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INTEGRATED HYDROLOGICAL
MODELING OF SURFACE -
GROUNDWATER INTERACTIONS
The case of Denpasar-Tabanan Basin in the
Southern Bali Island
Abenet Tadesse Teketel
March, 2017
SUPERVISORS:
Dr. Maciek W. Lubczynski
Dr. Zoltan Vekerdy
INTEGRATED HYDROLOGICAL
MODELING OF SURFACE -
GROUNDWATER INTERACTIONS
The case of Denpasar-Tabanan Basin in the
Southern Bali Island
Abenet Tadesse Teketel
Enschede, The Netherlands, March, 2017
Thesis submitted to the Faculty of Geo-Information Science and Earth Observation
of the University of Twente in partial fulfilment of the requirements for the degree of
Master of Science in Geo-Information Science and Earth Observation.
Specialization: Water Resource and Environment Management
SUPERVISORS:
Dr. Maciek W. Lubczynski
Dr. Zoltan Vekerdy
THESIS ASSESSMENT BOARD:
Dr. Ir. Christiaan van der Tol
Dr. W. van Verseveld (External Examiner, Deltares, The Netherlands)
DISCLAIMER
This document describes work undertaken as part of a programme of study at the Faculty of Geo-Information Science and
Earth Observation of the University of Twente. All views and opinions expressed therein remain the sole responsibility of the
author, and do not necessarily represent those of the Faculty.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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ABSTRACT
The Denpasar-Tabanan (D-T) Basin (2270 km2) located in the southern part of Bali Island, Indonesia, is a
densely populated area, also typical destination of international tourism. The basin is composed of
unconsolidated volcanic materials storing groundwater in an unconfined aquifer. That aquifer provides the
main water supply of the Bali Island although it often undergoes crises of water shortage. Therefore, it is
crucial to understand its complex dynamic of surface-groundwater (SW-GW) interactions and to evaluate
its groundwater resources to improve water management.
The dynamics of SW-GW- interaction was numerically simulated using three-dimensional steady-state and
transient models. For that purpose, MODFLOW-NWT with stream flow routing (SFR2) and unsaturated
zone flow (UZF1) packages were used. All data, including time series of rainfall, stream discharge, and
potential evapotranspiration for the four-year period from 1st January 2009 to 31st December 2012, were
simulated on a daily basis.
The steady-state model groundwater inflow consisted of: RUZF (95%) and qsg (5%). The groundwater outflow
consisted of: qgs (47.8%), ETss (23.4%), Exfgw (22.6%), and qg (6.1%) of total groundwater outflow. In the
transient model simulation, groundwater inflow consisted of Rg (75.4%), qsg and ∆Sgi were 3.3% and 21.3%
of total groundwater inflow respectively. Regarding transient model groundwater outflow, qgs (30.4%), Exfgw
(29.4%), ETg (14.1%) followed by ∆Sgout (18.9%) and qg (7.2%) of total groundwater outflow respectively. It
was observed that in the years analysed the net recharge was largely positive and that streams largely gain
groundwater, which reflects good groundwater potential of the D-T basin.
The calibrated transient model showed large spatiotemporal variability of groundwater fluxes. The Rg ranged
from 7.64 (January) to 2.30 mmday-1 (August) with the mean 3.36 mmday-1, Rn from 5.84 (January) to 0.26
mmday-1 (August) with the mean 1.34 mmday-1, ETg from 1.05 (February) to 0.65 mmday-1 (July), Exfgw from
1.48 (March) to 1.37 mmday-1 (December) and qgs from 1.48 (January) to 1.37 mmday-1 (August). The
temporal variability of fluxes was mainly due to seasonal variability of driving forces changing from dry to
wet season. The large spatial variability of groundwater fluxes was primarily due to large variety of land
covers and large spatial variability of rainfall.
Key Words: Surface-groundwater interactions, Bali, Volcanic aquifer, Water balance, MODFLOW-NWT
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ACKNOWLEDGEMENTS
The preparation and completion of this thesis work would not have been possible without the involvement
and contribution of kind persons around me. First, I thank the almighty God for the gift of life, good health
and for His guidance to this far. Many thanks to the Netherlands Fellowship Program (NFP) for the
generous financial support throughout my study period.
I would like to express my deep gratitude to my first supervisor, Dr. Maciek W. Lubczynski, for his
supervision, patience, words of encouragement, constructive ideas and invaluable remarks throughout this
research work. My deep gratitude also goes to my second supervisor Dr. Zoltan Vekerdy, for his supervision,
useful comments, remarks, and words of encouragement, throughout the thesis study. It would be so
difficult without their help. Sincere thanks to Dr. Tom H.M. Rientjes, Dr. ir. Suhyb Salama, and ir. Arno M.
van Lieshout for their valuable comments during the process of this research starting from thesis proposal.
You all patiently directed my wild imaginations to a worthwhile research item and ensured that I stayed
within the scope of the study by frequently correcting my work. Sincere thanks to Miss Novi Rahmawati
(Ph.D. candidate), who selflessly ensured I had all the necessary data, and for guiding me through the data
that are written in Balinese language. My thanks are extended to government of Indonesia especially to
Indonesian Agency for Meteorology, Climatology, and Geophysics Locally called DPPU; Biro of Geospatial
Information, “BIG”; and Ministry of Energy and Mineral Resources of Indonesia, “KLPU” for sharing the
meteorological and hydrological data for all station that are available in Bali Island.
Many thanks to the administrative and teaching staff of the ITC-WRM Program. It is here where I learned
most of my theoretical foundations in water resources management. To my fellow classmates, thank you
for the quality time spent together as one big ‘family’; in a way, you helped me in the completion of this
thesis. Last but not the least, my heartfelt gratitude to my family for their unconditional love, patience and
support to the seemingly endless journey. Special thanks to my dad and mom for this encouragement and
trust that forever keeps me strong. I am because you were. To my elder brother, my greatest source of
inspiration.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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TABLE OF CONTENTS
1. INTRODUCTION .............................................................................................................................................. 1
1.1. Background ...................................................................................................................................................................1 1.2. Problem statement ......................................................................................................................................................2 1.3. Research setting ...........................................................................................................................................................3
1.3.1. Research objectives ................................................................................................................................... 3
1.3.2. Research question ..................................................................................................................................... 3
1.3.3. Novelty of the study ................................................................................................................................. 3
1.3.4. Research hypothesis.................................................................................................................................. 3
1.3.5. Assumptions .............................................................................................................................................. 3
2. RESEARCH METHOD AND MATERIALS ............................................................................................... 4 2.1. Study area ......................................................................................................................................................................4
2.1.1. Location ...................................................................................................................................................... 4
2.1.2. Monitoring network .................................................................................................................................. 5
2.1.3. Climate ........................................................................................................................................................ 5
2.1.4. Topography and land cover .................................................................................................................... 6
2.1.5. Hydrology ................................................................................................................................................... 7
2.1.6. Hydrogeology ............................................................................................................................................ 8
2.1.7. Previous studies in the area ..................................................................................................................... 8
2.2. Data processing............................................................................................................................................................9
2.2.1. Watershed boundary .............................................................................................................................. 10
2.2.2. Precipitation ............................................................................................................................................ 10
2.2.3. Potential evapotranspiration ................................................................................................................ 12
2.2.4. Interception and infiltration rate ......................................................................................................... 13
2.2.5. Stream discharge .................................................................................................................................... 14
2.2.6. Hydraulic properties .............................................................................................................................. 15
2.2.7. Head observation ................................................................................................................................... 15
2.2.8. Groundwater abstraction ...................................................................................................................... 15
2.3. Modeling flow chart ................................................................................................................................................. 16 2.4. Conceptual model..................................................................................................................................................... 16
2.4.1. Defining Hydrostratigraphic units ...................................................................................................... 17
2.4.2. Defining the flow system ...................................................................................................................... 17
2.4.3. Defining preliminary water balance .................................................................................................... 18
2.4.4. Defining the boundaries of the model ............................................................................................... 18
2.5. Numerical model ...................................................................................................................................................... 18
2.5.1. Software selection .................................................................................................................................. 18
2.5.2. Aquifer geometry and grid design ....................................................................................................... 20
2.5.3. Driving forces ......................................................................................................................................... 20
2.5.4. State variables ......................................................................................................................................... 21
2.5.5. Parametric data ....................................................................................................................................... 21
2.5.6. Boundary conditions ............................................................................................................................. 22
2.6. Model calibration ...................................................................................................................................................... 24
2.6.1. Steady-state model calibration ............................................................................................................. 24
2.6.2. Warming-up period for transient model calibration ........................................................................ 24
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2.6.3. Transient model calibration .................................................................................................................. 25
2.7. Error assessment and sensitivity analysis ............................................................................................................. 25 2.8. D-T basin water balance ......................................................................................................................................... 26
3. RESULTS AND DISCUSSION ..................................................................................................................... 28 3.1. Data processing calculation results........................................................................................................................ 28
3.1.1. Filling missed data for precipitation .................................................................................................... 28
3.1.2. Consistency of the precipitation records ............................................................................................ 28
3.1.3. Spatial data interpolation of rainfall ..................................................................................................... 29
3.1.4. Interception and infiltration rate .......................................................................................................... 31
3.1.5. Potential Evapotranspiration [PET] .................................................................................................... 32
3.1.6. Consistency of stream discharge .......................................................................................................... 34
3.2. Steady-state model calibration ................................................................................................................................ 36
3.2.1. Calibrated head and error assessment ................................................................................................. 36
3.2.2. Calibrated stream discharges ................................................................................................................. 38
3.2.3. Hydraulic conductivities ........................................................................................................................ 39
3.2.4. Water budget of the steady-state simulation using GHB conditions at the sea coast ................. 39
3.2.5. Spatial variability of groundwater fluxes ............................................................................................. 42
3.2.6. Effects of changing GHB conductance upon lateral groundwater outflow to the ocean .......... 43
3.2.7. Water budget of the steady-state simulation using CHD boundaries at the sea coast ................ 43
3.2.8. Sensitivity analysis ................................................................................................................................... 45
3.3. Transient model calibration .................................................................................................................................... 46
3.3.1. Calibration heads and error assessment .............................................................................................. 47
3.3.2. Calibrated stream discharges ................................................................................................................. 50
3.3.3. Hydraulic conductivities and specific yield ......................................................................................... 55
3.3.4. Water budget of the transient-state simulation .................................................................................. 56
3.3.5. Temporal variability of groundwater fluxes ....................................................................................... 57
3.3.6. Spatial variability of groundwater fluxes ............................................................................................. 58
3.3.7. Yearly steady-state and transient variability of water fluxes ............................................................ 59
3.3.8. Sensitivity analysis ................................................................................................................................... 61
4. CONCLUSIONS AND RECOMMENDATIONS .................................................................................... 63 4.1. Conclusions ............................................................................................................................................................... 63 4.2. Recommendations .................................................................................................................................................... 64
Appendix I ................................................................................................................................................................. 69
Appendix II .................................................................................................................................................................. 69
Appendix III ................................................................................................................................................................ 70
Appendix IV ................................................................................................................................................................. 71
Appendix V .................................................................................................................................................................. 71
Appendix VI ................................................................................................................................................................. 74
Appendix VII ............................................................................................................................................................... 75
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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LIST OF FIGURES
Figure 1: Geological map and cross section across the study area (Modified after Purnomo & Pichler, 2015).
.......................................................................................................................................................................................... 2
Figure 2: Location and elevation map of the D-T basin. ........................................................................................ 4
Figure 3: Monitoring stations of D-T basin .............................................................................................................. 5
Figure 4: Mean monthly rainfall; maximum, minimum, and mean temperature at station Kuta of D-T basin.
For the location of the station see Appendix V. ...................................................................................................... 6
Figure 5: Land use map and percent area coverage of D-T basin. ........................................................................ 7
Figure 6: Watershed boundaries, stream segments and gauging location of D-T basin. For the name of each
station see Appendix V (B). ......................................................................................................................................... 7
Figure 7: Geology of the study area. ........................................................................................................................... 8
Figure 8: Potentiometric surface of Bali Island (Modified after Nielsen & Widjaya, 1989). ............................. 9
Figure 9: Double mass curve for a precipitation data (after Gómez, 2007). ..................................................... 11
Figure 10: Methodology of flow chart. ................................................................................................................... 16
Figure 11: Geological cross section across the study area (After Ministry of Energy and Mineral Resources
of Indonesia)................................................................................................................................................................ 17
Figure 12: Proposed boundary conditions and locations in the D-T basin. ..................................................... 23
Figure 13: Schematic diagram of MODFLOW-NWT setup of D-T basin model. ......................................... 26
Figure 14: Daily rainfall after filling missed data at station Kuta for the years from 2009 to 2013. For the
location of station see Appendix V (A)................................................................................................................... 28
Figure 15: Double mass curves of the precipitation gauges [units in mm]. The double mass curve in A & C
shows consistency in the data but B & D shows inconsistency in the data. For the location of stations see
Appendix V (A). .......................................................................................................................................................... 29
Figure 16: Sample significance test results of rainfall record on January 10, 2009. ......................................... 30
Figure 17: Standard model variogram; distance in a unit of [m] and semi-variance in a unit of [m2]. .......... 30
Figure 18: Kriged prediction and Kriging variance of D-T basin for long-term average rainfall from
01/01/2009 to 01/01/2012 [unit – mday-1]. .......................................................................................................... 31
Figure 19: Spatially variable interception (A) and infiltration rate (B) of D-T basin. ...................................... 32
Figure 20: Temperature coefficient of determination for Sanglah and Kuta stations. .................................... 32
Figure 21: Spatially variable crop coefficient (A) and extinction depth (B) for D-T basin. ........................... 33
Figure 22: Average Rainfall (P), Infiltration rate (Pr), Interception rate (I) and Potential evapotranspiration
(PET) for four hydrological years from 2009 to 2012. ......................................................................................... 33
Figure 23: Sample double mass curve and frequency distribution for the stream gauge discharge data [Q-
stream discharge in m3sec-1]. For the location of station and log transform see Appendix V. ...................... 35
Figure 24: Relation between rainfall and stream discharge. The oval shape indicates uncertainty on the
relation between measured stream flow and rainfall pattern. [RF – rainfall and Q – stream discharge]. For
the location of stream gauging stations see Appendix V. .................................................................................... 35
Figure 25: Relationship between simulated and observed heads in the D-T basin during steady-state IHM
for the year from 2009 to 2012. ............................................................................................................................... 36
Figure 26: Potentiometric surface with location of heads, stream segments of the D-T basin during steady-
state IHM. The stream segments with black lines indicates those that were not included during model
calibration. Heads in m a.s.l. ..................................................................................................................................... 37
Figure 27: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after steady-state
IHM [unit - mday-1]. ................................................................................................................................................... 39
Figure 28: Schematic representation volumetric water budget in case of steady-state IHM for the entire
model of D-T Basin [ All units - mmyear-1]. .......................................................................................................... 41
Figure 29: Spatially variable ETss of D-T Basin for calibrated steady-state IHM [Unit – mday-1]. ................ 42
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Figure 30: Spatially variable Rg map for calibrated steady-state IHM in D-T Basin [Unit – mday-1]. ............ 43
Figure 31: The relationship between GHB conductance and head dependent boundary flow rate. The GHB
conductance that masked by orange circle indicate the final value that was selected. In MODFLOW-NWT
the GHB conductance is calculated based on polyline objects as in Section 2.4.6. ......................................... 43
Figure 32: Sensitivity of model for horizontal hydraulic conductivity (A) & Vertical unsaturated zone
hydraulic conductivity (B). ......................................................................................................................................... 45
Figure 33: Sensitivity of model for UZF1 package parameter and driving forces: (C) extinction depth, (D)
infiltration rate, (E) extinction water content, (F) potential evapotranspiration. .............................................. 46
Figure 34: Sensitivity of model for (G) Brooks-Corey-Epsilon & (H) saturated water content. .................. 46
Figure 35: Relationship between simulated and observed heads for the transient IHM of 11 observation
points. ............................................................................................................................................................................ 47
Figure 36: The potentiometric surface and stream segments of the D-T basin during transient model
calibration at the last stress period, December 31, 2012. ...................................................................................... 48
Figure 37: Time series for the comparison of yearly observed and daily simulated heads for D-T basin. P –
rainfall, Hobs – observed heads, and Hsim – simulated heads. ............................................................................... 49
Figure 38: Relationship between observed and simulated discharge in the D-T basin for the transient-state
model calibration of 13 stream gauge (2009 - 2012). For the location of gauges see Appendix V (A & B).
The oval shape in Figure 37 (J, K, and L) show that uncertainty in the measured rainfall and stream
discharges. Because it is expected that at high rainfall records, stream discharge is higher and the opposite
is true. Q – stream discharge and RF – rainfall. ..................................................................................................... 54
Figure 39: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after Transient-
state IHM [unit - mday-1]............................................................................................................................................ 56
Figure 40: Temporal variability of groundwater fluxes in transient model calibration for gross recharge (Rg),
net recharge (Rn), surface leakage (Exfgw), and groundwater evapotranspiration (ETg). ................................... 57
Figure 41: Temporal variability of rainfall, actual infiltration and PET ............................................................ 58
Figure 42: Spatially variable ETg map for calibrated transient IHM during dry (A) and wet (B) period in D-
T Basin [Unit – mday-1]. ............................................................................................................................................. 59
Figure 43: Spatially variable Rg map for calibrated transient IHM during dry (A) and wet (B) period in D-T
Basin. ............................................................................................................................................................................. 59
Figure 44: Sensitivity of model for horizontal hydraulic conductivity [Kh], maximum unsaturated zone
vertical hydraulic conductivity [Kvun], extinction depth [EXTDP], extinction water content [EXTWC],
Saturated water content [WCsat], and Brooks-Corey-Epsilon [BC]. .................................................................... 61
Figure 45: Effects of changing unsaturated zone vertical hydraulic conductivity [Kvun] upon infiltration (A)
and Exfgw (B), effects of changing extinction depth [EXTDP] and GHB conductance upon ETg (C) and qg
(D) respectively. ........................................................................................................................................................... 62
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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LIST OF TABLES
Table 1: Available data from the year 2009 to 2012 (Tmax - maximum temperature, Tmin - minimum
temperature, RH – relative humidity, WS – wind speed, SS - sunshine duration, n.a - indicates that the data
are not available within the study periods, EXTDP – Extinction depth, Kh – saturated hydraulic
conductivity, and Sy - specific yield). ........................................................................................................................ 10
Table 2: Interception loss rate that used in D-T Basin......................................................................................... 14
Table 3: Aquifer characteristics value of the basin (T - transmissivity, Sy – specific yield, Kh - horizontal
hydraulic conductivity, SWL - surface water level). The location of bores can be seen in Appendix I. ...... 15
Table 4: D-T extinction depth based on land cover. ............................................................................................ 21
Table 5: Observed and simulated head with calculated error assessment for 11 piezometers, Hobs – Observed
head, Hsim – Simulated head [units – m]. ................................................................................................................. 36
Table 6: Observed and simulated stream discharge with calculated error assessment for 16 gauges: Qobs –
observed stream discharge; and Qsim – simulated stream discharge [unit - m3day-1]. Stations that are
highlighted by red colour indicate those station that are not used for model calibration and show the model
response for those stations........................................................................................................................................ 38
Table 7: Total water balance of D-T basin at steady-state IHM [mmday-1]. ..................................................... 40
Table 8: water balance of land surface and unsaturated zone [mmday-1]. ......................................................... 40
Table 9: Water balance of groundwater in steady-state IHM [mmday-1]. .......................................................... 41
Table 10: Water balance of groundwater in steady-state condition [mmday-1]................................................. 44
Table 11: Observed, Hobs and simulated head, Hsim with calculated error assessment for 11 piezometers.
[Units – m]. .................................................................................................................................................................. 48
Table 12: Observed and simulated stream discharge with GHB conductance of 0.1 m2day-1 per unit length
calculated error assessment for 16 gauges in m3day-1. Stations that are highlighted by red colour indicate
those station that are not used for model calibration and shows the model performance for those stations.
....................................................................................................................................................................................... 55
Table 13: Final calibration output for model parameters and model variables in the D-T basin: EXTDP –
extinction water content; EXTWC – extinction water content; THTS – saturated volumetric water content;
THTI – initial volumetric water content; STRTOP – streambed top; STRTHICK – streambed thickness;
SLOPE – stream slope; STRHC1 – streambed hydraulic conductivity; WIDTH1 – stream width; Kvun –
maximum unsaturated zone vertical hydraulic conductivity; Kh – horizontal hydraulic conductivity; Sy –
specific yield; and C – conductance. ........................................................................................................................ 56
Table 14: Long term average groundwater budget for entire model in transient-state IHM [mmday-1] for the
2009-2012. IN – inflow to the aquifer system, OUT – outflow from the aquifer system, GW – groundwater.
....................................................................................................................................................................................... 57
Table 15: The yearly variability of driving forces and different groundwater balance components over the
three hydrological periods 1st January 2009 till 31st December 2012 MODFLOW-NWT simulation period
[All units in mm year-1]. ............................................................................................................................................. 60
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LIST OF ABBREBATIONS
∆S Change in storage
BGI Biro of Geospatial Information
BMKG Indonesian Agency for Meteorology, Climatology, and Geophysics
CHD Time-Variant Specified-Head
DEM Digital Elevation Model
DPPU Ministry of Public Works
D-T Denpassar - Tabanan
ETg Groundwater Evapotranspiration
ETo Reference Evapotranspiration
ETun Unsaturated zone evapotranspiration
Exfgw Groundwater exfiltration
EXTDP Extinction depth
EXTWC Extinction water content
FAO Food and Agriculture Organization
GHB General Head Boundary
GUI Graphical User Interface
ho Head in the aquifer
hs Head in streams
I Interception
IHM Integrated hydrological modelling
Kc Crop coefficient
KESDM Ministry of Energy and Mineral Resources of Indonesia
Kh Horizontal hydraulic conductivity
Kvun Maximum unsaturated zone vertical hydraulic conductivity [UHC]
m a.s.l Meters above sea level
MAE Mean Absolute Error
ME Mean Error
MODFLOW Modular three dimensional finite-difference flow model
NS Nash-Sutcliffe efficiency
NWT Newtonian
P Precipitation
Pe Actual infiltration
PET Potential evapotranspiration
Pr Infiltration rate
q Stream discharge at the outlet of the catchment
Q Discharge
qd Dunnian saturated excess runoff
qg Lateral groundwater outflow
qgs Groundwater loss to the stream
qh Hortonian runoff
qsg Groundwater gain from the stream
Rg Gross recharge
RH Relative humidity
RMSE Root Mean Square Error
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Rn Net recharge
RUZF Unsaturated zone recharge
Ro Total runoff
RVE Relative Volumetric Error
SFR2 Surface flow routing package
SS Sunshine duration
SW-GW Surface water and groundwater
Sy Specific yield
Tmax Maximum temperature
Tmin Minimum temperature
UPW Upstream Weighting Package
UZF1 Unsaturated zone flow package
WCsat Saturated water content
WS Wind speed
Y Overall model performance
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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1. INTRODUCTION
1.1. Background
Surface water and groundwater and (SW-GW) are very crucial for the well-being of humans and for the
nature in general (Sophocleous, 2002). The significance of these resources is increasing through time, as the
number of population is rapidly increasing (Fitts, 2002 & Anderson et al., 2015). Recently, research effort
has been extended to understand the interaction between SW-GW and to quantify the flow between these
resources, since, understanding of the link between them is needed for effective management of the resource
(Lubczynski & Gurwin, 2005; Sophocleous, 2005; Hassan et al., 2014 & Ala-aho et al., 2015). The
hydrological interactions between SW-GW occur through the unsaturated zone and by infiltration into or
exfiltration from the saturated zone (Anibas et al., 2009).
The groundwater basin of D-T is located in the most developed area of Bali Island, Indonesia. The Island
is located at 80 south of the equator and has an area of 5,380 km2, while the area for D-T basin is 2270 km2.
The island of Bali has a variety of volcanic topographic units such as eroded early Quaternary volcanoes,
active stratovolcanoes, thick tephra deposits, pyroclastic flow slopes and closed caldera lakes (Nielsen &
Widjaya, 1989; Kayane et al., 1993 & Purnomo & Pichler, 2015). These topography types can be classified
into two categories. The Quaternary upper volcanic sequence and the Pliocene lower calcareous sequence
(Figure 1). The latter is composed of a sequence of limestone, the "prepatagung formation", and calcareous
sandstone. The thickness of this aquifer material is unknown, whereas the thickness of the Quaternary upper
formation is considered to be up to 150 m. This Quaternary upper formation is composed of different
materials of volcanic origin. It includes mainly unconsolidated sand & gravel, volcanic ash, lava flow, breccia,
lahar, "pumic", clay and tuff (Rai et al., 2015 & Purnomo & Pichler, 2015).
Cole (2012) stated that groundwater is the most widely used resource in Bali Island as aquifers are
characterized by high permeability. Mainly the Quaternary volcanic aquifer is the most productive and it can
produce up to 7862 m3day-1. Nielsen & Widjaya (1989), strongly recommended for the expansion of well
systems for irrigation and municipal demands, due to their finding that 75% of the recharge reaches to the
Quaternary upper formation called production aquifer. However, no research has been done regarding
integrated hydrological model [IHM].
This research focuses on assessing the interaction between SW-GW resources and estimate the groundwater
budget of the D-T basin. The interaction of SW-GW is best quantified through IHM (Lubczynski & Gurwin,
2005 & Kumar, 2015). MODFLOW-NWT is one of the models developed that link surface, unsaturated
and saturated zone in a reliable manner. The model is working under ModelMuse Graphical User Interface
(GUI) and merge with unsaturated zone flow package [UZF1] and stream flow routing package [SFR2]
(Niswonger et al., 2011 & Hassan et al., 2014). Therefore, in this study MODFLOW-NWT was conducted
to quantify the exchange flux between surface, unsaturated and saturated zones for the simulation period of
four years from 2009 to 2012. Groundwater study in D-T basin was selected because: (i) the basin is located
in the most developed area on the Bali Island and having high potential of groundwater resources but
sometimes suffers from water scarcity; (ii) it is representative of unconsolidated aquifer around the world,
i.e. it consists of volcanic aquifer with intergranular porosity and medium to high permeability; (iii) there is
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a four years of hydrological data available; (iv) groundwater recharge has been studied by Nielsen & Widjaya
(1989) using analytical methods and Artabudi (2012), that can be used for comparing the final findings.
Geological and cross section map of Bali Island
Figure 1: Geological map and cross section across the study area (Modified after Purnomo & Pichler, 2015).
1.2. Problem statement
Groundwater is the most popular water resources in Bali Island. However, Bali is affected by frequent crises
of water shortage (Purnomo & Pichler, 2015 & Straub, 2011). There is also a lack of knowledge and
mismanagement of SW-GW resources which causes decline of the water table, saltwater intrusion and
deterioration of water quality. Cole (2012) stated that the Island lacks official government statistics and
documentation regarding the available amounts of water resources. Furthermore, he mentioned the need
for reliable studies on SW-GW resources for successful water utilization and management. Besides, the
author of this study found that Bali groundwater has only been studied by Nielsen & Widjaya (1989) who
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
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did recharge assessment but only by analytical methods and Artabudi (2012) who estimated groundwater
recharge using remote sensing application. The interaction of SW-GW and groundwater recharge using
IHM has not been studied in Bali Island.
1.3. Research setting
1.3.1. Research objectives
The overall objective of the study is to develop an IHM of D-T basin for management purpose.
Specific objectives:
1. To set up the numerical model in D-T based on the data from 2009 till 2012.
2. To calibrate steady-state and transient IHM of the D-T basin.
3. To estimate the water balance of the D-T basin.
4. To characterize the dynamics of SW-GW interactions in the D-T basin.
1.3.2. Research question
1. How to integrate various sources of data in the IHM?
2. What are the key components of spatiotemporal variability of the water balances in the D-T basin?
3. How does the water balance of the D-T basin vary on daily and/or yearly basis?
4. How do the SW and GW resources interact?
1.3.3. Novelty of the study
The findings of this study will increase the understanding of an unconsolidated aquifer of the D-T basin
and can be used as an asset for management purpose by including the following novelties:
1. First-time use of IHM in the D-T basin. No research has been done in the area related to SW-GW
interactions.
2. Use of daily streamflow measurement for IHM calibration.
1.3.4. Research hypothesis
It is hypothesized that the calibration of the integrated transient numerical model of the D-T basin gives a
reliable estimate of the SW-GW exchange flux and groundwater budget.
1.3.5. Assumptions
- Eventual leakages across the bottom boundary of the volcanic aquifer have a negligible impact on the flow
system of the modeled aquifer.
- Eventual lateral fluxes across watershed boundaries are negligible.
- Variable density groundwater flow, advection and dispersive salt transport have a negligible impact on the
flow system of the modeled aquifer.
- Due to lack of groundwater abstraction data both the steady-state and transient-state IHM were calibrated
without groundwater abstraction data. Therefore, the impact of groundwater abstraction in the water budget
of D-T basin have a negligible impact.
4
2. RESEARCH METHOD AND MATERIALS
2.1. Study area
2.1.1. Location
The D-T basin is located in the south-west of Bali Island, Indonesia with geographical coordinates of 8º39'S
latitude and 115º13'E longitudes. It is part of the Bali Island with estimated area coverage of 2270 km2;
whereas the whole Bali Island has an estimated area of 5,380 km2. The D-T basin has elevation variation
from 0 to 2850 m a.s.l with the highest elevation located in the north and north-east of the basin and with
the lowest elevation located in the south (Figure 2). The study mainly focused on the southern part of the
area; where most population part of Bali lives in D-T basin, the study excluded Nusa Dua and Nusa Penida
peninsula.
Location of D-T Basin
Figure 2: Location and elevation map of the D-T basin.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
5
2.1.2. Monitoring network
The D-T basin, the southern Bali Island hydro-climatologically data such as rainfall, temperature, stream
level, groundwater level, and pumping test data were monitored and available. These hydro-climatological
data are available in the daily basis from 1st January 2009 to 31st December 2012 except for groundwater
level. In D-T basin there are 21 meteorological stations, of all this 18 of them have sparsely located rain
gauge stations and the remaining 3 are temperature, relative humidity, radiation and wind speed monitoring
stations. Stream level at the southern basin outlet was monitored on a daily basis using 16 discharge gauge
stations. The groundwater level was monitored by using 11 boreholes and dug wells (Figure 3).
Monitoring Stations
Figure 3: Monitoring stations of D-T basin
2.1.3. Climate
Based on average monthly rainfall, Bali has a pattern of monsoon type climate. Monsoon pattern occurs due
to the air circulation changing direction every six months across the Indonesian region. In the area, month
from April till the end of September is dry season and from October till the end of March is the wet season.
The air mass that brings the rain from the northwest equatorial wind in the wet season and the southeast
wind from Australia in the dry season (Figure 2) cause the seasonal pattern in the area (Kayane et al., 1993).
Bali has an average annual rainfall of 2150 mm. Generally, during the rainy season, part of rainfall will
evaporate, other part will be taken up by the plant, some will run as overland flow and the remaining infiltrate
to the subsurface. About 30 to 50% of total rainfall has been estimated to infiltrate into the Quaternary
terrains. In fact, the percentage which infiltrate depends upon geological conditions, vegetation cover, land
use, and slope (Nielsen & Widjaya 1989). On average, the temperature ranges from 27-30 0C (Figure 4) and
humidity 85-90 %. Moreover, in Bali soil and air temperature decreases at a lapse rate of 0.62 0C/100 m
with elevation (Kayane et al., 1993).
6
Figure 4: Mean monthly rainfall; maximum, minimum, and mean temperature at station Kuta of D-T basin. For the
location of the station see Appendix V.
2.1.4. Topography and land cover
The Island of Bali is a mountain chain that extends from the West to the East with volcanoes in Mount
Batur (1717m) and Gunung Agung (3142 m) still active (Figure 1). The mountain chain that runs along the
island of Bali causes morphological regions of Bali to be divided into several topographic and physiographic
units (Purnomo & Pichler, 2015). Since the Northern part is high elevated, major drainage network is located
in the south as well as the central part the D-T basin. In other respect, the most common land covers of D-
T basin are Forest, 6%; bare soil, 9%; Agriculture, 68.3%; buildings, 13%; grassland and others, 3.4% (Figure
5).
20
22
24
26
28
30
32
34
0
4
8
12
16
20
Jan
Feb
Mar
Ap
r
May
Jun
Jul
Aug
Sep
Oct
No
v
Dec
Tem
per
ature
[oC
]
Rai
nfa
ll [m
m m
on
th-1
]
A. Mean monthy RF & T in 2009
Kuta_RF 2009 Max. Temp
Min. Temp Mean. Temp
20
22
24
26
28
30
32
34
0
4
8
12
16
20
Jan
Feb
Mar
Ap
r
May
Jun
Jul
Aug
Sep
Oct
No
v
Dec
Tem
per
ature
[oC
]
Rai
nfa
ll [m
m m
on
th-1
]
A. Mean monthy RF & T in 2009
Kuta_RF 2010 Max. Temp
Min. Temp Mean. Temp
20
22
24
26
28
30
32
34
0
4
8
12
16
20
Jan
Feb
Mar
Ap
r
May
Jun
Jul
Aug
Sep
Oct
No
v
Dec
Tem
per
ature
[oC
]
Rai
nfa
ll [m
m m
on
th-1
]
A. Mean monthy RF & T in 2009
Kuta_RF 2011 Max. Temp
Min. Temp Mean. Temp
20
22
24
26
28
30
32
34
0
4
8
12
16
20
Jan
Feb
Mar
Ap
r
May
Jun
Jul
Aug
Sep
Oct
No
v
Dec
Tem
per
ature
[oC
]
Rai
nfa
ll [m
m m
on
th-1
]A. Mean monthy RF & T in 2009
Kuta_RF 2012 Max. Temp
Min. Temp Mean. Temp
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
7
Land use map
Percent area ratio
Figure 5: Land use map and percent area coverage of D-T basin.
2.1.5. Hydrology
The D-T watershed boundaries are defined by topographic divides and delineate areas where surface water
runoff drains into a common surface water body. The defined watershed boundaries are determined by
science-based hydrologic principles, not favoring any administrative boundaries (Figure 6). Streams flow
from the north side to the south direction following the valleys. Most of the streams are perennial (Rai et
al., 2015), while their discharges originated from groundwater and surface runoff formed by precipitation.
The data from 16 stream gauges were available in a daily basis from 01/01/2009 to 31/12/2012.
Watershed boundaries of D-T basin
Figure 6: Watershed boundaries, stream segments and gauging location of D-T basin. For the name of each station see Appendix V (B).
0.48%
3.43%
5.99%
8.96%
12.82%
68.32%
100.00%
Water
Grass
Forest
Bare Soil
Buildings
Aggriculture
Total
8
2.1.6. Hydrogeology
Geologically, the study area is part of the “Sunda-Banda" volcanic islands arc. The arc is caused by the Indo-
Australian and Eurasia plates. Since the late Tertiary, this process drives volcanism and produces a vast
distribution of volcanic rocks (Figure 7). The Quaternary upper volcanic sequence which is also called
unconsolidated layer and the Pliocene lower calcareous sequence also called consolidated layer, are the two
dominant geologic formations of the area (Figure 1 & Figure 11). These volcanic rocks are rich in mafic
minerals and exhibits considerable relief at the north (Purnomo & Pichler, 2015). Hills that surrounds
Northern area forms surface water divides that coincide with the groundwater divides. Consequently, there
is no flow contribution from outside of the basin and the outflow is the only through the streams discharge
and lateral groundwater outflow towards the Indian ocean.
Pumping tests were conducted by Ministry of energy and mineral resources of Indonesia, locally "KESDM"
to evaluate the characteristics of the aquifer systems and groundwater potential of the basin. All the pumping
tests were carried out in Quaternary layer and the Tertiary layer is considered to be an impervious layer.
Because of that, it was assumed that there is no hydraulic contact between the upper Quaternary and lower
Tertiary layer.
D-T basin Geological map
Figure 7: Geology of the study area.
2.1.7. Previous studies in the area
Nielsen & Widjaya (1989), estimated groundwater recharge in southern Bali through five different
techniques for the year from 1980 to 1983. Based on analysis of well hydrographs they found that the
recharge value of 468 mm per annum, annual infiltration (≈25% of rainfall) gave 437 mm year-1, base flow
separation gave 272 mm per annum, flow net analysis gave 492 mm per annum. Finally, they built an
analytical model based on land use and soil type and found recharge value of 645 mm per annum in light
soil, 538 mm per annum in medium soil and 376 mm per annuam in heavy clay soil. Based on the above
findings, they recommended the expansion of well systems for tourism, irrigation, and municipal demands.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
9
They also showed the piezometric/potentiometric map of the area, in which groundwater flows from
northern to the southern side of the basin (Figure 8). Additionally, Artabudi (2012) estimated the net
recharge of Denpasar in two ways: (1) using “the Global Satellite mapping for precipitation” for the data
from 2005 to 2009, the groundwater recharge value of 218 – 220 mmyear-1 was estimated; and (2) using in-
situ rainfall data the groundwater recharge value of 650 – 660 mmyear-1 was obtained.
In the study area, the Quaternary volcanic aquifer which is also called the unconsolidated layer is the most
productive and it can produce up to 7862 m3day-1. This unconfined aquifer is characterized by high
permeability and its volcanic rocks are characterized by intermediate hydraulic conductivity (Kh). Sand and
gravel of volcanic origin are highly permeable with transmissivity value of over 700 m2day-1 (Rai et al., 2015
& Purnomo & Pichler, 2015). Southern Bali piezometric map
Figure 8: Potentiometric surface of Bali Island (Modified after Nielsen & Widjaya, 1989).
2.2. Data processing
Data collection is a prerequisite in groundwater modeling. Meteorological and hydro-geological data need
to be collected as well as processed for effective model simulation of a given area (Kumar, 2015). In this
study, the meteorological and hydrogeological data are available as shown in Table 1. Data such as
groundwater depth, pumping test, hydrogeological and geological maps were collected from Ministry of
Energy and Mineral Resources of Indonesia (locally "KESDM"). Most of the meteorological data such as
daily rainfall, air temperature, relative humidity, streams level, and rating curves were collected from Ministry
of Public Works (Locally called "DPPU"). Additionally, the land use map and 2012 daily rainfall data were
collected from Biro of Geospatial Information (BIG) and Indonesian Agency for Meteorology, Climatology,
and Geophysics (Locally called "BMKG") respectively.
Initially, in the data processing step, the missing rainfall data was filled using the coefficient of correlation
method (Teegavarapu & Chandramouli, 2005). Then, a double mass curve was used to check the consistency
of rainfall and stream discharge data (Searcy & Hardison, 1960). Afterward, all the available data (Table 1)
10
was converted in a way that MODFLOW-NWT can accept it. For instance, the available point observation
of rainfall data was interpolated into rainfall map using kriging method. Kriged prediction was selected
because it is a best linear unbiased predictor (Sterk & Stein, 1997; Hengl et al., 2007; Webster & Oliver,
2007; & Zhang et al., 2012). Spatially variable crop coefficient (Kc), interception rate and infiltration rate
were estimated using the 2009 land use map of the D-T basin. Using FAO Penman-Monteith method the
available Tmax, Tmin, RH, WS, & SS together with spatially variable Kc data were used to calculate potential
evapotranspiration (PET). The hydraulic head was calculated from elevation and groundwater depths data.
Finally, the IHM was built and simulated in daily time steps for a four hydrological years from 1st January
2009 to 31st December 2012.
Table 1: Available data from the year 2009 to 2012 (Tmax - maximum temperature, Tmin - minimum temperature, RH –
relative humidity, WS – wind speed, SS - sunshine duration, n.a - indicates that the data are not available within the
study periods, EXTDP – Extinction depth, Kh – saturated hydraulic conductivity, and Sy - specific yield).
Required data Available data No. of stations
Required Units
Frequency of available data
Watershed boundary DEM - - -
Infiltration rate Rainfall 18 mday-1 daily
Potential evapotranspiration
Tmax, Tmin, RH, WS, SS
3 mday-1 daily
Stream discharge Stream level & rating curve
16 m³day-1 daily
Hydraulic head Groundwater depth
11 m yearly
Groundwater abstraction
n.a. n.a. m³day-1 n.a.
Tidal head Tidal head 1 m daily
Model top elevation DEM - m a.s.l. -
Crop coefficient Land use map - - -
Interception Land use map - - -
EXTDP Land use map - - -
Kh , Sy Kh, Sy 14, 2 mday-1, - n.a.
2.2.1. Watershed boundary
The D-T watershed boundaries were defined by topographic divides and delineating areas where surface
water runoff drains into a common surface water body. The defined watershed boundaries were determined
upon science-based hydrologic principles, not favoring any administrative boundaries. The SRTM (Shuttle
Radar Topographic Mission) 90 m DEM (digital elevation model) was used to delineate these watershed
boundaries. The SRTM 90 m DEM provided by NASA, has significant importance in determining the flow
direction and in delineating catchment areas according to their stream flow. This data is available on the
internet with free of charge by USGS, (http://srtm.csi.cgiar.org/). Initially, the available DEM data was
filled into remove small imperfections in the data using hydrology spatial analyst tool in ArcGIS, then using
the filled DEM map, a raster map of flow direction from each cell to its steepest downslope neighbor was
generated. Then, a raster map of accumulated flow into each cell was generated. Afterward, the steam gauges
were used as a snap pour points to the cell of highest flow accumulation within a 1000 m distance. Finally,
the contributing area above a set of cells or watershed boundaries was obtained (Figure 6).
2.2.2. Precipitation
Precipitation is one of the first essential input data in IHM. Precipitation is used in UZF1 package to be
partitioned into runoff, infiltration, evapotranspiration, unsaturated-zone storage and recharge. Precipitation
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
11
together with potential evapotranspiration is the input driving forces of UZF1 packages of MODFLOW-
NWT (Niswonger et al., 2006). The D-T basin rainfall was measured using tipping bucket at 18 sparsely
distributed rain gauge stations (Figure 3 and Appendix V). From the total number of stations, only the
station called Kuta has missed rainfall data.
Estimation of the Missing Precipitation Records
Rainfall records can be missed due to instrument malfunction, tree growth or other reason. Filling the missed
data is one of the most important tasks to be carried out in many hydrological studies. The most commonly
applied methods that are recently used for filling missed data are inverse distance, inverse exponential, the
coefficient of correlation weighted method, and others (ASCE, 1996). In this study, the “coefficient of
correlation weighted method” (CCWM) was used to fill missing data as proposed by Teegavarapu &
Chandramouli (2005) & Gómez (2007). Reliable estimation of missed data using CCWM is strongly
dependent on spatial autocorrelation in which the data nearby are more similar than that of far apart. Once
the correlation coefficient is determined, the missed data at a given station is calculated using equation 2.1.
n
1imir
mirn
1iiP
mP (2.1)
where Pm - precipitation at the base station m; Pi - precipitation at station i, n – number of nearby stations,
and rmi - correlation coefficient of station i with nearest n stations. The correlation coefficient, rmi, is obtained
from SPSS by using the method known as “Pearson - Moment Correlation Coefficient” between closest
stations (Appendix III).
Consistency of the precipitation records
Hydrological data consist of time series data that are collected at a particular location. The use of raw data
without checking for consistency in IHM can bring lots of error and uncertainty. Therefore, before
hydrological data are used in such study, they should be tested by the double-mass curve technique to ensure
their reliability (Searcy & Hardison, 1960). The Double-Mass curve is plotted as cumulative of one station
(y-axis) against the average cumulative of nearby stations (x-axis) as in Figure 9.
Figure 9: Double mass curve for a precipitation data (after Gómez, 2007).
12
Deviation from or break in the slope of the double mass curve means that there is a change in the
consistency of proportionality between the variables or simply it shows the degree of change in the relation.
Such deviation might be due to gauge location, observation method or exposure. The precipitation records
can usually be adjusted by coefficients determined from the double-mass curve (Equation 2.2).
bP
bδ
aδaP (2.2)
where Pa - adjusted precipitation, Pb - observed precipitation, δa - the slope of the graph at the time was
observed and δb - the slope of the graph to which records are adjusted.
2.2.3. Potential evapotranspiration
McMahon et al., (2013) define potential evapotranspiration [PET] as "the rate at which evapotranspiration
would occur from a large area completely and uniformly covered with growing vegetation which has access
to an unlimited supply of soil water, and without advection and heating effects." PET is one of the driving
forces in the UZF1 package. In the UZF1 package, the PET is applied at the land surface and decreases
linearly with depth down to the assigned extinction depth where evapotranspiration no longer occurs (Allen
et al., 1998). In most case PET calculated using FAO Penman-Monteith method (Equation 2.3). The
method is recommended by the scientific community as the best estimate of evapotranspiration with
minimum error compared to other methods (Wang et al., 2012). FAO Penman-Monteith method is
applicable if data such as daily air temperature, wind speed, relative humidity, atmospheric pressure and
relative sunshine duration are available. Consequently, the method was adapted for reference
evapotranspiration computation, since, the required data such as daily air temperature, wind speed, relative
humidity, atmospheric pressure and relative sunshine duration was available from the two stations namely
called station Sanglah and Kuta.
Before ETo computation using the equation 2.3, the correlation between Tmax, Tmin, and Tmean for the available
stations were constructed. A good coefficient of correlation between the station means that temperature is
uniform spatially. Then, the computed ETo would be spatially uniform but temporally variable. In the case
of low coefficient of correlation between Tmax, Tmin, and Tmean of the different stations kriging interpolation
method would be applied to generate the spatially variable ETo values.
Note that, the computation equations to estimate evapotranspiration as shown in Equation 2.3 and
Appendix II are the one that were applied in this study based on the available data. There are many possible
ways of determining one parameter based on the availability of data in a given area. For detail study
interested readers are referred to Allen et al.,(1998) & Raes & Munoz (2009).
)2U*0.34γ(1Δ
)aes(e2U273T
900*γG)n(R*Δ*0.408
oET
(2.3)
where ETo - reference evapotranspiration [mmday-1], ∆ - slope vapour pressure curve [kPa°C-1], Rn - net
radiation at the crop surface [MJm-2day-1], G - soil heat flux density [MJm-2day-1], 𝛾 - psychrometric constant
[kPaoC-1], T - mean daily air temperature at 2 m height [°C], U2 - wind speed at 2 m height [ms-1], es - vapour
pressure [kPa], ea - actual vapour pressure [kPa], es-ea, - saturation vapour pressure deficit [kPa], Rn again can
be calculated using the equations as in Appendix II.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
13
The computed ETo needs to be converted into PET since MODFLOW-NWT requires PET rather than
ETo. The single and dual crop coefficient (Kc) are the two approaches to converting ETo into PET (Allen
et al., 1998). The former approach calculates as in equation 2.4; in which the Kc depends on crop type and
growing stage, whereas, in the latter case the Kc splits it to two other factors. The first factor for evaporation
and second factor for transpiration difference between crop reference surface (Zehairy, 2014 &
Weldemichael, 2016). Dual crop coefficient requires sufficient data about crop/vegetation and soil and
hence for this study spatially variable but temporally invariable single crop coefficient approach was applied.
cK*oETPET (2.4)
where PET - potential evapotranspiration [mmday-1], and Kc- crop coefficient [-].
The spatially variable Kc in this study area was estimated based on the land use and vegetation cover. The
D-T basin mainly covered by agricultural land, forest, bare soil, and grass. The Kc value for bare soil which
is about 9 % of the study area was assigned as 0.61. About 6 % of the area covered with forest and the Kc
of trees was assigned as 1.0 (Allen et al., 1998). Agriculture land that covers 68% of the total area and the
majority of the agricultural land was covered by rice field. The Kc values of rice during initial, crop
development, mid-season, and late season stages were 0.62, 0.75, 1.16 and 0.67 respectively (Choudhury et
al., 2013). It was assumed that the Kc value for rice field to be during crop development stage. The Kc value
of 0.75 was used for agriculture land. After defining the crop coefficient for each land cover and vegetation
type, the spatially variable Kc was obtained for 500 * 500 grid cells. Then, the spatiotemporal variability of
PET was calculated using Equation 2.4.
2.2.4. Interception and infiltration rate
Interception rate is the amount of rainfall that is retained by vegetation above the surfaces. The rate depends
mainly on the rainfall duration, density, and morphology of vegetation cover. The interception loss from a
given land cover can be calculated by using Equation 2.5 (Zehairy 2014 & Weldemichael 2016).
)other
A*other
If
A*f
(I*PI (2.5)
where I - canopy interception per grid cell [mday-1], P - precipitation [mday-1], If, and Iother - interception loss
rate by forest, and agriculture respectively in [%] of precipitation, and Af other Aother - area ratios coverage
per grid for forest and agriculture respectively.
The D-T basin interception loss was calculated as in Equation 2.5. The spatial variability of interception rate
was calculated per grid cells and subtracted from spatially variable precipitation rate to get spatially variable
infiltration rate. Several kinds of the literature suggested interception ratio, i.e. If and Iother based on land
cover. For instance, Ghimire et al., (2012) determined rainfall interception by natural and planted forests in
the middle mountains of central Nepal. According to their finding, interception loss for the evergreen
natural forest was 22.4% of precipitation. Since similar forest type is present in the D-T basin (Heim, 2015),
this study adapted the value of interception ratio 22.4% of precipitation as a value for forest cover. Van Dijk
& Bruijnzeel (2001) also studied rainfall interception in upland West Java, Indonesia for mixed agricultural
cropping system involving cassava, maize, and rice. According to their finding interception loss for the
agricultural land was 14.4% of precipitation. The final finding of Van Dijk & Bruijnzeel (2001) for mixed
crops was conducted in this study as interception loss rate for agriculture farmland. Finally, Corbett et al.,
(1968) determined rainfall interception by annual grass and chaparral and found that grass has an
14
interception loss rate of 6.5% of the total rainfall. This finding for grass was used in this study as interception
loss from grassland. The values are summarized in Table 2.
Table 2: Interception loss rate that used in D-T Basin
D-T Land cover Interception loss Adapted literature
Forest cover 22.4% Ghimire et al., (2012)
Agriculture [mainly rice] 14.4% Van Dijk & Bruijnzeel (2001)
Grassland 6.5% Corbett et al., (1968)
As stated earlier the infiltration rate was calculated as the difference between rainfall and interception rate
(Equation 2.6). Infiltration is the amount of water that percolate to the unsaturated zone. The infiltration
rate highly depends on the vertical hydraulic conductivity and degree of saturation of the unsaturated zone.
The higher the vertical hydraulic conductivity, the easy through which water can pass through the soil, then
the higher the infiltration rate would be and vice versa. When the infiltration rate is higher than the vertical
hydraulic conductivity, the water hardly passes through the soil pores, then the excess rainfall will be
redirected to the streams.
IPPr (2.6)
where Pr - infiltration rate per grid cell [mday-1], P - precipitation [mday-1]. This infiltration rate is one of the
driving forces that was used in the UZF1 package to estimate the unsaturated zone storage and unsaturated
zone evapotranspiration, and groundwater recharge (Niswonger et al., 2006).
2.2.5. Stream discharge
According to Braca (2008), the stage-discharge relation or rating curve in an open channel flow is used to
convert the series of stage records into discharge records. Similarly, it is used to convert forecasted flow
hydrographs into stage hydrographs. The relationship is highly affected by section and channel controls.
The latter is due to hydraulic properties and roughness of the surface downstream. Such hydraulic properties
can be channel size, shape, slope, and curvature. On the other hand, the former can be caused by natural or
man-made processes. Rock ledge, sand bar, and debris are grouped under natural processes. Dam, Weir,
Flume, and Spillway are grouped under man-made processes. Because of the underlining reasons, the
knowledge of channel features and a time series of stage and discharge together with low and high flow
measurements are required to construct efficient rating curves. The stage-discharge relation can be calculated
using the simplified forms of Manning equation (ISO, 2010) as shown in Equation 2.7.
)( ahCQ (2.7)
where Q - discharge [m3day-1], h - stage [m], a - gauge height of zero flow [m], ah - effective depth of
water on the control, C - calibration coefficient [m2day-1], α - slope of rating curve [-].
The D-T basin has 16 sparsely located discharge stations (Figure 6 and Appendix V). The data that was
collected from "DPPU" was daily stream level for the year 2009 to 2012 together with rating curve for each
station but it lacks stream discharges data. The availability of rating curve that was constructed using
HYMOS (Sankhua & Srivastava, 2011) saves the time to convert the stages into stream discharges.
Therefore, the four-year daily stream level data were converted into stream discharge for each station and
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
15
then missing discharge data and its consistency was adjusted in the same manner as precipitation – section
2.1.1. Afterward, the final result was used as a state variable in SFR2 package (Niswonger & Prudic 2005).
2.2.6. Hydraulic properties
The pumping tests were used to obtain the aquifer characteristics such as transmissivity and storativity. Such
data together with other data was used to build a numerical modeling and evaluate the resources in the given
area. Table 3 shows the aquifer characteristics of D-T basin, this test value was used as an initial value in the
model and then adjusted during the model calibration.
Table 3: Aquifer characteristics value of the basin (T - transmissivity, Sy – specific yield, Kh - horizontal hydraulic
conductivity, SWL - surface water level). The location of bores can be seen in Appendix I.
ID
Latitude
Longitude
T
[m2day-1]
Sy
Kh
[mday-1]
SWL
[m]
Thickness
[m]
Bottom
elevation [m]
PZ1 8°25'29.21" 115°12'50.48" 1821.6 67.5 100.1 27.5 126.5
PZ2 8°30'56.37" 115°27'02.07" 2340.1 36.2 50.4 64.6 11.6
PZ3 8°20'9.69" 115°21'13.83" 134.8 2.7 89.8 50.2 140.1
PZ4 8°12'42.08" 115°17'17.63" 57.6 1.2 148.2 47.6 195.5
DP2 8°37'14.17" 115°14'0.91" 390.2 0.25 2.9 18.8 131.2 149.5
DP3 8°23'19.05" 115°13'20.55" 690.5 5.4 22.3 128.9 150.1
DP4 8°30'21.10" 115°12'33.51" 550.2 4.3 21.6 128.4 150.0
DP5 8°39'19.45" 115°11'46.89" 760.1 0.24 5.9 22.1 127.9 150.5
DP6 8°38'36.55" 115°13'56.06" 385.8 2.8 14.1 135.9 148.5
DP7 8°33'55.05" 115°10'50.25" 280.5 2.1 19.1 130.9 147.7
DP13 8°37'26.58" 115°14'09.05" 298.6 2.1 10.8 139.2 151.2
sbo1 8°31'44.41" 115°12'5.08" 7.1 0.1 62.0 62.2 130.2
sbo2 8°27'48.60" 115°11'15.25" 8.9 0.2 62.0 70.5 129.9
sbo3 8°32'18.33" 115°09'56.42" 5.4 0.1 4.2 111.0 115.2
sbo4 8°19'30.60" 115°22'00.83" 8.5 0.7 31.6 118.3 151.1
sbo9 8°22'33.38" 115°17'06.45" 110.1 0.8 9.9 140.1 151.0
sbe10 8°32'20.20" 115°06'54.27" 43.1 0.4 38.9 111.1 151.4
2.2.7. Head observation
In the study area, all groundwater level measurements are undertaken in Quaternary deposits and show
strong spatial variation to topographic altitude differences. However, such data were available neither daily
nor monthly rather monitoring records show one record per year besides, the monitoring stations have low
spatial coverage over the study area (Figure 3).
2.2.8. Groundwater abstraction
The D-T basin groundwater abstraction data could not be found in public services as well as from Ministry
of Energy and Mineral Resources of Indonesia, locally "KESDM". It was found out that the data is
confidential and the ministry is not willing to share the data even for study purposes. Because of the
underlining reason, the author builds the model without groundwater abstraction. Therefore, the result of
this model should be used with caution in case future model implemented using groundwater abstraction
data.
16
2.3. Modeling flow chart
The overall activities going to be applied to answer the research questions and to come up with the
targeted objectives is summarized in the flow chart (Figure 10).
Figure 10: Methodology of flow chart.
2.4. Conceptual model
According to Anderson & Woessner, (1992), there are three essential steps in modeling protocol. These are
(1) “to establish the purpose of the model”, (2) “formulation of the conceptual model of the system”, and
(3) “formulation of the numerical model of the system”. The purpose of the model is for better
representation of the flow between surface, unsaturated zone and saturated zone. It is useful in
understanding the interaction and estimating the water balance in the D-T basin. A conceptual model is a
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
17
“pictorial representation” of the flow system. It is used to configure the field problem into a simple and
meaningful schema and then, field problem can be easily analysed. Most of the errors in modelling arise
during formulation of a conceptual model and the generated error in the conceptual model can propagate
into the numerical model. Then, the final output of the model rarely represents real world scenarios.
Therefore, modelers should give attention in understanding field data and formulation of the conceptual
model. There are four steps to formulating conceptual model: defining hydrostratigraphic units, defining
the flow system, defining preliminary water balance, and defining the boundaries of the model.
2.4.1. Defining Hydrostratigraphic units
The hydrostratigraphic unit is used to define the aquifer type (Anderson & William, 1992). Stratigraphic
units can be merged into one hydrostratigraphic unit or treated as independent hydrostratigraphic units, this
depends on the hydrogeological formation of the layers. As stated earlier, the D-T basin consists of the
Quaternary and Tertiary geological strata. The upper Quaternary volcanic sequence consists of
unconsolidated sand & gravel, volcanic ash, lava flow, breccia, lahar, "pumic", clay and tuff (Figure 11),
whereas, Tertiary or Pliocene lower calcareous consists of a sequence of limestone, “prepatagung”
formation, calcareous sandstone, sand, and Graywacke, this layer also called the consolidated layer (Nielsen
& Widjaya, 1989 & Purnomo & Pichler, 2015). In this study, the individual geological
formation/stratigraphic unit was considered to be an independent hydrostratigraphic unit. This was due to
the fact that the stratigraphic units have different physical properties and have a different hydrogeologic
formation. The upper Quaternary volcanic sequence or the unconsolidated layer is a pervious layer where
most of the borehole are presented, whereas, the lower Tertiary layer consists of limestone and such
geological formation is impervious, so that groundwater is rarely present in this layer. Concluding, the upper
layer is considered as an unconfined aquifer. This aquifer type is bounded with the water table at the top
and with the impervious layer, an aquiclude at the bottom.
Geological cross section Bali Island, Indonesia
Figure 11: Geological cross section across the study area (After Ministry of Energy and Mineral Resources of Indonesia)
2.4.2. Defining the flow system
The mountain chain that runs along the island of Bali causes morphological regions of Bali to be divided
into several topographic and physiographic units (Purnomo & Pichler, 2015). Since the Northern part of
18
the D-T basin is high elevated, major drainage network of rivers/streams is located in the south as well as
in the central part of the basin (Figure 6). The groundwater flow system of D-T basin is directed from the
higher hydraulic head, in the North to the lower head, in the South as in Figure 8. However, close to the sea
coast the aquifer flow system is dependent on the tidal movement (Pauw et al., 2014). The influence of the
tidal movement on the groundwater head and flow, is taken into account using fresh/seawater boundaries
(Mulligan et al., 2011; Durden et al., 2013 & Pauw et al., 2014).
2.4.3. Defining preliminary water balance
In the D-T basin rainfall is the only source of water to the system. At first, part of the incoming rainfall is
intercepted and evaporated back to the atmosphere due to vegetation and others bodies; and then, part of
it becomes recharge and finally some will either evaporate or drain to the streams as overland flow. For
groundwater basin, recharge from unsaturated zone and stream discharge to the groundwater was
considered as the inflow to the aquifer system. Groundwater evapotranspiration, surface leakage, lateral
groundwater outflow and stream discharge from groundwater was considered as an outflow from the
system, the schematic representation of D-T basin is presented in section 2.7.
2.4.4. Defining the boundaries of the model
Model boundaries need to be defined critically since the defined boundaries can have a tremendous effect
on the final output of the model. In the study area there are physical and hydrological conceptual model
boundaries. The southern, south-eastern and south-western sides of the basin were surrounded by the
physical boundary, i.e. the Indian Ocean. The groundwater flow system near to the sea coast is highly
influenced by the tidal effect or forcing of the sea (Mulligan et al., 2011 & Pauw et al., 2014). Thus, the
impact of tidal forcing on the groundwater flow of D-T unconfined aquifer was take into account by
defining a reliable numerical boundary condition as in section 2.4.6. Apart from these, the lower Pliocene
calcareous sequence underneath the unconfined aquifer considered as the bedrock of the basin/impervious
layer and hence there is no flow out from basin bottom. The northern, north-eastern, and north-western
sides of basin is surrounded by hydrological boundaries. The defined hydrological boundaries are mountain
ranges/watershed divide at the north; streamlines at the north-east as well as north-west side (Figure 1). The
watershed boundaries are defined by topographic divides and they identify the surface water runoff divides.
Besides, they usually do represent groundwater flow dividers in the case of an unconfined aquifer (Heswijk,
2013). Therefore, flux along the watershed divide or streamlines was considered as zero or no in/outflow
from these boundaries.
2.5. Numerical model
According to Anderson & William (1992), the third step in modeling protocol is the formulation of the
numerical model of the system. Numerical modeling is actually the numerical representation of hydrological
system regime and considers the aquifer properties are divided in space and time. Numerical modeling
includes software selection, general model assumptions, grid design, aquifer geometry design, aquifer
parameterization and boundary conditions.
2.5.1. Software selection
Software selection is dependent on the environment being modeled and objectives. In this study,
MODFLOW-NWT software was used to develop the model. According to Niswonger et al., (2011)
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
19
MODFLOW-NWT is working under ModelMuse Graphical user Interface (GUI) and merged with UZF1;
SFR2 and other packages. It is a Newton formulation of MODFLOW-2005, is one of the models that
developed to link saturated and unsaturated zone. MODFLOW-2005 is block centered with finite difference
concept, that computes head with an average head for the cell that surrounds the node (McDonald &
Harbaugh, 1988). Therefore, this model was used to quantify the exchange flux between surface, unsaturated
and saturated zones. MODFLOW-NWT is selected for D-T basin because: (i) it will integrate surface,
unsaturated and saturated zone; (ii) it is a standalone and public domain with excellent documentation, and
(iii) it is MODFLOW base model, hence it can possibly be compared with other models.
UZF1 Package
Integrating and modeling the unsaturated zone and saturated zone/groundwater in three dimensions is quite
troublesome. Since modeling unsaturated zone based on Richards’s equation is highly nonlinear and it is
difficult to solve it (Niswonger et al., 2011). However, recently UZF1 package is developed to simulate the
flow in the unsaturated zone into one-dimension form of Richard’s equation. "The one-dimension form of
Richards’s equation is approximated by a kinematic wave equation to simulate the flow of water and storage
in vertical components in response to gravity potential gradients only and ignores negative potential
gradients", equation 2.8. This package is a substitution for the Recharge and Evapotranspiration Packages
of MODFLOW-2005, which integrate the flow with the three-dimensional groundwater flow system
(Niswonger et al., 2006). UZF1 Package in MODFLOW-NWT uses input data such as saturated water
contents, maximum unsaturated zone vertical hydraulic conductivity and Brooks-Corey exponents,
infiltration rate, evapotranspiration demand, extinction depth and extinction water content at specific stress
period. The Brooks-Corey exponents are used to define the relation between unsaturated zone vertical
hydraulic conductivity and water content. The extinction depth and extinction water content at specific
stress period are essential components to simulate evapotranspiration. Extinction depth is “defined based
on the dominant vegetation of the area in which the depth extends beneath the soil zone” and
evapotranspiration ceases underneath this depth (Hassan et al., 2014). Extinction water content is the water
content in unsaturated zone below which evaporation will be neglected. Using the above input data, the
package partition flows into evapotranspiration, recharge, and runoff into the stream. Nonetheless, the
package does not allow for parameter estimation, the parametric values are shown in section 2.4.5.
0)(
i
Z
K
t
(2.8)
where θ - volumetric water content [m3m-3], K(θ) - unsaturated hydraulic conductivity as a function of
water content [mday-1], i - ET rate per unit depth [m-1], t - time [day].
SFR2 Packages
SFR2 package is used to simulate the exchange flux between stream and groundwater as well as the flow
and storage in the unsaturated zone beneath the stream. In this package, the flow computation method
between stream and aquifer is the same as River Package in MODFLOW-2005 (Niswonger & Prudic 2005).
The “flow computation between the two resources is based on Darcy’s law and assuming uniform flow
between them” (Equation 2.9). Additionally, simulation of flow and storage in the unsaturated zone beneath
the stream is based on the kinematic wave approximation to Richards’s equation. In the approximation
techniques, it is assumed that the flow is in the vertically downward direction, horizontal flow component
is ignored. The zone assumed to be homogeneous and isotropic, and diffusion is neglected. Because the
20
flow is assumed to be vertical downward direction, SFR2 packages fill the unsaturated zone pores from the
top down sequence. Seepage across the streambed can exhibit either horizontal or vertical component of
flow.
SFR2 package in MODFLOW-NWT uses input data such as stream flow network, streambed top, stream
slope, streambed thickness, streambed hydraulic conductivity, stream width, channel roughness, bank
roughness, saturated and initial water contents, maximum unsaturated zone vertical hydraulic conductivity,
Brooks-Corey exponents, flow into upstream end, SFR2 packages parametric values were shown in section
2.3.5. The package can simulate volumetric water discharge, it allows the user to add or subtract water from
stream due to precipitation, runoff, and evapotranspiration (Niswonger & Prudic 2005).
)()( hohschohsM
KWLQl (2.9)
where Ql; - volumetric flow between a given section of streams and volume of aquifer [m3day-1]; K - hydraulic
conductivity of streambed sediment [mday-1]; W - width of the stream [m]; L - length of the stream [m]; M
- thickness of the streambed deposits extending from top to the bottom of streambed [m]; hs - the head in
stream [m]; ho - head in the aquifer [m]; and C – riverbed conductance [m2day-1].
2.5.2. Aquifer geometry and grid design
Block-centred steady/transient with a grid size of 500 * 500 m, one-layer unconfined IHM was developed
because of the single hydrostratigraphic unit. Small grid cell size was proposed in order to compromise the
model accuracy and computation time. Mehl & Hill, (2010) mentioned that “highly refined grids have a
better representation of the system and address more detailed resources management issues”. Aquifer
geometry design is in forms that defining top and bottom of the model layer and defining water table
distributions. This single layer is represented by layer type 1, which is utilized the uppermost layer of a
model, and only where unconfined conditions are expected to persist in the layer throughout the entire
period of simulation.
2.5.3. Driving forces
Driving forces can vary in space and time. The number of driving forces in a given model depends on the
intended purpose of the modeling. By fixing the model parameter value, the output of the model will be
affected due to change of driving forces through time. The proposed driving forces in this study area were
precipitation, infiltration rate, and PET. Initially, the driving forces are available on a daily basis for four
years (01/01/2009 – 31/12/2012). These time series data are point observation (Figure 3 and Appendix V;
A & B) but the MODFLOW-NWT required as interpolated map. Because of this, raster map was generated
for each driving force. For instance, from the available eighteen-point observation rainfall data, the
spatiotemporal rainfall map was generated using kriging interpolation method; this method was chosen
because it is a best linear unbiased predictor [BLUP] that gives a minimum error of variance (Sterk & Stein,
1997; Hengl et al., 2007; & Webster & Oliver, 2007). In order to generate spatiotemporal infiltration rate,
first spatially variable but temporally uniform interception rate was generated using the land use map of the
D-T basin. Then, spatiotemporal infiltration rate was generated by subtracting the interpolated interception
rate from spatiotemporal rainfall map- section 2.1.1 & 2.1.2. In addition to this, the spatiotemporal PET
was generated by simple multiplication of the spatiotemporal ETo and spatially variable but temporally
uniform Kc interpolated map – Section 2.23. Finally, the spatiotemporal infiltration rate and PET were
imported as ASCII raster file into UZF1 packages (Niswonger et al., 2011).
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
21
2.5.4. State variables
In this study, the defined state variables are hydraulic heads and stream discharges. As the driving forces can
have a different value at the different time and space, the state variables can also have a different value in
different time and space. In the D-T basin, there are 11 groundwater levels and 16 stream gauge records.
The daily basis of stream discharge record was available from locally called "DPPU". The four-year time
series stream discharge data show temporal variability for each station. Groundwater level records from 11
stations were not on a daily basis rather the records are once in a year. Since groundwater assessment
required groundwater monitoring stations, the available initial heads from 11 stations was used as starting
heads in the steady-state IHM. Then, these head again was used as an initial head value for transient IHM.
Since there is a shortage of time series groundwater fluctuation, the transient model is calibrated mainly
based on daily stream discharge data.
2.5.5. Parametric data
The UZF1 package is used to calculate vadose zone evapotranspiration, saturated zone evapotranspiration,
gross recharge, groundwater exfiltration, and change in storage in the vadose zone as a function of the inputs
assigned to the package including infiltration rate, PET, extinction water content [EXTWC], and extinction
depth [EXTDP]. First the package satisfying the evapotranspiration demand, then, the remaining water
moves to underlying aquifer as UZF recharge. In the steady-state model, the average infiltration rate over
the four years was calculated per grid cells after subtracting the spatially variable but temporally uniform
interception rate from kriging prediction rainfall map - section 3.1. In the transient model, the infiltration
input was calculated as a daily variable for each time step in order to account for the spatiotemporal
variability of subsurface fluxes. In the same manner, the spatially variable PET value assigned in the model
using spatiotemporal ETo and spatially variable but temporally uniform Kc. On top of that, spatially uniform
Brooks-Corey exponent as 3.5; maximum unsaturated vertical hydraulic conductivity as 0.35 m day-1 and
adjusted during model calibration; saturated water content as 0.5 m3 m-3; and the extinction water content
as 0.06 m3m-3 was used to all cells. The model top was taken as the land surface where the infiltration was
applied. In addition to these, the extinction depth was adapted from literature. The extinction depth was
assigned to each land cover (Table 4) and spatially variable extinction depth was generated for 500 * 500 m
grids. Furthermore, “the recharge and discharge location option” [NUZTOP] was selected as “Top active
cell (3)”; “vertical hydraulic conductivity source” [IUZFOPT] was assigned as “Specify vertical hydraulic
conductivity (1); “number of trailing waves” [NTRAIL2] was set to 16 (notice, it ranges between 10 to 20);
“number of wave sets” [NSETS2] was set to 20 since the infiltration rate varies through time, and finally
“route discharge to streams, lakes, or SWR reaches” [IRUNFLG]; “Simulate evapotranspiration”
[IETFLG]; “Print summary of UZF budget terms” [IFTUNIT]; and “calculate surface leakage” inverse of
[NOSURFLEAK] were selected. For Newton Solver the “Head tolerance” [HEADTOL] was set as 0.0001
m and adjusted during model calibration; “Flux tolerance” [FLUXTOL] set as 500 m3day-1 and adjusted
during model calibration; “Maximum number of outer iterations” [MAXITEROUT] 1000; and “Model
complexity” [OPTIONS] set as Complex (Hassan et al., 2014 & Niswonger et al., 2006).
Table 4: D-T extinction depth based on land cover.
D-T Land cover EXTDP [m b.g.s] Adapted literature
Forest 2.5 Shah et al., (2007)
Agriculture and Grass 1.45 Mishra et al., (1997) & Francis et al., (2014)
Bare soil 0.5 Shah et al., (2007) &Francis et al., (2014)
22
The D-T basin streams that flow from the north to the south were simulated by the SFR2 packages. Most
of the D-T streams are perennial and the stream segments are hydraulically connected with groundwater
(Rai et al., 2015). Prior to setting up the model, the map of each stream segments and reaches were prepared
in ArcGIS. Each stream segments were assigned a unique number and the numerical value that was assigned
in each stream segments was arranged from smallest to largest, in order to define the flow direction of the
streams. Then, the generated stream segments were imported into the model and required input data (section
2.4.1) were defined in each stream segments through the SFR2 package. In this package, spatially uniform
values such as “maximum unsaturated zone vertical hydraulic conductivity” [UHC]; “Brooks-Corey
exponents” [EPS]. “Saturated volumetric water content” [THTS]; “Initial volumetric water content” [THTI]
were used the same as in UZF1 package. “Streambed vertical hydraulic conductivity” [STRHC1] was set as
one-tenth of the horizontal hydraulic conductivity and adjusted during model calibration (Niswonger &
Prudic 2005). “Streambed top” [STRTOP] was set to be between 1m to 3.5 m and adjusted during model
calibration; “Streambed thickness” (STRTHICK) set between 0.35 to 0.5 and adjusted during model
calibration; and “stream slope” (SLOPE) set as 0.025 and adjusted during model calibration. “The stage
calculation” [ICALC] set as 1, this value represents the rectangular channel; the stream reaches were set a
width of 2 to 12 m and adjusted during model calibration. The length ranged from 1 km to 20 km in the
cells depending on the generated stream segments in ArcGIS. “Manning’s roughness coefficient for the
channel reaches” (ROUGHCH) and “Bank roughness” (ROUGHCBK) were set as 0.035 and 0.06
respectively. “Tolerance” [DLEAK] was set as 0.0001 m3day-1; “Number of trailing wave increments”
[NSTRAIL] was set to 20, “Maximum number of trailing waves” [NSFRSETS] set as 30, and “Maximum
number of cells to define unsaturated zone” [ISUZN] set to 10. Additionally, “Unsaturated flow
(ISFROPT); “Print streams (ISTCB2) as print flows in listing file”; “Streambed properties” (ISFROPT) as
“Specify some streambed properties by reach (can’t inactivate streams)” were selected.
Aquifers have different properties, which describe the capacities to transfer water through the soil medium.
The properties can vary by several orders of magnitude and show strong spatial variation. In the case of
unconfined aquifer these properties are explained by horizontal hydraulic conductivity (Kh) and specific
yield (Sy). For instance: (1) Sy, the difference of total porosity (n) and specific retention (Sr), is an important
parameter during model calibration. It is defined as “the volume of water that unconfined aquifer releases
by gravity forces from storage per unit surface area of the aquifer per unit decline in the water table”
(Kruseman & Ridder, 1994); (2) Kh is another core calibration parameter. It is defined by Fitts (2002) as the
easy with which water can pass through the soil. The higher Kh the easy water transmits through the medium
and vice versa. During steady-state IHM, thirty-four internally homogenous, uniform Kh zones were defined
based on hydraulic properties (section 2.1.7) and streambed hydraulic conductivity. The value as indicated
in Table 3 were used as a guideline for model calibration. During transient IHM, both Kh and Sy were defined
in the model. The Kh zonas and their value from steady-state IHM was used as an initial value and adjusted
during model calibration. Additionally, spatially uniform Sy was set as 0.24 in the modelled area and adjusted
during model calibration. Spatially invariant Sy was assigned, because the unconsolidated layer of the basin
shows nearly similar sorted aquifer materials (Figure 7).
2.5.6. Boundary conditions
Figure 12 shows the proposed boundary conditions of D-T basin. Two boundary condition type were
defined in the D-T basin. At the north, northeast, and northwest of the study area were no-flow boundaries
due to the presence of hydrological boundaries, i.e. watershed divide at the north and streamlines at the
northeast and northwest of the basin. A no-flow boundary condition was also defined at the bottom of
unconfined aquifer since the Quaternary deposit was considered as an impermeable geological formation.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
23
The area defined by no-flow boundaries were assumed to prevent water from entering or leaving the system
(Anderson & William 1992).
In the D-T basin the south, southeast, and southwest areas were bounded by Ocean. The numerical
boundary conditions at the sea coast and the effect of assigning different boundary condition on the
groundwater flow and head distribution were studied by Mulligan et al., (2011) & Pauw et al., (2014) using
SEWAT. According to them, the fresh/seawater boundary is represented in three ways: using time-variable
specified head (CHD); the general-head boundary (GHB) or periodic boundary condition (PBC) packages.
The CHD and GHB packages were supported by MODFLOW-NWT, however, the PBC package was not
supported by MODFLOW-NWT rather in SEWAT. In this study the PBC package was not covered,
interested readers are recommended the above articles. Mulligan et al., (2011) studied “Tidal boundary
conditions in SEWAT” and they found that the GHB have an advantages over CHD or PBC; (1) the CHD
or PBC boundaries reduce the amplitude of heads or create difficulty in matching the simulated and
observed heads; (2) incorrect simulation of fluxes and salt advection into the aquifer (salt advection is not
covered in this study); (3) reduce the high contrast in hydraulic conductivity and “eliminating potential
numerical problems”. Pauw et al., (2014) studied “regional scale impacts of tidal forcing on groundwater
flow in unconfined coastal aquifer”. Emphasizing the need to consider tidal forcing in the coastal aquifer
and that the assigned boundary condition at the fresh/seawater interface governs the amount of
groundwater flow from the groundwater divides to the intertidal area. The groundwater flow and head
distribution are best quantified through GHB conditions. Moreover, the USGS coastal aquifer studies such
as Bakker et al., (2013); Durden et al., (2013); & Masterson et al., (2016) strongly recommended the need
to use GHB to represent the ocean. They also refer that GHB condition is the most widely used numerical
boundary conditions at sea coast. Therefore, in this study, the numerical boundary condition at the sea coast
was assigned as GHB conditions (Figure 12).
Proposed boundary conditions in D-T basin.
Figure 12: Proposed boundary conditions and locations in the D-T basin.
The GHB conditions defined in the model as a polyline objects and the head at that boundaries was
represented as equivalent fresh-water head of sea level. In MODFLOW-NWT, the GHB conductance is
calculated as an average value between the GHB conductance per unit length* “object section intersected
24
length” and GHB condition parameter * “object section intersected length”. These GHB condition
parameter value of 10-4 was used as a recommended value and this was multiplied by user-specified
multipliers to determine the GHB conductance (Niswonger et al., 2011). Furthermore, a separate model was
built using the CHD boundaries and head along the coast was assumed to vary through position and time,
h = f(x,y,t) (Franke et al., 1987). Then, the water balance results of this model was compared with the GHB
model output results.
2.6. Model calibration
Calibration refers to the adjustment of model parameter values to find the best fit with the observations. It
is also called "model fitting" or "history matching" (Barnett et al., 2012). Model calibration is not an easy
task rather complex step because it needs the understanding of advanced mathematics, statistics and
software packages as well as proper characterization of the study area. Calibration of MODFLOW-NWT
model has been done by adjusting model parameters, i.e. hydraulic conductivity (Kh) and specific yield (Sy)
together with UZF1, SFR2 and GHB conductance input variables. In the case of steady-state IHM
calibration was carried out with objectives to minimize differences between observation and model
prediction heads and stream discharges, whereas, in the case of transient IHM, calibration was carried out
with the objective to reproduce pattern of stream discharges and minimize differences between observation
and model prediction stream discharges as well as heads. Barnett et al., (2012) suggested that manual
calibration has an advantage over automatic calibration; in which physically meaningful judgment could be
applied. Consequently, manual/trial and error calibration techniques were carried out in this study for a
better understanding of the real world behavior. A steady-state and transient model were simulated based
on the hydrological conditions for the period of 2009 till 2012.
2.6.1. Steady-state model calibration
Steady-state IHM was built based on the assumption that stream discharges and heads do not change with
time. Steady-state IHM was calibrated based on the average of the hydrological conditions in the study
period from 1st January 2009 to 31st December 2012. Thirty-four internally homogenous, uniform Kh zones
were defined based on pumping test result and streambed hydraulic conductivity. The value as indicated in
Table 3 were used as a guideline for model calibration. These values were assigned in “Upstream Weighting
Packages” [UPW] and adjusted during model calibration till model error assessment criterion was fulfilled -
section 2.6. The steady-state model calibration also adjust input parameters such as the maximum
unsaturated zone hydraulic conductivity (Kvun) in UZF1 package; GHB conductance in GHB package and
also the “Streambed vertical hydraulic conductivity” [STRHC1]; “Streambed top” [STRTOP]; “Stream
width”; “Streambed thickness” (STRTHICK); and “stream slope” (SLOPE) in SFR2 packages (Niswonger
& Prudic 2005). Moreover, all initial models calculations were set into meter and day.
2.6.2. Warming-up period for transient model calibration
One hydrologic year data from 1st January 2009 to 31st December 2009 or 365-time steps data were applied
as warming-up period, in such a way the model possible minimizing the influence of initial state conditions
on the transient simulation (Navarro & Playan, 2007). The model with one-year data was calibrated to assess
the model response to the daily variation of stream flows. Once, the model has response to the warming up
period, the transient model can be built. In this study, contrary to Hassan et al., (2014), the data that was
used in the warming up period was not discarded rather three-years data from 1st January 2010 to 31st
December 2012 were added into it and in total four-year from 1st January 2009 to 31st December 2012 was
considered as a transient model simulation period.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
25
2.6.3. Transient model calibration
Transients IHM is applied when pumping wells start up and shut down and/or in response to transient state
variables. In this study, the transient model is required due to the response to transient state variables. The
transient IHM simulation period from 1st January 2009 to 31st December 2012 which is equal to 1461 days
is considered as stress periods and by considering the variation of stream discharges daily time steps were
generated. As quoted by Anderson (1992); Schlumberger (2011); & Fitts (2002), the time step is important
because the size of time steps affects the error in the water balance as well as the stability of the solution. In
a nutshell, the initial conditions in the transient model were adapted from a steady-state model and the
stream discharges value for each stress period was given to MODFLOW-NWT through SFR2 packages.
Then, the Kh and Sy as a calibrated parameter together with other input variables as indicated in steady-state
model calibration were adjusted during model calibration till model error assessment criterion - section 2.6
riches.
2.7. Error assessment and sensitivity analysis
The model should be evaluated after calibration by statistical analysis to test how well the calibrated model
result fits with observed data. Model performance was carried out for both hydraulic heads and stream
discharges. To assess the difference between measured and observed heads three different measure errors
were used. These are the mean error (ME), mean absolute error (MAE) and root mean squared error
(RMSE) calculated by using equation 2.10 to 2.12. In most cases RMSE is used to check the performance
and when RMSE is close to zero then the model has good performance and when RMSE highly deviate
from zero the model has poor performance Anderson and Woessner (1992) and Mason & Hipke (2013).
ni iso hh
nME 1 )(
1 (2.10)
ni iso hh
nMAE 1 )(
1 (2.11)
ni iso hh
nRMSE 1
2)(1
(2.12)
where ho - observed head [m], hs - simulated head [m], n - umber of observation.
The model performance for stream discharges were evaluated using different objective functions, the
selection of objective functions depends on the calibration purpose. Equation 2.13 to 2.15 show the main
objective function as recommended by Nash and Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007);
Moriasi et al., (2007); & Akhtar et al., (2009). These are the relative volumetric error (RVE), Nash-Sutcliffe
efficiency (NS) and overall model performance (Y). RVE is used to evaluate the fitness in terms of volume
under hydrograph. According to them, when the RVE approximate to 0 the model has the best
performance; when the RVE ranges from ± 5 % the model has well performance; when the RVE is between
± 5 % ± 10 %, the model has reasonable performance. NS is used to evaluate the fitness of the shape of
hydrograph, NS between 0.9 and 1 mean that the model performs extremely well. NS between 0.8 and 0.9
means that the model performs very well. NS between 0.6 and 0.8 mean that the model performs reasonably
well. NS below 0.6 means the model has low performance.
100*)(1
1 1
ni obs
ni sim
niobs
Q
QQRVE (2.13)
26
2
1
12
)(
)(1
ni meanobs
ni simobs
QQNS (2.14)
||1 RVE
NSY
(2.15)
where Qobs - observed stream discharge [m3day-1], Qsim - simulated stream discharge [m3day-1], Qmean - mean
stream discharge [m3day-1], ho - observed head [m], hs - simulated head [m], n - the number of observation.
A sensitivity analysis is the process of varying model input parameters over a reasonable range, i.e. range of
uncertainty in the value of the model parameter and observing the relative change in model response. The
sensitivity analysis in the D-T basin were performed in order to assess the effects of model parameters and
adjusted variables (Section 2.4.5) on the calibrated model. The sensitivity of each model parameters were
established with a percent factor of -30 to 30%. When one parameter analysed, other model calibration
parameters will remain the same. Then, their effects of uncertainty on the calibrated model would be
interpreted.
2.8. D-T basin water balance
As stated earlier, MODFLOW-NWT integrate surface, unsaturated/vadose and saturated zone. It is
working under ModelMuse GUI and coupled with UZF1, and SFR2 (Niswonger et al., 2011; Hassan et al.,
2014; Tian et al., 2015; & Tian et al., 2016). The interaction of the three zone under MODFLOW-NWT
model in the D-T basin can be shown as in Figure 13. The schematic diagram and summary of the water
balance below follows (Hassan et al., 2014).
Water balance components of D-T basin
Figure 13: Schematic diagram of MODFLOW-NWT setup of D-T basin model.
where P - precipitation, I - canopy interception, ETuz - vadose zone evapotranspiration, ETg - groundwater
evapotranspiration, Exfgw - groundwater exfiltration, Rg - gross recharge, qH - hortonian runoff, qD - dunnian
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
27
saturated excess runoff, qgs - groundwater leakage into the stream, qsg - stream leakage to the groundwater, qg
- lateral groundwater outflow, all units are in [mday-1].
The water balance of D-T basin and the daily flux for surface, unsaturated and saturated zone can be
calculated as below. For the entire basin, the water balance can be calculated as in Equation (2.16).
SqqETP g (2.16)
where ET - total evapotranspiration, q - stream discharge at the basin outlet, and ∆S - change in basin
storage. Total evapotranspiration and change in basin storage can be estimated as in Equation (2.17) and
(2.18) respectively.
guz ETIETET (2.17)
guz SSS (2.18)
where, ∆Suz - the change in storage in the vadose zone and ∆Sg - the change in storage in the saturated zone.
Moreover, the general surface and unsaturated zone water balance of the area can be written as in Equation
(2.19).
uzuzge
eogw
SETRP
PRIExfP
OR uzuzgogw SETRRIExfP (2.19)
where Ro - the total runoff to streams, Pe - actual infiltration rate. Finally, the groundwater zone water balance
is expressed as in equation 2.20 below.
ggwgn
gggssgn
ETExfRR
SqqqR
OR ggwgggssgg ETExfSqqqR (2.20)
where Rn - net recharge to the groundwater. Sophocleous (2005) & Hassan et al.,(2014) stipulated that,
estimating net recharge give an advantage of understanding the dynamics and sustainability of groundwater
resources then estimating gross recharge.
28
3. RESULTS AND DISCUSSION
This chapter describes results and discussion of the three parts, namely data processing, steady-state model
calibration, and transient model calibration.
3.1. Data processing calculation results
The hydro-meteorological calculations were made for the model inputs which including precipitation,
interception rate, infiltration rate, and evapotranspiration. The consistency of the data was checked through
the double mass curve; that the commutative of a given station versus commutative of nearby stations
expected to be linearly correlated as in section 3.1.2. Spatial variability of rainfall data was generated using
the kriging interpolation method.
3.1.1. Filling missed data for precipitation
The correlation coefficient between station Kuta and the nearby stations such as Ubung and Sanglah was
0.72 and 0.75 respectively (Appendix III). Because the relation coefficient is good enough Equation 2.1 was
applied to fill the missed rainfall data. Figure 14 shows the rainfall distribution through the study period of
station Kuta after the missed rainfall data was filled using the CCWM.
Observed and filled rainfall data at station Kuta
Figure 14: Daily rainfall after filling missed data at station Kuta for the years from 2009 to 2013. For the location of
station see Appendix V (A).
3.1.2. Consistency of the precipitation records
The double mass curve technique as described previously – section 2.1.1., was carried out to check the
quality of the meteorological stations. For that reason, high-quality assessment of the recorded rainfall data
for each meteorological station was carried out. In such a way each year from 2009-2012 was treated
independently for consistency check. It was found that fifteen stations (Bedugul, Bonganica, Buagan,
Gadungan, Kedisan, Kuta, Mambal, Pempatan, Pengotan, Sading, Selishan, Tegallalang, Tiyin Gading,
Ubung, and Sanglah) have a very good control and should be treated as reliable data. There are three stations
(Tampaksiring, Rendang, and Klungkung) that show inconsistency in the data. As the scatter plots shown
in Figure 15, the rainfall data for Bedugul and Sanglah stations have linear trends and the data do not present
0
20
40
60
80
100
120
Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13
Rai
nfa
ll (m
md
ay-1
)
RF Observed at Kuta station RF filled at Kuta station
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
29
a break in slope. In contrary, in the case of Rendang and Tampaksiring stations a break in slopes clearly
shown, therefore the data from the break point were adjusted using Equation 2.2.
A. Double mass curve for station Bedugulu
B. Double mass curve for station Rendang
C. Double mass curve for station Sanglah
D. Double mass curve for station Tampaksiring
Figure 15: Double mass curves of the precipitation gauges [units in mm]. The double mass curve in A & C shows
consistency in the data but B & D shows inconsistency in the data. For the location of stations see Appendix V (A).
3.1.3. Spatial data interpolation of rainfall
The spatial data interpolation was carried out in R-Software. First and for most, hypothesis test, i.e. Ho: β1
= 0 and H1: β1 ≠ 0 (Ho – null hypothesis, H1 - alternative hypothesis, and β1 - elevation) was executed to
examine whether rainfall is dependent on elevation or not. The significance test was performed for daily
rainfall records form the year 2009-2012. A sample significance test result was presented as in Figure 16 and
it was found that; p = 0.23. This p-value corresponds to the F-test (Webster & Oliver, 2007) and when p>α,
means fail to reject the Ho hypothesis. It was concluded that at the α=5% level of significance the elevation
has no significant effect on rainfall distribution. Therefore, it was not critical to include elevation as a
covariate/auxiliary variable for rainfall interpolation. By using the above results, the rainfall type in the area
may be frontal but may not be orographic type of rainfall since, in the orographic type of rainfall, large mass
of air is forced to rise over the mountain ranges and cause heavy precipitation on the windward side. In case
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000 3500
Cum
ula
tive
pp
t fo
r B
edugu
l Sta
tio
n
Average cumulative ppt for a group of stations
0
500
1000
1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000 3500
Cum
ula
tive
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t fo
r R
end
ang
stat
ion
Average cumulative ppt for a group of stations
0
500
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1500
2000
2500
3000
0 500 1000 1500 2000 2500 3000 3500
Cum
ula
tive
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t fo
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glah
sta
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Average cumulative ppt for a group of stations
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0 500 1000 1500 2000 2500 3000 3500
Cum
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t fo
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amp
aksi
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atio
n
Average cumulative ppt for a group of stations
30
of frontal rainfall, the cold air mass from northwest equatorial and the dry air mass from southeast Australia
meet and the warm air is forced to rise over the denser, colder air. As the warm air is forced to rise further
condensation occurs and rain is formed (Ahrens, 2013).
Figure 16: Sample significance test results of rainfall record on January 10, 2009.
The standardized average sample variogram was estimated by averaging the individual sample variogram
(Appendix IV). After several trial and errors, the exponential variogram model was found as the best fit
model (Figure 17). The exponential model has slightly higher nugget effect compared to the partial sill, this
might bring uncertainity in the daily rainfall interpolated map. The model bounded asymptotically and
reached the sill with some effective range (Hengl et al., 2007; Webster & Oliver, 2007; & Zhang et al., 2012).
The effective range of spatial dependency is the distance at which the semi-variance is 95% of the sill. It is
assumed that while correlations may become arbitrarily small at a large distance, they never vanish and that
spatial dependencies never fall to zero. In this case, the effective range is 17772 m; meaning that the model
will reach 95% of the sill at 17772 m.
Model Variogram
Figure 17: Standard model variogram; distance in a unit of [m] and semi-variance in a unit of [m2].
Figure 18, shows the kriged prediction and kriging variance for long-term average rainfall. The results from
ordinary kriging show that it minimized the prediction error variance and smoothing the actual variability
(Sterk & Stein, 1997; Hengl et al., 2007; & Zhang et al., 2012). The yellow and dark blue color as in Figure
18 left, shows the areas with the highest and the lowest rainfall predicted concentrations respectively.
Observations that are closer to each other had higher correlation than the observations that are far apart
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
31
(Webster & Oliver, 2007). The result shows that the kriged prediction has similar results in the area where
there are dense observations than sparse observations. The point where no data or very few neighboring
points (south-west to north) shows that the predictions are influenced by covariance structure. Location
with no observation alters the value of the outcome of the contribution of neighboring measured values to
the prediction.
Kriging variance is dependent on the location of prediction, location of observation point and on the
variogram model (Webster & Oliver, 2007). The kriging variance was less in the locations where there is
rain gauge observation and high in area where there is no rain gauge observation (Figure 18, right). Dark
blue color shows low kriging variance while orange to yellow has high kriging variance. Thus it can be
concluded that areas having a high kriging variance are those areas that have observation far apart (south-
west to north) whereas areas having low kriging variance are those areas that have observation close to each
other. Due to the presence of lack of a number of observation points outside of the D-T basin, there is a
substantial increase in prediction uncertainty, thereby increasing the kriging variance. Moreover, it is clearly
seen in the output that the kriging variance is almost the same for each individual day. This is because that
the ordinary kriging method used just similar variogram.
Figure 18: Kriged prediction and Kriging variance of D-T basin for long-term average rainfall from 01/01/2009 to 01/01/2012 [unit – mday-1].
3.1.4. Interception and infiltration rate
The spatially variable interception rate of D-T basin was generated using the land use map of the area. The
land use map that was collected from office locally called “BIG”. It shows that the D-T basin is mainly
covered by agriculture and it has interception rate of 14.4% (Figure 5 & 19, A). Similarly, the interception
rate of 22.4% and 6.5% was assigned for forest, grass cover respectively. Zero percent of interception rate
was assigned for buildings and bare soil. The spatiotemporal infiltration rate was calculated from
interception and rainfall map - section 2.1.3. Mathematically, the infiltration rate was calculated as Kriged
prediction rainfall – (interception rate * Kriged prediction rainfall). This can be executed either in ArcGIS
spatial analysis tools (Figure 19, B) or the mathematical formula can be written in MODFLOW-NWT.
Consequently, the latter case was used and the spatially variable interception rate and rainfall map were
imported independently into the model to maintain the mathematical expression.
32
A. Spatially variable interception rate
B. Spatially variable infiltration rate
Figure 19: Spatially variable interception (A) and infiltration rate (B) of D-T basin.
3.1.5. Potential Evapotranspiration [PET]
Due to the presence of low number of microclimatic stations (Figure 3), the correlation between Tmax, Tmin,
Tmean for the two stations namely called station Sanglah and Kuta was carried out (Figure 20). A good
coefficient of determination (R2) was found between maximum, minimum and mean temperature of the
two stations. Because of this finding the ETo that was calculated using FAO Penman-Monteith method was
considered as an average of the two stations for the entire study area. A detail explanation of ETo calculated
using FAO Penman-Monteith was shown in section 2.1.3.
Figure 20: Temperature coefficient of determination for Sanglah and Kuta stations.
R² = 0.69
15
20
25
30
35
40
15 20 25 30 35
San
glah
_st
atio
n
Kuta_station
Max Temp. 10m [ºc]
R² = 0.32
15
20
25
30
35
40
15 20 25 30 35
San
glah
_Sta
tio
n
Kuta_station
Min Temp. 10m [ºc]
R² = 0.61
15
20
25
30
35
40
15 20 25 30 35
San
glah
-sta
tio
n
Kuta_station
Mean Temp. 10m [ºc]
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
33
Spatially variable but temporally invariable crop coefficient, Kc and extinction depth, EXTDP were assigned
based on the dominant vegetation of the D-T basin in a similar way as interception rate (Figure 21). The
assigned crop coefficient and extinction depth were adapted from different literature (Table 2 and Table 4).
Finally, PET was calculated as the product of spatially invariable but temporally variable ETo and spatially
variable but temporally invariable crop coefficient (Kc) in MODFLOW-NWT as in Equation 2.4.
A. Crop coefficient
B. Extinction depth
Figure 21: Spatially variable crop coefficient (A) and extinction depth (B) for D-T basin.
Figure 22 shows the relation between rainfall, infiltration, interception and PET. The maximum and
minimum PET value of 6.71 mmday-1 and 1.82 mmday-1 was found for the entire simulation period. The
calculated PET was proportional to temperature (Figure 4). Therefore, PET was reasonable to be applied
in the model as a driving force. The average interception loss by the forest, agriculture and grassland were
0.085, 0.62, 0.014 mmday-1 respectively. High infiltration rate was observed during the periods with a high
rate of precipitation, the estimated infiltration rate was the highest in January 2009 with 94.9 mmday-1 (Figure
22). The estimated infiltration rate ranged from 0 to 94.9 mmday-1 with an average value of 5.7 mmday-1.
Long-term average rainfall, interception, infiltration and PET
Figure 22: Average Rainfall (P), Infiltration rate (Pr), Interception rate (I) and Potential evapotranspiration (PET) for four hydrological years from 2009 to 2012.
0
1
2
3
4
5
0
20
40
60
80
100
1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13
PE
T
P, I,
an
d P
r
P (mm/day) Pr (mm/day) I (mm/day) PET (mm/day)
34
3.1.6. Consistency of stream discharge
The consistency of stream discharges data was carried out in the same way as precipitation records. The
double mass curve between one stream discharge data and average cumulative discharge of group stations
was generated for each stream gauge. It was found that thirteen out of sixteen stations namely called Yeh
Matan, Yeh Hoo, Yeh Empass, Tukad Penat, Tukad Oos, Tukad Petan, Sangsang, Melangit, Tukad Jinah,
Tukad Unda-cegeng, Yeh Otan, Yeh Aba, and Pekerisan have a very good consistency and should be treated
as reliable data. As in the scatter plot shown in Figure 23, the sample double mass curve for Melangit and
Yeh Hoo stations have a linear trends and it does not present a break in slope. The frequency distribution
graphs were also constructed for each station to show normality of the stream gauging records (Figure 23).
The results show those 13 stream discharge records have the uniform distribution but skewed to the right.
However, the log transform gives normal distribution (Appendix V, C). Additionally, the consistency of the
records was checked based on the relation between each stream flow against rainfall recorded at the
upstream (Figure 24). The result shows a few outliers, but in general the relation between stream flow and
the upstream rainfall record gives a logical statement that the stream flow increased when the rainfall
increases and the opposite is also true. Therefore, discharge for the above records were reasonable to be
applied in the model as a state variable.
A. Double mass curve for station Melangit
B. Double mass curve for station Yeh Hoo
C. Frequency distribution for station Melangit
D. Frequency distribution for station Melangit
0
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300
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600
0 100 200 300 400 500 600 700 800
Cum
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Q f
or
Mel
angi
t st
atio
n
Average cumulative Q for a group of stations
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0 100 200 300 400 500 600 700 800
Cum
ula
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Q f
or
Yeh
Ho
o s
tati
on
Average cumulative Q for a group of stations
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
35
Figure 23: Sample double mass curve and frequency distribution for the stream gauge discharge data [Q- stream
discharge in m3sec-1]. For the location of station and log transform see Appendix V.
Nevertheless, the remaining three streams gauge data, i.e. Balian, Ayung Buangga, and Badung Hilir show
inconsistency in the data (Appendix V; D, E and F). It was difficult to adjust these data since, the double
mass curve was quite erratic and there was no clear relation to apply equation 2.2. Apart from that, the graph
between stream flow and rainfall recorded at the upstream was unrelated. Such error may be due to exposure,
gauge location, or observation method. Due to the above facts, those stream gauges are not used for model
calibration rather incorporated in the model to assess the model response. Therefore, in this study only 13
out of 16 stream gauge records were used for model calibration and the remaining 3 included to see the
model response.
A. Relation between rainfall and stream discharge at station Yeh Hoo
B. Relation between rainfall and stream discharge at station Tukad Petanu
Figure 24: Relation between rainfall and stream discharge. The oval shape indicates uncertainty on the relation between
measured stream flow and rainfall pattern. [RF – rainfall and Q – stream discharge]. For the location of stream gauging
stations see Appendix V.
0
2
4
6
8
10
120
20
40
60
80
100
120
140
160
180
200
Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13
Q [
m3se
c-1]
RF
[m
md
ay-1
]
Gadungan_RF Yeh_Hoo_Q
0
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4
6
8
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20
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60
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140
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Jan-09 Jul-09 Jan-10 Jul-10 Jan-11 Jul-11 Jan-12 Jul-12 Jan-13 Jul-13 Jan-14
Q [
m3se
c-1]
RF
[m
md
ay-1
]
Tegallalang_RF Tukad_Petanu_Q
36
3.2. Steady-state model calibration
This was addressed into four main parts, namely: (1) calibration head and error assessment, (2) calibrated
stream discharge, (3) hydraulic conductivity, and (4) water budget of the steady-state simulation.
3.2.1. Calibrated head and error assessment
The assigned hydraulic conductivity value has been adjusted until the simulated heads matched with
observed heads. The steady-state observed and simulated heads were tested for correlation using a scatter
plot and by calculating R2 (Figure 25). A quantitative comparison of the head data in all the observation
points indicates a good match between the simulated and observed head values. The scatter plot exhibits a
random distribution and fall close to the 1:1 solid line, which indicates a reasonable match between observed
and simulated heads. The result is in the line with the Hill (1998) suggestion, he indicated that when the
observed and simulated discharge plotted they should fall close to a 1:1 solid line and the R2 should be ≥
0.9.
The coefficient of determination (R2) between observed and simulated heads
Figure 25: Relationship between simulated and observed heads in the D-T basin during steady-state IHM for the year
from 2009 to 2012.
Assessment of errors was based on the mean error (ME), mean absolute error (MAE), and root means
square error (RMSE) calculated from equation 2.10, 2.11, and 2.12 respectively. The values of ME, MAE,
and RMSE are respectively equal to 0.1 m, 0.41 m, and 0.52 m with the associated error shown in Table 5.
The water table in the D-T basin varies between 2.5 m a.s.l. to 361.5 m a.s.l. which makes the total head loss
of 359 m in the model area. The steady-state model calibration result was in line with the Anderson and
Woessner (1992) and Mason & Hipke (2013) model error criteria, where mean absolute error is less than
2% of the total head changes (7.2 m); the maximum absolute value of model residuals (0.9 m) should be less
than 10% of the total head changes (35.9 m); the root mean square error is less than 2% of the total head
changes (7.8 m); the ratio of RMSE to the total head difference is 0.11% which is also lower than the 10%
of total head difference (35.9 m). Besides, the model also satisfied the suggested by Anderson and Woessner
(1992) when RMSE closer to zero (0.52 m) the model has reasonable performance.
Table 5: Observed and simulated head with calculated error assessment for 11 piezometers, Hobs – Observed head,
Hsim – Simulated head [units – m].
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
37
Observation
Points Latitude Longitude Hobs HSim
Hobs -
Hsim
|Hobs-
Hsim|
[Hobs -
Hsim]²
WL1 8°43'43.65"S 115°10'36.44"E 2.52 1.94 0.58 0.58 0.34
WL3 8°40'48.55"S 115°13'50.04"E 5.38 6.18 -0.80 0.80 0.64
WL5 8°36'58.96"S 115°05'47.79"E 12.34 12.33 0.01 0.01 0.00
BOL13 8°33'19.18"S 115°02'14.96"E 10.20 10.27 -0.07 0.07 0.00
WL4 8°38'53.06"S 115°13'23.01"E 27.27 27.56 -0.29 0.29 0.08
WL7 8°34'19.78"S 115°03'37.99"E 74.61 75.47 -0.86 0.86 0.74
WL8 8°33'41.88"S 115°16'27.71"E 98.90 99.20 -0.30 0.30 0.09
WL10 8°30'14.47"S 115°10'45.12"E 178.09 177.51 0.58 0.58 0.34
WL11 8°29'21.68"S 115°24'09.22"E 227.77 227.99 -0.22 0.22 0.05
BOL5 8°26'14.57"S 115°01'43.26"E 361.50 361.45 0.05 0.05 0.00
WL2 8°42'24.68"S 115°13'36.69"E 3.79 2.97 0.82 0.82 0.67
Sum -0.55 4.53 2.95
ME MAE RMSE
-0.05 0.41 0.52
Median -0.07 0.30 0.09
STD 0.54 0.33 0.29
Min -0.86 0.01 0.00
Max 0.82 0.86 0.74
Figure 26 shows the potentiometric surface of D-T basin for steady-state IHM. According to the
groundwater heads results, the higher heads value start from the north and the lowest heads are in the south
of the study area. Consequently, the flow direction is from the north to south.
Figure 26: Potentiometric surface with location of heads, stream segments of the D-T basin during steady-state IHM. The stream segments with black lines indicates those that were not included during model calibration. Heads in m a.s.l.
38
The potentiometric surface results of this study was compared with Nielsen & Widjaya (1989). Generally
speaking, the potentiometric surface of this study followed the general trend of their analytical results and
the hydraulic head values near coast exhibit similarity. However, the pattern of head distribution in the
current study is influenced by the SW-GW interaction. The streamlines that are perpendicular to the
equipotential lines follow an irregular line, this shows the coupling between SW-GW. Comparatively, the
Nielsen & Widjaya (1989) studies show non-irregularity in streamlines (Figure 8). Finally, the water table
depth was compared to the topographic surface to check if it did not rise above the ground surface. The
water table depth, which is the difference of Model Top or DEM and model simulated head, was everywhere
below the ground surface.
3.2.2. Calibrated stream discharges
Calibration of stream discharge has been done simultaneously with groundwater heads. The average values
of stream flows were calibrated in the steady-state model (Table 6). The task of stream flow calibration was
complicated due to the presence of 13 stream gaging stations, besides many parameters involved.
Assessment of errors was based on the relative volumetric error (RVE), Nash-Sutcliffe efficiency (NS), and
overall model performance (Y) calculated from equation 2.13, 2.14, and 2.15 respectively. The steady-state
model stream flow calibration result was within the limit of model error criteria as indicated by Nash and
Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007); Moriasi et al., (2007); & Akhtar et al., (2009).
The value of NS and RVE were equal to 0.86 and 23.4 respectively. The overall steady-state model
performance was 70%. Therefore, the model has reasonable performance.
Table 6: Observed and simulated stream discharge with calculated error assessment for 16 gauges: Qobs –observed stream discharge; and Qsim – simulated stream discharge [unit - m3day-1]. Stations that are highlighted by red colour indicate those station that are not used for model calibration and show the model response for those stations.
Station Latitude Longitude Qobs Qsim RVE
Yeh Empas 8°34'44.25"S 115°05'11.22"E 74,963.00 52,399.50 0.301
Tukad Petanu 8°31'26.49"S 115°17'15.64"E 175,055.20 160,357.30 0.084
Melangit 8°33'10.93"S 115°21'54.48"E 127,639.90 39,500.70 0.691
Yeh Hoo 8°29'15.96"S 115°04'46.26"E 155,918.40 222,631.20 -0.428
Yeh Mata 8°27'42.69"S 115°02'36.43"E 132,288.20 137,879.50 -0.042
Tukad Oos 8°33'25.08"S 115°15'20.73"E 107,896.70 534,283.00 -3.952
Sangsang 8°33'13.29"S 115°20'47.97"E 103,104.40 137,410.10 -0.333
Tukad Jinah 8°29'42.09"S 115°22'59.21"E 89,363.90 49,861.10 0.442
Tukad Penat 8°31'06.55"S 115°12'01.88"E 363,702.30 313,330.10 0.138
Tukad Unda 8°29'11.11"S 115°26'08.18"E 208,907.40 303,573.10 -0.453
Balian 8°27'23.44"S 115°00'12.94"E 544,448.80 1,077,433.50 -0.979
Yeh Otan 8°28'22.15"S 115°01'48.37"E 136,354.30 150,918.40 -0.107
Badung Hilir 8°38'57.85"S 115°12'44.89"E 1,056,475.60 333,563.90 0.684
Pekerisan 8°23'51.75"S 115°19'09.33"E 118,150.10 102,296.30 0.134
Ayung Buangga 8°25'33.59"S 115°13'55.11"E 9,716,965.30 6,385,364.80 0.343
Yeh Aba 8°34'04.29"S 115°04'18.22"E 204,233.30 194,908.20 0.046
Mean 832,216.68 637,231.92 -0.214
Calculated NS RVE Y
0.86 23.4 69.6
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
39
3.2.3. Hydraulic conductivities
Initially, 34 hydraulic conductivity zones were assigned in the model. The zones consisted of similarly sorted
sediments in which a given sedimentary structure was dominant. Then, through the calibration process, the
number of zones increased to 78 hydraulic conductivity zones and the spatial distribution of Kh was shown
as in Figure 27. The value of Kh varied from 0.01 to 900 mday-1 in the D-T basin unconfined aquifer. Lower
Kh was observed over the streambeds ranging from 0.01 to 0.8 mday-1. Aquifer Kh varied over several orders
of magnitude and show strong spatial variation. Higher Kh was obtained in the southern and lower Kh in
the northern part of the modeled area. Based on Kruseman and de Ridder (1971), the geological class of the
D-T basin varied from medium sands to gravel; where sand and gravel aquifer materials were found close
to the sea, coarse to medium sand materials were found at the center and over the mountain range. The
result of aquifer Kh agrees with the geological cross section map of the D-T basin that was found from
locally called "KESDM" (Figure 11). The cross section map shows that sand and gravel material was
deposited at the south Sanur, whereas sand and gravel together with tuff, lava and breccias were deposited
at the north Denpasar.
Figure 27: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after steady-state IHM [unit - mday-1].
3.2.4. Water budget of the steady-state simulation using GHB conditions at the sea coast
The water budget of the steady-state simulation using the GHB conditions at the sea coast was presented
below. The GHB conductance has a large effect on the water budget as confirmed by its sensitivity analysis
– section 3.2.6. After several trial and error, a conductance of 0.1 m2day-1 per unit length was used as an
optimal value by considering the model error as small as possible and to get reliable groundwater budget of
D-T basin. Afterward, in the GHB package the optimal conductance 0.1 m2day-1 per unit length multiplied
with defined “object section intersected length” so, the model converted it into unit of m2day-1 as in
Appendix VI, A.
Water balance of the entire model
The daily average water balance of D-T basin was calculated (Table 7) by applying equation 2.16 to 2.20.
Rainfall was the only sources of inflow to the entire system. The percent contribution of the outflow
40
components from the entire system was; 17.1% of sub-surface evapotranspiration; 12.8% of interception
loss; 65.6% of stream discharge at the outlet, and 4.7% of lateral groundwater outflow. The percent
discrepancy of 0.05 indicates the closer of the water balance for the entire model. In steady-state IHM,
groundwater evapotranspiration, ETg and unsaturated zone evapotranspiration, ETun is not distinguish
clearly, rather the model simply gives as sub-surface evapotranspiration demand. However, in the case of
transient IHM the two components considered separately (Niswonger et al., 2006).
Table 7: Total water balance of D-T basin at steady-state IHM [mmday-1].
Budget component IN Budget component OUT
Precipitation (P) 6.72 Subsurface evapotranspiration (ETss) 1.21
Interception loss (I) 0.91
Stream discharge at the outlet (q) 4.65
Lateral groundwater outflow (qg) 0.32
TOTAL 6.72 TOTAL 7.10
IN-OUT -0.35
PERCENT DISCREPANCY -4%
Water balance of land surface and unsaturated zone
The land surface and unsaturated zone water balance were calculated using Equation 2.19 in Table 8. In the
inflow, component precipitation contributed the major part 85.1% and GW exfiltration 14.9% of the total
amount of water for land surface and unsaturated zone. In the outflow component, the major part was gross
recharge 61.1%, interception loss 11.5%, and total runoff 27.4%. The water balance at the land surface and
the unsaturated zone is closed with the percent discrepancy of 0.001.
Table 8: water balance of land surface and unsaturated zone [mmday-1].
Budget component IN Budget component OUT
Precipitation (P) 6.72 Interception loss (I) 0.91
GW exfiltration (Exfgw) 1.17 Gross recharge (Rg) 4.82
Total runoff (Ro) 2.16
TOTAL 7.89 TOTAL 7.88
IN-OUT 0.01
PERCENT DISCREPANCY 0.1%
Water balance of the saturated zone
The groundwater/saturated zone water balance reflects the long-term average from 1st January 2009 to 31st
December 2012 water flow into and out of the D-T basin. The components of water balance that flow into
the saturated zones are gross recharge (Rg) and stream leakage to the groundwater (qsg). The components of
water balance that flow out of the saturated zones are groundwater evapotranspiration (ETg), groundwater
exfiltration (Exfgw), groundwater discharge to the streams (qgs), and lateral groundwater outflow (qg). The
saturated zone water balance was calculated using Equation 2.20 as in table 9. The gross recharge constituted
nearly all inflow to saturated zone 95%, the remaining 5% of inflow contributed by stream leakage to
groundwater. The percent contribution of groundwater outflows: sub-surface evapotranspiration 23.7%,
GW exfiltration 22.6%, groundwater flow to streams 47.8%, and lateral groundwater outflow 6.1%.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
41
On average, the volumetric budget for groundwater discharge to the streams, qgs was higher than the
groundwater recharge by the streams, qsg. This shows that the interaction of the GW-SW is stream gaining
in most stream reaches and losing in few reaches. This result agrees with the Rai et al., (2015) suggestion,
who stated that stream gaining conditions is expected since most of the streams in Bali Island are perennial.
Table 9: Water balance of groundwater in steady-state IHM [mmday-1].
Budget component IN Budget component OUT
Stream discharge to GW (qsg) 0.25 Subsurface evapotranspiration (ETss) 1.23
Gross recharge (Rg) 4.82 GW exfiltration (Exfgw) 1.17
Stream discharge from GW (qgs) 2.47
Lateral groundwater outflow (qg) 0.32
TOTAL 5.07 TOTAL 5.17
IN-OUT -0.10
PERCENT DISCREPANCY -2%
The long term average net recharge was 2.44 mmday-1 as calculated using Equation 2.20. This value is 50.6
% of UZF recharge and 36.3% of average rainfall. The final findings of this study during the steady-state
IHM was compared with Nielsen & Widjaya (1989) and Artabudi (2012). They estimated a net recharge
value of 600 – 650 mmyear-1, whereas in this study the net recharge was 890 mmyear-1. The final finding of
this study was slightly higher than their findings. This may be due to simplification of UZF1 package in the
steady-state IHM, the package assigned the UZF recharge equals to infiltration rate. In the steady-state
model the UZF1 package does not consider storage change in either unsaturated or saturated zone and also
there is no clear difference between unsaturated zone evapotranspiration, ETun and groundwater
evapotranspiration, ETg.
The schematic representation shows the overall volumetric water budget of D-T basin (Figure 28). The
result shows the summary of the annual average flows of each water budget components for the
unconsolidated aquifer.
Figure 28: Schematic representation volumetric water budget in case of steady-state IHM for the entire model of D-T
Basin [ All units - mmyear-1].
42
3.2.5. Spatial variability of groundwater fluxes
The spatial variability of groundwater fluxes shown in Figure 29 to Figure 30. The steady-state subsurface
evapotranspiration, ETss loss varies spatially since the crop coefficient, Kc and extinction depth, EXTDP
varies through land covers. The ETss ranges from 0.0003 mmday-1 to 0.0047 mmday-1. Lower ETss was
observed in an area where there is bare soil since low Kc and EXTDP assigned whereas higher ETss demand
was observed in forest cover due to higher Kc and EXTDP assigned.
Figure 29: Spatially variable ETss of D-T Basin for calibrated steady-state IHM [Unit – mday-1].
Figure 30 shows that the distribution of groundwater gross recharge for the steady-state IHM. It was equal
to the actual infiltration rate because UZF1 package in MODFLOW-NWT over simplified the steady-state
model and gave zero unsaturated and saturated zone storage besides, no clear distinction between ETg and
ETun. The maximum gross recharge was 0.011 mmday-1 at the north, northeast of the modeled area and
minimum gross recharge was 0.0026 mmday-1 at central, south-east of the modeled area. The result shows
that the groundwater gross recharge highly influenced by the spatial distribution of rainfall and kriging
variance –section 3.1.3. Lower recharge rate that was observed may also be due to the modeled cell were
saturated and excess infiltration rate was routed as Hortonian or Dunnian flow.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
43
Figure 30: Spatially variable Rg map for calibrated steady-state IHM in D-T Basin [Unit – mday-1].
3.2.6. Effects of changing GHB conductance upon lateral groundwater outflow to the ocean
Intitally, the boundary at the sea coast was defined by GHB conditions and an arbitrary value was assigned
as GHB conductance. Then, the value was calibrated through trial and error method. During the process
the effect of GHB conductance on the water budget was examined and presented as in Figure 31. The result
depicts that the head dependent boundary rate/lateral groundwater outflow increase when the GHB
conductance increases. The percent contribution of lateral groundwater outflow was more than 80% of the
incoming rainfall when the GHB conductance was higher than 12.5 m2day-1 per unit length. The remaining
20% contributed to subsurface evapotranspiration, stream leakage, and groundwater exfiltration.
Consequently, lower GHB conductance was used to get a reasonable water budget of D-T basin – section
3.2.4.
Figure 31: The relationship between GHB conductance and head dependent boundary flow rate. The GHB conductance that masked by orange circle indicate the final value that was selected. In MODFLOW-NWT the GHB conductance is calculated based on polyline objects as in Section 2.4.6.
In this study, the water budget result using GHB conditions – section 3.2.4 and CHD boundaries –section
3.2.7 were compared and similar water budget results were found at a GHB conductance of 12.5 m2day-1
per unit length. This indicates the non-uniqueness of the D-T model. However, at a low GHB conductance
the two models show quite large difference on the groundwater budget.
3.2.7. Water budget of the steady-state simulation using CHD boundaries at the sea coast
Water balance of the entire model
The daily average water balance of D-T basin for the entire area was calculated as in Appendix VII (B).
From the total incoming rainfall, the percent contribution of the outflow components was; 3.8% of sub-
0
2500
5000
7500
10000
12500
15000
17500
20000
22500
0 2.5 5 7.5 10 12.5 15 17.5 20 22.5 25
Hea
d d
epen
det
bo
un
dar
y ra
te p
er g
rid
cel
l [m
3 m-1
]
GHB Conductance [m2day-1 per unit length]
Head dependent Boundary rate per grid cell VS GHB conductance per unit length
44
surface evapotranspiration; 13.9% of interception loss; 10.3% of stream discharge at the outlet, and 71.9 %
of lateral groundwater outflow.
Water balance of land surface and unsaturated zone
The calculated water balance of the land surface and unsaturated zone Appendix VII (C) also shows. In the
inflow, component precipitation contributed 89.3% and GW exfiltration 10.8% of the total amount of water
for land surface and unsaturated zone. In the outflow component, the prime part was gross recharge 81.2%,
interception loss 12.1%, and total runoff 6.8%.
Water balance of the saturated zone
Table 3.6 shows the saturated zone water balance was calculated using Equation 2.26. The gross recharge
constituted nearly all in flow to saturated zone, 95.4%, and the remaining 4.6% of inflow contributed by
stream leakage to groundwater. Sub-surface evapotranspiration 3.8%, GW exfiltration 12.7%, groundwater
flow to streams 10.7 %, and lateral groundwater outflow took the major part 72.9 %. The volumetric budget
for stream leakage into the groundwater was slightly higher than the stream leakage out of the groundwater.
The result confirmed that the D-T streams gaining in some reaches and losing in other reaches.
Table 10: Water balance of groundwater in steady-state condition [mmday-1].
Budget component IN Budget component OUT
Stream discharge to GW (qsg) 0.27 Sub-surface evapotranspiration (ETss) 0.22
Gross recharge (Rg) 5.54 GW exfiltration (Exfgw) 0.74
Stream discharge from GW (qgs) 0.61
Lateral groundwater outflow (qg) 4.25
TOTAL 5.81 TOTAL 5.82
IN-OUT -0.01
PERCENT DISCREPANCY -0.2%
The steady-state net recharge as equation 2.26 was 4.58 mmday-1. This value is 82.7% of gross recharge and
75.3% of long-term average precipitation. The discrepancy between the inflow and outflow was within the
limit of the acceptable range, ≤ 0.2 % (Weldemichael, 2016). Hence, the numerical model error is negligible
and the water balance of the model is closed.
In the current study, groundwater budget results using the GHB condition and CHD boundaries at the sea
coast were compared. It was found that that the assigned CHD boundaries overestimated lateral
groundwater outflow and underestimated the percent contribution of groundwater evapotranspiration,
stream leakage, and groundwater exfiltration (Table 10). However, the GHB conditions control the lateral
groundwater outflow and comparatively give a reasonable water budget result of D-T basin. This finding is
in the line with Bakker et al., (2013); Durden et al., (2013); Mulligan et al., (2011); Pauw et al., (2014); &
Masterson et al., (2016) – section 2.4.6. They emphasise that GHB condition is the most widely used
boundary condition at the sea coast and it has several advantages than CHD boundaries: (1) reduced the
high contrast in hydraulic conductivity and “eliminating potential numerical problems” (2) the CHD
boundaries reduced the amplitude of heads or arise difficulty in matching the simulated and observed heads;
(3) the CHD boundaries gave incorrect simulation of fluxes and salt advection into the aquifer, salt advection
is not covered in this study; (4) CHD boundaries at the sea coast have low control on the amount of
groundwater flow from the groundwater divides to the ocean.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
45
3.2.8. Sensitivity analysis
Sensitivity analysis was conducted in the steady-state IHM with the aim of assessment of groundwater in
the basin. The response of the model hydraulic head was assessed by varying model parameters as shown
in Figure 32. It was observed that the Kh and Kvun parameters showed a higher response to the model. The
Kh and Kvun follow a similar trend of the model response. The model response increase for both high and
low Kh and Kvun values. But when the two parameters are compared, the model response was higher to the
variation in the Kh parameter than the Kvun.
A. Sensitivity of Kh upon heads
B. Sensitivity of Kvun upon heads
Figure 32: Sensitivity of model for horizontal hydraulic conductivity (A) & Vertical unsaturated zone hydraulic conductivity (B).
The parameter and driving forces, i.e. infiltration rate, PET, extinction depth [EXTDP], extinction water
content [EXTWC], the Brooks-Corey-Epsilon [BC] and Saturated water content [WCsat] in the UZF1
packages were examined (Figure 33 and 34). It was observed that the infiltration rate, PET, and EXTDP
have a higher response to the model while the EXTWC, BC, and WCsat hardly showed any response. The
model was highly sensitive to infiltration rate to both higher and lower values, whereas in the case of PET
and EXTDP the model response higher to a lower value and lower response to higher values.
C. Sensitivity of EXTDP upon heads
D. Sensitivity of infiltration rate upon heads
E. Sensitivity of EXTWC upon heads F. Sensitivity of PET upon heads
0.2
0.4
0.6
0.8
1
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
Kh
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
0.61
0.62
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
Kvun
0.5278
0.5280
0.5282
0.5284
0.5286
0.5288
0.5290
0.5292
0.5294
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
EXTDP
0
2
4
6
8
10
12
14
16
18
20
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
Infiltration rate
46
Figure 33: Sensitivity of model for UZF1 package parameter and driving forces: (C) extinction depth, (D) infiltration rate, (E) extinction water content, (F) potential evapotranspiration.
In general, the model is more sensitive to parameters such as Kh, Kvsun, and EXTDP and insensitive to
EXTWC, BC, and WCsat. Those the sensitive parameters are good for model calibration whereas the
insensitive may create uncertainty in the model. Therefore, more effort is required to get reliable information
about the insensitive parameters.
G. Sensitivity of BC upon heads
H. Sensitivity of WCsat upon heads
Figure 34: Sensitivity of model for (G) Brooks-Corey-Epsilon & (H) saturated water content.
3.3. Transient model calibration
Calibration of transient IHM was carried out with objectives to reproduce the pattern of stream discharges
and minimize the difference between observed and simulated stream discharges as well as heads. Due to
lack of groundwater fluctuation data, the model does not include calibration of the daily variation of heads.
It is also not constrained by groundwater abstractions. Therefore, the result of this model should be used
with caution in case future studies incorporating daily variation of groundwater heads and abstraction.
Before the transient model calibration, one-year data from 1st January 2009 to 31st December 2009 or 365
daily stress period was used as a warming period. The model with one-year data was calibrated to assess the
model response to the daily variation of 13 stream discharges. This model has used the final steady-state
heads and Kh’s as initial heads. Additionally, Sy was assigned as 0.24 for the entire modeled area – as in
section 2.4.5. At the first try, the model response was not good enough, but then the Kh, Sy and other
parameters in UZF1, as well as SFR2 packages, were adjusted. After several trial and error, the model shows
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
EXTWC
0.52
0.53
0.54
0.55
0.56
0.57
0.58
0.59
0.60
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
PET
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
BCE
0.0
0.1
0.2
0.3
0.4
0.5
0.6
-30% -20% -10% 0% 10% 20% 30%
RM
SE
[m
]
Sensitivity change factor
WCsat
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
47
a reasonable response to the daily stream discharges. Then, the transient model run for four-years simulation
periods. In this study, contrary to Hassan et al., (2014), the data that was used in the warming up period was
not discarded rather three-years data from 1st January 2010 to 31st December 2012 were added into it and
in total four-year from 1st January 2009 to 31st December 2012 was considered as a transient model
simulation period. In a nutshell, the transient IHM has considered daily stream discharge records from 1st
January 2009 to 31st December 2012, this simulation period is equal to 1461 daily stress periods. The
transient model calibration having 13 streams, 11 heads and several parameters in UZF1and SFR2 packages
is complicated and time-consuming process besides, most of the input data such as rainfall, interception
rate, PET, EXTDP were spatiotemporally variable. Each calibration takes more an hour and produced huge
output files ~ 4 GB. Notepad++ was used to open the file because such file could not be open through
standard Notepad.
3.3.1. Calibration heads and error assessment
As stated earlier, the groundwater fluctuation data available neither daily nor monthly rather monitoring
records show one record per year. Hence, the final transient-state heads calibration was examined for
correlation with the observed heads using the actual date of monitoring heads (Table 11). The result shows
a good match between the simulated and observed head values since the heads fall close to the solid line
(Figure 35). The transient-state heads calibration result was in the line with Hill (1998) suggestion, who
stated based on the scatter plot that the observed and simulated heads should fall close to a line with a slope
of 1:1 and the R2 should be greater than 0.9.
Figure 35: Relationship between simulated and observed heads for the transient IHM of 11 observation points.
Table 11 shows the mean error (ME), mean absolute error (MAE), and root means square error (RMSE)
calculated from equation (2.10), (2.11), and (2.12) respectively. The values of ME, MAE, and RMSE are
respectively equal to -0.22 m, 0.57 m, and 0.6 m. The water table in the D-T basin varies between 2.5 m a.s.l.
to 361.5 m a.s.l., which makes the total head loss of 358.9 m in the model area. The transient model
calibration result fits Anderson & William, (1992) and Mason & Hipke (2013) model error criteria, where
mean absolute error is less than 2% of the total head changes (7.2 m); the maximum absolute value of model
residuals (0.9 m) should be less than 10 % of the total head changes (35.9 m); the root mean square error is
less than 2% of the total head changes (7.2 m); the ratio of RMSE to the total head difference is 0.17%
which is also lower than the 10 % of total head difference (35.9 m). The model performance with respect
to simulating groundwater heads is not as good as for the steady-state simulations possible because the
model was not calibrated sufficiently.
48
Table 11: Observed, Hobs and simulated head, Hsim with calculated error assessment for 11 piezometers. [Units – m].
Observation Points
Latitude Longitude Date of observation
Hobs Hsim Hobs.- Hsim.
|Hobs-Hsim|
[Hobs. - Hsim.]²
WL1 8°43'43.65"S 115°10'36.44"E 5-May-09 2.5 2.4 0.1 0.1 0
WL3 8°40'48.55"S 115°13'50.04"E 8-Jun-09 5.4 4.8 0.6 0.6 0.4
WL5 8°36'58.96"S 115°05'47.79"E 4-Sep-09 12.3 12.0 0.4 0.4 0.1
BOL13 8°33'19.18"S 115°02'14.96"E 13-May-09 10.2 11.1 -0.9 0.9 0.8
WL4 8°38'53.06"S 115°13'23.01"E 14-May-11 27.3 27.5 -0.2 0.2 0.1
WL7 8°34'19.78"S 115°03'37.99"E 9-May-12 74.6 75.0 -0.4 0.4 0.2
BOL3 8°33'41.88"S 115°16'27.71"E 21-Feb-09 176.8 176.0 0.7 0.7 0.6
WL10 8°30'14.47"S 115°10'45.12"E 31-Dec-09 178.1 176.8 1.3 1.3 1.6
WL11 8°29'21.68"S 115°24'09.22"E 15-May-09 227.8 227.4 0.4 0.4 0.1
BOL5 8°26'14.57"S 115°01'43.26"E 12-May-12 361.5 362.1 -0.6 0.6 0.3
WL2 8°42'24.68"S 115°13'36.69"E 6-May-11 3.8 3.2 0.6 0.6 0.4
Sum 1.9 6.2 4.5
ME MAE RMSE
0 0.1 0.6
Median 0.4 0.6 0.3
STD 0.6 0.3 0.5
Min -0.9 0.1 0
Max 1.3 1.3 1.6
Figure 36 shows the potentiometric surface of D-T basin for transient-state model simulation at the last
stress period, 31st December 2012. The potentiometric surface result was almost the same with the steady-
state potentiometric surface but slightly lower over the norther part of modeled area (Figure 25). According
to the groundwater heads result, higher heads value was observed over the mountainous area and lower
heads near to the sea coast. Consequently, the flow direction is from the north to south of the modeled area.
Figure 36: The potentiometric surface and stream segments of the D-T basin during transient model calibration at the last stress period, December 31, 2012.
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
49
The hydrographs of simulated groundwater heads are shown in Figure 37. In most of the monitored
piezometers, there was delayed hydrograph response to rainfall. The amplitude or the fluctuation of the
heads was higher over the north ~ 2.5 m than the south ~ 1.5 m. This fluctuation of the hydrographs is due
to the recharge of the groundwater during the rainy/wet periods from October to March.
A. Simulated head for station BOL3
B. Simulated head for WL5
C. Simulated head WL2
Figure 37: Time series for the comparison of yearly observed and daily simulated heads for D-T basin. P – rainfall, Hobs – observed heads, and Hsim – simulated heads.
0
20
40
60
80
100
120
9.5
10
10.5
11
11.5
12
12.5
13
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
P [
mm
day
-1]
Hea
d [
m]
P Hsim Hobs
0
20
40
60
80
100
120
0
0.5
1
1.5
2
2.5
3
3.5
4
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
P [
mm
day
-1]
Hea
d [
m]
P Hsim Hobs
0
20
40
60
80
100
120
175.5
176
176.5
177
177.5
178
178.5
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
P [
mm
day
-1]
Hea
d [
m]
P Hsim Hobs
50
3.3.2. Calibrated stream discharges
Transient-state model calibration was carried out to match the daily simulated stream discharges with the
observed stream discharges. Thirteen stream gauging station were calibrated using four-years period from
1st January 2009 to 31st December 2012. Figure 38 and Appendix VII show the hydrograph of observed and
simulated discharges in relation to daily rainfall patterns. The hydrographs of observed and simulated
discharges are reasonably fit for the year 2009 – 2012 (Figure 38). In most cases, the stream discharges
calibration result is in the line with Nash and Sutcliffe (1970); Seibert (1999); de Vos and Rientjes (2007);
Moriasi et al., (2007); & Akhtar et al., (2009) model error criteria as depicted in Table 12. However, the
model has the incapability to produce peak flows, despite it gives good efficiency and model performance
for thirteen stations namely called Yeh_Empass, Yeh Matan, Yeh Hoo, Tukad Penat, Tukad Petan, Sang
Sang, Melangit, Tukad Unda-cegeng, Yeh Otan, Yeh Aba, and Pekerisan. Several reasons exist for the
incompetence of the model to simulate high flows. As model itself is the simplified representation of the
real world hydrological processes, several processes are ignored in the mathematical model for example
perched flow, macro-pore flow and other. The parameters are just the estimation of the catchment
characteristics, and may not fully consider the heterogeneity of the catchment. In addition, the
meteorological information may also not well represent the whole catchment and result in the reduced values
of peak flow.
0
40
80
120
160
2000
2
4
6
8
10
12
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12R
F [
mm
day
-1]
Q [
m3se
c-1]
A. Station Melangit
Pengotan_RF Observed_Q Simulated_Q
0
40
80
120
160
2000
1
2
3
4
5
6
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
B. Station Sang Sang
Observed_Q Simulated_Q Sanglah_RF
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
51
0
40
80
120
160
2000
1
2
3
4
5
6
7
8
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3 s
ec-1
]
C. Station Tukad Jineh
Observed_Q Simulated_Q Selishan_RF
0
40
80
120
160
2000
1
2
3
4
5
6
7
8
1-Jan-09 20-Jul-09 5-Feb-10 24-Aug-10 12-Mar-11 28-Sep-11 15-Apr-12 1-Nov-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
D. Station Tukad Oos
Observed_Q Simulated_Q Mambal_RF
0
40
80
120
160
2000
2
4
6
8
10
12
1-Jan-09 20-Jul-09 5-Feb-10 24-Aug-10 12-Mar-11 28-Sep-11 15-Apr-12 1-Nov-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
E. Station Tukad Petanu
Observed_Q Simulated_Q Tegallalang_RF
52
0
40
80
120
160
2000
1
2
3
4
5
6
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
F. Station Yeh Empas
Observed_Q Simulated_Q Gadungan_RF
0
40
80
120
160
2000
2
4
6
8
10
12
14
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
G. Station Yeh Hoo
Observed_Q Simulated_Q Gadungan_RF
0
40
80
120
160
2000
1
2
3
4
5
6
7
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
H. Station Yeh Mata
Observed_Q Simulated_Q Pempatan_RF
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
53
0
40
80
120
160
2000
5
10
15
20
25
30
35
40
45
50
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
I. Station Tukad Penat
Observed_Q Simulated_Q Tampaksiring_RF
0
40
80
120
160
2000
2
4
6
8
10
12
14
16
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
J. Station Tukad Unda
Observed_Q Simulated_Q Rendang_RF
0
40
80
120
160
2000
10
20
30
40
50
60
70
80
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
K. Station Pekerisa
Observed_Q Simulated_Q Kedisan_RF
54
Figure 38: Relationship between observed and simulated discharge in the D-T basin for the transient-state model
calibration of 13 stream gauge (2009 - 2012). For the location of gauges see Appendix V (A & B). The oval shape in
Figure 37 (J, K, and L) show that uncertainty in the measured rainfall and stream discharges. Because it is expected
that at high rainfall records, stream discharge is higher and the opposite is true. Q – stream discharge and RF – rainfall.
The oval shape in Figure 38 (A) shows that the model hardly reaches the base flows. This may be due to
that the excess rainfall was stored in the different model zones. Additionally, for station Yeh Hoo, Tukad
Penat, and Tukad Petanu the simulated stream discharge was somewhat higher than the observed stream
discharge but follow similar pattern. This may be caused by the assigned streambed top elevation, or width
in the SFR2 package, due to lack of time the result was taken as it is but for further study parameters should
be optimized for better represent with the observed stream discharges.
The model hardly performs in terms of hydrograph, model efficiency and mean difference for stations
Balian, Ayung Buanga, and Badung Hilir (Appendix VII). Nevertheless, the model represents the base flow
of those stations. For instance, in station Ayung Buanga the model reproduces the base flow from 1st January
2011 to 31st December 2012; in station Badung Hilir from 1st January 2010 to 31st December 2012, and in
station Balian from 1st January 2009 to 1st January 2010. The model performance of those stations as in
Table 12 shows very high relative volumetric error (RVE), and low Nash-Sutcliffe efficiency (NS) and overall
0
40
80
120
160
2000
5
10
15
20
25
30
35
40
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
L. Station Yeh Aba
Observed_Q Simulated_Q Gadungan_RF
0
40
80
120
160
2000
4
8
12
16
20
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
M. Station Yeh Otan
Observed_Q Simulated_Q Pempatan_RF
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
55
model performance (Y), calculated from equation 2.13, 2.14, and 2.15. As stated earlier in section 3.1.6, for
those stations the hydrological information was not representative. This was discovered by the inconsistency
in the double mass curve and frequency distribution analysis (Appendix V; D, E & F). The main reason may
be due to exposure, observation method, or gauging location.
In a nutshell, the main reasons for the mismatch between observed and simulated streams discharge are due
to uncertainty in the measured stream level and groundwater heads; unaccounted surface and groundwater
abstraction, unaccounted temporal variability of land cover and heterogeneity; and also modeled grid cell
size (Mehl & Hill, 2010).
Table 12: Observed and simulated stream discharge with GHB conductance of 0.1 m2day-1 per unit length calculated error assessment for 16 gauges in m3day-1. Stations that are highlighted by red colour indicate those station that are not used for model calibration and shows the model performance for those stations.
Station Name Latitude Longitude NS RVE Y
Melangit 8°34'44.25"S 115°05'11.22"E 0.63 27.62 49.58
Sangsang 8°31'26.49"S 115°17'15.64"E 0.89 -8.67 82.13
Tukad_Jineh 8°33'10.93"S 115°21'54.48"E 0.73 17.86 61.66
Tukad_Oos 8°29'15.96"S 115°04'46.26"E -0.35 -56.44 -22.37
Tukad_Petanu 8°27'42.69"S 115°02'36.43"E 0.76 -23.32 61.75
Yeh_Empas 8°33'25.08"S 115°15'20.73"E 0.71 7.05 66.35
Yeh_Hoo 8°33'13.29"S 115°20'47.97"E 0.51 -39.66 36.78
Yeh_Mata 8°29'42.09"S 115°22'59.21"E 0.99 -2.59 96.69
Tukad_Penat 8°31'06.55"S 115°12'01.88"E 0.86 -33.26 64.77
Tukad_Unda 8°29'11.11"S 115°26'08.18"E 0.99 -4.60 94.82
Ayung Buangga 8°27'23.44"S 115°00'12.94"E -0.37 95.25 -18.74
Badung Hilir 8°28'22.15"S 115°01'48.37"E -0.38 54.33 -24.92
Balian 8°38'57.85"S 115°12'44.89"E 0.59 -28.24 46.11
Pekerisa 8°23'51.75"S 115°19'09.33"E 0.85 -63.18 52.39
Yeh_Aba 8°25'33.59"S 115°13'55.11"E 0.93 -27.86 73.10
Yeh_Otan 8°34'04.29"S 115°04'18.22"E 0.83 9.61 75.29
3.3.3. Hydraulic conductivities and specific yield
The horizontal hydraulic conductivity that was calibrated in the steady-state model was gently modified and
the result is shown in Figure 39. Generally, the spatial variability of transient Kh was almost the same as
calibrated steady-state Kh. Minor changes were made over the southern part of the basin. The value of Kh
varied from 0.01 to 580 mday-1. Riverbed hydraulic conductivity ranges from 0.01 to 0.35 mday-1.
The D-T basin aquifer materials were early Quaternary deposits. This Quaternary upper formation was
composed of different materials of volcanic origin. It includes mainly unconsolidated sand & gravel, volcanic
ash, lava flow, breccia, lahar, "pumic", clay and tuff (Nielsen & Widjaya, 1989 & Purnomo & Pichler, 2015).
The study area aquifer materials are spatially uniform so that, spatially uniform Sy, 0.24 was used during
transient model calibration. The final model parameter values and model variables that were used in the
transient calibration of the D-T basin numerical model are shown in Table 13.
56
Figure 39: Calibrated horizontal hydraulic conductivity (Kh) distribution map of D-T basin after Transient-state IHM
[unit - mday-1].
Table 13: Final calibration output for model parameters and model variables in the D-T basin: EXTDP – extinction water content; EXTWC – extinction water content; THTS – saturated volumetric water content; THTI – initial volumetric water content; STRTOP – streambed top; STRTHICK – streambed thickness; SLOPE – stream slope; STRHC1 – streambed hydraulic conductivity; WIDTH1 – stream width; Kvun – maximum unsaturated zone vertical
hydraulic conductivity; Kh – horizontal hydraulic conductivity; Sy – specific yield; and C – conductance.
Vertical zones Parameters Minimum value Maximum value Unit
Unsaturated zone EXTDP 0 2.5 m
(MODFLOW-NWT, UZF1) EXTWC 0.05 0.07 m3m-3
Kvun 0.1 0.1 mday-1
Streams THTS 0.4 0.4 -
(MODFLOW-NWT,SFR2) THTI 0.2 0.2 -
STRTOP 2.5 2.5 m
STRTHICK 0.5 0.5 m
SLOPE 0.025 0.025 -
STRHC1 0.05 0.8 mday-1
WIDTH1 2 12 m
Groundwater zone Kh 8 900 mday-1
(MODFLOW-NWT) Sy 0.24 0.24 -
C 6 44 m2day-1
3.3.4. Water budget of the transient-state simulation
The average groundwater budget during the four-year model simulation was shown in Table 14. The rainfall
recharge was the major supply to the aquifer system and Rg contributes 75% of total groundwater inflow
followed by ∆Sgin (21.4%) and qsg (3.3%). The majority of the outflow from the aquifer system was qgs
(30.4%), Exfgw (29.4%), ∆Sgout (18.94%) and ETg (14.1%) followed by 7.5% of qg. Comparatively, the
calibrated transient-state qg (7.5%) was slightly higher than the calibrated steady-state qg (6.1%). In transient-
state Rn contributes 42.4% of Rg. The Rn value is slightly lower as compared to steady-state Rn (50.6%).
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
57
Table 14: Long term average groundwater budget for entire model in transient-state IHM [mmday-1] for the 2009-
2012. IN – inflow to the aquifer system, OUT – outflow from the aquifer system, GW – groundwater.
IN m3day-1 OUT m3day-1
Storage 2203881 Storage 1965919
Lateral GW outflow 0 Lateral GW outflow 742374
Stream leakage 346467 stream leakage 3157223
GW ET 0 GW ET 1462588
UZF recharge 7827765 UZF recharge 0
Surface Leakage 0 Surface Leakage 3049997
TOTAL IN 10378113 TOTAL OUT 10378100
IN-OUT 13
3.3.5. Temporal variability of groundwater fluxes
The temporal variability of groundwater fluxes for gross recharge (Rg), net recharge (Rn), surface leakage
(Exfgw), and groundwater evapotranspiration (ETg) is shown in Figure 40. The net recharge was calculated as
the sum of Exfgw and ETg subtracted from the Rg. The result shown that both Rg and Rn were influenced by
the rainfall intensities. The Rn follows the Rg path for low and high values but it is influenced by ETg and
Exfgw. “Exfgw occurs whenever the altitude of the water table exceeds the soil zone and it can be lost as ETun,
qd or becomes storage in the soil zone” (Hassan et al., 2014). The temporal variability of groundwater fluxes
corresponds mainly with the seasonal variability of driving forces changing from wet to dry periods.
Figure 40: Temporal variability of groundwater fluxes in transient model calibration for gross recharge (Rg), net recharge (Rn), surface leakage (Exfgw), and groundwater evapotranspiration (ETg).
0
20
40
60
80
100
1200
1
2
3
4
5
6
7
8
9
1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13P
[m
md
ay-1
]
Rgan
d R
n[m
md
ay-1
]
Rainfall, Gross recharge and Net recharge
P Rg Rn
0
20
40
60
80
100
1200
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
P [
mm
day
-1]
ET
gan
d E
xf gw
[m
md
ay-1
]
Rainfall, Gross recharge and Net recharge
P ETg Exfgw
58
Figure 41 shown the applied rainfall (P), PET, and the calculated actual infiltration rate (Pe). The result shows
that the Pe value depends on the rainfall intensities, the degree of saturation in the unsaturated zone, and the
vertical hydraulic conductivity of the soil. The peaks in the Pe rate correspond to the high P value and at
first, this water subdivided into Rg, ETun, and ETg then the remaining excess infiltration rate routed to the
streams and store in the unsaturated zone.
Figure 41: Temporal variability of rainfall, actual infiltration and PET
3.3.6. Spatial variability of groundwater fluxes
The spatial variability of groundwater fluxes was compared during dry (April – September) and wet (October
- March) periods. For comparison purpose fluxes were taken randomly from both periods. The transient-
state groundwater evapotranspiration, ETg loss varies spatially as shown in Figure 42. The ETg demand
ranging from 0.003 mmday-1 to 0.004 mmday-1 in the dry season, example in 26-July-2010. The ETg demand
ranging from 0.004 mmday-1 to 0.006 mmday-1 in the wet season, 5th-Febrary-2009. The spatial distribution
of ETg, was highly depend on land cover. For instance, lower ETg was observed in an area where there is
bare soil than forest since, low Kc and EXTDP assigned
A. Spatially variable ETg in 26-July-2010
A. Spatially variable ETg in 5-Febrary-2009
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
0
20
40
60
80
100
120
140
160
1-Jan-09 1-Jul-09 1-Jan-10 1-Jul-10 1-Jan-11 1-Jul-11 1-Jan-12 1-Jul-12 1-Jan-13
PE
T [
mm
day
-1]
P a
nd
Pe
[mm
day
-1]
Rainfall (P), Actual infiltration (Pe) and PET
P Pe PET
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
59
Figure 42: Spatially variable ETg map for calibrated transient IHM during dry (A) and wet (B) period in D-T Basin [Unit – mday-1].
Figure 43 shows that the distribution of groundwater gross recharge for the transient-state IHM. Seasonally,
the gross recharge was higher during wet than dry season since rainfall was higher during wet season but
also during dry period (Figure 4). During the dry period, as an example in 17th – August -2009, Rg ranged
from 0.0002 mmday-1 to 0.003 mmday-1 while in the wet period, 21st –December-2009, Rg from 0.03 mmday-
1 to 0.003 mmday-1. The result shows that the spatial distribution of groundwater gross recharges was highly
influenced by the spatial distribution of rainfall and its kriging variance –section 3.1.3.
A. Spatially variable Rn in 17-August-2009 B. Spatially variable Rn in 21-December-2009
Figure 43: Spatially variable Rg map for calibrated transient IHM during dry (A) and wet (B) period in D-T Basin.
3.3.7. Yearly steady-state and transient variability of water fluxes
As stated earlier, the Newtonian formulation of MODFLOW-05 was used to run transient IHM.
MODFLOW-NWT links unsaturated and saturated zone and also simulate the interaction of GW-SW
(Niswonger et al., 2011). Initially, during transient model calibration the model stopped running and show
message “failed to meet solver convergence criteria”. This was due to UZF1 package solver criteria. In order
to solve the problem, the recommended value for flux tolerance and head tolerance as in section 2.4.5 were
increased from 500 m3day-1 and 0.0001 m into 5,000 m3day-1 and 0.001 m respectively and then model
converged.
In this study, mean of the four-year net recharge was 491 mmyear-1, this result was comparable with the
final findings of Nielsen & Widjaya (1989) who estimated groundwater recharge of southern Bali based on
(1) analysis of well hydrographs as 468 mmyear-1; (2) flow net analysis as 492 mmyear-1; (3) annual infiltration
gave 437 mmyear-1. However, the estimated net recharge of this study somewhat deviates from Nielsen &
Widjaya (1989), who estimated net recharge (1) from base flow separation as 272 mmyear-1; (2) from
analytical model using land cover map as 645 mmyear-1 in light soil, 538 mmyear-1 in the medium soil, and
376 mmyear-1 in heavy soil. In addition, the result of this study slightly varies from Artabudi (2012) final
findings, who estimated groundwater recharge as 218-220 mmyear-1 when the driving forces extracted from
satellite sensor products and as 650-660 mmyear-1 when the driving forces were obtained from in situ data.
60
Table 15: The yearly variability of driving forces and different groundwater balance components over the three hydrological periods 1st January 2009 till 31st December 2012 MODFLOW-NWT simulation period [All units in mm year-1].
where P – precipitation, PET – potential evapotranspiration, I – interception, Inf – infiltration rate, Rn – net recharge, qsg – stream leakage to the groundwater system, Rg – gross recharge, qg – lateral groundwater outflow, qgs – groundwater flow to the streams, ETg – groundwater evapotranspiration, Exfgw – surface leakage/exfiltration, ∆Sg – groundwater storage, Ro – runoff, Pe – Actual infiltration rate, ETun – Unsaturated zone evapotranspiration, and ∆Sun – Unsaturated zone storage.
Table 15 show the average yearly rainfall, PET, interception, infiltration rate, groundwater budget, and unsaturated zone budget for the simulation period from 1st
January 2009 to 31st December 2012. The result depicts that there was annual variability in groundwater fluxes and difference with the steady-state model simulation
results. The result of steady-state and the mean of the four-year transient model simulation was comparable for some flux components such as lateral groundwater
outflow and stream leakage into the groundwater. However, for the remaining fluxes, there is a dissimilarity due to oversimplification of the steady-state model;
where all the driving forces and state variables are taken as an average value. Additionally, there might be an oversimplification of UZF1 packages during steady-
state IHM in which it does not take into account the water storage, and unsaturated zone evapotranspiration. However, in the transient model simulation estimated
those groundwater budget components.
P PET I Inf Rn qsg Rg qg qgs ETg Exfgw ∆Sg Ro Pe ETun ∆Sun
Steady-state IHM 2452.8 1311.3 332.2 2120.7 890.6 91.5 1759.2 116.8 901.6 441.7 427.1 0.0 795.7 1759.2 0.0 0.0
1st Jan. 2009 – 31st Dec. 2009 2380.0 1420.6 273.7 2106.3 591.0 53.3 1343.9 119.3 476.5 258.2 494.8 48.5 281.0 2320.1 421.3 554.9
1st Jan. 2010 – 31st Dec. 2010 3206.7 1316.0 368.8 2837.9 539.1 50.7 1279.7 119.4 488.6 245.6 495.0 -18.2 420.3 2912.6 1511.1 121.8
1st Jan. 2011 – 31st Dec. 2011 2187.7 1305.7 251.6 1936.1 471.6 55.6 1214.1 120.1 480.1 241.3 501.2 -73.0 279.1 2158.2 480.8 463.3
1st Jan. 2012 – 31st Dec. 2012 2172.9 1135.3 249.9 1923.0 360.7 57.4 1074.2 120.3 478.9 207.6 505.9 -181.1 284.7 2144.3 822.8 247.3
Minimum 2172.9 1135.3 249.9 1923.0 360.7 50.7 1074.2 119.3 476.5 207.6 494.8 -181.1 279.1 2144.3 421.3 121.8
Maximum 3206.7 1420.6 368.8 2837.9 591.0 57.4 1343.9 120.3 488.6 258.2 505.9 48.5 420.3 2912.6 1511.1 554.9
Average 2486.8 1294.4 286.0 2200.8 490.6 54.3 1228.0 119.8 481.0 238.1 499.2 -55.9 316.3 2383.8 809.0 346.8
Standard deviation 423.6 102.3 48.7 374.9 86.1 2.5 100.0 0.4 4.6 18.7 4.7 84.1 60.1 313.0 433.4 171.3
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
61
3.3.8. Sensitivity analysis
Sensitivity analysis was conducted in the transient IHM with the aim of assessment of groundwater in the
basin. The response of the model hydraulic head was assessed by varying model parameters in the same way
as steady-state IHM (Figure 44). It was observed that the Kh and Kvun parameters showed a higher response
to the model. The Kh and Kvun follow a similar trend of the model response. The model response increase
for both high and low Kh values and to some degree for low Kvun. The model response was higher to the
variation in the Kh parameter than the Kvun. Apart from this the model hardly response for EXTDP, EXTW,
WCsat and BC values. Those the insensitive parameters may create uncertainty in the model. Therefore,
more effort is required to get reliable information about the insensitive parameters.
A. Sensitivity of Kh, Kvun, EXTDP, EXTWC, WCsat,& BC upon heads
Figure 44: Sensitivity of model for horizontal hydraulic conductivity [Kh], maximum unsaturated zone vertical hydraulic
conductivity [Kvun], extinction depth [EXTDP], extinction water content [EXTWC], Saturated water content [WCsat],
and Brooks-Corey-Epsilon [BC].
Sensitivity analysis was also conducted in the transient-state IHM with the aim of assessment of groundwater
in the basin. The response of the groundwater budget components was assessed by varying model
parameters as shown in Figure 45. It was observed that the Kvun parameter showed a higher response to the
model. The Kvun parameter has the same response to the infiltration rate and Exfgw. The response for
groundwater budget components increase for high Kvun values and decrease for low Kvun values. This is
because that when the unsaturated zone vertical hydraulic conductivity increases then the water can pass
through the soil easily than in the case of low hydraulic conductivity. Then the infiltration rate also increases.
0.40
0.45
0.50
0.55
0.60
0.65
0.70
0.75
0.80
0.85
0.90
-45% -30% -15% 0% 15% 30% 45%
RM
SE
[m
]
Sensitivity change factor
Kh
Kvun
EXTDP
EXTWC
Wcsat
BC
62
A. Sensitivity of Kvun upon Infiltration
B. Sensitivity of Kvun upon Exfgw
C. Sensitivity of EXTDP upon ETg
D. Sensitivity of GHB conductance upon qg
Figure 45: Effects of changing unsaturated zone vertical hydraulic conductivity [Kvun] upon infiltration (A) and Exfgw (B), effects of changing extinction depth [EXTDP] and GHB conductance upon ETg (C) and qg (D) respectively.
5.8
6.0
6.2
6.4
6.6
6.8
7.0
7.2
-45% -30% -15% 0% 15% 30% 45%
Infi
ltra
tio
n [
mm
day
-1]
Sensitivity change factor
Kvun
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
-45% -30% -15% 0% 15% 30% 45%
Ex
f gw[m
md
ay-1
]
Sensitivity change factor
Kvun
0.64
0.65
0.66
0.67
0.68
0.69
0.70
-45% -30% -15% 0% 15% 30% 45%
ET
g[m
md
ay-1
]
Sensitivity change factor
EXTDP
0.0
0.1
0.2
0.3
0.4
0.5
-45% -30% -15% 0% 15% 30% 45%
q g[m
md
ay-1
]
Sensitivity change factor
Conductance
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
63
4. CONCLUSIONS AND RECOMMENDATIONS
4.1. Conclusions
The main objective of this research was to develop an IHM of D-T basin for management purpose. For
that reason, MODFLOW-NWT under ModelMuse environment was used. MODFLOW-NWT is a
Newtonian formulation of MODFLOW-05 that with UZF1 and SFR2 packages simulates water flow
between ground surface and aquifer throughout unsaturated zone, groundwater flow and SW-GW
interaction. The steady-state and transient-state IHM was built and calibrated manually using daily data from
1st January 2009 to 31st December 2012. The most important findings of this study are listed below:
The steady-state model calibration ‘produced’ heads and stream flows with RMSE of 0.52 m and
NS of 0.86 respectively. In this model the groundwater budget components: RUZF contributed 95%
of total inflow to the aquifer system and the remaining 5% was covered by qsg. The main outflows
of the aquifer systems were and qgs and ETg which contributed 47.8% and 23.4% of total outflow
respectively. The remaining outflows were: Exfgw ~22% and qg ~6.1%.
The transient model was calibrated to reproduce patterns of stream discharge and to minimize the
difference between simulated and observed stream discharges as well as heads. The calibration
process produced stream flows with NS ranging from 0.51 to 0.99 (Table 12). Besides, the RMSE
of groundwater heads calibrated simultaneously with stream discharges was ~0.58 m.
The four-years (1st January 2009 to 31st December 2012) precipitation (P) was 6.8 mm day-1; the
corresponding groundwater fluxes were as follows: Rg=3.45 mm day-1 (50.5% of P), ETg=0.64
mmday-1 (9.5% of P), Exfgw=1.34 mmday-1 (19.7% of P), Rn 1.46 mmday-1 (21.4% of P), qgs=1.39
mmday-1 (20.4% of P); ∆S=0.11 mmday-1 (1.6% ofP), and qg=0.33 mmday-1 (4.8% of P).
The temporal variability of groundwater fluxes obtained in the transient model calibration can be
illustrated by: Rg ranging from 7.64 (January) to 2.30 mmday-1 (August) with the average value of
3.36 mmday-1; Rn ranging from 5.84 (January) to 0.26 mmday-1 (August) with the average value of
1.34 mmday-1; ETg ranging from 1.05 (February) to 0.65 mmday-1 (July) whereas, and also qgs ranging
from 1.48 (January) to 1.37 mmday-1 (August). Exfgw ranging from 1.48 (March) to 1.37 mmday-1
(December). The spatiotemporal variability of groundwater fluxes is constrained by seasonal
variability of driving forces, changing from wet season (October – March) to dry season (April –
September). The spatial variability of groundwater fluxes is mainly attributed to spatial variability
of rainfall and land cover.
The effect of boundaries at the sea coast was examined through two independent models with two
different boundary conditions at the sea coast. For the first model, the boundary was simulated by
GHB and in the second model, the CHD boundary. When the sea coast was simulated as CHD
boundary, the corresponding groundwater fluxes were as follows: Rg contributed 95%, followed by
qgs 5% of total groundwater inflow. Regarding groundwater outflow, ETg contributed 4%, Exfgw
12.7%, qgs 10.7%, and qg 72.9% of total groundwater outflow. However, when the GHB
conductance was < 12.5 m2day-1 per unit length, then the qg (5.8%) contribution was much lower
than the percent contribution of CHD boundaries besides, the percent contribution of ETg,
(33.2%), Exfgw, (12.8%) and qgs (48.3%) was reasonably higher than CHD boundaries. In a nutshell,
64
the GHB conditions at the sea coast give a more reliable water balance as compared to CHD
boundaries; this is because that at a low GHB conductance the model has a high control on the
lateral groundwater outflow to the ocean.
The UZF1 package in the steady-state IHM oversimplified UZF recharge assuming it equal to
infiltration rate. In addition to this, it lacks to estimate storage in different model zones and to
separate the sub-surface evapotranspiration, ETss into two: unsaturated evapotranspiration, ETun
and groundwater evapotranspiration, ETg. Because of that, the steady-state evapotranspiration was
higher than the transient-state groundwater evapotranspiration.
The IHM is a useful and effective tool for water resources management especially when the SW-
GW are hydraulically interconnected. It gives good results that may lead to proper planning and
management of water resources.
4.2. Recommendations
In this study, the standardized average sample variogram was estimated by averaging the individual
sample variogram. For further study, each sample and model variogram should be treated
independently for spatial data interpolation.
The temporal variability of land use map should be taken into account to assess its effect on the
groundwater budget of D-T basin.
Microclimatic data of only two stations was used to generate PET map. For further study, it is
recommended to integrate the in-situ data with satellite products, e.g. FEWSNET Global Potential
Evapotranspiration.
The effect of different density of sea water as compared to density of the fresh water at the sea
coastline, should be implemented in future model; nevertheless, quick tests with Seawater Intrusion
package [SWI2] indicated negligible impact of that condition upon the water balances of the D-T
basin.
The daily variation of groundwater fluctuation and abstraction data were not available and Ministry
of Energy and Mineral Resources of Indonesia as those data was confidential; if this data cannot
be used to upgrade this model, then such data should acquire from the field by installation of the
groundwater monitoring network.
To better close the water balance, it is recommended that model calibration should aim at both
matching hydrograph peaks and improve model overall performance (Y).
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
65
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APPENDICES
APPENDIX I
D-T Basin boreholes location.
APPENDIX II
The computation equations to estimate evapotranspiration (FAO Penman-Monteith equation)
2237.3)(T
)]237.3T
T*17.27exp(*[(0.6108*4098
Δ
P*3
10* 0.664742γ
)237.3T
T*17.27exp(*0.6108(T)
0e
)100
meanRH]mean[T
0e(T)ae
5.42)z*ln(67.8
4.87ZU2U
70
Where ETo - reference evapotranspiration [mm day-1], Tmax - maximum daily air temperature [°C], Tmin -
minimum daily air temperature [°C], Ra - extraterrestrial short wave radiation [MJm-2day-1] (divide the value
by 2.45 to obtained Ra in mmday-1), Rn - net radiation at the crop surface [MJm-2 day-1], G - soil heat flux
density [MJ m-2day-1], 𝛾 - psychrometric constant [kPaoC-1], T - mean daily air temperature at 2 m height
[°C], U2 - wind speed at 2 m height [ms-1], es - vapour pressure [kPa], ea – actual vapour pressure [kPa], es-ea -
saturation vapour pressure deficit [kPa], ∆ slope vapour pressure curve [kPa°C-1]. Rn again can be calculated
using equation (2.8).
sR*α)(1lnRnsRnR
a]RN
nsbs[asR
)s(ω)cos(δcos(cos()sin(δssin(s[ωrdscGπ
24(60)aR
0.35)soR
sR)(1.35ae0.14](0.34
2
kmin,4
Tkmax,4
Tσ[lnR
where Rns - net solar or shortwave radiation [MJm-2day-1], Rln - net outgoing long wave radiation [MJm-2day-
1], Rs - solar or shortwave radiation [MJm-2day-1], Ra - extraterrestrial radiation [MJm-2day-1], Rso - clear sky
solar radiation [MJm-2day-1], Rs/Rso - relative shortwave radiation (limited to ≤ 1.0), α - albedo or canopy
reflection coefficient for the reference crop [-], n - actual duration of sunshine [hr.], N - daylight hours [hr.],
n/N - relative sunshine duration [-], Gsc - solar constant = 0.0820 [MJm-2min-1], dr - inverse relative distance
Earth-sun, ωs - sunshine hour angle [rad], ϕ - latitude [rad], δ - solar declination [rad], as - regression
constant, expressing the fraction of extraterrestrial radiation reaching the earth on overcast days (n=0), as +
bs - fraction of extraterrestrial radiation reaching the earth on clear days (i.e. n=N). In case of site specific
information, as and bs can be used as 0.25 and 0.50 respectively.
APPENDIX III
Pearson-correlation coefficient between rainfall stations in the D-T basin based on the data from 2009-2012.
Bedugul Bonganica Buagan Gadungan Kedisan
Klungkung
dpu Kuta Mambal Pempatan Pengotan Rendang Sading Selishan Tampaksiring Tegallalang
Tiying
Gading Ubung Sanglah
Bedugul 1
Bonganica 0.038 1
Buagan .135**
.215** 1
Gadungan 0.095 .297**
.323** 1
Kedisan .445**
.126*
.152**
.177** 1
Klungkung dpu .234**
.204**
.384**
.473**
.277** 1
Kuta .209**
.232**
.585**
.478**
.242**
.527** 1
Mambal .171**
.132*
.310**
.520**
.220**
.641**
.573** 1
Pempatan .130*
.242**
.131*
.239** 0.097 .210
**.232
**.284
** 1
Pengotan .359**
.195**
.324**
.303**
.488**
.396**
.437**
.374**
.192** 1
Rendang 0.072 .202**
.168**
.439**
.150**
.408**
.303**
.402**
.293**
.249** 1
Sading .129*
.165**
.489**
.605**
.194**
.674**
.593**
.727**
.265**
.439**
.370** 1
Selishan .109*
.137**
.451**
.364**
.125*
.486**
.381**
.362**
.122*
.305**
.386**
.462** 1
Tampaksiring .117*
.254**
.165**
.459**
.144**
.505**
.388**
.636**
.349**
.218**
.442**
.523**
.336** 1
Tegallalang 0.099 .185**
.231**
.537**
.180**
.532**
.399**
.671**
.278**
.324**
.574**
.559**
.375**
.643** 1
Tiying Gading .160**
.194**
.286**
.311**
.143**
.324**
.298**
.372**
.238**
.217**
.391**
.347**
.208**
.331**
.378** 1
Ubung .280**
.134*
.509**
.436**
.281**
.548**
.712**
.671**
.334**
.484**
.316**
.686**
.361**
.444**
.512**
.349** 1
Sanglah 0.119 0.061 .454**
.411** 0.113 .567
**.749
**.621
**.402
**.394
**.367
**.628
**.256
**.434
**.501
**.401
**.782
** 1
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
71
APPENDIX IV
Sample Variogram
Model Variogram
APPENDIX V
A. Spatial distribution of rain gauge stations with their names in the D-T basin
72
B. Stream segments overlaying the DEM of D-T basin and stream gauging stations with their names.
The yellow circle indicates three reference gauges that are not used for model calibration.
C. The log transformation of rainfall at station Melangit [units m3sec-1]
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
73
D. Sample double mass curve and frequency distribution for the gauge discharge data [Q - m3sec-1].
Double Mass curve for station Balian Double Mass curve for station Ayung Buangga
Frequency distribution for station Balian Frequency distribution for station Ayung
E. Relation between rainfall and stream discharge
0
20
40
60
80
100
120
140
160
180
2000
100
200
300
400
500
600
700
800
900
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
Station Ayung Buangga
Ayung_Q Tiying Gading_RF
0
100
200
300
400
500
600
0 200 400 600 800
Cum
ula
tive
Q f
or
Bal
ian
stat
ion
Average cumulative Q for a group of stations
0
100
200
300
400
500
600
0 50 100 150 200 250
Cum
ula
tive
Q f
or
Ayu
ng
Buan
gga
stat
ion
Average cumulative Q for a group of stations
74
F. Relation between rainfall and stream discharge
APPENDIX VI
A. GHB conductance at the sea coast for both steady-state and transient-state model [unit - m2day-1]
0
20
40
60
80
100
120
140
160
180
2000
10
20
30
40
50
60
70
80
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
Station Balian
Balian_Q Pempatan_RF
INTEGRATED HYDROLOGICAL MODELING FOR SURFACE AND GROUNDWATER INTERACTION
75
B. Total water balance of D-T Basin at steady-state condition using CHD boundaries [mmday-1].
Budget component IN Budget component OUT
Precipitation (P) 6.10 GW evapotranspiration (ETg) 0.22
Unsaturated zone ET (ETun) 0.00
Interception loss (I) 0.82
Stream discharge at the outlet (q) 0.61
Lateral groundwater outflow (qg) 4.25
TOTAL 6.10 TOTAL 5.89
IN-OUT 0.2
PERCENT DISCREPANCY 3%
C. Land surface and unsaturated zone water balance using of D-T Basin at steady-state condition using CHD boundaries
[mmday-1]. Budget component IN Budget component OUT
Precipitation (P) 6.10 Unsaturated zone ET (ETun) 0.00
GW exfiltration (Exfgw) 0.74 Interception loss (I) 0.82
Gross recharge (Rg) 5.55
Total runoff (Ro) 0.47
TOTAL 6.84 TOTAL 6.83
IN-OUT 0.01
PERCENT DISCREPANCY 0.1%
APPENDIX VII
Hydrograph of observed and simulatd stream discharges.
0
40
80
120
160
2000
100
200
300
400
500
600
700
800
900
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
Station Ayung Buangga
Observed_Q Simulated_Q Tiying Gading_RF
76
0
40
80
120
160
2000
20
40
60
80
100
120
140
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
Station Badung Hilir
Observed_Q Simulated_Q Ubung_RF
0
40
80
120
160
2000
10
20
30
40
50
60
70
80
1-Jan-09 2-Jul-09 1-Jan-10 2-Jul-10 1-Jan-11 2-Jul-11 1-Jan-12 1-Jul-12 31-Dec-12
RF
[m
md
ay-1
]
Q [
m3se
c-1]
Station Balian
Observed_Q Simulated_Q Pempatan_RF