A travel time model for estimating the water budget of complex catchments
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Transcript of A travel time model for estimating the water budget of complex catchments
A travel time model for water budget of complex catchments
Candidate: Supervisors: Marialaura Bancheri Prof. Riccardo Rigon Matr.: 169091 Eng. Giuseppe Formetta
Doctoral School in Civil, Environmental and Mechanical Engineering - 29°Cycle
A travel time model for water budget of complex catchments
Getting the right answers for the right reasons: toward many
“embedded” reservoirs.
Age-rankedhydrologicalbudgetsandatravel6medescrip6onofcatchment
hydrology
JGrass-NewAge: a replicable
hydrological model
Bancheri M., A travel time model for the water budgets of complex catchments
Overview
Travel time T
Residence time Tr Life expectancy Le
Injection time tin
Exit time tex
tTime
Travel time: the time a water particle takes to travel across a catchment
T = (t� tin
)| {z }Tr
+(tex
� t)| {z }Le
Bancheri M., A travel time model for the water budgets of complex catchments
Travel times as random variables
dS(t)
dt= J(t)�Q(t)�AET (t)
S(t) =
Z min(t,tp)
0s(t, tin)dtin AET (t) =
Z min(t,tp)
0aeT (t, tin)dtin
J(t) =
Z min(t,tp)
0j(t, tin)dtin Q(t) =
Z min(t,tp)
0q(t, tin)dtin
ds(t, tin)
dt= j(t, tin)� q(t, tin)� aeT (t, tin)
Bancheri M., A travel time model for the water budgets of complex catchments
“Bulk” water budget VS “age-ranked” water budget
Backward probability conditioned on the actual time t
Travel time T
Exit time tex
tTimeInjection
time tin
Looks backward to tin
Travel time T
Exit time tex
tTimeInjection
time tin
Looks backward to tin
Bancheri M., A travel time model for the water budgets of complex catchments
Backward probabilities
Time
Time
J(t)
S(t)
S(t)
Residence time
ttin
s(t, tin)Residence timebackward probabilities
pS(t� tin|t) :=s(t, tin)
S(t)[T�1]
Bancheri M. , A travel time model for the water budgets of complex catchments
Backward probabilities
Time
J(t) ttin
TimeResidence time
Q(t)
Q(t)
Travel timebackward probabilities
q(t, tin)
pQ(t� tin|t) :=q(t, tin)
Q(t)[T�1]
Bancheri M. , A travel time model for the water budgets of complex catchments
Backward probabilities
On the shape of the backward pdfs
Z min(t,tp)
0pQ(t� tin|t)dtin = 1
• Time-variant
•
• not always true for other classical distributions , e.g., Z min(t,tp)
0
(t� tin)↵+1e(t�tin)
�
�↵�(↵)dtin 6= 1
8t⇤ 2 [0,min(t, tp)]
Bancheri M. , A travel time model for the water budgets of complex catchments
Backward probabilities
After the previous definitions and some proper substitutions, the water budget equation for the control volume can be written as:
d
dtS(t)pS(Tr|t) = J(t)�(t� tin)�Q(t)pQ(t� tin|t)�AEt(t)pET (t� tin|t)
obtaining a linear ordinary differential equation that can be solved exactly, once assigned the SAS values :
d
dtS(t)pS(Tr|t) = J(t)�(t� tin)�Q(t)
SASz }| {!Q(t, tin) pS(Tr|t)| {z }
pQ(t�tin|t)
�AEt(t)
SASz }| {!ET (t, tin) pS(Tr|t)| {z }
pET(t�tin|t)
Bancheri M. , A travel time model for the water budgets of complex catchments
Backward probabilities
The formalism developed is applicable, in principle to any substance, say indicated by a superscript i.
If the substance is diluted in water, it is usually treated as concentration in water, which is known once the concentration of the solute in input is known together with the backward probability:
d
dtSi(t)p(t� tin|t) = J i(t)piJ(t� tin|t)�Qi(t)!Q(t, tin)p(t� tin|t)
Ci(t) =
Z t
0p(t� tin|t)Ci
J(tin)dtin
Bancheri M. , A travel time model for the water budgets of complex catchments
Passive solute transport
Forward probability conditioned on the injection time tin
Travel time T
Exit time tex
tTimeInjection
time tin
Looks forward to t
Travel time T
Exit time tex
tTimeInjection
time tin
Looks forward to t
Bancheri M. , A travel time model for the water budgets of complex catchments
Forward probabilities
Thanks to Niemi’s relationship (Niemi, 1977) we can connect the backward and forward pdfs:
Where:
We can also define the forward travel time pdfs as:
pQ(t� tin|tin) :=q(t, tin)
⇥(tin)J(tin)
⇥(tin) := limt!1
⇥(t, tin) = limt!1
VQ(t, tin)
VQ(t, tin) + VET (t, tin)
Q(t)pQ(t� tin|t) = ⇥(tin)pQ(t� tin|tin)J(tin)
Bancheri M. , A travel time model for the water budgets of complex catchments
Forward probabilities
Bancheri M. , A travel time model for the water budgets of complex catchments
Getting the right answers for the right reasons: toward many “embedded” reservoirs.
R S
Ssnow
M
SCanopy
E
Tr
SRootzone
TRZ
SRunoff
TR
Re
SGroundwater
QR
QG
U
R S
Ssnow
M
SCanopy
E
Tr
SRootzone
TRZ
SRunoff
TR
Re
SGroundwater
QR
QG
U
The entire model is based on the assumption that the water budget has been solved and the fluxes are known.
Flux Expression
Tr(t) H(Scanopy
(t)� Imax
)ac
Scanopy
(t)
E(t)S
canopy
S
Canopy
max
(1� SCF )ETp
U(t) pSRootzone
TRZ
(t) S
Rootzone
S
Rootzone
max
ETp
Re
(t) Pmax
S
Rootzone
S
Rootzone
max
QR
(t) ARt
0 uW (ut� ⌧)↵(⌧)Tr
(⌧)d⌧
TR
(t)S
Runoff
S
Runoff
max
ETp
QG
(t) aSGroundwater
Process Component Geomorphological model setup Jgrastools
Meteorological interpolation tools KrigingIDW, JAMI
Energy balance Shortwave radiation balance
Clearness IndexLongwave radiation balance
Evapotranspiration Penmam-Monteith
Priestley-TaylorFao-Etp-model
Snow melting Rain-snow separationSnowmelt and SWE model
Runoff production Adige "Embedded" reservoirs
Travel times descriptionBackward travel times pdfsForward travel times pdfs
Solute trasport
Automatic calibration LUCA
Particle swarmDream
Geomorphological model setup
Meteorological interpolation tools
Energy balance
Evapotranspiration
Runoff production and Snow Melting
Travel times and passive solute transport
Automatic calibration
JGrass-NewAge
Bancheri M. , A travel time model for the water budgets of complex catchments
uDig-Jgrasstools-Horton Machine
GEOSTATISTICS Kriging
DETERMNISTICSIDW,JAMI
SHORTWAVE (SWRB) Iqbal+Corripio model
Decomposition
LONGWAVE(LWRB) Brutsaert with
10 parametrizations
Penmam-Monteith Priestley-Taylor Fao-Etp-model
Adige model Snowmelt and SWE model
LUCA Particle swarm Dream
“Embedded”reservoirs
Backward travel times pdfs
Forward travel times pdfs
Solute transport Bancheri M. , A travel time model for the water budgets of complex catchments
JGrass-Newge: hydrological modelling with components
• Rewrote according to the Java object orienting programming;
• Increased their flexibility using design patterns;
• Gradle integrated;
• Travis CI integrated;
• Documentation wrote to obtain a variety of modelling solutions;
• OMS project example published for reproducing the results.
Source code Project examples
Community blog Documentation
Bancheri M. , A travel time model for the water budgets of complex catchments
Replicability of JGrass-NewAge
http://geoframe.blogspot.com
Bancheri M. , A travel time model for the water budgets of complex catchments
GEOframe: a system for doing hydrology by computer
Bancheri M. , A travel time model for the water budgets of complex catchments
Application to real cases: River Net3 for the Posina river case
14HRUsA=36km2
42HRUsA=112km2
Bancheri M. , A travel time model for the water budgets of complex catchments
Applications: Posina River
0
100
200
300
1995 1996 1997 1998 1999
Pre
cipi
tatio
n [m
m]
0
10
20
30
40
1995 1996 1997 1998 1999Time [h]
Dis
char
ge [m
3/s]
Measured
Simulated
Bancheri M. , A travel time model for the water budgets of complex catchments
Applications: Posina River
0
5
10
15
20
1995 1996 1997 1998 1999
Rainfall[mm]
Upper layer
0
50
100
150
1995 1996 1997 1998 1999
Mea
n TT
[d]
ω Preference for new water Uniform preference Preference for old water
Beta(↵,�) : prob(x|↵,�) = x
↵�1(1� x)��1
B(↵,�)
B(↵,�) =
Z 1
0t↵�1(1� t)��1dt
T
ω
Uniform preference: α=1,β=1
1
T
ω
1
Preference for new water α=0.5,β=1
T
ω
1
Preference for old water α=3,β=1
Bancheri M. , A travel time model for the water budgets of complex catchments
Applications: Posina River
0
10
20
1995 1996 1997 1998 1999Pre
cipi
tatio
n [m
m] Precipitation [mm]
010203040
1995 1996 1997 1998 1999
Mea
n TT
[d]
Canopy
0255075100
1995 1996 1997 1998 1999
Mea
n TT
[d]
Rootzone
Bancheri M. , A travel time model for the water budgets of complex catchments
Applications: Posina River
0.25
0.50
0.75
1.00
Gen 1994 Apr 1994 Lug 1994 Ott 1994 Gen 1995Time
Par
titio
ning
coe
ffici
ent Θ
January
February
March
April
May
June
July
August
September
October
November
Jan 94 Apr 94 Jan 95 Oct 94 Jul 94
Bancheri M. , A travel time model for the water budgets of complex catchments
Applications: Posina River
Further valida6ons of the travel 6mes theory are required,especiallytotestthesolutetransport.However,sincethelackofdata,itwasnotpossible6llnow.ThereforeIaskedtoadeferralof6monthsofthesubmissionofthethesis.Hopefullytheisotopedataarearrivingintheweeks…(maybewithSanta!)
Bancheri M. , A travel time model for the water budgets of complex catchments
Research outcomes
Journals paper
Rigon, R., Bancheri, M., Formetta, G., and de Lavenne, A. (2016) The geomorphological unit hydrograph from a historical-critical perspective. Earth Surf. Process. Landforms, 41: 27–37. doi: 10.1002/esp.3855.
Rigon R., Bancheri M., Green T., Age-ranked hydrological budgets and a travel time description of catchment hydrology, in discussion, HESSD, 2016
Formetta, G., Bancheri, M., David, O., and Rigon, R.: Performance of site-specific parameterizations of longwave radiation, Hydrol. Earth Syst. Sci., 20, 4641-4654, doi:10.5194/hess-20-4641-2016, 2016.
Bancheri, M., Serafin, F., Abera, W., Formetta, G., Rigon R., A well engineered implementation of Kriging tools in the Object Modelling Sisytem v.3., in preparation, 2016
Bancheri M. , A travel time model for the water budgets of complex catchments
Research outcomes
Conference abstract
M. Bancheri, G.Formetta, W.Abera, R. Rigon, Componenti della radiazione solare ad onda lunga: NewAge-LWRB, XXXIV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2014
W. Abera, G. Formetta, M.Bancheri, R.Rigon, 2014, The effect of spatial discretization on hydrological response, the case of Semi-distributed Hydrological modelling, AGU chapman conference, 2014.
M.Bancheri, W. Abera, G. Formetta, R.Rigon & F. Serafin , Implementing a Travel Time Model for the Entire River Adige: the Case on JGrass-NewAGE, American Geophysical Union, Fall Meeting 2015, abstract \#H11K-03.
M.Bancheri, Rigon, R., Formetta, G. & Green T.R., Implementing a travel time model for water and energy budgets of complex catchments: Theory, software, and preliminary application to the Posina River, Hydrology Days 2016.
Serafin, F., Bancheri M., Rigon R. and David O. "A Java binary tree data structure for environmental modelling." (2016), International Congress on Environmental Modelling and Software, 2016
Bancheri, M., et al. "Replicability of a modelling solution using NewAGE-JGrass.", International Congress on Environmental Modelling and Software, 2016
Bancheri M. and Rigon R. “Implementing a travel time model for the water budget of complex catchment: theory and preliminary results.” , XXXV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2016
Bancheri M., Formetta G., Serafin, F., and Rigon R. “Rasearch reproduciblity and replicability: the case of JGrass-NewAge”, XXXV Convegno nazionale di Idraulica e Costruzioni Idrauliche, 2016
Bancheri M. , A travel time model for the water budgets of complex catchments
Research outcomes
Organized meetings
- PhD Days di Ingegneria delle Acque 2015, University of Trento, Italy
- Hydrological Modeling with the Object Modelling System (OMS) International Summer Class Short Course, University of Trento, Italy, July 18-21, 2016
Teaching activity
- Supervision of undergraduates at Hydrology course A.A 2013-2014
- Supervision of undergraduates at Hydraulic Construction course A.A 2013-2014 - Supervision of undergraduates at Hydrology course A.A 2014-2015
- Supervision of undergraduates at Hydraulic Construction course A.A 2014-2015