IX. Transient Forward Modeling
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IX. Transient Forward Modeling
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IX. Transient Forward Modeling. Ground-Water Management Issues. Recall the ground-water management issues for the simple flow system considered in the exercises: - PowerPoint PPT Presentation
Transcript of IX. Transient Forward Modeling
IX. Transient Forward Modeling
Ground-Water Management Issues
Recall the ground-water management issues for the simple flow system considered in the exercises:
Water-supply wells are to be installed, but the effect of pumping on the river is of concern, because there is a minimum required discharge from the ground-water system to the river.
A landfill is proposed in one corner. The landfill developers claim (a) the landfill is outside the capture zone of the wells and (b) any leaking effluent will reach the river sufficiently diluted.
Analysis of predicted advective transport from the landfill using the steady-state model suggested that a flow model with pumping conditions is needed for making a final decision about landfill approval.
Thus, pumping wells were drilled in aquifers 1 and 2, and a 283-day aquifer test has been conducted, during which drawdown and river discharge data were collected. A transient model of the flow system will be recalibrated using these data and the previous steady-state data, and will be used to predict the advective flow path from the proposed landfill.
Transient Ground-Water Flow System
See Figure 2.1a of Hill and Tiedeman.
As at steady-state, inflow occurs primarily as areal recharge; there
is also a very small amount of inflow across the boundary with the
hillside.
Outflow occurs as discharge to the river and as ground-water
withdrawal by pumping.
The well is roughly in the center of the model area. An aquifer test
has been performed for 283 days, using a total pumping rate of 2.0
m3/sec (1.0 m3/sec from each confined aquifer).
Transient Ground-Water Flow Model
See flow model setup in Figure 2.1b of Hill and Tiedeman.
The well is in row 9, column 10; the pumping rate is 1.0m3/sec from each
model layer.
See transient model parameter definition and starting values in Table 9.2.
See true simulated conditions in Figure 9.3 and 9.4.
Transient Parameters and Starting Values
Modified from Table 9.2 of Hill and Tiedeman (page 231)
Flow-system property Parametername
True value Starting value
Specific storage in layer 1 SS_1 2.0 x 10-5 2.6 x 10-5
Specific storage in layer 2 SS_2 2.0 x 10-6 4.0 x 10-6
Pumping rate in each of model layers 1 and 2, in m3/s Q_1&2 -1.0 -1.1
Do exercise 9.3
True Simulated Conditions
With pumping, near steady-state
-5
-4
-3
-2
-1
0
1
2
3
4
5
0 50 100 150 200 250 300
Time (minutes)
Flow
(m3/d
ay)
Storage
General Head Boundary
Recharge
Wells
River
True Simulated Conditions
Fig. 9.3, p. 229
True Simulated Conditions
Figure 9.4 of Hill and Tiedeman (page 230)
Transient Flow Model Observations
10 steady-state head observations, and
22 transient drawdown observations at the 10 wells.
Observed values shown in Table 9.3 of Hill and Tiedeman, p. 232
1 steady-state and 2 transient flow observations
of ground-water discharge to the river.
Observed values shown in Table 9.4 of Hill and Tiedeman, p. 234
Transient Head and Drawdown Observations
Observation name Lay Row
Col Time of observation,
after beginning of simulation
(days)
Reference stress period
Time of observation,
after beginning of reference stress period
(days)
Observed head (m)
Total variance of head
measurement error (m2)
Variance of
drawdown (m2)
1.ss 1 3 1 0.0 1 0.0 101.804 1.0025 --
1.tr1 1 3 1 1.0088 1 1.0088 101.775 1.0025 0.005
1.tr2 1 3 1 282.8595 1 282.8595 101.675 1.0025 0.005
2.ss 1 4 4 0.0 1 0.0 128.117 1.0025 ---
2.tr1 1 4 4 1.0088 1 1.0088 128.076 1.0025 0.005
2.tr2 1 4 4 4.0353 1 4.0353 127.560 1.0025 0.005
2.tr3 1 4 4 107.6825 1 107.6825 116.586 1.0025 0.005
2.tr4 1 4 4 282.8595 1 282.8595 113.933 1.0025 0.005
Part of Table 9.3 of Hill and Tiedeman (page 232)
MODFLOW
Transient Head and Drawdown Observations
Observation name Lay Row
Col Time of observation,
after beginning of simulation
(days)
Reference stress period
Time of observation,
after beginning of reference stress period
(days)
Observed head (m)
Total variance of head
measurement error (m2)
Variance of
drawdown (m2)
1.ss 1 3 1 0.0 1 0.0 101.804 1.0025 --
1.tr1 1 3 1 1.0088 1 1.0088 101.775 1.0025 0.005
1.tr2 1 3 1 282.8595 1 282.8595 101.675 1.0025 0.005
2.ss 1 4 4 0.0 1 0.0 128.117 1.0025 ---
2.tr1 1 4 4 1.0088 1 1.0088 128.076 1.0025 0.005
2.tr2 1 4 4 4.0353 1 4.0353 127.560 1.0025 0.005
2.tr3 1 4 4 107.6825 1 107.6825 116.586 1.0025 0.005
2.tr4 1 4 4 282.8595 1 282.8595 113.933 1.0025 0.005
Part of Table 9.3 of Hill and Tiedeman (page 232)
UCODE_2005
Transient Head and Drawdown Observations
Observation name Lay Row
Col Time of observation,
after beginning of simulation
(days)
Reference stress period
Time of observation,
after beginning of reference stress period
(days)
Observed head (m)
Total variance of head
measurement error (m2)
Variance of
drawdown (m2)
1.ss 1 3 1 0.0 1 0.0 101.804 1.0025 --
1.tr1 1 3 1 1.0088 1 1.0088 101.775 1.0025 0.005
1.tr2 1 3 1 282.8595 1 282.8595 101.675 1.0025 0.005
2.ss 1 4 4 0.0 1 0.0 128.117 1.0025 ---
2.tr1 1 4 4 1.0088 1 1.0088 128.076 1.0025 0.005
2.tr2 1 4 4 4.0353 1 4.0353 127.560 1.0025 0.005
2.tr3 1 4 4 107.6825 1 107.6825 116.586 1.0025 0.005
2.tr4 1 4 4 282.8595 1 282.8595 113.933 1.0025 0.005
Part of Table 9.3 of Hill and Tiedeman (page 232)
UCODE_2005MODFLOW BothBoth
Transient Flow Observations
Table 9.4 of Hill and Tiedeman (page 234)
Observation name Time of observation, after
beginning of simulation (days)
Reference stress period
Time of observation, after beginning of
reference stress period (days)
Observed gain in river flow (m3/s)
Coefficient of variation of river gain
Standard deviation of river gain
(m3/s)
flow.ss 0.0 1 0.0 4.4 0.10 --
flow.tr1 10.0882 5 0.0 4.1 -- 0.38
flow.tr2 282.8595 5 272.7713 2.2 -- 0.21
Weights on Observations
Head observation weights are the same as for steady-state model: Elevation of each observation well has a variance of measurement error
of 1.00 m2. Each water-level measurement has a variance of of measurement error
of 0.0025 m2. Thus, total variance of head measurement error = 1.0025 m2.
Drawdown observation weights: Drawdowns are obtained by subtracting one head measurement from
another. Well elevation measurement error is constant in time, so it subtracts out. Water-level measurement error is random in time, so the variances of these errors must be added to obtain the total variance of measurement error for the drawdowns.
Statistics used to weight flow observations: Coefficients of variation and standard deviations for flows are given in
Table 9.4 of Hill and Tiedeman.
DO EXERCISE 9.4b: Calculate weights on transient observations.
Model fit to heads using starting parameter values
Figure 9.5
p. 236
DATA AT HEAD LOCATIONS OBSERVATION OBSER- SIMUL. WEIGHTED OBS# NAME VATION EQUIV. RESIDUAL WEIGHT**.5 RESIDUAL * * 1 hd01.ss 102. 100. 1.58 0.999 1.58 2 dd01.1 -0.290E-01 -0.153E-04 -0.290E-01 14.1 -0.410 3 dd01.tr2 -0.129 -0.906E-01 -0.384E-01 14.1 -0.543 4 hd02.ss 128. 139. -11.2 0.999 -11.2 5 dd02.tr1 -0.410E-01 -0.949E-02 -0.315E-01 14.1 -0.446 6 dd02.tr2 -0.557 -0.276 -0.281 14.1 -3.97 7 dd02.tr3 -11.5 -13.0 1.43 14.1 20.3 8 dd02.tr4 -14.2 -18.8 4.59 14.1 64.9 9 hd03.ss 157. 174. -17.7 0.999 -17.7 10 dd03.tr1 -4.38 -3.67 -0.715 14.1 -10.1 11 dd03.tr2 -42.5 -56.2 13.7 14.1 194. 12 hd04.ss 125. 139. -14.4 0.999 -14.4 13 dd04.tr1 -0.670E-01 -0.163E-01 -0.507E-01 14.1 -0.718 14 dd04.tr2 -14.3 -18.8 4.54 14.1 64.3 15 hd05.ss 141. 157. -16.2 0.999 -16.2 16 dd05.tr1 -0.600E-01 -0.368E-01 -0.232E-01 14.1 -0.328 17 dd05.tr2 -21.7 -28.5 6.79 14.1 96.0 18 hd06.ss 127. 140. -13.1 0.999 -13.1 19 dd06.tr1 0.500E-02 -0.125E-01 0.175E-01 14.1 0.247 20 dd06.tr2 -14.4 -19.2 4.82 14.1 68.2 21 hd07.ss 101. 103. -1.76 0.999 -1.75 22 dd07.tr1 0.480E-01 -0.109E-02 0.491E-01 14.1 0.694 23 dd07.tr2 -0.568 -1.38 0.813 14.1 11.5 24 hd08.ss 158. 174. -15.8 0.999 -15.8 25 dd08.tr1 -5.53 -5.81 0.277 14.1 3.91 26 dd08.tr2 -43.2 -57.3 14.0 14.1 199. 27 hd09.ss 176. 190. -13.9 0.999 -13.9 28 dd09.tr1 -0.992E-03 -0.506E-01 0.496E-01 14.1 0.702 29 dd09.tr2 -38.2 -49.5 11.3 14.1 159. 30 hd10.ss 142. 157. -15.0 0.999 -15.0 31 dd10.tr1 -0.130E-01 -0.436E-02 -0.864E-02 14.1 -0.122 32 dd10.tr2 -19.9 -26.1 6.21 14.1 87.8 …………………………………………DATA FOR FLOWS REPRESENTED USING THE RIVER PACKAGE OBSERVATION MEAS. CALC. WEIGHTED OBS# NAME FLOW FLOW RESIDUAL WEIGHT**.5 RESIDUAL 33 flow01.ss -4.40 -4.86 0.461 2.27 1.05 34 flow01.10 -4.10 -4.72 0.618 2.63 1.63 35 flow01.283 -2.20 -2.86 0.663 4.76 3.16
Model Fit Using Starting Parameter ValuesSTATISTICS FOR HEAD RESIDUALS : MAXIMUM WEIGHTED RESIDUAL : 197. OBS# 26 MINIMUM WEIGHTED RESIDUAL : -17.7 OBS# 9 AVERAGE WEIGHTED RESIDUAL : 25.6 # RESIDUALS >= 0. : 15 # RESIDUALS < 0. : 17 SUM OF SQUARED WEIGHTED RESIDUALS (HEADS ONLY) 0.13131E+06 DATA FOR FLOWS REPRESENTED USING THE RIVER PACKAGE OBSERVATION MEAS. CALC. WEIGHTED OBS# NAME FLOW FLOW RESIDUAL WEIGHT**.5 RESIDUAL 33 flow.ss -4.40 -4.86 0.461 2.27 1.05 34 flow.tr1 -4.10 -4.72 0.622 2.63 1.64 35 flow.tr2 -2.20 -2.87 0.670 4.76 3.19 STATISTICS FOR RIVER FLOW RESIDUALS : MAXIMUM WEIGHTED RESIDUAL : 3.19 OBS# 35 MINIMUM WEIGHTED RESIDUAL : 1.05 OBS# 33 AVERAGE WEIGHTED RESIDUAL : 1.96 # RESIDUALS >= 0. : 3 # RESIDUALS < 0. : 0 SUM OF SQUARED WEIGHTED RESIDUALS (RIVER FLOWS ONLY) 13.958 SUM OF SQUARED WEIGHTED RESIDUALS (ALL DEPENDENT VARIABLES) 0.13133E+06
From MODFLOW-2000 output file.
EXERCISE 9.5: Evaluate model fit using the starting parameter values.
