1. IX. Transient Forward Modeling

2. 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.

3. 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 m 3 /sec (1.0 m 3 /sec from each confined aquifer).

4. 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 1.0m 3 /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.

5. Transient Parameters and Starting Values Modified from Table 9.2 of Hill and Tiedeman (page 231) Flow-system propertyParameter name True valueStarting value Specific storage in layer 1SS_12.0 x 10 -5 2.6 x 10 -5 Specific storage in layer 2SS_22.0 x 10 -6 4.0 x 10 -6 Pumping rate in each of model layers 1 and 2, in m 3 /sQ_1&2-1.1 Do exercise 9.3

6. True Simulated Conditions With pumping, near steady-state

7. True Simulated Conditions Fig. 9.3, p. 229

8. True Simulated Conditions Figure 9.4 of Hill and Tiedeman (page 230)

9. 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

10. Transient Head and Drawdown Observations Observation nameLayRo w ColTime 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 (m 2 ) Variance of drawdown (m 2 ) 1.ss1310.01 101.8041.0025-- 1.tr11311.00881 101.7751.00250.005 1.tr2131282.85951 101.6751.00250.005 2.ss1440.01 128.1171.0025--- 2.tr11441.00881 128.0761.00250.005 2.tr21444.03531 127.5601.00250.005 2.tr3144107.68251 116.5861.00250.005 2.tr4144282.85951 113.9331.00250.005 Part of Table 9.3 of Hill and Tiedeman (page 232) MODFLOW

11. Transient Head and Drawdown Observations Observation nameLayRo w ColTime 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 (m 2 ) Variance of drawdown (m 2 ) 1.ss1310.01 101.8041.0025-- 1.tr11311.00881 101.7751.00250.005 1.tr2131282.85951 101.6751.00250.005 2.ss1440.01 128.1171.0025--- 2.tr11441.00881 128.0761.00250.005 2.tr21444.03531 127.5601.00250.005 2.tr3144107.68251 116.5861.00250.005 2.tr4144282.85951 113.9331.00250.005 Part of Table 9.3 of Hill and Tiedeman (page 232) UCODE_2005

12. Transient Head and Drawdown Observations Observation nameLayRo w ColTime 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 (m 2 ) Variance of drawdown (m 2 ) 1.ss1310.01 101.8041.0025-- 1.tr11311.00881 101.7751.00250.005 1.tr2131282.85951 101.6751.00250.005 2.ss1440.01 128.1171.0025--- 2.tr11441.00881 128.0761.00250.005 2.tr21444.03531 127.5601.00250.005 2.tr3144107.68251 116.5861.00250.005 2.tr4144282.85951 113.9331.00250.005 Part of Table 9.3 of Hill and Tiedeman (page 232) UCODE_2005 MODFLOW Both

13. Transient Flow Observations Table 9.4 of Hill and Tiedeman (page 234) Observation nameTime 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 (m 3 /s) Coefficient of variation of river gain Standard deviation of river gain (m 3 /s) flow.ss0.01 4.40.10-- flow.tr110.088250.04.1--0.38 flow.tr2282.85955272.77132.2--0.21

14. 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 m 2. Each water-level measurement has a variance of of measurement error of 0.0025 m 2. Thus, total variance of head measurement error = 1.0025 m 2. 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.

15. 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

16. Model Fit Using Starting Parameter Values STATISTICS 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.