# Presentation: 673010

## 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)

- Do exercise 9.3

## True Simulated Conditions

- With pumping, near steady-state

## 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

- Part of Table 9.3 of Hill and Tiedeman (page 232)

- MODFLOW

## Transient Head and Drawdown Observations

- Part of Table 9.3 of Hill and Tiedeman (page 232)

- UCODE_2005

## Transient Head and Drawdown Observations

- Part of Table 9.3 of Hill and Tiedeman (page 232)

- UCODE_2005

- MODFLOW

- Both

- Both

## Transient Flow Observations

- Table 9.4 of Hill and Tiedeman (page 234)

## 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 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.