Exercise 2 Solution: Lower Ratio of Streamflow to Pumping

The problem:

The Base Case analysis of Exercise 1 assumed that the streamflow was much greater than the well pumpage. What if the pumping rate was higher than in Exercise 1 and the ratio of streamflow to pumping (withdrawal) rate was much lower? In the Base Case, river inflow is about ten times greater than the well pumpage. Consider a case in which the well pumpage is increased by a factor of three (two more wells are drilled close to the original well to form a well field, and each well has the same pumping capacity, so the total Q in that cell of the model grid is -6,078 m3/d) and the river inflow is reduced by a factor of three (Qin = 6,667 m3/d instead of 20,000 m3/d). The ratio of streamflow entering the system to pumping out of the aquifer would then be about 1.1. How would that affect (1) the streamflow in space and time, (2) the drawdown in the aquifer, (3) the head distribution in the aquifer, and (4) the hydrograph for the pumping well? How does that affect (5) the water budget of the aquifer and (6) the fractional sources of water to the well? Is this pumping scenario sustainable?

How to run and analyze the model results:

If you have not already done so, it is useful to read Box 3, then run and post-process the results of the Base Case model of Case Study 1 before undertaking Exercise 2. To do this, first put the input files, MODFLOW-NWT executable code, and ModelMuse files for the Base Case of Case Study 1 on a Microsoft-OS computer by downloading the zip file “CaseStudy1–Models.zip“ from the online Supplementary Information for this book. Extract the “Case Study 1” folders and subfolders onto your personal computer. Then go through the steps described in Box 3.

Acquiring a file folder for Exercise 2:

Next download the zip file “Exercise2.zip“ from the online Supplementary Information for this book. To get you started, we have already copied the Base.Case input files into a new folder under the folder “Exercise 2” (Revised Base Case–Change.Qs); you can use these to simulate the case with more pumping and less streamflow. However, the files have not been modified yet, so if you execute these files without changes, you will get the base case result. We suggest you work from this folder to analyze and develop solutions to Exercise 2. For convenience, we have also installed a copy of the executable code for MODFLOW-NWT in a location that will work with the batch files in these two folders.

Modifying Input Files

To determine the effect and importance of the relative strength of the pumping stress to the magnitude of streamflow, copy the Base Case input files into a new folder for Exercise 2 and modify the input parameters to match the assumptions of the above exercise. Also, to more clearly assess the impact on streamflow, it is suggested that you add an additional stream gage to a location in the river close to the well. The results of Exercise 1 indicated a minimum streamflow in reach 46, so place the gage there. These modifications can be accomplished by:

  • Increase the pumping rate for the well on the last line of the WEL Package input file “Base.Case.wel” by changing the value “-2.026000000000E+003” to “-6.078000000000E+003”.
  • Reduce the streamflow entering the river for both stress periods in the file “Base.Case.sfr” by changing both occurrences of the value “2.000000000000E+004” to “0.666700000000E+004”.
  • Add a stream gage by (1) changing the number on the first line of the “Base.Case.gag” file to “2”, (2) adding a third line to the “Base.Case.gag” file “1 46 20206 1”, and (3) adding a line to the “Base.Case.nam” file after the similar line for the first gage that says “DATA 20206 ..\Output.Files\Base.Case.sfrg2 REPLACE”).

Next, run the model by double clicking on the batch file “Base.Case.bat” in the Input.Files folder.

Assessing Streamflow:

In assessing the effects of pumping on streamflow for the case with increased pumping and less incoming streamflow, we see that after 200 years, the streamflow along the river (from the upstream to downstream ends) is much lower than for the previous Base Case (Figure ExSol 2-1). This difference appears to be explainable primarily by the difference in the specified inflow at the upstream end of the river. To more fully understand the changes in streamflow, we can look at the records of the two stream gaging stations in the GAG output files (Figure ExSol 2-2). These results show that flow at the gage located near the middle reach of the river (Gage no. 2) declines rapidly for 5 years until the river goes dry at that location; it stays dry (no flow) for the remainder of the simulation period. The gage at the downstream end of the river (Gage no. 1) similarly declines rapidly at first, but then the rate of decline decreases after 5 years — at the same time that the upstream reach has ceased flowing. At that time — starting in year 6 — the streamflow depletion is influenced only by the decreased groundwater discharge and is no longer affected by decreased infiltration in the upper reaches.

The nature of the cessation of streamflow in selected parts of the river can be analyzed by plotting the streamflow profiles along the river at various times (Figure ExSol 2-3). These results illustrate that the river first goes dry in a short 7-km central reach of the river at 6 years. The length of the dry section subsequently expands in both an upstream and downstream direction. After 200 years of pumping, 40 kilometers of the river are dry, and the expansion trend seems to be continuing. Therefore, with the smaller ratio of streamflow to pumping, the effects on the flow in the river are much more severe, noticeable, and environmentally damaging.

Graph showing streamflow variations with distance
Figure ExSol 2-1 – Streamflow variations with distance after 200 years (Konikow and Bredehoeft, 2020).
Graph showing streamflow changes
Figure ExSol 2-2 – Streamflow changes for 200 years at two gaging stations. Gage No. 1 is located at the outflow from the modeled area (reach 80) and Gage No. 2 is located at reach 46 (37km) downstream from where the river enters the modeled area) (Konikow and Bredehoeft, 2020).
Graph showing changes in the streamflow profile
Figure ExSol 2-3 – Changes in the streamflow profile during the 200-year simulation period showing growth in the length of the dry central reaches after year 5 (Konikow and Bredehoeft, 2020).

Assessing Drawdown:

The drawdown in the pumping well would be expected to be greater than in the Base Case. As seen in Figure ExSol 2-4, that is indeed the case, although the differences are relatively small. Whereas the Base Case drawdown indicates that it is close to equilibrium before 200 years, with the higher pumping rate in Exercise 2 that is not the case and drawdown is still increasing measurably. But in both cases the maximum drawdown is small compared to the average saturated thickness of the aquifer (150 m), so even with the higher pumping rate, additional long-term drawdown would not be a major concern to water managers.

Graph showing calculated drawdown in the pumping well
Figure ExSol 2-4 – Calculated drawdown in the pumping well for Base Case and Exercise 2 (with higher pumping rate) (Konikow and Bredehoeft, 2020).

Assessing Heads:

The head distribution calculated after 200 years of pumping (Figure ExSol 2-5) indicates that even though the pumping rate is higher and drawdown is greater than in the base case, all of the groundwater entering the well is ultimately derived from the upstream reaches of the river; the pumping well does not capture any of the water derived from mountain front recharge along the system’s western boundary. Comparison to the base case heads (Figure 20b) indicates that the most visible differences include more drawdown, lower heads in most areas, stronger convergence of flow close to the pumping well, and head contours perpendicular to the river where it has gone dry (indicating a lack of exchange between the aquifer and the river along those dry reaches of the river).

Contours of calculated heads in the aquifer
Figure ExSol 2-5 – Calculated heads (in m) in the aquifer after 200 years for conditions of Exercise 2 (with higher pumping rate). The contour interval is 0.5 m, with a supplementary contour at 28.75 m (Konikow and Bredehoeft, 2020).

Assessing the Water Budget:

The water budgets (Tables ExSol 2-1 and ExSol 2-2) have changed substantially from those of the Base Case (Tables 1 and 2 in the book), mostly because of the different assumptions about incoming streamflow and well pumpage. A comparison of water budgets for the two cases indicates that the biggest changes are (1) the much higher storage depletion rate and (2) the reduced outflow to the river at 200 years — both of which result directly from the higher imposed pumping rate than in the Base Case.

Table ExSol 2-1 – Groundwater budgets for Exercise 2 for predevelopment conditions and after 200 years of pumping one well. All flux values are in m3/d.

Predevelopment t = 200 Years
IN Mountain Front Recharge 1,688 1,688
Change in Storage 0 2,299
Stream infiltration 5,842 6,667
Total 7,530 10,654
OUT Wells 0 6,078
Outflow to stream 7,534 4,577
Total 7,534 10,655

Table ExSol 2-2 – Streamflow budgets for Exercise 2 for predevelopment conditions and after 200 years of pumping one well. All flux values are in m3/d.

Predevelopment t = 200 Years
River Inflow 6,667 6,667
River Outflow 8,232 4,577

As in the Base Case (Figure 21), the components of the water budget change substantially during the 200-year transient simulation period (Figure ExSol 2-6). Compared to the Base Case, in this new simulation the increase in induced infiltration from the river to the aquifer (a type of recharge) has reached its maximum possible value at about 6 years, and then ceases to change after that. The maximum increase in induced infiltration from the river is the difference between the inflow to the river (6,667 m3/d) and the stream infiltration (or seepage loss from the river) under predevelopment conditions (5,842 m3/d) — a difference of 825 m3/d. Once that reaches its maximum, the growth in capture is derived solely from continued decreases in groundwater discharge to the river in its downstream reaches. An inflection in the capture and groundwater storage depletion curves occurs at 6 years also when the increase in recharge stabilizes. The system becomes capture dominated at about 100 years (compared to almost 20 years in the Base Case).

The fractional sources of water to the well under the conditions of Exercise 2 are shown in Figure ExSol 2-7. After 200 years, 38 percent of well pumping is balanced by groundwater storage depletion while 62 percent of pumping is balanced by capture — substantially less than in the Base Case. This indicates that it will take a much longer time for the system to reach a new equilibrium.

Graph showing calculated changes in the water budget
Figure ExSol 2-6 – Calculated changes in the water budget of the hypothetical desert-basin aquifer during the 200-year simulation period for the Exercise 2 case. Capture is the sum of its components represented by the dashed lines (Konikow and Bredehoeft, 2020).
Graph showing nondimensional sources of water being pumped based on annual rates
Figure ExSol 2-7 – Nondimensional sources of water being pumped based on annual rates for the conditions of Exercise 2 (Konikow and Bredehoeft, 2020).

Assessing Sustainability:

The well is still deriving water from increasing amounts of capture after 200 years of pumping. The water budget analysis and system responses indicate that from a hydraulic perspective solely of the aquifer, the pumping is sustainable. However, the capture rates are high relative to the flow in the river, and part of the river goes dry after just 5 years of pumping. The extent of the dry reach grows continually over time. This would likely constitute unacceptable surface water impacts and environmental/ecological damage to most hydrologists and water managers.

Return to exercise 2


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