Scenario 1: Scaled-EPS-Groundwater-Withdrawal Scenario

Ellis (2018a) developed a 20-year EPS groundwater-withdrawal scenario by using the Rush Springs aquifer groundwater-flow model. For the 20-year EPS groundwater-withdrawal scenario, existing simulated wells were replaced with a simulated well for each active cell representing the Rush Springs aquifer within the groundwater-flow model. The use of a simulated well for each active cell facilitated the hypothetical application of groundwater withdrawals on an equal basis over the spatial extent of the aquifer. The simulated wells then withdrew water at a uniform rate that was incrementally scaled until half of the model cells retained a saturated thickness at least 15 ft after 20 years. The 20-year-EPS-groundwater-withdrawal rate (hereinafter referred to as “baseline EPS rate”) from this scenario was used as the basis for assessing the effects on base flows in Cobb, Lake, and Willow Creeks by scaling that rate by selected percentages. For consistency with the previously published groundwater-flow model (Ellis, 2018a), the LAK package (not the CHD package) was used to simulate Fort Cobb Reservoir for the scaled-EPS-groundwater-withdrawal scenario documented in this report. Ellis (2018a, b) used constant long-term (1979–2015) mean stresses for package inputs (except for groundwater withdrawals), which were then used for the scaled-EPS-groundwater-withdrawal scenario.

The scaled-EPS-groundwater-withdrawal scenario consisted of six simulations scaling the baseline EPS rate by 25, 40, 50, 75, 100, and 120 percent for a period of 50 years to see the effects of these EPS rates over a longer time period than the 20-year period simulated in Ellis (2018a). For the 50-year simulations, streams (1) never ceased flowing under the 25-percent scaling scenario (fig. 12A); (2) ceased flowing after about 26 years under the 40-percent scaling scenario (fig. 12B); (3) ceased flowing after about 12 years using the 50-percent scaling scenario (fig. 12C); (4) ceased flowing after about 4 years using the 75-percent scaling scenario (fig. 12D); (5) ceased flowing after about 2 years using the baseline EPS rate (fig. 12E); and (6) ceased flowing after about 1 year using the 120-percent scaling scenario (fig. 12F).

As the EPS-rate scaling factor increased, base flows generally declined more sharply until approaching no flow (fig. 12). Cobb Creek began each simulation with the largest amount of base flow and sustained the largest losses in base flows when increasing the EPS-rate scaling factor. Lake Creek base flows often decreased in the same manner as Cobb Creek base flows, but by a smaller amount. Willow Creek base flows remained close to zero for most of the scaled-EPS-rate simulations, although base flows remained low (about 1 ft³/s) even after 50 years when using an EPS-rate scaling factor of 25 percent (fig. 12A). As the EPS-rate scaling factor increased, however, base flows for Lake and Willow Creeks declined more rapidly than base flows for Cobb Creek, likely because base flows for Cobb Creek are generally greater than the base flows in Lake and Willow Creeks and therefore can withstand greater groundwater withdrawals. The simulated EPS rates in this report represent a high volume of groundwater withdrawals that tend to quickly (often in less than 10 years) cause dry streams. To maintain stream base flow, the EPS rate would likely need to be much less than the EPS rate determined by using MAY targets (50 percent of the aquifer with less than 15 ft saturated thickness over 20 years of continuous EPS withdrawals).

Scenario 2: Scaled-Historical-Groundwater-Withdrawal Scenario

To investigate the effects of groundwater withdrawals on base flows in Cobb, Lake, and Willow Creeks, a scenario was developed to modify historical groundwater withdrawals implemented in the Ellis (2018a) groundwater-flow model. The scaled-historical-groundwater-withdrawal scenario consisted of 10 simulations scaling the Ellis (2018a) historical groundwater-withdrawal rates by 50, 60, 70, 80, 90, 100, 125, 150, 175, and 200 percent. The scenario with 100-percent scaled historical-groundwater-withdrawal rates (hereinafter referred to as the “historical baseline rate”) was identical to the Ellis (2018a) groundwater-flow model except that the CHD package was used to simulate Fort Cobb Reservoir instead of the LAK package. The outputs from the historical-baseline-rate simulation were used for comparison with the results from the Ellis (2018a) groundwater-flow model (table 5). Ellis (2018b) estimated 500 gallons per minute (gal/min) as the maximum groundwater-withdrawal rate that the Rush Springs aquifer could sustain over longer periods of continuous pumping (such as monthly or annually). Therefore, scaled-groundwater-withdrawal rates were not permitted to exceed 500 gal/min. Historical groundwater withdrawals for the steady-state stress period were not scaled for each simulation to ensure identical starting conditions for each simulation.

Base flows were more sensitive to increases in groundwater withdrawals than to decreases in groundwater withdrawals; that is, the absolute magnitude of the change in base flow was greater for simulated increases in groundwater withdrawals than for simulated decreases in groundwater withdrawals (fig. 13A–C). Changes in base flows were generally highest for Cobb Creek (fig. 13A), intermediary for Lake Creek (fig. 13B), and lowest for Willow Creek (fig. 13C). Changes in base flow for Lake Creek were similar to those for Cobb Creek during some years. Base flows for Lake and Willow Creeks resulted in small streamflows approximating no-flow conditions for a few years, which would mean a lack of water available for diversions from each stream. For the simulation with the highest groundwater withdrawals, total inflows into Fort Cobb Reservoir declined about 16 ft³/s during some years (fig. 13D) with corresponding decreases in base flow of as much as 70 percent. Lake and Willow Creeks combined contributed about the same quantity of base flow as Cobb Creek.

The largest percentage changes in base flow were simulated for streams with the smallest overall flow (fig. 14A–C). Percentage change was calculated by using

where Thus, equal reductions in base flow would result in a larger negative percentage change for streams with less base flow. However, a large negative percentage change in base flow would indicate that a stream is susceptible to undergoing sustained periods of no flow. Willow Creek was most susceptible to periods of low base flow transitioning to no flow (fig. 14C). The percentage change in base flow for Cobb Creek (fig. 14A) was lower compared to the percentage change in base flow for Lake Creek (fig. 14B) and Willow Creek (fig. 14C). Percentage change in base flows for total inflows into Fort Cobb Reservoir ranged from about 40 to 60 percent for the highest and lowest groundwater withdrawal simulations (fig. 14D). This was slightly more than Cobb Creek but generally less than Lake and Willow Creeks.

For observed long-term (1979–2015) base-flow changes, the slope of the relation between the percentage change in groundwater withdrawals and the percentage change in mean annual base flows was negative (fig. 15). A more negative slope in the curves depicted in figure 15 indicates that mean annual base flows declined by a greater percentage for a given percentage change in groundwater withdrawals. Slopes were generally more negative for increasing groundwater withdrawals (positive percentage change in groundwater withdrawals) than for decreasing groundwater withdrawals (negative percentage change in groundwater withdrawals). Base flows were thus more affected by simulated increases in groundwater withdrawals than they were to simulated decreases in groundwater withdrawals. Percentage changes in mean annual base flow (fig. 15) followed similar patterns to those of annual base flow (fig. 14); the percentage changes in Willow Creek base flows were highest, followed by Lake Creek base flows, then total inflows into Fort Cobb Reservoir, and lastly Cobb Creek base flows. Simulating an increase in groundwater withdrawals generally reduced base flows more in Cobb Creek than in Lake Creek or Willow Creek. Additional groundwater withdrawals near Cobb Creek would likely reduce inflows to the Fort Cobb Reservoir more appreciably compared to the reductions in inflows caused by additional groundwater withdrawals near Lake and Willow Creeks.

Scenario 3: Zonal-Scaled-Historical-Groundwater-Withdrawal Scenario

A scenario was developed to assess the effects of increased historical groundwater withdrawals within eight zones that compose the Cobb Creek watershed. Groundwater withdrawals outside the Cobb Creek watershed were assumed to negligibly affect base flows in streams within the watershed (fig. 1). Zones were created by using a k-means spatial clustering algorithm for the location of historical groundwater withdrawals (as represented as the model cell centroid; QGIS, 2022). The k-means spatial clustering algorithm facilitates the creation of a user-specified number of groups or zones of points such that the distance between each point in a group and the mean location for points assigned to the same group is smallest relative to the distance to the mean locations of points assigned to other groups (QGIS, 2022). Use of the k-means spatial clustering algorithm method made it possible to maintain relatively similar total groundwater withdrawals for each zone (fig. 16B).

The total historical groundwater withdrawals during 1979–2015 were divided among the eight zones of the Cobb Creek watershed (fig. 16). For simulating future scenarios, groundwater-withdrawal rates were scaled to 50, 80, 100, 150, and 200 percent of the historical groundwater-withdrawal rates (Ellis, 2018a) for each zone. Because Ellis (2018b) estimated that 500 gal/min was the maximum groundwater-withdrawal rate that the Rush Springs aquifer could sustain over longer periods of continuous pumping (such as monthly or annually), groundwater-withdrawal rates were set to 500 gal/min if they exceeded this value when scaled. Groundwater withdrawals for the steady-state stress period were not changed from the Ellis (2018a) groundwater-flow model to maintain identical starting conditions for each groundwater-flow simulation. Because of long simulation run times (9 hours or more), the scenario used PEST++ version 4 parameter estimations software. PEST++ version 4 was modified from PEST++ version 3 (Welter and others, 2015) and is available from the USGS Github repository at https://github.com/usgs/pestpp/releases/tag/4.3.17. PEST++ version 4 includes a utility program that can be used to evaluate sets of parameter values in parallel (PESTPP-SWP). The PESTPP-SWP utility program was used to run the 40 groundwater-flow simulations in parallel using a high-performance computing environment (Condor Team, 2012). The simulations using unscaled historical groundwater withdrawals from each of the eight zones of the Cobb Creek watershed were used for error checking and simplifying after processing because outputs were referenced to these simulations.

To observe how each zone affects total inflows to the Fort Cobb Reservoir, total inflows from each scaled-historical-baseline rate simulation were subtracted from total inflows from the historical-baseline-rate simulation and divided by total inflows from the historical-baseline-rate simulation represented as a percentage of total inflows (fig. 16). Larger percentage changes in the contribution to total inflows from a given zone indicate that increasing groundwater withdrawals in that zone resulted in a larger increase of total inflows compared to other zones. Percentage changes in total inflows for zones farther upgradient in the watershed were generally greater than for zones farther downgradient (fig. 16). Percentage changes in total inflows for zones farther upgradient in the watershed were generally greater than for zones farther downgradient (fig. 16), possibly because with sufficient pumping, groundwater withdrawals could act as a barrier to groundwater flow, restricting downgradient water flow (Heath, 1983). Simulated stream seepage in the Cobb Creek watershed was frequently farther upgradient in the watershed than closer to the Fort Cobb Reservoir (Ellis, 2018b). Greater stream seepage provides more groundwater available for capture, which is likely the reason why base flows responded more to changes in groundwater withdrawals in the upgradient parts of the watershed compared to the parts of the watershed closer to the Fort Cobb Reservoir.

To further investigate how changes in groundwater withdrawals within each zone affect total inflows, linear regression equations were used to compare mean annual groundwater withdrawals to mean annual changes in total inflows for individual wells grouped by zone (fig. 17). The slopes of the linear regression equations represent the sensitivity of base flows to changing groundwater withdrawals for each zone. Zones where the regression-equation slopes were more negative (for example, zones 1, 4, and 5, where the slopes ranged from −0.41 to −0.70) indicate that reductions in groundwater withdrawals in these zones tend to have a larger effect on total inflows compared to other zones where the slopes of the regression equations were less negative (for example, zones 2, 3, 6, 7, and 8, where the slopes ranged from −0.0025 to −0.24).

Total inflows to the Fort Cobb Reservoir were most responsive to changes in groundwater withdrawals near Cobb Creek, followed by changes in groundwater withdrawals near Lake Creek and then Willow Creek (fig. 16A). Groundwater withdrawals in zones 1 and 4 affected base flows more than withdrawals in the other zones (table 6; figs. 16–17). This is likely because zone 1 covers much of Cobb Creek farther upgradient in the watershed (where base flows were higher [Ellis, 2018b]) and zone 4 covers the area between Cobb and Lake Creeks which constitute the majority of total inflows to the Fort Cobb Reservoir (about 90 percent of total inflows, where mean annual base flow was 17.6 ft³/s and mean annual total inflows were 37.9 ft³/s; fig. 2). Base flows were next most affected by groundwater withdrawals in zone 5 (figs. 16–17). Base flows in zone 5 were not as responsive to changes in groundwater withdrawals as those in zone 4 likely because zone 5 covered an area between Cobb and Lake Creeks but was closer to Lake Creek, whereas zone 4 covered an area that overlapped both Cobb and Lake Creeks where more base flow was available for capture. Base flows in zones 3, 7, and 8 were about equally responsive to changing groundwater withdrawals (table 6; figs. 16–17), likely because these zones included areas upgradient from the start of the simulated streams for zone 7 (Lake Creek) and zone 3 (Willow Creek) or areas mostly downgradient of the inflows to the Fort Cobb Reservoir (zone 8 for Cobb and Lake Creeks). Base flows were minimally affected by groundwater withdrawals in zones 6 and 2 (figs. 16–17). Zone 6 was mostly near Willow Creek, and Willow Creek generally contributes a small percentage of inflows to the Fort Cobb Reservoir (fig. 2), which is likely why this zone was not very responsive. Zone 2 was a control zone used to verify that groundwater use downgradient of the streams would not influence base flows, indicated by the nearly flat slope of the regression equations for this zone (fig. 17).

The relations between reducing groundwater withdrawals and increasing groundwater withdrawals in the simulations were similar for the zonal-scaled-historical-groundwater-withdrawal scenario and the scaled-historical-groundwater-withdrawal scenario (table 6; figs. 15–16). When increases in groundwater withdrawals were simulated, total inflows tended to decrease by a greater amount than the equivalent increase in total inflows caused by a reduction in groundwater withdrawals (fig. 16). When fitting a linear regression equation to annual change in groundwater withdrawals and annual change in total inflows to the Fort Cobb Reservoir, the relation between increasing and decreasing groundwater withdrawals was not as strong (less negative slope) for zones farther downgradient within the Cobb Creek watershed and zones farther away from Cobb Creek (fig. 17). Years with the greatest absolute change in total inflows to the Fort Cobb Reservoir were those when the simulated groundwater withdrawals were increased (fig. 17). The simulation with the 50-percent scaling factor for historical groundwater withdrawals produced greater absolute changes in total inflows to the Fort Cobb Reservoir than the simulation using the 150-percent scaling factor for historical groundwater withdrawals (which would imply equal changes in groundwater withdrawals between both simulations). Because groundwater withdrawals were capped at 500 gal/min and because using the WEL package results in gradually decreasing groundwater-withdrawal rates when hydraulic head altitudes were also decreasing under a certain threshold for solver stability (Niswonger and others, 2011), the groundwater-withdrawal rates for the 50- and 150-percent scaling factors may not simulate equivalent changes in historical groundwater withdrawals. Smaller simulated increases in annual groundwater withdrawals (about 1,000 acre-ft per year) still resulted in declines in total inflows to the Fort Cobb Reservoir greater than any increase in base flows from reducing groundwater withdrawals (fig. 17), which likely indicates that increasing groundwater withdrawals affects total inflows to the Fort Cobb Reservoir more than reducing groundwater withdrawals.

Linear regression equations were computed to show the general responsiveness of base flows in each zone of the Cobb Creek watershed to simulated changes in groundwater withdrawals; the sum of the base flows from each zone equals the total inflows to the Fort Cobb Reservoir (table 6; fig. 17). Regression equations with larger negative slopes correspond to zones where the base flows were more affected by groundwater withdrawals compared to zones with less negatively sloped regression equations. Overall, Cobb Creek (zones 1, 4, and 8) base flows were most responsive to zonal changes in groundwater withdrawals, followed by those of Lake Creek (zones 4, 5, 7, and 8) and Willow Creek (zones 3 and 6). In general, groundwater withdrawals nearest Cobb Creek more greatly affected total inflows to the Fort Cobb Reservoir compared to groundwater withdrawals nearest Lake and Willow Creeks.

Scenario 4: Simulated Base-Flow Depletion Scenario

A base-flow-depletion scenario (Barlow and Leake, 2012) for the Rush Springs aquifer using the Ellis (2018a) groundwater-flow model was constructed by simulating additional pumping of a hypothetical well in each model cell within the Cobb Creek watershed (fig. 1). The base-flow-depletion scenario totaled 36,638 cells and thus the same number of simulations. The goal of this scenario was to assess the spatial sensitivity of groundwater withdrawals on base flows while holding parameters other than groundwater withdrawals (such as climate parameters) constant. In doing so, the effects of groundwater withdrawals can be isolated. Inflows from Cobb, Lake, and Willow Creeks to the Fort Cobb Reservoir (from the SFR package) were used as the basis for calculating base-flow depletion. A base-flow-depletion fraction equation was developed by following the steps of the “Constructing Capture Maps” section of Leake and others (2010):

where

The base-flow-depletion fraction is calculated for each cell by using the amount of groundwater withdrawn from the hypothetical well in that cell and the corresponding change in base flow at a specified point (which represents net base flow for all stream segments upstream from that point). The results of the simulations can be used to compute capture maps—a matrix with the dimensions of the groundwater-flow model grid containing a base-flow-depletion fraction for each cell for which a hypothetical well was simulated (Leake and others, 2010; Barlow and Leake, 2012). For this report, base-flow depletion was represented as a percentage, where each cell indicated how much base flow would decrease as a percentage of how much groundwater was withdrawn. If groundwater withdrawals from the hypothetical well resulted in 100 percent base-flow depletion, then all groundwater withdrawn from the hypothetical well was captured from base flow. A base-flow depletion of 0 percent indicated that groundwater withdrawn from the hypothetical well captured no base flow. Groundwater withdrawals can capture groundwater from a variety of sources, including groundwater that would have otherwise been lost to evapotranspiration, groundwater in storage, and groundwater that would have otherwise contributed to base flow (Barlow and Leake, 2012); however, this study focused on the capture associated with base flow (that is, groundwater withdrawals resulting in base-flow depletion). Several capture maps were constructed for total inflows to the Fort Cobb Reservoir (fig. 18) and for each inflow to the Fort Cobb Reservoir from Cobb, Lake, and Willow Creeks (figs. 19–20). Because the simulations for this scenario used the SFR package (which routes base flow downstream), the simulated base flows from each of the three major streams that drain into the Fort Cobb Reservoir represent the net base flow for the entire Fort Cobb Reservoir watershed as explained in the “Introduction” section of this report.

The base-flow depletion scenario was created by using the steady-state simulation from the Ellis (2018a) groundwater-flow model with the CHD package for simulating Fort Cobb Reservoir and the historical groundwater withdrawals used in that simulation. Timing of base-flow depletion cannot be determined from a steady-state simulation because a steady-state simulation lacks a time component. Therefore, base-flow depletion calculations derived from the steady-state simulation represent conditions after an equilibrium is established between the additional groundwater withdrawals, the groundwater system, and the groundwater discharges that form the base flows in streams.

PESTPP-SWP was used to run the simulations associated with the base-flow depletion scenario in parallel using a high-performance computing environment to complete the 36,638 simulations that were needed to construct the capture map. The groundwater-withdrawal rate used for the analysis was approximately 20 gal/min (3,876.45 cubic feet per day), which was the mean historical groundwater-withdrawal rate for the steady-state simulation of the Ellis (2018a) groundwater-flow model. This rate was considered a moderate, realistic groundwater-withdrawal rate that is less likely to create issues with nonlinearity ascribed to higher groundwater-withdrawal rates when calculating the base-flow-depletion fraction (Barlow and Leake, 2012). The groundwater-withdrawal rate was applied to layer 3 for each simulation. Layer 3 represented most of the Whitehorse Group (the main unit of the Rush Springs aquifer), and layer 2 represented the upper 30 ft of the Whitehorse Group and the alluvium and terrace deposits (where present) to facilitate the simulation of lateral groundwater flow between the alluvium and terrace deposits and the Rush Springs aquifer (fig. 3; Ellis, 2018b). Wells were not simulated in layer 2 (for groundwater-flow model cells representing the Whitehorse Group) to reduce the effect of structural noise associated with the base of layer 2, because the base of layer 2 was set to an arbitrary altitude for groundwater-flow model cells representing Whitehorse Group where the aquifer system is not overlain by the alluvium and terrace deposits.

Barlow and Leake (2012, p. 65) describe conditions where nonlinearity related to groundwater flow with respect to base flow may occur as

Nonlinearity was likely minimal for the approximately 20-gal/min groundwater-withdrawal rate because it was unlikely that (1) such a low groundwater-withdrawal rate would cause large changes in saturated thickness, (2) water levels would be drawn below the streambed or below the evapotranspiration extinction depth, and (3) the groundwater-withdrawal rate would be sufficient to dry the stream.

The capture maps created from the base-flow-depletion scenario were used to assess the response of base flows caused by hypothetical groundwater withdrawals (in addition to historical groundwater withdrawals for the steady-state simulation). For figure 18, the sum of base flows for Cobb, Lake, and Willow Creeks (total inflows) was used to calculate base-flow depletion. Thus, the base-flow-depletion percentages shown in figure 18 represent the responsiveness of total inflows to additional groundwater withdrawals. Figure 19A represents the base-flow depletion capture map for Cobb Creek when only Cobb Creek base flows were used to determine base-flow depletion. Figures 19B, C represent the same concept as figure 19A, except figures 19B, C use Lake Creek base flows and Willow Creek base flows, respectively, when calculating base-flow depletion. Thus, the maps in figure 19 show the responsiveness of base flows to additional groundwater withdrawals for each stream individually.

Cobb Creek base flows were more responsive to groundwater withdrawals over a broader area compared to the responsiveness of base flows in Lake and Willow Creeks to groundwater withdrawals (figs. 18, 19A–C). This is likely because the inclusion of the two main tributaries to Cobb Creek in the simulation provided more sources for base-flow capture over a broader area compared to the areas of base-flow capture for Lake and Willow Creeks. Proximity to other streams may be a contributing factor to base-flow-depletion response for a specific stream. For example, when groundwater withdrawals from wells are nearer to Lake Creek, base-flow-depletion quickly declines for Cobb and Willow Creeks (fig. 19). Although wells nearer to Lake Creek likely capture most of the base flow from Lake Creek or intercept groundwater that would otherwise flow into Lake Creek, the potential for additional base-flow capture remains high when considering ungaged locations where inflows to the Fort Cobb Reservoir from Cobb, Lake, and Willow Creeks were simulated because a given well might withdraw groundwater from the watersheds of multiple streams (figs. 18–19).

To assess how base-flow depletion varied among streams, various offset distances were constructed and the cell centroids within those offset distances were used to calculate base-flow depletion summary statistics. Offset distances were arbitrary distances created to help summarize the base-flow depletion statistics as a function of distance away from the stream. A groundwater-flow model cell was considered to be within the offset distance if its centroid was within the offset distance from the stream. The data shown on each capture map in figure 20 were used to calculate mean base-flow depletion and mean base-flow depletion scaled by mean annual base flow as a fraction of mean annual inflow (hereinafter referred to as “scaled mean base-flow depletion”) for each stream (fig. 21). The data shown on the capture maps for each individual stream were used to remove the influence of base-flow depletion for the other streams.

Groundwater wells can only capture a finite amount of water from streams. To contextualize base-flow depletion for each stream, scaled mean base-flow depletion was used to normalize the potential effects of base-flow depletion and to better represent how each stream contributes to total inflows to the Fort Cobb Reservoir. Scaling mean base-flow depletion contextualizes how each stream would contribute to total inflows. Because a small groundwater-withdrawal rate was used for each base-flow depletion simulation, only small quantities of base flow would be captured. If higher groundwater-withdrawal rates were used, streams with less base flow could become dry and no longer yield water to the aquifer, therefore producing a smaller base-flow depletion value than when simulating a smaller groundwater-withdrawal rate. Thus, scaling mean base-flow depletion for Cobb, Lake, and Willow Creeks to their proportion of total inflows contextualizes how base-flow depletion for each stream would affect total inflows. Mean base-flow depletion decreases to about 60 percent for Cobb Creek and to less than 50 percent for Lake and Willow Creeks when an offset distance ranging from more than 9,000 to 10,000 ft is applied (fig. 21). Mean base-flow depletion moderately declined from about 90 percent near the streams for offset distances of less than 1,000 ft to about 35 to 50 percent at the offset distance ranging from more 9,000 to 10,000 ft. Scaled mean base-flow depletion for Cobb Creek was the highest by about a factor of three, followed by Lake Creek (scaled mean base-flow depletion of about one-third of Cobb Creek), then Willow Creek (scaled mean base-flow depletion of about one-tenth of Cobb Creek). Groundwater withdrawals near Cobb Creek likely affect total inflows to the Fort Cobb Reservoir much more than those near Lake and Willow Creeks.

Overall, high base-flow depletion (more than 80 percent) covers a broader watershed area for Cobb Creek compared to base-flow depletion for Lake and Willow Creeks. When considering the contributions of each stream to total inflows for Fort Cobb Reservoir, additional groundwater withdrawals near Cobb Creek are more likely to reduce total inflows to the Fort Cobb Reservoir compared to additional withdrawals in areas near Lake and Willow Creeks (fig. 19). However, base-flow depletion was consistently high (more than 80 percent) for all three major streams (Cobb, Lake, and Willow Creeks) for offset distance ranging from 0 to about 2,000 ft (fig. 21). For areas downgradient from Cobb, Lake, and Willow Creeks and in the northwest corner of the Cobb Creek watershed, changes in groundwater withdrawals resulted in minimal changes to base flow (base-flow depletions were typically less than 10 percent); therefore, total inflows to the Fort Cobb Reservoir were minimally reduced compared to other areas within the Cobb Creek watershed (figs. 18–19). Results from the groundwater-flow model demonstrated that additional groundwater withdrawals closer to the Fort Cobb Reservoir were not as likely to reduce inflows to the reservoir by as much as additional groundwater withdrawals further upgradient in the Cobb Creek watershed.

Model Assumptions and Limitations

Limitations are associated with the groundwater-flow model scenarios for the Rush Springs aquifer because the groundwater-flow model approximates the complex, real-world groundwater-flow regime of the Rush Springs aquifer. Many of the limitations for the calibrated groundwater-flow model apply to the scenarios in this report. Limitations of the groundwater-flow model used for the scenarios and the limitations for the scenarios themselves are summarized herein. Refer to Ellis (2018b) for a more detailed discussion of the limitations of the groundwater-flow model.

MODFLOW-NWT simulates groundwater flow by using Darcy’s Law which assumes that groundwater is of uniform density and incompressible and that groundwater flow is laminar and occurs through porous media (Heath, 1983). Although groundwater flow in Rush Springs aquifer is governed by Darcy’s Law, groundwater flow could deviate from some of the inherent assumptions of Darcy’s Law in some locations; for example, groundwater flow may not be laminar for fractured rocks contained in the Rush Springs aquifer. Groundwater withdrawals are not metered in Oklahoma, and the groundwater withdrawals for the calibrated Rush Springs groundwater-flow model were from reported groundwater use (Ellis, 2018b). OWRB does not require permitting for domestic groundwater use, so any domestic groundwater use was unknown and not included in the calibrated Rush Springs groundwater-flow model (Ellis, 2018b). Domestic groundwater withdrawals were assumed to be a relatively minor component of total groundwater withdrawals (Ellis, 2018b).

The uncertainty associated with construction of the bases of aquifers in the study area and the spatial discretization required to represent those bases in a model can inhibit matching groundwater-flow model outputs to observations (Doherty, 2015). The Rush Springs aquifer groundwater-flow model consists of 500-ft by 500-ft cell spacing. Properties and boundary conditions for each cell are assumed to be uniform. Ellis (2018b) implemented streams and lakes into the calibrated Rush Springs groundwater-flow model that were best represented at a regional to subregional scale. Although the streams implemented in the groundwater-flow simulation likely contained most of the base flow from the Rush Springs aquifer, the quantity of base flow in smaller ordered streams that were not included in the modeling scenarios is an unknown and thus a source of some uncertainty. The LAK package was replaced with the CHD package for the Fort Cobb Reservoir for the groundwater-flow models in this study. As a result of the change to the CHD package, changes in reservoir storage and changes in stage cannot be observed and were outside the scope of this report.

Uncertainty also arises from the limited availability and quality of groundwater altitude and base-flow data used to calibrate the groundwater-flow model. Relatively few parameter and observation data were available, and the available data were not distributed uniformly temporally or spatially. Calibration targets and observations were sparse throughout certain locations of the groundwater-flow model that were typically outside of the Cobb Creek watershed (the focus of this report; Ellis, 2018b). All groundwater-flow model inputs and observations have uncertainty associated with them. The base-flow separation inputs and observations, Soil-Water-Balance climate inputs, hydraulic properties, groundwater withdrawals, groundwater altitude observations, and stream properties were all estimated and therefore subject to measurement and human error. Ellis (2018b) modified many of those parameters during calibration to better match calibration targets (observations). Many of these parameters affect base flow and can affect the results of the simulations done for this study; however, automated calibration should reduce the effect of this uncertainty because parameters in the model should be closer to their “true” values (Doherty, 2015).

Ellis (2018b) completed a sensitivity analysis for the calibrated Rush Springs groundwater-flow model by incrementing individual parameters by 1 percent and recording the response. Ellis (2018b) identified that recharge, hydraulic conductivity, and evapotranspiration were most sensitive with respect to base flows. Recharge, hydraulic conductivity, and the rates specified for the EVT package were not modified for the scenarios in this study. These values could be different from their “true” values. In such instances, base-flow responses may differ from the “true” response. Ellis (2018b) also completed an identifiability analysis for parameters modified during calibration. Doherty and Hunt (2009) provide a detailed discussion of identifiability analyses in groundwater models. Parameters affect observations to a lesser extent when the parameter identifiability is lower compared to parameters with higher identifiability. The hydraulic-conductivity parameters and the evapotranspiration extinction-depth parameter were considered less identifiable (Doherty and Hunt, 2009) compared to the other parameters used in the model, so the hydraulic-conductivity parameters and the evapotranspiration extinction-depth parameter were relatively uncertain. Hydraulic conductivity and extinction depth contribute the most to capture map bias (Nadler and others, 2018). Thus, uncertainties associated with simulated base flows may be higher than if those parameters were more certain. However, Nadler and others (2018) calculated higher capture map bias for low hydraulic conductivities. The Rush Springs aquifer model contained moderate hydraulic conductivities; about 75 percent of the Rush Springs aquifer was simulated with hydraulic conductivities greater than 3 ft per day (Ellis, 2018b).

Because the intent of the EPS scenario is to dry aquifer cells (which can no longer yield water) and not all cells become dry at the same time, the mean EPS rate (total volume pumped divided by the area of the aquifer and the number of years of the simulation) likely differs from the rate specified in the WEL package. This implies that the EPS rate is not applied uniformly over the entire aquifer. Therefore, mean EPS rates for the simulations in scenario 1 (the scaled-EPS-groundwater-withdrawal scenario) might not be equivalent to multiplying the baseline EPS rate by the specified percentage used to scale groundwater withdrawals for the simulations in scenario 1. Additionally, the mean EPS rate for scenario 1 will be different if calculated over the first 20 simulated years or over the entire simulated 50-year period as a result of the progressive reduction in groundwater availability.

For the zonal-scaled-historical-groundwater-withdrawal scenario (scenario 2), zones were created to contain approximately equal groundwater withdrawals to attempt to reduce bias. This was difficult to achieve because dissimilar groundwater withdrawals had to be discretized spatially and temporally. That is, not all groundwater withdrawals persist through time and are therefore difficult to group spatially while maintaining equal groundwater-withdrawal rates for all zones. Some zones contained more groundwater withdrawals than other zones, so some bias was still present because the relation between groundwater withdrawals and base flows is not always linear (Barlow and Leake, 2012).

The base-flow-depletion scenario (scenario 4) was completed by using mean climatic conditions. It is possible that other climatic conditions (such as droughts or flooding) would produce different base-flow-depletion fractions (particularly if no-flow conditions prevailed in the streams during drought conditions or if there was no flow in certain reaches that subsequently began flowing during flooding conditions). The base-flow-depletion scenario was done by using a steady-state simulation. When a well first begins withdrawing water, there is a time delay until the water levels in the aquifer reach equilibrium with the groundwater being withdrawn (Heath, 1983; Barlow and Leake, 2012). The timing of the changes to base flows and other groundwater-flow components cannot be determined by using the simulation because the steady-state simulation assumes no time component. Because the Rush Springs simulation was designed for a subregional to regional scale, base-flow depletion may not be appropriate when assessing the effects on base flows by groundwater withdrawals from individual wells. Depletion fraction calculations rely on the principle of superposition and, thus, assume that groundwater flow is linear within a groundwater system (Barlow and Leake, 2012). Somewhat nonlinear groundwater systems can still be approximated by using superposition (Reilly and others, 1987). Groundwater flow from the base-flow-depletion scenario was assumed to be linear or only somewhat nonlinear because a small groundwater-withdrawal rate was used (about 20 gal/min). Nonlinearity (for a base-flow depletion simulation) is, in large part, a result of changes in transmissivity caused by a declining water table (Barlow and Leake, 2012; Nadler and others, 2018); a small groundwater-withdrawal rate would not likely produce a large decline in the water table.