6.0 Analysis of Applicant's Ground Water Model Predictions

Information concerning the predictions made by the Applicant with its mathematical models of the South Park ground water system was assembled from a variety of produced materials, and analyzed. The results of such analysis are presented in the following topic categories as graphical images created by Principia and accompanied by brief descriptions. Figures 6-1 depicts the initial potentiometric heads employed by the model for NOCUP conditions within each of the five model layers, and the corresponding flow velocity vectors. The values of potentiometric head are displayed using a background color as well as with contour lines. The flow vectors indicate the local direction and velocity of ground water flow.

The identical variables based upon the model predictions at the end of water year 21, measured from the starting year of model simulation runs, are presented in Figures 6-2. Likewise, Figures 6-3, 6-4 and 6-5 depicts predicted conditions at the end of model years 47, 68, and 94, all measured from the starting year of model simulations. It should be noted that year 21 in the NOCUP1B run sequence corresponds to year 68 in the overall NOCUP sequence. The Applicant has indicated that impacts for this year are considered significant in magnitude.

The NOCUP1A and SPCUP1H model runs are started with very similar conditions. Using an identical format to the sequence of figures above, Figures 6-6 through 6-9 depict potentiometric heads predicted by the model for SPCUP conditions for model years 21, 47, 68 and 94, respectively. Flow velocity vectors based upon prescribed distributions of potentiometric head and hydraulic conductivity are also superimposed upon each figure.

Figures 6-10 through 6-18 display the vertical flows between model layers for the same set of conditions as Figures 6-1 through 6-9. Figures 6-10 depicts vertical flows for the NOCUP initial conditions, and corresponds to the horizontal flows depicted in Figure 6-1. The colors employed in Figure 6-10 represent variations in the rate of vertical flow between the model layers. Upward flows from a lower model layer to the layer above it are represented by the green-yellow-orange-red-black color sequence. Downward flows are represented by the blue-magenta-purple color sequence. The flow rate is indicated in inches per year for ready comparison with recharge rates which have been depicted in the same units.

Figures 6-11, 6-12, 6-13 and 6-14 depict the vertical flows for model years 21, 47, 68 and 84 of the NOCUP simulation, respectively. The corresponding horizontal flows have been presented previously as Figures 6-2, 6-3, 6-4 and 6-5. Likewise, Figures 6-15, 6-16, 6-17 and 6-18 depict predicted vertical flows for model years 21, 47, 68 and 84 of the SPCUP simulation, respectively. The corresponding horizontal flows have been presented previously as Figures 6-6, 6-7, 6-8 and 6-9.

The predicted flow pattern throughout the model domain can be readily discerned by examining the image sequence from Figures 6-1 through 6-18. A number of ground water recharge source areas can be identified. In model layer 1, ground water flow is generally directed from the north-west to the south-east. Sub-surface flows enter layer 1 through the general head boundaries along the northern edges of layer 1 as indicated in Figure 4-11a. Such flows also enter layer 1 through recharge and leakage from streams. Since the bottom of layer 1 is prescribed as impermeable to flow except where it overlies layer 2, ground water along the north-western section of model layer 1 is forced to flow either to the south-east or be discharged through evaporation or surface streams. The "a" components of Figures 6-10 through 6-18, i.e. for example such as Figure 6-10a, depict the flow as predicted to occur between model layers 1 and 2. Blue-magenta-purple colors indicate where this flow is directed downward from model layer 1 into layer 2 beneath it. Areas within the domain of model layer 1, indicated with a white background, are zones where layer 2 has been prescribed as inactive and hence model layer 1 has been assigned an impermeable bottom in these zones. Comparisons between the prescribed initial vertical flows depicted in Figure 6-10a with the terminal flows predicted under NOCUP conditions as depicted in Figure 6-14a and with predicted terminal SPCUP flows as depicted in Figure 6-18a indicates that vertical flows predicted by the Applicant's model are generally directed more from layer 1 to layer 2, in both area and magnitude, than the other way around.

Flows predicted in model layer 2 have many local exceptions to the generally north-west to east predicted flow pattern. Horizontal sub-surface flows to or from layer 2 can only occur through the general head boundaries prescribed along the eastern edges of model layer 2 as indicated in Figure 4-11b. Ground water also enters layer 2 vertically through recharge and leakage from streams. A number of recharge source areas prescribed with high water levels and closed water level contours can be readily identified in the "b" components of Figures 6-1 through 6-9. Specifically the area of Michigan Hills to the northwest, another area to the north-east and a complex near the center of the model domain indicate elevated levels of predicted ground water in model layer 2. Ground water flow is usually directed radially outwards from these recharge source areas as predicted by the Applicant's model. In the Michigan Hills area, such flows are directed south-easterly as a consequence of the chosen model geometry.

Model layers 3, 4 and 5 have not been assigned any general head boundary cells. Thus, sub-surface flows within these layers, by prescription, can only occur by vertical exchanges with other model layers. As described above, model layers 1 and 2 have been assigned some sub-surface connections with surrounding materials. The total rate of inflows through general head boundaries into model layers 1 and 2 in the Applicant's model, averages about 1,475 acre-feet per year, while the outflow averages about 455 acre-feet per year. These average flow rates differ by approximately an acre-foot between NOCUP and SPCUP simulations. For comparison purposes, the average recharge prescribed within the model domain is 8,204 acre-feet per year. Through the choices embedded in it, the Applicant's model therefore represents the ground water system as essentially a closed basin.

In the north half of model layer 3, predicted ground water flow is generally directed west to east. Such flow is generally directed downwards on the west side of the domain from model layer 2 to layer 3, and upward from layer 3 to layer 2 on the east side of the domain. The predicted sub-surface flow in the southern half of layer 3 appears dominated by several convergence zones. In these zones, predicted flows are upward into model layer 2, while around these zones, predicted flows are directed downward from model layer 2.

The pattern of sub-surface flows predicted by the model in layers 4 and 5 are similar to that of model layer 3. The northern half of the domain in these layers is predicted to have predominantly west to east flows, resulting from predicted downward flow on the west and predicted upward flow to the east. In the southern half of the domain, the convergence zones predominate, where there is upward flow, with downward flow in the surrounding areas.

As part of the Applicant's SPCUP model simulation runs, withdrawals of ground water through pumping are represented as occurring from model layers 4 and 5. In the vicinity of this prescribed well pumping, such withdrawals causes the predicted NOCUP flows to be altered into a converging pattern around these pumping centers. This causes significant vertical flows, both up and down, near the pumping centers.

Results predicted by the Applicant's model of the South Park ground water system were further analyzed. As part of such analysis, the predicted depths to water table based upon the top-most active model layer and the ground surface elevations used for ET representations are presented in Figures 6-19. Figure 6-19a depicts the initial depth to water distribution as employed for the NOCUP conditions. The sequence from Figures 6-19b through 6-19e presents the predicted results, as depths to water, for NOCUP conditions at the end of water years 21, 47, 68 and 94 respectively. Likewise, the sequence from Figures 6-19f through 6-19i presents predicted results expressed in the same manner for SPCUP conditions at the end of water years 21, 47, 68 and 94 respectively. The predicted depths to water table based upon the same model predictions but using the ET layer array instead of the top-most active model layer are presented as a next group of figures. Figure 6-20a depicts this initial depth to water distribution as employed for the NOCUP conditions. The sequence from Figures 6-20b through 6-20e presents the predicted results, as depths to water, for NOCUP conditions at the end of water years 21, 47, 68 and 94 respectively. Likewise, the sequence from Figures 6-20f through 6-20i presents predicted results expressed in the same manner for SPCUP conditions at the end of water years 21, 47, 68 and 94 respectively.

In Figures 6-19 and 6-20, the spatial distribution of depth to water predicted by the model is depicted using a fill color. The blue-purple color sequence represents a negative depth to water, i.e. a predicted water level that lies above the local ground surface as defined in the Applicant's own ET package. If the results predicted by the model were proper and accurate, these locations would constitute either wetland areas or lakes and ponds fed by ground water. The green color in the figures displays areas where the predicted depth to water lies between zero to six feet. Six feet of course was the extinction depth using the linear function prescribed by the Applicant for ET. Evapotranspiration is therefore predicted by the model to occur within these areas. Of course, evapotranspiration will also occur at the maximum specified rate in the blue-purple areas where the water level is above the ground surface.

Using results predicted by the Applicant's model in the same runs as described previously, the confining pressure represented as acting upon model layer 2, was analyzed. This confining pressure is defined here for purposes of discussions as the difference between the elevation of potentiometric heads in model layer 2 and the prescribed elevation of the top surface of this layer when it is positive, both of course as spatial distributions. The results of this analysis are presented in Figures 6-21. Figure 6-21a depicts the initial confining pressure utilized to represent NOCUP conditions. The sequence from Figures 6-21b through 6-21e depicts the predicted confining pressure under the same NOCUP conditions for model years 21, 47, 68 and 94, respectively. Figure 6-21f depicts the initial confining pressure utilized to represent SPCUP conditions and the remaining sequence from Figures 6-21g through 6-21j depicts the predicted confining pressure under the same SPCUP conditions for model years 21, 47, 68 and 94, respectively. The percentage of time during which model layer 2 is in fact predicted to be under confining pressure is presented in Figure 6-21k for NOCUP conditions and in Figure 6-21l for SPCUP conditions.

Examination of Figures 6-21 indicates that on the east side of the model domain, layer 2 was prescribed as predominantly unconfined. A notable exception in this prescription was along the stream channels wherever model layer 1 overlies layer 2. Wherever the unconfined layer 1 is active, specific yield should actually be used in layer 1 to calculate its ground water storativity changes, while storage coefficient should be used in the confined layer 2 to calculate its storativity changes. In all areas of the model domain where layer 2 is the topmost layer and the potentiometric head in layer 2 is either prescribed or calculated to lie below the elevation of the top of layer 2, as is the case in most of the eastern side of the domain, specific yield should be used to calculate storativity changes. However, comparisons between the specific yield prescribed by the Applicant for model layer 2 as depicted in Figure 4-7b and the storage coefficient prescribed in model layer 2 as depicted in Figure 4-8b, indicate that the specific yield and storage coefficient values have been interchanged. The values for storage coefficient prescribed by the Applicant on the east side of the model domain are typical specific yield values, while the specific yield values are typical storage coefficient values. When such an interchange is prescribed, the specific yield values will be applied whenever model layer 2 remains confined, whereas the storage coefficient values will be applied whenever layer 2 becomes unconfined. The consequence of such an interchange is the use of extraordinarily low storage coefficient values in unconfined areas, and the use of extraordinary values in confined areas, thereby mis-representing the actual behavior of the aquifer system. In fact, in areas where layer 1 overlies layer 2, the interchange will actually result in the model accounting doubly for ground water storage.

In further analysis of predictions made by the Applicant's model, Figure 6-22a illustrates predicted potentiometric head values within model layers 1 through 4 at ten chosen model grid cell locations. For clarity, Figures 6-22b through 6-22k present the individual hydrographs at each of these grid cell locations. It will be observed that each of these figures includes the predicted potentiometric heads for all four layers and under both NOCUP and SPCUP conditions. Additional insight into the ground water flow patterns predicted the Applicant's model, both as they vary with time and between the NOCUP and SPCUP series of model runs, can be gained from Figures 6-22. At model grid cell (54,30), the predicted flow in model layers 1 to 4 under NOCUP conditions varies within a year but maintains an upward gradient from model layer 4 to layer 1. However, under SPCUP conditions, the predicted results for the same grid cell show a gradient reversal during most of the simulation time period. Significant impacts simulated by the model as caused by the SPCUP pumping can be observed at a number of other locations. Hydrographs such as that presented for model grid cells (88,23), (74,24) and (72,19), among others, suggest that impacts beyond the 94 years of simulation are likely to be even greater.

Predicted ground water flows interacting with the domain boundaries of the Applicant's model were also analyzed. These flows represent interactions of this domain with portions of the South Park ground water system lying outside it, through the assignment of general-head boundary conditions. These flows include both inflows, i.e. recharges treated as positive, and outflows, i.e. discharges treated as negative. The results of such analysis are presented in Figures 6-23a and 6-23b respectively. The differences between the NOCUP and SPCUP simulations are imperceptible at this scale. It is noteworthy that the vertical axes of the graphs presented in Figures 6-23 does not extend to zero, and hence the variations in predicted general head flows throughout the simulation period are actually quite small.

Predictions of stream flows obtained by the Applicant through the ground water model were analyzed. The status of these simulated streams as predicted by this model is depicted in the Figures 6-24. These figures indicate the percentage of time during the simulation period when the steam is prescribed to operate under the specified condition. The first figure of this group presents the status as a percent of time during the simulation time period, under NOCUP conditions, in which streams are predicted to be gaining, that is predicted flow is from the aquifer to the stream. The second figure of the group presents the status as a percent of time during the simulation time period, under SPCUP conditions, in which streams are predicted to be gaining. The third and fourth figures present the status as a percent of time, respectively under NOCUP and SPCUP conditions, in which streams are predicted as having broken their connection with the aquifer. The connection with the aquifer is said to be broken when the water level in the aquifer has declined to the point that additional declines will not increase the leakage from the stream. In the MODFLOW computer program, this condition occurs when the aquifer water level declines below the specified stream bottom elevation shown in Figure 4-25c. For those stream cells where the connection is predicted to be broken in the NOCUP simulation, no impacts in the form of stream depletions can be occur in the model.

Figures 6-25 presents the flows predicted by the model in a number of stream segments exactly as defined by the Applicant. The stream segments are identified by name. In the case of streams such as Tarryall, the names Tarryall 1 through Tarryall 6 refers to different segments of the stream, numerically numbered from upstream to downstream. In the ground water model, the North Branch Collection System is called the Aurora Ditch. Where the stream is connected to the ground water model Layer 1, the stream cells are shown filled in green. Where the stream is connected to the ground water model Layer 2, the stream cells are shown filled in blue. The reach number within each segment appears as a number in the cell. Each figure shows two hydrographs, one representing the NOCUP and the other the SPCUP simulations. The blue line in the hydrograph represents inflow into top of the segment, while a green line represents flow out of the bottom of the segment. A red line represents leakage from the segment into the aquifer. Negative leakage values indicate a gaining stream.

The dominant headwater flows for the Tarryall Creek system, as represented in the ground water model, are presented in Figures 6-25. Figure 6-25a depicts the Aurora Ditch, Figure 6-25b the Tarryall 1 stream segment and 6-25q the Park Gulch 1 segment. Flow down Tarryall Creek proceeds from the flow specified at the edge of the model domain, i.e. Tarryall 1, after its confluence with Packer Gulch, i.e. Tarryall 5, at almost the same flow rate. The constant flow rate assigned at the top of Segment 16 then becomes a flow rate that varies by about 2 cfs during SPCUP simulations and about 1 cfs during NOCUP simulations at the confluence of Tarryall Creek and Park Gulch. The circumstance is illustrated in Figure 6-25i. The stream flow in Park Gulch at this point is depicted in Figure 6-25y. Figure 6-25z depicts the flow rate in Tarryall Creek beyond its confluence with Park Gulch. As a result of mis-routing stream flow from Tarryall Creek 5 in the NOCUP simulation, flow rate in the SPCUP simulation is predicted as being significantly greater than flow rate in the NOCUP simulation.

Figure 6-25f depicts the flow rate in Segment 83, which represents the Link Ditch. This ditch is prescribed to divert water from Tarryall Creek 3 which is predicted to carry in excess of 12 cfs of flow rate during both NOCUP and SPCUP simulations. However, the diverted amount has been assigned as precisely zero in the Applicant's model. Therefore, the model ends up by predicting no impacts upon this ditch caused by the Applicant's proposed project.

The evapotranspiration (ET) rates, describing vegetative consumptive use, as predicted by the Applicant's model of the South Park ground water system were analyzed. The status of ET as predicted by this model is presented in the two groups of four figures each as represented by Figures 6-26 and 6-27. Using the ET indicator array for reference, Figure 6-26a identifies the percent of time during the model simulation time period, under NOCUP conditions, when model grid cells are predicted to discharge ground water as a result of ET. This figure therefore shows how often ET occurs in the various model grid cells at any rate greater than zero. Figure 6-26b identifies the similar status for SPCUP conditions. Figure 6-26c identifies the percent of time during the model simulation time period, also under NOCUP conditions, when the maximum ET is predicted to occur in model grid cells. The maximum ET rate occurs when the predicted water level is at or above the specified local ground surface elevation. Thus, this figure also indicates the percent of time that the water level is at or above the ground surface. Figure 6-26d identifies the similar status for SPCUP conditions. Using the top active model layer for reference in calculating the depth to water instead of the ET indicator array, an identical group of four figures is presented as Figures 6-27. They depict differences from the previous set of four in predicted ET status.

The rates of evapotranspiration from ground water predicted by the model, under both NOCUP and SPCUP conditions, were analyzed. The results of such analysis are illustrated as a series of graphical images representing predicted ET rates at the end of June during selected years within the model simulation time period. These ET rates are a function of the maximum ET rate and extinction depth specified to the model, and the depth to water calculated by the model based on a specified ground surface and the ET layer array. Figures 6-28a through 6-28e depicts the distribution of predicted ET rates, under NOCUP conditions, for water years 1, 21, 47, 68 and 94 respectively. Using the identical format, Figures 6-28f through 6-28j depicts the distribution of predicted ET rates, under SPCUP conditions, also for water years 1, 21, 47, 68 and 94 respectively. The ET rate is represented as a color fills. The gray area represents areas where no ET occurs. White cells inside the model domain indicate cells where the layer indicated by the ET layer array is inactive.

Figure 6-29a depicts the ground water ET rates predicted by the model at eight chosen model grid cell locations, during the time period from start to 94 years of the model simulations. Figures 6-29b through 6-29i present the hydrographs representing predicted ET rates at the eight individual grid cell locations. In all these figures, results for both NOCUP and SPCUP conditions are included. It is noteworthy that the ET rate varies considerably from location to location. This is a result of both the depth to water predicted by the model and the maximum ET rate specified. It is also noteworthy that the maximum ET rate includes factors such as the percent cover in the cell as shown in Figure 4-32a.

The flows in springs as represented in the Applicant's model of the South Park ground water system were analyzed. The results of this analysis are presented as a group of images grouped under Figures 6-30. Figure 6-30a depicts the spring flows predicted by the model, through its so-called drain package, at eight chosen model grid cell locations during the time period from start to 94 years of the model simulations. Figures 6-30b through 6-30i present the eight hydrographs representing predicted spring flow rates at the eight individual grid cell locations. In all these figures, results for both NOCUP and SPCUP conditions are included. Flow under NOCUP conditions are displayed as a blue line, while a red line shows the flow under SPCUP conditions. All these drain cells are located in model Layer 2. It is noteworthy that drain flows are adversely impacted in all the locations shown, except for the model grid cell (124,43) where there is a approximately 50% increase in drain flows during model year 92.

The volumetric budget is a term employed in the computer program MODFLOW to denote the accounting for all ground water recharge and discharge rates, predicted by the model at defined intervals of time or over the entire model simulation time period. The volumetric budget for runs made with the Applicant's model of the South Park ground water system was analyzed. The results of this analysis are presented in Figures 6-31. Figures 6-31a and 6-31b present the components of the budget, in monthly intervals, respectively for the NOCUP and SPCUP conditions. Figures 6-31c and 6-31d present the components, in annual intervals, respectively for the NOCUP and SPCUP conditions.

Last but not least, the differences between NOCUP and SPCUP conditions in predictions made with the Applicant's model of the South Park ground water system, were analyzed. These results of such analysis are presented as a group of graphical images from Figure 6-32 through 6-37, described as follows. Figures 6-32 depicts the differences in potentiometric head distributions predicted by the model for each of the model layers from 1 through 5, at the end of the water year 21, measured from the start of model simulations. Likewise, Figures 6-33, 6-34 and 6-35 depict the differences in potentiometric head distributions predicted by the model at the end of the model year 47, 68 and 94, respectively. Figure 6-36 depict the maximum differences over the entire simulation period between the predicted potentiometric head distributions for the NOCUP and SPCUP conditions for each of the model layers 1 through 5.

The difference in the water table at various times are depicted in Figure 6-37. The water table is calculated as the top-most active layer in the model at that instant in time. After calculating the cell by cell water table for elevation for both the NOCUP and SPCUP simulation, the difference is taken. Figures 6-37a through 6-37d depict these differences at the end of model year 21, 47, 68 and 94, respectively. Figure 6-37e depicts the maximum value that the water table difference attains at any instant in time. It should be mentioned that the maximum differences at all locations are not necessarily attained at the same instant of time.


Index | Introduction | Information Reviewed | Spatial Data | Framework | Framework Supplement | Calibration | Calibration Supplement | Predictions | Predictions Supplement | Surface Water | Findings | Findings Supplement | Glossary | Figures
Created 10-Mar-2000 by webmaster@prinmath.com
Copyright © 2000, Principia Mathematica, Inc. - All Rights Reserved