Information concerning attempts by the Applicant to calibrate the mathematical model of the South Park ground water system was assembled from produced materials, and analyzed by Principia. This information includes the sets of data concerning both the so-called quasi-steady-state (QSS) and the transient calibrations of the model. The results of such analysis are presented below as graphical images grouped together in topic categories for convenience.
The Applicant's attempts at model calibrations involved two model runs. The first was called QSS16, and comprises both the Quasi-Steady State calibration and the Transient-1 (1960-1979) calibration in a single run. The second run was called SPTR96G and covers the period 1980 to 1996. The QSS model run was actually a 480-year transient run provided with information broken down into 28 stress periods. Of these, stress period 1 covers one day and stress period 28 covers 120 years, in progressively increased interval sizes. The last QSS stress period leads directly into the Transient 1 calibration time period. According to deposition testimony provided by Dr. Harvey Eastman, the two stress periods, 29 and 30, cover the decades from 1960 to 1969 and from 1970 to 1979, respectively. Stress period 29 is 3,650 days long and is traversed in 80 individual time steps. The first of these time steps covers 18.8 days and the last time step covers 90.0 days. Stress period 30 is 3,660 days long and is traversed in 160 time steps. The first of these time steps is 3.2 days long and the last time step is 74.9 days long. The SPTR96G model calibration run covers the time period 1980 to 1996 divided into 17 stress periods. Each of these stress periods is 365.25 days long and is traversed in 80 time steps. The first of these time steps is approximately 15.9 hours long and the last time step is approximately 14.7 days long.
In the groups of figures that follow, the quasi-steady-state portion of the QSS16 run will hereafter be referred to as QSS, while the transient portion from 1960 to 1979 will be referred to as Tr60-79. The transient calibration run from 1980 to 1996 will be referred to as Tr80-96. The group of figures show the aquifer parameters used during the simulations used to calibrate the model. In these figures, differences between the prescribed calibration set and the corresponding prediction set for the same South Park ground water conditions have been noted.
Figures 5-1 depict the model domain and numerical grid cell system as used in the model calibration process. Differences between the model domain as represented in the QSS, Tr60-79 and NOCUP simulations are indicated using different colors to identify appropriate grid cells.
Figures 5-2 shows the model layer top assignment in the model. The top of Layer 1 is taken to be the ground surface as specified in the ET package. Figures 5-2 also highlight differences in the assigned layer tops between the QSS, Tr80-96 and NOCUP runs. It is noteworthy that these differences actually occur in each of the five model layers. Likewise, Figures 5-3 present the bottom elevation distributions for model layers 2 through 5. In these layers the assignment of the bottom elevation distributions differ between the various model runs.
Figures 5-4 represents the specific yield values prescribed by the Applicant for model layers 1 and 2 and used in the transient calibration runs. Hatching is used in this figure to indicate grid cell locations where the specific yield values differ from the values used in the NOCUP simulation. Figures 5-5 represents the storage coefficient values prescribed for model layers 2 and 4 and used in the transient calibration runs. Hatching is also adopted in this figure to indicate where the storage coefficient values differ from the values used in the NOCUP simulation.
Figure 5-6 depicts the hydraulic conductivity values prescribed for layer 1 used in the QSS and transient calibration runs. Again, hatching is used to depict different values prescribed by the Applicant for the various model runs undertaken. Figure 5-7 depicts the prescribed vertical conductance values between model layers 1 and 2 and used in both the QSS and transient calibration runs. Once again hatching is used to depict different values used between the various runs.
A group of figures which follow presents analysis of information on rates of well pumping assigned by the Applicant for purposes of model calibrations. Figure 5-8 depicts the variations with time of total pumping rates so assigned. No well pumping was prescribed for the QSS calibration run. Figures 5-9 illustrate the pumping rates assigned to wells simulated within designated model grid cells for each of the five model layers during the decade from 1960 through 1969. Similarly, Figures 5-10 illustrate the pumping rates during the decade from 1970 through 1979. Figures 5-11 and 5-12 illustrate the assigned well pumping rates during the years 1980 and 1996, respectively. As can be seen in these figures, well pumping has been assigned to all five layers in the model. Figure 5-8 depicts the monotonic increase in the assigned well pumping rate over time.
Figures 5-13 depict the ground water recharge rates prescribed by the Applicant for purposes of model calibrations. Figure 5-13a illustrates the recharge rates so prescribed spatially for the QSS and for transient calibrations during the time span from 1960 through 1969. The recharge rates prescribed spatially for the subsequent decade from 1970 through 1979 are illustrated in Figure 5-13b. A sequence of seventeen figures which follow, from Figure 5-13c through 5-13s illustrate the recharge rates prescribed spatially for each year from 1980 through 1996 and used for purposes of model calibrations. The total recharge by year from pre-1960 to 1996 is shown in Figure 5-13t. It is noteworthy that 1981 and 1984 represent extremes in the assigned recharge rates.
Figure 5-14 depicts the representation of streams by the Applicant for purposes of calibrating the ground water model. The legend to this figure illustrates the designation of stream segment and its interactions with the aquifer. Details of stream routing adopted by the Applicant for calibrations of the ground water model are presented in Figure 5-15.
In a manner similar to ground water recharge Figures 5-16 have been prepared by Principia to illustrate analysis of the rates of ground water ET prescribed by the Applicant for purposes of model calibrations. Figure 5-16a depicts the ET rates prescribed spatially for the QSS calibration as well as for transient calibrations to both decades from 1960 through 1969 and from 1970 through 1979. A following group from 5-16b through 5-16r illustrates the ground water ET rates prescribed spatially for each year from 1980 through 1996. Figures 5-17 identifies the spatial distribution of the model ET layer from which vegetative consumption is prescribed to occur. Hatching is used in this figure to identify locations where ET is prescribed to occur in the different layers and for the various model runs undertaken.
Results predicted by the model as a consequence of the Applicant's calibration attempts were also analyzed. These results were evaluated both as potentiometric head distributions and as corresponding distributions of ground water flow vectors superimposed upon them. Five figure groups represent the heads and flow vectors at various times during the calibration period. Figures 5-18 depict the predicted results under QSS calibrations. Figures 5-19 and 5-20 represent conditions at the end of each decade of the initial transient calibration, showing results for 1969 and 1979. Figures 5-21 and 5-22 show two results from the 1980 to 1996 transient calibration. Figure 5-21 depicts the results at the end of water year 1989 and Figure 5-22 depicts the results at the end of water year 1996. In addition, the vertical flow distributions between adjacent model layers, also predicted by the model as a consequence of model calibrations were also analyzed. Figures 5-23 through 5-27 depict the predicted inter-layer vertical flows, for the QSS, 1969, 1979, 1989 and 1996 conditions respectively.
The depth to the water table below the ground surface predicted by the model as a consequence of the Applicant's calibration attempts were also analyzed. These results were evaluated in two ways: first by using the predicted head in the top-most active layer in the model; and second, by using the array identified by the Applicant as denoting the ET layer. Figures 5-28 depict the depth to water evaluated by the former method and Figures 5-29 depict the depth to water evaluated by the latter method. Each of these figures presents the spatial distribution of depth to water as predicted by the model at various times during its calibration. In particular, results are shown for QSS conditions and progress through the years 1969, 1979, 1989 and 1996 respectively. Differences may be observed between the two groups of images for the identical conditions depicted in corresponding figures.
The confining pressure exerted upon model layer 2 in the model calibration results was also analyzed. This pressure is defined as the difference between the potentiometric head elevation within model layer 2 and the elevation of this layer's top surface. At issue here is the model's use of the storage coefficient or specific yield values. When the confining pressure is positive, the predicted head is above the top of the model layer and the model uses the storage coefficient to compute changes in aquifer storage. When confining pressure is negative, the predicted head is below the top of the model layer and the model uses the specific yield value to compute changes in aquifer storage. Results extracted from the model calibrations are presented as Figures 5-30.
In order to evaluate the status of calibration of the model, Figure 5-31 shows calibration hydrographs for 650 calibration targets prepared by the Applicant. Each image in this sequence shows model prediction hydrographs covering the time period from 1960 through 1996 at ten locations. The measurement value is shown as a symbol when the actual date of the measurement was provided. For those values for which a date was not provided, the measurement level is shown as a dashed line. In addition to the measurement value and hydrograph, the ground surface associated with the measurement, the elevation of the bottom of the well, and the ET ground surface is also shown if it fits within the scale of the plot. The depth to water shown on the hydrograph is calculated from the ground surface supplied with the measurement. The hydrograph elevation is computed by interpolating horizontally between adjacent grid cell center predicted head values to the actual location shown for the measurement. The model layer designated in the Applicant's data is used in the interpolation.
The Applicant has selected a subset of available measurement locations as calibration targets. The Applicant has also added a number of calibration targets of unknown origin to the target set and, further, computed the difference between these calibration targets and values predicted by the model during calibration runs. These differences are usually referred to as calibration residuals. The goal of calibration attempts by the Applicant was to achieve zero residuals.
Figures 5-32 through 5-50 depict spatial displays of the calibration residual at discrete time instants. Figure 5-32 shows the calibration residuals by layer for the QSS calibration. It is noteworthy that the actual residuals are calculated only at point locations designated by black symbols. In order to display these residuals, the point values were spatially interpolated by Principia using the regular kriging technique. The values of the residuals are displayed using color fills. In areas where there are no calibration point close by, the residual is a spatial interpretation of the trends in the residuals.
Figures 5-33 shows the residuals at the end of the 1960 to 1979 transient calibration by model layer. Figures 5-34 through 5-50 shows the residuals at the end of each year of the 1980 to 1996 transient calibration by layer. When a layer is not shown it indicates that no calibration points for that layer were apparently selected by the Applicant for that year.
The calibration residuals are summarized in Figure 5-51 for each of the times shown in the group of figures from Figures 5-32 through 5-50. The horizontal axis denotes the observed potentiometric head value, and the vertical axis denoted the value of the residual at each location. In this figure, calibration points for each layer are identified by a distinct color and shape. The scale of all figures in the Figures 5-51 group are identical. A perfect model calibration would be represented by a status wherein all residuals are identically zero. This status is designated by the bold horizontal line. Solid lines at 5 and 10 feet above and below the zero line are also indicated in this figure, as well as dotted horizontal lines placed at 50-foot intervals.
Last but not least, the volumetric budget for the model calibration time period is shown in Figure 5-52. The budget for the QSS period and from 1960 through 1969 is very similar, differing only as a result of a small magnitude of prescribed well pumping. From 1970 through 1979, the prescribed well pumping increases, while stream gains and recharge rates decrease. During the 1980 to 1996 period, recharge rates as well as stream gains and losses indicate the most significant changes, and on average decline from the prescribed QSS values.
A careful examination of the modelling framework, including the model layer domains, layer geometry, the adjusted property values assigned to grid cells in all five layers, etc., adopted as a consequence of the Applicant's attempts to calibrate the model, has been undertaken by Principia. This framework, so essential to any model's reliability, has been compared with that employed by the Applicant in the model used to make the NOCUP and SPCUP series of predictive runs. Such a comparison indicates that significant modifications to the model's framework were implemented apparently after the model calibration runs were accomplished. The resulting differences are presented here as Table 1.