The Corpus Christi Bay estuary system is currently being studied under the Corpus Christi Bay National Estuary Program (CCBNEP). As part of the program a research project entitled Estimation of Total Constituent Loadings to the Corpus Christi Bay System is being conducted at The University of Texas at Austin. Besides estimating total constituent loadings to the bay system, the project includes the calculation of a constituent mass balance in the bay system. For that calculation water, quality modeling parameters like dispersion coefficients and segment volumes are needed. The estimation of those parameters is documented here.
The constituent mass balance of the system is calculated using BALANCE, a map based surface water quality model. The model is written in ArcView's Avenue programming language and runs inside the GIS environment. The parameter estimation is done with ArcView as well. The procedure for establishing each parameter is described in detail below. The programs used for calculations and the final data can be downloaded as well.
This study presents a first estimate at the parameters and it is likely that as the project continues some parameters will be changed.
The Bay System has been segmented by Ward and Armstrong for the purpose of cataloging water, sediment and tissue quality as shown in Figure 1 (Ward and Armstrong, 1996). The segmentation consists of 160 segments.
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Figure 1. Segmentation Developed by Ward and Armstrong (1996).
The segmentation developed by Ward and Armstrong extends onto the land surface in many areas. Those parts of the segmentation located on the land surface were clipped off with the outline of the bay. The ARC/INFO CLIP command was used with the EPA's River Reach File 1 (RF1). Figure 2 shows the resulting segmentation. Note that this eliminated some segments completely. A total of 14 segments were eliminated. The two most upstream segments of Oso Bay, for example, have been eliminated. Oso Bay drains into the southern part of Corpus Christi Bay (see the 'Middle' figure).
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Figure 2. Ward and Armstrong Segmentation Clipped with RF1.
The segmentation shown in Figure 2 was considered for the model. However, a water quality model at this level of detail was determined to be beyond the scope of the project. The main reasons for not using this segmentation were:
A coarser segmentation was therefore constructed. After consultation with Dr. Ward, the segment boundaries were chosen to coincide with those of the more detailed segmentation. An additional segment called Upper Laguna Madre South (ulms) was added to the bottom of the segmentation, because that part of the system receives direct runoff from the CCBNEP study area. The shoreline was smoothed out using ARC/INFO's ArcEdit module. The segmentation used in this study is shown in Figure 3. Table 1 lists how the segmentation relates to the one developed by Ward and Armstrong.
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Figure 3. Model Segmentation used in the BALANCE Model.
----------------------------------------------------------------------- |BALANCE | | | |Segments |ID |Ward and Armstrong Segments | ----------------------------------------------------------------------- |St. Charles | stc | SC1, SC2, SC3 | | | | | |Copano | cop | M1, M2, AR1, PB1, PB2, CP01, CP02, CP03, | | | | CP04, CP05, CP06, CP07, CP08, CP09, CP10 | | | | | |Aransas North | aran | I1, I2, I3, AYB, MB1, MB2, CB, CBY1, CBY2| | | | | |Aransas Middle | aram | A1, A2, A3, A4, A5, I4, I5, A8, A9, A10, | | | | LB | | | | | |Aransas South | aras | A6, A11, A12, A13, I6, I7, I8, LAC | | | | | |Redfish | red | RB1, RB2, RB3, RB4, RB5, RB6, RB7, RB8, | | | | RB9, CBH, HI1, HI2 | | | | | |Inlet | inl | INL | | | | | |Nueces West | nuew | ND1, ND2, ND3, ND4, NB1 | | | | | |Nueces Middle | nuem | NR1, NR2, NR3, NR4, NR5, NB2, NB3, NB4 | | | | | |Nueces East | nuee | NB5, NB6, NB7, NB8, NB9 | | | | | |Inner Harbor | inh | IH1, IH2, IH3, IH4, IH5, IH6, IH7 | | | | | |Corpus North | ccbn | LQ1, LQ2, C15, C16, C17, C18, C19, C20, | | | | C21, C22, C23, CCC3, CCC4, CCC5, CCC6, | | | | CCC7, CCC8 | | | | | |Corpus Middle | ccbm | C01, C02, C03, C04, C05, C06, C07, C08, | | | | C10, C11, C13 | | | | | |Corpus East | ccbe | CCC1, CCC2, EF, C12, C09, C14 | | | | | |Corpus South | ccbs | C24, I9, C25 | | | | | |Oso | oso | OS1, OS2, OS3, OS4, OS5, OS6, OS7 | | | | | |ULM North | ulmn | UL01, UL02, UL03, UL04, UL05, UL06, UL07,| | | | UL08, UL09, UL10, I10, I11, I12, I13, I14| | | | | |ULM Middle | ulmm | UL11, UL12, UL13, UL14, I15, I16, I17, | | | | I18 | |ULM South | ulms | none | | | | | |Baffin | baf | GR1, GR2, LS1, LS2, AL1, AL2, BF1, BF2, | | | | BF3 | | | | | -----------------------------------------------------------------------Table 1. Segmentation Table for the BALANCE Model.
Bathymetry data for the Bay System was taken from the input file of a hydrodynamic model of the system. The input file was obtained from Junji Matsumoto of the Texas Water Development Board (1996). The data were taken from NOAA charts. A graphical user interface called Surface Water Modeling System (SMS) was used to calculate the mean depth for each segment and line manually. Nodes belonging to a segment or interface line were select with SMS' 'Select with Polygon' function. SMS automatically displays the average value of the nodes. Figure 4 shows the depth of each segment. Table 3 (Section 5) lists the segment depths.
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Figure 4. Segment Depths.
Segment surface areas were calculated using the calcarea program described further in the Developer's Corner of the BALANCE documentation. As stated above, RF1 was used to clip of parts of the segmentation that are located on the land surface. The shoreline is however subject to interpretation in certain areas of the system. This becomes apparent when comparing RF1 with the USGS' Digital Line Graph file for the ULM South (ulms) segment. Figure 5 shows the two files. A manual adjustment was made to the area of the ULM South (ulms) and Aransas North (aran) segments. The area calculated using the RF1 shoreline was multiplied by an adjustment factor. See Table 2 for the adjustment factors. Table 3 (Section 5) lists the segment areas.
------------------------------------- | |Segment Area | |Segment |Adjustment Factor | |------------------------------------ |ULM South |0.25 | |Aransas North |0.6 | -------------------------------------Table 2. Segment Area Adjustment Factors.
Segment volumes were calculated as the product of surface area and segment depths. The volume of the Inlet (inl) segment was small compared to the other segments. The Inlet (inl) segment therefore controlled the numerical stability of the model. Since the model was solved for a steady state solution without decay the segment volume does not effect the final results. The volume of the Inlet (inl) segment was therefore increased by a factor of 1000 to allow for the model to be run with a larger time step. Table 3 lists the segment volumes.
------------------------------------------------------------------ |Name |ID |Depth |Area |Volume | | | |[m] |[m^2] |[m^3] | ------------------------------------------------------------------ |St. Charles | stc | 0.7 | 33173293 | 23221305 | |Copano | cop | 1.3 | 191930588 | 249509765 | |Aransas North | aran | 1.4 | 38094550 | 53332370 | |Aransas Middle | aram | 2.2 | 110235428 | 242517942 | |Aransas South | aras | 2.6 | 120451154 | 313173001 | |Redfish | red | 1.6 | 98067488 | 156907981 | |Inlet | inl | 14.0 | 4117508 | 57645100000 | |Nueces West | nuew | 0.7 | 12096637 | 8467646 | |Nueces Middle | nuem | 0.8 | 20349579 | 16279663 | |Nueces East | nuee | 1.0 | 37515710 | 37515710 | |Inner Harbor | inh | 14.0 | 6204909 | 86868719 | |Corpus North | ccbn | 5.3 | 108540903 | 575266787 | |Corpus Middle | ccbm | 3.4 | 200240004 | 680816013 | |Corpus East | ccbe | 3.4 | 101090366 | 343707243 | |Corpus South | ccbs | 0.6 | 35924644 | 21554787 | |Oso | oso | 0.7 | 17746600 | 12422620 | |ULM North | ulmn | 1.5 | 173796230 | 260694000 | |ULM Middle | ulmm | 1.8 | 78999499 | 142199098 | |ULM South | ulms | 1.8 | 217413081 | 391344000 | |Baffin | baf | 1.3 | 239474381 | 311316695 | ------------------------------------------------------------------Table 3. Segment Depths, Areas and Volumes.
Interface lengths are the horizontal lengths of the lines representing the interface (connection) between segments. The lengths were calculated using the calclength program described further in the Developer's Corner of the BALANCE documentation. Note that the lines of the segmentation do not always represent the length of the interface available for mass transfer by dispersion. The interface lengths for some interfaces were adjusted manually. The line between the Corpus South (ccbs) and ULM North (ulmn) segments will serve as an example. That line represents the location of the JFK Causeway, connecting the mainland to the barrier islands. There are only a couple of openings under the causeway available for dispersive mass transport. Figure 6 shows the area. Table 4 lists the interface lengths.
----------------------------------------------------------------- |Interface |Line |Interface | | |--------------------------------|Length |length |Depth | |From |To |[m] |[m] |[m] | |---------------------------------------------------------------- |St. Charles |Aransas Middle | 3924 | 1600 | 0.8 | |Copano |Aransas Middle | 2946 | 2946 | 1.6 | |Aransas North |Aransas Middle | 4257 | 4257 | 1.7 | |Aransas Middle |Aransas South | 5953 | 5953 | 3.0 | |Aransas South |Redfish | 16607 | 830 | 2.1 | |Aransas South |Inlet | 2211 | 800 | 7.5 | |Redfish |Corpus North | 353 | 353 | 3.6 | |Redfish |Inlet | 1552 | 200 | 3.0 | |Inlet |Corpus East | 2281 | 1100 | 9.3 | |Corpus North |Corpus Middle | 21123 | 21223 | 6.7 | |Corpus North |Corpus East | 978 | 978 | 10.1 | |Corpus North |Inner Harbor | 522 | 522 | 14.0 | |Nueces West |Nueces Middle | 2618 | 2600 | 0.8 | |Nueces Middle |Nueces East | 4574 | 4100 | 0.9 | |Nueces East |Corpus North | 3458 | 2900 | 1.2 | |Corpus Middle |Oso | 685 | 200 | 1.3 | |Corpus Middle |Corpus East | 19070 | 18070 | 3.5 | |Corpus East |Corpus South | 5637 | 4000 | 1.4 | |Corpus South |ULM North | 6449 | 1000 | 5.5 | |ULM North |ULM Middle | 3588 | 3000 | 1.6 | |Baffin |ULM Middle | 6798 | 6700 | 1.5 | |ULM Middle |ULM South | 5990 | 4200 | 1.9 | -----------------------------------------------------------------Table 4. Interface Geometry.
Interface areas were calculated as the product of interface depth and length. See Section 3 for a description on how the interface depths were calculated.
Evaporation data was obtained from a grid of mean annual evaporation provided by Reed et al. (1996). The grid was calculated using the Priestley-Taylor Method. The segmentation polygon coverage was converted to a zone grid using the ARC/INFO POLYGRID function and the mean evaporation for each segment was calculated using the ARC/INFO Grid ZONALMEAN function. The mean evaporation was multiplied by the surface area of the segment to get the evaporation in the units of flow. Figure 7 shows the evaporation for the system. Table 5 (Section 9) lists the evaporation values for each segment as well as some comparison data.
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Figure 7. Segment Evaporation.
Precipitation data was obtained from a grid of mean annual precipitation provided by Reed et al. (1996) in the same manner as the evaporation was calculated. Figure 8 shows the precipitation for the system. Table 5 lists the precipitation values for each segment as well as some comparison data.
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Figure 8. Segment Precipitation.
--------------------------------------------------------------- |Segment |Evaporation [m/yr] |Precipitation [m/yr] | | |-----------------------------|---------------------| | |Reed Pan |Reed PT |TWDB |Reed |TWDB | --------------------------------------------------------------- |stc | 1.55 | 1.38 | 1.58 | 0.82 | 0.83 | |cop | 1.57 | 1.38 | 1.58 | 0.85 | 0.83 | |aran | 1.55 | 1.38 | 1.58 | 0.82 | 0.83 | |aram | 1.55 | 1.38 | 1.58 | 0.85 | 0.83 | |aras | 1.62 | 1.43 | 1.58 | 0.80 | 0.83 | |red | 1.63 | 1.58 | 1.58 | 0.73 | 0.83 | |ccbn | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |nuee | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |nuew | 1.63 | 1.65 | 1.58 | 0.78 | 0.83 | |nuem | 1.63 | 1.65 | 1.58 | 0.78 | 0.83 | |inl | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |ccbe | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |inh | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |ccbm | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |oso | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |ccbs | 1.63 | 1.65 | 1.58 | 0.71 | 0.83 | |ulmn | 1.63 | 1.65 | 1.58 | 0.73 | 0.83 | |baf | 1.63 | 1.67 | 1.58 | 0.70 | 0.83 | |ulmm | 1.63 | 1.67 | 1.58 | 0.71 | 0.83 | |ulms | 1.62 | 1.68 | 1.58 | 0.69 | 0.83 | ---------------------------------------------------------------
Evaporation
Runoff Inflows
The inflows were obtained by summing the mean annual runoff for the watershed of each segment. The mean annual runoff was calculated by Ann Quenzer from data obtained from Reed et al.(1996). Figure 9 shows the system runoff inflows. Table 6 lists the runoff for each segment obtained in that manner. Two other sources of runoff inflow are also listed for comparison.
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Figure 9. Runoff Inflows.
----------------------------------------- |Segment |Runoff Inflows [m^3/s] | | |-----------------------------| | |Reed |USGS | TWDB | ----------------------------------------- |stc | 2.89 | 2.94 | 3.28 | |cop | 17.56 | 25.94 | 17.53 | |aran | 11.95 | 0.00 | 0.00 | |aram | 0.25 | 0.00 | 0.00 | |aras | 0.09 | 0.00 | 0.00 | |red | 0.09 | 0.45 | 0.00 | |ccbn | 0.25 | 16.54 | 0.00 | |nuee | 0.20 | 0.00 | 0.00 | |nuew | 10.11 | 19.99 | 13.54 | |nuem | 0.09 | 0.00 | 0.00 | |inl | 0.00 | 0.00 | 0.00 | |ccbe | 0.09 | 0.00 | 0.00 | |inh | 0.03 | 0.00 | 0.00 | |ccbm | 0.03 | 0.00 | 0.00 | |oso | 0.76 | 0.00 | 2.72 | |ccbs | 0.03 | 0.00 | 0.00 | |ulmn | 0.37 | 0.00 | 0.00 | |baf | 9.80 | 4.16 | 2.07 | |ulmm | 0.03 | 0.00 | 0.00 | |ulms | 4.98 | 0.17 | 0.00 | |---------|---------|---------|---------| |Total | 59.58 | 70.20 | 39.13 | -----------------------------------------
Table 6. Segment Runoff Inflows.
The flows were obtained by routing runoff downstream into the bay segments. Since the grid extends further north and south, flow which actually ends up in parts of the bay not modeled here can make it's way into the bay. This happened at the North boundary as is illustrated in Figure 10. The flow into the Aransas North (aran) segment was initially set to zero. Later the flow was set to a positive number. See section 11 for more detail.
Boundary Flows
The interface between the ULM South (ulms) and ULM Middle (ulmm) segments and the North boundary were set as a no-flow boundaries. The Gulf boundary was set to close the water mass balance. See the BALANCE documentation instructions on how to change parameters like boundary flows.
Interface flows and dispersion coefficients were calibrated against observed salinity data. A trial-and-error approach was used where interface flows and dispersion coefficients were assigned, BALANCE was run, and the modeled salinity concentrations were compared to the observed ones. Then the interface flows and dispersion coefficients were modified as needed. The process was repeated until the modeled salinity concentrations matched the observed ones. Note that we are dealing with mean annual conditions.
For the calibration observed salinity concentrations had to be obtained which is discussed in the next section. Then the calibration is described in detail, followed by the results.
11.a. Computation of Observed SalinityAn electronic file of salinity measurements was obtained from George Ward (1997). The measurements were grouped by the segmentation developed by Ward and Armstrong (1996) and listed in chronological order. To obtain estimates of the observed salinity for each of the segments the data had to be averaged in two dimensions: Time and Space. The time period for averaging was chosen to be the period of record, consistent with the other parts of the project. Six different averaging methods were employed and compared:
Time Averaging Scheme
The results for each averaging scheme are listed in Table 7. Note that the data is sensitive to the averaging method employed for certain segments. Certain differences can be easily explained. Consider for example the Nueces Middle (nuem) segment. The averages calculated using the simple space averaging method are all lower than the averages calculated using the area weighted space averaging method. That is because the low values are measured in the Nueces River (which drains into and is part of the segment). However, because the river is not part of the RF1 outline of the bay, the segments corresponding to the Nueces River are assigned zero area (and thus no weight). A similar logic can be applied to the Oso (oso) segment.
----------------------------------------------------------------------- |Time |Simple |Time |Max Ctrl |Simple |Time |Max Ctrl | |Averaging| |Weighted |Time | |Weighted |Time | |Scheme | | |Weighted | | |Weighted | |---------|-----------------------------|-----------------------------| |Space |Simple |Area Weighted | |Averaging| | | |Scheme | | | |---------------------------------------------------------------------| |Segment |Salinity [ppt] | ----------------------------------------------------------------------- |cop | 14.29 | 13.56 | 13.97 | 14.45 | 13.67 | 14.20 | |stc | 13.20 | 13.08 | 13.61 | 13.52 | 13.32 | 13.85 | |aran | 19.05 | 20.89 | 19.26 | 18.72 | 20.11 | 19.08 | |aram | 18.60 | 19.00 | 18.57 | 18.20 | 19.29 | 18.16 | |aras | 23.31 | 23.12 | 23.40 | 23.37 | 23.10 | 23.45 | |red | 26.27 | 26.06 | 26.61 | 26.36 | 25.97 | 26.54 | |inl | 29.27 | 28.29 | 28.77 | 29.27 | 28.29 | 28.77 | |nuew | 21.88 | 19.84 | 21.33 | 24.18 | 19.31 | 22.37 | |nuem | 14.71 | 11.56 | 14.07 | 25.24 | 18.44 | 23.90 | |nuee | 25.59 | 24.45 | 25.06 | 25.71 | 24.53 | 25.08 | |inh | 29.16 | 28.64 | 28.59 | 28.53 | 28.24 | 27.82 | |ccbn | 28.85 | 27.74 | 28.83 | 28.90 | 27.78 | 28.88 | |ccbm | 28.24 | 26.45 | 29.12 | 28.11 | 25.20 | 29.13 | |ccbe | 29.69 | 29.24 | 29.87 | 29.80 | 30.63 | 30.02 | |ccbs | 30.47 | 29.83 | 31.19 | 30.50 | 30.29 | 31.34 | |oso | 26.13 | 26.70 | 26.29 | 31.85 | 30.72 | 31.98 | |ulmn | 35.52 | 34.00 | 35.37 | 35.76 | 34.29 | 35.57 | |ulmm | 36.88 | 35.32 | 36.87 | 37.41 | 35.95 | 37.57 | |ulms | no data | no data | no data | no data | no data | no data | |baf | 38.51 | 37.37 | 38.12 | 38.19 | 35.59 | 37.58 | |---------------------------------------------------------------------| |Boundary |Salinity [ppt] | |---------------------------------------------------------------------| |Gulf | 30.04 | 29.64 | 29.37 | n/a | n/a | n/a | |North | no data | no data | no data | no data | no data | no data | |South | no data | no data | no data | no data | no data | no data | -----------------------------------------------------------------------Table 7. Period of Record Observed Salinity.
The time weighted average with a maximum weight of one month was chosen as the best method for time averaging and the area weighted methods was chosen as the best method for averaging in space. Figure 11 shows the observed salinity in the system.
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Figure 11. Observed Salinity.
11.b. CalibrationAs mentioned above, interface flows and dispersion coefficients were calibrated against measured salinity data using a trial-and-error approach. First the boundary conditions were entered into the system. The calibration procedure is outlined below, followed by an illustrative example.
BoundariesSince observed concentrations for the North and South boundary were not available they were assigned values close to the observed value of the adjacent segment and the dispersion coefficient was set high to force the concentration in the adjacent segment to the observed one. The Gulf boundary was assigned the observed concentration of 29.37 ppt. The North and South boundaries were modeled as no-flow boundaries. The Gulf boundary was a flow boundary with the flow chosen to close the water mass balance.
ProcedureFirst reasonable estimates of the interface flows were entered into the model. Care was taken not to violate the water mass balance for each segment. For that purpose a table of net inflows was constructed (Table 8)
--------------------------------------------------- | |Flow [m^3/s] | | |---------------------------------------| | |Runoff |Evapo- |Precip- |Net | |Segment |Inflow |ration |itation |Inflow | --------------------------------------------------- |stc | 2.89 | 1.45 | 0.87 | 2.30 | |cop | 17.56 | 8.40 | 5.16 | 14.31 | |aran | 11.95 | 2.78 | 1.66 | 10.83 | |aram | 0.25 | 4.83 | 2.96 | -1.61 | |aras | 0.09 | 5.44 | 3.06 | -2.29 | |red | 0.09 | 4.92 | 2.28 | -2.55 | |ccbn | 0.25 | 5.68 | 2.46 | -2.97 | |nuee | 0.20 | 1.96 | 0.85 | -0.92 | |nuew | 10.11 | 0.63 | 0.30 | 9.78 | |nuem | 0.09 | 1.06 | 0.50 | -0.47 | |inl | 0.00 | 0.22 | 0.09 | -0.12 | |ccbe | 0.09 | 5.30 | 2.28 | -2.93 | |inh | 0.03 | 0.32 | 0.14 | -0.16 | |ccbm | 0.03 | 10.48 | 4.52 | -5.93 | |oso | 0.76 | 0.93 | 0.40 | 0.24 | |ccbs | 0.03 | 1.88 | 0.81 | -1.04 | |ulmn | 0.37 | 9.11 | 4.00 | -4.73 | |baf | 9.80 | 12.68 | 5.28 | 2.40 | |ulmm | 0.03 | 4.18 | 1.78 | -2.38 | |ulms | 4.98 | 11.55 | 4.79 | -1.78 | ---------------------------------------------------Table 8. Segment Net Freshwater Inflows.
Dispersion coefficients were initially assigned a value of 800 m^2/s for interfaces near the inlet area and 400 m^2/s for other interfaces. Then the following procedure was run until the modeled concentrations matched the observed ones.
Illustrative Example
Figure 12 shows the modeling error in Nueces Bay after hypothetical run A. Blue segments indicate the model underestimates salinity and red segments indicate the model overestimates salinity. The red arrows represent flow and the green and blue arrows represent advective and dispersive mass flux. The green and blue boxes are a measure of the net advective and dispersive loads into the segment, respectively.
Note that the model underestimates the salinity concentration in the upstream segments. This part of the model is one dimensional and the interface flows are therefore fixed. Our only control are the dispersion coefficients. For the concentration in the upstream segments to increase the dispersive flux from Corpus Christi Bay has to increase. Note that the model overestimates the concentration in Corpus Christi Bay. That means that the low dispersive mass flux is not due to a low concentration in Corpus Christi Bay. The dispersion coefficients in Nueces Bay have to be low. The dispersion coefficients in Nueces bay are increased from 250 to 300 m^2/s and the model is rerun.
Figure 13 shows the modeling error in Nueces Bay after the rerun. The model now overestimates the concentration in all of the three segments. The trial-and-error instinct would tell the modeler that he or she made too big of an adjustment. A possible solution would be to go back and decrease the dispersion coefficients to a value around maybe 275 m^2/s. However, the dispersive mass flux into Nueces Bay is also a function of the concentration in Corpus Christi Bay, which is still overestimated by the model. If the modeled concentration in Corpus Christi bay can be decreased to a value closer to the observed the one in Nueces Bay will decrease as well. The focus is therefore shifted to adjusting the concentration in Corpus Christi Bay.
Comparison of Modeled and Observed Concentrations
After about 50 runs the difference in modeled and measured concentration was less than 1 ppt for most segments. That is an error of less than 5% which is well below the estimated error in the input data to the model and therefore acceptable. Figure 14 shows the modeled salinity for the system and Figure 15 shows the modeling error. Table 9 compares the modeled and observed concentrations.
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Figure 14. Modeled Salinity.
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Figure 15. Model Error.
---------------------------------------- | |Salinity [ppt] | | | |-------------------| | |Segment |Observed |Modeled |% Error | ---------------------------------------- |cop | 14.20 | 14.35 | 1.05 | |stc | 13.85 | 14.14 | 2.06 | |aran | 19.08 | 19.08 | 0.01 | |aram | 18.16 | 18.52 | 2.02 | |aras | 23.45 | 23.93 | 2.05 | |red | 26.54 | 26.72 | 0.70 | |inl | 28.77 | 29.36 | 2.05 | |nuew | 25.08 | 22.63 | 1.14 | |nuem | 23.90 | 23.99 | 0.35 | |nuee | 22.37 | 25.54 | 1.83 | |inh | 27.82 | 29.58 | 6.34 | |ccbn | 28.88 | 29.58 | 2.41 | |ccbm | 29.13 | 29.71 | 1.96 | |ccbe | 30.02 | 29.77 | 0.85 | |ccbs | 31.34 | 31.67 | 1.05 | |oso | 31.98 | 32.37 | 1.23 | |ulmn | 35.57 | 35.29 | 0.78 | |ulmm | 37.57 | 37.54 | 0.08 | |ulms | n/a | 37.55 | n/a | |baf | 37.58 | 36.42 | 3.07 | ----------------------------------------Table 9. Comparison of Observed and Modeled Salinity.
The salinity in the Inner Harbor (inh) segment could not be modeled to within 1 ppt. The Inner Harbor (inh) segment does not receive enough freshwater inflow to cover net evaporation. The flow (and advective mass flux) is therefore into the segment. The concentration has to be higher than the adjacent downstream segment. However, the observed concentrations indicate the concentration in the Inner Harbor (inh) segment is lower than the adjacent downstream segment, Corpus North (ccbn). The error is probably due to: (a) An error in the estimate of the inflow. The segment could receive more inflow. (b) An error in the estimate of the net evaporation. This could be due to an error in the estimation of the surface area.
11.c. ResultsThe calibrated interface flows and dispersion coefficients are shown in Figures 15 and 16 and listed in Table 10.
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Figure 16. Salinity Mass Balance.
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Figure 17. Dispersion Coefficients.
--------------------------------------------------------------------------- | | |Bulk | | |Interface |Dispersion |Dispersion | | |--------------------------------|Coefficient|Coefficient|Flow | |From |To |[m^2/s] |[m^3/s] |[m^3/s] | |-------------------------------------------------------------------------- |St. Charles |Aransas Middle | 80 | 7.4 | 2.3 (south) | |Copano |Aransas Middle | 150 | 49.1 | 14.3 (east) | |Aransas North |Aransas Middle | 100 | 55.1 | 0.0 | |Aransas Middle |Aransas South | 40 | 45.7 | 15.0 (south) | |Aransas South |Redfish | 300 | 54.4 | 8.9 (west) | |Aransas South |Inlet | 40 | 22.4 | 3.8 (east) | |Redfish |Corpus North | 200 | 13.8 | 4.3 (south) | |Redfish |Inlet | 80 | 5.0 | 1.0 (east) | |Inlet |Corpus East | 600 | 455.0 | 4.2 (south) | |Corpus North |Corpus Middle | 100 | 1545.0 | 9.6 (south) | |Corpus North |Corpus East | 100 | 62.0 | 0.0 | |Corpus North |Inner Harbor | 5000* | 2419.0 | 0.2 (west) | |Nueces West |Nueces Middle | 250 | 163.1 | 9.8 (east) | |Nueces Middle |Nueces East | 250 | 144.0 | 9.3 (east) | |Nueces East |Corpus North | 150 | 53.0 | 8.4 (east) | |Corpus Middle |Oso | 100 | 2.6 | 0.2 (south) | |Corpus Middle |Corpus East | 50 | 245.0 | 3.4 (south) | |Corpus East |Corpus South | 250 | 99.0 | 5.7 (south) | |Corpus South |ULM North | 150 | 45.9 | 4.7 (south) | |ULM North |ULM Middle | 40 | 7.3 | 0.0 | |Baffin |ULM Middle | 100 | 78.7 | 2.4 (east) | |ULM Middle |ULM South | 5000* | 909.1 | 0.0 | ---------------------------------------------------------------------------
* - a dispersion coefficient was used for boundaries to force the concentration of the adjacent segment. The interface to the Inner Harbor (inh) segment was chosen high to correct the suspected error in the interface flow.
Table 10. Interface Dispersion and Advection Parameters.
Note that care has to be taken when using these dispersion coefficients for different boundary conditions. For different boundary conditions an error in a dispersion coefficent can have a different effect on the error in the modeled concentration. This means the calibrated dispersion coefficient for a certain interface line might be off by 50%, which was not noticed during the salinity calibration, because under these boundary conditions the modeled salinity is not very sensitive to this dispersion coefficent. Under a different set of boundary conditions, however, this error might have a significant effect on the modeled concentration.
The calibrated dispersion coefficients can be compared to those in other systems. Before doing so several issues have to be discussed. (1) The model is mean annual, which means the dispersion coefficients include molecular diffusion, eddy diffusion, turbulent dispersion and tidal mixing. The dispersion coefficients can only be compared to coefficients taking into account these processes as well. (2) Errors in the estimation of mixing lengths and areas are reflected in the dispersion coefficients. (3) Numerical dispersion in the model causes the calibrated dispersion coefficients to underestimate actual dispersion. Numerical dispersion is discussed below in greated detail.
Numerical Dispersion
Each segment is modeled as a completely mixed tank. The dispersion inside every tank is infinitely large. Therefore the model disperses mass even if the dispersion coefficients are set to zero. This dispersion is termed numerical dispersion. For this model the magnitude of the numerical dispersion (Enum) can be estimated using the following formula (Thomann and Mueller, 1987):
Enum = U * (dx / 2)
In the above formula U is the mean velocity and dx is the length of the segment. The numerical dispersion is a function of velocity and segment length. If we keep those parameters constant from the calibration to the application our calibrated dispersion coefficients are applicable. The dispersion coefficients will have to be recalibrated if the segmentation or the flows are altered.
It is important to note that our estimates of the dispersion coefficients were made with this numerical dispersion present. The effect of numerical dispersion in the model is that the calibrated dispersion coefficients are lower than the actual dispersion coefficients in the system. Our dispersion only models what is left of the actual dispersion after the numerical dispersion has done its part. To illustrate the order of magnitude the estimated numerical dispersion for different velocities and segment lengths is plotted in Figure 18.
For Nueces Bay, for example, The through flow is approcimately 10 m^3/s. For a cross sectional area of about (4,000 m x 0.8 m) 3,200 m^2 this results in an average velocity of 0.003 m/s. Given a segment length of about 4 km and using the relationship in Figure 18 we can see that the numerical dispersion coefficient is about 6 m^2/s. When compared to the calibrated dispersion coefficient, 250 m^2/s, in the bay we can see that numerical dispersion is not significant in magnitude to the calibrated dispersion for this segment.
Table 11 shows that the estimated dispersion coefficients are reasonable compared to other systems.
--------------------------------------------------- | |Dispersion Coefficient | |Estuary |[m^2/s] | |-------------------------------------------------- |Hudson River, NY |600 | |East River, NY |300 | |Cooper River, SC |900 | |South River, NJ |150 | |Houston Ship Channel, TX |800 | |Compton Creek, NJ | 3 | |River Foyle, N. Ireland |150 | |Rio Quayas, Ecuador |750 | ---------------------------------------------------Table 11. Published Dispersion Coefficients (Thomann and Mueller, 1987).
Matsumoto, J., Personal Conversation, 10/21/96.
Reed, S., Maidment, D.,and Patoux, J., Spatial Water Balance of Texas, Center for Research in Water Resources, University of Texas at Austin, 2/20/96.
Thomann, R., V., and Mueller, J. A., Principles of Surface Water Quality Modeling and Control, Harper Collins, New York, 1987.
Ward, G. H., and Armstrong, N. E., Corpus Christi Bay National Estuary Program, Ambient Water, Sediment and Tissue Quality of Corpus Christi Bay Study Area: Present Status and Historical Trends, Summary Report, Draft, Center for Research in Water Resources, The University of Texas at Austin, November 1996.
Ward, G. H., Personal Conversation, 02/11/97.
This section documents the programs used in the study. All programs are written in ArcView's Avenue programing language. More related programs can be found in the Developer's Corner of the BALANCE documentation.
Ward Data Import Utility (wardimp)Description: This is an import utility for CCBNEP data compiled by George Ward. Sample points are written to a table.
Status: Done. Could be modified to create a point shape file of the measurement points. This would make point and click access to the data possible.
Source Code: wardimp.txt
Description: This is a simple averaging utility for sample data.
Status: Done.
Source Code: simpleave.txt
Description: This is a time averaging utility for sample data.
Status: Done. The way the weight is calculated could be modified. Now the weight is calculated as the length of time from the last measurement to this measurement. A better way would be to take the length of time from the point halfway between the last measurement and this measurement to the point halfway between this measurement and the next measurement.
Source Code: timeave.txt
Description: This is a time averaging utility for sample data. Maximum weight assigned is one month.
Status: Done.
Source Code: timeavem.txt
Description: This is a segment averaging utility for sample data.
Status: Done.
Source Code: segave.txt
Description: This is a segment averaging utility for sample data. Average is weighted by area.
Status: Done.
Source Code: segavea.txt
The result of the study consists of an ARC/INFO coverage of the segmentation of the system attributed with the water quality modeling parameters. The coverage is in ARC/INFO export format. The file can be downloaded from our anonymous ftp site and imported with the ARC/INFO IMPORT command or the ArcView IMPORT71 utility program.
Note: If you are new to ftp you might want to read the page entitled Getting Data From CRWR's Anonymous FTP Site.
Address: ftp.crwr.utexas.edu
Login: anonymous
Password: your e-mail address
Directory: /pub/crwr/gishydro/ccbparam
Transfer Mode: binary
File: bay.e00