Application Scenarios

 

Basic steps typically involved in applying BATHTUB to a reservoir are discussed below.  Three application scenarios can be defined, based upon reservoir status and data availability:

 

    Data Availability
Scenario Reservoir Water/Nutrient
 Balance Data		 Pool Water
Quality Data
A Existing Yes Yes
B Existing No Yes
C Existing or Proposed Yes No

 

 

Scenario A normally applies to an existing reservoir with nutrient balance data and pool water quality data.  Under Scenario B, nutrient balance (loading) information is lacking; in this case, the program can be used for diagnostic purposes (e.g., assessing pool nutrient/chlorophyll relationships and ranking vs. the CE reservoir data used in model calibration (Walker, 1985).  Scenario C is distinguished by lack of pool water quality data, which would otherwise be used for preliminary testing and calibration.  The user is referred to the Theory section for a discussion of basic concepts that underlying the steps.

For each scenario, application procedures can be summarized in terms of the following basic steps:

These steps are designed to be executed sequentially.  Reiteration of previous steps is common in typical modeling projects.  As described below, not all modeling steps are applicable to each scenario.  The procedures are intended to provide general indications of factors to be considered during the modeling process.  They are not intended as a rigid framework for applying the model.  User judgment must be exercised to account for unique aspects of each application.  The Theory section describes model formulations, options, and other background information required to support applications.  Before considering each scenario, a few general aspects of developing model applications are discussed.

 

It is important to define purpose and scope prior to undertaking the modeling effort.  This includes specifying management issues to be evaluated and types of model output required to support the evaluations.  In typical applica­tions, most of the effort and cost is devoted to data collection and data reduction.  In situations where modeling is undertaken after the monitoring data have been acquired, model results may be severely limited by data.  This situation can be avoided by initiating modeling before designing and undertaking addi­tional monitoring.  Modeling can be conducted in two phases.  The first phase is based upon historical data and helps to define data gaps that can be filled in subsequent monitoring.  The second phase is based upon more complete data.  Chapter 1 contains guidance for designing monitoring programs to support model applications.
 

In defining study scope, the user must decide which components will be modeled.  In the most general case, a model application involves specification of tributary loads (flows and concentrations) for a conservative tracer, total phosphorus, ortho phosphorus, total nitrogen, and inorganic nitrogen.  Of these, only total phosphorus is absolutely necessary.  Based upon the CE reservoir data set used in developing the phosphorus sedimentation models, additional consideration of ortho phosphorus loads reduces the standard error of predicted reservoir-mean phosphorus concentrations by 16 to 32 percent, depending upon model formulation.  Considering total phosphorus loads only will provide unbiased predictions of reservoir response, however, if the ratio of tributary ortho phosphorus load to tributary total phosphorus load is in the range of 15 to 50 percent.  Considering nitrogen loads provides additional descriptive information, but may not contribute significantly to predicting the trophic response of the reservoir, as measured by chlorophyll a because nitrogen may not be limiting algal growth or because external nitrogen loads may be supplemented by fixation of atmospheric nitrogen (see Eutrophication response models).  Modeling a conservative tracer, such as chloride or conductivity, provides a means for calibrating and testing diffusive transport terms and for testing overall water balances.


BATHTUB provides a facility for calibrating the empirical models to account for site-specific conditions (see Calibration factors).  Calibration should be attempted only by experienced users working with intensive moni­toring data sets.  A potential need for site-specific calibration is indicated when significant differences between observed and predicted concentrations are found during initial model runs.  A conservative approach to calibration is recommended (adjusting the fewest number of coefficients within reasonable ranges).  Differences between observed and predicted concentrations result from two basic sources:  data errors and model errors.  Random data errors always occur in the specification of model input values (tributary loads, observed reservoir water quality, flows, morphometry, etc.).  Omission of important nutrient sources in formulating the reservoir nutrient balance is another type of random error.  These are essentially artifacts of study design, data collection, and data reduction.  Model errors reflect true differences between model predictions and reservoir response.  Calibration to account for model errors may be justified, but calibration to account for data errors is generally not justified.  One possible exception to this rule occurs when data errors are not random, but are biases attributed to differences in measurement  methods; for example, calibration of the chlorophyll a model may be appro­priate to account for differences in measurement technique.  BATHTUB error analyses can help to distinguish between model and data errors.  Calibration is generally not necessary when there is considerable overlap between observed and predicted distributions.

 

Each application should start with construction of a schematic diagram show­ing major reservoir regions, inflow streams, point sources, outflow streams, and monitoring stations.  Examples of schematic diagrams are given in the Documented Session and Instructional Cases sections at the end of this chapter. The diagram can be overlaid on a reservoir map.  Initial definitions of model segments should be shown; these may be revised based upon subsequent review and summary of monitoring data.  Segments and tributaries should be labeled and numbered.  The diagram provides a useful frame of reference for subsequent data reduction and modeling steps.

 

Scenario A - Existing reservoir with loading and pool water quality data

 

Step 1 involves reduction of watershed data used in modeling. Formulation of a drainage area “balance” is an important first step in summarizing water­shed characteristics.  The FLUX program (Walker, 1999; Chapter 2) can be used for estimating seasonal and/or annual loadings for gauged tributaries, point sources, and discharges.  An averaging period for calculating tributary inflows must be selected.  This is typically 1 year for reservoirs with relatively long hydraulic residence times and one growing season (April-September or May-September) for reservoirs with relatively short residence times (see Nutrient residence time and turnover ratio).  Sensitivity to choice of averaging period can be tested by creating separate input files for different averaging periods.Ungauged inflows and stream concentrations can be estimated by drainage-area proportioning using data from other regional watersheds with similar land uses.  Alternatively, ungauged inflows and concentrations can be estimated by calibrating and applying the nonpoint source model provided with BATHTUB (TYPE=2 tributaries).  Calibration requires specification of typical runoff rates and concentrations as a function of land use (Edit Export Coefficients  procedure).

Step 2 involves reduction of reservoir morphometric and water quality data.  Morphometric information can be estimated from contour maps and/or sediment accumulation surveys.  PROFILE (Walker, 1999; Chapter 3) can be used to summarize observed water quality conditions by segment and calculate oxygen depletion rates in stratified reservoirs.  Segment boundaries depicted on the schematic diagram may be revised based upon review of pool monitoring data. Generally, it is appropriate to aggregate adjacent reservoir areas with similar water quality into a single segment.  Box plots summarizing water quality data by station can be useful for this purpose (Walker, 1999; Chapter 3) .  Even if significant spatial variations in water quality are apparent, division of the reservoir into multiple segments is not necessary for modeling.  Modeling the entire reservoir with one segment provides predictions of area-weighted mean concentrations, which may be adequate to support management decisions.  In such situations, it will be particularly important to apply spatial weighting factors when averaging observed water quality data.  Defining multiple segments may be required to support management decisions.  Simulating spatial variations within the reser­voir can provide evidence of model applicability and reliability that is not available in single-segment applications.

 

In Step 3, an input data file is create using the Edit screens.  The input file should be listed and checked for data-entry errors and completeness.  Default model options should be modified to reflect the components being modeled (conservative substance, phosphorus, nitrogen).  If ortho phosphorus and/or inorganic nitrogen concentrations for all stream inflows are not supplied, availability factors should not be used in calculating nutrient balances.  This is achieved by setting the availability factor option to 0.

Water balances are checked and adjusted in Step 4 using the List Balances Overall procedure.  Measured flows for all major inflow and outflow streams must be specified in order to check the water balance.  It may be appropriate to adjust certain inflow, outflow, and/or increase-in-storage terms until balances are established.  The appropriate terms to adjust vary from case to case, depending upon watershed characteristics and flow monitoring networks.  Based upon familiarity with the flow data sources, the user should assess the most likely source(s) of water balance error and adjust the appro­priate value(s) in the Case file.  Flow-balance errors are often attributed to ungauged surface or groundwater inflows.  If a water balance cannot be established with reason­able adjustments, additional monitoring with refine­ments to flow gauging networks may be required.

 

Nutrient turnover ratios are checked in Step 5 using List Balances Overall procedure.  The appropriate averaging period for mass-balance calculations is determined by the observed turnover ratio of the limiting nutrient (usually phosphorus).  A seasonal averaging period (April/May through September) is usually appropriate if it results in a turnover ratio exceeding 2.0. An annual averaging period may be used otherwise.  The turnover ratio criterion is an approximate guideline, which may be adjusted from case to case.  Other con­siderations (such as comparisons of observed and predicted nutrient levels) can also be used as a basis for selecting an appropriate averaging period, particularly if the turnover ratio is near 2.0.  Note that if the reservoir is vertically stratified and significant hypolimnetic accumulations of phosphorus occur, seasonal phosphorus turnover ratios calculated from mixed-layer concentrations will be over-estimated.  In this situation, mixed-layer nutrient levels during the growing season may reflect nutrient transport from the bottom waters via diffusion or mixing processes, as compared with nutrient inputs from external sources.  Both annual and seasonal balances should be tested in this situation.  Depending upon results of Step 5, it may be necessary to repeat the calculation of tributary loadings (Step 1) using a different averaging period.

 

Step 6 involves checking and possible calibration of diffusive transport terms using the List Hydraulics procedure.  If numeric dispersion exceeds the estimated dispersion in a given segment, the user should consider revising the segmentation scheme (e.g., increasing segment numbers and thus decreasing segment lengths) until this criterion is satisfied.  In some cases, this may be difficult to achieve with a reasonable number of segments, particularly in upper-pool segments, where advective velocities tend to be greater.  The cri­terion may be waived if the sensitivity of predicted nutrient profiles to alterna­tive segmentation schemes is shown to be minimal.


Conservative tracer data (typically chloride or conductivity), may be used to calibrate diffusive transport terms in problems involving more than one segment.  An overall tracer mass balance should be established (List Balances Overall) prior to calibrating transport terms.  Calibration involves adjusting the global calibration factor for dispersion (Edit Model Coefficients) and/or segment calibration factors (Edit Segments) to match observed tracer profiles.  Generally, predicted concentration gradients will decrease with increasing dispersion rates.  The Run Sensitivity procedure shows the sensitivity of predicted tracer concentrations to four-fold variations in dispersion rates.  Where possible, adjustments should be made only to the global calibration factor (keeping segment calibration factors at their default setting of 1.0); this is a more conservative calibration approach than adjusting values for each segment individually.  For Dispersion Model 1, the global calibration factor should be in the range of 0.25 to 4.0, the approximate 95-percent confidence limit for dispersion estimated from Fischer’s equation.  If adjustment outside this range is required, other dispersion models and/or alternative segmentation schemes should be investigated.

 

If there is a long wind fetch and segments are aligned along predominant wind directions, upward adjustment of the dispersion factors may be necessary.  Conversely, downward adjustment may be necessary in reservoirs or reservoir areas that are sheltered from winds.  The segment calibration factor for disper­sion can be adjusted downward to reflect local restrictions caused by weirs, bridges, etc.  Calibration of dispersion rates based upon tracer data is feasible only if significant tracer gradients are detected in the reservoir as a result of the tracer loading distributions.

 

Step 7 involves selecting, testing, and possibly calibrating nutrient sedimenta­tion models using List and/or Plot procedures.  Calibrating dispersion rates to match observed nutrient gradients is also feasible, provided that tracer data are not available in Step 6.  As discussed above, differences between observed and predicted nutrient profiles may reflect random errors in the data, as well as true differences between the model predictions and reservoir responses.  As discussed above, a conservative approach to calibration is recommended.

 

The List T-tests and List Calibration Statistics  procedure provides statistical comparisons of observed and predicted concentrations.  These are computed using three alternative mea­sures of error: observed error only, T(1); error typical of model development data set, T(2); and observed and predicted error, T(3).  Tests of model applicability are normally based upon T(2) and T(3).  If their absolute values exceed 2 for the comparison of area-weighted mean concentrations, there is less than a 5-percent chance that nutrient sedimentation dynamics in the reservoir are typical of those in the model development data set, assuming that input conditions have been specified in an unbiased manner.  The applicability of the models would be questionable in this case.  If the discrepancy cannot be attri­buted to possible errors in the input data file (particularly, inflow concentrations), other options for modeling nutrient sedimentation should be investigated.

 

Lack of fit may also result from unsteady-state loading conditions, particularly if the nutrient turnover ratio is less than 2 based upon annual loadings. In such cases, averaging periods longer than a year may be required to establish a valid load/response relationship.  This situation is more likely to occur for nitrogen than phosphorus because unit sedimentation rates tend to be lower for nitrogen.  
 

Once an appropriate sedimentation model is selected, T(1) can be used as a basis for deciding whether calibration is appropriate.  If the absolute value of T(1) exceeds 2, then there is less than a 5-percent chance that the observed and predicted means are equal, given the error in the observed mean.  In this situa­tion, it may be desirable to calibrate the model so that observed and predicted nutrient concentrations match.  See the overview for additional discussion on calibration.

 

As outlined in Table 4.2, two calibration methods are provided for phos­phorus and nitrogen:  Method 0 - calibrate decay rates and Method 1 - calibrate concentrations.  In the first case, the segment-specific calibration factors are applied to estimated sedimentation rates in computing nutrient balances.  In the second case, the factors are applied to estimated concentrations.  In Method 0 (default), it is assumed that the error is attributed primarily to the sedimentation model.  In Method 1, the error source is unspecified (some combination of input error, dispersion error, and sedimentation model error). The latter may be used when predicted nutrient profiles are insensitive to errors in predicted sedi­mentation rate because the mass balance is dominated by inflow and out­flow terms (low hydraulic residence times, see Figures 1.3 and 1.4).  Regardless of the selected calibration option, global calibration factors for phosphorus and nitrogen ( Edit Model Coefficients) are always applied to the nutrient sedimentation rates.

 

Nutrient Sedimentation Models 1 and 2 have been empirically calibrated and tested for predicting reservoir-mean conditions.  Error analysis calculations indicate that sedimentation rates predicted by these models are generally accurate to within a factor of 2 for phosphorus and a factor of 3 for nitrogen (Walker 1985).  To account for this error, nutrient calibration factors ( Edit Model Coefficients) can be adjusted within the nominal ranges of 0.5 to 2.0 and 0.33 to 3 for phosphorus and nitrogen, respectively.

 

In some cases, nutrient retention coefficients for phosphorus or nitrogen may be negative.  Even after setting the nutrient calibration coefficient to zero (essentially treating the nutrient as a conservative substance), the model will under-predict the observed nutrient concentration in the reservoir.  This may reflect net nutrient releases from bottom sediments (phosphorus or nitrogen) or fixation of atmospheric nitrogen by bluegreen algae.  These “internal loadings” can be represented in the model (Edit Segments). Apparent negative retention coefficients may reflect use of an improper averaging period or under-estimation of significant external loads.  Independent evidence and estimates of sediment nutrient sources should be obtained before specifying internal sources in the model.  As discussed in the theory section, reservoirs with negative nutrient retention coefficients were rarely encountered in the supporting research (Walker 1985).  If internal sources are specified, estimates of model error derived from the supporting research are invalid.  While it is usually possible to “tune” the model predictions using the internal source terms, this does not provide a way of predicting how the internal sources will change in response to changes in external loads or other manage­ment strategies evaluated in Step 11.

 

Once nutrient balances have been established, eutrophication responses (as measured by chlorophyll a, transparency, and hypolimnetic oxygen depletion rate) are developed in Step 8. This involves model selection, testing, and possi­ble calibration.  As outlined in Tables 4.2 and 4.3, several options are available for predicting chlorophyll a concentrations and Secchi depths as a function of nutrient levels and other controlling factors.  If nitrogen balances are considered in addition to phosphorus, chlorophyll a Models 1 or 3 can be used; otherwise, chlorophyll a Model 2 (default) is the most general for application to reser­voirs.  Secchi Model 1 (default) requires an estimate of non-algal turbidity for each model segment (see Theory).  The interpretation and use of t-statistics in testing and calibrating the chlorophyll a and Secchi sub-models follow the above discussion for nutrients (Step 7).

 

With the completion of Step 8, the model has been set up and possibly calibrated using pool and tributary data from a particular year or growing season. Step 9 involves testing of the model based upon an independent data set derived from a different monitoring period.  Model options and calibration factors are held constant, and performance is judged based upon a comparison of observed and predicted nutrient, chlorophyll a, and transparency profiles. This procedure is especially recommended in systems with significant year-to-year variations in hydrology, loading, and pool water quality conditions or in cases where extensive calibration is necessary. Generally, multiyear reservoir studies are necessary in order to obtain adequate perspectives on water quality variations driven by variations in climate or flow.  A separate model input file can be created for each study year; each file uses the same segmentation scheme, model options, and calibration coefficients.  Successful simulation of year-to-year variations is important evidence of model validity.  Reiteration of previous modeling steps may be required to improve model performance over the range of monitored conditions.

 

Step 10 involves application of the model for diagnostic purposes using the List Predicted + Observed procedure.  Observed and predicted variables are listed and ranked against the model development data set.  Diagnostic variables (Table 4.5) reflect the relative importance of phosphorus, nitrogen, and light as factors controlling algal productivity.  Results are reviewed to ensure that controlling factors are consistent with the chlorophyll a and transparency submodels employed.

 

The model is applied to predict the impacts of alternative loading scenarios or management strategies in Step 11.  Typically, a separate input file is created for each management strategy and hydrologic condition (e.g., wet year, average year, dry year).  Effects of management strategies under different hydro­logic conditions can be evaluated by comparing model predictions.  Model output from multiple runs can be routed to disk files and subsequently read into a spreadsheet for tabulation, comparison, and display.  In simple cases, multiple loading scenarios can be specified within a single file (see Scheme 4)

Sensitivity to critical assumptions made in the modeling process can be evaluated by repeating Steps 1-11 using alternative assumptions and comparing results.  If the application has involved substantial calibration in Steps 6-8, management scenarios should also be evaluated using model runs with the uncalibrated model (all calibration coefficients set to 1.0).  In many cases, the relative impacts of alternative management strategies (expressed as percentage differences in predicted mean chlorophyll a, for example) will be insensitive to whether they are based upon the calibrated or the uncalibrated model.

 

Error analyses can be run to quantify uncertainty in each predicted response variable for each scenario and hydrologic condition.  Uncertainty is expressed in terms of the mean coefficient of variation (CV = standard error / mean).  The error analysis will over-predict this uncertainty in cases where the model has been calibrated to site-specific conditions.  In all cases, the uncertainty associ­ated with relative predictions (e.g., expressed as percent change in chlorophyll a resulting from different management strategies) will be substantially lower than that associated with absolute predictions (expressed in ppb).

 

In applying the model to predict future conditions, diagnostic variables are checked to ensure that controlling factors are consistent with the chlorophyll a and transparency submodels.  For example, if a phosphorus-limited chlorophyll a model (e.g., 4 or 5 ) is applied to existing conditions in Step 8, model predictions will be invalid for a future loading condition, which causes a switch from phosphorus- to nitrogen-limited conditions.  Similarly, if the phosphorus sedimentation model does not account for inflow phosphorus availability, predictions of future conditions involving a significant change in the Ortho-P/Total P load ratio may be invalid.

 

Scenario B - Existing reservoir with pool water quality data only

 

BATHTUB can be used to summarize and rank water quality conditions and to evaluate controlling factors in segments representing different reservoirs or different areas within one reservoir.  Comparisons are based upon observed water quality conditions and morphometric features specified for each segment.  Various nutrient/chlorophyll a and other eutrophication response models can be tested.  This type of analysis can be applied in the absence of nutrient loading and water balance information.  It is essentially descriptive or diagnostic in nature and does not provide a predictive basis.  Because water-balance and nutrient-balance calculations are not involved, Steps 4-7 and 11 are not performed.

 

Scenario C - Reservoir with loading data only

 

BATHTUB can be used to predict water quality conditions in a future reser­voir or in an existing reservoir lacking observed water quality data.  Lack of observed water quality data precludes calibration and testing of diffusive transport, nutrient sedimentation, and eutrophication-response models.  If the application is to an existing reservoir, a monitoring program should be implemented to obtain data for calibration and testing before using the model to evaluate management strategies.  If the application is to a proposed reservoir, the accuracy and credibility of model projections would be enhanced by first applying it successfully to an existing reservoir in the same region and, if possible, with similar morphometry and watershed characteristics.

 

Model predictions for a future reservoir refer to steady-state conditions and do not apply to the initial “reservoir aging” period, during which significant “internal” loadings may occur as a result of nutrient releases from inundated soils and vegetation.  The reservoir aging period is inherently dynamic and not suited for direct simulation via the steady-state algorithms used in BATHTUB. Approximate estimates of conditions during the reservoir aging period may be derived by specifying additional internal nutrient sources of appropriate magnitudes to reflect sediment releases during this period, based upon literature reviews and/or field data.