Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 1 Estuaries



# Appendix E: Uncertainty Analysis for Water Quality Simulation Modeling

November 30 , 2012Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

Volume 1 Estuaries



### Contents

Appendix E. Uncertainty Analysis for Mechanistic Modeling

.......................................... E-1

E.1 Introduction

................................................................................................................... E-1

E.2 Watershed (LSPC) Model Parameters

.......................................................................... E-2

E.2.1 Watershed Hydrology Model Parameters

......................................................... E-2

E.2.2 Watershed Water Quality Model Parameters

................................................... E-4

E. 3 Procedure

....................................................................................................................... E-5

E.3.1 Parameter Uncertainty

...................................................................................... E-5

E.3.2 Monte Carlo Sampling

...................................................................................... E-6

E.3.3 Input to WASP7

................................................................................................ E-7



### Figures

Figure E -1. Example of a cumulative likelihood function that summarizes the range of TN loadings produced by an advance sensitivity analysis of a LSPC

watershed model

....................................................................................................... E-7



### Tables

Table E -1. LSPC watershed model parameters investigated and ranges defining the 95 percent confidence intervals employed in ad vanced sensitivity analyses of the Pensacola and Tampa watershed

- estuary system models

........................................ E-5

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### Appendix E. **Uncertainty Analysis for Mechanistic**  **Modeling**

**E.1 Introduction** 

Florida watershed estuary systems are modeled using Loading Simulation Program in C++ ( LSPC ), Environmental Fluid Dynamics Code ( EFDC ), and Water Quality Analysis Simulation Program Version 7.3 ( WA SP7 ) . LSPC simulates watershed hydrology and water quality and

estimates the water flow and nutrient loading at inlets to a coupled estuary. EFDC and WASP7 simulate the water flow and quality, respectively, within the estuary system. Th o se system models were calibrated to effectively simulate hydrological and water quality conditions observed in the system. For instance, the values of hydrological and water quality parameters of a watershed are adjusted within reasonable bounds until the hydrological and wa ter quality conditions observed at one or more USGS gauges in the watershed are replicated with reasonable

accuracy. The resulting c alibrated watershed estuary systems accurately simulate the impact of upstream watershed conditions on downstream estuary wa ter quality.

Because the calibration of the system model requires the adjustment of hydrological and water quality model input parameter values, it is logical to assume that there is uncertainty associated

with the parameters. Moreover, because model parameters values are adjusted to achieve

simulated results that reasonabl y replicate target conditions, it follows that simulated outputs are sensitive to model input values. As such, it is unreasonable to presume that the set of model input parameter values that produce the best calibrated model is, in fact, the true set of parameter values that most exactly reflects the real system being modeled. Alt hough the set of calibrated model parameter values is likely close to reality, the variability of simulated mod el conditions due to variability in model input parameter valu es can be investigated to demonstrate the degree to which simulated downstream estuarine water quality conditions can change with respect to changes in hydrological and water quality parameter values within realistic ranges. Such an analysis is herein termed an advanced sensitivity analysis

.

Whereas traditional model sensitivity analyses perturb a subset of model input parameters within a small range of values to gauge the robustness of the calib rated model, an advanced sensitivity analysis adjusts model input parameters within a larger range that reflects the values that model parameters can take in nature. Subsequently, simulated results include a range in model outcomes that can plausibly occur.

In an advanced sensitivity analysis , the process of adjusting model parameters and assessing resulting model outcomes is guided by Monte Carlo sampling, wh erein a single value is defined, or sampled, for each queried model input parameter, and the resulting model is executed;

simulation outcomes are then tabulated and assessed. That process is repeated numerous times

until the suite of values defined (sampled) for each input model parameter sufficiently reflects the prescribed range of realistic values. T he numerous sets of simulation outcomes are aggregated and reduced to a range of outcomes (lower and upper bounds). Such an analysis applied to an LSPC model, for instance, could produce a range of nutrient loads at estuary inlets.

Alt hough ranges of model results can be informative for describing the worst and best case scenarios, it is often desirable to understand the likelihood of tho se scenarios; perhaps the lower and upper bounds on a model outcome are highly improbable , whereas model outcomes between

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th ose bounds are more likely to occur. Thus, an element of probability must be introduced into

the advanced sensitivity analysis. The calibrated model introduces such probability where one assumes the calibrated value for a input model parameter is the me an, or expected value for that parameter in the system being modeled. By definition, the calibrated model outcomes reflect the expected simulated conditions. Variability is introduced by prescribing 95 percent confidence

interval s for key input model param eters; the values for the 95 percent confidence intervals are generally guided by published parameter ranges, modeler insight, and field data.

The purpose of applying an advanced sensitivity analysis to Florida watershed- estuary systems is

to characterize the impact of varying watershed characteristics on corresponding downstream estuary water quality and ultimately assess how much estuary water quality can vary in reality. Specifically, watershed hydrology and water quality inputs are adjusted within presc ribed ranges, the range of simulated biochemical oxygen demand (BOD), TN, and TP loadings to the corresponding estuary are probabilistically assessed, and various percentiles (e.g., 5 th percentile,

95 th percentile) of simulated constituent loadings are input into the WASP estuary water quality model, and subsequent estimates estuary endpoint are calculated. The advanced sensitivity analysis wa s applied to the Pensacola and Tampa watershed

- estuary systems

. Th o se two systems represent relative extremes in watershed land use: mostly forested and mostly urban, respectively. By applying the advanced sensitivity analysis to tho se two systems

, one can reasonably assess a full range of the potential variability in predictions of estuarine water quality

across all modeled Florida estuaries.



### E.2 **Watershed (LSPC) Model**  **Parameters**

As previously mentioned, watershed model parameter values are varied to produce variability in model simulated constituent loadings to t he linked estuary. Modelers identified a subset of watershed model parameters to which simulated constitue nt loadings are most sensitive. The parameters fall into two categories: hydrology and water quality. The parameters adjusted in the advanced sensitivity analyses are briefly described below.

**E.2.1 Watershed Hydrology Model**  **Parameter s**  The following parameters characterize the hydrological aspects of the modeled watershed, and

, as such

, they predominantly affect the simulated watershed hydrology; it follows logically that simulated water quality conditions are sensitiv e to these parameters, as well.

• Lower zone nominal soil moisture storage (LZSN)

, inches , is related to both precipitation pa tterns and soil characteristics.

• Index to mean soil infiltration rate (INFILT)

, inches/hour , controls the partitioning of available moisture from precipitation into surface flow, subsurface flow, and storage components and is a function of so il characteristics and land use.

• Variable groundwater recession rate parameter (KVARY)

, inches -1 , is employed to characterize the groundwater recession rate that varies wit h season and groundwater

levels.

• Base groundwater recession rate (AGWRC)

, days -1 , is the ratio of current groundwater discharge to that 24 hours prior.

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• Deep infiltration fraction (DEEPFR)

, unitless , is the fraction of infiltration that is apportioned to deep aquifers; {1 – DEEPFR} is infiltration retained in active groundwater storage and is related to geology and groundwater recharge.

• Streambed -based riparian vegetation evapotranspiration ( ET ) frac tion (BASETP)

, unitless , is the fraction of potential ET that str eam

- adjacent vegetation uptakes.

• Model land ET fraction (AGWETP)

, unitless , is the fraction of modeled land that is susceptible to groundwater storage- based ET because of a s hallow groundwate r table (e.g., fraction of model covered by wetlands).

• Vegetation

- retained rainfall fraction (CEPSC), unitless , is the percentage of rainfall that never reaches land surface and eventually evaporates (monthly varying parameter), and is related to type of vegetation present on a parcel of land; all monthly values of

CEPSC s for each land use and soil class are adjusted by a single factor

.

• Nominal upper

- zone soil moisture storage (UZSN)

, inches , dictates the amount of water stored in the upper zone and made av ailable for ET (monthly varying parameter); related to surface soil conditions and land use; all monthly values of UZSN for each land use and soil class are adjusted by a single factor

.

• Interflow

- from

- surface coefficient (INTFW)

, unitless , determines the a mount of water

that enters the subsurface from surface detention storage and becomes interflow (monthly varying parameter); related to soils, topography , and land use. All monthly values of

INTFW for each land use and soil class are adjusted by a single factor

.

• Interflow recession coefficient (IRC)

, unitless

, is the ratio of current daily interflow discharge to that of the previous day (monthly varying parameter); like INTFW, it is

related to soil s topography and land use. All monthly values of IRC for each land use and soil class are adjusted by a single factor

.

• Index to lower zone ET (LZETP)

, unitless , is a coefficient that governs ET potential (monthly varying parameter) and is related to vegetation type and root depth; to preserve the calibrated temporal variation, all monthly values of LZETP for each land use and soil class are adjusted by a single factor.

Each modeled watershed has a number of prescribed land uses (e.g. , urban pervious, agricu ltural) and soil classes (e.g.

, sandy, clayey). The Pensacola watershed model has 15 land uses and 3 soil classes; the Tampa watershed model has 16 land uses and 5 soil classes. Each of th o se parameter s can have a unique value for each land use and soil cl ass, al though certain land uses behave similarly and their parameters for th o se tied land uses take the same value. On the basis

of th ose considerations, 300 hydrological parameters were adjusted in the advanced sensitivity analysis for the Pensacola water shed model and 525 hydrological parameters were adjusted in the advanced sensitivity analysis for the Tampa watershed model.

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**E.2.2 Watershed Water Quality Model Parameters** 
The following parameters describe the water quality characteristics of the modeled watersh ed. Variation in the values of these parameters produces variability in simulated watershed water quality (BOD, TN, and TP loadings), al though simulated watershed hydrology is not sensitive to these parameters.

• Rate of surface runoff to remove 90 percent of stored constituent (WSQOP)

, inches/hour

, is the amount of runoff necessary to remove 90 percent of the accumulated

constituent on land surface.

• Constituent accumulation rate (ACCUM) , pounds/acre/day

, is the rate at which a constituent builds up on the ground surface in a watershed; varying monthly, the temporal variation in this parameter is more important than the magnitude of the individual monthly values. A s such

, all mont hly values of ACCUM for each land use, soil class, and

constituent are adjusted by a single factor.

• Storage limit of constituent (SQOLIM) , pounds/acre

, is the maximum constituent mass that can be stored on the ground surface in a watershed; al though this parameter varies monthly, in modeling the monthly varying values are a multiple o f the ACCUM value assigned to the corresponding constituent, land use, and soil class.

• Interflow constituent concentration (INTERCONC)

, mg/L , is the monthly varying concentration of a constituent in the upper part of the unsaturated zone; varying monthly, the temporal variation in this parameter is more important than the magnitude of the individual monthly values. A s such , all monthly values of INTERCONC for each land use, soil class

, and constituent are adjusted by a single factor; th at single factor is q ueried

in th e advanced sensitivity analysis.

• Groundwater constituent concentration (GRNDCONC) , mg/L , is the monthly varying concentration of a constituent in the subsurface saturated zone; varying monthly, the temporal variation in this parameter is more important than the magnitude of the individual monthly values. A s such , all monthly values of GRNDCON C for each land use, soil class

, and constituent are adjusted by a single factor . T his parameter must be less than or equal to the INTERCONC value assigned to the corresponding constituent, land use, and soil class.

• Constituent first

- order decay rate (DECA Y) , day -1

, is the rate at which the in

- stream concentration of a constituent is chemically mitigated because of the transformation of the constituent into a product; this parameter varies by stream type.

• Temperature correction for first

- order decay (TCDECAY)

, unitless

, a temperature

based adjustment that affects the in

- stream decay rate of a constituent; this parameter varies by stream type.

• BOD decay rate at 20 ° C (KBOD 20)

, hour -1

, is the rate at which BOD decays at standard temperature; this parame te r varies by stream type.

• BOD settling rate (KBODSET)

, meters/hour

, th e removal rate of in

- stream BOD due to settling; this parameter varies by stream type.

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- 4Table E-1

. LSPC watershed model par ameters investigated and ranges defining

the 95 percent confidence intervals employed in advanced sensitivity analyses
of the Pensacola and Tampa watershed

- estuary system models

Parameter Pensacola Watershed Tampa Watershed

INFILT [0.05, 0.5] ± 50%

AGWRC [0.950, 0.999] [0.850, 0.999]

BASETP [0, 0.1] [0, 0.2]

AGWETP (only wetlands) [0.2, 0.8] [0.5, 0.9]

CEPSC ± 50% ± 50%

INTFW ± 50% ± 100% LZSN [6, 15] [6, 15]

KVARY [0, 1] ± 50%

DEEPFR [0, 0.2] [0, 0.6]

UZSN [0, 2] ± 100% Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

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As with the hydrological parameters defined above, the water quality parameters can vary with

land use and soil class. Additionally, the parameters can vary by constituent, and s ome var y by

stream type . On the basis of th o se consideration s, in addition to the fact that some land uses and constituents are modeled to behave similarly with respect to some of the water quality parameters, 1

, 387 water quality parameters we re investigated in the advanced sen sitivity analysis

of the Pensacola watershed

- estuary system ; 1,870 water quality parameters we re investigated in the advanced sensitivity analysis of the Tampa watershed

- estuary system.



### E.3 **Procedure**

**E.3.1 Parameter Uncertainty** 
As stated previously, the desired outcome of the advanced sensitivity is to understand how estuary water quality varies because of variability in upstream watershed hydrology and water quality. More pointedly, it is desirable that the likelihood associated with predicted estuary water

qua lity be characterized. T o characterize model outcomes probabilistically, uncertainty in watershed model inputs must be defined. Such uncertainty is warranted by the fact that whereas the set of calibrated watershed model parameters provides the best solution, the set of parameter

values m ight not exa ctly reflect watershed conditions in reality. However, it is assumed that the calibrated parameter values are the expected, or mean, parameter values.

In addition to identifying the parameters that require attention in the advanced sensitivity analysis, mo delers prescribed ranges of values within which the parameters could plausibly vary. For a model parameter, that range of values is informed by modeling insight, a knowledge of the modeled watershed, and published data. For the purposes of Monte Carlo anal ysis

, th o se ranges of values were interpreted as the 95 percent confidence interval. In conjunction with the assumption that a parameter’s calibrated value is the expected ( e.g ., mean value) and assumption of normality in the stochastic distribution of wat ershed model parameters, the prescribed 95 percent confidence intervals characterize the likelihoods associated with each model parameter listed above. The 95 percent confidence intervals prescribed for the Pensacola and Tampa

watershed models are listed in Table E -1.

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- 5Parameter Pensacola Watershed Tampa Watershed

IRC [0.50, 0.85] [0.5, 0.85]

LZETP ± 50% ± 50%

WSQOP [0.1, 0.9] [0.1, 0.9]

ACCUM ± 100% ± 100%

SQOLIM [1, 6] [1, 6]

INTERCONC ± 100% ± 100%

GRNDCONC ± 100% ± 100%

DECAY (only TN, TP) TN: [0.00, 0. 25] TN: [0.00, 0. 25]
TP: [0.000, 0.025] TP: [0.000, 0.025]

TCDECAY (only TN, TP) [1.00, 1.07] [1.00, 1.07]

KBOD20 [0, 0.2] [0, 0.2]

KBODSET [0, 0.1] [0, 0.1] Technical Support Document for U.S. EPA’s Proposed Rule for Numeric Nutrient Criteria,

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**E.3.2 Monte Carlo Sampling** 
To convey the prescribed uncertainty in model input parameters to model outputs, a Monte Carlo sampling approach wa s employed. Monte Carlo sampling execution begins with selectin g (sampling) of a single value for each uncertain model parameter between the modeler

- defined lower and upper bounds. The collection of selected values comprises a complete set of model inputs necessary to execute a single instance of the watershed model; that set of sampled values is alternatively called a realization. The model is subsequently executed and the resulting model outcomes are tabulated. In this application of Monte Carlo analysis, the model outcomes of

interest a re the simulated annual BOD, TN, and TP loadings at subwatersheds that are inlets to the coupled estuary system. The process of sampling a realization from the set of stochastic parameters, executing the resulting model, and tabulating the model outcomes i s repeated many times until the set of sampled realizations sufficiently reflects the prescribed uncertainty in model input parameters. The sampling of a parameter is guided by the probability distribution

defined for th at parameter; values associated with higher probabilities are sampled more frequently than those assoc iated with lower probabilities.

After Monte Carlo sampling is complete, the many instances in key model prediction s (BOD, TN, TP loadings at estuary inlets) are aggregated probabilistic ally such that a likelihood curve can be constructed to represent both the range in plausible model outcomes and the likelihood associated with the outcomes within that range. Figure E -1 is an example of such a cumulative likelihood curve reflecting the variability in TN loadings produced by an advanced sensitivity analys is of a non- Florid ian watershed. For all values in the range of simulated TN loadings, the

cumulative lik elihood curve defines the probability of occurrence, solely on the basis of variability in model input parameter values. For instance, the curve suggests that it is 95 percent likely that the predicted s pring TN loading will be less than 7 ,000 lb and 5 percent likely that the predicted s pring TN loading will be less than 5 ,500 lb. The median predicted TN loading is approximately 6 ,200 lb. Whereas traditional modeling would produce a single predicted s pring TN loading, the advanced sensitivity analysis provides a range of values and likelihoods associated with predictions within th at range.

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0 10 20 30 40 50 60 70 80 90 100

0 5000 10000 15000 20000Cumulative Likelihood



### Total Nitrogen Spring Loading (lb) 

## Total Nitrogen Spring Loading Likelihood Function

Figure E-1

. Example of a cumulative likelihood function that summarizes the range of TN loadings produced by
an advance sensitivity an alysis of a LSPC watershed model

**E.3.3 Input to WASP7** 
The results of the Monte Carlo sampling are cumulative likelihood curves, similar in structure to that presented in Figure E -1 . The curves define the range of plausible predicted watershed BOD, TN, and TP loadings to the coupled estuary, as well as the likelihood associated with the predicted loadings from each watershed subbasin that is an inlet to the coupled estuary.

To further simulate the range in plausible estuarine water quality predictions, the probabilistic information must be input to the WASP7 model of the coupled estuary. The multiday run times associated with the WASP7 models for the Pensacola and Tampa watersheds preclude a complete Monte Carlo analysis, wherein the uncertain constituent loadings are exhaustively sampled and resulting realizations inform numerous WASP7 model executions.

To expedite the analysis and simplify the desired predictions, the 5 th and 95 th percentile loadings predicted for the estuary inlets we re gleaned from the suite of cumulative likelihood curves. Intuitively, the 5 th percentile loadings reflect plausibly low constituent source conditions in the estuary; conversely, the 95 th percentile loadings reflect plausibly high constituent source conditions in the estuary. The calibrated WASP7 estuary model wa s executed for both conditions. The resulting set of WASP7 predictions reflect a plausible range in estuarine water quality with res pect to BOD, TN, and TP concentrations.

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