Final Report V2 November 13, PREPARED BY: Tetra Tech, Inc Powers Ferry Rd. SE, Suite 202 Atlanta, Georgia Phone: (770)

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1 PREPARED BY: Tetra Tech, Inc Powers Ferry Rd. SE, Suite 202 Atlanta, Georgia Phone: (770) Final Report V2 November 13, 2015 PREPARED FOR: Department of the Army Savannah District, Corps of Engineers 100 W Oglethorpe Avenue Savannah, Georgia Contract: 100-ATL-T32468

2 Table of Contents TABLE OF CONTENTS... I REVISION HISTORY... III LIST OF FIGURES... IV LIST OF TABLES... IX 1.0 EXECUTIVE SUMMARY INTRODUCTION FIRST ORDER VARIANCE ANALYSIS (FOVA): BACKGROUND IMPLEMENTATION BASELINE CONDITIONS MODEL COMPONENTS UNDER EVALUATION ESTIMATES OF INPUT DATA AND PARAMETRIC UNCERTAINTY Model Bathymetry Freshwater Inflows Water Surface Elevations (Ocean Tide) EFDC temperature boundary conditions Open Boundary Salinity Concentration Solar Radiation Bottom Roughness Background dispersion coefficient Marsh Size Sediment Oxygen Demand WASP Input Temperature from EFDC Dissolved Oxygen Boundary Concentrations Wind Scaling Factor DIMENSIONLESS SENSITIVITY COEFFICIENTS (DSC) WATER SURFACE ELEVATION CURRENT SPEED FLOW TEMPERATURE SALINITY DISSOLVED OXYGEN UNCERTAINTY ESTIMATES WATER SURFACE ELEVATION CURRENT SPEED FLOW TEMPERATURE SALINITY DISSOLVED OXYGEN PSU SALINITY BOUNDARY Prepared by Tetra Tech, Inc. i

3 7.0 CONCLUSIONS REFERENCES Prepared by Tetra Tech, Inc. ii

4 Revision History The following table presents the revision history of the 2015 SHEP model Uncertainty Analysis Report. Table i-1 Revision History of 2015 SHEP model Uncertainty Analysis Report Revision Number Release Date Comments 0 February 27, 2015 Initial report release. 1 May 5, 2015 Final V1 report release. 2 November 13, 2015 Final V2 report release. Prepared by Tetra Tech, Inc. iii

5 List of Figures Figure 4-1 Location of stations used for the uncertainty analysis... 7 Figure 5-1 DSCs for Water Surface Elevation at station USGS (Front River at I-95 Bridge) Figure 5-2 DSCs for Water Surface Elevation at station USGS (Front River at Houlihan Bridge) Figure 5-3 DSCs for Water Surface Elevation at station USGS (Middle River at Houlihan Bridge) Figure 5-4 DSCs for Water Surface Elevation at station USGS (Little Back River at Houlihan Bridge) Figure 5-5 DSCs for Water Surface Elevation at station USGS (Front River at USACE Dock) Figure 5-6 DSCs for Water Surface Elevation at station USGS (Front River at Fort Pulaski) Figure 5-7 DSCs for Current Speed at surface layer at station USGS (Front River at I-95 Bridge) Figure 5-8 DSCs for Current Speed at surface layer at station USGS (Front River at Houlihan Bridge) Figure 5-9 DSCs for Current Speed at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 5-10 DSCs for Current Speed at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-11 DSCs for Current Speed at surface layer at station USGS (Front River at USACE Dock) Figure 5-12 DSCs for Current Speed at surface layer at station USGS (Front River at Fort Pulaski) Figure 5-13 DSCs for Flow at surface layer at station USGS (Front River at I-95 Bridge) 23 Figure 5-14 DSCs for Flow at surface layer at station USGS (Front River at Houlihan Bridge) Figure 5-15 DSCs for Flow at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 5-16 DSCs for Flow at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-17 DSCs for Flow at surface layer at station USGS (Front River at USACE Dock) Figure 5-18 DSCs for Flow at surface layer at station USGS (Front River at Fort Pulaski)25 Figure 5-19 DSCs for Temperature at surface layer at station USGS (Front River at I-95 Bridge) Figure 5-20 DSCs for Temperature at bottom layer at station USGS (Front River at I-95 Bridge) Figure 5-21 DSCs for Temperature at surface layer at station USGS (Front River at Houlihan Bridge) Figure 5-22 DSCs for Temperature at bottom layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. iv

6 Figure 5-23 DSCs for Temperature at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 5-24 DSCs for Temperature at bottom layer at station USGS (Middle River at Houlihan Bridge) Figure 5-25 DSCs for Temperature at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-26 DSCs for Temperature at bottom layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-27 DSCs for Temperature at surface layer at station USGS (Front River at USACE Dock) Figure 5-28 DSCs for Temperature at bottom layer at station USGS (Front River at USACE Dock) Figure 5-29 DSCs for Temperature at surface layer at station USGS (Front River at Fort Pulaski) Figure 5-30 DSCs for Temperature at bottom layer at station USGS (Front River at Fort Pulaski) Figure 5-31 DSCs of Salinity at surface layer at station USGS (Front River at I-95 Bridge). DSCs are 0 because simulated salinity was close to 0 PSU at this station Figure 5-32 DSCs of Salinity at bottom layer at station USGS (Front River at I-95 Bridge). DSCs are 0 because simulated salinity was close to 0 PSU at this station Figure 5-33 DSCs of Salinity at surface layer at station USGS (Front River at Houlihan Bridge) Figure 5-34 DSCs of Salinity at bottom layer at station USGS (Front River at Houlihan Bridge) Figure 5-35 DSCs of Salinity at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 5-36 DSCs of Salinity at bottom layer at station USGS (Middle River at Houlihan Bridge) Figure 5-37 DSCs of Salinity at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-38 DSCs of Salinity at bottom layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-39 DSCs of Salinity at bottom layer at station USGS (Front River at USACE Dock) Figure 5-40 DSCs of Salinity at surface layer at station USGS (Front River at USACE Dock) Figure 5-41 DSCs of Salinity at bottom layer at station USGS (Front River at Fort Pulaski) Figure 5-42 DSCs of Salinity at surface layer at station USGS (Front River at Fort Pulaski) Figure 5-43 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at I- 95 Bridge) Figure 5-44 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at I- 95 Bridge) Figure 5-45 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. v

7 Figure 5-46 Figure 5-47 Figure 5-48 Figure 5-49 Figure 5-50 Figure 5-51 Figure 5-52 Figure 5-53 Figure 5-54 Figure 6-1 Figure 6-2 Figure 6-3 Figure 6-4 Figure 6-5 Figure 6-6 Figure 6-7 Figure 6-8 Figure 6-9 Figure 6-10 Figure 6-11 Figure 6-12 Figure 6-13 Figure 6-14 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at Houlihan Bridge) DSCs of Dissolved Oxygen at surface layer at station USGS (Middle River at Houlihan Bridge) DSCs of Dissolved Oxygen at bottom layer at station USGS (Middle River at Houlihan Bridge) DSCs of Dissolved Oxygen at surface layer at station USGS (Little Back River at Houlihan Bridge) DSCs of Dissolved Oxygen at bottom layer at station USGS (Little Back River at Houlihan Bridge) DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at USACE Dock) DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at USACE Dock) DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at Fort Pulaski) DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at I-95 Bridge) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at USACE Dock) Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at Fort Pulaski) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at USACE Dock) Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. vi

8 Figure 6-15 Figure 6-16 Figure 6-17 Figure 6-18 Figure 6-19 Figure 6-20 Figure 6-21 Figure 6-22 Figure 6-23 Figure 6-24 Figure 6-25 Figure 6-26 Figure 6-27 Figure 6-28 Figure 6-29 Figure 6-30 Figure 6-31 Figure 6-32 Figure 6-33 Figure 6-34 Figure 6-35 Figure 6-36 Figure 6-37 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. vii

9 Figure 6-38 Figure 6-39 Figure 6-40 Figure 6-41 Figure 6-42 Figure 6-43 Figure 6-44 Figure 6-45 Figure 6-46 Figure 6-47 Figure 6-48 Figure 6-49 Figure 6-50 Figure 6-51 Figure 6-52 Figure 6-53 Figure 6-54 Figure 6-55 Figure 6-56 Figure 6-57 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Median surface salinity concentrations predicted for the month of August of The lower limits of the blue legend separates the region of salinity concentrations below 0.5 PSU (upstream) and above 0.5 PSU (downstream) Median surface salinity concentrations predicted for the month of August of The medians were computed for each cell using the time series of baseline predictions (calibrated model) +1 standard deviation error estimate Median surface salinity concentrations predicted for the month of August of The medians were computed for each cell using the time series of baseline predictions (calibrated model) -1 standard deviation error estimate Prepared by Tetra Tech, Inc. viii

10 List of Tables Table i-1 Revision History of 2015 SHEP model Uncertainty Analysis Report... iii Table 4-1 List of stations used for the uncertainty analysis... 6 Table 4-2 Summary of input variables and model parameters included in the uncertainty analysis.. 8 Table 4-3 Estimates of uncertainty in input variables and model parameters of the 2015 SHEP model... 9 Table 5-1 Summary of model perturbations conducted to obtain the DSCs Table 6-1 Statistic summary of model output uncertainty for WSE for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-2 Statistic summary of model output uncertainty for Current Speed for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-3 Statistic summary of model output uncertainty for Flow for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-4 Statistic summary of model output uncertainty for temperature for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-5 Statistic summary of model output uncertainty for salinity predictions for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-6 Statistic summary of model output uncertainty for Dissolved Oxygen predictions for the 2015 SHEP model calibration period of 1/1/2013 4/30/ Table 6-7 Statistic summary of model output uncertainty for Dissolved Oxygen predictions for the 2015 SHEP model summer calibration period of 7/1/2013 9/30/ Prepared by Tetra Tech, Inc. ix

11 1.0 EXECUTIVE SUMMARY Uncertainty analysis is a complementary activity to model calibration and validation, performed to investigate the impacts of different sources of error on the predictions of a calibrated model (McIntyre et al and Refsgaard et al. 2007). This analysis evaluates the potential uncertainty in the model predictions resulting from the propagation of epistemic sources of uncertainty such as errors in the model structure, input data, and model parameter values. An uncertainty analysis was performed for the 2015 Savannah Harbor model, which was developed for the 2015 Savannah Harbor Expansion Project (SHEP), and herein identified as the 2015 SHEP model. The three-dimensional hydrodynamic and water quality 2015 SHEP model was calibrated to water surface elevations, current speeds (velocity), flows, temperature, salinity, and dissolved oxygen at monitoring stations located throughout the Savannah Harbor and River from January 1, 2013 through April 20, While three-dimensional hydrodynamic and water quality models can be used for predictive purposes, there is some level of uncertainty in the model predictions due to variability in model input variables and model parameters. Therefore, it is highly useful to estimate the level of confidence that may be associated to the model predictions in the presence of different sources of variability or uncertainty. The purpose of the uncertainty analysis presented herein is to provide a compressive assessment of the potential level of uncertainty or otherwise level confidence that may be placed in the 2015 SHEP model predictions given existing uncertainties or variability in critical aspects of the model such as bathymetry, boundary conditions, and model parameterizations. It is important to note that the uncertainty estimates should not be used to accept or reject a calibrated model, but to document the most important sources of errors involved in a model application and to estimate the level of confidence that may be expected in the model predictions due to these sources of uncertainty. The uncertainty analysis evaluated the impacts of existing errors in the 2015 SHEP model structure variables, input variables, and model parameters, and parameters on the 2015 SHEP model predictions. For example, the level of confidence on the predictions of salinity was estimated by evaluating uncertainties in the model bathymetry, marsh area size, freshwater flows, temperature boundary conditions, salinity boundary conditions, bottom roughness, and dispersion coefficient. Literature and reference values were used to determine the estimate of uncertainty for each model component evaluated in the uncertainty analysis. The estimates of confidence around the model predictions were evaluated using the First Order Variance Analysis (FOVA), which is a robust and a less computer-intensive alternative to the traditional Monte Carlo Analysis (Blumberg and Georgas 2008; Sucsy et al 2010; Camacho et al 2014). Overall, results from the FOVA analysis showed that existing uncertainties in the 2015 SHEP model were low and will likely cause a level of uncertainty of less than 10% in the model predictions values. In other words, the confidence in the 2015 SHEP model predictions is approximately 90%. The 2015 SHEP model will be used to evaluate future deepening of the harbor and the associated impacts on DO and salinity. Because of this deepening, the salinity intrusion may move further upstream and impact freshwater marshes and upstream water supplies. The uncertainty analysis indicated that existing uncertainties in the model input data and parameters caused a minimal change in the predictions of the upstream boundary of the salinity intrusion. The potential uncertainty or level of confidence in the predictions of DO was approximately ±0.5 mg/l, which is typically for this type of model. The 2015 SHEP model salinity predictions can be impacted the most by errors in open boundary salinity concentrations, model bathymetry, and freshwater flows, while the DO predictions can be impacted the most by errors in input temperatures, DO boundary conditions, bathymetry, salinity open boundary concentrations, and SOD. Prepared by Tetra Tech, Inc. 1

12 2.0 INTRODUCTION In 2014, the U.S. Army Corps of Engineers (USACE) Savannah District contracted Tetra Tech to update the 2006 Savannah Harbor Expansion Project (SHEP) hydrodynamic and water quality models to reflect new data collected over the last 7 years (2008 through 2014). The updated models, referred to as the 2015 SHEP calibrated model, will be used to evaluate navigation and mitigation features outlined in the General Re-evaluation Report (USACE 2012) for the Savannah Harbor, and how they impact salinity and Dissolved Oxygen (DO). As part of these modeling efforts, Tetra Tech was contracted to perform an uncertainty analysis of the updated model to determine the potential impacts of different sources of error on the predictions of Water Surface Elevations, Current Speeds (velocity), Flows, Temperature, Salinity and DO. Uncertainty analysis is a complementary activity to model calibration and validation, performed to investigate the impacts of different sources of error on the predictions of a calibrated model (McIntyre et al and Refsgaard et al. 2007). This analysis evaluates the potential uncertainty in model predictions resulting from the propagation of epistemic sources of uncertainty, such as errors in model structure, input data, and model parameter values. The strategies for uncertainty analyses are generally classified into analytical and approximate methods, and the latter provide the most practical analysis (Matott et al. 2009; Camacho et al. 2014). The approximate methods include stochastic strategies such as Bayesian Monte Carlo Analysis (BMC) (Kennedy and O'Hagan 2001 and Camacho and Martin 2013), Bayesian Total Error Analysis (BATEA) (Kuczera et al. 2007), and the Generalized Uncertainty Estimation Method (GLUE) (Beven and Binley 1992), and deterministic strategies such as First Order Variance Analysis (FOVA) (Blumberg and Georgas 2008). Stochastic strategies are robust strategies of general applicability, but have the limitation of being computationally intensive, requiring hundreds and often thousands of simulations to obtain meaningful estimates of uncertainty. For this reason, most applications of BMC, BATEA, GLUE and similar methods are related to aggregated or conceptual models of climatology, meteorology, hydrology and groundwater hydrology, rather than to distributed or gridded models such as those of estuarine hydrodynamics. FOVA represents an effective and pragmatic approach for these latter complex models because of its high efficiency and low computational requirements. FOVA performs a first order Taylor Series expansion of the model around the calibrated predictions to obtain estimates of uncertainties (e.g. uncertainty bounds such as ± 1 standard deviation prediction error) due to model structure errors, errors in input datasets, and/or errors in model parameter values (Blumberg and Georgas 2008). This process is performed for each model component presumed to cause uncertainty in the model predictions. Then, the total uncertainty is computed as the linear superposition of the uncertainty caused by each individual model component. The process described above typically requires few model executions and the resulting uncertainty estimates are comparable to those obtained using traditional Monte Carlo simulations (Camacho et al. 2014). In the 2015 SHEP model, a mechanistic modeling approach was used to investigate the fundamental processes governing the circulation, transport, and biochemical processes. The mechanistic model is a coupled hydrodynamic and water quality model based on the Environmental Fluid Dynamics Code (EFDC) and the Water Quality Analysis Simulation Program Version 7.0 (WASP7). The coupled model represents a state-of-the-art predictive system of high sophistication. Given the complexity of the model, FOVA was selected as the most appropriate approach to conduct the uncertainty analysis. Similar studies have also identified FOVA as the most cost-effective alternative to perform uncertainty analysis in hydrodynamic studies (Blumberg and Georgas 2008; Thomson et al. 2008; Camacho et al. 2014). Prepared by Tetra Tech, Inc. 2

13 3.0 FIRST ORDER VARIANCE ANALYSIS (FOVA): BACKGROUND First Order Variance Analysis (FOVA) is a strategy to compute the total variance associated to a model prediction as a result of input data and parameter errors. Within FOVA, the variance associated to input datasets and/or model parameters (i.e. input data and parameter uncertainty respectively) is propagated to the model predictions using a first-order Taylor series approximation of the predictive model. Then, after the output variances are computed for each individual source of uncertainty, they are summed up to generate the total variance of the model prediction. In addition, FOVA can also provide estimates of model sensitivity to the input data or parameters of interest which are useful to identify the most relevant features of a model for a given application. FOVA is a less computationally intensive alternative to other commonly used uncertainty analysis strategies such as Bayesian Monte Carlo (BMC) and Markov Chain Monte Carlo (MC 2 ), particularly in cases where the complexity of the models preclude the use of these later strategies. In addition, recent hydrodynamic investigations show that the results of FOVA are comparable to those obtained using traditional Monte Carlo simulations (Camacho et al. 2014). A detailed explanation of FOVA is presented below. In order to calculate the uncertainty in the predictions of a variable ( Y ) due to uncertainty in a set of input data ( X ) or model parameters ( θ ), FOVA computes the first two statistical moments of a first-order Taylor expansion of the function Y F( X, θ) (Blumberg and Georgas, 2008). For sake of generality, F constitutes a mathematical model representation of Y (e.g. water surface elevation), X a matrix of p-input variables x x,...,, 2 x p 1 (e.g. freshwater flows, open boundary water levels), and θ a vector of q-model parameters θ 1, θ2,..., θ q (e.g. bottom roughness, dispersion coefficients). The expansion of the function F (X) is performed around a baseline simulation (e.g. calibrated model prediction) Y0 F( X0, θ0) where X 0 ( x1 o, x2o,..., x po) denotes the baseline set of input variables and θ the baseline parameters values. The 0 expansion is given by, p q F F F( X ) f ( x1 o, x2o... x po, 1 o, 2o..., qo) xi xio i io (1) x i 1 i xi xio i 1 i xi xio where p and q represent the number of input variables and parameters under analysis respectively; x io and are the baseline or unperturbed values of the i-th input variable and model parameter respectively; and io F / x i and F / are the local changes of the model predictions Y due to changes in the input variable i respectively. The mean and variance of the model predictions Y are x i, and model parameter i estimated by computing the first two moments of Eq. (1) as (e.g. Blumberg and Georgas 2008), E Y] E[ F( X )] f ( x, x... x,,..., ) (2) [ 1e 2e pe 1e 2e qe Var( Y) q i 1 F 2 Y i i o p i 1 2 F x i x x E( i io ) i o E( xi xio ) q q i 1 j 1, j i 2 2 F p i 1 j 1, j i i i o p F F x j x x j i x x jo i io E F x i j x x j io jo E j x x x x i jo io j jo (3) Prepared by Tetra Tech, Inc. 3

14 A common strategy to implement FOVA, and in particular to obtain a more tractable form of Eq. (3) is to assume that the input variables ( x 1o, x2o,..., x po) and model parameters ( 1 o, 2o..., qo) are statistically independent. This assumption reduces Eq. (3) to, Var 2 2 p q 2 F F ( Y) Y xi i i 1 xi i i xi x 1 io i o (4) 2 where is the variance associated with the model predictions (i.e. output model uncertainty), and Y 2 and i are the variances of the i-th input variable (i.e. input uncertainty) and model parameter (i.e. parametric uncertainty). The terms F / x i and F / quantify the changes in the output x i x io i i io variable Y as a result of a perturbation in the input variable x i and model parameter i from the baseline conditions x o and o respectively. The derivative term F can be evaluated numerically using a simple difference scheme. For example, using forward differencing F F( xio xi ) F( xio), where F( x io xi ) is the model prediction obtained after perturbing the input variable x i in a magnitude equivalent to xi from the baseline value x io. This same procedure can be used to evaluate the changes in the model predictions due to changes in the parameters values. Note that Eq. 4 can be alternatively expressed in terms of coefficients of variation (CV) if the standard deviations are normalized by the mean or baseline values of their corresponding variables (i.e. CV Y Y / Yo, CV xi i / xio, CV i / io ). In this case Eq. 4 can be rewritten as CV 2 Y p q F 2 xi xo F DSC i CVxi DSC CV i i i o * * i 1 i 1 As part of the FOVA analysis, dimensionless sensitivity coefficients (DSC) are also computed using Eq. (6) to identify the degree of sensitivity of the model predictions to changes in a particular model component such as model structure, input data, or model parameters. The DSC represents the ratio between the percentage change of a model prediction from the calibrated prediction, and the percentage change of a model component (e.g. a model parameter) from the calibrated value. The interpretation of the DSCs is straightforward. A DSC of 1 suggests that an x % change on a model component causes the same x % change on the model prediction. Likewise, a DSC of 0.5 suggests that an x % change on a model component causes a 0.5x % change on the model prediction, and a DSC of 2 suggests that an x % change on a model component causes a 2x % change on the model prediction. The evaluation of DSC is an effective approach to understand the relative sensitivity of model output variables to different model components. Where DSC represent dimensionless sensitivity coefficients that quantify the relative importance of changes in the input variable x i and model parameter i on the model predictions. These coefficients can be computed by (Blumberg and Georgas, 2008) DSC (6) F i xi xo F i o F / xi / F( xi ) / xi and DSCi F / i / F( i ) / i i o xi xo The implementation of FOVA can be summarized in the following five steps (Blumberg and Georgas 2008): 2 2 xi (5) Prepared by Tetra Tech, Inc. 4

15 a) Define the baseline values of the model parameters, input variables and model predictions. Typically, the baseline conditions are obtained by calibrating the model. b) Identify the model parameters and input and output variables of interest. c) Estimate the standard deviation i (or alternatively the coefficient of variation CV i ) for each input variable and model parameter under analysis (i.e. estimate the degree of uncertainty in each parameter and input variable). d) Define a perturbation magnitude for each input variable, and run the model for the perturbed conditions. Use the resulting model predictions to compute the DSC with Eq. 6. e) Propagate the uncertainty in the input variables and parameters to the output variables using Eqs. 4 or 5 (i.e. compute the CV (Eq. 5) or standard deviation i (Eq. 4) of the output variable of interest). Prepared by Tetra Tech, Inc. 5

16 4.0 IMPLEMENTATION This section presents a detailed description of the implementation of FOVA for the 2015 SHEP model. The method was implemented following the procedure described in Section 3.0 (steps a-e). Section 4.1 describes the baseline conditions for the uncertainty analysis. Section 4.2 identifies the output variables of interest and the model locations where the analyses are performed. Section 4.2 also identifies the input variables and model parameters considered in this investigation as the most relevant sources of uncertainty impacting the prediction of the target output variables. Section 4.3 presents an analysis of error on the input variables and model parameters identified in Section 4.2. The estimates of error in this section are expressed in terms of a standard deviation or a coefficient of variation for the implementation of FOVA. Section 5.0 presents the sensitivity analysis of the output variables of interest due to perturbations in the input variables and model parameters defined in Section 4.2. Finally, Section 6.0 presents the evaluation of uncertainty estimates in the output variables of interest. 4.1 Baseline conditions The uncertainty analysis was performed as a complementary activity to the 2015 SHEP model calibrationvalidation in order to quantify the potential impacts of existing uncertainties in input datasets and model parameters on the predictions of the model (Tetra Tech 2015). These impacts are expressed by means of confidence bounds around the predictions of the calibrated model. The analysis focused on the following output variables: Water Surface Elevation (WSE), Current Speed (CS), Temperature (Temp), Salinity (Sal), and Dissolved Oxygen (DO). To implement FOVA, the uncertainty analysis used model predictions from the calibration period (January 1, 2013 April 30, 2014) of the 2015 SHEP model (Tetra Tech 2015). The uncertainty analysis results are presented at six United States Geological Survey (USGS) and Dial-Cordy stations located along the Front River, Middle River and Little Back River (Table 4-1 and Figure 4-1). The results at these stations are representative of the potential uncertainty in other regions of the estuary. Table 4-1 List of stations used for the uncertainty analysis USGS ID Dial-Cordy ID Station Description EFDC-WASP cell location I J FR-26 Front River at Fort Pulaski FR-21 Front River at USACE Dock FR-09 Front River at Houlihan Bridge Middle River at Houlihan Bridge Little Back River at Houlihan Bridge SR-14 Front River at I-95 Bridge Prepared by Tetra Tech, Inc. 6

17 Figure 4-1 Location of stations used for the uncertainty analysis Prepared by Tetra Tech, Inc. 7

18 4.2 Model components under evaluation The model structure variables, input variables, and model parameters listed in Table 4-2 represent the most important factors controlling the ability of the model to predict WSE, CS, Flow, Temp, Sal, and DO. The uncertainty analysis was focused on evaluating the impacts of existing errors in these variables, and parameters on the predictions of the 2015 SHEP model. The estimates of error in each of the variables included in the first column of Table 4-2, is provided in Table 4-3 and discussed in Section 4.3. These error estimates represent the input uncertainty for the model. Table 4-2 Summary of input variables and model parameters included in the uncertainty analysis Model component Model Output variable WSE CS Flow Temp Sal DO Model structure Model bathymetry EFDC x x x x x x Marsh area size EFDC x x x x x Input variable Freshwater flows at Clyo EFDC x x x x x x WSE at open boundary (Ocean tide) EFDC x x x EFDC temperature boundary conditions EFDC x x Open boundary salinity concentration EFDC x x x x Solar radiation EFDC x WASP input temperature (from EFDC) WASP x DO boundary concentrations WASP x Model parameter Bottom roughness EFDC x x x x x Background dispersion coefficient EFDC x x x x x Initial bed temperature EFDC x Sediment Oxygen Demand (SOD) WASP x Wind scaling factor in WASP WASP x Indicates if the variables listed in the first column are included in the uncertainty analysis 4.3 Estimates of input data and parametric uncertainty For the FOVA analysis, the level of uncertainty in the model structure components, input variables, and model parameters must be defined. This uncertainty can be expressed in terms of a standard deviation (σ) or in terms of a coefficient of variation (CV), as explained in Section 3.0. The standard deviation (σ) is useful to describe the errors in input variables and model parameters when the errors are independent of the magnitude of the input variable or model parameter. For example, water levels can be measured with errors of less than 0.01 cm regardless the magnitude of the measurement. Therefore, a standard deviation of σ = 0.01 cm could effectively describe the level of error in the measurements of water levels. On the other hand, the coefficient of variation (defined mathematically as the ratio between the standard deviation and the mean of the variable:cv = σ/x ), is useful to describe errors that vary with the magnitude of the input variable or model parameter. For example, the errors in flow measurements typically increase with the magnitude of the flow, with low flows potentially having a CV of 5%, and high flows having a CV of 20%. Therefore, for flows the CV constitutes a more appropriate description of the errors expected in the measurements. Prepared by Tetra Tech, Inc. 8

19 For the 2015 SHEP model, the estimates of uncertainty for each one of the input variables and parameters of interest (Table 4-2) are summarized in Table 4-3. These estimates are similar to those reported for other estuaries such as the New York Harbor, NY (Blumberg and Georgas 2008), St Johns River Estuary, FL (Sucsy et al. 2010), Weeks Bay Estuary, AL (Camacho et al. 2014), and other waterbodies (Zhao et al. 2011). For instance, literature values of CV for the hydraulic and water quality variables typically range between 5% and 15%. Estimates used for the 2015 SHEP uncertainty analysis are within reported ranges, with the exception of the scaling factor for wind and the sediment oxygen demand which had error estimations of 20%. A detailed discussion on the input variables and parameters, along with the metrics used for the estimate of uncertainty, is provided in Section through Section Table 4-3 Estimates of uncertainty in input variables and model parameters of the 2015 SHEP model Model component Estimate of uncertainty Metric Value Model structure Model bathymetry σ e (m) 0.15 if depth < 7 m 0.25 if depth > 7 m Marsh area size C v (%) 15 Input variable Freshwater flows at Clyo C v (%) 15 WSE at open boundary (Ocean tide) C v (%) 5 EFDC temperature boundary conditions C v (%) 5 Open boundary salinity concentration σ e (psu) 0.8 Solar radiation C v (%) 10 WASP input water temperature (from EFDC) C v (%) 5 DO boundary concentrations C v (%) 15 Model parameter Bottom roughness σ e (m) Background dispersion coefficient σ e (m) Initial bed temperature C v (%) 15 Sediment Oxygen Demand (SOD) C v (%) 20 Wind scaling factor in WASP C v (%) Model Bathymetry The uncertainty in the model bathymetry is usually caused by measurements errors and by errors resulting from the implementation of gridding procedures to define an effective bathymetry for the model scale. The later process refers to interpolation or extrapolation of data through data average techniques. The measurement errors refer to inaccuracies in the estimation of the horizontal position of a bathymetric measurement and also to inaccuracies in the actual estimation of the bottom depth. By using modern acoustic devices, the errors in the horizontal position of an individual measurement generally fall in the range ±2 m, while the errors in the measurement of the bottom depth can range between ±15 cm for depths of less than 7 m and between ±25 cm in deeper areas (Byrnes et al. 2002; International Hydrographic Organization 2008, Hare et al. 2011). Some of the reasons for these errors include positioning errors, range and beam errors, errors in vessel heading, errors in the beam pointing angle, sensor position offset errors, errors in the vertical datum, tidal measurement errors, fluid mud reflections, vessel draught, and vessel settlement among others. Prepared by Tetra Tech, Inc. 9

20 The errors associated to the gridding of the bathymetry depend on the type of gridding procedure implemented (i.e. interpolation or extrapolation), the spatial density of the available data measurements, and the resolution of the model grid (Hare et al. 2011). Combined, these errors may contribute to approximately 1 10% of the total model bathymetric errors, but can be minimized by creating a grid capable of representing the fundamental features of the bathymetry, by having a good coverage of measurements, and by avoiding the extrapolation of data (Maleika et al. 2012). In the 2015 SHEP model, the model bathymetry is assumed to be mostly affected by measurement errors. The level of error introduced by the gridding process is small because the resolution of the model is able to capture in detail the main channel and the main features of the system and the coverage of bathymetric measurements is very detailed, which typically resulted in thousands of points within each cell to compute the model bathymetry. Therefore, for this uncertainty analysis, the total expected error in the model bathymetry is 15 cm in areas where the depth, referred to MLLW is less than 7 m and 25 cm in deeper areas Freshwater Inflows The errors associated to freshwater flows typically vary from 5 to 25% (Baldassarre and Montanari 2009). The lower errors are generally representative of actual measurements of flows obtained under optimal conditions, such as using optimal current meters or acoustic current profilers in small cross sections with low macro-vegetation. The largest errors are associated with estimates derived from rating curves, particularly during high flow conditions. The rating curves are typically generated with data collected under normal or low flow conditions, and extrapolated to high flow conditions. For high flow there is little or no data to constrain the parameterization of the curves, which can cause the higher percent errors. The freshwater inputs for the Savannah River in the 2015 SHEP model were obtained from the USGS Station Savannah River near Clyo, GA. The level of uncertainty in these monitoring stations is usually moderate to low given the continuous maintenance of the stations, the periodic refinement of the rating curves, and the quality controls on the data. Reported flow values at station are described as fair in the 2013 USGS Water-Data report (USGS 2014). Therefore, the potential errors in flow measurements at this station are likely to represent approximately 15% of the reported values. This level of uncertainty was used for the uncertainty analysis Water Surface Elevations (Ocean Tide) Errors in WSE at the open boundary are fundamentally caused by the absence of measurements close to the boundaries of the 2015 SHEP model. As discussed in Tetra Tech (2015), the boundary conditions of ocean tide were created using the 6-min records of water level available at the National Oceanic and Atmospheric Administration (NOAA) station located at Fort Pulaski. To create these boundary conditions, Aa time delay (or phase lag) in the series of water levels at NOAA was introduced and the amplitude of the simulations were adjusted to match the observations at USGS station Savannah River at Fort Pulaski, GA. The Normalized Root Mean Square Error (RMSE), or difference between the model simulations and observations of ocean tide at USGS (i.e. RMSE 0.05), was used as an estimate of the potential uncertainty associated with this boundary forcing. The above estimate is reasonable taking into account that the errors in measured datasets of water elevations typically range between 1 and 3% (Thomson et al. 2008). Therefore, the RMSE value of 0.05, or 5%, was used for the WSE input variable in the uncertainty analysis EFDC temperature boundary conditions Temperature boundary conditions for 2015 SHEP calibrated EFDC model were created using observed records of temperature at station NOAA for the open boundary, and at stations NOAA and USGS for the upstream and tributary boundaries (Tetra Tech 2015). Temperature measurements are generally reliable with measurement errors ranging between 0.1 and 1ºC, which represent Prepared by Tetra Tech, Inc. 10

21 a confidence level of more than 95% in individual measurements. This means that the uncertainty in Temperature measurements is approximately 5%. This level of confidence was used to define the potential uncertainty in the records of temperature used to force the boundaries of the 2015 SHEP model Open Boundary Salinity Concentration As discussed in Tetra Tech (2015), the salinity boundary conditions for the 2015 SHEP model were defined based on measurements collected during the period 2005 through 2007 at station R2 of the SABSOON monitoring system. After a basic statistical analysis of the observations, a constant salinity concentration of PSU was selected to force the model, given the low variability of the salinity observations during the analyzed period. In this investigation, the level of error associated to the open boundary salinity concentration of PSU fundamentally expresses the variability expected around this constant estimate. The standard deviation of the measurements between 2005 and 2007 (σ e = 0.8 psu) was used in the uncertainty analysis as an effective estimate of this variability. The level of error from measurements inaccuracies is assumed to be negligible given that salinity can be estimated with high precision with appropriate instrumentation Solar Radiation The solar radiation input variable is used by EFDC to predict daily and seasonal temperature variations in the 2015 SHEP model. Existing research on the potential errors associated to measurements and model derived solar radiation values suggest that the level of uncertainty that can be expected in individual estimates of solar radiation is approximately 10% (Myers 2005). This estimate of uncertainty was used in this investigation to express the level of error in the available input datasets of solar radiation Bottom Roughness Literature values for the bottom roughness thickness of estuarine systems usually range between m and 0.05 m (Ji 2008). This information was used to define, through calibration, the bottom roughness of the 2015 SHEP model (Tetra Tech 2015). For this investigation, it is assumed that the level of uncertainty in the calibrated roughness values varies between ± m which represents an error between 7% and 15% of the calibrated estimates. These estimates of error are reasonable and within the ranges reported in similar investigations (Lacy et al and Sucsy et al. 2010), and reflect a moderate level of uncertainty on the calibrated roughness Background dispersion coefficient Literature values for the background dispersion coefficient typically range between 1.0 x 10-5 m 2 /s and 1.0 x 10-4 m 2 /s (Ilicak et al and Ji 2008). Similar to the bottom roughness, the above information was used to calibrate the background dispersion coefficient in the 2015 SHEP model. The final calibrated value was set to 1.3 x 10-4 m 2 /s. During the calibration, the predictive performance of the model was evaluated using dispersion coefficients between 1.0 x 10-4 and 1.0 x 10-3, which is a plausible range for estuarine models (Ilicak et al. 2008). The model performed well with dispersion coefficient values approximately between 1.18 x 10-4 m 2 /s and 1.45 x 10-4 m 2 /s, and the best model performance was achieved using a dispersion coefficient of 1.3 x 10-4 m 2 /s (Tetra Tech 2015). The above results were used to assign an estimate of uncertainty in the calibrated dispersion coefficient of ±1.3 x 10-5 m 2 /s, which represents approximately 10% of the calibrated value Marsh Size The sizes of the marsh cells in the 2015 SHEP model were defined using soils and land use maps. However, the marsh cell size is an approximation to the actual size and configuration of the marsh areas in the estuary. For this investigation, it was assumed that the error expected in the marsh sizes is 15%. Prepared by Tetra Tech, Inc. 11

22 Sediment Oxygen Demand The estimates of sediment oxygen demand (SOD) are subject to a high level of uncertainty due to the high variability of the distribution of organic sediments in estuarine ecosystems, (Di Toro 2001), the dependence of SOD to temperature, and the lack of measurements to determine the actual values and distribution of SOD in the 2015 SHEP model. An unpublished database of SOD measurements from the Environmental Protection Agency (EPA) shows that in estuarine ecosystems the medium rates of SOD range between 1.8 go/m 2 /day and 3.1 go/m 2 /day with an average value of 2.4 go/m 2 /day. These values reflect a compilation of SOD measurements in different estuaries nationwide including Sarasota Bay FL, Mobile Bay AL, St. Johns River FL, St. Louis Bay, MS among others. The values of SOD used in the 2015 SHEP model were initially obtained from the Savannah TMDL model (USEPA 2010) and updated through calibration using the EPA SOD ranges to match the time series and vertical profiles of DO available at different stations within the estuary. The final calibrated values of SOD varied between 0.6 go/m 2 /day and 2.2 go/m 2 /day in the 2015 SHEP model, and mostly fell within the ranges observed in related studies (Park et al and Garcia et al. 2010). Considering the high variability of SOD in estuaries, the level of uncertainty or error in the SOD values implemented in the 2015 SHEP model can range between 10 and 20 %. A 20% error has been used for the purposes of this uncertainty analysis. This error estimate is conservative and within the ranges reported for calibrated SOD rates in similar studies (Ambrose et al. 1993, Zheng et al. 2004; Kalin and Hantush 2007; Utley et al. 2008) WASP Input Temperature from EFDC Uncertainty in the prediction of water temperature can impact the predictive capacity of a water quality model as several processes such as nutrient cycling, phytoplankton production, and SOD are highly driven by temperature (Chapra 2008). In the 2015 SHEP model, temperature is computed within the hydrodynamic model (EFDC) based on solar radiation inputs, boundary temperature values, and parameterizations related to how fast solar heat is diffused through the water column (Hamrick 1992). The existence of errors in the above input variables reduces the capacity of the model to accurately predict the variations of temperature in the estuary. Given that in this investigation the temperature predictions from EFDC are used as inputs by the water quality model WASP, estimates of uncertainty in the EFDC model can be computed by performing a statistical analysis of the residuals between the EFDC predictions and the available observations at different stations. The calibration results discussed in Tetra Tech (2015) indicated that the errors between the predictions of temperature from EFDC and the available observations usually fall below 1.0 C, and represent less than 4% of the predicted magnitude. For the uncertainty analysis, the above information was used to assign a level of uncertainty of 5% in the predictions of temperature Dissolved Oxygen Boundary Concentrations As discussed in Tetra Tech (2015), the boundary conditions of DO at the upstream boundary of the 2015 SHEP model were defined using a combination of data from the Georgia Environmental Protection Division (GaEPD) station (one to three observations per month) and USGS station Meanwhile, the boundary conditions at the open boundary are DO concentrations at 100% DO saturation. In general, the uncertainty in the DO boundary conditions reflect the lack of measurements at the actual boundaries of the model and also the errors in the estimates of DO saturation used to force the model at the open boundary. The uncertainty in the estimates of DO saturation reflect the high sensitivity of DO saturation to salinity conditions particularly during low temperatures <10 C (Chapra 2008). For instance, a change in salinity conditions from 20 PSU to 40 PSU at 10 C changes the DO saturation concentration Prepared by Tetra Tech, Inc. 12

23 in approximately 13%. Meanwhile, this change in salinity at 20 C only changes the DO saturation concentration in 0.9% (Chapra 2008). The estimates of DO saturation at the open boundary are considered approximate due to the lack of temperature and salinity measurements to obtain exact estimates. In this investigation, the level of uncertainty in the DO boundary conditions was assumed to be 15% and represented the potential variability of the DO saturation concentrations particularly during low temperatures Wind Scaling Factor Wind velocity is used by WASP to estimate wind-driven reaeration rates in surface water. Reaeration is a natural process by which oxygen is transferred from the atmosphere to the water as a result of concentration gradients. This process occurs across the interface between the water and the atmosphere, and its velocity is fundamentally driven by turbulence intensity. The more stable and quiescent the water atmosphere interface, the slower the rate of oxygen transfer in a given water body. Conversely, the more unstable or turbulent the water - atmosphere interface, the faster the rate of oxygen transfer. In estuaries, reaeration is driven by current velocities and wind shear, and constitutes an important source of DO in these systems. In WASP, reaeration rates are first computed using empirical equations based on flow velocity and depth (flow-induced reaeration) and also based on wind speed (wind-induced reaeration). The larger of these two rates is then used by WASP to compute the mass balance of DO in every model segment (Ambrose et al. 1993). While flow-driven reaeration is computed internally based on the temporal evolution of currents in an estuary, the evaluation of wind-driven reaeration requires the input of wind speeds to WASP. Wind-driven reaeration rates are computed by WASP using the O'Connor (1983) model and based on estimates of wind speed at 10cm above the water surface. Given that in practice the measurements of wind velocity are collected in land stations and at a specific height above ground level, they require some level of correction to represent the effective wind speed at the water surface. Some level of correction is also generally required to describe the highly variable spatial distribution of wind speeds resulting from local obstructions surrounding estuaries and the presence of macrovegetation (Rueda et al. 2009). These corrections represent relevant sources of input uncertainty which are difficult to evaluate from the available datasets of wind speeds collected in the nearby stations of the Savannah estuary. In order to take into account the spatial variability of wind speed in the 2015 SHEP model, the water quality model uses scaling factors to increase or reduce the wind inputs by zones (offshore area, upstream riverine portion, etc.). These factors, presented in Tetra Tech (2015), were adjusted during the model calibration to achieve the best possible agreement between the model predictions and the observations of DO in the surface layers. Although these scaling factors are intended to represent the spatial variability of the wind field, they ultimately aggregate other sources of error more difficult to evaluate in an explicit way. To reflect this level of uncertainty, it was assumed in this investigation that the errors associated with wind scaling factors were 20%. This estimate is reasonable compared to other studies where the errors associated to wind datasets can range between 10% and 20% (Sucsy et al and Blumberg and Georgas 2008). Prepared by Tetra Tech, Inc. 13

24 5.0 Dimensionless Sensitivity Coefficients (DSC) As described in Section 3.0, the DSC are useful to estimate the relative sensitivity of model output variables to different model aspects such as model structure, input data and model parameters. The DSC represents the ratio between the percent change of a model prediction from the calibrated prediction, and the percent change of a model component (e.g. a model parameter) from the calibrated value. A DSC of 1 suggests that an x % change on a model component causes the same x % change on the model prediction. Likewise, a DSC of 0.5 suggests that an x % change on a model component causes a 0.5x % change on the model prediction. In the uncertainty analysis, Eq. 6 in Section 2.0 was used to evaluate the level of sensitivity of the predictions of WSE, CS, Flow, Temp, Sal and DO to errors in the input variables and parameters listed in Table 4-2. The baseline conditions used for the analysis were the model predictions from the 2015 SHEP model during the calibration period of January 1, 2013 through April 30, Following the implementation guidelines found in FOVA applications (Melchin 1995; Blumberg and Georgas 2008), the baseline inputs and parameters of the 2015 SHEP model were increased and reduced by 15% (Table 5-1). The perturbed model output predictions were used to estimate the model prediction changes from the calibrated condition (i.e. F in Eq. 6). Therefore, in this case a DSC of 1.0 meant that a 15% perturbation of an input variable/parameter caused a 15% change in the model prediction, while a DSC of 0.5 meant that such perturbations only caused a 7.5% change in the model prediction. The DSCs were computed for every output time step at the surface and bottom layers of the stations of interest (Table 4-1). In order to compare the relative importance of each variable listed in Table 4-2 on the SHEP 2015 model output parameters, the daily median value of each DSC was then computed and plotted in a time series graph. The results of this activity for a 15% increment perturbation are presented from Figure 5-1 to Figure The results for a 15% reduction perturbation were similar to those for a 15% increase and thus, are omitted from this report. Table 5-1 Summary of model perturbations conducted to obtain the DSCs. Input variable or model parameter Perturbation scenario Model bathymetry Marsh area size Freshwater flows at Clyo WSE at open boundary (Ocean tide) EFDC temperature boundary conditions Open boundary salinity concentration Solar radiation WASP input water temperature from EFDC DO boundary concentrations 15% increment/reduction of model bathymetry. Changes applied simultaneously to all cells. 15% increment/reduction of mash sizes. Changes applied simultaneously to all marshes. 15% increment/reduction of time series of flows from USGS % increment/reduction of time series of ocean tide levels. 15% increment/reduction of input temperatures from tributaries, point sources and ocean water. Changes were applied simultaneously in all of the model boundaries. 15% increment/reduction of salinity concentration at the open boundary. 15% increment/reduction of solar radiation radiation time series 15% increment/reduction of output temperature from EFDC. 15% increment/reduction of DO boundary conditions. Changes were applied simultaneously to the open boundary and the freshwater boundaries. Prepared by Tetra Tech, Inc. 14

25 Input variable or model parameter Bottom roughness Background dispersion coefficient Initial bed temperature Sediment Oxygen Demand (SOD) Wind scaling factor in WASP Perturbation scenario 15% increment/reduction of roughness coefficients. Changes applied simultaneously to all cells. 15% increment/reduction of background dispersion coefficient. 15% increment/reduction of initial bed temperature. Initial bed temperature is assumed to be homogeneous throughout the system 15% increment/reduction of sediment oxygen demand SOD. 15% increment/reduction of wind scaling factors in WASP. 5.1 Water Surface Elevation The sensitivity analysis indicated that the WSE in the 2015 SHEP model was primarily driven by the ocean tide conditions, followed by the bottom bathymetry. Freshwater flows also influenced the dynamics of the WSE, although only during wet periods and in upstream or non-tidal regions of the system (USGS in Figure 5-1). The results indicated that WSE was sensitive to ocean tide and model bathymetry at the mouth and the middle portion of the estuary (Figure 5-2 to Figure 5-5), and only sensitive to ocean tide in the offshore area and close to the estuary entrance (Figure 5-6). Changes in the ocean tide generally resulted in nearly constant DSCs around 1.0 at most stations, suggesting that uncertainty in this variable reflects in the same proportion in the model predictions. The bathymetric DSCs generally oscillated between 0.2 and 1.2 at most stations except USGS , where the DSCs were constant around 0.2. The larger values were associated to spring periods and flood tides, while the lower values were associated to neap periods and ebb tides. The relevance of the ocean tide and the bottom bathymetry in governing WSE was expected given that these are the main factors controlling the propagation and dissipation of surface waves in coastal systems. The celerity of a surface wave depends on bathymetry, as it is proportional to the square root of the water depth. Also, other factors such as wave length and amplitude depend on bathymetry. Prepared by Tetra Tech, Inc. 15

26 Figure 5-1 DSCs for Water Surface Elevation at station USGS (Front River at I-95 Bridge) Figure 5-2 DSCs for Water Surface Elevation at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 16

27 Figure 5-3 DSCs for Water Surface Elevation at station USGS (Middle River at Houlihan Bridge) Figure 5-4 DSCs for Water Surface Elevation at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 17

28 Figure 5-5 DSCs for Water Surface Elevation at station USGS (Front River at USACE Dock) Figure 5-6 DSCs for Water Surface Elevation at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 18

29 5.2 Current Speed At station USGS , CS are predominantly sensitive to freshwater flows, model bathymetry, ocean tide, and to marsh size to a lesser extent (Figure 5-7). CS in this upstream region of the estuary seem to be particularly sensitive to freshwater flows during wet periods, and slightly more sensitive to bathymetry and ocean tide during normal or dry periods than to freshwater flows or marsh size. The sensitivity of CS to freshwater flows diminishes in downstream areas below McCoys Cut regardless of the hydrologic conditions. Near Houlihan Bridge (stations USGS , and ) changes in freshwater flows resulted in DSCs between 0.1 and 0.4, while changes in bathymetry and ocean tide usually resulted in DSCs between 0.4 and 1.4 (Figure 5-8 to Figure 5-10). These results suggest that uncertainties in bathymetry and ocean tide can impact the predictions of CS twice as much as uncertainties in flow estimates in this region of the Savannah estuary. The existence of multiple marshes in this region also increases the sensitivity of the CS to the marsh size estimates, as suggested by the marsh size DSCs between 0.2 and 0.5. This result is explained by a significant variation of flow exchanges between the marshes and the main channels due marsh size variations. Current speed was most sensitive to bathymetry and ocean tide in the lower portion of the Savannah estuary, although the results at stations USGS and also indicated a significant sensitivity of current speed to open boundary salinity concentrations (Figure 5-11 and Figure 5-12). At station USGS , for example, changes in the open boundary salinity concentrations resulted in DSCs between 0.4 and 1.0 which were equivalent to the DSCs obtained by perturbing the ocean tide. The above results could be associated to changes in internal wave circulation and transport caused by density changes, such as baroclinic transport. Figure 5-7 DSCs for Current Speed at surface layer at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 19

30 Figure 5-8 DSCs for Current Speed at surface layer at station USGS (Front River at Houlihan Bridge) Figure 5-9 DSCs for Current Speed at surface layer at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 20

31 Figure 5-10 DSCs for Current Speed at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-11 DSCs for Current Speed at surface layer at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 21

32 Figure 5-12 DSCs for Current Speed at surface layer at station USGS (Front River at Fort Pulaski) 5.3 Flow The sensitivity analysis showed that CS and Flow predictions from the 2015 SHEP model had a similar response to changes in model bathymetry, ocean tide, freshwater flows and marsh size (Figure 5-13 to Figure 5-18, and Section 5.2). This result was expected given that Flow is computed as the product between CS and the effective flow area. In the upstream portion of the Savannah estuary, close to station USGS , Flow was sensitive to bathymetry and ocean tide, as well as to freshwater flows from Clyo during wet periods (Figure 5-13). The importance of freshwater flows was reduced below McCoys Cut, and in the middle portion of the estuary around the Houlihan Bridge, Flow was primarily driven by bathymetry, ocean tide and marsh size (Figure 5-14 to Figure 5-16). Bathymetry was relevant in the main channel with DSCs between 0.6 and 1.8 at USGS (Figure 5-14), while ocean tide were the largest driver of Flows in the Middle River and the Little Back River, with DSCs between 0.8 and 1.2 (Figure 5-15 and Figure 5-16). The above DSCs values indicated that the uncertainties in bathymetry and ocean tide can cause a similar level of uncertainty in the predictions of Flow. In the lower part of the estuary at stations USGS and , Flow was sensitive to the open boundary salinity concentrations, even though results were predominantly driven by bathymetry and ocean tide (Figure 5-17 and Figure 5-18). Salinity can impact Flow because of internal currents caused by density gradients between the ocean water and the freshwater flows from the watershed. The strength of the density gradients and the bathymetry of the system usually determines the level of salinity intrusion in estuarine systems. Prepared by Tetra Tech, Inc. 22

33 Figure 5-13 DSCs for Flow at surface layer at station USGS (Front River at I-95 Bridge) Figure 5-14 DSCs for Flow at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 23

34 Figure 5-15 DSCs for Flow at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 5-16 DSCs for Flow at surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 24

35 Figure 5-17 DSCs for Flow at surface layer at station USGS (Front River at USACE Dock) Figure 5-18 DSCs for Flow at surface layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 25

36 5.4 Temperature The sensitivity analysis suggested that Temp predictions from the 2015 SHEP model were predominantly driven by the temperature boundary conditions at Clyo and at the open boundary. In the upstream portion of the estuary for example, changes in temperature boundary conditions typically caused DSCs to be close to 1.0 (station USGS in Figure 5-19 and Figure 5-20), while changes in other variables such as bathymetry and flows typically resulted in DSCs below 0.1. The above results indicated that the temperature boundary conditions at Clyo can explain most of the variability of the water temperature in this part of the estuary. In the middle and lower portions of the estuary below Houlihan Bridge, water temperature was more sensitive to bathymetry and solar radiation, although changes in these variables generally resulted in DSCs below 0.2 (Figure 5-19 to Figure 5-28). Nevertheless, temperature boundary conditions remained the most important factors explaining the variability of water temperature predictions in these regions with DSCs values between 0.5 and 0.9. The relatively low importance of variables such as bathymetry and solar radiation on the predictions of water temperature may be attributed to the fact that horizontal transport in the Savannah Harbor occurs at a much faster rate than transport in the vertical as a result of the shallow character of the system compared to thermally stratified systems such as lakes. In addition, the active transport resulting from the interactions of freshwater flows and ocean tide typically result in short flushing times. Therefore, model predictions have a larger sensitivity to perturbations propagating in the horizontal dimensions than to perturbations propagating in the vertical dimension, such as changes in solar radiation. Figure 5-19 DSCs for Temperature at surface layer at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 26

37 Figure 5-20 DSCs for Temperature at bottom layer at station USGS (Front River at I-95 Bridge) Figure 5-21 DSCs for Temperature at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 27

38 Figure 5-22 DSCs for Temperature at bottom layer at station USGS (Front River at Houlihan Bridge) Figure 5-23 DSCs for Temperature at surface layer at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 28

39 Figure 5-24 DSCs for Temperature at bottom layer at station USGS (Middle River at Houlihan Bridge) Figure 5-25 DSCs for Temperature at surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 29

40 Figure 5-26 DSCs for Temperature at bottom layer at station USGS (Little Back River at Houlihan Bridge) Figure 5-27 DSCs for Temperature at surface layer at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 30

41 Figure 5-28 DSCs for Temperature at bottom layer at station USGS (Front River at USACE Dock) Figure 5-29 DSCs for Temperature at surface layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 31

42 Figure 5-30 DSCs for Temperature at bottom layer at station USGS (Front River at Fort Pulaski) 5.5 Salinity The sensitivity analysis indicated that the predictions of salinity in the 2015 SHEP model were predominantly sensitive to perturbations in the open boundary salinity concentration, the model bathymetry, and the freshwater flows. The relative importance of these perturbations varies within the estuary. At the Savannah estuary entrance, the predictions of salinity were predominantly impacted by perturbations in the open boundary conditions, followed by perturbations in the model bathymetry, and freshwater flows (Station USGS in Figure 5-42 and Figure 5-41). In the main channel between Stations USGS and USGS , the model bathymetry had a greater impact on the predictions of salinity followed by the open boundary conditions and the freshwater flows (Figure 5-40 to Figure 5-38). In more upstream regions of the estuary, such as station USGS at I-95 Bridge, the predictions of salinity are insensitive to any perturbations in the evaluated variables because salinity intrusion is minimal in these regions (Figure 5-31 and Figure 5-32). The smallest temporal variations occurred at station USGS at Fort Pulaski where the DSCs at the surface layer varied between 1.0 and 1.6 for perturbations in the open boundary conditions, between 0.3 and 1.4 for perturbations in the model bathymetry, and between 0.2 and 0.9 for perturbations in the freshwater flows. These results were expected given that station USGS is the closest station to the open boundary, and as such the variability in the predictions of salinity was mostly driven by the open boundary conditions. At this station, the DSCs at the surface were greater than at the bottom layer, indicating that surface predictions of Salinity were more sensitive to model inputs than those at the bottom. In upstream areas above Station USGS , the predictions of salinity become more sensitive to changes in the bathymetry, followed by changes in the open boundary salinity and freshwater flows. Results indicated that perturbations in these input variables were amplified in the predictions of salinity as suggested by the values of the DSCs greater than 1.0. At station USGS at the USACE Dock, the DSCs in the surface layer reached values of up to 10 by perturbing the model bathymetry, and values of up to Prepared by Tetra Tech, Inc. 32

43 approximately 6 by perturbing the open boundary salinity. Generally, the largest DSCs were associated with low salinity predictions. For example, on February 15, 2013, the salinity predictions for baseline condition in the surface layer were below 2 PSU. By perturbing the model bathymetry by 15%, the salinity predictions increase from approximately 2 PSU to around 4 PSU. These increments represented about % of the baseline condition or in terms of DSCs, about 7 10 times the perturbation in the model bathymetry (15%). These results were similar at other stations, suggesting that in general, the lower the model predictions of salinity, then the more sensitive the model predictions were to perturbations in the model components, even though the absolute change in the model prediction were small. These results also explain why the model predictions in the surface layers were more sensitive than those at the bottom. The high DSCs were also caused by timing changes on the propagation of salinity fronts. Even if the extent and magnitude of a salinity front has low sensitivity to model perturbations, changes in the travel time may cause high DSC values. In these cases, the DSCs reflect time shifts in the signals of salinity predicted by the model. The DSCs in stations located on the Front, Middle, and Back Rivers at the Houlihan Bridge (USGS , USGS and ) also indicated that the predictions of salinity in this portion of the estuary were mostly impacted by perturbations in the model bathymetry, the open boundary salinity, the freshwater flows, and the size of the marshes although to a lesser extent (Figure 5-33 to Figure 5-38). In this region, the computed DSCs had a wide range of variability in response to bathymetry perturbations (DSCs between 0.0 and above 10.0) and perturbations in the salinity boundary conditions (DSCs between 0 and approximately 6). The largest DSCs were generally associated with small salinity concentrations around 1 PSU, while the lowest DSCs were associated with salinity concentrations close to 0.0 PSU. DSCs of 0 occurred at stations where the modeled salinity concentrations were close to 0.0 PSU. The sensitivity of the salinity predictions at the Houlihan Bridge stations to perturbations in the bathymetry, the open boundary salinity, and the freshwater flows was expected given that these variables control the transport of salinity in estuarine ecosystems. Perturbations in these variables can change the amount, distribution, and residence time of salt predicted by the model. For example, it is reasonable to expect higher salinity intrusions by over estimating the model bathymetry (deeper) and by underestimating freshwater flows. Finally, in upstream regions of the model such as at station USGS at the I-95 Bridge where salinity intrusion was minimal, the results indicated that the predictions of salinity were not sensitive to perturbations in the evaluated input variables and parameters (Figure 5-31 and Figure 5-32). Prepared by Tetra Tech, Inc. 33

44 Figure 5-31 DSCs of Salinity at surface layer at station USGS (Front River at I-95 Bridge). DSCs are 0 because simulated salinity was close to 0 PSU at this station. Figure 5-32 DSCs of Salinity at bottom layer at station USGS (Front River at I-95 Bridge). DSCs are 0 because simulated salinity was close to 0 PSU at this station. Prepared by Tetra Tech, Inc. 34

45 Figure 5-33 DSCs of Salinity at surface layer at station USGS (Front River at Houlihan Bridge). Figure 5-34 DSCs of Salinity at bottom layer at station USGS (Front River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 35

46 Figure 5-35 DSCs of Salinity at surface layer at station USGS (Middle River at Houlihan Bridge). Figure 5-36 DSCs of Salinity at bottom layer at station USGS (Middle River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 36

47 Figure 5-37 DSCs of Salinity at surface layer at station USGS (Little Back River at Houlihan Bridge). Figure 5-38 DSCs of Salinity at bottom layer at station USGS (Little Back River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 37

48 Figure 5-39 DSCs of Salinity at bottom layer at station USGS (Front River at USACE Dock). Figure 5-40 DSCs of Salinity at surface layer at station USGS (Front River at USACE Dock). Prepared by Tetra Tech, Inc. 38

49 Figure 5-41 DSCs of Salinity at bottom layer at station USGS (Front River at Fort Pulaski). Figure 5-42 DSCs of Salinity at surface layer at station USGS (Front River at Fort Pulaski). Prepared by Tetra Tech, Inc. 39

50 5.6 Dissolved Oxygen The sensitivity analysis indicated that DO predictions from the 2015 SHEP model were predominantly sensitive to input temperature from EFDC and the DO boundary conditions (Figure 5-43 to Figure 5-54). The DSCs associated with temperature perturbations varied at most stations from 0.5 during cooler months to nearly 5.0 during warmer months. The DSCs associated with perturbations in the DO boundary conditions had a smaller variability, and typically varied from 0.5 in surface layers and areas far from the model boundaries to approximately 1.0 in bottom layers and regions close to the model boundaries. The sensitivity of the DO predictions to perturbations in the DO boundary conditions was relatively higher during the winter period when DO saturation was higher (Figure 5-43 to Figure 5-54). Temperature impacts the predictions of DO because temperature controls the rates of the biological processes associated to the decomposition of organic matter in the water column (reflected in the biochemical oxygen demand (BOD)) and the bottom sediments (reflected in the SOD), as well as processes such as nitrification and phytoplankton production. For example, SOD rates increase as temperature increases above 20 C and hence, need to be corrected accordingly (Chapra 2008). An SOD rate of 1 g/m 2 /day at 20 C would increase to 1.85 g/m 2 /day at a water temperature of 28 C using a temperature correction factor of 1.08 (Chapra 2008). If the hydrodynamic model temperature input is 28 C and perturbed by +15% (i.e. 28 * 1.15 = 32.2 C), the perturbation would cause an initial SOD rate of 1.85 g/m 2 /day to increase to 2.55 g/m 2 /day. This exponential nature of temperature dependent biological procceses mean that a 15% increase in temperature causes a 40% increase in the baseline SOD rate (2.55 g/m 2 /day vs 1.85 g/m 2 /day). Other biological processes such as BOD decay and nitrification rates, are also corrected for changes in temperature and perturbations in input temperatures cause these processes to be magnified as well. DO predictions were relatively sensitive to bathymetry, salinity open boundary conditions, and SOD. At stations USGS (Figure 5-49) and USGS (Figure 5-51Figure 5-49Figure 5-34), changes in bathymetry and salinity open boundary conditions resulted in DSCs between 0.1 and 0.6, and between 0.1 and 0.5 respectively. These variables control estuarine circularion and the propagation of internal waves resulting from density gradients and can therefore impact the transport of DO masses within the main channel. SOD had a lower impact on the predictions of DO with DSCs, typically varying between 0.1 and 0.3. Prepared by Tetra Tech, Inc. 40

51 Figure 5-43 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at I-95 Bridge). Figure 5-44 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at I-95 Bridge). Prepared by Tetra Tech, Inc. 41

52 Figure 5-45 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at Houlihan Bridge). Figure 5-46 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 42

53 Figure 5-47 DSCs of Dissolved Oxygen at surface layer at station USGS (Middle River at Houlihan Bridge). Figure 5-48 DSCs of Dissolved Oxygen at bottom layer at station USGS (Middle River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 43

54 Figure 5-49 DSCs of Dissolved Oxygen at surface layer at station USGS (Little Back River at Houlihan Bridge). Figure 5-50 DSCs of Dissolved Oxygen at bottom layer at station USGS (Little Back River at Houlihan Bridge). Prepared by Tetra Tech, Inc. 44

55 Figure 5-51 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at USACE Dock). Figure 5-52 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at USACE Dock). Prepared by Tetra Tech, Inc. 45

56 Figure 5-53 DSCs of Dissolved Oxygen at surface layer at station USGS (Front River at Fort Pulaski). Figure 5-54 DSCs of Dissolved Oxygen at bottom layer at station USGS (Front River at Fort Pulaski). Prepared by Tetra Tech, Inc. 46

57 6.0 Uncertainty Estimates Uncertainty analyses and estimates should not be used to accept or reject a calibrated model, but should be used to document the most important sources of errors involved in a model application, and to estimate the level of confidence that may be expected in the model predictions due to these sources of uncertainty. The uncertainty estimates also represent the possible errors in the 2015 SHEP model predictions that could be caused by existing errors and uncertainties in the model structure, input variables, and model parameters. Equations 4 and 5 in Section 2.0 were used to compute the expected uncertainty on the predictions of WSE, CS, Flow, Temp, Sal, and DO in the 2015 SHEP model. In this investigation the estimates of uncertainty around the calibrated model predictions were expressed as ±1 standard deviation, which is approximately equivalent to a 68% level of confidence around the prediction. Although the selection of a confidence level is in general subjective and project-specific, in TMDL studies and other common hydrodynamic model applications the uncertainty estimates typically range between ±1 and ±2 standard deviations (Zhang and Yu 2004 and Blumberg and Georgas 2008). As discussed in Section 2.0, the variance and standard deviation of the predictions represent the expected uncertainty after propagating the errors in model structure, input variables, and model parameters listed in Table 4-2 and Table 4-3. The uncertainty estimates were computed for each calibrated model prediction obtained during the calibration period from the 2015 SHEP model. The results of the corresponding analyses are presented in the sections below. 6.1 Water Surface Elevation The calibrated predictions of WSE for the period January 1, 2013 through April 30, 2014 including ± 1 standard deviation confidence bounds, are presented for the evaluated stations in Figure 6-1 through Figure 6-6. The narrow shape of the confidence bounds indicated that existing uncertainties in the ocean tide, model bathymetry, freshwater flows and marsh size caused a low level of uncertainty on the predictions of WSE (Table 4-2 and Table 4-3). Results also suggested that the predictions of WSE during flood tide periods have a larger uncertainty than the predictions of WSE during ebb tide periods. This was likely caused by uncertainties in the model bathymetry, as this variable controls the amplitude and speed of the propagation of shallow waves. A statistical summary of the uncertainty estimates is presented in Table 6-1 and includes a comparison of the standard deviations to the calibrated model predictions at the mean, median, and 75th and 90th percentiles. The uncertainty in the predictions of WSE was slightly higher in upstream regions of the estuary than that in downstream regions close to the open boundary. At station USGS (I-95 Bridge), the average potential uncertainty on the predictions of WSE was approximately ±0.11 m, while at USGS (Fort Pulaski) the potential uncertainty was ±0.06 m. These levels of uncertainty are small relative to the magnitude of the model predictions (Figure 6-1 through Figure 6-6), and within the ranges reported in similar hydrodynamic studies (Sucsy et al. 2010). For instance, at USGS , a level of uncertainty of ±0.11 m on the predictions of WSE during flood periods ( 3 m) represents only approximately 3.6% of the model prediction. A comparison of Table 6-1 against the statistics of model performance obtained during the calibrationvalidation (Tetra Tech 2015) indicated that existing uncertainties in the ocean tide, model bathymetry, freshwater flows and marsh size can explain an important fraction of the average differences between the model predictions and the observations of WSE achieved in the model calibration. For instance, at station USGS the Mean Absolute Error (MAE), or difference between the predictions and observations of WSE, was approximately 0.2 m (Tetra Tech 2015), while the potential average uncertainty in this station was approximately 0.11 m. These values suggest that uncertainties in the ocean tide, model bathymetry, freshwater flows and marsh size could explain approximately 55% of the differences between the model predictions and observations of WSE at this station. Prepared by Tetra Tech, Inc. 47

58 Additional complex sources of uncertainty likely impacted the predictive capacity of the model and/or the statistics of model performance achieved during model calibration-validation beyond the model components reviewed in the uncertainty analysis. For example, the absence of flood plains in the upper portion of the model above USGS limited the capacity of the model to reproduce the attenuation of freshwater flood levels such as those observed during July 2013 (Tetra Tech 2015). This limitation increased the differences between the predictions and observations of WSE during July 2013 as well as the MAE for the calibration period. The existence of uncertainties in the datum at station USGS could also impact the statistics of model performance achieved during calibration-validation as this type of uncertainty introduced an artificial bias in the observations of WSE increasing the calibration MAE. In other stations, such as at USGS , the differences between the model predictions and observations of WSE could be fully caused by the existing uncertainties in the ocean tide, model bathymetry, freshwater flows, marsh size and model roughness. At this station in particular, the MAE achieved during calibration was 0.07 m, while the average estimated level of uncertainty around the model prediction was 0.06 m. Figure 6-1 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 48

59 Figure 6-2 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at Houlihan Bridge) Figure 6-3 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 49

60 Figure 6-4 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Little Back River at Houlihan Bridge) Figure 6-5 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 50

61 Figure 6-6 Calibrated predictions of Water Surface Elevation ± 1 standard deviation at station USGS (Front River at Fort Pulaski) Table 6-1 Statistic summary of model output uncertainty for WSE for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Average (m) Median (m) %tile (m) %tile (m) Current Speed Predictions of CS for the period January 1, 2013 through April 30, 2014 and the ± 1 standard deviation confidence bounds are presented in Figure 6-7 through Figure Results suggest that uncertainties in freshwater flows, model bathymetry, ocean tide, marsh size, and open boundary salinity concentrations may be the cause of the error in the model predictions of CS. Uncertainty results were similar during both flood and ebb periods, however, the level of uncertainty increased during high flow periods, particularly in the upper portion of the estuary as seen at station USGS (Figure 6-7). A statistical summary of the uncertainty estimates is presented in Table 6-2 and includes a comparison of the standard deviations to the calibrated model predictions at the mean, median, and 75th and 90th percentiles. These statistics show that uncertainty in the predictions of CS was small relative to the magnitude of the prediction. At stations USGS and USGS for example, the average level of uncertainty on the predictions of CS was 3.89 cm/s and 7.92 cm/s respectively, which represented approximately 8% of the predictive speeds during flood tide periods (approximately 50 cm/s at USGS and 100 cm/s at USGS ). Prepared by Tetra Tech, Inc. 51

62 Figure 6-7 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at I-95 Bridge) Figure 6-8 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 52

63 Figure 6-9 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Middle River at Houlihan Bridge) Figure 6-10 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 53

64 Figure 6-11 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at USACE Dock) Figure 6-12 Calibrated predictions of Current Speed ± 1 standard deviation in the surface layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 54

65 Table 6-2 Statistic summary of model output uncertainty for Current Speed for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Average (cm/s) Median (cm/s) %tile (cm/s) %tile (cm/s) Flow Predictions of surface Flows for the period January 1, 2013 through April 30, 2014, including ± 1 standard deviation confidence bounds, are presented from Figure 6-13 to Figure The results indicated that uncertainty in Flow predictions was small relative to the magnitude of the model predictions, and that potential data errors in freshwater flows, model bathymetry, ocean tide, marsh size, and open boundary salinity concentrations did not cause a large uncertainty in the predictions of Flow. Uncertainty in Flow predictions was greater during periods of high freshwater flows at station USGS (Figure 6-13). Below Houlihan Bridge, the uncertainty predictions were more homogeneous and less influenced by the freshwater flow conditions. At station USGS , predictions of ebb flows had a slightly higher uncertainty than the predictions of flood flows. A statistical summary of the uncertainty estimates is presented in Table 6-3 and includes a comparison of the standard deviations to the calibrated model predictions at the mean, median, and 75th and 90th percentiles. These statistics indicated that uncertainty in the Flow predictions represented between 5 and 10% of the predicted flow value. At station USGS for example, an average uncertainty of m 3 /s (Table 6-3) represented approximately 10% of the flow prediction during flood flows (Figure 6-13). At station USGS (Middle River at Houlihan Bridge), an average uncertainty of m 3 /s represented approximately 7% of the flow prediction. Prepared by Tetra Tech, Inc. 55

66 Figure 6-13 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Figure 6-14 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 56

67 Figure 6-15 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 6-16 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 57

68 Figure 6-17 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Figure 6-18 Calibrated predictions of Flow ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 58

69 Table 6-3 Statistic summary of model output uncertainty for Flow for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Average (m 3 /s) Median (m 3 /s) %tile (m 3 /s) %tile (m 3 /s) Temperature The calibrated predictions of Temp for the period January 1, 2013 through April 30, 2014, including ± 1 standard deviation confidence bounds, are presented in Figure 6-19 through Figure Results indicated that the existing uncertainties in temperature boundary conditions, solar radiation, freshwater flows and model bathymetry potential caused a small level of uncertainty in the model predictions of water Temp. Although the level of uncertainty in all regions of the model was greater during the summer period and lower in the winter, the uncertainty in model predictions rarely exceeded 1 C. A statistical summary of the uncertainty estimates is presented in Table 6-4 and includes a comparison of the standard deviations to the calibrated model predictions at the mean, median, and 75th and 90th percentiles. These results showed that the level of uncertainty in the predictions of Temp was less than 1 C in most regions of the estuary, and that existing input errors caused the same level of uncertainty in the predictions at the surface and bottom layers of the model. A comparison of Table 6-4 against the statistics of model performance obtained during the model calibration (Tetra Tech 2015) suggested that the average differences between the model predictions and the measured observations of Temp could be attributed to existing uncertainties and potential measurement errors in temperature boundary conditions, solar radiation, freshwater flows and model bathymetry. For instance, the MAE between the predictions and observations of Temp at stations USGS and (0.44 C and 0.9 C respectively) was similar to the average levels of uncertainty that may be expected in these stations (0.77 C and 0.58 C respectively). Prepared by Tetra Tech, Inc. 59

70 Figure 6-19 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Figure 6-20 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 60

71 Figure 6-21 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Figure 6-22 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 61

72 Figure 6-23 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 6-24 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 62

73 Figure 6-25 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 6-26 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 63

74 Figure 6-27 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Figure 6-28 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 64

75 Figure 6-29 Calibrated predictions of Temperature ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Figure 6-30 Calibrated predictions of Temperature ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 65

76 Table 6-4 Statistic summary of model output uncertainty for temperature for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Average ( C) Median ( C) %tile ( C) %tile ( C) Salinity The calibrated predictions of Sal, including ± 1 standard deviation uncertainty bounds, are presented in Figure 6-31 through Figure The analysis is presented for the period January 1, 2013 through April 30, Qualitatively, the narrow shape of the uncertainty bounds at most stations indicated that that the expected uncertainty on the predictions of Sal was small relative to the model prediction. A statistical summary of the uncertainty estimates is presented in Table 6-5. This table shows by station, the mean, median, and 75th and 90th percentiles of the time series of +1 standard deviation from the calibrated predictions of Sal. Table 6-5 suggests that uncertainties in the open boundary salinity concentrations, model bathymetry and freshwater flow (Table 4-2) caused a low level of uncertainty in the predictions of Sal. For example, the average uncertainty on the predictions of Sal at the surface and bottom layers of station USGS (Fort Pulaski) was 1.54 PSU and 1.2 PSU respectively. The uncertainty was greatest at higher Sal concentrations, and at this station the 90th percentile uncertainties for the surface and bottom layers was 2.6 PSU and 2.23 PSU respectively. Sal model predictions at USGS generally oscillated between 10 and 30 PSU at the surface and between 20 and 30 PSU in the bottom layers, so the uncertainties represented between 10 and 15% of the calibrated model prediction. This level of uncertainty in Sal predictions is within the ranges reported in similar modeling applications (McCutcheon et al. 1990). The uncertainty in the Sal predictions diminished in the upper regions of the model domain. At station USGS (Houlihan Bridge), the average uncertainty in the predictions of salinity at the surface and bottom layers was 0.43 PSU and 0.8 PSU respectively. At station USGS (I-95 Bridge) where salinity intrusion was negligible, the uncertainty in the model predictions was 0 PSU. In addition, the estimates obtained in this investigation are within the ranges reported for other predictive hydrodynamic models (Sucsy et al. 2010) Average differences between model Sal predictions and measured Sal concentrations (Tetra Tech 2015) could be attributed to existing uncertainties in the open boundary salinity concentrations, the model bathymetry and the freshwater flows. For example, at station USGS (USACE Dock), the MAE between the predictions and observations of Sal was approximately 3.7 PSU, while the average level of uncertainty expected in the predictions of Sal at this station was approximately 0.89 PSU at the surface and 1.63 PSU at the bottom. The above results indicated that the existing input uncertainties and potential data errors explain an important fraction of the MAE achieved during calibration at this station. Similar results are obtained for the remaining stations. Prepared by Tetra Tech, Inc. 66

77 Figure 6-31 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Figure 6-32 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 67

78 Figure 6-33 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Figure 6-34 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 68

79 Figure 6-35 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Figure 6-36 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 69

80 Figure 6-37 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Figure 6-38 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 70

81 Figure 6-39 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Figure 6-40 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 71

82 Figure 6-41 Calibrated predictions of Salinity ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Figure 6-42 Calibrated predictions of Salinity ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 72

83 Table 6-5 Statistic summary of model output uncertainty for salinity predictions for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Average (PSU) Median (PSU) %tile (PSU) %tile (PSU) Dissolved Oxygen The calibrated predictions of DO for the period January 1, 2013 through April 30, 2014, including ± 1 standard deviation uncertainty bounds, are presented in Figure 6-43 through Figure Uncertainties in the model predictions of DO were typically less than 0.5 mg/l and can be attributed to existing uncertainties and data errors from input temperatures, DO boundary conditions, bathymetry, salinity open boundary concentrations and SOD. Uncertainty in the DO predictions was typically higher in the winter period and lower in the summer season when the model predicts the lowest DO concentrations. This may be explained by uncertainties in the DO boundary conditions, given that, as discussed in Section , the estimates of DO saturation used as open boundary conditions are subject to a larger uncertainty during low temperatures (winter) than during high temperatures (summer). A statistical summary of the uncertainty estimates for the entire SHEP 2015 calibration period is presented in Table 6-6 and includes a comparison of the standard deviations to the calibrated model predictions at the mean, median, and 75th and 90th percentiles for DO. The same statistics are present for the period of July 1, 2013 through September 30, 2013 as well in Table 6-7. The full period reflects the overall uncertainty estimates for the calibration period while the summer period reflects the uncertainty in the predictions of low or critical DO levels. Table 6-6 and Table 6-7 show that uncertainty in the predictions of DO was homogeneous throughout the estuary and typically ranged from 0.45 to 0.65 mg/l. The results for the critical conditions (Table 6-7) indicated that uncertainties in input temperatures from EFDC and the DO boundary conditions caused an average uncertainty in the predictions of DO of approximately 0.45 mg/l at the surface and of approximately 0.5 mg/l at the bottom. The 90 th percentiles reported in Table 6-7 show that 90% of the deviations from the calibrated model predictions of DO were less than or equal to 0.5 mg/l at the surface and less than or equal to 0.58mg/L at the bottom. The level of uncertainty in the DO predictions is low, especially since the errors in field and lab measurements can vary between ±0.1 mg/l and ±1 mg/l (Katznelson 2004). Expected uncertainty in the predictions of DO was slightly lower in the Middle River and Little Back River (Figure 6-47 to Figure 6-50) than that in the Front River (Figure 6-45 and Figure 6-46), which was likely due to a lower influence of the boundary conditions in the Middle River and Little Back River and to a larger influence of marsh river interactions. Also, bottom DO predictions typically had slightly higher uncertainty than the surface DO predictions, likely due to the influence of SOD. Prepared by Tetra Tech, Inc. 73

84 A comparison of Table 6-7 against the statistics obtained during model calibration (Tetra Tech 2015) suggest that existing uncertainties in input temperatures from EFDC, DO boundary conditions, bathymetry, salinity open boundary concentrations and SOD, could explain the average differences between the model predictions and the observations of DO achieved in the model calibration. For example, at station USGS (Front River at Houlihan Bridge) the MAE between the predictions and observations of DO is 0.5 mg/l (Tetra Tech 2015), which was the same as the average level of uncertainty that may be expected in the predictions of DO at this station (0.5 mg/l) as a result of uncertainties in input temperatures from EFDC, DO boundary conditions, bathymetry, salinity open boundary concentrations and SOD. Figure 6-43 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at I-95 Bridge) Prepared by Tetra Tech, Inc. 74

85 Figure 6-44 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at I-95 Bridge) Figure 6-45 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 75

86 Figure 6-46 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at Houlihan Bridge) Figure 6-47 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Middle River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 76

87 Figure 6-48 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Middle River at Houlihan Bridge) Figure 6-49 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Little Back River at Houlihan Bridge) Prepared by Tetra Tech, Inc. 77

88 Figure 6-50 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Little Back River at Houlihan Bridge) Figure 6-51 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at USACE Dock) Prepared by Tetra Tech, Inc. 78

89 Figure 6-52 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at USACE Dock) Figure 6-53 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at surface layer at station USGS (Front River at Fort Pulaski) Prepared by Tetra Tech, Inc. 79

90 Figure 6-54 Calibrated predictions of Dissolved Oxygen ± 1 standard deviation at bottom layer at station USGS (Front River at Fort Pulaski) Table 6-6 Statistic summary of model output uncertainty for Dissolved Oxygen predictions for the 2015 SHEP model calibration period of 1/1/2013 4/30/2014 Statistic USGS USGS USGS USGS USGS USGS Average (mg/l) Median (mg/l) 75%tile (mg/l) 90%tile (mg/l) Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Prepared by Tetra Tech, Inc. 80

91 Table 6-7 Statistic summary of model output uncertainty for Dissolved Oxygen predictions for the 2015 SHEP model summer calibration period of 7/1/2013 9/30/2013 Statistic USGS USGS USGS USGS USGS USGS Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Bott Surf Average (mg/l) Median (mg/l) %tile (mg/l) %tile (mg/l) PSU Salinity Boundary In the Savannah Harbor estuary, a median 0.5 PSU Sal boundary was developed to estimate the limits of salt water intrusion in the marsh areas. The critical location, associated with low freshwater flow conditions and a limited flushing capacity of the system, was estimated by computing the median salinity concentration during the month of August 1999 using the 2015 SHEP model. The August 1999 month was considered a representative dry period in the Savannah Harbor region. In this investigation, FOVA was implemented to evaluate the expected level of uncertainty in the predicted location of the 0.5 PSU salinity boundary due to errors in the input variables and model parameters listed in Table 4-2. To determine the level of uncertainty in the boundary, the calibrated model was run for the 1999 year, and the resulting predictions constituted the baseline model predictions for August The FOVA technique was applied using the procedures outlined in Section 3.0 and using the estimates of input uncertainty in Table 4-3. The results of the FOVA analysis were the uncertainty bounds around the calibrated or baseline model predictions. To define the baseline prediction of the 0.5 PSU salinity boundary, the median surface salinity concentration for August 1999 was estimated from the time series of calibrated predictions at each cell within the model domain. The results of this exercise are presented in Figure 6-55 where the regions of salinity below 0.5 PSU are colored in blue. The uncertainty estimates were obtained by computing the median surface salinity concentration from the time series of calibrated salinity predictions + 1 standard deviation as well as from the time series of calibrated salinity predictions -1 standard deviation. The results of the above computations are presented in Figure 6-56 and Figure 6-57 respectively, and again, the regions of salinity below 0.5 PSU are colored in blue. A comparison between Figure 6-55, Figure 6-56 and Figure 6-57, indicated that it is unlikely that the predicted location of the 0.5 PSU boundary was underestimated by the model due to existing uncertainties in the 2015 SHEP model. Results suggest that existing uncertainties in the 2015 SHEP model were more likely to cause an overestimation of the 0.5 PSU boundary location, meaning that the boundary is further downstream that the actual model prediction, particularly in the Middle and Little Back Rivers. Due to uncertainties in the model, Figure 6-57 showed that the 0.5 PSU boundary could be located close to the Houlihan Bridge in the Middle River, and downstream of the Houlihan Bridge in the Little Back River, as opposed to being upstream of the bridge as predicted by the 2015 SHEP model (Figure 6-55). This suggests that the 2015 SHEP model prediction of the 0.5 PSU salinity boundary is a conservative estimate of the boundary location. Prepared by Tetra Tech, Inc. 81

92 Figure 6-55 Median surface salinity concentrations predicted for the month of August of The lower limits of the blue legend separates the region of salinity concentrations below 0.5 PSU (upstream) and above 0.5 PSU (downstream). Prepared by Tetra Tech, Inc. 82

93 Figure 6-56 Median surface salinity concentrations predicted for the month of August of The medians were computed for each cell using the time series of baseline predictions (calibrated model) +1 standard deviation error estimate. Prepared by Tetra Tech, Inc. 83