Critical Ecosystem Studies Initiative Final Project Report

Salinity is a fundamental and key characteristic of the physical conditions of estuarine and coastal ecosystems. Salinity affects water quality, the make-up and spatial distribution of vegetative communities, and the life history of most animal species in these ecosystems. Simulations and forecasts of salinity are an important tool in the assessment of ecological resources in the Everglades, Florida Bay, and the estuaries on the Gulf of Mexico (CROGEE, 2002). Water managers use forecasts to evaluate the expected benefits and impacts of ecosystem restoration activities. Ecosystem restoration involves aspects of adaptive management (NRC 2004), uncertainty analysis (CERP 2002), and risk assessment (Thom et al. 2004), and these all rely on the application of predictive models.

This report reviews models for which information is currently available on a broad basis (June 2006) for simulating and forecasting salinity in Florida Bay, Whitewater Bay, and the Gulf coast estuaries. For the salinity evaluations that have taken place thus far, there have been two general approaches to constructing such models. The first is empirical and relies on accurately describing observed salinity variations and correlative relationships. The second is mechanistic-based and relies on accurately accounting for the physical processes that drive changes in salinity. In both approaches the accuracy of the forecasts is limited by the data available to describe patterns of salinity variation and the driving processes.

Various statistical techniques can be employed in the empirical approach, the simplest being descriptive analysis. Both regression and time series modeling techniques have been applied to derive models for Florida Bay and Gulf coast salinity. Regression models exploit linear relationships in records of driving processes and systems response. Time series models utilize the serial correlation that is present in many hydrologic parameters. The statistical models that have been developed thus far for Florida Bay and the Gulf coast estuaries are based on a coastal aquifer conceptual model and have been used successfully for evaluating water management alternatives and for performance measure development.

Mechanistic salinity models for south Florida estuaries include both mass-balance models and more complex hydrodynamic models. Mass balance models of salinity, in their discretized numerical form, are similar in form to autoregressive time series models. Mass balance models account for the inputs and outputs of water from basins delineated by geomorphologic features. Mass balance models have been used for ecological evaluations and for minimum flows and levels modeling.

Hydrodynamic models have been developed for both Everglades hydrology and the salinity in the downstream estuary. Hydrodynamic models are based on the solution of simultaneous differential equations of continuity and hydrodynamics (momentum) in one, two, or three dimensions, and can be used for both surface and groundwater applications. Hydrodynamic models have been used for modeling the freshwater portion of the Everglades / Florida Bay hydrologic system for about the past decade, and are in the process of being updated with better data and techniques. Only recently have hydrodynamic models been available that are capable of adequately simulating the salinity regime in south Florida Bay and the mangrove / salinity transition zone. Work is currently underway on the Florida Bay hydrodynamic models, while work on hydrodynamic models for the transition zone of the Gulf coast estuaries is still in preliminary stages.

A summary table presenting general model information and a summary evaluation table is included with this Executive Summary. In the evaluation table the Florida Bay Science Program model evaluation factors have been used and a score of 1 to 5 has been assigned to each model for each factor, with 1 being poor and 5 being excellent in application.

Executive Summary
Contents

1 Introduction
1.1 General
1.2 Background
1.2.1 Approaches to Simulation and Forecasting
1.2.2 Forecast Uncertainty
1.3 Previous Report
1.4 Objectives and Scope of this Study

2 Salinity Patterns and Processes
2.1 Salinity Variation
2.2 Driving Processes
2.2.1 Net Freshwater Supply
2.2.2 Exchange Processes
2.2.3 Boundary Salinity
2.3 Available Salinity Data
2.4 Estimating Inflow from the Everglades to Florida Bay

3 Statistical Models
3.1 Regression Models
3.2 Time Series and Frequency Domain Models

4 Mechanistic Models
4.1 Mass Balance (Box) Models
4.1.1 Four Box Model of Florida Bay
4.1.2 PHAST
4.2 Hydrodynamic Models
4.2.1 Initial Hydrodynamic Modeling Efforts
4.2.2 EFDC
4.2.3 SICS / TIME

5 Summary and Discussion

6 Findings

7 References

1.1 General

Ecological forecast models play an essential role in efforts to restore and preserve natural resources. This role is analogous to the role that hydrologic forecast models have played in the management of water resources for human benefit (Lettenmaier and Wood 1993). Ecosystem restoration involves aspects of adaptive management (NRC 2004), uncertainty analysis (CERP 2002), and risk assessment (Thom et al. 2004), and these all rely on the application of predictive models. In south Florida, the Everglades and estuarine ecosystems in Everglades National Park have been altered by water supply and flood protection for agricultural and urban activities (CROGEE 2002). The restoration effort for these ecosystems is currently centered on the activities of the Comprehensive Everglades Restoration Plan (CERP).

For CERP, ecologists and water managers use salinity forecasts as one tool to evaluate the expected benefits and impact of restoration activities. These benefits and impacts to coastal ecosystems are reflected in potential future changes in wetland communities, estuarine water quality, and coastal fisheries that are expected for water management activities and for alternative management scenarios. Forecasts provide managers with quantitative information needed for evaluation of alternative actions under consideration and to choose the course of action that best meets objectives.

The study area for this review of models includes the freshwater marshes and mangrove eco-tone areas of the Everglades, the estuarine and near-marine basins of Florida Bay, the estuarine areas of Whitewater Bay, and the estuaries the discharge into the southeastern-most portion of the Gulf off Mexico (Gulf coast). The hydrologic features in the upstream Everglades that are important to salinity modeling include Shark River Slough, Taylor Slough, and the C-111 Canal system.

The ability to forecast how Everglades restoration will affect the ecology of Florida Bay, Whitewater Bay, and the Gulf coast of south Florida depends on first being able to forecast how changes in regional water management alter the bay's salinity. Changes in salinity reflect changes in the amount or timing of the net supply of freshwater to an estuary, i.e. the sum of rainfall plus inflow minus evaporation, hydrodynamics and mixing, and exchange with the ocean. Salinity is a key characteristic of physical conditions (including water quality) in estuarine and coastal ecosystems; it affects the composition and spatial distribution of vegetative communities and life history of most animal species. Because salt is a conservative tracer, changes in salinity signal possible changes in the concentrations of other substances, such as nutrients and contaminants that enter estuarine and coastal waters through the inflow of freshwater or mixing with the coastal ocean.

This report reviews models for which information was currently available (June 2006) for forecasting salinity in Florida Bay. This constitutes part of the work being performed by the Cetacean Logic Foundation, Inc. for Everglades National Park (ENP) with support from the Critical Ecosystem Science Initiative (CESI) program. The purpose of this study is to update information in a similar report compiled for Everglades National Park by The Cadmus Group (Nuttle 2002). The present work expands the coverage of the earlier report by incorporating the recent improvements in hydrology and salinity modeling including statistical, mass balance, and hydrodynamic models.

1.2 Background

In general, the formulation and application of forecasting models serve three roles. First, the formulation and development of predictive models helps to confirm a common understanding of the system and its behavior in response to changes in driving processes. Second, the predictive model functions as one of the primary mechanisms for investigating possible future structure and behavior of the system that can may result from proposed restoration activities. Finally, predictive models are used to understand uncertainties about the present and future state of the system and the variation in driving processes, and translate these into corresponding uncertainties of meeting restoration goals.

Forecasting ability increases with improved scientific understanding through the synthesis of research results. Therefore, formulation and refinement of predictive models serves an essential function in the development of knowledge through research and in the application of that knowledge toward the practical goals of ecosystem restoration. This is the motivation for building predictive salinity models for the southern Everglades and Florida Bay region.

Recurrent patterns in the data, such as the annual cycle of wet and dry seasons, are predictive in their own right in the mode of a null model. The underlying assertion of a null model is that the mechanisms driving the phenomenon will continue unchanged. Models used in restoration planning must go beyond the description of a null model, if only to test the proposition that the null model is or is not the best model for describing the observed data.

1.2.1 Approaches to Simulation and Forecasting

Making accurate forecasts of salinity in Florida Bay, the mangrove transition zone of the Everglades, Whitewater Bay, and the Gulf coast estuaries depends on knowledge of patterns of salinity variation in the past and of the underlying driving processes that produced them. Forecasts derive from the driving processes and a representation of the relationship between these processes and salinity in the bay. For Everglades restoration, driving processes include water management alternatives that affect freshwater inflow to the estuaries from the Everglades, tied to different proposed management strategies.

There are two general approaches currently employed to construct salinity models. The first is empirical and relies on accurately describing observed salinity variations. Analysis of the available data identifies basic patterns that characterize the phenomenon of interest. The second is mechanistically-based and relies on accurately portraying the processes that drive changes in salinity. Typically, a numerical model describes the physical relationship between driving processes and salinity. In both approaches the accuracy of the forecasts is limited by the data available to describe patterns of salinity variation and the driving processes.

Various statistical techniques, including descriptive analysis and correlation, are employed in the empirical approach. These techniques help in understanding the relationship between driving processes and resulting salinity variation and can be used in deriving a mathematical description embodied in a linear combination model. Correlation does not necessarily establish a causal link between characteristics of the ecosystem and the driving processes that incorporate the effects of human activities. However, descriptive analysis and correlation are the foundation for models capable of reproducing patterns of variation. Descriptive analysis also serves to diagnose bias and other problems related to the methods of observation and measurement. Patterns identified through descriptive analysis and correlations provide clues to the underlying mechanisms by their proximity in time and space.

Both regression and time series modeling techniques have been applied to models for Florida Bay salinity. Regression models exploit linear relationships in records of driving processes and systems response. A number of statistical modeling tools are available, ranging from simple linear regression to more complicated analytical techniques such as multivariate regression, linear transfer function models, and frequency domain models. Time series models utilize the distribution of variation with time and serial correlation to model system behavior. By nature, useful time series models require enough data such that the variation over time can be adequately analyzed statistically. Classical time series modeling begins by allocating the variation in a set of data ordered by time into different components, such as mean, trend, seasonal, etc. Times series models also include an explicit representation for irreducible error represented ideally as uncorrelated white noise error term.

The mechanistic approach relies on knowledge of the physical processes that influence estuarine salinity. The structure of mechanistic models reflects this understanding. Explicit mathematical representation of cause and effect based on general physical principles means that a mechanistic model can predict the behavior of the system beyond the range that has been observed. For this approach, there are various models that exhibit different levels of complexity depending on the detail employed in the numerical description of the processes at work.

Mechanistic models have only been developed for Florida Bay and the southern Everglades mangrove zone. Mechanistic models include both relatively simple mass-balance models and more complex hydrodynamic models. Mass balance models of salinity, in their discretized numerical form, are similar in form to autoregressive time series models. Mass balance models ignore momentum effects which are negligible at time steps greater than daily. Complex mechanistic models are based on the solution of simultaneous differential equations of continuity and hydrodynamics (momentum). A hydrodynamic forecast model is used where additional temporal and spatial detail or coverage are required for forecasts.

1.2.2 Forecast Uncertainty

Uncertainty in salinity forecasts falls into the category of “Knowledge Uncertainty” (NRC, 2000a). Knowledge uncertainty encompasses sources of uncertainty from imperfect knowledge of processes, model structure, model parameter values and data used as input in generating the forecasts. These sources of uncertainty are often not independent of each other. Uncertainties in the data can be derived in part from the mismatch between the temporal and spatial scales represented by the model and the scales on which data are collected. And finally, the uncertainty in the data contributes to the uncertainty in the optimally selected model parameters. All sources of uncertainty must be considered when evaluating alternative approaches or making improvements to forecasting.

Uncertainty in forecasts can be characterized by various statistics calculated from the differences between measured and forecast values of salinity, i.e. the set of residuals (R). For this study, five error statistics are reported:

average error (avg e),
root mean squared error (rmse),
average absolute error (abs e),
coefficient of determination (r²), and
model efficiency (eff).

The average error, the average of R, measures bias between simulated and observed values; a mean error of zero means no bias. Even if the average error is zero there can still be significant differences between simulated and observed values; these differences may simply cancel out in the calculation of the average error.

The root mean squared error and the average absolute error are measures of the deviation between simulated and observed values, reported in the units of the simulated variable. The root mean squared error (RMSE) is calculated as the square root of the mean of the squared residuals (MSE). The average absolute error is calculated as the mean of the absolute values of the R values. These measures better reflect the expected magnitude of the difference between calculated and measured salinity at a particular location and time.

Model efficiency and the coefficient of determination, R-squared, or R² are similar. The coefficient of determination measures the fraction of the variance in the observations that can be explained by a linear transformation of the simulated salinity values; therefore it is a measure of the correlation between the simulated and observed values. In contrast, model efficiency is calculated from the mean square error normalized by the variance of the observed salinity:

eff = 100* (1 - MSE / Var(obs)) 1

where MSE is the mean of the squared residual errors and Var(obs) is the variance of the observed salinity data.

Model efficiency, also known as the Nash-Sutcliffe efficiency (c.f. Nash and Sutcliffe 1970, Weglarczyk 1998), can be interpreted broadly as the percentage of the variance in the data that is accounted for directly by the model. A model efficiency of zero indicates that the model accounts for no more of the variation than does the mean of the data. An efficiency of 100 indicates that the model accounts for all of the variation in the data. However, model efficiency can take on negative values if, for example, the model produces a biased estimate of the data. In this case, the mean of the data offers a better forecast than the model.

1.3 Previous Report

The salinity modeling status report by Nuttle (2002) reviewed and evaluated work prior to 2002 that could be applied to forecast salinity in the coastal mangroves of Everglades National Park and in Florida Bay. The report focused on approaches for formulating models needed to support the development and application of ecological performance measures. The goal was to identify an approach for linking coastal salinity prediction to changes in Everglades hydrology that could be implemented quickly and so satisfy the immediate need for predictive tools in planning. Different approaches were evaluated based on both predictive ability and practical considerations related to needs of the multi-agency planning process for ecosystem restoration in south Florida.

Accordingly, Nuttle (2002) evaluated the alternative approaches to forecasting salinity in Florida Bay based on the following set of practical requirements drawn from experience in the Florida Bay Science Program (PMC 2000):

Portability - The model chosen should be widely available for evaluation and application.
Validity - The predictive capability of the model must be generally known and accepted.
Fidelity - The model must be consistent with understood mechanisms of cause and effect within the limitations of the underlying approach to prediction.
Focus - Model predictions must relate directly to the ecosystem attributes defined as performance measures.
Ease of use - Model results must be able to be obtained quickly within the typically short time period allotted for analysis of alternatives within the planning process.

The Nuttle (2002) report recommended adopting the mass balance modeling approach, and this recommendation led to the development of the aggregated wetland basin hydrology and estuarine basin salinity model (PHAST) for ENP, and more recently used as a planning tool for the Biscayne Bay Coastal Wetlands Project (Nuttle 2005).

1.4 Objectives and Scope of this Study

Resource managers need reliable salinity forecast models to use in evaluating the benefits of alternative project designs for water management through the CERP program. As planning progresses and the understanding of the system matures, modeling activities will focus more on assuring the predictive capability of the model. For example, the future activities of the SFWMD Interagency Modeling Center will extend to reviewing modeling needs and advising project management teams on the application of models used for planning activities of individual CERP projects (CERP 2004).

This CESI task report provides general information about the options currently available from models that can be applied at sub-regional levels. The models that will be described in this task report will have the following characteristics:

The primary models that will be reviewed are salinity models; Everglades freshwater hydrology models are included to the extent they have been utilized with the salinity models being described;

Status of modeling efforts will be reported as of June 30, 2006;

Salinity models for the southern Everglades mangrove zone, Florida Bay, Whitewater Bay, and the southwest Gulf coast areas only will be reviewed (the subject area for this CESI project);

Information will be gathered primarily from abstracts and papers that are available from the sofia.usgs.gov website, the evergladesplan.org website, the latest Greater Everglades Ecosystem Restoration (GEERS) conference proceedings, the latest Florida Bay Science Program conference proceedings, and from personal communications; and Models reviewed will include models currently in use by ENP as well as models not currently being used by ENP that have the potential for use.

---

Figures

Figure 1: Map showing the location of Marine Monitoring Network stations with MLR salinity models (from Everglades National Park). [larger image]

---

Figure 2: The box model divides Florida Bay into four regions based on observed patterns in water quality (Boyer et al 1997, Nuttle et al. 2000). [larger image]

---

Figure 3: Map identifying the basins and the aggregated regions used in FATHOM for salinity calculations. [larger image]

Figure 4. Domain of the EFDC model, coarse grid (from TetraTech, 2003) [larger image]

Figure 5: South Florida satellite image showing SICS and TIME model domains (USGS). [larger image]

Figure 6. Map showing the domain of the SoFLA-HYCOM model (Kourafalou, 2005) [larger image]

Figure 7. A comparison of observed salinity (SERC), monthly average salinity (MMN), and simulations by FATHOM and MLR salinity models (monthly average) at Long Sound. [larger image]

Figure 8. A comparison of observed salinity (SERC), monthly average salinity (MMN), and simulations by FATHOM and MLR salinity models (monthly average) at Whipray Basin. [larger image]

View the PDF version (1 MB) of this publication. (Please note: you will need the free Adobe Acrobat Reader in order to view this file.)