Scientific Investigations Report 2008-5029


Prepared in cooperation with the
South Florida Water Management District

Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TaRSE) for Spatially Distributed Modeling of Phosphorus in South Florida Peat Marsh Wetlands

James W. Jawitz, Rafael Muñoz-Carpena, Stuart Muller, Kevin A. Grace, and Andrew I. James


     Select an option:

     Purpose and Scope
     Description of Study Area
     Previous Studies
Model Conceptualization
     Model Notation
          Water Column
     Physical and Biological Transfer Mechanisms
          Physical Transfer Processes
               Water Flows
               Atmospheric Deposition
               Pore-water/Surface-Water Transfer
               Settling and Entrainment of Particulate Material
               Sloughing and Cohesion of Biofilm
              Mineral Precipitation
          Biological Transfer Processes
               Growth of Biological Tissues
               Senescence and Decay of Biological Tissues
               Soil Oxidation and Mineralization and Burial
     Feedbacks and External Environmental Factors
          Light Limitation
          Temperature Effects
          Vegetation Effects on Flow Restriction
     Reaction Equations
Model Calibration and Validation
     Level 1—Soil Cores
     Level 2—Outdoor Mesocosms
     Level 3—Stormwater Treatment Area-1W, Cell 4
Global Sensitivity Analysis
     Techniques and Screening Methods
          Morris Method
          Extended Fourier Amplitude Sensitivity Test (FAST)
     Effects of Changing Model Structure and Flow Velocity on Global Model Output Sensitivity
          Analysis Procedure
          Flow Domain
          Description of Inputs and Outputs
          Morris Method Results
               Screening of Parameters
               Ranking of Parameters
               Effect of Flow Velocity
               Effect of Model Complexity
          Extended Fourier Amplitude Sensitivity Test (FAST) Results
              Surface-Water Soluble Reactive Phosphorus (CswP]o,tf) Case Study
              General Trends Observed in Sensitivity Dynamics
Analysis and Assessment of Model Uncertainty from Fourier Amplitude Sensitivity Test (FAST) Simulations
     Level-1 Uncertainty
     Level-2 Uncertainty
     Level-3 Uncertainty
Summary and Conclusions
References Cited
Appendix 1: Model Nomenclature Used in this Study
Appendix 2: Model Parameter Values for Levels 1, 2, and 3
Appendix 3: Equations and XML Input Files for Complexity Levels 1, 2, and 3
Appendix 4: Fourier Amplitude Sensitivity Test (FAST) for Additional Model Outputs


     Alterations to the predevelopment delivery of water and nutrients into the Everglades of southern Florida have been occurring for nearly a century. Major regional drainage projects, large-scale agricultural development, and changes to the hydrology of the Kissimmee River-Lake Okeechobee watershed have resulted in substantial phosphorus transport increases by surface waters. Excess phosphorus has accumulated in the soils of northern Everglades marshes to levels that have impaired the natural resources of the region. Regulations now limit the amount of phosphorous that enters the Everglades through an extensive network of water-control structures.
     This study involved the development and application of water-quality modeling components that may be applied to existing hydrologic models of southern Florida to evaluate the effects of different management scenarios. The result of this work is a spatially distributed water-quality model for phosphorus transport and cycling in wetlands. The model solves the advection-dispersion equation on an unstructured triangular mesh and incorporates a wide range of user-selectable mechanisms for phosphorus uptake and release parameters. In general, the phosphorus model contains transfers between stores; examples of stores that can be included are soil, water column (solutes), pore water, macrophytes, suspended solids (plankton), and biofilm. Examples of transfers are growth, senescence, settling, diffusion, and so forth, described with first order, second order, and Monod types of transformations. Local water depths and velocities are determined from an existing two-dimensional, overland-flow hydrologic model. The South Florida Water Management District Regional Simulation Model was used in this study.
     The model is applied to three case studies: intact cores of wetland soils with water, outdoor mesocosoms, and a large constructed wetland; namely, Cell 4 of Stormwater Treatment Area 1 West (STA-1W Cell 4). Different levels of complexity in the phosphorus cycling mechanisms were simulated in these case studies using different combinations of phosphorus reaction equations. Changes in water column phosphorus concentrations observed under the controlled conditions of laboratory incubations, and mesocosm studies were reproduced with model simulations. Short-term phosphorus flux rates and changes in phosphorus storages were within the range of values reported in the literature, whereas unknown rate constants were used to calibrate the model output.
     In STA-1W Cell 4, the dominant mechanism for phosphorus flow and transport is overland flow. Over many life cycles of the biological components, however, soils accrue and become enriched in phosphorus. Inflow total phosphorus concentrations and flow rates for the period between 1995 and 2000 were used to simulate Cell 4 phosphorus removal, outflow concentrations, and soil phosphorus enrichment over time. This full-scale application of the model successfully incorporated parameter values derived from the literature and short-term experiments, and reproduced the observed long-term outflow phosphorus concentrations and increased soil phosphorus storage within the system.
     A global sensitivity and uncertainty analysis of the model was performed using modern techniques such as a qualitative screening tool (Morris method) and the quantitative, variance-based, Fourier Amplitude Sensitivity Test (FAST) method. These techniques allowed an in-depth exploration of the effect of model complexity and flow velocity on model outputs. Three increasingly complex levels of possible application to southern Florida were studied corresponding to a simple soil pore-water and surface-water system (level 1), the addition of plankton (level 2), and of macrophytes (level 3). In the analysis for each complexity level, three surface-water velocities were considered that each correspond to residence times for the selected area (1-kilometer long) of 2, 10, and 20 days. Various of model outputs were studied that could be potentially useful to the model user: surface-water soluble reactive phosphorus (SRP) outflow, soil pore-water SRP variation, soil organic accretion, soil adsorbed phosphorus, plankton outflow, and macrophyte variation.
     Results show that a simple soil pore-water and surface-water system modeled with and without plankton exhibits little change in sensitivity, owing to the plankton-based processes. Effects in both cases are primarily linear (additive), and the degree of interactions among parameters is minimal. The sensitivity ranking of the parameters, however, changes with the introduction of plankton-related modeling processes, because the plankton growth parameters dominate the simulated response of the system for most outputs studied. The introduction of macrophytes substantially alters the parameter sensitivity, tempering much of the linear effects and generating nonlinear interactions among all components. Although it is possible to reduce the number of important parameters to about half of the total model parameters for levels 1 and 2, the presence of interactions prevents such simplification for level 3.
     Among the important parameters for level 1, the organic soil oxidation rate, kox, was consistently ranked most important followed by three other parameters: diffusion coefficient, kdf, soil bulk density, pb, and mass fraction of phosphorus in organic soil, XsoP. These results agree well with current understanding of the physical system, because the principal source of new phosphorus to the level-1 system is from oxidation of the soil (controlled by kox) and the pore-water SRP and, hence, the adsorbed phosphorus is controlled by the other three parameters. The SRP in the water column is more sensitive to kdf because this parameter represents the limiting process of diffusion through which the surface water gains new phosphorus. These trends across outputs persist in the level-2 results, with the only notable difference being the prominence of plankton growth parameters in the ranking for mobile outputs (outflow of surface-water SRP and plankton biomass). Level-3 results do not exhibit any pattern of parameter dominance across the different outputs.
     Model sensitivity to velocity is correlated with model complexity; that is, as velocity increases, the model sensitivity to the important parameters changes the most for the most complex case. The complex interactions that occur in level 3 complicate the process of identifying sensitive parameters with the Morris screening method. This technique, however, was found to be computationally efficient for qualitatively evaluating global model sensitivity and linear or nonlinear effects of important parameters. In cases where many parameters appear to be important, as when interactions predominate, the extended FAST method provides quantitative measures of the linear and nonlinear contributions of each parameter to the observed global output variance.

Suggested Citation:

Jawitz, J.W., Muñoz-Carpena, Rafael, Muller, Stuart, Grace, K.A., and James A.I., 2008, Development, Testing, and Sensitivity and Uncertainty Analyses of a Transport and Reaction Simulation Engine (TaRSE) for Spatially Distributed Modeling of Phosphorus in South Florida Peat Marsh Wetlands: U.S. Geological Survey Scientific Investigations Report 2008-5029, 109 p.

For additional information, contact:

U.S. Geological Survey
Florida Integrated Science Center
3110 SW 9th Avenue
Ft. Lauderdale, FL 33315

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