PATUXENT WATERSHED MODEL

• Spatial Design
• Temporal Design
• Structural Design
• Calibration

When developing a model we first need to formulate the goal. In our case our prime goal is to be create an integrated approach to economic and ecological processes in a watershed.

We want to be able to analyze both ecological and economic processes in their interrelation and be able to account for changes in the system that are generated by both components. The goal of the study very much determines the spatial, temporal and structural resolution of the model.

Spatial Design

In the spatial domain we need to make sure that the ecological, hydrological heterogeneity in the area can be represented as well as the socio-economic heterogeneity. Two types of spatial representation have been mostly used in watershed modeling.

• Lumped network based units. The whole area is subdivided into regions based on certain hydro-ecological criteria. These maybe subwatersheds of certain size, hillslopes, areas with similar soil and habitat properties, etc. This is the approach used in such models as HSPF, RHESys or TOPMODEL.
• Grid-based units. The landscape is partitioned into a spatial grid of unit cells. The cells may have different size but their geometry is the same. This is the approach used in the ANSWERS model.

The second approach suits our goals best, because it allows cell attributes to change during the model run. The coverages that drive the model do not need to be entirely defined for the whole model run, they may be modified in response to the simulated behavior.

In this way, for example, the Landuse map can be modified within the Economic module and then immediately fed into the Ecological module. We do not need to restart the simulation. The Ecological Module will then respond to changes in the Landuse patterns and feed back to the Economic Module.

Temporal Design

We assume that in time we can represent the system as a sequence of independent discrete events. Every next event depends on the current and past states of the system but there are no events occuring simulataneously.

Event based temporal design

Click on a module to see more details

Human population model
Major model components and interaction between them

The modeled landscape is partitioned into a spatial grid of square unit cells. The model is hierarchical in structure, incorporating an ecosystem-level "unit" model that is replicated in each of the unit cells representing the landscape. While the unit model simulates ecological processes within a unit cell, horizontal fluxes link the cells together across the landscape to form the full PLM. Such fluxes are driven by cell-to-cell head differences of surface and ground water in saturated storage. Within this spatial context, the water fluxes between cells carry dissolved and suspended materials, determining water quality in the landscape.

Spatial organization of the model

The same general unit model structure runs in each cell. Individual models are parameterized according to habitat type and georeferenced information for a particular cell. The habitat-dependent information is stored in a parameter database which includes initial conditions, rate parameters, stoichiometric ratios, etc. The habitat type and other location-dependent characteristics are referenced through links to geographic informations system (GIS) files. The vegetation community type in the cells responds to changing hydrologic and nutrient regimes via successional switching algorithms which are defined by current ecological knowledge. Thus, when run within the spatial framework of the PLM, the landscape response to hydrology and water quality is effectively simulated as material flows between adjacent cells.

The model incorporates a modular structure. This allows individual modules to be designed and tested independently, prior to running the full model with all modules. The PLM uses an integrated spatial simulation modeling approach and was constructed using the Spatial Modeling Environment (SME).

Calibration

Much of the time involved in developing spatial process-based models is devoted to calibration and testing of the model behavior against known historical or other data. Calibrating and running a model of this level of complexity and resolution requires a multi-stage approach. We performed the calibration and testing at several time and space scales.

Multi-tier calibration process for a complex spatial model.
Different modules are calibrated independently at a
variety of spatial scales and resolutions.

Taking advantage of the model modularity, these tests were carried out for various parts of the model as well as for the whole model. The unit ecological model has undergone rigorous testing using newly-developed calibration software, which calculates a comprehensive Model Performance Index (MPI) . The index integrates an array of variable-specific tests into a single score which expresses the overall fit with data and hypotheses. Each test considers a different aspect of the model's output, e.g. fit to data, known patterns of autocorrelation, meaningful boundary values, or steady states.

Unit model calibration using the Model Performance Index

The left hand side figure shows a sample of the parameter search sequence in the MPI. Each graphed line represents the change in the fit of a model variable relative to a set of calibration data and other semi-quantitative calibration criteria. Increasing MPI values indicate a successively better match. Each vertical line marks the change in the value of a single parameter in the sequential search process. As an example, at step 7 along the X axis the daily rate of leaf loss at end of the growing season was changed by the search algorithm from the initial guess of 0.1 kg of carbon per day to 0.01. This change in the parameter value created an approximately 20% better fit for the net primary productivity (PHBIO_NPP) variable as measured by the partial MPI. The same change caused a smaller (~ 8%) decrease in the fit of the macrophyte leaf area index (MACLAI). This drop was recovered at step 13 by changing the initial biomass of non-photosynthetic tissue from 0.5 kg of carbon per square meter to 3.0. The search algorithm evaluates the sensitivity of the global MPI to changes in each parameter, then tries different parameter values according to the results of the sensitivity analysis.

The right hand figure presents the cooresponding model output for net primary productivity (NPP; left axis) compared to the Normalized Difference Vegetation Index data (NDVI, right axis). The initial guess was created by visual comparison of model output and reference data. The Model Performance Index (MPI) method was applied to search a 37-dimensional subset of the 119-dimensional parameter space to improve upon the initial guess. An early fit and the best fit resulting from the MPI search algorithm are shown as MPI 0.13 and MPI 0.29 representing points in the search sequence as shown in figure on the left. The MPI values represent the composite fit for all 97 calibration variables. All data and model output are 10-day maxima .

Sample Output of Full Model

Click here to explore SME project structure and data

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