Evaluating regional landscape change, including the driving forces of and interactions between ecological and economic systems is the aim of our modeling efforts. The Patuxent Landscape Model (PLM) was designed to serve as a tool in a systematic analysis of the interactions among physical and biological dynamics of the watershed, conditioned on socioeconomic behavior in the region. A companion economic model of the region's land use dynamics was developed to link with the PLM and provide a means of capturing the feedbacks between ecological and economic systems. The economic model estimates land development patterns and effects on human decisions from site characteristics, ecosystem properties, and regulatory paradigms. For the ecological model, a process-based unit model calculates stocks and flows for hydrology, nutrients, plants, and animal populations within each cell of the 2,500 km2 Patuxent River watershed and cells are linked in a spatial model to simulate water and material fluxes across the landscape at several scales. Dynamic models examine the numerous competing effects of human and naturally imposed variation to suggest potential long term impacts to system function and resiliency. Model results will be used to inform land use policy and evaluate goals for ecosystem quality indicators.
Some of our most significant progress to date has been in the development of tools and data bases which have greatly facilitated model calibration.
These advances have increased our efficiency and will eventually
simplify model transport to other watersheds.
Calibration of the model at several spatial and complexity scales has improved model robustness and overall performance.
Efforts to link the ecological model to policy analyses has led to the development of new methods. Preliminary scenario results show the effects of spatial development patterns.
The Simulation Performance Index is a composite index of several tests of model performance. The index is user-defined in the sense that its value is a linear combination of variable scores, each one pertaining to a different model output variable and weighted to take the experimenter's priorities into account. Each variable score is in turn a composite score from a series of tests defined for that particular variable. The family of tests includes rough tests to establish initial boundaries in parameter space and rigorous statistical tests of the agreement between observed and simulated data in both the time and frequency domains. Examples of such information include minima and maxima of stock variables, seasonality, or other frequencies in behavior.
Algorithms have been developed for directing the search for combinations of parameter values that maximize the Simulation Performance Index. The software identifies the range of parameter sensitivity within the user-defined acceptable range, resamples the range, and searches for the parameter value that maximizes the SPI. The parameter value is fixed and the process is continued for each parameter in the array. Once all parameters have been defined, the parameters are reshuffled and the whole search process begins again. Initial experiments have shown that the process is not often sensitive to parameter array order but occasionally shows dramatic shifts from parameter reordering.
The directed search algorithm has been used for calibration of the ecological components of the PLM and has shown encouraging results. In addition to identifying the best parameter sets, these methods provide statistics about the behavior of the model, such as estimating regions of maximum predictability of behavior across the parameter space. The methods include quantitative measures of "goodness of behavior" for application of the model, and estimates of the range of parameter values where the model gives a reliable, meaningful output. Documentation is at http://kabir.cbl.cees.edu/~villa/svp/svp.html.
The graphical, object-oriented user interface is a module in
the Collaborative Modeling Environment (CME) which promotes easy
integration with state-of-the-art GIS packages and sharing and
reuse of input and output data. The interface environment allows
users to prepare unit models to run spatially, define data input
and output configurations, choose among display options, and set
calibration data sets. (Collaborative Modeling Environment http://kabir.cbl.cees.edu/~villa/cme/cme.html)
Our main goal this year was to calibrate the spatial model in preparation for running the land use and management scenarios. The hydrology portion of the landscape model, which serves as the major vector for movement across the landscape, has been calibrated at several spatial extents and the full ecosystem model has been implemented and tested for general conformity to expected variable ranges for a Patuxent subwatershed. Hydrology model runs show good agreement between estimated and measured streamflow data for an initial 2-year testing period from 1981-82 (Fig. 1). Several nested subwatersheds were used to test model behavior at a range of spatial extents (23, 940 and 2300 km2). Figure 2 shows surface water flow for the smallest sub-watershed. The model performed well in describing overall surface and ground water flow at all spatial extents with model predictions generally falling within 10% of daily values, although some large flood peaks deviated to a larger extent, which is typical for process-based grid-cell models. This modular approach to calibration worked well for the hydrologic component, with little fine tuning required when switching scales. Further statistical tests are being applied to the spatial hydrologic model calibration.
Figure 1: Calibration results for two gaging stations in Cattail subwatershed. The model is generally able to predict the timing of storms and magnitude of total runoff. Flow during fall and winter is being overestimated in this subwatershed, due to seasonal parameters not adjusted for this scale.
Figure 2: Spatial animation of surface water flow response to a storm event in Cattail Creek (June-July.1981). This corresponds to the time period between day 530 and day 560 in Fig.1 with snapshots generated every four days.
The full ecosystem model displayed expected orders of magnitude in ecosystem stock variables, and appropriate seasonal dynamics in plant growth and nutrient cycling after the initial calibration period. Spatial calibration data on annual increment to forest biomass, which will be used to calibrate the full ecological model, were developed using species-specific tree ring records and spatial distributions in the Patuxent watershed. Tree ring data we collected and analyzed augments existing forest service data and allowed us to evaluate the feasibility of more detailed tree growth studies to evaluate land use effects on growth. Seasonal and longitudinal dynamic records for phosphorus and nitrogen concentrations in the river were compiled for calibration from numerous sources.
The unit model was calibrated non-spatially before it was implemented spatially. State variables and rates were matched to field and literature values using the SPI and directed search algorithm described above. Calibration focused on constraining primary productivity, nutrient fluxes and deposited matter to boundary conditions, including seasonal variation. Calibration data included 10 day maxima in Normalized Difference Vegetation Index (NDVI) measurements which were supplemented with data on stand characteristics from the Forest Inventory Analysis (FIA) database. The unit model was calibrated for two years at a daily timestep.
Unit model calibrations were carried out to test the general model performance for forest typical of the Patuxent watershed. Within the macrophyte sector, calculated forest biomass remained within acceptable bounds established from literature and field data. Figure 3 shows that the model captures important seasonal dynamics in plant growth that are also expressed in stem diameter increases for a similar temperate mixed hardwood forest (Coweeta). Data from the Patuxent watershed sites provided boundary conditions for biomass but seasonal dynamics to track forest nutrients and primary productivity were not readily available. Data from Coweeta proved useful for comparing general dynamics. Data being developing from satellite imagery will be used for calibrating NPP in the spatial model.
The unit model captures the dynamics in soil phosphate but fails to do so for soil dissolved inorganic nitrogen (DIN) (fig. 4). DIN is not well captured by the unit model because the horizontal hydrologic fluxes which control dissolved materials are not part of the unit model. We expect our estimates of nitrogen dynamics to improve once the nitrogen sector is calibrated for the spatial model.
Figure 3: Model net primary production (NPP) plotted against tree diameter at breast height (DBH) data from Coweeta forest to compare seasonal growth dynamics. Stem growth displays a more integrated response to conditions than the daily fluctuations seen in photosynthetic rates. The fit between NPP and stem growth degrades during the second half of the year when stem growth decreases as photosynthetic products are allocated from structural tissue to reproductive and storage tissue. The abrupt drop in NPP seen later is from leaf shedding and is not expressed in stem growth, leading to the divergence between time series. Coweeta data from: F. Day & C. Monk, Recording the stem diameter growth of different species of trees with aluminum vernier tree bands. Coweeta Databank #28.
Figure 4: Seasonal dynamics of phosphate and dissolved inorganic nitrogen for soil interstitial water in a single forest cell, measured as total stock per cell in the model output (black line), and as concentration in Coweeta pine-hardwood forests (grey line). The unit model captures the dynamics of soil phosphate but fails to do so for soil DIN. Soil phosphorus, in contrast to DIN, is controlled by local processes of sorption, allowing dynamics to be modeled non-spatially with higher accuracy. DIN is more likely to be controlled by hydrology and denitrifying conditions at the landscape scale.
As of the beginning of calendar year 1997, the Maryland Office of Planning completed the digitizing of the locations of the centroids of (almost) all land parcels in the State. Since land parcels are the basic unit in any economic study of the landscape, this step was necessary to make economic modeling of the behavior of land owners possible at a spatially disaggregated level. Prior to this, we had used address matching routines that produced variable success, with a strong bias towards non-rural parcels.
During the year we addressed the first of a series of spatial econometrics problems that arise when estimating models using spatially disaggregated data. Spatial econometrics is a relatively new branch of econometrics and, to date, most of the spatial econometrics advances have been made in terms of maximum likelihood estimation. However, our sample sizes are such that the MLE approach is not feasible. We currently have under review one of the first papers in which the Kelejian and Prucha generalized method of moments estimation approach is applied to micro-level spatial data. (See Bell and Bockstael, 1997b).
Economic models of land use change have largely been developed in the urban economics literature in which distance to employment center is expected to drive land prices and ultimately land use pattern. We have begun a series of papers that investigate the process of price determination and land use pattern for the exurban fringe, where most conversion activity is now taking place. Bockstael and Irwin, 1997, is the first step, with subsequent work in progress.
Our preliminary models of land prices and land use conversion have been estimated using the new geocoded parcel level data and adopting some of the appropriate corrections for spatial autocorrelation. These models explain the factors that have the most effect on land values in different uses and therefore the factors that affect pressures for land use conversion. The physical location of the parcel as well as the spatial pattern of regulations affect the value of a parcel in different uses and therefore the likelihood that a parcel will be developed or kept in a natural state or used in agriculture. To date we have investigated the role of the following factors in affecting land use pattern:
To expand the usefulness of dynamic modeling results, model output will either be used directly or in combination with empirical relationships to create indicators with which to judge ecosystem function. Empirical models relating land use configuration to fish habitat were developed and found statistically valid relationships between land use pattern and fish habitat where other work in the region has not. The findings suggests that correlations between land use and in-stream habitat may be more detectable when watersheds are small and similar in hydrologic respects, and when data are used in a time-series cross-sectional model rather than as multi-year means.
An adaptation of the hydrologic model, which had previously been calibrated to an urban-suburban coastal plain watershed (Wainger et al., 1996), was used to evaluate hydrologic indicators of land use change. Change in stream baseflow and in peak storm magnitudes were used to evaluate hydrologic impacts from development in hydrologically important zones of the watershed. Sensitivity to land use proportions and pattern decreased sharply above 60% high density residential and commercial uses. Stream buffers in particular lost the ability to mitigate storm peak flows although they were seen to mitigate stream peak flows at low-moderate levels of development (Wainger 1997). High fragmentation of land use increased stream baseflow but did not mitigate peak flow. The indicators and methods that were developed will be used to test effects of development in the full landscape model on indicators identified as important.
We continue to add important components necessary for scenarios of management or land use change while removing redundant or insensitive components. The macrophyte sector has been updated to improve representation of agricultural practices. The model and database were expanded to include the region's most prevalent crops and rotation methods.
Databases associated with the EPIC agricultural model have been tapped to provide agricultural input and calibration data. The EPIC model output will be compared to the ecosystem model's estimates to evaluate the impact of the lower level of complexity within the GEM model. EPIC has been shown to have low error margins during tests throughout the U.S. during the last 20 years and is structured to analyze issues of crop productivity, and effects of management practices on erosion and water pollution. We will use EPIC variables with low (7-10%) error margins to inter-calibrate: total biomass, nitrogen and phosphate in biomass, crop residue on soil surface, and standing crop residue. In addition, we will compare the orders of magnitude of erosion and soil phosphate and nitrogen levels.
A habitat map and an age-structured population model have been developed and will be integrated into the simulation model over the next year. The deer model provides another means to link ecological and economic impacts.
The extensive database necessary to support the model continues to be updated as new data become necessary or available.
The Spatial Modeling Environment (SME) is an integrated software environment we developed to link georeferenced and other databases to the model for input and calibration (Maxwell and Costanza 1995; http://kabir.cbl.umces.edu/SME3). Recent advances include:
A test comparing SME output from the non-spatial model to commercially
available software (STELLA™, High Performance Systems) found
that the SME output deviated less than 5% from the STELLA model
output for most of the state variables. Larger deviations occurred
in soil nutrient concentrations and in the photosynthetic biomass.
The magnitude of the differences found between SME and STELLA
model runs does not indicate any major problems with the SME code
and appears to be due to differences in equation ordering and
algorithms for preventing negative fluxes.
Bell, K. 1997. A Spatial Analysis of the Transportation-Land Use Linkage: Land Use Pattern and Returns from Highway Investments. Ph. D. Dissertation, University of Maryland.
Bell, K and N. Bockstael. 1997a. An Example of Spatial Economic Modeling: Land Use Conversion in Howard County, MD. Presented at Allied Social Sciences Association meetings, New Orleans
Bell, K. and N. Bockstael. 1997b. Applying the Generalized Methods of Moments Approach to Spatial Problems Involving Micro-Level Data, under review with Review of Economics and Statistics.
Bockstael, N. and K. Bell. 1997. Land Use Patterns and Water Quality: The Effect of Differential Land Management Controls. In International Water and Resource Economics Consortium, Conflict and Cooperation on Trans-Boundary Water Resources, Richard Just and Sinaia Netanyahu, editors. Kluwer Publishing.
Bockstael, N. and E. Irwin. 1997. Modeling Change in the Pattern of Land Use: A Discussion of spatial Models and Models of Spatial Processes. Paper presented at symposium on spatial modeling in economics. Duke University.
Maxwell, T. and Costanza, R., 1995. Distributed Modular Spatial Ecosystem Modelling. International Journal of Computer Simulation: Special Issue on Advanced Simulation Methodologies, 5(3):247-262.
Pickett, S. T. A. et al. 1997. Human Settlements as Ecosystems: Metropolitan Baltimore, MD, 1797-2100. Proposal to NSF. http://chesapeake.usgs.gov/lter/proposal.html.
Wainger, L., T. Maxwell and R. Costanza. 1996. Development of a Landscape Model to Evaluate the Effects of Land Conversion on Hydrology in Sawmill Creek Watershed, Anne Arundel County, Maryland. Final Report to MDNR.
Wainger, L. A. 1997. The Effects of Land Use Pattern on Ecosystems: Development of Hydrologic Simulation and Empirical Habitat Models for Multi-Criteria Policy Analysis. Ph. D. Dissertation. University of Maryland.
Spatial and Unit Model Development, Economic Model: http://kabir.cbl.umces.edu/PLM
Spatial Modeling Environment: http://kabir.cbl.umces.edu/SME3
Collaborative Modelling Environment: http://kabir.cbl.umces.edu/~villa/cme/cme.html
Simulation Performance Index and software: http://kabir.cbl.umces.edu/~villa/svp/svp.html.