Chapter 8: Modeling Physical Systems
Helena Mitasova, Ph.D
Research Associate
Geographic Modeling Systems Laboratory,
Department of Geography,
University of Illinois at Urbana-Champaign,
Urbana, IL, 61801 USA
Lubos Mitas, PhD
Research Scientist
National Center for Supercomputing Applications,
University of Illinois at Urbana-Champaign,
Urbana, IL, 61801 USA
Summary
Human society and ecosystems depend on the quantity and quality of water, air, soil and other natural resources. Our understanding of atmospheric, hydrologic and landscape processes is therefore crucial for environmental sustainability and ecological stability. Besides being key components of life, water and air are also the main carriers of pollutants and modeling of these physical systems is an inherent part of modern environmental research. In this chapter, the general principles used for building models of physical systems are introduced and illustrated by examples describing distribution of surface water and sediment. The role of computational modeling and simulations in providing better understanding of physical processes is discussed and key modeling approaches are explained. Modeling of physical processes is based on representation of spatial phenomena as fields and their discretization, according to the approach used for the solution of governing differential equations. The equations are usually solved by numerical approaches, such as finite difference, finite element and path sampling methods. The role of GIS remains primarily in the area of input data processing, analysis, visualization and management of model results. Simpler models, especially raster-based, can be developed and run within the GIS, using GIS commands, map algebra tools or modeling languages. Several modeling systems include specialized GIS capabilities used for creating the conceptual site models and for customized visualization, analysis and presentation of the results. Because of their role in the environment, models of physical systems are often the core modules in integrated models and decision support systems.
How this chapter fits into the book
This chapter describes how the principles and concepts presented in previous chapters are applied to modeling of physical systems and focuses on the approaches which are specific to these systems. It also explains the importance of physical systems as core modules for integrated environmental modeling, which is described in Chapter 9. Issues of calibration, validation and sensitivity analysis are mentioned, with more details described in Chapter 5. Different levels of coupling with GIS are explained, with more comments on this topic found in chapter 1. The examples are presented for surface water flow and related processes, while dynamic systems and 4D models of physical processes are described in more detail in Chapter 6 and more case studies are given in Chapter 10. The text is accompanied by figures and snapshots from animations created using some techniques described in the Chapter 11.
8.1. INTRODUCTION
One of the key challenges in environmental research is the description of interacting physical processes with sufficient accuracy and efficiency. It is clear, that a rapid development of computer technology offers new opportunities to tackle extremely complex environmental problems. In fact, computational simulation and modeling is becoming a third way of doing scientific research complementing the traditional experiments and analytical theories. Computational approaches belong to "young" methodologies which were developed only over the past few decades and their progress is closely tied to the advances in computer capabilities. As such, they have their own rules, challenges, successes and limitations. The role of algorithms, data structures, computationally efficient methods, advanced visualization and exploration of parallelism are crucial for new advances in environmental research and require close collaboration between traditional research disciplines and computational science.
Originally, GIS applications were focused on static spatial data processing, analysis and computer cartography. However, development of new geospatial data collection technologies and computer capabilities together with acute environmental problems have pushed the GIS applications into more sophisticated levels. Advanced geoscientific applications involve multidimensional phenomena (see chapter 6, also Mitasova et al 1995), dynamics (chapter 6, Mitas et al. 1997), supercomputing class simulations as well as real-time processing of huge amount of measured data (Catin and Fortin 2000). Nevertheless, the process-based modeling of the geospatial phenomena involves substantially more uncertainty than modeling in physics or chemistry. One of the key reasons is the above mentioned complexity of studied phenomena. The practical solutions then have to rely on the best possible combination of physical models, empirical evidence, intuition and available measured data. In physics, the accuracy is usually understood in a much stricter sense, because many fundamental laws are known over a broad range of scales in energy, distance or time. For example, Schrodinger equation describes the matter at the electronic level virtually exactly, that means, within spectroscopic accuracy of 6 to 12 digits. This is seldom the case in complex geoscientific applications where 50% differences between measurements and model predictions can be in many instances considered satisfactory.
8.2 PHYSICAL PROCESSES IN ENVIRONMENTAL MODELING
The physical processes relevant for environmental modeling can be categorized, for example, as
These categories are conveniently based on disciplines, however, many important processes permeate more than one or even all of them. One of the examples is the water cycle which involves the movement of water between the atmosphere and earth surface/subsurface layers. Another case is the carbon cycle which describes the evolution of carbon in the full variety of its forms: generation and transport of gases such as carbon dioxide and methane, life cycles of organic matter of plants and animals, organic matter in soil, etc. It is becoming obvious that water and carbon cycles will play a key role for sustainability of life on Earth and they are the focus of large efforts in environmental modeling (Krysanova 2000).
8.2.1 Model types and components
Computational approaches to investigations of physical systems are based on simulation and modeling. By simulation we understand a computer representation of reality in which the simulated system is governed by a set of known physical laws expressed in mathematical language. In this case the model is already in place and its range of validity and accuracy is supposed to be well-known and verified. The task of simulation is to solve it for a particular realistic situation. The fact that the fundamental laws are known does not mean that simulations are straightforward or easy. The corresponding equations are often difficult to solve and barriers in computational feasibility and efficiency often limit accuracy, resolution or size of the modeled system.
On the other hand, by modeling we understand a process by which the scientist is trying to build a simplified version of reality for phenomenon for which the fundamental laws are either unknown, impractical to use or simply do not exist. This typically involves systems which are very complex, with many constituents and variety of interactions between them and with limited amount of available experimental information. Typical examples are many ecological models, and systems which involve anthropogenic activities. Modeling process often involves trial and error effort and in some cases its predictive power, accuracy and relation to reality might be a research problem on its own.
Physical systems are often described by a combination of deterministic (physically based) and empirical models. Empirical models are based on observations and statistical analysis of observed data and their applicability is limited to the conditions for which they were developed. They can provide a rough picture of the phenomenon under study, but they cannot explain how the system works. Because of their simplicity, they are widely used for practical applications and as components of more complex models for the sub-processes for which the physical model is unknown or too complicated. Physically based models take into account the nature of physical processes behind the observed phenomena and are usually based on:
Models can be further categorized according to several criteria. Based on the treatment of spatial distribution models can be divided essentially into two classes.
Models based on homogeneous or spatially averaged units. In hydrologic applications, the units represent watershed hierarchies, channels and stream networks, lakes, wetlands or hillslope segments (Helleweger and Maidment, 1999; Flanagan, 2000; Band 2000). The processes are then described by unit-to-unit transport rules or by ordinary differential equations for quasi-1D flow. This approach is very effective for systems which include man-made structures (urban hydrology, agricultural fields), however, adequate selection of units, their network topology and hierarchies can be time consuming for larger areas and can require substantial expertise. This is true especially for complex, natural environments which cannot be easily described by simple geometrical features (e.g., a complex hillslope by a tilted plane, curved stream by a line segment).
Distributed models rely on different discretizations of fields/multivariate functions, such as regular or irregular grids or meshes, derived from the numerical methods used for solving the governing equations. The most common approaches are based on finite differences, finite elements and variety of spectral projection methods. Very recently, path sampling strategies were employed for some of the water and soil transport problems because of their simplicity, robustness and scalability.
8.2.2 Equation examples
Many physical processes can be described by partial differential equations which are "built" according to the complexity of the underlying system. A simple 2D continuity equation approximately describes steady state shallow water flow over a hillslope :
Ñ × [h(r) v(r)] = i (r) (8.1)
where Ñ is the divergence operator, r =(x,y) is a position, h(r) is the water depth, v(r) is the water flow velocity vector field and i(r) is the rainfall excess. If we assume uniform flow velocity, the explicit solution of this equation can be expressed as a function of upslope contributing area, which can be computed using standard GIS flow tracing functions (Figure 8.1b,c). More realistic solution which takes into account variable flow velocity (due to topography and land cover) requires numerical solution of the equation (8.1) (Figure 8.1d,e,f).
¶ h(r,t)/¶ t + Ñ × [h(r,t) v(r,t)] = i (r,t) (8.2)
where the first term represents the change of water depth due to time t, and the second term represents the change in water depth due to space.
Surface water flow can detach soil and transport it over landscape, which can be described by an equation similar to equation (8.2) with additional terms
¶ c(r,t)/¶ t + Ñ × [c(r,t) v(r,t)] - D D c(r,t) = sources (r,t) - sinks(r,t) (8.3)
where c(r,t) is the sediment concentration and the term D D c(r,t) describes the diffusion which is a result of random influences. On the right side is the sources/sinks term which describes inflows or outflows of the quantity c(r,t). This equation includes both deterministic and stochastic influences, which is typical for most natural processes. Even more general equation would include a rate term
¶ c(r,t)/¶ t + Ñ × [c(r,t) v(r,t)] - D D c(r,t) + U (r,t) c(r,t) = sources (r,t) - sinks(r,t) (8.4)
where U (r,t) is a "potential" which describes the local rate of proliferation or diminishing of c(r,t) .
8.2.4 Methods of solution
The differential equations describing the spatial processes are usually solved in a discretized form. Typical approaches include finite difference (see chapter 5) and finite element methods (Burnett, 1987). The detailed description of these standard methods is beyond the scope of this paper, but we briefly introduce a newer method, which has a real potential for many geoscientific applications. The approach is called path sampling (other names such as random walks are also common, Gardiner (1985)) and relies on the duality: field ó particle density. Suppose that we have an equation
L [c(r,t)] = S(r,t) (8.5)
where L is an operator, c(r,t) is the unknown quantity and S denotes sources-sinks. Suppose that L is linear, such as in equation (4), (although weak non-linearities can be treated too). Symbolically, the solution can be written as
c(r,t) = L-1 S (r,t) (8.6)
where L-1 is the operator inverse to L. That, of course, implies that the inverse operator is known, which is seldom the case. Nevertheless, we are able to simulate what is the action of L-1 on S(r,t). This can be done by
i) sampling the source term field by a set of points in the configuration space,
ii) applying the action of L-1 on S (r,t) by using appropriate expression for the Green’s function (Stakgold 1987); points representing S (r,t) evolve and create paths,
iii) transform the solution represented by the path samples to continuous field c(r,t ) by evaluating the path densities.
The path sampling method has been successfully used for many transport type problems. It has several important advantages when compared with more traditional approaches. The method is very robust, can be easily extended into arbitrary dimension, is mesh-free and is very efficient on parallel architectures. Because the method does not rely on meshes it is also rather straightforward to implement in a multi-scale framework . The Figure 8.2 illustrates the approach and the solutions obtained for sediment flow, the applications which use this approach are in Figures 8.5, 8.6.
8.2.4 Problem of multiple scales
Many of the natural processes involve more than a single scale and exhibit multiscale, multiprocess type of phenomena (Steyaert 1993, Green et al. 2000). Problem of multiple scales now permeates a number of scientific disciplines such as materials research, geosciences, and biology. Some multiscale problems can be partitioned into a system of nested models in the direction from fine to coarse scales. This basically requires to develop effective model on each scale level which incorporates simplified or "smoothed out" effects coming from finer, more accurate levels. On the other hand, in the direction from coarse to fine scales, one develops a set of effective embeddings which determine boundary and/or external conditions for the processes on finer scales. The high accuracy, resolution and processes of fine scales are then used only in "hot spots" of the studied system which require such a treatment.
It is interesting that in many cases such partitioning/model nesting might be very difficult. This is true whenever the system exhibits fluctuations which appear over large range of scales which can reach up to the size of the whole system. Such examples exist in nature: an onset of magnetism in magnetic materials, self-organized criticality (Favis-Mortlock et al. 1998) and others. In these cases one has to carefully "filter-out" the inherently multi-scale effects first. Such models are being studied and have been constructed, however, their investigation is a research problem by itself. Another case for which a simple scale decomposition and nesting might not work are nonlinear and unstable systems. Whenever a small perturbation can rapidly overtake a large part or even the whole system (detonation phenomena, collapse of a large engineering or natural structure, avalanches, etc) accurate description and decomposition is difficult and often crude approximation have to be made to enable feasible studies.
8.3. MODELS AND GIS
The use of GIS for environmental modeling has substantially increased over the past 5 years, moving from research to routine applications (Goodchild et al, 1993,1996, 1997). The implementation of new modeling functions, improvements in capabilities to import/export data in various formats, and the introduction of object oriented technology facilitate more efficient use of GIS functionality and support coupling of models with GIS at different levels. The type of coupling usually depends on the model complexity as well as on the target audience. Developers and researchers with full understanding of the underlying theory, algorithms and source code, often work with "GIS independent" models, while using a wide range of software tools (including GIS) to support the model development and applications. Land owners, decision makers, and public in general need a different modeling environment, with easy to use models, analysis and visualization tools, supporting adequate understanding and interpretation of results. With the growing use of GIS by users with different backgrounds, the linkage between GIS and models has taken many forms and levels of complexity.
Full integration of models within GIS: embeded coupling. Models which are useful for a wide range of GIS applications are often developed and implemented within a GIS using its programming tools, such as Application Programming Interface (API), scripting language, or map algebra operations. Model is then run as a GIS function or command, the inputs and outputs are stored in a GIS database and no data transfer is needed. Portability of the model is restricted, and the enhancements as well as the maintenance of the model is dependent on the GIS. This type of model development is further supported by customization and application development tools (ESRI, 1996), extensions to map algebra (Wesseling et al., 1996; Park and Wagner, 1997) and visual modeling tools (Murray et al., 2000).
Implementation of simple models within a raster GIS is relatively easy using the combination of map algebra operations and raster GIS functions. Site-based models, which are location dependent but do not incorporate spatial interaction, can be implemented as spatial models by applying the underlying equation(s) to each spatial unit (grid cell or polygon) using map algebra. Models, which involve spatial interactions, such as approximation of steady state water flow, can be computed using a flow tracing function (Mitasova et al., 1995; Moore et al., 1993 ) or the neighborhood syntax of the map algebra (Shapiro and Westervelt, 1992). Accuracy and realism of the resulting water flow pattern is then dependent on the underlying algorithm used for the flow tracing and on the quality of input data, as illustrated by Figure 8.1b,c and Figure 8.3.
Map algebra operations have been successfully used for the development of simple dynamic models using cellular automata or finite difference methods for solving underlying partial differential equations. This type of dynamic models have been developed both within the the general GIS as well as for more specialized systems and GIS extensions, such as the PCRaster with its high level programming language supporting development of dynamic models (Wesseling et al., 1996; Burrough et al, 2000, Sluiter, 2000), or cellular automata extension of IDRISI (Park and Wagner, 1997).
Full integration of complex models involving solutions of coupled partial differential equations has been limited, in spite of several successful implementations (Saghafian, 1995; Doe et al., 1996; Vieux, 1995). Among the basic obstacles is the fact that the support for double precision floating point data, an essential requirement for effective modeling of nonlinear phenomena, is less than adequate. For example, in the most widely used GIS, the floating point grids are supported, however, the tools for creating suitable nonlinear color tables or categories are not available and the number of significant digits can be cut-off during processing without giving any warning leading to the loss spatial variability for entire regions (Mitasova and Mitas, 1999). With the growing number of 3D dynamic models (Rogowski, chapter 6) better and/or cheaper support for temporal 3D data and finite element meshes would be needed. Even with all the necessary capabilities available within the GIS, the biggest disadvantage of full integration of complex models is that the models become too dependent on the development and fate of a particular GIS. Changes in the GIS data structures, functionality, interface, libraries or programming tools, which are beyond the control of the model developers, may require time consuming changes in the models or the models become incompatible with the latest version of the GIS software. Also, the fully integrated model is less portable and users have to install entire GIS even if they need the model only for a one-time application. Therefore, alternative methods of coupling have been more widely adopted, for complex models.
Integration under a common interface: tight coupling. This level of integration has been widely used for existing models which were developed outside GIS. GIS and model are linked through a common interface which guides the user through the steps needed for input data processing, running the models and analyzing and presenting the results. The model has its own data structures and the interface provides the tools to extract the input data from the GIS layers and create the associated databases in a format required by the model. The interface also allows the user to visualize the results using both the GIS display tools and specialized graphical and numerical outputs. This type of integration has proven to be effective for several hydrologic and non-point source pollution models (Khairy et al 2000, Srinivasan and Arnold 1996: SWAT, Rewerts and Engel 1996: ANSWERS, Srinivasan and Engel 1991: AGNPS, EPA 2000: BASIN-2). Several models have been coupled with more than one GIS (e.g., SWAT, ANSWERS with both GRASS and ArcView). This approach have been used not only for coupling of a single model with GIS but also for development of modeling systems supporting simulation of numerous interacting processes (Frysinger, chapter 9).
Linkage through the import/export of data: loose coupling. Improvements in GIS import/export capabilities as well as the increased availability of digital geospatial data have made the loose coupling a routine procedure used with almost any stand-alone landscape process model. In this case, the model is developed and run independently of GIS while input data are processed and exported from GIS and results are imported to GIS for analysis and visualization. Using a common data format (e.g. regular grid or a vector data structure designed consistently with a given GIS) makes this coupling more efficient. However, changing the input data for simulation of different scenarios is not very convenient and this approach is therefore suitable for applications where the need for modifications of input data is small. The model is to the large extent independent from GIS, it can therefore be used with different systems and changes in GIS will have minimal impact on the functionality of the model. There is a large number of models with this type of GIS coupling, for example SIMWE-erosion and deposition model (Mitas and Mitasova, 1998), SWMS2D for hydrologic modeling of watersheds with drainage (Badiger et al., 2000).
Incorporation of GIS functionality into the modeling systems. Large, professional modeling systems, most often aimed at engineering applications, use both loose coupling with a GIS and its own, specialized GIS capabilities. A general GIS is used for storing, managing and processing of basic topographic data and for generating the cartographic output. The modeling system includes support for GIS functions where tight coupling with the model is necessary, such as the design of a conceptual model for the given site, adjustment of finite difference/finite element grids and meshes, as well as modifications of the model parameters (conditions of simulations) based on the simulation results. Because many of the professional systems are dynamic and 3D, they also have their own visualization capabilities specific to a given discipline. State of the art systems with this type of GIS coupling have been developed for groundwater and surface water modeling (Holland and Goran, 2000; Environmental Modeling Research Laboratory: GMS/SMS/WMS, Danish Hydrologic Institute 2000: MIKE11,21), urban hydrology (Danish Hydrologic Institute 2000: MOUSE; Johnston and Srivastava, 1999: HydroPEDDS) or oil spill simulation (Cantin and Fortin, 2000). Several geoscientific models are coupled with systems which are not considered a GIS, however, they have spatial data processing and visualization capabilities, and a high level programming language which allows the users to write the models efficiently - for example, the landscape evolution model CHILD (Tucker et al, 1999) is coupled with MATLAB.
GIS and the web based models With the explosive growth of the Internet, physical proces models useful for a wider range of users, such as farmers, land owners, city planners or public land managers are being implemented as web-based applications. The successful applications include not only the modeling tools but also the databases with input data and model parameters so that the user does not have to deal with the time consuming tasks of finding, processing and submitting the input data for the model runs. Usually only selection of the location and land use management scenario is needed from the given set of options. Spatial data are stored in a GIS on the server and the digital maps, representing the inputs and model results, are served using internet map serving technology, such as ArcView IMS, MapObjects IMS (ESRI 1999/2000) or GRASSlinks (Neteler 2000). The web-based models of physical systems were developed for example for long-term hydrological impact assessment LTHIA (Engel 2000), watershed based hydrology and pollution modeling BASIN-2 (EPA 2000) or terrain analysis based hydrologic modeling TOPOG (CSIRO 2000).
8.4. CASE STUDIES
To illustrate the presented concepts, examples of models, modeling systems and applications with different levels of complexity and GIS coupling are described. The case studies are focused on modeling of surface water flow and its impact of soil erosion and deposition. Case studies which include global climate, ocean, fresh water and related land use and ecological modeling are presented by Mackey in chapter 10.
8.4.1 Modeling erosion and deposition pattern using standard GIS tools
Cost effective land maintenance and rehabilitation at military installations requires identification of critical areas which should be targeted for erosion prevention. High resolution, process-based simulations provide valuable tool for assessing the current situation and predicting erosion and deposition patterns for various land management conditions. In this case study, the erosion deposition pattern was estimated using GRASS GIS and its interpolation, flow tracing, topographic analysis, visualization and map algebra tools. The erosion and deposition pattern was computed using Unit Stream Power Based erosion/deposition model USPED (Mitasova et al. 1998, Mitasova and Mitas upcoming). It is a simple model which predicts the spatial distribution of erosion and deposition rates for a steady state overland flow, with uniform rainfall excess, for transport capacity limited case of erosion process. The model is based on the theory originally outlined by Moore and Burch (1986) with numerous improvements. For the transport capacity limted case, we assume that the sediment flow rate is at the sediment transport capacity T(r), r=(x,y) which is approximated as a function of upslope area A(r), slope b(r)
T(r) = R(r) K(r) C(r) P(r) A(r)m (sin b(r))n (6)
where R(r), K(r), C(r) are the spatially variable RUSLE rainfall, soil and cover factors, used as weights to incorporate the impact of rainfall intensity, soil, and cover, while and m and n are constants, with m=1.6, n=1.3 used for prevailing rill erosion and m=n=1 for prevailing sheet erosion. Then the net erosion/deposition E(r) is estimated as
E(r) = Ñ × [T(r) .s(r)] = ¶ (T(r)*cos a(r))/¶ x + ¶ (T(r)*sin a(r))/¶ y (7)
where s(r) is the unit vector in the steepest slope direction and a(r) [deg] is aspect of the terrain surface. Caution should be used when interpreting the results because the RUSLE parameters were developed for simple plane fields and detachment limited erosion, and to obtain accurate quantitative predictions for complex terrain conditions they need to be re-calibrated.
The model can be implemented using a sequence of GIS commands and map algebra operations. Assume that the elevation, K, C are given as raster data and R=120 and resolution=10 are constants. Then the model can be comupted in GRASS5.0 as follows: (see Mitasova and Mitas 1999: http://www2.gis.uiuc.edu:2280/modviz/erosion/usped.html for more detailed description of implementation in both ArcView Spatial Analyst and GRASS5.0)
1. r.flow elevation dsout=flow (computes upslope area) 2. r.slope.aspect elevation slope=slope aspect=aspect (derive slope/aspect) 3. r.mapcalc sflow=exp(flow*res,1.6)*exp(sin(slope),1.3) (transport capacity term) qsx = 120 * K * C * sflowtopo * cos(aspect) (sediment flow vector) qsy = 120 * K * C * sflowtopo * sin(aspect) 4. r.slope.aspect qsx dx = qsx.dx (components of sediment flow divergence) 5. r.slope.aspect qsy dy = qsy.dy 6. r.mapcalc erdep = qsx.dx + qsy.dy (net erosion/deposition = div of sediment flow) 7. r.colors erdep rast=old.erdep (assign nonlinear color table)
Slope, aspect, and partial derivatives dx, dy are computed using Horn's formula (Horn 1981, Shapiro and Westervelt 1992) implemented in r.slope aspect, but they can be also computed using the neighborhood syntax of map algebra (Westervelt and Shapiro 1992). The implementation will be similar in any raster GIS, however the results of the model will greatly depend on the quality of the DEM (Figure 8.3) and the slope and flow algorithms used in the specific GIS (Figure 8.1). As a one time application, this model is easy to run as a sequence of commands. For routine, repeated applications for different locations or different land use patterns, the model can be implemented as a script with suitable interface for selecting the input data and viewing the results.
The results of the application of this model to a military installation with combination of high intensity use and well preserved areas is in Figure 8.4. The model predicts severe erosion on the upper convex parts of hillslopes with bare soil and in areas with concentrated flow. Significant portion of soil eroded from hillslopes has a potential for being deposited before entering the streams, however, the potential for deposition of soil eroded by concentrated flow is much smaller. This type of analysis is being used for designing the training areas and implementation of conservation and mitigation measures to prevent negative impacts of erosion on soil and water quality.
8.4.2 Process based simulation of water depth and erosion/deposition using models with loose GIS coupling
Simulation of spatial distribution of water depth provides valuable information for identification of locations which require drainage to prevent negative impact of standing water on yields. Using a high accuracy DEM interpolated from rapid kinematic survey data by the RST method (Mitas and Mitasova 1999) within GRASS5.0, the water depth distribution was simulated for a typical rainfall for Midwestern agricultural fields (9mm/hr) under saturated conditions. The simplified water flow approximation by kinematic wave, e.g. by using the r.flow command in GRASS5.0 was not sufficient for a flat terrain with depressions (as explained by Figure 8.1b,c,d) and a two dimensional approximate diffusive wave simulation implemented in a GIS independent model SIMWE (Mitas and Mitasova 1998) had to be used. The gradual accumulation of water in depressions is shown by the 3 snapshots from the simulation during the uniform, steady rainfall (Figure 8.5a,b,c) and locations where water will stand several hours after the rainfall (taking into account also simplified infiltration) is in the Figure 8.5d. The resulting water depth maps were used to evaluate suitability of the locations of current drainage and to plan the location of new drainage network in the negatively affected field. While the model was very useful for evaluating and planning of spatial pattern of the drainage network, detailed soil data and more complex dynamic simulations with coupled surface and subsurface flow (Badiger et al., 2000) are necessary to optimize the size, depth, structure and other drainage network parameters.
Recently, benching effect of hedges has gained an increased interest as a cost effective alternative to more complex terraces. Hedges are about 1-1.5m wide strips of dense vegetation installed along contour lines and the field data suggest that the combination of water erosion and tillage leads to natural creation of terraces along these hedges (Dabney et al., 2000). Modeling the impact of hedges poses a special challenge - the deposition is observed within and above the hedges which means that backwater effect is present, erosion is observed below the hedges due to the cleaner water coming from hedges. Moreover, increased deposition above the hedges is observed in swales with convergent flow and increased erosion is observed on noses with dispersal flow. Interaction of these complex phenomena make it difficult to predict these effects using the traditional approaches based on 1D flow over predefined hillslope segments and a 2D continuous diffusive wave approximation which incorporates also the terrain change is needed. We have used a time series of SIMWE (Mitas and Mitasova 1998) simulations which included the change of terrain due to erosion and deposition, to evaluate the suitability of the model for predicting the functioning of hedges. Terrain and erosion/deposition pattern development after 7 steady state events with uniform rainfall excess 36mm/hr, and Mannings n=0.2 (hedge) and n=0.15 (field) results in deposition above and within the hedge and erosion below the hedge (Figure 8.6). The impact of swales and noses is also correctly simulated due to the use of 2D flow in simulation. These results are preliminary and are used to further develop the model so that the dynamics during the event as well as the temporal change in terrain can be properly simulated.
8.4.3 Hydrologic modeling using systems with GIS capabilities
Groundwater, Surface Water and Watershed Modeling Systems (Environmental Modeling Research Laboratory) and the MIKE/MOUSE family of hydrologic programs (Danish Hydrologic Institute) are excellent examples of systems which incorporate their own set of GIS tools. For example, GMS is a groudwater modeling system developed by Department of Defense which provides interface and tools for performing simulations with several groudwater models such as MODFLOW. Specialized GIS cabilities are provided within the Map module which uses data model similar to ArcInfo, facilitating efficient exchange of data between the GMS and ArcInfo/ArcView. The Map module is designed for development of conceptual model of the modeled site - a task which would be possible, but more time consuming with general GIS tools. Map module provides the tools to define the locations of sources/sinks, model boundaries, and specific layer parameters, which are then used to automatically construct a finite difference grid for the simulation. GIS objects are then overlaid on the conceptual model and the relevant information (stresses: rivers, wells, recharge zones, etc.) is inherited by the grid cells in the format used by the groundwater model While it is still necessary to use GIS for such tasks as data projection, if the data are not in the form directly usable by Map module, shifting some of the specific data preparation tasks from GIS to GMS makes modification of model configuration much faster and simpler, so the model can be run for different scenarios efficiently. GMS has also its own tools for multivariate interpolation and visualization - tools which either are not widely available in GIS or are expensive. DoD has been developing similar systems for modeling surface water in rivers and lakes (SMS, Figure 8.7) and watersheds (WMS).
8.5 CONCLUSIONS AND LESSONS LEARNED
The current research and development in physical systems modeling is focused on distributed, process-based models, often dynamic in 3D space. This trend has been stimulated by the availability of geospatial data and supporting GIS tools. GIS has greatly reduced the time for preparation of inputs, however, this task can still be rather tedious and time consuming. Artifacts from interpolation remain a perennial problem and the support for high precision floating point, temporal and mutidimensional data is still inadequate. Therefore coupling of GIS and models is done at various levels and incorporation of GIS functionality within the modeling systems is now quite common. The models of physical processes are often core modules for integrated modeling systems, due to their impact on ecosystems and society. Models of physical systems are also important components of decision support systems.
The current research in the area of coupled GIS and physical systems modeling focuses on object oriented model development (e.g., Band 2000, Helleweger and Maidment 1999, Naumov 2000), real-time simulations (e.g., Cantin and Fortin 2000), multiscale simulations and modeling with heterogeneous data (e.g., Mitasova and Mitas, 2000, Green et al. 2000), as well as distributed on-line modeling (Engel 2000). At the same time, GIS as a single general system is disappearing and GIS is melting into the general computing infrastructure. We can see assimilation of GIS into end-user applications rather than integrating applications into the GIS and we can expect this trend also in modeling of physical systems.
Just a few years ago, there were numerous efforts to built comprehensive modeling and problem solving environments which would provide essentially everything for doing both the routine processing and advanced modeling as well as development of new methods and technologies. The practice, however, seems to be going in other directions as well. The large, universal, thought-through, all-powerful systems which were expected to support almost every possible research or development need ("research cathedral" , Raymond, 1999) are, in fact, not practical. The maintenance of large software package is expensive, rigid and inefficient. More successful is a concept of cooperation between a number of smaller software units and tools, environments and program packages. This concept enables to create more independent smaller pieces of software with simplified interdependencies. It enables for a number of groups or individuals to contribute and work on various parts simultaneously. If some branch of development proves to be uninteresting or unproductive it rapidly dies out without necessity to go through decision hierarchies usually present in the other paradigm. In contrast to the "cathedral" such a framework creates a "research bazaar" which offers variety of combinations and provides in effect a market of tools which can be combined together or used for data processing, modeling, method development and their combination. This in many cases is more useful for new advances in scientific exploration as the most exciting and influential research breakthroughs happen through stepping outside the established routes.
Acknowledgments We would like to acknowledge the long term support for environmental modeling research from Geographic Modeling Systems Laboratory director Douglas M. Johnston as well as GIS assistance by William M. Brown. The funding was provided by the USArmy CERL, Strategic Environmental Research and Development Program and Illinois Council on Food and Agricultural Research (CFAR). We greatly appreciate the sharing of data by S. Warren, K. Drackett and S. Dabney.
8.6 REFERENCES
Badiger S.M, Cooke R.A.C (2000) Application of integrated GIS and numerical models in subsurface drainage studies. Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Band L.E., (2000 ) Urban watersheds as spatial object hierarchies. Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Burrough, P.A. (1998). Dynamic Modelling and GIS, Chapter 9, In: P.Longley et al.(Eds) Geocomputation: a Primer. Wiley, pp165-192.
Burrough, P.A., da Costa, J.R., Haurie, A., Fedra, K., Salvemini, M., & Hauska, H. (2000) MUTATE: a web-based distance learning programme for environmental modelling with GIS. Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Burnett D. S. (1987). Finite Element Analysis: From Concepts to Applications, Addison-Wesley, Reading, MA.
Cantin J.-F., Fortin P. (2000) Integration of Numerical Models and Field Characterization into a Georeferenced System for Oil Spill Emergency Response in the St. Lawrence River, Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Dabney, S.M. (1999) Lanscape Benching from Tillage Erosion Between Grass Hedges. Proceedings from ISCO Conference, CDROM, Lafayette: Purdue University.
Doe, W.W., B. Saghafian, and P.Y. Julien (1996). Land Use Impact on Watershed Response: The Integration of Two-dimensional Hydrological Modeling and Geographical Information Systems. Hydrological Processes, 10, 1503-1511.
ESRI (1999/2000) Four software products feature web-mapping functionality. Arc News 21, p. 7.
ESRI (1994) Cell-based Modeling with GRID. Redlands: ESRI.
ESRI (1996) Avenue: Customization and application development for ArcView. Redlands: ESRI.
Favis-Mortlock D., Boardman J., Parsons, T., Lascelles, B. (1998) Emergence and erosion: a model for rill initiation and development. Proceedings of the 3rd conference on GeoComputation (CDROM), University of Bristol, UK.
Gardiner, C. W., (1985) Handbook of Stochastic Methods for Physics, Chemistry, and the Natural Sciences. Berlin: Springer.
Goodchild, M.F, L. T. Steyaert, and B. O. Parks, eds., (1993) Geographic Information Systems and Environmental Modeling. New York: Oxford University Press.
Goodchild, M.F., L. T. Steyaert, and B. O. Parks, eds.,(1996) GIS and Environmental Modeling: Progress and Research Issues. Ft. Colins: GIS World, Inc.
Goodchild, M.F., L. T. Steyaert, and B. O. Parks, eds, (1997) GIS and Environmental modeling .Proceedings of the 3rd conference on GIS and Environmental modeling (Santa Fe), NCGIA, CDROM .
Green, T. R., Ascough, J. C. and Erskine, R.H. (2000) AgSimGIS for integrated GIS and agricultural system modeling: II. Application to soil-water dynamics in an undulating landscape in Colorado, Proceedings of 4th conference on GIS and Environmental modeling . CDROM, Banff, Canada.
Heinzer ,T.J., Sebhat, M., Feinberg, B. (2000) Case Studies using Geographis Information Systems to Facilitate Data Integration with MIKE21 when Modeling Flood Inundation Scenarios, Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Helleweger, F.L., Maidment, D.R. (1999) Definition and Connection of Hydrologic Elements Using Geographic Data, Journal of Hydrologic Engineering 4, 10-18.
Holland J and Goran W (2000) Development of a Land management system in support of natural resources management. Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Horn B. K. P. 1981 Hill shading and the reflectance map. Proc. IEEE 69, 14-46.
Johnston, D.M. and Srivastava, A. (1999) Decision Support Systems for Design and Planning: The Development of HydroPEDDS (Hydrologic Performance Evaluation and Design Decision Support ) System for Urban Watershed Planning, 6th International Conference on Computers in Urban Pl anning and Urban Management (CUPUMS'99), Venice, Italy
Khairy, W., Hannoura, A.P., Cothren, G.M. (2000). Application of Information Systems in Modelling of non-point pollution, Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Krysanova V., Wechsung F., (2000) Analysis of global change impacts at the regional scale by means of integrated ecohydrological modelling. Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Mitas, L., Mitasova, H., (1999) Spatial Interpolation. In: P.Longley, M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Information Systems: Principles, Techniques, Management and Applications, Wiley, 481-492.
Mitasova, H., and Mitas, L. (1999) Erosion/deposition modeling with USPED. WWW tutorial.http://www2.gis.uiuc.edu:2280/modviz/erosion/usped.html
Mitas, L. and Mitasova, H. (1998) Distributed erosion modeling for effective erosion prevention. Water Resources Research, 34, 505-516.
Mitas, L., Brown, W. M., Mitasova, H. (1997) Role of dynamic cartography in simulations of landscape processes based on multi-variate fields. Computers and Geosciences, 23, 437-446 http://www2.gis.uiuc.edu:2280/modviz/lcgfin/cg-mitas.html
Mitasova, H., L. Mitas, B.M. Brown, D.P. Gerdes, I. Kosinovsky (1995) Modeling spatially and temporally distributed phenomena: New methods and tools for GRASS GIS. International Journal of GIS, 9 , 443-446.
Moore, I. D., A. K. Turner, J. P. Wilson, S. K. Jensen, and L. E. Band (1993) GIS and land surface-subsurface process modeling, in Geographic Information Systems and Environmental Modeling, edited by M. F Goodchild, L. T. Steyaert, and B. O. Parks, 196-230, Oxford University Press, New York.
Murray , S., Miller W., Breslin P. (2000) Visual framework for spatial modeling. Proceedings from the 4th conference on GIS and Environmental Modeling, CDROM, Banff, Canada.
Naumov, A. (2000) Design of high-level GIS data types for hydroecological modeling in GRASS. . Proceedings from the 4th conference on GIS and Environmental Modeling, CDROM, Banff, Canada.
Neteler, M. (2000). Advances in open source GIS software. Proceedings from the "1st National Geoinformatics Conference of Thailand, Bangkok.
Rewerts, C.C. and Engel, B.A. (1991) ANSWERS on GRASS: Integrating a watershed simulation with a GIS. ASAE Paper No.91-2621. American Society of Agricultural Engineers, St.Joseph, Missouri, 1-8.
Saghafian, B., (1996) Implementation of a Distributed Hydrologic Model within GRASS, in GIS and Environmental Modeling: Progress and Research Issues, edited by M. F Goodchild, L. T. Steyaert, and B. O. Parks, GIS World, Inc., 205-208.
Sluiter, R., Karssenberg,D, Burrough,P.A., Wesseling,C., de Jong, K., Van der Meer, M., van Steijn, H. & Jetten,V. (2000). GMOR: interactive computer models for teaching dynamic geomorphological processes, . Proceedings of 4th conference on Environmental modeling and GIS, CDROM, Banff, Canada.
Srinivasan, R. and B. A. Engel, (1991) A knowledge based approach to extract input data from GIS, ASAE Paper No. 91-7045, American Society of Agricultural Engineers, St.Joseph, Missouri, 1-8.
Srinivasan, R., and J. G. Arnold, (1994) Integration of a basin scale water quality model wi th GIS, Water Resources Bulletin, 30, 453-462.
Stakgold, I., (1979) Green's Functions and Boundary Value Problems, Wiley, New York.
Steyaert L. T., (1993) A perspective on the State of Environmental Simulation Modeling. Geographic Information Systems and Environmental Modeling, Oxford University Press, New York, 16-30
Raymond, E. S. (1999). The cathedral and the bazaar. O’Reilley.
Tucker, G., Gasparini, N., Bras, R., and Rybarczyk, P. (1999) An object-oriented framework for distributed hydrologic and geomorphic modeling using triangulated irregular networks. 4th International Conference on GeoComputation Fredericksburg: Mary Washington College
Vieux, B. E., N. S. Farajalla, and N. Gaur (1996) Integrated GIS and distributed storm water runoff modeling, in GIS and Environmental Modeling: Progress and Research Issues, edited by M. F. Goodchild, L. T. Steyaert, and B. O. Parks, GIS World, Inc., pp. 199-205.
C.G. Wesseling, D. Karssenberg, P.A. Burrough & W. van Deursen 1996, Integrating dynamic environmental models in GIS: the development of a Dynamic Modelling language. Transactions in GIS Vol 1: 40-48, 1996.
6. Information Resources
IDRISI - raster based GIS and its applications
Danish Hydrologic Institute MIKE system
SWAT: Soil and Water Assessment Tool
IDOR2D,3D: Hydrodynamic and pollutant transport simulations
Hydrologic modeling integrated with GIS at EMGIS Laboratory, University of Oklahoma
Environmental Modeling Research Laboratory - hydrologic models GMS, SMS, WMS linked to ArcView
Hydrologic models linked to GIS
LTHIA - on-line, long term hydrologic impact assessment
Stochastic modeling of petrophysics
Geographic Modeling Systems Laboratory
ESRI-GRID, Avenue, Spatial Analyst
IDRISI - raster based GIS and its applications
Dr. Helena Mitasova is a Research Associate in the Geographic Modeling Systems Laboratory, Department of Geography, University of Illinois at Urbana-Champaign. Her research has been focused on modeling of landscape processes, spatial interpolation and multidimensional visualization for GIS. She has been partcipating in the development of OPEN source GRASS GIS since 1991.
Dr. Lubos Mitas is a Research Scientist at the National Center for Supercomputing Applications, University of Illinois at Urbana-Champaign. His research involves computational materials research, quantum Monte Carlo methods and development of methods for spatial interpolation and simulation of landscape processes.