SYSTEM DYNAMICS (SD) MODELING

System Dynamics (SD) is a rigorous method of system description, which facilitates feedback analysis via a simulation model of the effects of alternative system structures and the control policies of system behaviour (Simonovic, 2009). The advantages of system dynamics simulation include: (a) facilitating the simplicity of use of system dynamics applications; (b) a greater applicability of the general principles of system dynamics to social, natural, and physical systems; (c) the ability to address how structural changes in one part of a system might affect the behaviour of the system as a whole; (d) a combined predictive (determining the behaviour of a system under particular input conditions) and learning (the discovery of unexpected system behaviour under particular input conditions) functionality; and (e) an active involvement of stakeholders in the modeling process. The strength of the system dynamics approach is

largely in representing temporal processes. SD models, however, do not adequately represent spatial processes. For example, SD models can be used for the analysis of different flood management policies and the estimation of flood damages (as a function of time). However, SD modeling provides no easy way to represent damage topographically. A simple SD model is therefore inadequate for developing an overland flood model that can capture both spatial and temporal variability in the propagation of flood flows. Given that SD is adept at representing temporal processes (with a limited capacity for spatial modeling), and GIS is useful for spatial modeling (with a limited capacity for temporal representation), the logical step in the development of a more comprehensive methodology is the integration of SD with GIS to model the spatio- temporal dynamics of engineering systems.

System dynamics has a long history as a modeling paradigm with its origin in the work of Forrester (1961), who developed the subject to provide an understanding of strategic problems in complex dynamic systems. System dynamics is grounded in control theory and the modern theory of nonlinear dynamics. More details on SD modeling can be found elsewhere (Sterman, 2000; Ford, 1999; and Coyle, 1996). System Dynamics is a promising approach for modeling complex dynamic systems. SD has been successfully applied to policy analysis in the area of business (Sterman, 2000), health care (Royston et al., 1999), and environmental management (Ford, 1999; and Sudhir et al., 1997). The concepts and applications of system dynamics approaches to a variety of problems have been discussed by several authors (Sterman, 2000; Forrester, 1961; and Coyle, 1996). System dynamics is becoming increasingly popular for modeling water resource systems.

Palmer (1998) has done extensive work in river basin planning using SD. Keyes and Palmer (1993b) used SD simulation modeling for drought studies. Matthias and Frederick (1994) have used SD techniques to model sea-level rise in coastal areas. Fletcher (1998) has used system dynamics as a decision support tool for the management of scarce water resources. Simonovic, et. al., (1997) and Simonovic and Fahmy (1999) have used a SD approach for long-term water resources planning and in policy analysis for the Nile River Basin in Egypt. The SD approach has been used to model reservoir operation for flood control (Ahmad and Simonovic, 2000a), operation of multiple reservoirs for hydropower generation (Teegavarapu and Simonovic, 2000), calculation of flood damages (Ahmad and Simonovic, 2000b), and analysis of the economic aspects of flood management policies (Ahmad and Simonovic, 2000c). Simonovic (2002) has used SD to develop a world water model. Li and Simonovic (2001) have developed a SD model for predicting floods from snowmelt in North American prairie watersheds. Ahmad and Simonovic (2001c) used SD as a decision support tool for the evaluation of impacts of flood management policies. The spatial system dynamics approach (SSD) developed by Ahmad and Simonovic (2004) can model dynamic processes in time and location in space with certain limitations.

The strength of the system dynamics approach is in its ability to represent temporal processes. SD models are excellent tools for planning and policy analysis. SD models, however, do not adequately represent spatial processes. For example, system dynamics models can be used for the analysis of different flood management policies and the estimation of flood damages (as a function of time). Given the strength of SD in

representing temporal processes with restricted spatial modeling capabilities, and the competency of GIS for spatial modeling with limited representation of temporal aspects, a logical alternative is the integration of system dynamics with GIS to model spatial dynamic systems. Attempts have been made to add spatial dimensions to system dynamics models. These attempts can be divided into two categories: (a) introducing spatial dimensions into the system dynamics model (implicit approach) or (b) translating system dynamics model equations to run in GIS. The first approach does not represent spatial dimensions in an explicit manner. The Mono Lake model is an example of this approach (Ford, 1999). In this model spatially important features of the system are represented with one or two aggregate relationships. The complex shape of the Mono basin affects the water flow, which is modeled by two non-linear functions: (a) surface area – volume curve; and (b) elevation - volume curve. The second approach of adding a spatial dimension to the system dynamics models involves translating SD model equations into a programming language and interfacing with GIS. For instance, Costanza et al. (1990) combined a GIS with a system dynamics model for ecological modeling. They used Stella (HPS Inc., 2001) to develop ecological models and then translated the model into Fortran through a separate program to interface with the GIS. To study the effects of fire on landscape patterns Baker (1992) interfaced four models with a GIS to control the simulation, data handling, and display. A decision support software package, Extend and EML (Environmental Modeling Language), were used by Theobald and Gross (1994) to explore landscape dynamics (a fire spread and population model). They combined SD, GIS and CA to provide spatial-temporal modeling capabilities for landscape dynamics. Work on modeling mobile individuals in dynamic landscapes is

reported by Westervelt and Hopkins (1999) using software packages IMPORT/ DOME, GRASS, and SME (Spatial Modeling Environment). In these studies, the work is focused on spatial modeling (emphasis on GIS) and SD is used to bring the dynamic modeling (temporal aspect) capability into the GIS environment. Since system dynamics model equations are translated to run within a GIS, a drawback of the approach used in these studies is the loss of the interactive power of SD (changes cannot be made during simulation). The main limitation in all the attempts that have been made so far for a combined spatio-temporal dynamic modeling, is that the relationship between time and location in space is not explicit.