An GIS-based Many-Region Disaster Preparedness Model for the United States

Sam Cole,

National Center for Geographic Information and Analysis,

University at Buffalo

Paper to be presented at the Third International Conference/Workshop on Integrating GIS and Environmental Modeling, Santa Fe, New Mexico, USA,

January 21-25, 1996. Sam Cole

An GIS-based Many-Region Disaster Preparedness Model for the United States


This paper describes the construction, solution, and application of a many-region county-level social accounting matrix of the United States to be used to assess economic damage arising from natural disasters, such as floods, hurricanes, or earthquakes, (including economic earthquakes), and to improve the viability and efficiency of subsequent recovery efforts. Since the full empirical model is extremely large, concepts drawn from Geographic Information Systems are used to aggregate and view transactions by geography and sector so as to focus the model on the target locality and its immediate linkages. Thus the system is organized as a "virtual model" whereby the many-region accounts are condensed to a set of basic data associated with each locality and a set of estimated parameters which allow selected local accounts to be re-constructed and solved as required. Digitized national data sets for states and counties, are used to estimate county-level social accounts and inter-county spatial interactions. The approach may be extended to sub-county localities, such as urban neighborhoods. As a complete set of transactions between the 3000-plus counties the United States, the model may be used to explore how major disasters propagate through the national economy.

Creating such a system in a GIS-like environment presents a major challenge. In principle, every locality described in the model is connected to every other through structure, time, and space - changing any variable in one region affects every variable in all other regions. Even though specific sectorial locality to locality impacts may be small (say, the impact of a small earthquake in Santa Barbara on Buffalo, New York), the aggregate effects across regions of the nation (say, the Northeast) can be substantial. Most GIS deal well only with variations in structure, and do not deal well with time varying and place-to-place flows. Moreover, since many data are missing or must be estimated there remains a question of how the virtual model, and the metadata that describes it, should be organized. Last, for real-world applications, the system should be manipulated via a relatively straightforward Decision Support System (DSS) interface. There are thus several critical choices to be made, and the paper describes these choices and their rationale.

Section One explains the approach which is directed initially at estimating medium-term economic and social costs and losses to populations and institutions in small localities, where ready-made planning instruments and proactive contingency plans may not be available. Section Two describes the construction of the social accounts, to include estimates of economic transactions within and between counties and regions, as well as details of economic distribution across households, businesses, and lifelines. Section Three describes the solution procedures using a time-dependent approach for conceptualizing economic processes. This offers consistency between the construction and solution of the many-region social accounts, and allows the magnitude and time-scale of failures arising from natural disasters and subsequent reconstruction efforts to be integrated into the solution of the model in situations where damage from a disaster is spatially and temporally distributed across infrastructure and delivery systems of several localities. Finally, Section Four considers the appropriate DSS, drawing a distinction between controlled research applications and the chaotic circumstances of a natural disaster.


The rationale for the specification of the modeling system being developed in this paper, arises from the following considerations.

In many cases, natural disasters have their most severe impacts on isolated localities and small and impoverished communities. In the United States natural disasters are a national problem, experienced at the local level (Berke and Beatley, 1992). For example, a major disaster like the "500-year" Midwest floods of 1993 had minimal impact at the national, or even at the state level, yet many small communities may never be able to recover. As a fraction of annual income or even normal business cycle swings, even Hurricane Andrew had modest impact on Dade County, Florida - yet South Dade County and Homestead were devastated. This alone demands that models of relatively small districts be made available.

Disasters often impact most severely on poor and marginal populations. In many cases, this can be traced to poverty and inappropriate development, such as inferior infrastructure or housing, or limited insurance and other defensive resources (Cuny, 1983). For similar reasons, disasters tend to impact small businesses more severely than large enterprises. Ideally, a model should describe the situation of these groups and activities explicitly, as well as their links with the wider economy and community.

Even when they not impacted directly, people and businesses may be affected through damage to lifelines such as water supply or roads, or through indirect effects such as the loss of livelihood or markets. Even in aggregate, the indirect effects on a community are often far larger than the direct effects (Eguchi et al, 1992). Therefore, models need to be economy wide, so as to account for all sectors of an economy and all segments of a population (see e.g. NRC, 1990).

In general, the smaller a community, the greater will be the importance of its linkages to neighboring districts, and the more vulnerable it will be to damage to lifelines, such as power and water supplies, or transport and other communications. Moreover, the smaller a community the greater will be the spill-over effects to other communities, the more likely it is that neighbors also will be impacted directly by the disaster, or that feedback effects through their economies will be important. Thus, models must have an explicit account of a locality's links to its neighbors and the world beyond, and in many cases models must be multi-regional.

Disasters affect populations for an extended period of time. Most disasters and recovery activities operate on a variety of time scales that are characteristic of the physical, social, economic, and technological systems involved. As far as possible, it is necessary to represent these within a model, through the manner in which the impacts are calculated. Ultimately, the analysis of disasters presents an almost intractable network problem. Even so, one vital aspect of recovery programs or pro-active measures is to recognize that the vulnerability of the locality to disasters can be reduced though the application of various systems principles to the physical, economic, and social aspects of disaster preparedness (Kameda and Shinozuka, 1989).

Models need to be situated within the overall development process. While the immediate priority must be to attend to the life-threatening consequences of the disaster (such as medical and shelter needs), it is also necessary to plan for an economic recovery which provides an opportunity to improve the quality of development if the hardship from future disasters is to be reduced. In the past, victims and places often have been disadvantaged even further by deficient recovery programs. For this reason, disasters are best viewed as part of the development process, providing opportunities, as well as tragedy (Jones, 1989). A model based on this perspective must bring together relevant social and economic categories, so that both the damage caused by the disaster, and the proposed recovery strategy, can be assessed in the context of the long-term goals and institutional structures of the community.

Since natural disasters typically take place with rather little specific warning, it must be possible to provide the relevant planning tools that are adaptable to the situation of any community and type of damage, and become available as soon as possible after the disaster, so that they can be used to evaluate alternative proposals for recovery, before irreversible commitments are made. Even after a disaster has occurred, there remains considerable uncertainty as to the extent of damage or the most appropriate recovery strategy, the model should be updatable and flexible, so as to respond to evolving community needs.

All of the above - the need to provide analysis quickly, to provide models for small localities, describing specific sectors or lifelines, and particular types of household or community - suggests a rather high level of empirical detail and technical sophistication. This conflicts with several practicalities - the availability of data, the understanding of complex systems, and the needs of the planning process. The last cannot be ignored since, when the separation between the modeling and policy making becomes too great, the modeling loses much of its potential use (United Nations, 1994). While many expert and other decision support system have been developed in an attempt to bridge this gap (see e.g. Batty and Yeh, 1991), they have yet to confront the empirical and institutional chaos and complexity of much disaster planning.

Even though the above is an incomplete list of the challenges for addressing the consequences of major natural disasters, it presents a formidable task for economic modeling. While the present project has faced most of these issues, the exercise described in this paper focuses largely on questions of model construction and application in the context of a specific disruption to a lifeline systems in a metropolitan region of the United States.

The underlying theoretical question being addressed here is how do perturbations to an economic system propagate through structure, time, and space, and how well can regional modeling capture this process. Geographic Information Systems offer one promising means for bringing together the various data indicated, and to link the decision support system and directly to other studies and data bases.

Modeling Economic Disasters

The social accounting method used in this paper is a variety of input-output model (see e.g. Pyatt and Roe, 1979), and widely recommended as a core empirical device for national, regional and local planning (United Nations, 1994). Input-output models have been applied at the national or regional level for disaster assessment, with some recent efforts at the county level (e.g. West and Lenze, 1993) and small territories and islands (Cole, 1993).

Social accounting models have the particular advantage that, given the requisite data, both the supply and the demand sides of the economy can be described as a network that can be mapped onto its physical and social counterparts. It was argued earlier that this is necessary to describe and evaluate the consequences of specific types of damage in a useful fashion. The potential contribution of the methods adopted in this paper is that it extends the possibilities for constructing detailed input-output type models for small localities, and for introducing fairly complex disaster and reconstruction scenarios, taking account of changes in the internal structure of the economy.

Most economic transactions depend directly on physical lifeline systems - for example, purchases of power and water by businesses and households, the trucking of goods between industrial areas and to markets, the flow of information within and without the region via telecommunication links. The impacts of earthquakes on lifeline systems involves not only earthquake resistant constructions of individual components but also system recovery with the aid of network redundancy, back-up facilities, and restoration work, that are to be followed by reconstruction and improvement for the future earthquake (Kameda and Shinozuka, 1989). Because the nodes in the input-output tables represent localized production and consumption activities and the links shows flows of goods and services, such tables are especially appropriate for representing production, exchange, and consumption activities.

In order to address the complexity of the consequences of natural disasters it is necessary to reformulate the assumptions used in standard input-output calculations. This is especially so when there is a complex of events arising from the partial failure of several activities, resulting in a more general failure of the economic network as a whole.


The above considerations place a very demanding set of requirements for model construction, especially when it is recognized that data at a small spatial scale are often restricted (for confidentiality and other reasons), and information on the direct effects of disasters are usually incomplete and collected in an ad-hoc fashion. On the other hand, since the damage caused by a major natural disaster can affect the structure of an economy in dramatic ways (through the loss of entire industries or lifeline systems) so that even a model which captures the key features and linkages within an area's economy, before and after a disaster, and allows the broad outlines of a reconstruction strategy to be developed, can be useful. To this extent the requirements on precision for the model may be somewhat less than for a conventional economic impact calculations. Thus, the initial goal has been to make possible the rapid construction of a first-cut social accounts based impact model for any locality within the United States, using readily available data, while providing for the subsequent improvement and extension of the model, to sub-county localities.  (Figure 2) (Figure 3)

Development of the Model

In order to develop the requisite analytic procedures, it has been necessary to construct a detailed county-level many-region model of the entire United States. While this may appear a somewhat convoluted procedure, it provides the parameters necessary to estimate models for smaller, sub-county localities, and transactions between counties across the entire United States, providing indirect estimates of information that are otherwise not readily available.

The basic techniques used to construct the present model are relatively straightforward. Total supply and demand for each commodity and factor of production are estimated for every county and by scaling the accounts in the United States table. These supply-demand imbalances are then used to estimate the parameters of a spatial allocation model for each activity, and to provide bilateral inter-regional trade matrices. These flows are combined with the scaled regional matrices to give the many-region social accounts. Finally, the accounts are aggregated so as to highlight the locality of immediate interest within an overall matrix of manageable size. The main principles of the approach described here have been piloted in earlier phases of the project (NCEER, 1993). Whereas these pilot studies required considerable "hands-on" treatment using some specially collected data, the present approach is largely automatic or mechanical using national data sets available in digitized form (e.g. on CD-ROM) with data handling and presentation manipulated through geographic information system (GIS) techniques, and using generalizable algorithms to scale and solve the models (Miller and Blair, 1985).

Representation as a Virtual Model

The principal difficulties with extending the techniques to the many-region United States model arise in management of large volumes of data: a model of the transactions between the 3000 counties of the United States, each with up to 20 activities per region could requires a matrix with 36x108 entries (a table covering several footballs fields!). The size of this matrix is increased several fold when the results of the model, the corresponding changes in transactions for the years following a disaster event are also inventoried. Even though many of the transactions are zero, this would still require a vast amount of data, To deal with this the system is organized as a "virtual model" whereby the many-region accounts are condensed to a set of basic data associated with each locality and a set of estimated parameters which allow selected local accounts to be re-constructed and solved as required. Typically, only a small part of the total United States model is required in full detail at any one time - i.e. that describing the locality impacted by a disaster and its neighbors. The rest of the model may be aggregated according to the distance and direction from the target locality, for example, along major radial routes from the area. Thus, the system is designed to focus in on the segment of the matrix that describes the disaster area, in much the same way that a GIS system allows us to zoom a particular geography. A key task has been to devise appropriate estimation, and aggregation rules for this process.

Overview of Empirical Implementation

The empirical implementation of model construction and application is carried out through a series of computer programs. The procedure falls into several steps, each comprising a group of programs; data preparation, model estimation, model assembly, and model solution. The assumptions described below allow these steps to be carried out recursively. More elaborate scaling might require this part of the calculation to be iterated.

During the initial data preparation, information is extracted from the national data base which is carried on two CD-ROMs. Geographic data (county coordinates) and economic data (i.e. selected county level data required for matrix scaling) are transferred to separate state files (AreaCoo and AreaData respectively). These data are then used to construct a data file focused on the states in which the target counties are clustered (AreaBloc), and a second file (BlocDist) giving the bilateral distances (or alternative measures of impedance) between. A similar file is prepared for the national level, comprising states and clusters of states, or sub-county data. County or sub-state clusters for are then combined to a single file (for example, Mississippi, Tennessee, and Arkansas, as well as state data are combined in the Memphis file). This file (BlocData) has the same output format as those prepared at the county level (AreaBloc) in order that following steps are unchanged. The national social accounts (US-SAM) are scaled to the regions using data from the BlocData files in order to estimate domestic demand and supply for all regions (BlocScale). Equivalent information comprise the data base for the virtual model.

These estimates and the bilateral distances then are used in the calibration program (BlocGrav) to derive the bilateral transaction matrices for selected regions. A balancing program (BlocRAS, not shown) can be used at this stage. For the assembly of the final accounts, data from BlocGrav (or BlocRAS) are aggregated to final regions and sectors (BlocAgg), and the corresponding domestic data are prepared (BlocComb). These data are then combined into the final table using BlocSAM. Last, the model is solved (BlocImp) either to provide characteristic multipliers for the target region, of by introducing data on specific events (BlocEvent). A master program to input data and control program flow from within the GIS window is being developed.

Regional Supply and Demand

The supply and demand for commodities and factors by region and sector are the core data set for the virtual model - that is they provide the information from which the local models are extracted as required. Supply and demand are estimated by scaling a total requirements table for each county or regional bloc in turn scaled from a national table for the United States. The data required to build local area tables are not generally available (because they are too expensive to collect, or because they cannot be disclosed legally). The underlying assumption behind this scaling is that technologies (measured in terms of total factor and commodity inputs) across similar production sectors are uniform nationwide. A similar assumption is used for household consumption propensities.

The overall procedure for constructing the model includes two steps which involve the spatial aggregation of the model. The first is carried out prior to the calibration of the model parameters simply to reduce the number of entities involved in the calibration. Typically this procedure includes about one hundred clusters made up of single counties, within-state groups of counties, individual states, and multi-state blocs, such that the level of aggregation increases with distance from the target region. Collectively, these blocs comprise the entire United States. With this approach, the blocs of counties and states may be superimposed on the radial transportation networks which are ubiquitous in US cities, or modified to correspond to other systems, so that the regional clusters correspond to nodes on the lifeline network. The selection of the target county, and neighbors, is automated via a GIS interface.

Inter-regional Transactions

As there are no data on commodity flows between small localities, these too must be imputed. The estimation of inter-regional flows rests on the tremendous variation in the size, sectorial composition, and spatial disposition of county level economies in the United States. All localities exhibit an imbalance between amount of goods and service they produce and the amount they consume: excess supply from each locality is exported to other districts, and abroad, and vice versa, workers commute from districts where there is an excess of labor supplied by households, and so on. These spatial patterns have complex underlying causes, and there are several theoretical explanations of why the intensity of transactions should tend to decline with increasing distance between actors. This includes the need to limit the adverse consequences of unexpected delays, the presumption that underlies the method used to solve the present model. Throughout the estimation, a principle concern is to retain sufficient empirical information to estimate the model (see e.g. Griffith, 1991) since it is well known that any aggregation scheme introduces difficulties and ambiguities in the estimation of even simple models, manifestations of ecological fallacy, modifiable areal unit type concerns (see e.g. Fotheringham and Wong, 1991).

The inter-regional transactions in the social accounting matrix may be estimated by fitting parameterized spatial interaction models to the previously-estimated supply and demand for each commodity and factors. Once a plausible estimation of the bilateral transactions between regions is obtained, and anomalous results dealt with, the matrix for each commodity is re-balanced (see e.g. Cole, 1994).

Focusing Locality Specific Models

The above procedures for scaling levels of supply and demand and inter-county flows provides accounts for some 40 county-level models and a comparable number of regional and county clusters. This is still a relatively large model, and most of the information is not needed for consideration of any particular county. A second aggregation is used to focus the model onto an individual county (e.g. that which is closest to the epicenter of an earthquake or has suffered the most severe damage), or a string of counties (e.g. along a particular lifeline or natural phenomenon, such as an earthquake fault or river). In effect, this procedure targets a particular segment of the county-by-county United States economic model, just as a GIS zooms on a selected area of a map.  (Figure 1)

Refocussing the model to a new locality involves repeating this second aggregation, but does not require that the model be re-estimated. For the second aggregation, total demand commodity-by-production tables first are scaled to the new combinations of regions as described earlier, and the bilateral trade matrices are organized by commodity and region into a commodity-by-commodity trade matrix which is then combined with the domestic commodity-by-activity matrices. This provides a combined many-region commodity-by-activity matrix, with the domestic economy of the selected region shown in full detail.


Distributed Disruptions, Transaction Costs, and Uncertainty

The technique for solving the model rests on a time-dependent approach for conceptualizing input-output tables. The first important notion here is that the network of activities in any economy sets up a 'round-by-round' process that distributes income throughout the economy (see e.g. Miller and Blair, 1985). Thus, a change anywhere in the economy is magnified and transmitted throughout the community (and in some measure, throughout the world). This is the basis of the multiplier effect, that underlies all input-output type calculations, and provides an especially useful way of conceptualizing the propagation of events through structure, time, and space. The second underlying idea is that all economic processes involve a characteristic transaction lag - reflecting the time taken to design, finance, transport or produce goods, or simply to adjust to new circumstances (see ten Raa, 1986; Cole, 1988). As a consequence of the complex system of delayed feedback, it contains the multiplier process in any economic network always takes some time to build up to its full effect.

The prevailing spatial structure of any economy is in part a reflection of this system of delays, and of the effort by economic actors to minimize costs arising from it. Practically, actors seek to avoid the consequences of unexpected delays. Even under normal circumstances some proportion of transactions will be delayed unacceptably, and suppliers and their customers reduce losses by maintaining buffer stocks, or concentrating their business in nearby markets. In the event of a disaster, the proportion of failed transactions is increased beyond the capability of the normal system to cushion the event. Formalizing this process allows the magnitude and time-scale of lifeline and sectorial failures, and mitigation, or reconstruction efforts, to be integrated into the solution of the social accounting matrix. This includes situations where damage from a disaster is spatially and temporally distributed across infrastructure and delivery systems. The method can be related to Shinozuka et al's (1994) formulation of the fragility curve for a linearly connected lifeline systems, and to the method of Bates (1994) for analysis of travel time reliability. (Figure 4)

Decision Support Systems versus Expert Systems

The events to be simulated include the following:

i) Simple Disasters (or recovery) where the changes in output, income, and employment directly and indirectly can be calculated using standard input-output techniques (i.e. requires information on the proportion of each transaction affected directly by the disaster).

ii) Complex Disasters where the composition or source of inputs to particular sectors or households are changed or constrained in a non-linear fashion (requires e.g. information on household trade-offs, and the criticality or capacity constraints on production).

iii) Recovery Scenarios involving reconstruction of the activity over some specified time period (requires e.g. information about additional delays in performing transactions because of lifeline failure, the time taken for the transaction to recover to its previous or some specified level, or new links to enhance the robustness of the economy against future disaster).

iv) Prioritized Recovery incorporating recovery into a broader development strategy involving many conflicting interests (may require additional information on discount rates and trade-offs to minimize losses, for example within a discounted cost-benefit analysis).

The way in which the social accounts and the event matrix are used to aid decisions depend on the precise application. It is useful to distinguish here between two types of application in "well defined" and "poorly defined" or "chaotic" situations. The first approximates to the circumstances of a region as a research laboratory for disaster preparedness. The second corresponds to the type of situation that the modeling system developed here ultimately is designed to contribute to. These distinctions dictate the type of expert system that might be usefully employed. emphasize the balance between quantitative and qualitative representation, and the degree to which problems are well or ill-defined, and this the extent to which they can be modeled in a mechanical fashion (see e.g. Batty and Yeh, 1991). The promise of expert systems based on concepts of artificial intelligence has proved hard to realize and increasingly, even for well defined situations, the literature increasingly speaks of decision support systems rather than expert systems. The approach of this project falls into the generally accepted definition of aiming to help a community do for itself what otherwise an experts might be asked to do, but this nevertheless leaves open many issues of system interface design.


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This work was supported in part by the National Center for Earthquake Engineering Research (NCEER) under National Science Foundation (NSF) Master Contract BCS90-25010 and New York State Science and Technology Foundation (NYSSTF) Grant Number NEC-91029. Travel support and software also have been provided the NSF grant to the National Center for Geographic Information and Analysis (NCGIA) SBR- 88-10917.

Sam Cole,

National Center for Geographic Information and Analysis,

Department of Geography,

Wilkeson Quadrangle,

Ellicott Complex,

University at Buffalo,

NY 14620.

Phone/Fax 716-837-3924.