Spatial Impact Analysis through Qualitative Calculus: An Exploration

W O R K I N G P A P E R

SPATIAL IMPACT ANALYSIS THROUGH

QUALITATIVE CALCULUS: AN EXPLORATION

H. Voogd

September 1 9 8 2 WP-82-82

I n t e r n a t ~ o n a l I n s t ~ t u t r for Applied Systems Analysis

NOT FOR QUOTATION WITHOUT P E R M I S S I O N OF THE AUTHOR

S P A T I A L IMPACT ANALYSIS THROUGH

QUALITATIVE CALCULUS: AN EXPLORATION

H . V o o g d

S e p t e m b e r 1 9 8 2 WP-82-82

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INTERNATIONAL I N S T I T U T E FOR A P P L I E D SYSTEMS ANALYSIS A - 2 3 6 1 L a x e n b u r g , A u s t r i a

SPATIAL IMPACT ANALYSIS THROUGH QUALITATIVE CALCULUS: AN EXPLORATION

Henk Voogd

ABSTRACT

In this paper the usefulness of qualitative calculus for spatial impact analysis will be explored. The major issue of qualitative cal- culus concerns the sign-solvability problem. Its basic question is whether, and under what conditions, the direction of changes in a set of dependent variables in an interconnected system may be determined solely from the direction of changes in the indepen- dent variables and a knowledge of the signs, but not the magni- tudes, of the relevant partial derivatives. After an elaboration of this problem in Section 2, an overview will be given in Section 3 of the conditions under which full or partial sign-solvability may occur. A discussion of how this approach might be applied in urban and regional planning is given in Section 4, and the paper con- cludes with some suggestions for further research.

1. Introduction

The critical assessment of proposed courses of action is an important part of a planning process, and many impact analysis models are available to support these assessments (see, for instance, Batty, 1976; Putman, 1979; and Wilson, 1974). Here the term impact analysis means the a priori determination of the relevant consequences of system changes that would arise from specific policy measures. Spatial impact analysis may be seen as a particular type of impact analysis in that it emphasizes the spatial dimension of these consequences (see also Nijkamp, 1979, 1981, 1982).

Planning-oriented research in general, and spatial impact analysis in partic- ular, must usually be carried out under a number of constraints (see also Voogd, 1982), which include:

+ the speed with which results have to be produced;

+ the limited amount of suitable quantitative data;

+ the limited availability of (skilled) research (support) staff.

As a consequence, very few quantitative mathematical models have actually been used successfully in urban and regional planning. During the last few years, increasing attention has therelore been paid to approaches which:

+ are able to deal with qualitative information, so that cumbersome data- gathering activities are no longer required in order to reach meaningful conclusions;

+ are flexible with respect to the inclusion of new information and/or to new circumstances;

+ enable decision-makers to assess (the consequences of) the underlying ( ~ ~ s u m p t i o n s and value judgements.