State Space Analysis
Abstract
When a major change occurs in the region, it is important to assess how much the system has been altered. The change may result from a natural disaster, such as a hurricane, or from a management decision, such as forbidding crop agriculture on steep slopes. The State Space method provides a way to measure how far the environmental quality of each watershed has been moved. This makes it possible to determine where degradation is likely to be greatest or management decisions are likely to make major improvements.
Method Details
Accurately assessing change in the environmental quality and vulnerability of watersheds requires maximum use of all available variables. The state of a watershed is represented by a vector of numbers, one for each of the measured or modeled variables. The distance between two vectors can be measured by a multidimensional Euclidean distance. However, correlations among the variables must also be considered. The State Space approach uses all of the variables and corrects the calculation to account for covariances using a multivariate approach developed by Mahalanobis. The method basically calculates a Euclidean distance between the 'before' and 'after' vector of variables, corrected for covariances.
Limitations
The Mahalanobis distance is a well-established method for calculating the distance between two vectors in multivariate space. Therefore, limitations in our ability to calculate change is not limited by the method but by the accuracy of the data and how completely the data characterized the state of the watershed.
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