3.2.5.3 Statistical Approach to Define Developed Imperviousness

A statistical methodology is designed for the specific purpose of relating the imperviousness training statistics to statistics derived from coincidentally located Thematic Mapper imagery. Figure 24 illustrates one of the sample sites, and its corresponding Thematic Mapper composite, along with the statistics generated. Through some simple plotting of airphoto statistics versus TM statistics for the 15 sites, some strong linear trends are observed. (Figure 25) This prompted the pursuit of a multiple linear regression approach using the airphoto interpreted imperviousness as the response, and some combination of the TM statistics for the sample sites as the explanatory variables.

Selection of a regression was based upon the dual criteria of goodness of fit through the adjusted R-squared statistics, balanced with a desire for a set of explanatory variables that are not overly extensive, fitting expectations of what set of TM bands would be required. The first selected regression included TM Bands 3, 4, and 5, the ratio of band 4 to band 3, and the variance in TM band 5 (Table 7). While this produced favourable predictive results on the 15 sample sites, this selection did not take into account how the regression might operate on substantially different sets of TM statistics, found throughout the watershed.

Testing the performance of the regression for a large number of possible combinations of TM statistics is implemented by using a kernel aggregation approach. GRASS's r.mfilter module is used to generate all possible combinations of TM statistics of a given sample size in the watershed.(Figure 26).

One consideration is that the sample statistics for 11x11 kernels of TM pixels might be different from the round sample of pixels. Correlation experiments on the 15 sample sites (Figure 27) show statistics for the round 800 hectare sample and the 11x11 kernel sample to be virtually identical (Table 8).

The resulting regressed imperviousness map revealed many prediction errors resulting from this regression (Figure 29). Thus while this first regression is the best choice based upon the 15 member sample set, it does not perform well in the many possible statistical scenarios found throughout the watershed. Examination of the areas of extreme prediction errors (imperviousness above 100 and below 0) revealed that most errors are coincident with areas of high TM 5 variance, an included parameter. Another regression, reducing this type of error is calculated, using the criterion that no variance parameters be included. The explanatory variables of this next best regression were TM bands 3, 4, 5 and band 5 over 3. (Table 9)

This new regression, when subjected to the same 11x11 kernel testing methodology, produced maps of impervious similar to the previous attempt with far fewer extreme errors (Figure 30). The new regression still distinguished between more and less impervious land covers within the selected areas (as based upon visual comparison with the high resolution airphotos), producing similar patterns of percent imperviousness, and did not suffer from the extreme sensitivity to a single explanatory parameter (Figures 31, 32, and 33).