discussion:
The disappointing results for the Kriging methods requires some further analysis. As noted in the initial data exploration results, there were some deviations from the strict requirements for Kriging applications, especially for both the 1 Hour and 10 Hour fuel data. However, the near normal distribution for the 1 Hour data and the low kurtosis, skewness, and variance permitted reasonable results for the 1 Hour data when Cokriged with elevation. This is reasonable because trend analysis suggested that there was some correlation with elevation. The strong deviation of the 10 Hour fuel data from the strict criteria for Kriging, especially the skewness and kurtosis, resulted in poor estimations, even for Cokriging (Table 8).
A number of data transformation can be applied to correct for the deviations from a normal distribution noted in the 10 Hour fuel data. Data transformation are called for when any of the following conditions occur (Kleinbaum et al. 1998):
1. the variance is not constant
2. the data distribution deviates significantly from normal
3. a non-linear model is suggested by the data
The extreme kurtosis of the 10 Hour data violates the assumption of constant variance, and therefore violates Intrinsic Stationarity that is necessary for Kriging. The observed skewness also violates the requirement of a near normal distribution. However, the kurtosis has a stronger affect on modeling than skewness (Kleinbaum et al. 1998). Although some form of data transformation is called for in the case of the 10 Hour data, this is outside the scope of this investigation and remains to be explored further.
These Kriging results represent problems commonly encountered when applying this process. Merks (2005) has been a critic of the over-application of Kriging as an interpolation method. In particular problems arise when Kriging is applied without adequate testing for a true spatial correlation in the data by applying Fisher’s F-Ratio Test (Merks 2005). The assumption that parameters measured at adjacent points represent spatially continuous data is often incorrect Merks and Merks 1991).
Complications also arise from sampling. Flores-Garnica (2001) acknowledged the possibility of poor quality control in sampling, due to the variable skills of the individual sampling teams. However, the accuracy of fuel measurements is not the only consideration. Kriging is heavily dependant upon Sampling Theory, but its practitioners disregard the importance of establishing the degrees of freedom used to calculate the variance, and its implications for measuring anisotropy (Mardia 1980; Merks 2005; Boogaart 2009). Mardia (1980) suggests several specific data transformation to correct for different cases of anisotropy. The Geostatistical Analyst Wizard has transformation options to correct for non-normal data distributions and data anisotropy.
