Some difficulties and prospects

This chapter discusses several difficulties as well as several prospects that are related to the FS methodology and that were not treated explicitly earlier in the book. First, the problem of dealing with a large number of factors is common to atmospheric research but becomes a serious computational burden when 2_n simulations are required. The most important point here is that we can limit our calculation to second-order interactions at the first stage and choose the most important factors, and only then continue toward a full factor separation. Another somewhat related problem is how to deal with unchosen factors and with factor dependency. A further related problem is the fractional treatment that allows a finer analysis of potential non-linear effects of some factors. Particularly, how to reveal a significant variation in the effect of some factor due to change in a potential threshold. A comparison of the FS against a different statistical factorial modeling (FM) method is performed. It is shown that the FS method has two clear advantages over the FM method. First, the sum of all 2ⁿ contributions in an n-factor problem equals the full run result. This allows a closure of the separation as well as a percentage-wise analysis of all 2ⁿ contributions that sum up to 100%. Second, the contribution by the zero- or basic-state is calculated and is one of the 2ⁿ contributions. It is shown here and in many earlier FS studies that in the atmosphere the zero-state contribution can be significant and should be calculated.