I have been working on the WBGT calculation with some success.
- Iterative method can be described by a linear function
- Using this function, WBGT can be calculated directly
- The calculation is much much faster than iterating (important for Matthias’ volume)
- The function is suitably accurate ( +/- 0.5 degrees) for over 90 % of the cru database (and 100 % of 2010, 2011 data)
- The accuracy of the fit depends on the relative values of Ta and Td
- A simple adjustment factor has been found that improves the fit.
While the fit isn’t perfect, it is potentially a viable alternative to the iterative method. Further experimentation and refinement would be required to prove this claim.
UPDATE TO POST:
Since this post, we have found that we can use a linear model for WBGT to significantly reduce the number of iterations required to reach an accurate approximation of WBGT. We were able to derive an initial value of WBGT (w`) that was very close to the final value (wf)and then refine w` until it neared the limit of wf. One day I will write this up properly.