# Approximation Method for WBGT

Today I ran a test of Aaron McGowan’s approximation method for calculation WBGT. If this turns out to be accurate, it will provide a much much quicker way to calculate WBGT, with tighter bounds on the running time.

BACKGROUND
The climate chip project is using Bernard’s model for calculating WBGT(indoors). This uses an iterative approach to slowly relax Tw and provides a reliable and accurate measure for indoors WBGT. The down side is that the current approach depends on how close Ta and Tw are initially, with a greater spread resulting in a longer relaxation process. Over 30 years and 25 million calculations, this can be the difference between seconds and hours.

Bruno Lemke has been communicating with Aaron McGowen at RIT in New York State. Aaron is using Stull’s approximation method for calculating WBGT and is interested in comparing this method with the iterative method we are using. For my own project, this would be a huge improvement, giving significantly faster results and a tighter bound on the running time.

METHOD
Control values for WBGT were extracted from the cru database. These were initially calculated using Bernard’s iterative model for WBGT and have been proven to be accurate in many many case studies.

10000 Tmax and Tdew values were extracted from the database, and these values were passed to the approximate WBGT function. The resulting WBGT values were compared to the control WBGT from the database.

RESULTS
Overall running time for the approximate method was impressive. 10000 calculations were finished in less than 0.5sec.

At low – moderate temperatures of Tmax and Tdew, the approximate method was reasonably consistent with the control WBGT. However at higher values (> 30 o Celcius) of Tmax and Tdew, the approximated WBGT varied by as much as 20 %.

CONCLUSION
The running time for the approximate method was as good as hoped for. However, the accuracy is doubtful. At this stage, I do not think I can use this method in the project. I would love to explore alternative methods, or explore this approximation method more, but I think this may be outside the scope of the project at this stage.