# Deciphering the calculation of WBGT

This week has been interesting. I have spent a significant part of the week reading the publications of the Climate Chip group, particularly those that concern the calculation of the heat stress indicators. Lemke and Kjellstrom published an interesting article comparing the accuracy of various models for calculating WBGT(1). In this paper Lemke and Kjellstrom stipulate their criteria for a valid model of WBGT and conclude by citing Liljegren’s model. Oddly, Lemke annd Kjellstrom did not publish Liljegren’s model, though they did publish various others. Unfortunately, the paper in which Liljegren published this model is not freely available and the NMIT library do not hold a subscription for the Journal of Occupational and Environmental Hygiene. Thankfully I was able to source this from a colleague.

Liljegren’s model is not straight forward, and looking over it I begin to see where some of the “unpredictability” that Matthias has mentioned comes from. Liljegren calculates WBGT as follows:

$WBGT = 0.7T_{w} \times 0.2T_{g} \times 0.1T_{a} \newline \indent where \newline \indent \indent T_{w} = wet\, bulb\, temperature \newline\; \indent \indent T_{g} = globe\, temperature \newline\; \indent \indent T_{a} = ambient\, temperature$

However, T(w) and T(g) are calculated iteratively, where an initial estimation is refined to a defined accuracy.

This afternoon, Matthias also sent through the C# code that he uses to calculate WBGT and UTCI. Despite Lemke’s assertions that they use the Liljegren model, the calculation bears no obvious resemblance. So my challenge is going to be to make sense of Otto / Lemke’s formula and see if, with closer inspection, it is actually equivalent to Liljegren’s. I am sure it is, but this is not immediately recognisable.

The Challenge
Compare Otto / Lemke’s calculation with Liljegren’s model.

• Assuming that they are equivalent, figure out how Otto/ Lemke have managed to abbreviate it so nicely π
• Code the algorithm
• Run the algorithm and attempt to identify any patterns in the iteration that may allow us to prematurely short circuit the loop and arrive at the answer more quickly

What do I do if I can’t show that Otto / Lemke’s formula is equivalent to Liljegren’s?

• Gulp!
• Talk to Matthias, and go and see Lemke (he is a lecturer of physiology at NMIT – handy!)
• Find the remaining few constants I need to complete Liljegren’s and make some assumptions as to one or two of them

References:

(1) Lemke, B., & Kjellstrom, T. (2012). Calculating workplace WBGT from meteorological data: a tool for climate change assessment. Industrial Health, 50(4), 267-278.

(2) Liljegren, J. C., Carhart, R. A., Lawday, P., Tschopp, S., & Sharp, R. (2008). Modeling the wet bulb globe temperature using standard meteorological measurements. Journal of Occupational and Environmental Hygiene, 5(10), 645-655.