A linear sensitivity framework to understand the drivers of the wet-bulb globe temperature changes

Better understanding of the physical drivers of sufficiently realistic representation of human heat stress is crucial for improving prediction and enhancing preparedness. Wet-bulb globe temperature (WBGT) is a standard metric for workplace heat stress, however, its calculation involves complex parameterizations of radiative and convective energy exchange. Thus it is difficult to understand the driving mechanisms behind WBGT changes. To address this issue, we introduce a sensitivity framework to analytically evaluate WBGT's response to meteorological input changes. By examining the form of sensitivity coefficients we gain insights into the interactive effects of multiple environmental parameters in controlling WBGT. Given constant wind and solar radiation, the natural wet-bulb and black globe temperatures change at the same rate and direction as the wet- and dry-bulb temperatures, despite considerable differences in their absolute values. The framework, while having state-dependent sensitivity coefficients, can be linearized, transforming WBGT into a linear combination of temperature, specific humidity, surface pressure, and terms representing wind and solar radiation effects. These explicit and mathematically tractable relations between WBGT and more intuitively understandable variables enable us to leverage established theories and methods to understand the driving mechanisms of WBGT changes. We apply the framework to understand the physical drivers of regional WBGT scaling with global warming and extreme WBGT synoptic events. The sensitivity framework also provides a universal approach to develop locally tuned linear approximations of WBGT and can be used to diagnose the sources of biases in other empirically derived approximations.