Does urban canopy air temperature increase with anthropogenic heat flux linearly?

Anthropogenic heat flux (Q_AH) refers to the heat release associated with energy consumption caused by human activities, and it is an important control of urban temperatures. Its magnitude is expected to increase with urbanization, which interacts with regional climate change to exacerbate heat hazards in cities. In this research, we focus on whether the increase of anthropogenic heat flux causes a linear or non-linear increase in urban canopy air temperature (T_C). We use the Weather Research and Forecasting (WRF) model to simulate the effect of anthropogenic heat flux of varying magnitude (ranging from 1 to 100 W/m²) on the urban canopy air temperature over Boston, Los Angeles, and Chicago under heat wave conditions. Results show that the urban canopy air temperature increases as the anthropogenic heat flux gradually increases from 1 to 100 W/m². While a near-linear relation between changes in Q_AH and changes in T_C is observed across the three cities, the sensitivity of T_C to Q_AH (or the slope of the relation between change in Q_AH and changes in T_C) does vary with Q_AH in Boston and Chicago. Boston shows a decrease in the sensitivity as Q_AH increases, and Chicago shows a decrease first and then an increase, indicating nonlinear relations between changes in Q_AH and changes in T_C in these two cities. A decomposition analysis is conducted to quantify the contributions to the sensitivity of T_C to Q_AH. For Boston and Chicago, the contributions from surface temperatures and air temperature are not constant, particularly at lower Q_AH values, thereby contributing to the nonlinear relations between changes in Q_AH and changes in T_C in these two cities. In conclusion, while urban canopy air temperature generally increases with anthropogenic heat flux, the linearity of this increase varies depending on the city.