Modeling of thermal runoff response from an asphalt-paved plot in the framework of the mass response functions

During hot summer months, impervious surfaces within urban areas may store significant amounts of thermal energy, which may be rapidly transferred to stream waters during runoff events. Modeling of heat release from impervious areas to stream waters thus represents a first, necessary step to quantify possible negative impacts of increased stream water temperature on nearby aquatic ecosystems. In this paper, a stochastic Lagrangian approach is developed to simulate heat transfer from an impermeable surface to runoff. The approach is based on the framework of the mass response functions (MRFs), which was originally developed for modeling nonpoint source pollutant transport in watersheds. The MRF approach has been adapted to describe heat transfer from impervious surfaces to runoff by coupling a heat balance at the asphalt/water interface and a one-dimensional heat diffusion equation within the asphalt. The model incorporates a simplified, physically based description of all the heat fluxes possibly affecting the ensuing thermal response of impervious areas (e.g., solar radiation and evaporation). The model was applied to an asphalt-paved plot of 90 m2 where it was able to accurately reproduce the temperature variation of the asphalt surface and runoff during an artificially produced rainfall event. Model prediction uncertainty introduced by the estimate of some key parameters involved in the heat balance is analyzed by sensitivity analysis and by checking a posteriori the consistency of the estimated heat fluxes through an overall heat conservation equation. The effect of the heat diffusivity on the surface temperature response to rainfall input was also examined, showing that the effect could be significant depending on vertical temperature distributions of the plot.