A mathematical model for the energy stored in green roofs

A simple mathematical model to estimate the energy stored in a green roof is developed. Analytical solutions are derived corresponding to extensive (shallow) and intensive (deep) substrates. Results are presented for the surface temperature and energy stored in both green roofs and concrete during a typical day. Within the restrictions of the model assumptions the analytical solution demonstrates that both energy and surface temperature vary linearly with fractional leaf coverage, albedo and irradiance, while the effect of evaporation rate and convective heat transfer is non-linear. It is shown that a typical green roof is significantly cooler and stores less energy than a concrete one even when the concrete has a high albedo coating. Evaporation of even a few millimetres per day from the soil layer can reduce the stored energy by a factor of more than three when compared to an equivalent thickness concrete roof.