**4.2 Actual evapotranspiration models**

Potential evapotranspiration represents the ET rate limited only by energy supply instead of water supply. In current practices such as stormwater management, it is common to use PET or pan evaporation to represent *ETa* [100, 104, 113–116] and calculate other unknowns in the water balance [62]. However, without the adjustment for the substrate moisture content, *ETa* will be overestimated for unsaturated conditions [89, 117]. Therefore, the water stress coefficient [105] is used to take account of moisture dynamics, and has been used as the benchmark for assessing other predictive *ETa* models in lieu of physically monitored data [90, 97]. Actual evapotranspiration can be achieved by multiplying *ETo* by *Ks*. Simpler equations have been applied to green roof, such as the Thornthwaite-Mather version neglecting the rooting depth and moisture stress [83], or the soil moisture extraction function (SMEF) that further removes the restriction of wilting point [59, 74, 93, 97]. All these methods tend to exaggerate the magnitude of ET reduction during dry periods, since they do not account for processes that could increase the moisture availability such as depression storage, interception, vegetation storage, and ponding water, or factors that alter ET fluxes like the subsurface moisture movement and non-ideal environmental conditions [81]. A fundamental assumption behind these water stress models is that ET from plant and medium should follow a linear response curve with the moisture content. The linear assumption, however, may not well reflect the plant's real response, since plant's stomatal activity also depends on other factors as discussed above. This linear trend and becomes much more problematic when representing special species such as succulent plants with distinct metabolism mechanism [49, 78].
