Evaluation of three energy balance-based evaporation models for estimating monthly evaporation for five lakes using derived heat storage changes from a hysteresis model

The heat storage changes ( Q _t) can be a significant component of the energy balance in lakes, and it is important to account for Q _t for reasonable estimation of evaporation at monthly and finer timescales if the energy balance-based evaporation models are used. However, Q _t has been often neglected in many studies due to the lack of required water temperature data. A simple hysteresis model ( Q _t = a^*Rn + b + c^* d Rn/ d t ) has been demonstrated to reasonably estimate Q _t from the readily available net all wave radiation (Rn) and three locally calibrated coefficients ( a–c ) for lakes and reservoirs. As a follow-up study, we evaluated whether this hysteresis model could enable energy balance-based evaporation models to yield good evaporation estimates. The representative monthly evaporation data were compiled from published literature and used as ground-truth to evaluate three energy balance-based evaporation models for five lakes. The three models in different complexity are De Bruin-Keijman (DK), Penman, and a new model referred to as Duan-Bastiaanssen (DB). All three models require Q _t as input. Each model was run in three scenarios differing in the input Q _t (S1: measured Q _t; S2: modelled Q _t from the hysteresis model; S3: neglecting Q _t) to evaluate the impact of Q _t on the modelled evaporation. Evaluation showed that the modelled Q _t agreed well with measured counterparts for all five lakes. It was confirmed that the hysteresis model with locally calibrated coefficients can predict Q _t with good accuracy for the same lake. Using modelled Q _t as inputs all three evaporation models yielded comparably good monthly evaporation to those using measured Q _t as inputs and significantly better than those neglecting Q _t for the five lakes. The DK model requiring minimum data generally performed the best, followed by the Penman and DB model. This study demonstrated that once three coefficients are locally calibrated using historical data the simple hysteresis model can offer reasonable Q _t to force energy balance-based evaporation models to improve evaporation modelling at monthly timescales for conditions and long-term periods when measured Q _t are not available. We call on scientific community to further test and refine the hysteresis model in more lakes in different geographic locations and environments. (letter)