A unified framework of water balance models for monthly, annual, and mean annual timescales

At present, many conceptual water balance models have been proposed on monthly, annual, and mean annual timescales. With the increasing applications of these models, an emerging question is whether the water balance models on different timescales have some commonalities and can be integrated. To this end, this study established and applied a practical unified framework of water balance models that can be applied to different timescales. The framework was first developed on monthly timescale, where the water balance was captured by combining the abcd model and Budyko hypothesis with four parameters. Then, this framework was extended to annual and mean annual timescales under which certain parameters can be eliminated or assumed to be certain values. To be specific, on the annual timescale, the water balance was simulated by a Budyko-type model incorporating the water storage change; on the mean annual timescale the water balance was further simplified into a Budyko-type model which neglects the water storage change. Thus, all of the three typical water balance models on different timescales were unified to a general framework. The models were applied to 437 catchments in the contiguous United States with satisfying results achieved. Considering the water storage changes can improve the performance of annual water balance models in regions with clear interannual carrying water storage. Furthermore, the water balance models on different timescales share common supply and demand limits which is similar to Budyko hypothesis.