A Null‐Parameter Formula of Storage‐Evapotranspiration Relationship at Catchment Scale and its Application for a New Hydrological Model

Different formulas have been developed to estimate the mean annual evapotranspiration ratio ( E / P ) from the mean annual aridity index ( E p / P ) based on the Budyko framework. A major challenge in using the Budyko framework for the interannual behaviors of a catchment is the missed storage. Here we develop a null‐parameter formula of the storage‐evapotranspiration relationship based on the simplified proportionality hypothesis, which takes the storage in the soil‐plant‐atmosphere continuum as the accessible water for the evapotranspiration processes. In this formula, the annual E / P depends on the annual E p / P and S / P values where S is the soil‐plant‐atmosphere continuum storage. An annual water balance model including groundwater storage is required to estimate the annual runoff and S / P . We develop a new conceptual hydrological model with only three parameters in addition to the null‐parameter formula. The model performs well in the case study of the North Loup River Basin in Nebraska. It is found that the annual E / P increases with the increasing E p / P around a path that is different from conventional Budyko curves. For mean annual water balance, the triparameter model results in one‐parameter formulas to estimate both of the mean annual E / P and S / P so that the status of storage can be included in the Budyko framework. This study presents a new simple approach to investigate the interannual variability of catchments with varying dryness.