Modeling interannual variability of seasonal evaporation and storage change based on the extended Budyko framework

Abstract

[1] Long-term climate is the first-order control on mean annual water balance, and vegetation and the interactions between climate seasonality and soil water storage change have also been found to play important roles. The purpose of this paper is to extend the Budyko hypothesis to the seasonal scale and to develop a model for interannual variability of seasonal evaporation and storage change. A seasonal aridity index is defined as the ratio of potential evaporation to effective precipitation, where effective precipitation is the difference between rainfall and storage change. Correspondingly, evaporation ratio is defined as the ratio of evaporation to effective precipitation. A modified Turc-Pike equation with a horizontal shift is proposed to model interannual variability of seasonal evaporation ratio as a function of seasonal aridity index, which includes rainfall seasonality and soil water change. The performance of the seasonal water balance model is evaluated for 277 watersheds in the United States. The 99% of wet seasons and 90% of dry seasons have Nash-Sutcliffe efficiency coefficients larger than 0.5. The developed seasonal model can be applied for constructing long-term evaporation and storage change data when rainfall, potential evaporation, and runoff observations are available. On the other hand, vegetation affects seasonal water balance by controlling both evaporation and soil moisture dynamics. The correlation between NDVI and evaporation is strong particularly in wet seasons. However, the correlation between NDVI and the seasonal model parameters is only strong in dry seasons.Citation: Chen, X., N. Alimohammadi, and D. Wang (2013), Modeling interannual variability of seasonal evaporation and storage change based on the extended Budyko framework, Water Resour. Res., 49,[6067][6068][6069][6070][6071][6072][6073][6074][6075][6076][6077][6078]

The Budyko functions under non-steady-state conditions

“…In these cases, the catchment is considered to be under non-steady-state conditions ( Fig. 1) and the basin water balance should be written as P = E + Q + S. Table 2 shows some recent formulations of the Budyko framework extended to take into account the change in catchment water storage S. Chen et al (2013) (used in Fang et al, 2016 and Du et al (2016) proposed empirical modifications of the TurcMezentsev and Fu-Zhang equations, respectively, precipitation P being replaced by the available water supply defined as (P − S), with Du et al (2016) including the interbasin water transfer into S. Greve et al (2016) analytically modified the Fu-Zhang equation in the standard Budyko space (E p / P , E / P ) introducing an additional parameter, whereas Wang and Zhou (2016) proposed in the same Budyko space a formulation issued from the hydrological ABCD model (Alley, 1984), but with two additional parameters.…”

“…First, we present the new formulation under non-steady-state conditions: its upper and lower limits, its generic equations under restricted evaporation in the Budyko space (E p / P , E / P ) and in the space [E p / (P − S), E / (P − S)]. Second, we compare the new formulation to the analytical solution of Greve et al (2016) in the standard Budyko space and to the formulations of Chen et al (2013) and Du et al (2016) in the space [E p / (P − S), E / (P − S)].…”

“…Hydrological processes leading to changes in water storage are not represented and the catchment is considered closed without any anthropogenic intervention: precipitation is the only input and evaporation and runoff Q the only outputs (P = E + Q). Recently, the Budyko framework has been downscaled to the year (Istanbulluoglu et al, 2012;Wang, 2012;Carmona et al, 2014;Du et al, 2016), the season (Gentine et al, 2012;Chen et al, 2013;Greve et al, 2016) Published by Copernicus Publications on behalf of the European Geosciences Union. 4868 R. Moussa and J.-P. Lhomme: The Budyko functions under non-steady-state conditions Table 1.…”

“…It represents a generic framework, easy to use at various time steps (year, season or month), with the only data required being E p , P and S. For the particular case where the Fu-Zhang equation is used, the ML formulation with S ≤ 0 is similar to the analytical solution of Greve et al (2016) in the standard Budyko space (E p / P , E / P ), a simple relationship existing between their respective parameters. The ML formulation is extended to the space [E p / (P − S), E / (P − S)] and compared to the formulations of Chen et al (2013) and Du et al (2016). The ML (or Greve et al, 2016) feasible domain has a similar upper limit to that of Chen et al (2013) and Du et al (2016), but its lower boundary is different.…”

“…The ML formulation is extended to the space [E p / (P − S), E / (P − S)] and compared to the formulations of Chen et al (2013) and Du et al (2016). The ML (or Greve et al, 2016) feasible domain has a similar upper limit to that of Chen et al (2013) and Du et al (2016), but its lower boundary is different. Moreover, the domain of variation of E p / (P − S) differs: for S ≤ 0, it is bounded by an upper limit 1 / H E in the ML formulation, while it is only bounded by a lower limit in Chen et al.…”