Abstract
Abstract. Bouchet's complementary relationship and the Budyko hypothesis are two classic frameworks that are inter-connected. To systematically investigate the connections between the two frameworks, we analyze precipitation, pan evaporation, and potential evaporation data at 259 weather stations across the United States. The precipitation and pan evaporation data are from field measurement and the potential evaporation data are collected from a remote-sensing dataset. We use pan evaporation to represent “apparent” potential evaporation, which is different from potential evaporation. With these data, we study the correlations between precipitation and potential evaporation, and between precipitation and “apparent” potential evaporation. The results show that 93 % of the study's weather stations exhibit a negative correlation between precipitation and “apparent” potential evaporation. Also, the aggregated data cloud of precipitation vs. “apparent” potential evaporation with 5312 warm-season data points from 259 weather stations shows a negative trend in which “apparent” potential evaporation decreases with increasing precipitation. On the other hand, no significant correlation is found in the data cloud of precipitation vs. potential evaporation, indicating that precipitation and potential evaporation are independent. We combine a Budyko-type expression, the Turc–Pike equation, with Bouchet's complementary relationship to derive upper and lower Bouchet–Budyko curves, which display a complementary relationship between “apparent” potential evaporation and actual evaporation. The observed warm-season data follow the trend of the Bouchet–Budyko curves. Our study shows the consistency between Budyko's framework and Bouchet's complementary relationship, with the distinction between potential evaporation and “apparent” potential evaporation. The formulated complementary relationship can be used in quantitative modeling practices.
Highlights
Potential evaporation (Ep) is a widely used physical variable in hydrologic frameworks
In order to explore the connections between the Budyko framework and the complementary relationship (CR), our study investigates the relationships between precipitation and potential evaporation as well as between precipitation and “apparent” potential evaporation
In the 259 weather stations, 93 % of the stations have a negative correlation between P and Epa (Fig. 4a), but only 43 % of the stations are statistically significant (p < 0.05; Fig. 4b)
Summary
Potential evaporation (Ep) is a widely used physical variable in hydrologic frameworks. It is the evaporation rate under unlimited land surface water supply (Thornthwaite, 1948). Pan evaporation (Epan) measurement is often used as a surrogate of potential evaporation. These two variables are not the same (Brutsaert and Parlange, 1998; Roderick et al, 2009). A stipulation is added in the potential evaporation definition in Van Bavel (1966) and further clarified in Brutsaert (2015) that “the surface vapor pressure be saturated, so that it can be found from the surface temperature.”. The main difference between potential evaporation and pan evaporation is that pan evaporation is not measured under saturated surface vapor pressure.
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