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Exploring the relationships between warm-season precipitation, potential evaporation, and “apparent” potential evaporation at site scale

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.
