Positive or negative correlation between actual and potential evaporation? Evaluating using a nonlinear complementary relationship model

Abstract

Understanding whether a positive or negative correlation between actual (E) and potential (E p ) evaporation is of great importance in detecting changes of E from E p . In this study, such correlation was evaluated via the linear regression slope (k) between E and E p derived from a nonlinear complementary relationship model. k varies with the relative degree of variability in the radiation term (E rad ) and aerodynamic term (E aero ) of E p , and is further affected by water availability. The sign of k is always positive under conditions with high E rad variability but at the same time with low E aero variability (commonly true on an hourly basis). Under conditions with high E aero variability but at the same time with low E rad variability, the sign of k tends to change from negative to positive with more readily water availability. On a daily or annual basis, the sign of k would be related with water availability. Under water-limited conditions, the E aero variability is more significant than the E rad variability, and negative k is expected. Under energy-limited conditions, the E rad variability is compared to or even much obvious than the E aero variability, and positive k is expected. This implies a negative correlation between E and E p under water-limited conditions but a positive correlation under energylimited conditions on the daily or annual basis. The above analysis is confirmed in a grassland site in Northeast China at daily and half-hourly time scales. The correlation between annual E and E p over China was evaluated using data of 690 meteorological stations from 1956 to 2005. The k values change from negative in arid regions to positive in humid regions. According to k and the decreasing trends in annual E p , it is deduced that E increased for most stations in arid regions but decreased for most stations in humid regions.

Complementary‐Relationship‐Based Modeling of Terrestrial Evapotranspiration Across China During 1982–2012: Validations and Spatiotemporal Analyses

“…The increase in CR‐modeled ET a for most parts of western and northeastern China and the decrease for most parts of southern and eastern China are overall consistent with the results of a long‐term water‐balance analysis by Gao et al (), who concluded that ET a had a decreasing trend in most areas east of 100°E but showed an increasing trend in the western and the northern parts of northeastern China. Furthermore, Han, Tian, et al () also identified obvious decreasing trends in annual ET a over the past few decades for most stations in the humid regions while found the opposite for most stations in the arid regions. The decrease of ET a over the last three decades reported in the present study for the North China Plain is supported by the significant decline in topsoil water content during 1983–2012, which was due partially to the intensification of agricultural activities, as was demonstrated by Liu et al ().…”

“…The CR method has been widely used to estimate ET a at annual (Hobbins et al, ), monthly (Liu et al, ; Szilagyi & Jozsa, ; Szilagyi, ; Xu & Singh, ), weekly (Crago & Qualls, ), daily (Ma, Zhang, Szilagyi, et al, ; Ma, Zhang, Xu, et al, ; Ozdogan & Salvucci, ), and subdaily (Crago & Crowley, ; Han, Tian, et al, ) scales. However, Morton () suggested to avoid using the CR for periods shorter than 5 days over extended periods of time and/or over a large regional scale since large‐scale weather fronts may bring air masses over the land with a moisture signature decoupled from the underlying surface, which thus may temporarily disrupt the dynamic equilibrium of air humidity and surface fluxes in the land‐atmosphere system.…”

A scaling approach to Budyko's framework and the complementary relationship of evapotranspiration in humid environments: case study of the Amazon River basin

“…4) was carried out under the assumption that ∂P /∂E p = 0. Such an assumption is questionable given the well-known complementary relationship of evapotranspiration (Bouchet, 1963;Morton, 1983;Hobbins et al, 2001;Xu and Singh, 2005;Szilagyi and Jozsa, 2009;Han et al, 2014;Lintner et al, 2015), but also having in mind the important role of evapotranspiration in the recycling of precipitation (Shuttleworth, 1988;Elthair and Bras, 1994;Dominguez et al, 2006;Zemp et al, 2014). This paper presents a 3-D generalization of the Budyko hypothesis, intended to capture the mutual interdependence among E, E p , and P by involving the complementary relationship of evapotranspiration.…”

“…A strong body of literature has been dedicated to study the relationship between E and E p , in particular the complementary relationship hypothesis (Bouchet, 1963;Morton, 1983;Hobbins et al, 2001;Xu and Singh, 2005;Szilagyi and Jozsa, 2009;Han et al, 2014). Before the study of Bouchet (1963) it was thought that a higher E p implied a greater E. He corrected this misconception based on energy balance arguments, demonstrating that as a surface dries up from initially wet conditions, E p increases while E decreases as the available water drops.…”

Integration of Penman approach with complementary principle for evaporation research

“…The complementary principle reveals that the land surface wetness can be indirectly represented by the large‐scale advection of the drying power of air with a constant radiation energy input (Brutsaert, ). On the basis of this principle, Han et al (Han, Tian, & Hu, , Han, Hu, & Tian, ; Han, Hu, & Yang, ) extended the complementary relationship to a generalized form that expresses E / E Pen as a function of E rad / E Pen , shown as follows: …”