At which time scale does the complementary principle perform best on evaporation estimation?

At which time scale does the complementary principle perform best on evaporation estimation? Abstract 1 The complementary principle has been widely used to estimate evaporation under different 2 conditions. However, it remains unclear that at which time scale the complementary principle 3 performs best. In this study, evaporation estimation was assessed over 88 eddy covariance 4 (EC) monitoring sites at multiple time scales (daily, weekly, monthly, and yearly) by using 5 the sigmoid and polynomial generalized complementary functions. The results indicate that 6 the generalized complementary functions exhibit the highest skill in estimating evaporation at 7 the monthly scale. The uncertainty analysis shows that this conclusion is not affected by 8 ecosystem types nor energy correction methods. Through comparisons at multiple time 9 scales, we found that the slight difference between the two generalized complementary 10 functions only exists when the independent variable ( x ) in the functions approaches 1. The 11 difference results in different performance of the two models at daily and weekly scales. 12 However, such difference vanishes at monthly and annual time scales as few high x 13 occurrences. This study demonstrates the applicability of the generalized complementary 14 functions across multiple time scales and provides a reference for choosing the suitable 15 timestep for evaporation estimation in relevant studies. 16 than 0. At the annual scale, the mean value decreases 350 to −0.37 ± 0.25, and 63% of the c values are lower than 0. These results support our


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Terrestrial evaporation (E) including soil evaporation, wet canopy evaporation, and plant 22 transpiration, is one of the most important components in global water and energy cycles 23 (Wang and Dickinson, 2012). The evaporation process affects the atmosphere by a series of 24 feedbacks on humidity, temperature, and momentum (Brubaker and Entekhabi, 1996;Neelin 25 et al., 1987; Shukla and Mintz, 1982). Quantifying evaporation is crucial for a deep 26 understanding of water and energy interactions between the land surface and the atmosphere. 27 Generally, the meteorological studies focus on the evaporation change at hourly and daily 28 scales; the hydrological applications need evaporation data at weekly, monthly or longer time 29 scales (Morton, 1983); and the climate change researches pay more attention to the 30 interannual variation. The observation of E can be operated at different time scales. For 31 example, the Eddy covariance, lysimeter, and scintillometer can measure the evaporation at 32 the half-hour scale, and the water balance methods can observe the evaporation at monthly to 33 yearly scales (Wang and Dickinson, 2012). However, in most situations the observation is 34 unavailable and the estimation of E is necessary. There are several types of methods for 35 evaporation estimation, for example, the Budyko-type methods (Budyko, 1974;Fu, 1981), 36 and the atmosphere, the complementary principle assumes that the limitation of the wetness 48 state in the underlying surface on evaporation can be synthetically reflected by the 49 atmospheric wetness . Bouchet (1963) first proposed the "complementary 50 relationship" (CR), which suggested that the apparent potential evaporation (Epa) and the 51 actual E depart from potential evaporation (Epo) in equal absolute values but opposite 52 directions (Epa − Epo = Epo − E). Subsequently, the CR was extended to a linear function with 53 an asymmetric parameter (Brutsaert and Parlange, 1998). Further studies found that the linear     environments. In this study, xmax and xmin were set as 1 and 0, respectively, for convenience.

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The Epen term is defined by Penman's equation (Penman, 1950;Penman, 1948), which can be respectively; z is the measurement height (Table S1); d0 is the displacement height; z0m and 147 z0v are the roughness lengths for momentum and water vapor, respectively, which are 148 estimated from the canopy height (hc , Table S1), 0 = 0.67ℎ , 0 = 0.123ℎ , and 0 =  around the world were analyzed. The detailed information on these sites is listed in Table S1.

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These sites were selected from the FLUXNET database because they have observations for  Table S1.    (equation (5)) and the observed E of the 88 sites at multiple time scales is shown in Figure 3.

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The slopes of the regression increase from 0.9 to 1 as the timescale changes from day to      for the PGC function, when x is in the range of 0 to 1/α, most part of it is a concave function.

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For example, in the situation that c is equal to 0, the second derivative is higher than 0 as long 365 as x is lower than 2/3.  Table S2.  (Table 1). For the PGC functions, the regression result 402 at the seasonal scale is extremely close to that at the yearly scale ( Figure S1b and Figure 3d).

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The evaluation merits (NSEB = 0.31; R 2 B = 0.63; RMSEB = 9.94 W m −2 ) also range between 404 the monthly results and the yearly results (Table 1). These results indicate that the decline of   estimated Eest and observed site mean E also support this conclusion for the PGC function.

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The variations among different ecosystem types or between different energy balance 452 correction methods generally have no effect on this conclusion.