Complementary relationship with a convective boundary layer model to estimate regional evaporation

An idea to use a simple convective boundary layer (CBL) model in the complementary relationship to estimate regional evaporation was explored. The CBL model simulated the potential specific humidity deficit D in CBL when the bulk stomatal resistance r(st) = 0. This value of D was then used in the Penman-type equation to derive evaporation E-po that would occur with ample soil moisture under the prevailing weather condition. The same equation was also used to produce the potential evaporation E with the actual humidity deficit, and these E-p and E-po values allowed the evaluation of the actual evaporation E by applying the complementary relationship E = etaE(po) - E-p,, where eta is assumed as 2.0. This was tested with the data set obtained in Hexi Corn desert area in northwestern China with a modified version of a simple CBL model developed by Lhomme [1997]. It was found that the method produced better estimates of the daytime mean E values with smaller bias than those obtained from a conventional application of the complementary relationship without the CBL model. Also, it was shown that the assumption of eta = 2.0 in the complementary relationship was only approximate in most cases. To take this into account, an additional procedure was explored in which eta was treated as a variable, and an iteration process with the CBL model determined the final 77 and E values. It was found that this process produced E values that have smaller systematic error and agree better with the measurements on average, but the unsystematic error got worse than that found with 77 = 2.0, probably because of use of the CBL model with r(st) not equal 0 in the iteration process.