Comment on Two Papers About the Generalized Complementary Evaporation Relationships by Crago et al. Issue 3 (16th March 2020) - Liu, Wenzhao; Zhou, Haixiang; Han, Xiaoyang; Li, Zhi
Abstract: Crago et al. published two papers in Water Resources Research in 2016 and 2018, respectively, which discussed recent generalized complementary evaporation relationships; they recommended that the lower boundary condition of the Generalized Nonlinear Advection‐Aridity (GNAA) model proposed by Brutsaert (2015, https://doi.org/10.1002/2015WR017720 ) should be modified to y = 0 at x = xmin, where xmin ∈[0, 1]. First, it is shown herein that the rescaled complementary relationship (CR) y = X, proposed by Crago et al., does not advance the analysis forward, but that instead the rescaling is tantamount to a reversion to an earlier linear and more traditional asymmetric complementary model, in which the parameter b is a function of xmin . In fact, at xmin = 0, y = X the rescaled formulation becomes physically unrealistic. The second part of this comment deals with the extended quartic form of GNAA model. The nature of the adjustable parameter c in this extended formulation is further explored, and it is shown that while its lower limit is −1, calibration with actual data can result in values in excess of 2. Such calibration allows then the estimation of xmin as a function of c, that is, xmin = f (c). This way, in addition to satisfying the original four boundary conditions, the extended GNAA model also satisfies the boundary condition of y = 0 at x = xmin . The physical variables affecting the nature of the parameter c and its relationship with Epo /Epmax will require further investigation. Key Points: We raise concerns about Crago's study of the rescaled complementary relationship (CR) and the modified lower boundary condition The rescaled CR y = X is a linear asymmetric AA model with the parameter b as a function of xmin, and dy/dx depends on both xmin and x There is a relationship between xmin and parameter c of GNAA at xmin > 0; calibration with actual data can result in values of c in excess of 2