The generalized nonlinear advection aridity model (GNAA) for evaporation (E) estimation can be expressed in a basic form with a single parameter α_e-0, or an extended form using two parameters, α_e-c and c. The implications of these model parameters in the model and the accurate estimation of E are receiving increasing attention. Our study shows that α_e-0 and α_e-c are affected by precipitation (P), the aridity index (E_pa/P) and the climate seasonality and asynchrony index (SAI), etc, with which α_e-0 has stronger correlations. This demonstrated that annual α_e-0 and α_e-c could cover the α parameter in the Priestley–Taylor formula, as well as other factors, particularly the aridity index. For the basic GNAA form, annual α_e-0 is smaller than 1.00 in most catchments, but the GNAA model with the developed empirical formula between α_e-0 and E_pa/P can accurately estimate E at an annual scale. For the extended GNAA form, most annual α_e-c were larger than 1.00, with a mean value of 1.08 for the Loess Plateau; α_e-c tended to restore the original α values in the Priestley-Taylor equation. Functional differences exist between the basic and extended GNAA forms in estimating E and explaining the complementary relationship. Our results bridge some gaps in understanding the GNAA model from previous studies, and provide useful information to extend the application of the GNAA model.