Natural Resources, School of


Date of this Version



Szilagyi, J., Crago, R., Ma, N. (2020). Dynamic scaling of the generalized complementary relationship (GCR) improves long-term tendency estimates in land evaporation. Advances in Atmospheric Sciences, 37(9).

doi:10. 1007/s00376-020-0079-6.



© The Author(s) 2020. This article is published with open access at


Most large-scale evapotranspiration (ET) estimation methods require detailed information of land use, land cover, and/or soil type on top of various atmospheric measurements. The complementary relationship of evaporation (CR) takes advantage of the inherent dynamic feedback mechanisms found in the soil−vegetation−atmosphere interface for its estimation of ET rates without the need of such biogeophysical data. ET estimates over the conterminous United States by a new, globally calibrated, static scaling (GCR-stat) of the generalized complementary relationship (GCR) of evaporation were compared to similar estimates of an existing, calibration-free version (GCR-dyn) of the GCR that employs a temporally varying dynamic scaling. Simplified annual water balances of 327 medium and 18 large watersheds served as ground-truth ET values. With long-term monthly mean forcing, GCR-stat (also utilizing precipitation measurements) outperforms GCR-dyn as the latter cannot fully take advantage of its dynamic scaling with such data of reduced temporal variability. However, in a continuous monthly simulation, GCR-dyn is on a par with GCR-stat, and especially excels in reproducing long-term tendencies in annual catchment ET rates even though it does not require precipitation information. The same GCR-dyn estimates were also compared to similar estimates of eight other popular ET products and they generally outperform all of them. For this reason, a dynamic scaling of the GCR is recommended over a static one for modeling long-term behavior of terrestrial ET.

• A temporally variable dynamic scaling of the GCR yields better long-term behavior than a static one. • The dynamic scaling accounts for the aridity of the environment in each time step and thus improves land evaporation estimates. • The dynamic scaling does not require precipitation information.