Actual evapotranspiration (ETa) is important since it is an important link to water, energy, and carbon cycles. Approximately 96% of the Qinghai-Tibet Plateau (QTP) is underlain by frozen ground, however, the ground observations of ETa are particularly sparse-which is especially true in the permafrost regions-leading to great challenge for the accurate estimation of ETa. Due to the impacts of freeze-thaw cycles and permafrost degradation on the regional ET process, it is therefore urgent and important to find a reasonable approach for ETa estimation in the regions. The complementary relationship (CR) approach is a potential method since it needs only routine meteorological variables to estimate ETa. The CR approach, including the modified advection-aridity model by Kahler (K2006), polynomial generalized complementary function by Brutsaert (B2015) and its improved versions by Szilagyi (S2017) and Crago (C2018), and sigmoid generalized complementary function by Han (H2018) in the present study, were assessed against in situ measured ETa at four observation sites in the frozen ground regions. The results indicate that five CR-based models are generally capable of simulating variations in ETa, whether default and calibrated parameter values are employed during the warm season compared with those of the cold season. On a daily basis, the C2018 model performed better than other CR-based models, as indicated by the highest Nash-Sutcliffe efficiency (NSE) and lowest root mean square error (RMSE) values at each site. On a monthly basis, no model uniformly performed best in a specific month. On an annual basis, CR-based models estimating ETa with biases ranging from -94.2 to 28.3 mm year(-1), and the H2018 model overall performed best with the smallest bias within 15 mm year(-1). Parameter sensitivity analysis demonstrated the relatively small influence of each parameter varying within regular fluctuation magnitude on the accuracy of the corresponding model.

Accurately quantifying large-scale terrestrial evapotranspiration (ET) remains hampered by poor parameterization of the physical processes that relate to ET. Previous studies suggested that the calibration-free complementary relationship (CR) method that requires only routine meteorological data performed better than main-stream atmospheric reanalyses, land surface or remote sensing models in estimating large-scale ET. Here we simultaneously evaluate the latest machine learning-based upscaling of eddy-covariance measurements (FLUXCOM) and the CR estimates against the water-balance derived ET rates of 18 large Hydrologic Unit Code-2 (HUC2) and 327 medium HUC6 basins across the conterminous United States. Overall, CR and FLUXCOM perform comparably in representing the multiyear mean and temporal variations in annual ET at both, HUC2 and HUC6, scales for the 1979-2013 period. Such equally good skills also hold true for the 2003-2015 period, during which FLUXCOM was driven solely by remote sensing data. However, the CR generally captures the longterm linear tendencies in annual ET rates somewhat better than FLUXCOM. Because of its minimal data requirement, the calibration-free version of the CR may continue to serve as a benchmarking tool for large-scale ET simulations.

Accurate simulation of the daily actual evaporation (E) is important for understanding and predicting the hydrological climate and terrestrial water-carbon cycle. However, the inclement environment and sparse observation network in the high-altitude areas of the Tibetan Plateau hinder the reliable estimation of actual evaporation. The Complementary Relationship (CR) of evaporation, which is a simple method for estimating the actual evaporation implemented with only routine meteorological data, can be used to study the complex feedback between the atmosphere and the surface. In this study, the eddy covariance and meteorological data were used to test the existence of the CR in the Fenghuo Mountains in the permafrost regions of the Tibetan Plateau. We further compared the application of the generalized nonlinear CR (B2015) and the latest calibrationfree CR (S2017) in estimating the actual daily evaporation. The results show that a nonlinear CR of evaporation exists in the Tibetan Plateau. The calibration-free nonlinear principle implemented improvements in the boundary condition shows a more robustness advantage than the generalized method. In addition, we also found that, except rainfall, the freezing-thawing process of active layer is a main reason of seasonal variation characteristics in energy fluxes. These findings broaden our understanding of the applicability of the CR theory and provide a simple and promising method for simulating evaporation on the Tibetan Plateau with the minimum data sets.