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  1. Abstract. Evapotranspiration (ET) is critical in linking global water, carbon andenergy cycles. However, direct measurement of global terrestrial ET is notfeasible. Here, we first reviewed the basic theory and state-of-the-artapproaches for estimating global terrestrial ET, including remote-sensing-based physical models, machine-learning algorithms and land surfacemodels (LSMs). We then utilized 4 remote-sensing-based physical models,2 machine-learning algorithms and 14 LSMs to analyze the spatial andtemporal variations in global terrestrial ET. The results showed that theensemble means of annual global terrestrial ET estimated by these threecategories of approaches agreed well, with values ranging from 589.6 mm yr−1(6.56×104 km3 yr−1) to 617.1 mm yr−1(6.87×104 km3 yr−1). For the period from 1982 to 2011, boththe ensembles of remote-sensing-based physical models and machine-learningalgorithms suggested increasing trends in global terrestrial ET (0.62 mm yr−2 with a significance level of p<0.05 and 0.38 mm yr−2 with a significance level of p<0.05,respectively). In contrast, the ensemble mean of the LSMs showed nostatistically significant change (0.23 mm yr−2, p>0.05),although many of the individual LSMs reproduced an increasing trend.Nevertheless, all 20 models used in this study showed that anthropogenicEarth greening had a positive role in increasing terrestrial ET. Theconcurrent small interannual variability, i.e., relative stability, found inall estimates of global terrestrial ET, suggests that a potentialplanetary boundary exists in regulating global terrestrial ET, with the valuemore »of this boundary beingaround 600 mm yr−1. Uncertainties among approaches were identified inspecific regions, particularly in the Amazon Basin and arid/semiaridregions. Improvements in parameterizing water stress and canopy dynamics,the utilization of new available satellite retrievals and deep-learning methods,and model–data fusion will advance our predictive understanding of globalterrestrial ET.« less