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Accurate quantification of terrestrial evapotranspiration (ET) is essential to understand the Earth's energy and water budgets under climate change. However, despite water and carbon cycle coupling, there are few diagnostic global evapotranspiration models that have complete carbon constraint on water flux run at a high spatial resolution. Here we estimate 8-day global ET and gross primary production (GPP) at 500 m resolution from July 2002 to December 2017 using a coupled diagnostic biophysical model (called PML-V2) that, built using Google Earth Engine, takes MODIS data (leaf area index, albedo, and emissivity) together with GLDAS meteorological forcing data as model inputs. PML-V2 is well calibrated against 8-day measurements at 95 widely-distributed flux towers for 10 plant functional types, indicated by Root Mean Square Error (RMSE) and Bias being 0.69 min d(-1) and -1.8% for ET respectively, and being 1.99 g C m(-2) d(-1) and 4.2% for GPP. Compared to that performance, the cross-validation results are slightly degraded, with RMSE and Bias being 0.73 mm d(-1) and -3% for ET, and 2.13 g C m(-2) d(-1) and 3.3% for GPP, which indicates robust model performance. The PML-V2 products are noticeably better than most GPP and ET products that have a similar spatial resolution, and suitable for assessing the influence of carbon-induced impacts on ET. Our estimates show that global ET and GPP both significantly (p < 0.05) increased over the past 15 years. Our results demonstrate it is very promising to use the coupled PML-V2 model to improve estimates of GPP, ET and water use efficiency, and its uncertainty can be further reduced by improving model inputs, model structure and parameterisation schemes.