Abstract. Diagnostic terrestrial biosphere models (TBMs) forced by remote sensing observations have been a principal tool for providing benchmarks on global gross primary productivity (GPP) and evapotranspiration (ET). However, these models often estimate GPP and ET at coarse daily or monthly steps, hindering analysis of ecosystem dynamics at the diurnal (hourly) scales, and prescribe some essential parameters (i.e., the Ball–Berry slope (m) and the maximum carboxylation rate at 25 °C (Vcmax25)) as constant, inducing uncertainties in the estimates of GPP and ET. In this study, we present hourly estimations of global GPP and ET datasets at a 0.25° resolution from 2001 to 2020 simulated with a widely used diagnostic TBM – the Biosphere–atmosphere Exchange Process Simulator (BEPS). We employed eddy covariance observations and machine learning approaches to derive and upscale the seasonally varied m and Vcmax25 for carbon and water fluxes. The estimated hourly GPP and ET are validated against flux observations, remote sensing, and machine learning-based estimates across multiple spatial and temporal scales. The correlation coefficients (R2) and slopes between hourly tower-measured and modeled fluxes are R2=0.83, regression slope =0.92 for GPP, and R2=0.72, regression slope =1.04 for ET. At the global scale, we estimated a global mean GPP of 137.78±3.22 Pg C yr−1 (mean ± 1 SD) with a positive trend of 0.53 Pg C yr−2 (p<0.001), and an ET of 89.03±0.82×103 km3 yr−1 with a slight positive trend of 0.10×103 km3 yr−2 (p<0.001) from 2001 to 2020. The spatial pattern of our estimates agrees well with other products, with R2=0.77–0.85 and R2=0.74–0.90 for GPP and ET, respectively. Overall, this new global hourly dataset serves as a “handshake” among process-based models, remote sensing, and the eddy covariance flux network, providing a reliable long-term estimate of global GPP and ET with diurnal patterns and facilitating studies related to ecosystem functional properties, global carbon, and water cycles. The hourly GPP and ET estimates are available at https://doi.org/10.57760/sciencedb.ecodb.00163 (Leng et al., 2023a) and the accumulated daily datasets are available at https://doi.org/10.57760/sciencedb.ecodb.00165 (Leng et al., 2023b).