The sensitivity of photosynthesis to environmental changes is essential for understanding carbon cycle responses to global climate change and for the development of modeling approaches that explains its spatial and temporal variability. We collected a large variety of published sensitivity functions of gross primary productivity (GPP) to different forcing variables to assess the response of GPP to environmental factors. These include the responses of GPP to temperature; vapor pressure deficit, some of which include the response to atmospheric CO2 concentrations; soil water availability (W); light intensity; and cloudiness. These functions were combined in a full factorial light use efficiency (LUE) model structure, leading to a collection of 5600 distinct LUE models. Each model was optimized against daily GPP and evapotranspiration fluxes from 196 FLUXNET sites and ranked across sites based on a bootstrap approach. The GPP sensitivity to each environmental factor, including CO2 fertilization, was shown to be significant, and that none of the previously published model structures performed as well as the best model selected. From daily and weekly to monthly scales, the best model's median Nash-Sutcliffe model efficiency across sites was 0.73, 0.79 and 0.82, respectively, but poorer at annual scales (0.23), emphasizing the common limitation of current models in describing the interannual variability of GPP. Although the best global model did not match the local best model at each site, the selection was robust across ecosystem types. The contribution of light saturation and cloudiness to GPP was observed across all biomes (from 23% to 43%). Temperature and W dominates GPP and LUE but responses of GPP to temperature and W are lagged in cold and arid ecosystems, respectively. The findings of this study provide a foundation towards more robust LUE-based estimates of global GPP and may provide a benchmark for other empirical GPP products.