## 1 Introduction
The instantaneous temperature response of leaf-level photosynthesis is unimodal with photosynthesis inhibited at low and high temperatures, reaching an optimum somewhere in between [20]. But the optimum acclimates to growth conditions [21], and it is challenging to determine whether foliage is operating above or below the current optimum. There can also be differences between the temperature of the leaf and that of the ambient air [22]; those differences (or deltas) are influenced by radiation, transpiration and boundary-layer conductance [23; 24]. It would be desirable to replace measures of air temperature with remotely sensed land surface temperature (LST): theoretically, because LST is expected to be closer to the actual temperature of leaf tissue relevant for physiological processes; and practically, because remotely sensed LST is retrieved at a high spatial resolution relative to weather-station or meteorological analysis data. Stomata are the conduits both for CO\({}_{2}\) into the leaf, and for the loss of water vapour via transpiration. Stomata respond to an increase in vapour pressure deficit (VPD) by progressively closing to limit transpiration and this entrains a reduction in photosynthesis [25; 26]. Drought events, such as those experienced in central Europe in 2018 [27], can have further profound effects on vegetation and its productivity by causing earlier stomatal closure in response to VPD. [PERSON] et al. [28] estimated that the 2003 heatwave instigated a 30% reduction in GPP across Europe, upsetting the continental carbon balance and, in the short-term, converting the region from a sink to a source of CO\({}_{2}\). This effect of drought can interact with elevated temperatures to create a positive feedback loop--soil water depletion reducing evaporative cooling. In common with many LUE models, the P model does not take account of soil moisture effects, except as manifested through changes in fAPAR. Existing remotely sensed measures of soil moisture [29] are unable to give information about the moisture content of deeper soil layers that can be essential for plant function. The incremental predictive power of soil moisture estimates for GPP, when VPD values are available, is open to question [30]. Indeed, in the field and on relatively moist soils, soil moisture content has little or no effect on LUE. Analysis of flux-based GPP measurements at the sites considered by [PERSON] et al. [14], including a number of sites with pronounced dry seasons, confirmed that there is no universal decline of LUE with decreasing soil moisture, the implication being that any drought-induced reduction of GPP is already largely accounted for through the response of fAPAR. Changes in vegetation function, however, may not always be accompanied by changes in the state or extent of the foliage. A number of studies have reported the inability of remote sensing products to accurately capture drought effects on productivity. [PERSON] et al. [31] compared the performance of a suite of 11 satellite-based products (including fAPAR and prevalent greenness indices) in predicting GPP for a decadal timeseries (ca. 2000-2012) at four European sites (a mix of forests and grassland) and reported contrasting results--no single product proved capable of capturing each drought event at each site. Independent of leaf cover, some ecosystems (for example, tropical savannas and Mediterranean-type forests) regularly show reduced LUE during part or all of the dry season [32]. Moreover, extreme droughts to which ecosystems are not well adapted are expected to suppress LUE via a combination of reduced \(C_{\text{i}}\) and (under the most severe drying) reduced carboxylation capacity, as has been observed in drying-down experiments [33]. Therefore, in common with other operational products, the P model, when driven by air temperature, is likely to overestimate dry-season GPP in some ecosystems, and to underestimate the negative effect of extreme droughts on GPP [34].