## 1 Introduction  
Knowledge of how global vegetation takes up atmospheric carbon dioxide is crucial for understanding the Earth's carbon cycle processes. Gross primary production (GPP), which is equivalent to the amount of carbon fixed during photosynthesis, constitutes the largest global land carbon flux that maintains ecosystem functions such as growth and respiration [1; 2; 3]. GPP is also closely related to crop yield, and hence can be considered the basis for food production, thus supporting human welfare. Despite the model simulations to provide GPP estimates [4; 5; 6; 7], the lack of observational datasets and analyses limits our ability to validate these model outputs. Moreover, as drought events are projected to increase over both the US and other regions [8; 9; 10; 11] in future, it is important to quantify their effects on plant productivity [12; 13]. Challenges remain due to the complexity of plants' biophysical and physiological processes associated with droughts [14]. Many researchers have used solar-induced chlorophyll fluorescence (SIF) in studies of plant photosynthesis [15; 16; 17; 18]. As a fraction of the solar energy that is re-emitted at longer wavelengths after being absorbed by chlorophyll molecules, SIF can provide information on the plant functional state [19; 20; 21]. As a result, SIF measurements have been long used to assess changes in plant physiology, in both lab- and field-scale studies [15; 16]. In the last decade, satellite SIF retrievals have demonstrated that chlorophyll fluorescence exhibits a strong correlation with GPP [22]. This high correlation was found to hold for both natural vegetation [23] and croplands [22]; in addition, it was also shown to be valid from an individual leaf level [24] to the ecosystem level [25]. It is recognized that the relationship between SIF and GPP is mainly driven by absorbed photosynthetically active radiation (APAR), as both SIF and GPP depend on it. In addition, the light use efficiencies for photochemistry and fluorescence are expected to co-vary in the absence of other protective mechanisms [22; 26]. [PERSON] et al. [22] and [PERSON] et al. [27] have shown that the linear regression method using SIF and GPP as independent and dependent variables, respectively, produces reasonably good GPP estimates for croplands and grasslands over the US and Europe. These estimates are shown to produce good agreement with GPP at flux tower sites, as well as net primary production (NPP), based on the agricultural yield statistics provided by the US Department of Agriculture (USDA) [28]. [PERSON] et al. [22] used GPP observations from FLUXNET stations over Europe and the US to derive global crop and grass GPP estimates using a linear SIF-based equation, and it was demonstrated that data- and process-based biogeochemistry models, compared to the above-mentioned SIF-based approach, tend to underestimate crop GPP by 50-75%. Given this level of success, the question remains as to whether such a linear relationship can be further improved? Currently, the mechanistic link between SIF and GPP remains unclear [29] and such a SIF-GPP relationship might vary from region to region due to local differences, such as prevalent vegetation types [30] and environmental conditions [31]. The relationship between SIF and GPP would also reflect impacts of all other parameters that influence SIF. For example, one of the major physiological limits controlling plant functioning is water availability [32; 33; 33], which translates to soil moisture availability, as plants do not ingest water directly from the atmosphere. The drought-induced deficit in soil moisture causes stomatal closure and a reduction in CO\({}_{2}\) uptake [34] and by extension photosynthesis. A decrease in photosynthesis can modulate fluorescence via several mechanisms, one of which is non-photochemical quenching (NPQ) [35; 36].