Gross primary production (GPP)-the uptake of carbon dioxide (CO) by leaves, and its conversion to sugars by photosynthesis-is the basis for life on land. Earth System Models (ESMs) incorporating the interactions of land ecosystems and climate are used to predict the future of the terrestrial sink for anthropogenic CO . ESMs require accurate representation of GPP. However, current ESMs disagree on how GPP responds to environmental variations , suggesting a need for a more robust theoretical framework for modelling . Here, we focus on a key quantity for GPP, the ratio of leaf internal to external CO (χ). χ is tightly regulated and depends on environmental conditions, but is represented empirically and incompletely in today's models. We show that a simple evolutionary optimality hypothesis predicts specific quantitative dependencies of χ on temperature, vapour pressure deficit and elevation; and that these same dependencies emerge from an independent analysis of empirical χ values, derived from a worldwide dataset of>3,500 leaf stable carbon isotope measurements. A single global equation embodying these relationships then unifies the empirical light-use efficiency model with the standard model of C photosynthesis , and successfully predicts GPP measured at eddy-covariance flux sites. This success is notable given the equation's simplicity and broad applicability across biomes and plant functional types. It provides a theoretical underpinning for the analysis of plant functional coordination across species and emergent properties of ecosystems, and a potential basis for the reformulation of the controls of GPP in next-generation ESMs.

INTRODUCTION Reliable estimation of gross primary production (GPP) from landscape to global scales is pivotal to a wide range of ecological research areas, such as carbon-climate feedbacks, and agricultural applications, such as crop yield and drought monitoring. However, measuring GPP at these scales remains a major challenge. Solar-induced chlorophyll fluorescence (SIF) is a signal emitted directly from the core of photosynthetic machinery. SIF integrates complex plant physiological functions in vivo to reflect photosynthetic dynamics in real time. The advent of satellite SIF observation promises a new era in global photosynthesis research. The Orbiting Carbon Observatory-2 (OCO-2) SIF product is a serendipitous but critically complementary by-product of OCO-2’s primary mission target—atmospheric column CO 2 ( X CO 2 ). OCO-2 SIF removes some important roadblocks that prevent wide and in-depth applications of satellite SIF data sets and offers new opportunities for studying the SIF-GPP relationship and vegetation functional gradients at different spatiotemporal scales. RATIONALE Compared with earlier satellite missions with SIF capability, the OCO-2 SIF product has substantially improved spatial resolution, data acquisition, and retrieval precision. These improvements allow satellite SIF data to be validated, for the first time, directly against ground and airborne measurements and also used to investigate the SIF-GPP relationship and terrestrial ecosystem functional dynamics with considerably better spatiotemporal credibility. RESULTS Coordinated airborne measurements of SIF with the Chlorophyll Fluorescence Imaging Spectrometer (CFIS) were used to validate OCO-2 retrievals. The validation shows close agreement between OCO-2 and CFIS SIF, with a regression slope of 1.02 and R 2 of 0.71. Landscape gradients in SIF emission, corresponding to differences in vegetation types, were clearly delineated by OCO-2, a capability that was lacking in previous satellite missions. The SIF-GPP relationships at eddy covariance flux sites in the vicinity of OCO-2 orbital tracks were found to be more consistent across biomes than previously suggested. Finally, empirical orthogonal function (EOF) analyses on OCO-2 SIF and available GPP products show highly consistent spatiotemporal correspondence in their leading EOF modes across the globe, suggesting that SIF and GPP are governed by similar dynamics and controlled by similar environmental and biological conditions. CONCLUSION OCO-2 represents a major advance in satellite SIF remote sensing. Our analyses suggest that SIF is a powerful proxy for GPP at multiple spatiotemporal scales and that high-quality satellite SIF is of central importance to studying terrestrial ecosystems and the carbon cycle. Although the possibility of a universal SIF-GPP relationship across different biome types cannot be dismissed, in-depth process-based studies are needed to unravel the true nature of covariations between SIF and GPP. Of critical importance in such efforts are the potential coordinated dynamics between the light-use efficiencies of CO 2 assimilation and fluorescence emission in response to changes in climate and vegetation characteristics. Eventual synergistic uses of SIF with atmospheric CO 2 enabled by OCO-2 will lead to more reliable estimates of terrestrial carbon sources and sinks—when, where, why, and how carbon is exchanged between land and atmosphere—as well as a deeper understanding of carbon-climate feedbacks. The marked ecological gradients depicted by OCO-2’s high-resolution SIF measurements along a transect of temperate deciduous forests, crops, and urban area from Indiana to suburban Chicago, Illinois.

Recent studies have utilized coarse spatial and temporal resolution remotely sensed solar‐induced fluorescence (SIF) for modeling terrestrial gross primary productivity (GPP) at regional scales. Although these studies have demonstrated the potential of SIF, there have been concerns about the ecophysiological basis of the relationship between SIF and GPP in different environmental conditions. Launched in 2014, the Orbiting Carbon Observatory‐2 (OCO‐2) has enabled fine‐scale (1.3 by 2.5 km) retrievals of SIF that are comparable with measurements recorded at eddy covariance towers. In this study, we examine the effect of environmental conditions on the relationship of OCO‐2 SIF with tower GPP over the course of a growing season at a well‐characterized natural grassland site. Combining OCO‐2 SIF and eddy covariance tower data with a canopy radiative transfer and an ecosystem model, we also assess the potential of OCO‐2 SIF to constrain the estimates of Vcmax, one of the most important parameters in ecosystem models. Based on the results, we suggest that although environmental conditions play a role in determining the nature of relationship between SIF and GPP, overall, the linear relationship is more robust at ecosystem scale than the theory based on leaf‐level processes might suggest. Our study also shows that the ability of SIF to constrain Vcmax is weak at the selected site.

Key words: A-C i curve, leaf respiration during the day (R day ), maximum carboxylation rate (V cmax ), net photosynthetic rate at saturating irradiance and at ambient atmospheric CO 2 concentration (A sat ). SummarySimulations of photosynthesis by terrestrial biosphere models typically need a specification of the maximum carboxylation rate (V cmax ). Estimating this parameter using A-C i curves (net photosynthesis, A, vs intercellular CO 2 concentration, C i ) is laborious, which limits availability of V cmax data. However, many multispecies field datasets include net photosynthetic rate at saturating irradiance and at ambient atmospheric CO 2 concentration (A sat ) measurements, from which V cmax can be extracted using a 'one-point method'.We used a global dataset of A-C i curves (564 species from 46 field sites, covering a range of plant functional types) to test the validity of an alternative approach to estimate V cmax from A sat via this 'one-point method'.If leaf respiration during the day (R day ) is known exactly, V cmax can be estimated with an r 2 value of 0.98 and a root-mean-squared error (RMSE) of 8.19 lmol m À2 s À1 . However, R day typically must be estimated. Estimating R day as 1.5% of V cmax, we found that V cmax could be estimated with an r 2 of 0.95 and an RMSE of 17.1 lmol m À2 s À1 . The one-point method provides a robust means to expand current databases of fieldmeasured V cmax , giving new potential to improve vegetation models and quantify the environmental drivers of V cmax variation.