Global datasets of leaf photosynthetic capacity for ecological and earth system research

The maximum rate of Rubisco carboxylation (V_cmax) determines leaf photosynthetic capacity and is a key parameter for estimating the terrestrial carbon cycle, but its spatial information is lacking, hindering global ecological research. Here, we convert leaf chlorophyll content (LCC) retrieved from satellite data to V_cmax, based on plants' optimal distribution of nitrogen between light harvesting and carboxylation pathways. We also derive V_cmax from satellite (GOME-2) observations of sun-induced chlorophyll fluorescence (SIF) as a proxy of leaf photosynthesis using a data assimilation technique. These two independent global V_cmax products agree well ($r^{\mathrm{2}}=\mathrm{0.79},\mathrm{RMSE}=\mathrm{15.46}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001) and compare well with 3672 ground-based measurements ($r^{\mathrm{2}}=\mathrm{0.69},\mathrm{RMSE}=\mathrm{13.8}\mathrm{\mu }$mol m⁻² s⁻¹ and P<0.001 for SIF; $r^{\mathrm{2}}=\mathrm{0.55},\mathrm{RMSE}=\mathrm{18.28}\mathrm{\mu }$mol m⁻² s⁻¹ and P<0.001 for LCC). The LCC-derived V_cmax product is also used to constrain the retrieval of V_cmax from TROPical Ozone Mission (TROPOMI) SIF data to produce an optimized V_cmax product using both SIF and LCC information. The global distributions of these products are compatible with V_cmax computed from an ecological optimality theory using meteorological variables, but importantly reveal additional information on the influence of land cover, irrigation, soil pH, and leaf nitrogen on leaf photosynthetic capacity. These satellite-based approaches and spatial V_cmax products are primed to play a major role in global ecosystem research. The three remote sensing V_cmax products based on SIF, LCC, and SIF+LCC are available at https://doi.org/10.5281/zenodo.6466968 (Chen et al., 2022), and the code for implementing the ecological optimality theory is available at https://github.com/SmithEcophysLab/optimal_vcmax_R and https://doi.org/10.5281/zenodo.5899564 (last access: 31 August 2022) (Smith et al., 2022).

1 Introduction

The Farquhar-von Caemmerer–Berry (FvCB) leaf photochemistry model (Farquhar et al., 1980) is widely used for simulating vegetation photosynthesis in ecological studies. The maximum carboxylation rate (V_cmax) that determines leaf photosynthetic capacity is an essential parameter in the FvCB model. The current state of the art (Rogers 2014, Rogers et al., 2017) in regional and global ecosystem modeling is to assign V_cmax at 25 ^∘C (V_cmax25) as a fixed parameter that varies by plant functional type (PFT), and is typically estimated from a ground-based database (Kattge et al., 2009, 2020), even though observations show 2–3-fold variation in V_cmax25 for the same PFT. As the total simulated photosynthesis of a canopy is highly sensitive to V_cmax, this simple approach causes considerable distortion in modeled spatial distributions of the terrestrial carbon cycle (Bonan et al., 2011; Walker et al., 2017; Luo et al., 2017; Chen et al., 2019), hindering advancement in global ecological and Earth system research.

In recent studies, two independent satellite remote sensing approaches have been developed to estimate V_cmax at the global scale. Since the first demonstration of sun-induced chlorophyll fluorescence (SIF) as a proxy of gross primary productivity (GPP) at the global scale (Frankenberg et al., 2011), the use of SIF for global carbon cycle estimation has been a highly active research field (Mohammed et al., 2019). He et al. (2019) attempted the first global mapping of V_cmax from SIF after converting SIF observations into GPP that is related to V_cmax. A time series of daily V_cmax maps was derived using SIF measured by the Global Ozone Monitoring Experiment-2 (GOME-2) sensor from 2007 to 2017 at 36 km resolution (see Methods). The second space-based approach to deriving V_cmax is via leaf chlorophyll content (LCC). Chlorophyll harvests light that provides energy for the reactions in the Calvin–Benson–Bassham (CBB) cycle of photosynthesis, and therefore is likely coordinated with leaf carboxylation capacity (V_cmax) as plants optimize their photosynthetic nitrogen resources (Croft et al., 2017). The retrieval of LCC from satellite imagery offers the means of reliable and accurate LCC estimation over different spatiotemporal scales. Data from the medium resolution imaging spectrometer (MERIS) in red, near infrared, and red-edge bands at 300 m resolution at 7 d intervals have been used to produce a global LCC map series from 2003 to 2012 (Croft et al., 2020). In a temperate broadleaf forest, it was found that LCC is better correlated with V_cmax than leaf nitrogen content (LNC) over a growing season (Croft et al., 2017), and similar correlations between V_cmax and LCC were established from empirical data for various PFTs (Luo et al., 2019; Lu et al., 2020). In this study, we use this new LCC time series with existing empirical LCC-V_cmax relationships to derive another independent source of information for global V_cmax assessment.

The V_cmax products derived from SIF and LCC have different strengths and weaknesses. SIF contains strong signals for V_cmax because it is directly related to the vegetation photosynthesis rate, but the spatial and temporal resolutions of existing satellite SIF observations are low. LCC can be derived reliably from multispectral satellite data at much higher spatial and temporal resolutions than those of SIF. Chlorophyll pigments have broad absorption features in the visible range and also affect the fine positioning of red-edge wavelengths. However, the derivation of LCC from remote sensing data is influenced by errors in vegetation structural parameters used in the derivation. The conversion from LCC to V_cmax depends on empirical relationships for different PFTs, which have considerable uncertainties (Luo et al., 2019). In order to make the best use of available satellite data for mapping V_cmax, we combined SIF and LCC data to produce a single global V_cmax time series. We derived a global V_cmax time series using SIF data from the TROPical Ozone Mission (TROPOMI) at 0.1^∘ resolution in daily intervals for 2019 with LCC-derived V_cmax as a constraint in the derivation using a parameter optimization technique (He et al., 2019; see also Methods). The constraint is made with LCC-derived V_cmax aggregated to each 0.1^∘ grid every 7 d as the initial value, which is then replaced when good quality TROPOMI SIF data are available. In this way, the best information on V_cmax from both SIF and LCC is combined. The combined global V_cmax product is highly correlated with that produced from LCC ($r^{\mathrm{2}}=\mathrm{0.87},\mathrm{RMSE}=\mathrm{12.04}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001), suggesting that much of the LCC information is transferred to this product by filling in its data gaps.

The global distribution of V_cmax has also been derived theoretically. Based on a new ecological optimality theory (Wang et al., 2017), Smith et al. (2019) calculated a global V_cmax map from meteorological variables of radiation, air temperature, and vapor pressure deficit using a monthly climate dataset (Harris et al., 2014). The theory proposes that leaves optimize the use of available resources so that the photosynthetic rate limited by V_cmax equals that limited by the electron transport to generate ribulose-1,5,-bisphosphate (RuBP) needed in photosynthesis under average daytime conditions. In this theory, the electron transport rate is computed from meteorological conditions, and is independent of soil nutrient and water conditions. Evaluation against 3672 ground observations shows that the model can capture about $\mathrm{2}/\mathrm{3}$ of the variance in the observed V_cmax ($r^{\mathrm{2}}=\mathrm{0.66},\mathrm{RMSE}=\mathrm{13.37}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001), while the model bias is most significantly correlated to leaf nitrogen content among several leaf and soil parameters (Smith et al., 2019). The validity and reliability of V_cmax information derived from the theory are yet to be evaluated outside of the limited amount of ground data.

Here we provide assessment of the reliability of these products for global ecological and Earth system studies. The specific objectives of this study are (1) to derive new global V_cmax products using satellite data; (2) to assess the accuracy of these products against a ground-based dataset; (3) to mutually assess these products; and (4) to evaluate the V_cmax product-derived ecological optimality theory using satellite-derived V_cmax products, as the theory would be useful for estimating V_cmax in prognostic terrestrial ecosystem models (TEMs) which are often used in Earth system models.

2 Methods

2.1 Deriving V_cmax from SIF

During photosynthesis, plant leaves dissipate part of the excess light energy that is not used in photochemistry in the form of chlorophyll fluorescence (Porcar-Castell et al., 2014). Under conditions without strong moisture and/or thermal stress, the SIF emission from a leaf increases with its instantaneous photosynthetic rate (Frankenberg et al., 2011; Guanter et al., 2014; Sun et al., 2017; Li et al., 2018; Wang et al., 2020), although SIF signals are small (1 %–5 % of reflected radiation at near infrared wavelengths, Colombo et al., 2016) and contain noise from various sources including the variations in solar illumination angle and sensor viewing angle (Dechant et al., 2020). In a plant canopy, sunlit leaves are the predominant sources of SIF (Pinto et al., 2016). For the purpose of deriving leaf-level information, the total SIF measured from a canopy was first separated into sunlit and shaded leaf components according to sun-target-sensor observation geometry and canopy architectural parameters. The observation geometry was determined by satellite and solar zenith and azimuthal angles. The main canopy architectural parameters were leaf area index (LAI), which quantifies the amount of leaf area in the canopy per unit ground surface area, and the clumping index (CI), which characterizes the non-random spatial distribution of leaves in the canopy. Both LAI and CI were used to separate sunlit and shaded leaf fractions in the canopy, and the observation geometry determined the proportion of sunlit leaves observed by a satellite sensor (Chen et al., 1999). Leaf reflectance at the SIF wavelength was used to estimate the strength of multiple scattering of emitted SIF in the canopy that enhances SIF observed from sunlit leaves (He et al., 2019). The sunlit SIF component derived in this way was then converted into the average sunlit leaf photosynthetic rate, from which V_cmax is derived using a data assimilation technique (He et al., 2019). An ensemble Kalman filer (EnKF) was developed using an ecosystem model (Chen et al., 2012) and used in the data assimilation technique to optimize V_cmax based on the difference between SIF-derived and modeled average sunlit leaf photosynthetic rates. In the optimization, it was assumed that the error in modeling the photosynthetic rate was caused by both inaccuracy in the initial V_cmax input (constants by PFT or estimated based on LCC) and the collective errors in other parameters, including environmental conditions (meteorology and soil) used in the model. An error matrix was therefore developed to determine the amount of adjustment to the initial V_cmax value (He et al., 2019). Optimized V_cmax values often differed considerably from the initialized values beyond their error ranges, suggesting that SIF observations provided reliable and strong signals for its optimization, even though other model errors are also present.

The data assimilation methodology was first applied to GOME-2 SIF data and generated a global daily V_cmax map series from 2007 to 2017 at 36 km resolution (He et al., 2019). In this study, this methodology was refined and applied to TROPOMI SIF data to produce global daily V_cmax maps in 2019 at 0.1^∘ resolution (≈10 km). The refinements included the conversion from SIF to GPP using non-linear relationships (Liu et al., 2022) rather than linear relationships used in He et al. (2019) and the initialization of V_cmax using the LCC product (Croft et al., 2020) rather than constant V_cmax by PFT. Although the V_cmax map series produced using TROPOMI SIF + LCC data is available for only one year, it has a much higher spatial resolution than that produced from GOME-2, and therefore has broader applications in global ecological research.

2.2 Deriving V_cmax from LCC

LCC is responsible for light harvesting and providing excitation energy to drive photosynthesis in leaves, while V_cmax defines the capacity of leaves to utilize the excitation energy for photosynthesis. These two leaf traits are dynamically optimized to local environmental conditions to achieve an optimal use of nitrogen resources (Xu et al., 2012). LCC is a relatively stable trait without much day-to-day and diurnal variations, while V_cmax is sensitive to temperature. Empirical data show close relationships between LCC and V_cmax25 (Houborg et al., 2017; Croft et al., 2017; Lu et a., 2020), which is V_cmax normalized to its value at 25 ^∘C using a temperature function (Smith et al., 2019, see also Sect. 2.4 below). A two-step radiative transfer model inversion method was developed for retrieving LCC from multispectral satellite data (Zhang et al., 2008; Croft et al., 2020). In step 1, the canopy-level reflectance was inverted to leaf-level reflectance with a lookup table (LUT) constructed using canopy radiative transfer model for canopies with turbid media (Verhoef, 1984) and a geometrical optical model for clumped canopies (Chen and Leblanc, 1997, 2001) that computed observed sunlit leaf fraction according to canopy structure and sun-target-view geometry. In step 2, the leaf-level PROSPECT model (Feret et al., 2008) was inverted to obtain LCC from the inverted multi-spectral leaf reflectance. This two-step model inversion algorithm avoids issues with empirical methods that directly link LCC to canopy-level remote sensing data, which lack generality because of variable canopy structure and sun-target-view geometry. The first time-series of global LCC maps were retrieved using MERIS data from 2003 to 2011 at 300 m resolution and 7 d intervals (Croft et al., 2020). A validation using 248 ground sites in 5 PFTs suggests that this product is reliable ($r^{\mathrm{2}}=\mathrm{0.5},p\mathit{<}\mathrm{0.01},\mathrm{RMSE}=\mathrm{10.79}\mathrm{\mu }$g cm⁻² or mean error 23 %). Using empirical relationships between LCC and V_cmax25 for various PFTs (Luo et al., 2019), this global LCC time series was converted into V_cmax25.

2.3 Ground-based V_cmax dataset

In this study, we use the same ground-based V_cmax dataset as that used by Smith et al. (2019). It consisted of 3672 entries for 1474 plant species that are grouped into seven PFTs in this study. Each entry consisted of V_cmax measured from one or more leaves with companion data of air temperature, humidity, incoming PAR, longitude, and latitude. V_cmax was derived from several pairs of photosynthesis (A) and intercellular CO₂ concentration (C_i) (to construct an $A/C_{\mathrm{i}}$ curve) (56 %) or from a single pair of A and C_i using the method of De Kauwe et al. (2016) (44 %).

To match with V_cmax maps derived from SIF, LCC, and EOT, the ground-based data were aggregated in two ways: (1) the data points of the same PFT as that in the PFT map (Fig. 4b) used for LCC and SIF processing were grouped to form an average V_cmax for a grid, while mismatched data points within the grid were ignored; and (2) all existing data points within each grid were averaged and labeled as the dominant PFT. We found that the second way resulted in better correlation with all three types of V_cmax maps. After the aggregation to 0.5^∘ resolution, there were 180 data points for all PFTs used in the final analysis of all V_cmax products.

2.4 Temperature normalization

For the same leaf, V_cmax varies exponentially with leaf temperature, and hence it is more meaningful to compare V_cmax25 between leaves or different estimates. In this study, all global V_cmax products are derived at the growth temperature. To facilitate their comparisons with ground databases and their future use in models, V_cmax is converted to V_cmax25 using a common temperature function (Eq. 22 in Smith et al., 2019).

Figure 1 Global distributions of $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ at the mean growing season temperature derived using (a) GOME-2 SIF (2007–2011), (b) TROPOMI SIF+LCC (2019) constrained by leaf chlorophyll content (LCC), (c) LCC (2017), and (d) ecological optimality theory (1901–2015). White areas are missing data.

Table 1 Correlations by plant function type between V_cmax at growing season mean temperature (T_g) in four products (GOME-2 SIF, TROPOMI SIF, LCC, and EOT) and a ground database with 3672 individual data points aggregated to 180 grids of 0.5^∘ resolution. ENF signifies evergreen needleleaf forest, DNF deciduous needleleaf forest, DBF deciduous broadleaf forest, EBF evergreen broadleaf forest, GRS grassland, CRP cropland, SHR shrub, and RMSE root mean square error.

3 Results

3.1 Evaluation of four global V_cmax products

The global distributions of the growing season mean V_cmax obtained from GOME-2 SIF, MERIS LCC, and TROPOMI SIF are shown in Fig. 1 in comparison with V_cmax calculated from the ecological optimality theory (EOT) at the growing season mean temperature. For this comparison, V_cmax25 derived from LCC is converted to V_cmax at the mean growing temperature. The growing season is defined as the period when monthly mean air temperature is above 0 ^∘C. These four global V_cmax distributions derived at different spatial resolutions at 36 km, 300 m, 0.1, and 0.5^∘ from GOME-2 SIF, LCC, TROPOMI SIF, and EOT, respectively, and aggregated to 0.5^∘ resolution in Fig. 1, are highly correlated spatially, although their details differ to some extent. The distribution derived from the optimality theory appears to be spatially smooth, reflecting the fact that meteorological variables used for V_cmax prediction do not vary abruptly in space. The three remote sensing products show mutually-consistent patchy patterns, suggesting that they have all captured some realistic variability on the ground associated with PFT distribution patterns. However, all four products show remarkable similarities in the overall geographic patterns and mutually well correlated with each other ($R^{\mathrm{2}}=\mathrm{0.76}-\mathrm{0.90}$, p<0.001). Among three remote sensing products, SIF-derived products correlate best with the product based on the ecological optimality theory (EOT) ($r^{\mathrm{2}}=\mathrm{0.85},\mathrm{RMSE}=\mathrm{11.69}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001 for GOME-2; $r^{\mathrm{2}}=\mathrm{0.76},\mathrm{RMSE}=\mathrm{15.77}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001 for TROPOMI). We further evaluate these products below.

Figure 2 Comparisons of V_cmax at growing season mean temperature (T_g) derived from GOME-2 SIF, TROPOMI SIF+LCC, LCC, and optimality theory (EOT) against a ground database with 3672 individual data points aggregated to 180 grids of 0.5^∘ resolution. The root mean square error (RMSE) is in unit of µmol m⁻² s⁻¹.

All four V_cmax products compare well with ground-based measurements (Fig. 2) after they are aggregated to the corresponding 0.5^∘ grids (see Methods). The correlation of optimality-based V_cmax with the ground measurements is similar to that shown in Smith et al. (2019) ($r^{\mathrm{2}}=\mathrm{0.66},\mathrm{RMSE}=\mathrm{13.37}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001), and correlations of other three V_cmax products with the same ground measurements are similar ($r^{\mathrm{2}}=\mathrm{0.69},\mathrm{RMSE}=\mathrm{13.80}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001 for GOME-2; $r^{\mathrm{2}}=\mathrm{0.80},\mathrm{RMSE}=\mathrm{8.99}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001 for TROPOMI; $r^{\mathrm{2}}=\mathrm{0.55},\mathrm{RMSE}=\mathrm{18.28}\mathrm{\mu }$mol m⁻² s⁻¹, P<0.001 for LCC). It is encouraging to see that three of the four products captured about $\mathrm{2}/\mathrm{3}$ of the variance in the ground data, despite the large-scale mismatch between the grids of these products and the ground data points. Some errors would also be expected from temporal mismatches as the differences in the years of ground and remote sensing data acquisitions are not considered (in order to have as many data points as possible in the comparisons), although data outside of the growing season are excluded. While V_cmax for individual leaves may vary greatly among plant species within the same functional type and with environmental conditions over the landscape, their locally averaged values would be expected to display a consistent spatial pattern at large scales that are determined more or less by meteorological conditions – permitting the success of the optimality theory for predicting V_cmax based on meteorological variables alone. Coarse-resolution remote sensing data, such as GOME-2 SIF data at 36 km resolution and TROPOMI at 0.1^∘ resolution, can also capture the spatial variability in V_cmax at large scales.

The correlation statistics of the four products shown in Fig. 2 with the ground database by plant function type are given in Table 1. Forest PFTs of ENF, DNF, and DBF are combined in order to have a sufficient number of data points for the statistical analysis. Correlations for most PFTs are highly significant for all products (p<0.001), but for forest PFTs and SHR, the correlations are weak for most products except for TROPOMI. The TROPOMI V_cmax product (https://doi.org/10.5281/zenodo.6466968) compares best with the ground database in terms of the Pearson correlation coefficient (r²), RMSE, and the p value from two-tailed paired t tests, suggesting that the combination of SIF and LCC information is effective in capturing the spatial variability of V_cmax for the various PFTs. It is therefore most ready for global ecological studies among the four products.

Figure 3 Comparisons of SIF-derived and LCC-derived V_cmax values for a group of three PFTs and four individual PFTs, and all PFTs combined. These two sets of V_cmax derived independently using two different remote sensing techniques are very well correlated for all PFTs except for the evergreen broadleaf forests (EBFs) in tropical areas where frequent clouds degrade the quality of both SIF and LCC datasets.

Figure 4 The influence of irrigation on V_cmax over cropland and grassland, detected by TROPOMI SIF+LCC at 0.5^∘ resolution, where (a) is the actual area irrigated in percent of cell area (aai pct cell area) in recent decades, (b) the relative difference in V_cmax (ΔV_cmax) between TROPOMI and ecological optimality theory (EOT), i.e., ΔV_cmax=(TROPOMI-EOT)/EOT, (c) the correlation coefficient (r) between actual irrigated area percentage and ΔV_cmax within sliding windows of 10×10 pixels, and (d) the histograms of r and R² values in (c) for cropland and grassland. ΔV_cmax is significantly correlated with percent area irrigated in both cropland (r=0.32, p<0.001) and grassland (r=0.30, p<0.001) at the global scale.

The V_cmax values derived independently from GOME-2 SIF and MERIS LCC at the mean growing season temperature are well correlated overall (r²=0.79) and for individual PFTs ($r^{\mathrm{2}}=\mathrm{0.77}-\mathrm{0.88}$) except for EBF (r²=0.26) (Fig. 3). These high correlations suggest that the signals contained in both SIF and multi-spectral reflectance data used for LCC retrieval are strong and useful for deriving V_cmax. This is particularly encouraging because both types of remote sensing data are increasingly available with existing and forthcoming satellite sensors providing improved SIF (Mohammed et al., 2019) and multi-spectral data (such as the Sentinel sensor series, https://sentinel.esa.int/web/, last access: 31 August 2022). The differences between these two independent retrievals of V_cmax are still considerable, especially for EBF in the tropics due to frequent cloud cover, and there is room for improvement not only in the retrieval algorithms but also in providing improved SIF and spectral data at higher spatial and temporal resolutions. Much more ground-based data of V_cmax, LCC, and associated structural parameters (leaf area index and clumping index) are still needed for refining and validating the retrieved V_cmax. However, these existing products are already a large step forward from the current state of the art and can be employed immediately for parameterizing and benchmarking TEMs. In other words, these products may have already overcome the V_cmax bottleneck in accurate modeling of the spatio-temporal patterns of the terrestrial productivity and carbon cycle.

3.2 Influence of environmental factors on V_cmax

V_cmax values derived from all three remote sensing products shown in Fig. 1 are most obviously larger than those produced by EOT over croplands and grasslands in the Americas, India, and China. Cropland and grassland management, including fertilization and irrigation, may explain part of this divergence. To explore the possible influences of cropland and grassland irrigation on V_cmax, we used a global irrigation map (https://www.fao.org/aquastat/en/geospatial-information/global-maps-irrigated-areas/latest-version/, last access: 31 August 2022) at 0.5^∘ resolution to compare with the relative difference (ΔV_cmax) between TROPOMI SIF+LCC V_cmax and EOT-based V_cmax, i.e., (TROPOMI-EOT)/EOT (Fig. 4). Globally, ΔV_cmax increases with irrigated area percentage. The regression coefficient (R) between the actual values of percent irrigated area and ΔV_cmax for the areas of irrigation greater than 5 % at the global scale is +0.32 (p<0.01) and +0.3 (p<0.01) for croplands and grasslands, respectively. In some regions, including China, India, and the Middle East, the correlation coefficient is considerably higher ($\mathrm{0.25}-\mathrm{0.5},p\mathit{<}\mathrm{0.001}$). Irrigation in cropland and grassland would reduce water stress and increase leaf photosynthetic capacity (Reed and Loik, 2016; Chen et al., 2019; Song et al., 2021), giving rise to the positive correlation between ΔV_cmax and percent of irrigation area in a pixel. For crops, fertilization would generally co-occur with irrigation (Sela, 2021), so this positive correlation could also include the effect of fertilization on V_cmax.

Figure 5 Soil pH has significant influence on V_cmax detected by TROPOMI SIF+LCC at 0.5^∘ resolution. (a) Soil pH in the top 0–5 cm layer, (b) relative difference in V_cmax (ΔV_cmax) between TROPOMI and ecological optimality theory (EOT), i.e., ΔV_cmax= (TROPOMI-EOT)/EOT, (c) correlation coefficient (r) between soil pH and ΔV_cmax within sliding windows of 10×10 pixels, (d) PFT distribution, (e) summary of mean correlation coefficient r and R² values in (c) by PFTs, and (f) histograms of r and R² values in (c) for grassland (GRS) and cropland (CRP). In 40.3 % of GRS and CRP pixels, ΔV_cmax is positively and significantly (p<0.1) correlated with soil pH.

Soil properties may also influence V_cmax (Reich et al., 2007, Maire et al., 2015; Ali et al., 2015, Smith and Dukes, 2018). Among soil properties available in the global SoilGrids database (Hengl et al., 2017), we found that soil pH best correlates with ΔV_cmax. Soil pH is spatially variable (Fig. 5a), and we found that ΔV_cmax is positively and significantly correlated to soil pH in most regions, with 40.3 % (11 163 out of 27 681 pixels) of cropland and grassland areas having r>0.1 and p<0.1 (Fig. 5). Similar statistics are found for other PFTs, suggesting that soil pH has similar effects on V_cmax across PFTs. However, ΔV_cmax is not significantly correlated with other soil properties, including soil carbon content, nitrogen content, and cation exchange capacity. Soil pH is a key control on soil biochemical reactions affecting nutrient uptake (Hall et al., 1998; Gentili et al., 2018), and has an optimum range for plant growth from 5.5 to 7.5 (Islam, 1980). As soil pH varies in a wide range (4 to 8, Fig. 5), its effect on V_cmax is therefore detectable from remote sensing signals. Plants on acidic soils tend to have higher ratios of leaf-internal to ambient CO₂ (Wang et al., 2017; Dong et al., 2020; Pailassa et al. 2020), and therefore would be expected to have lower V_cmax. These results suggest that V_cmax derived from SIF has captured much of the spatial variability in V_cmax due to irrigation and soil properties that are not captured by optimality theory. Remote sensing products can therefore provide more nuanced information on plant responses to non-meteorological environmental drivers, and can therefore provide more accurate V_cmax estimates and additional information on its spatial variability.

Figure 6 The relative difference in $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ (ΔV_cmax) between TROPOMI and ecological optimality theory (EOT), i.e., ΔV_cmax= (TROPOMI-EOT)/EOT, is significantly correlated to leaf chlorophyll content (LCC) as a proxy of the leaf nutrient condition. All PFTs are included. The correlation is statistically highly significant with p<0.001 for individual PFTs and for all PFTs combined.

Figure 7 Influence of leaf nitrogen content on the relative difference between $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ values measured at ground sites and derived from an ecological optimality theory (EOT) using the available database (Smith et al., 2019). The influence is highly significant for all plant functional types (i.e., p<0.001). The slopes of the regressions of the relative difference in V_cmax against LCC or ground leaf nitrogen data are similar, in agreement with the global modeling results that levels of nutrient limitation to plant growth are similar among different PFTs (Fisher et al., 2012).

In addition to soil properties, leaf traits are expected to be more directly related to V_cmax. We use LCC, which contains part of the leaf photosynthetic nitrogen pool (Xu et al., 2012), as an indicator of the effect of leaf traits on V_cmax. We found that ΔV_cmax is significantly and positively correlated to LCC for individual PFTs ($r^{\mathrm{2}}=\mathrm{0.0004}-\mathrm{0.35},P\mathit{<}\mathrm{0.001}$ for TROPOMI) and for all PFTs combined ($r^{\mathrm{2}}=\mathrm{0.25},P\mathit{<}\mathrm{0.001}$) (Fig. 6). Similarly, the relative difference in EOT-derived V_cmax and ground measurements is also significantly correlated with leaf nitrogen content ($r^{\mathrm{2}}=\mathrm{0.21},P\mathit{<}\mathrm{0.001}$, Fig. 7), in agreement with the finding of Smith et al. (2019). These positive relationships suggest that LCC as a proxy of the photosynthetic nitrogen content in leaves can explain part of the spatial variability in V_cmax due to the variations in environmental conditions that are not captured by the optimality theory. The added information from LCC due to plants' optimal allocation of nutrient resources would be useful to improve optimality-based modeling of V_cmax.

The global distribution patterns of growing season V_cmax shown by the four products (Fig. 1) have common latitudinal gradients, i.e., V_cmax is generally largest near the Equator and decreases away from the Equator. This latitudinal dependence is simulated in EOT through considering radiation, i.e., stronger radiation leading to larger V_cmax. This influence of radiation on V_cmax is well captured by the three remote sensing products. According to analyses of the leaf economics spectrum (Wright et al., 2004; Sack et al., 2013; Osnas et al., 2013; Reich, 2014), leaf photosynthetic capacity increases with mean annual rainfall, and therefore V_cmax in dry areas is expected to be smaller than that in wet areas. However, several semi-arid regions, such as India, the Middle East, Southeast Brazil, and areas near the southern border of the Sahara desert, have large V_cmax values. We found that these are mostly irrigated agricultural areas (Fig. 4), and the high V_cmax values there are due to crop management and are not in contradiction to existing leaf economics spectrum data. The V_cmax distribution pattern in Australia is compatible with the rainfall distribution, i.e., the lowest V_cmax is found in central Australia where rainfall is lowest and the highest V_cmax is located in northern Australia where rainfall is largest. The EOT product can also capture this pattern to some extent through meteorological variables (e.g., radiation and temperature). There are many spatial details in these V_cmax products that are of great interest to leaf economic studies.

Table 2 Mean and standard deviation (SD) of V_cmax at the growing temperature ($V_{\mathrm{cmax}{T}_{\mathrm{g}}}$) and normalized to 25 ^∘C (V_cmax25) for different plant functional types (PFTs) calculated from the TROPOMI and ecological optimality theory (EOT) products in comparison with two ground-based databases (Smith et al., 2019; Kattge et al., 2009).

Figure 8 Distribution of ground sites of the database of Smith et al. (2019) after aggregation to 0.5 grids for the different plant functional types.

3.3 Global mean values of V_cmax for different biomes

We compared the mean V_cmax values of the TROPOMI SIF+LCC product, denoted by $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$, representing the three remote sensing products, and the EOT product over the growing season grouped by PFT with ground-based datasets at the mean growth temperature and at 25 ^∘C after temperature normalization using the same scheme of Smith et al. (2019) (Table 2). The agreement between TROPOMI and EOT is best for EBF, DBF, SHR, and GRS, for which the difference between the two products is smaller than their mean standard deviation. For ENF, DNF, and CRP, the difference between the two products exceeded their mean standard deviation. TROPOMI $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ is also considerably smaller than the ground datasets because of the large contributions of high-latitude conifer forests with low $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ that are underrepresented in the ground datasets (Fig. 8). Since the TROPOMI $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ product compares well with the ground database (Fig. 1 and Table 1) and has complete coverage for each PFT, it provides more reliable global averages than the ground database shown in Table 2. Ground data for DNF are too few (Fig. 8) to make sound evaluation for this PFT. TROPOMI $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ is considerably larger than EOT $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ for CRP, and GRS to a less extent, mostly because of the positive impact of irrigation on $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ as demonstrated in Fig. 4. Although the same temperature function is used in the normalization for all products, the relative changes from $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ to V_cmax25 for the various PFTs differed slightly among the four global products (Table 2) as the differences in $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ among the products vary spatially with different growth temperatures, creating different weights in the calculation of the global averages of V_cmax25.

Figure 9 Mean and standard deviation of $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ at growth temperature and V_cmax25 (normalized to 25 ^∘C) derived from GOME-2 SIF, TROPOMI SIF+LCC, LCC, and ecological optimality theory (EOT) in comparison with two ground databases (Smith, 2019; Kattge, 2009) for the main PFTs at growth temperature. Kattge (2009) contains more V_cmax25 than $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$, so only V_cmax25 is included in (a). The EOT product has considerably smaller $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ in grassland (GRS) and crops (CRP) than the three remote sensing products. All four products have considerably higher $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ than the ground site measurements in grassland mostly because the number of site measurements are too small to be representative of the global average. After the temperature normalization, the differences among the products become much smaller.

In addition to the TROPOMI V_cmax product, the other two remote sensing products are also compared in Fig. 9. The magnitude of V_cmax25 in the TROPOMI product is generally in between those from GOME-2 SIF and LCC for the various PFTs (Fig. 9a) because it uses information of LCC which tends to be converted to lower values of V_cmax using existing empirical relationships. For forest PFTs, both V_cmax25 and $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ of the EOT product is generally larger than those of remote sensing products. This is likely due to the fact that EOT considers only meteorological variables while soil nutrients and other variables could impose limitations on plant growth and hence leaf traits, while remote sensing techniques could be responsive to these soil effects on plants. For the same reason, V_cmax25 and $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ values of the EOT product for CRP are smaller than those of remote sensing products because crop irrigation and soil pH could have positive effects on leaf V_cmax that are captured by the remote sensing products but not by EOT (Figs. 3 and 4). The mean values of V_cmax25 and $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ from the ground databases (Smith et al., 2019; Kattge et al., 2009) are given in Fig. 9 for comparison purposes, but they do not represent the true global averages for the various PFTs because of their limited spatial distributions (Fig. 8 for Smith et al., 2019). We therefore do not yet have true ground averages to determine which product provides the most reliable global averages for the various PFTs. However, based on the point-to-point comparisons (Fig. 1 and Table 1), we believe that the TROPOMI product is most reliable in providing the global averages of V_cmax25 and $V_{\mathrm{cmax}{T}_{\mathrm{g}}}$ for the various PFTs.

4 Discussion

The V_cmax datasets derived from SIF and LCC represent the in situ leaf-level V_cmax that is the collective outcome of meteorological conditions and other environmental properties. These datasets can therefore be used directly in TEMs without further adjustment. The TRY database (Kattge et al., 2009) contains both V_cmax normalized to 25 ^∘C (V_cmax25) and total LNC, and they are well correlated. Empirical studies have also shown this correlation (Ryan, 1995; Medlyn et al., 1999; Walker et al., 2017; Prentice et al., 2014). LNC has therefore been used to adjust V_cmax25 within the same PFT in some TEMs. However, such an adjustment can only recover part of the spatio-temporal variability in V_cmax25 because only a small part of LNC is closely linked to carboxylation capacity. LNC can be separated into four components: photosynthetic, structural, storage, and respiratory nitrogen pools (Xu et al., 2012; Ali et al., 2016). The photosynthetic nitrogen pool can be further divided into sub-pools for light harvesting, electronic transport, and carboxylation, and its fraction to the total LNC is variable depending on meteorological and soil conditions and possibly also atmospheric CO₂ concentration (Ali et al., 2016). For fully grown leaves in balance with environmental conditions, these sub-pools are naturally optimized so that the investment of resources in light-harvesting optimally satisfies the need for electron transport or carboxylation (Xu et al., 2012). In other words, photosynthetic sub-pools are highly correlated, giving rise to the experimental evidence that LCC containing the light-harvesting nitrogen is highly correlated to V_cmax and J_max (Croft et al., 2017). The daunting and complex task of mapping the spatio-temporal distributions of leaf photosynthetic capacity could therefore be accomplished by mapping LCC that contains nitrogen in balance with carboxylation nitrogen in Rubisco, and multispectral or hyperspectral remote sensing data that are highly sensitive to light absorption by the chlorophyll pigments would be a reliable way to obtain such highly desirable information. The LCC product shown in this study could therefore be used in conjunction with V_cmax products derived from SIF and optimality theory to parameterize V_cmax models with consideration of the nitrogen cycle.

Our remote sensing algorithms derive V_cmax from SIF and LCC from multi-spectral data from sunlit leaves after considering the sun-target-view geometry (He et al., 2019; Croft et al., 2020), and hence the remote sensing V_cmax products represent sunlit leaves observed by the sensors. The observed sunlit leaves are mostly located near the top of the canopy, and hence these V_cmax products could be considered to represent the average condition of leaves near the top of the canopy. In applying a V_cmax value to a canopy, it would be necessary to consider the vertical variation of V_cmax in the canopy. A mathematical scheme to integrate the vertical variation for average sunlit and shaded leaves at different LAI values and solar zenith angles is available from Chen et al. (2012).

The growing season mean V_cmax products are available at https://doi.org/10.5281/zenodo.6466968, but seasonal variation of V_cmax is not yet ready for distribution. Reliable seasonal variation of V_cmax is not yet produced at the global scale due to several reasons: (1) SIF data are often not reliable over non-growing seasons and near the beginning and end of the growing season; (2) LCC derivation is considerably affected by the inaccuracy in the input LAI data outside of the growing season, and near the beginning and end of the growing season the separation of LCC and LAI signals in remote sensing data is still an issue; (3) the ecological optimality theory that provides the basis for evaluating remote sensing V_cmax products can so far be used for calculating growing season mean V_cmax and is not yet ready for calculating its seasonal variation; and (4) few ground-based data with seasonal variation of V_cmax are available for validation. While efforts are being made to overcome these issues, it will take a while to accumulate sufficient ground-based datasets and to improve remote sensing algorithms and the optimality theory before reliable seasonal variation of V_cmax can be derived at the global scale.

5 Code and data availability

The V_cmax datasets presented in this paper are available at https://doi.org/10.5281/zenodo.6466968 (Chen et al., 2022). It includes the following three global 0.5 ^∘ V_cmax datasets at growth temperature:

1. V_cmax from GOME-2 SIF: GOME2_V_cmax_Tg_05deg.tif

2. V_cmax from TROPOMI SIF+LCC: TROPOMI_Vmax_ Tg_ mean.mat

3. V_cmax from global leaf chlorophyll content map (Croft et al., 2020, RSE): LCC_V_cmax_Tg_mean.mat.

The geographic reference is the same for all three datasets, conforming to that in the geotiff file.

For any questions on the dataset, please contact Jing M. Chen, jing.chen@utoronto.ca.

The functions written in R for calculating V_cmax using the ecological optimality theory are available at https://github.com/SmithEcophysLab/optimal_vcmax_R (Smith et al., 2019) and https://doi.org/10.5281/zenodo.5899564 (Smith et al., 2022).

6 Conclusions

The two RSV_cmax products used in this research were derived independently from separate satellite observations of SIF and LCC, and yet show close agreement in their magnitudes and spatial patterns of modeled V_cmax. These remotely sensed V_cmax products (https://doi.org/10.5281/zenodo.6466968) also closely agree in large-scale spatial patterns with those calculated from the ecological optimality theory using meteorological variables, providing support for the use of the theory for prognostic modeling of terrestrial ecosystem function under future climate scenarios. However, the optimality-based V_cmax product does not show the local-scale spatial distribution patterns that are consistently found in all three remote sensing products because of patchy land cover distributions, implying that meteorological variables alone do not capture all spatial variability. Importantly, the relative difference in V_cmax (ΔV_cmax) between SIF and optimality-based products is found to be significantly correlated to the fraction of irrigation area in a pixel, soil pH, and leaf nitrogen content, highlighting the impacts of environmental conditions on V_cmax that are not captured within optimality theory. From these results, we conclude: (1) the remote sensing products shown in this study have reliably captured the spatial variability in V_cmax and therefore are directly useful for diagnostic ecological modeling at the global scale; and (2) in comparison to the optimality-based product, the remote sensing products provide additional information on how V_cmax varies according to local environmental conditions, which is useful for prognostic modeling purposes. Furthermore, understanding the dynamic in situ response of plant photosynthetic capacity to soil water and nutrient availability, independent of meteorological drivers, is important to monitoring plant photosynthetic potential. The LCC product shown in this study could be used in conjunction with V_cmax products derived from SIF and optimality theory to parameterize V_cmax models with consideration of the nitrogen cycle. This work demonstrates the power of global-scale satellite-based and ecological optimality approaches to reveal crucial spatial information on V_cmax, thereby removing a barrier in global ecological and Earth system research.