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# Decoupling of greenness and gross primary productivity as aridity decreases

Zhongmin Hu, Shilong Piao, Alan Knapp, Xuhui Wang, Shushi Peng, Wenping Yuan, Steve Running, Jiafu Mao, Xiaoying Shi, Philippe Ciais, et al.

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## To cite this version:

Zhongmin Hu, Shilong Piao, Alan Knapp, Xuhui Wang, Shushi Peng, et al., Decoupling of greenness and gross primary productivity as aridity decreases. Remote Sensing of Environment, 2022, 279, pp.113120. 10.1016/j.rse.2022.113120. hal-04624457

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Decoupling of greenness and gross primary productivity as
aridity decreases

Zhongmin Hu¹, ², ³*, Shilong Piao⁴, Alan K. Knapp⁵, Xuhui Wang⁴, Shushi Peng⁴,

Wenping Yuan⁶, ³, Steve Running⁷, Jiafu Mao⁸, Xiaoying Shi⁸, Philippe Ciais⁹,

Deborah N. Huntzinger¹⁰, Jia Yang¹¹, Guirui Yu¹²

¹ School of Geography, South China Normal University, Shipai Campus, Guangzhou 510631,
China;

² Key Laboratory of Agro-Forestry Environmental Processes and Ecological Regulation of
Hainan Province (Hainan University), Haikou, 570228, China;

³Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Guangdong 519082,
China.

⁴Department of Ecology, College of Urban and Environmental Science, and Key Laboratory
for Earth Surface Processes of the Ministry of Education, Peking University, Beijing
100871, China;

⁵Department of Biology and Graduate Degree Program in Ecology, Colorado State University,
Fort Collins, CO 80523, USA;

⁶School of Atmospheric Sciences, Sun Yat-Sen University, Guangzhou 519082, China

⁷NTSG, College of Forestry and Conservation, University of Montana, Missoula, MT 59812,
21 United States

22 Climate Change Science Institute and Environmental Sciences Division, Oak Ridge National

23 Laboratory, Oak Ridge, Tennessee 37831, USA;

24 Laboratoire des Sciences du Climat et de l'Environnement, Gif-sur-Yvette, France;

25 School of Earth Sciences and Environmental Sustainability, Northern Arizona University,

26 Flagstaff, Arizona 86011, USA;

27 Department of Natural Resource Ecology and Management, Oklahoma State University,

28 Stillwater, OK 74078, USA;

29 Synthesis Research Center of Chinese Ecosystem Research Network, Key

30 Laboratory of Ecosystem Network Observation and Modeling, Institute of Geographic

31 Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing

32 100101, China

33

34 *Correspondence:

35 Zhongmin Hu, Email: huzm@igsnrr.ac.cn

36

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38

39
40 Abstract

41 Ecosystem primary productivity is a key ecological process influencing many
42 ecosystem services, including carbon storage. Thus, clarifying how primary
43 productivity in terrestrial ecosystems responds to climatic variability can reveal key
44 mechanisms that will drive future changes in the global carbon budget. Satellite
45 products of canopy greenness are widely used as proxies for vegetation productivity to
46 evaluate how ecosystems respond to climate variability. However, to what degree inter-
47 annual variations in productivity are consistent with greenness and how this
48 relationship varies spatially remains unclear. Here we investigated the strength of the
49 coupling between inter-annual variations in leaf area index (LAI, a measure of
50 greenness) and ecosystem gross primary productivity (GPP) derived from eddy
51 covariance towers, i.e., the r² of the LAI-GPP relationship. Overall, inter-annual GPP
52 and LAI were highly coupled (i.e., high r²) in arid grasslands, but were fully decoupled
53 in mesic evergreen broadleaf forests, indicating that this relationship varies strongly
54 along aridity gradients. A possible mechanism of the spatial variation in the LAI-GPP
55 relationship is that the tradeoff between ecosystem structure (LAI) and physiology
56 (photosynthesis per unit leaf area) becomes stronger in more humid climates. Land
57 models overestimated the r² of LAI-GPP correlation for most ecosystem types and
58 failed to capture the spatial pattern along aridity gradients. We conclude that relying on
59 greenness products for evaluating inter-annual changes in vegetation productivity may
60 bias assessments, especially in tropical rainforest ecosystems. Our findings may also
61 reconcile observed disparities between responses in greenness and GPP during drought
62 in Amazon forests.

63 Key worlds: gross primary productivity, greenness, leaf area index, inter-annual variability, land models, light-use efficiency

65

66 **Introduction**

67 Primary productivity is the principal path carbon dioxide is ‘fixed’ into organic material
68 in terrestrial ecosystems (Le Quéré et al., 2014) and terrestrial gross primary
69 productivity (GPP) is the dominant process driving inter-annual variability in net land
70 carbon flux globally, which in return determines the temporal variability of CO2 growth
71 rate in the atmosphere (Piao et al., 2020b). Therefore, identifying how GPP in terrestrial
72 ecosystems responds to climatic variability is critical for identifying the mechanisms
73 underlying variability is atmosphere CO2 concentrations and the global carbon budget
74 (Piao et al., 2013; Schimel et al., 2015).

75

76 Clarifying the temporal dynamics of GPP at regional and global scales is challenging,
77 because the most reliable in-situ measurements, e.g., the eddy covariance towers, tend
78 to be established in sites that are not representative of the global distribution of
79 ecosystem types (Baldocchi et al., 2018). Remote sensing approaches to estimating GPP,
80 however, can provide insights into ecosystem dynamics in response to climatic
81 variation at both regional and global scales. Vegetation greenness, usually represented
82 by the leaf area index (LAI) or vegetation index, is a canopy structural property directly
linked to harvesting solar radiation for photosynthesis. Early studies reported strong relationships between vegetation greenness and photosynthetic activity (Tucker and Sellers, 1986), and today satellite products of vegetation greenness are widely used to evaluate the temporal dynamics of GPP at large spatial scales (Beck and Goetz, 2011; Schwalm et al., 2012; Forkel et al., 2016). For example, vegetation greenness is considered a key approach to detect the impacts of extreme climate events e.g., droughts and heat waves on ecosystem productivity (Hilker et al., 2014; Yuan et al., 2016). Further, some research has suggested that GPP can be estimated directly from vegetation greenness with no other data required (e.g., Sims et al., 2006; Shi et al., 2017).

It is noteworthy then that vegetation greenness has also been reported to be weakly correlated with GPP in some ecosystems (Shi et al., 2017; Walther et al., 2019). In Amazonian rainforests, for example, it was found that greenness decreased but vegetation productivity remained constant in the 2010 drought year (Xu et al., 2011; Doughty et al., 2015), and that little change in greenness was measured in contrast to substantial decreases in canopy photosynthesis in the 2015-2016 drought period (Yang et al., 2018). The causes of such variable relationships between greenness and productivity is still debated, but satellite data artifacts are often invoked (Samanta et al., 2010; Asner et al., 2011). An alternative explanation is that the coupling of greenness and vegetation productivity might be weaker than previously expected. For example, tradeoffs between leaf quantity, LAI and leaf quality, leaf photosynthesis capacity, may
result in this decoupling in wet tropical forests (Wu et al., 2016). If the dependency of
GPP on greenness is overestimated, assessments of vegetation productivity in response
to climatic variability would be biased.

108

To clarify the extent to which greenness controls on the inter-annual variability of GPP
across global ecosystems, we addressed two questions: (1) how does the interannual
GPP-greenness coupling vary across ecosystem types and along climate gradients? And
(2) what is the mechanism underlying spatial variability? We investigated the
robustness of the inter-annual LAI-GPP relationship for the period 1982 to 2011 at a
global scale by using satellite LAI products (GIMMS3g and MODIS) (Zhu et al., 2013),
GPP estimated from eddy covariance (EC) at flux tower sites (referred to as Fluxnet),
and EC-based GPP datasets available at a global extent (referred as MTE; Jung et al.,
2011). In addition, we investigated the performance of seven state-of-the-art land
models in capturing the LAI-GPP relationship in different biomes. Finally, we focused
on the long-debated Amazon drought responses and specifically investigated the
relationship between GPP and LAI in the 2010 severe drought year. Our rationale for
using LAI as a metric of greenness is that this variable has explicit ecological meaning,
and it is also simulated by models, facilitating comparison with the performance of land
models (Zhu et al., 2016).

124

Data and methods

125

MTE GPP dataset
We chose a 30-year eddy covariance flux-based GPP product as a largely independent observation-based GPP dataset, which has been widely used as a global scale benchmark GPP (Jung et al., 2011). This dataset was derived from a model calibrated using global flux site-level data by means of a model tree ensemble machine learning technique (MTE). Explanatory variables used in training include the remotely sensed fraction of absorbed photosynthetically active radiation, climatic fields, land cover data, and indicator variables for the photosynthetic pathway. This dataset was generated at a monthly time step in 2008-2011 with a spatial resolution of 0.5°. Note that we did not use the newer version of the MTE dataset, i.e., the FLUXCOM dataset (Jung et al., 2020), because we found the newer version largely underestimated the inter-annual variations in GPP (see also in O'Sullivan et al., 2020). Therefore, we adopted the original MTE dataset for analysis in this study.

138

139 *Fluxnet2015 dataset*

The eddy covariance technique is a key approach to estimating GPP by measuring ecosystem-atmosphere exchange of CO₂ (Baldocchi et al., 2001). We used GPP data from 213 flux tower sites available in the Fluxnet2015 Database (Tier 1), the latest collection of global eddy flux observations (www.fluxdata.org). The database was a combination of measurements from regional networks, with a time period of 1993-2014. Daily GPP was used to calculate monthly and then annual GPP in this study. If the number of days with missing data was < 10 in a month, the missing daily GPP
was calculated from the mean of all other days in that month. We excluded months and years when missing data exceeded this threshold. In addition, if the total days with missing data > 60 in a year, that year was excluded. To investigate inter-annual relationships between LAI and GPP at the flux sites, we only selected the sites with ≥4 year's of continuous measurements of GPP. In addition, we also excluded the sites with no satellite LAI data available due to cloud contamination or some other issues during the same period of flux measurements. Overall, meeting these criteria allowed us to analyze data from 102 sites (881 site-years), including 31 evergreen needleleaf forests (ENF), 15 deciduous broadleaf forests (DFB), 13 grasslands, 10 croplands, 8 evergreen broadleaf forests (EBF), 8 savannas, 7 mixed forests (MF), 7 shrublands, and 3 wetlands.

MsTMIP model data

Modelled GPP and LAI were from MsTMIP—the Multi-scale synthesis and Terrestrial Model Intercomparison Project (http://dx.doi.org/10.3334/ORNLDAAC/1225). MsTMIP uses a standardized simulation protocol, with uniform historical forcing data, boundary conditions, and spin-up across all models for facilitating inter-model comparisons. Models of MsTMIP run globally (0.5° spatial resolution) with outputs at monthly steps from 1901 to 2010 (Huntzinger et al., 2013). All models were run diagnostically, i.e., the LAI used to quantify modeled GPP-LAI relationships was simulated by the models, rather than prescribed
168 with satellite products. In our study, the model outputs that include all time-varying
169 factors except nitrogen deposition (simulation SG3) were used. We compared the
170 model outputs with (BG1) and without (SG3) nitrogen deposition, finding similar
171 spatial LAI-GPP relationships with the two treatments. For the sake of consistency
172 (some models do not have the BG1 outputs), we used SG3 outputs for all models. We
173 first excluded models in which LAI or GPP were not included in the outputs. Second,
174 we excluded models in which the simulated global average LAI-GPP relationship was
175 negative (we assumed this result was incorrect). Finally, the outputs from seven
176 models (Biome-BGC, CLASS, CLM, LPJ, ORCHIDEE, SibCASA, VEGAS) were
177 used for analysis. Ensemble averages of GPP and LAI in 1982-2010 as simulated by
178 the selected seven models were used to compare with the data-driven datasets.

179

180 Satellite LAI products

181 The Global Inventory Modeling and Mapping Studies (GIMMS) LAI was generated by
182 an Artificial Neural Network model (available at http://sites.bu.edu/cliveg). The
183 GIMMS LAI3g dataset provides LAI observations at 15-day temporal resolution and
184 1/12 degree spatial resolution for global vegetation from July 1981 to December 2011
185 (Zhu et al., 2013). We calculated annual LAI with the 15-day GIMMS LAI3g data by
186 averaging the composites in the same year, and then resampled the data to 0.5° spatial
187 resolution. This dataset was used to analyze the GPP-LAI relationship at a global scale.
188 MODIS LAI data are satellite products starting in 2001 acquired from the website of
189 ORNL DAAC (8-day, 1 km, http://daac.ornl.gov) (Yan et al., 2016). Using geographic
190 location, we extracted continuous time series LAI (1-km resolution) for each Fluxnet
191 site to construct temporal LAI-GPP relationship for the Fluxnet sites. The MODIS LAI
192 contain some cloud-contaminated or missing data. Therefore, before using the data
193 these products were processed using the software package TIMESAT3.0 (an
194 asymmetric Gaussian method) to exclude noise and fill gaps (Jonsson and Eklundh,
195 2004) and then the annual mean was calculated. This dataset was also resampled at 0.5
196 degrees to analyze the GPP-LAI relationship at a global scale.

197

198 Land cover data

199 The MODIS land cover product was used to estimate the r² of LAI-GPP relationship
200 for different ecosystem types (Friedl et al., 2010). The advantage of this product is that
201 is provides a suite of land cover types by exploiting the information content of MODIS
202 data in the spectral, temporal, spatial, and directional domains. This data set (0.5°
203 spatial resolution) was generated using a full year of MODIS data from October 2000
204 to October 2001. This product described the geographic distribution of the 17 land
205 cover classification scheme proposed by the International Geosphere-Biosphere
206 Programme (IGBP). The percentage of the dominant land cover was provided for each
207 pixel in the dataset. Note that the information of land cover was provided for the flux
208 tower sites in the FLUXNET2015 dataset. Therefore, the MODIS land cover product
209 was not used to determine the ecosystem types of the flux sites.
210 Aridity index data

211 Because aridity is a result of two of the primary climatic drivers of global patterns of
212 productivity, temperature and precipitation, we used an aridity index with a spatial
213 resolution of 10 arc minutes and resampled to a resolution of 0.5° (data is available at
214 https://data.apps.fao.org). The aridity index we used represents the average yearly
215 precipitation divided by average yearly potential evapotranspiration, as defined by the
216 United Nations Environmental Programme (UNEP).

217 SIF product

218 Satellite-retrieved solar-induced chlorophyll fluorescence (SIF) has shown great
219 potential for monitoring the GPP of terrestrial ecosystems (Mageney et al., 2019). In
220 this study, SIF products were used in the Amazon rainforests to clarify whether SIF and
221 LAI responded differently to the severe drought in 2010. Global spatially contiguous
222 SIF (CSIF, 0.05° 4-day, 2000-2018) data were derived by Zhang et al. (2018) by
223 training a neural network (NN) with surface reflectance from the MODIS and SIF
224 provided by the Orbiting Carbon Observatory-2 (OCO-2). Annual CSIF was calculated
225 as the mean of 4-day data within each year. CSIF was resampled to 0.5 degrees as with
226 other datasets.

227

228 Data analysis

229 Linear regression analyses between LAI and GPP was used to quantify the dependency
230 of GPP on LAI at an annual time scale. For example, we fitted the LAI-GPP relationship
with 30-years (1982-2011) of annual GPP and mean annual LAI for each pixel. The coefficient of determination ($r^2$) of the linear regression was used as the metric quantifying the coupling between GPP and LAI. The ratio of GPP to LAI, $GPP_{leaf}$, was then calculated as a canopy-level physiological property, i.e., canopy mean leaf photosynthesis capacity. To minimize autocorrelation, instead of calculating $GPP_{leaf}$ directly with annual GPP and LAI, we first calculated monthly $GPP_{leaf}$ (i.e., ratio of monthly GPP to monthly LAI), and then averaged the monthly $GPP_{leaf}$ as annual $GPP_{leaf}$.
Since MODIS LAI begins in 2001, GPP measured before this year at a few Fluxnet sites was not used to derive the LAI-GPP relationship.

Uncertainty may exist in the MTE dataset, especially the inter-annual variability (IAV) in GPP, due to shortcomings in the process of spatial and temporal scaling-up (Piao et al., 2013; Kauwe et al., 2017). To verify the reliability of the MTE dataset for estimating temporal variability in GPP, we compared the IAV of GPP at the Fluxnet sites and that in the pixels containing the flux sites in the MTE datasets. If < 80% of vegetation type in the 0.5° pixel was consistent with the vegetation type of the flux site (vegetation types of the flux sites were provided in the FLUXNET2015 dataset), the flux data was excluded for the comparison. Considering the fact that very few flux sites have GPP measurements before 2001 and the periods of measurement are inconsistent among sites, we made the comparison by bulk-averaging the Fluxnet GPP at the flux sites and the MTE GPP in corresponding pixels in 2001-2011. The result shows that the two datasets illustrated consistent patterns of inter-annual variability despite the difference in magnitude (Fig. S5).
253 **Results**

254 *Variations in the strength of LAI-GPP relationships across biomes and aridity gradient*

255 Both the MTE and Fluxnet data indicated that the mean *r*² of the inter-annual LAI-GPP relationship was quite low (< 0.4) in most ecosystem types, suggesting a weak dependency of GPP on LAI (Fig. 1a). The overall average temporal *r*² for all the ecosystem types was 0.30 for the MTE grid data and 0.21 for the Fluxnet site data, which was obviously smaller than *r*² of the spatial LAI-GPP relationship (0.81 for MTE data, and 0.61 for Fluxnet data, respectively, Fig. S1). Calculated *r*² values also illustrated different relationships among the ecosystem types. For example, ecosystems in water-limited environments, e.g., grassland, savanna, and shrub showed stronger dependency of GPP on LAI (i.e., larger *r*²) than more mesic forest ecosystems (Fig. 1a).
260
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264 In contrast, forest ecosystems, especially evergreen broadleaf forests (EBF), had non-significant LAI-GPP relationships (*p* > 0.05 at >80% pixels), suggesting a weak LAI dependency.
266
267

268 Land models predicted stronger LAI-GPP coupling (with a global average *r*² of 0.54) than the MTE (0.30) and Fluxnet (0.21) datasets (*p* < 0.05, Fig. 1a). This suggests that the land models overestimate the dependency of GPP on LAI at an annual time scale.
269
270
271 By calculating yearly global mean GPP and LAI, we found the same result: the models yielded a mean value as large as 0.89 (with the range 0.70-0.96) for the inter-annual GPP-LAI relationship in 1982-2011, compared to a value of 0.42 estimated by MTE
272
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274 (Fig. 1b). Moreover, the model-derived r² was less variable among biomes (0.46-0.59, 275 std=0.04) than from the MTE analysis (0.1-0.55, std=0.12). This suggests that the 276 models did not capture the inter-biome differences in the temporal dependency of GPP 277 on LAI. 278

279 For the sensitivity of GPP to LAI, i.e., the slope of the LAI-GPP relationship, both the 280 MTE and Fluxnet datasets show that sensitivity was lower in forests than all other 281 ecosystems (Fig. S2). In comparison, the land models predicted 2-10 fold higher LAI 282 sensitivity than that predicted by the MTE data on a global average basis (Fig. 1b), 283 suggesting that land models overestimate the overall degree of dependency, as well as 284 the sensitivity of GPP on LAI. 285

286 In order to investigate further these model-data differences, we analyzed the frequency 287 distribution of the r² for all pixels. We found both MTE and Fluxnet data had the largest 288 number of pixels with the lowest r² (ca. 0.02) and declined exponentially with r² (Fig. 289 1c). In comparison, most models predicted larger number of pixels with high r² (> 0.5), 290 with the average model predictions illustrating a gaussian-like distribution of r² at a 291 mean of 0.52 (Fig. 1c). This means that most models overestimated the number of pixels 292 with high LAI dependency but underestimate the number of pixels with low LAI 293 dependency. 294
<figure><img src="image_4.png" /></figure>

<figure><img src="image_5.png" /></figure>

<figure><img src="image_6.png" /></figure>

294

295 Figure 1. Comparison of the strength of the inter-annual LAI-GPP coupling between

296 observations (Fluxnet), data-driven method (MTE), and model simulations. a, Mean $r^2$
of the temporal LAI-GPP relationship for different plant functional types identified by three data sources, i.e., MTE dataset, Fluxnet observations, and models (ModelAvg indicates the bulk mean of seven member models). ENF: evergreen needleleaf forest, EBF: evergreen broadleaf forest, DNF: deciduous needleleaf forest, DBF: deciduous broadleaf forest, MF: mixed forest. b, r² of global average LAI-GPP temporal relationship (1982-2010) predicted by MTE and different models. c, frequency distributions of the r² predicted by MTE and models for all pixels in global terrestrial ecosystem. The inset panel indicates the frequency distributions of r² for the fluxnet sites and the pixels containing the flux sites derived from the three data sources.

To clarify the spatial distribution of LAI dependency across the globe, we investigated the global distribution of r² of the LAI-GPP relationship. The r² derived from MTE were large in arid and semi-arid regions, e.g., the Great Plains in North American, Eurasian temperate steppe area, Australia, and northern African (Fig. 2a, Fig. S3). On the contrary, low values of r² were generally found in humid regions, e.g., tropical rainforest areas, southeast Asia and eastern North American, and the boreal regions. With another indicator of vegetation greenness, NDVI (normalized difference vegetation index), we found a similar global spatial pattern of r² of NDVI-GPP relationships (Fig. S4). Both the MTE and flux tower data indicated that, with the exception of when AI < 0.25, the r² and slope of the temporal LAI-GPP relation increased with aridity (Fig. 2c). This result indicates that both the dependency and sensitivity of GPP on LAI increased with climatic aridity. In comparison, the land models predicted a contrasting global
pattern of the $r^2$ of the LAI-GPP relationship, with higher values in humid regions, e.g.,
tropical rainforet areas and the high latitude boreal forests (Fig. 2b). Specifically,
modelled $r^2$ increased, but sensitivity remained relatively constant with humidity,
contrary to spatial pattern derived from observations (Fig. 2d).

323

<figure><img src="image_7.png" /></figure>

324

<caption>Figure 2. Global distributions of $r^2$ of the temporal LAI-GPP relationship derived from observation-based datasets (a) and land models (b), and the spatial pattern of $r^2$ along an aridity gradient (group average of 0.05 interval) derived from Fluxnet data and MTE</caption>

325

326

327
datasets (c) and models (d). The stars with PFTs indicate values derived from
measurements at Fluxnet sites. Shaded areas indicate one standard deviations within
each 0.05 interval of aridity index.

331

Three tests were conducted to verify the reliability of the spatial pattern of r² of the temporal LAI-GPP relationship. First, considering uncertainty in MTE dataset, especially in terms of the inter-annual variability (IAV) (Piao et al., 2013; Anav et al., 2015; Kauwe et al., 2017), we compared the IAV of GPP derived from the MTE and in-situ flux tower measurements. The result indicated a consistent IAV of GPP between the two products, suggesting that the MTE product reproduced the IAV of GPP with high reliability (Fig. S5). Second, the mismatch in temporal periods between MTE data, GIMMS LAI, and flux tower measurements may also introduce uncertainty. Therefore, in addition to GIMMS LAI, MODIS LAI was used to analyze the global pattern of the r² of GPP-LAI relationship. Using the overlapping period (2001-2011), the two datasets showed consistent global distributions of the r², with high values distributed in arid regions and low values in tropical areas (Fig. S6), Finally, with the site-level Fluxnet tower GPP dataset and MODIS LAI, we also found the r² of GPP-LAI relationships increased with climate aridity, consistent with the results shown in Fig. 2c (Fig. S7). Therefore, all the above tests support the finding that the coupling of the temporal LAI-GPP relationship increases with aridity.

348
349 *Mechanism of the spatial variations in the strength of LAI-GPP relationship*

350 Two hypothesis may explain the increase of the inter-annual LAI-GPP correlation along
351 aridity gradient. First, in tropical evergreen broadleaf forests, the canopy is already very
dense and thus LAI remains relatively constant across years whereas GPP varies much
352 more due to changes in leaf physiology as a result of climatic fluctuations. The second
353 mechanism might be that a tradeoff exists between LAI (quantity of leaves) and average
354 leaf photosynthesis, GPP<sub>leaf</sub>, (quality of leaves). This tradeoff may become stronger in
355 more humid ecosystems, and cause weaker LAI-GPP coupling. Our further analysis
356 rejected the first hypothesis, showing that with the decrease of climate aridity, the IAV
357 of GPP decreased steadily but IAV of LAI kept relatively conservative, suggesting that
358 LAI was more variable than GPP in mesic forest ecosystems (Fig. 3).
359

<figure><img src="image_8.png" /></figure>

360

361 Figure 3 Inter-annual variability (coefficient of variance: the ratio of standard deviation
362 to mean) of GPP (a) and LAI (b) for different ecosystem types. Error bars indicate the
363 inter-site standard deviation within the biomes. The numbers above the error bars
364 indicate the r² of temporal LAI-GPP relationship for the ecosystem types.

365

366 For the second hypothesis, we identified high positive LAI- GPP<sub>leaf</sub> relationships in arid
367 regions but high negative LAI- GPP<sub>leaf</sub> relationships in humid regions (Fig. 4a). On
368 average, the Pearson correlation coefficient steadily decreased from 0.22 (p > 0.05) at
369 the AI of 0.25 to strong negative (r = -0.92, p < 0.05) in the mesic end (Fig. 4c).
370 Therefore, it is possible that consistent changes for both LAI and leaf photosynthesis
371 capacity occur in response to climate fluctuations in arid ecosystems but there is a
372 stronger tradeoff between the two components in mesic ecosystems. Canopy light-use
373 efficiency (LUE) is another indicator of leaf photosynthesis capacity, and to further
374 confirm this mechanism, we investigated the spatial distribution of the correlation
375 coefficient between LAI and LUE (the ratio of GPP to absorbed photosynthetically
376 active radiation, APAR, the latter of which was calculated as FPAR × PAR). We found
377 the spatial pattern of the LAI-LUE relationship was similar to that of the LAI-GPP<sub>leaf</sub>
378 relationship, with positive values in arid regions that steadily declined to negative at the
379 wet end of the climate gradient (Fig. 4b, c). This confirms that the degree of the tradeoff
380 increases with the decrease of aridity. In Amazonian rainforests, the wettest ecosystem
381 type, we found that the 2010 severe drought caused a large reduction in LAI but had
382 less impact on GPP and SIF owing to the increase in canopy LUE, especially in the
383 northern part of this region (Fig. 5). This suggests that the tradeoff in changes between
384 the structural factor (LAI) and physiological factor (LUE) caused GPP-LAI decoupling

385 in the drought year.

386

<figure><img src="image_9.png" /><figcaption>b</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>c</figcaption></figure>

<figure><img src="image_11.png" /></figure>

387

388 Fig. 4 Spatial distributions of the temporal correlation (r) between LAI and (a) GPP per unit area, GPP<sub>leaf</sub>, and (b) canopy light use efficiency, and the patterns of r along spatial

389
390 aridity gradient (c). Shaded areas indicate one standard deviations within each 0.05

391 interval of aridity index

392

393

<figure><img src="image_12.png" /></figure>

394 Fig. 5 Relative reduction (a) and distributions of LAI (b), canopy LUE (c), GPP (d), and solar-induced fluorescence (SIF) (e) in the 2010 drought year in comparison to 395 2009 in forests of the Amazon. Error bars indicate standard deviations of all the pixels
397 in Amazonian forest region. Positive values suggest reductions and negative values
398 suggest increases.

399

400 **Discussion**

401 Our results suggest that ecosystems in water-limited environments, e.g., grasslands,
402 savannas, and shrublands showed high inter-annual dependency of GPP on LAI (i.e.,
403 larger r²) (Fig. 1a). This is consistent with previous studies reporting both primary
404 productivity and vegetation index are highly variable across years in ecosystems in arid
405 environments (Ahlström et al., 2015; Kauwei et al., 2017; Hu et al., 2018). This implies
406 that changes in LAI is a key strategy for ecosystems in arid environments to cope with
407 climatic fluctuations. However, weaker LAI-GPP relationships were found in forest
408 ecosystems, especially the evergreen broadleaf forest. This finding implies that relying
409 only on greenness products to evaluate changes in ecosystem carbon uptake in response
410 to climatic variabilities may result in biased assessments, especially in mesic forest
411 ecosystems. In recent years, several studies have suggested that new satellite products,
412 e.g., solar-induced fluorescence (SIF) (Zhang et al., 2018) and near-infrared reflectance
413 of terrestrial vegetation (NIRv) (Badgley et al., 2017) may be able to capture canopy
414 physiological conditions (Mageney et al., 2019). Thus, these products have the potential
415 to track inter-annual variations in regional GPP. For example, our results on Amazon
416 tropic rainforest suggest more consistent responses of SIF than LAI with GPP to the
417 2010 drought year (Fig. 5). Thus, in addition to conventional greenness, we suggest that
these products should be used together to provide more robust assessments (e.g., Piao et al., 2020a).

420

Our results suggest that the tradeoff between leaf quantity (i.e., LAI) and quality (i.e., canopy LUE or GPP<sub>leaf</sub>) caused the weak GPP-LAI relationship in mesic forest ecosystems, e.g., the Amazonian tropic forest (Fig. 5). The cause of differences in greenness and plant growth in response to droughts in Amazon forests has been debated for years (e.g., Samanta et al., 2010; Saleska et al., 2016). Our results are consistent with studies reporting tradeoffs between LAI and canopy LUE, which determine changes in canopy carbon uptake in dry seasons and drought years, and thus lead to inconsistent responses in LAI and GPP (Wu et al., 2016; Yang et al., 2018). We speculate the spatial pattern of tradeoff between LAI and GPP<sub>leaf</sub> along climate gradients is linked to canopy physical structure. For ecosystems in arid and semi-arid environments, vegetation canopies are sparse with most plant leaves under light exposure, thus both the IAV of LAI and GPP<sub>leaf</sub> are controlled by water availability (Hu et al., 2008). In ecosystems in humid environments, e.g., tropical rainforests, the canopy is dense and growth of plants is limited by light availability. Decreases in LAI in drought years can permit solar radiation to be transmitted throughout the canopy, facilitating C uptake by lower canopy leaves, and enhancing overall canopy light use efficiency, i.e., GPP<sub>leaf</sub> (Tang and Dubayah, 2017; Walther et al., 2019). In addition, leaf development and demography may also contribute to the discrepancy between inter-annual variations in greenness and carbon uptake, especially in the tropical rainforests
440 (Wu et al., 2016). Therefore, our findings have the potential to reconcile the observed discrepancies between greenness and ecosystem photosynthesis during drought seasons and years in Amazon forests (Xu et al., 2011; Doughty et al., 2015).

443

444 We realize that uncertainties in the LAI products may affect the $r^2$ of GPP-LAI relationships (Liu et al., 2018). To minimize these uncertainties, we adopted the most recently version of the GIMMS product, LAI3g (Zhu et al., 2013). In addition, we also used the most recent version of MODIS LAI product (collection 6) as supplementary evidence. These two products yielded the same global spatial patterns of the $r^2$ values (Fig. S6), supporting the main results that the GPP-LAI coupling was stronger in more arid areas of the globe. We also note that the values of $r^2$ derived from MODIS LAI were overall higher than that from GIMMS LAI in the arid regions. This suggests that the MODIS LAI yielded higher GPP-LAI coupling than the GIMMS product in ecosystems in the arid regions. Considering the generally recognized higher quality of MODIS than GIMMS, the GPP-LAI coupling may be higher than shown in Fig. 2.

455

Comparing the three data sources, Fluxnet data showed overall lower GPP-LAI coupling than the MTE data (Fig. 1a). This may be because MTE uses satellite FPAR products in training (Jung et al., 2011), and may therefore have a higher correlation with LAI. In comparison, land models predict much stronger dependency of the IAV of GPP on LAI than both Fluxnet and MTE. This indicates that, possibly due to failing to
capture tradeoffs between LAI and GPP<sub>leaf</sub>, these models failed to reproduce the change in dependency of GPP on LAI across ecosystem types and along aridity gradients.

Clarifying the reasons for this remains a challenge. We suggest the modelling community focuses on some focal ecosystems with extensive observations as examples, e.g., temporal grasslands (high GPP-LAI coupling) and tropical rainforest (low GPP-LAI coupling), to further investigate model performance relating to how GPP, LAI, and leaf physiology in respond to climate anomalies. Possible modules in land models that may affect GPP-LAI relationships include leaf development and demography (e.g., Wu et al., 2016), radiation allocation within canopy (affect understory photosynthesis and hence canopy level light-use efficiency), carbon allocation between leaf and other organs (we would expect full GPP-LAI coupling if all carbon were allocated to leaves, and *vice versa*), etc. In addition to the degree of coupling, *r*<sup>2</sup>, the sensitivity (i.e., the slope) of the GPP-LAI relationship is also important to address. In this study, we focused primarily on the *r*<sup>2</sup>, and thus the results on sensitivity was not fully presented.

However, we suggest that further analysis might clarify spatiotemporal variations in the sensitivity of GPP-LAI relationships, and how land models can capture the variations.

477

478 Conclusions

Using 30 years of different and complimentary data streams, e.g., remote sensing datasets, outputs from seven land models, and global in-situ flux measurements, we found that the strength of the coupling between inter-annual variations in LAI and GPP,
482 increased with aridity, and that relationships were overall much weaker than model
483 simulations. Inter-annual GPP and LAI are highly coupled in arid grasslands, but are
484 apparently fully decoupled in mesic forests, e.g., Amazonian rainforests. Our study has
485 three implications. First, using only products of greenness for evaluating changes in
486 ecosystem carbon uptake in response to climatic variabilities may result in biased
487 assessments, especially in mesic forest ecosystems. Second, our findings have the
488 potential to reconcile the long-lasting debate on the observed disagreement between
489 greenness and productivity responses in Amazonian forests during drought years. In
490 addition, our findings highlight the need to re-investigate the coupling between canopy
491 structure properties and vegetation productivity in land models.

492

493 ACKNOWLEDGEMENTS

494 This study was jointly supported by National Natural Science Foundation of China
495 (Grant No. 31922053), National Key R&D Program of China (Grant No.
496 2017YFA0604801), the Second Tibetan Plateau Scientific Expedition and Research
497 Program (Grant NO. 2019QZKK0405), and the start-up fund of Hainan University
498 (Grant NO. KYQD(ZR)21096). Funding for the Multi-scale synthesis and Terrestrial
499 Model Intercomparison Project (MsTMIP; https://nacp.ornl.gov) activity was provided
500 through NASA ROSES Grant no. NNX10AG01A. Data management support for
501 preparing, documenting and distributing model driver and output data was performed
502 by the Modeling and Synthesis Thematic Data Center at Oak Ridge National
Laboratory (ORNL; http://nacp.ornl.gov), with funding through NASA ROSES Grant no. NNH10AN681. Finalized MsTMIP data products are archived at the ORNL DAAC (http://daac.ornl.gov). This work used eddy covariance data acquired and shared by the FLUXNET community, including these networks: AmeriFlux, AfriFlux, AsiaFlux, CarboAfrica, CarboEuropeIP, CarboItaly, CarboMont, ChinaFlux, Fluxnet-Canada, GreenGrass, ICOS, KoFlux, LBA, NECC, OzFlux-TERN, TCOS-Siberia, and USCCC.

The ERA-Interim reanalysis data are provided by ECMWF and processed by LSCE.

The FLUXNET eddy covariance data processing and harmonization was carried out by the European Fluxes Database Cluster, AmeriFlux Management Project, and Fluxdata project of FLUXNET, with the support of CDIAC and ICOS Ecosystem Thematic Center, and the OzFlux, ChinaFlux and AsiaFlux offices.

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