Emergent constraints on climate—carbon cycle feedbacks from tropical atmospheric aridity

1 The vulnerability of the terrestrial tropical carbon cycle to changes in climate, especially 2 temperature and moisture, remains one of the largest sources of uncertainty in future climate 3 projections. Harnessing new satellite-driven global carbon reanalysis, we show here that 4 tropical atmospheric aridity, which is directly related to the atmospheric vapor pressure deﬁcit 5 (VPD), is a causal driver of the interannual variability of the tropical net carbon balance and 6 consequently the CO 2 growth rate with observed present-day sensitivities of -3.2 ± 0.62 GtC 7 mb − 1 yr − 1 . Our results provide evidence that a large part of tropical net biome exchange 8 variability is indirectly driven by land-atmospheric coupling via VPD variations that can not 9 be explained by tropical temperatures alone. Furthermore, we ﬁnd that there is an emergent 10 relationship between the sensitivity of the tropical carbon balance to VPD and the long-term 11 response of tropical-land carbon storage to increase in VPD across an ensemble of Earth 12 System Models used in the Climate Model Intercomparison Project 6 (CMIP6). Employing 13 a hierarchical emergent constraint, the global carbon—climate feedback from aridity is -22 ± 14 11 GtC mb − 1 , which represents a substantial reduction in uncertainty relative to the CMIP6 15 ensemble. Our ﬁndings show that atmospheric aridity is an important proxy for the combined 16 eﬀects of both water and temperature on the terrestrial carbon balance and a key predictor 17 of carbon—climate feedbacks. 18

tem productivity loss than temperature (Zhou et al., 2019b). The study by Konings et al. (2017) 48 highlighted that increases in VPD rather than changes in precipitation substantially influenced 49 vegetation productivity. 50 In the tropics, observational records indicate that VPD is increasing over the rainforests of 51 the Amazon Basin with values well beyond the range of trends attributable to natural variability 52 of the climate system (Barkhordarian et al., 2019). Increasing VPD is observed to be associated 53 with more incoming solar radiation, which naturally increase the demand for photosynthesis and 54 transpiration. However, with recent trends in the observed soil water deficit from reduced dry-55 season precipitation (Barkhordarian et al., 2018), the risk of mortality from physiological and 56 hydraulic failure substantially increases (Anderegg et al., 2015) with the potential to upset the 57 tropical carbon balance (Sulman et al., 2016). Persistent changes in atmospheric aridity and 58 seasonal moisture availability could fundamentally change Amazon forest function that may augur 59 a "tipping point" (Lenton et al., 2008). 60 VPD is often overlooked in carbon cycle research despite its critical role in terrestrial water 61 use and carbon uptake (Novick et al., 2016). In contrast, in this study we show that atmospheric 62 demand for ecosystem water, which is directly related to the atmospheric vapor pressure deficit, is 63 an important control on the variability of the tropical carbon balance and consequently the CO 2 64 growth rate (CGR). In order to distinguish between causal and correlative linkages between VPD (for simplicity CGR is converted to equivalent GtC/yr). The gradient of the ordinary least squares 89 linear regression between de-trended anomalies in the CGR and the tropical VPD defines γ CGR V P D = 90 dCGR/dV P D. We calculate VPD from two independently-developed datasets: (1) VPD from 91 ERA5 reanalysis temperature and dew point (Hersbach et al., 2020) and (2)  are associated with also high CGR, which suggest a weakening of the land carbon uptake. 98 We calculated how γ CGR V P D changes with time using a 30-yr moving window between 1960 and 99 2018 (Fig 1b) (both variables detrended). We exclude data for 2 years following large volcanic 100 eruptions (Mount Agung, 1963;El Chichon, 1982;and Mount Pinatubo, 1991). Within each 30-yr 101 moving window, there is a significant positive correlation between CGR and VPD in the range 102 of [0.52 -0.71] (P ≤ 0.01). Furthermore, γ CGR V P D increased by a factor of 1.6, from 1.40 ± 0.58 GtC/yr/mb to 2.28 ± 0.42 GtC/yr/mb between 1960-1995and 1989-2018 (CMS-Flux;Liu et al. (2020)). CMS-Flux is a carbon cycle data assimilation system that incor-116 porates global satellite-driven measurements across the carbon cycle to attribute CO 2 variability 117 to spatially-resolved processes (Liu et al., 2014a(Liu et al., , 2017Bowman et al., 2017).  We also note that the correlation is higher than the observed 133 coupling between NBE and near surface (2m) temperature (r = -0.78). For each VPD time series, 134 the correlation is -0.86 (P = 0.00) and -0.80 (P = 0.00) with ERA5 and CRUv4, respectively.

135
The high correlation between VPD and NBE indicates that high atmospheric demand for water 136 weakens the terrestrial carbon sink. Based upon the previous regression, we quantify the observed 137 yearly sensitivity to be γ N BE V P D = -3.2 ± 0.62 GtC/yr/mb (Fig 2a). In other words, for 1 mb increase 138 in water vapor pressure deficit, there is 3.2 grams less carbon uptake. the correlation coefficient between predicted (CGR-reconstructed VPD) and observed values of 153 VPD.

154
We limit the analysis to CGR as the tropical NBE record is too short, but we have shown  The CCM results (Fig 1c) indicates that the CGR-reconstructed VPD curve (the prediction skill) 164 gradually converges to a statistically significant values (ρ CCM = 0.73, P = 0.00 ) as time-series 165 length increases. Since convergence is a key property that distinguishes causation from simple 166 correlation we conclude that CGR variations are causally linked to VPD variations.  2016)). The name of the models are given in Extended data and its dependence on both temperature and moisture processes.

194
In addition to a partial correlation analysis, we can also look at the surface energy partitioning.

195
The partitioning of available energy at the land surface into sensible (Q s ) and latent heat ( 4). These results solidify the conclusion that that tropical VPD is substantially impacted 212 by surface moisture processes through land-atmospheric coupling.
where subscript "TL" represents "Tropical Land", γ T L and β T L are the carbon-climate and car-228 bon-concentration feedback parameters, respectively. In contrast to previous studies, we use 229 changes in tropical mean VPD (atmospheric aridity), ∆V P D T L , as a proxy for carbon-climate 230 feedbacks. This approach is also slightly different from earlier work in that the feedbacks are 231 confined to sensitivities of tropical land carbon storage to climate change and direct CO 2 effects 232 (Friedlingstein et al., 2003(Friedlingstein et al., , 2006. Extratropical terrestrial carbon feedbacks are not considered 233 here. We estimate γ T L parameters from 12 ESMs (Extended data an expression for the atmospheric aridity-carbon cycle feedback parameter (γ T L ): The changes are computed for the tropical band ( previously, we map current climate, x t → γ N BE V P D , and future climate, z t+τ → γ T L , which is the 286 impact of atmospheric aridity on the long-term tropical land carbon storage. The observational 287 constraint, y t →γ N BE V P D , is calculated from the sensitivity of NBE from CMS-Flux to atmospheric 288 aridity (γ N BE V P D , whereγ denotes an estimate of γ, Fig 2a). The observed short-term sensitivity, y t 289 = -3.2 GtC/yr/mb with an observational uncertainty of σ nt = 0.62 GtC/yr/mb.

296
The larger uncertainty in the CMIP6 ensemble makes the null hypothesis (i.e., VPD has no 297 substantial impact on carbon storage) to be far more likely than the HEC constraint. For the 298 projected VPD increase of 8.6 mb (Fig. 3), the tropical carbon storage would decrease by 189.2 ± 299 89.04 GtC. HEC with about a factor of 2 reduction in uncertainty relative to CMIP6 models alone.

310
While ESMs broadly represent NBE dependencies on VPD, these analysis reveal substantial 311 differences between models. In most cases their partial correlation analysis is substantially lower 312 than observed, often by 0.5 or more. This suggests that more complex carbon-water interactions 313 are not getting captured-and that temperature is a more dominant role than is warranted in 314 the data. However, process deficiency also leads to caution in the interpretation of the HEC. If Observation and model data used in this study are presented in Table 1. We calculate VPD on the  In the CCM method, the first step is to determine the optimal embedding dimension (E), which 361 describes the size of the time window used for prediction. Extended data Fig. 2b presents the 362 variation in the prediction skill, ρ, as a function of E, which shows that the ρ asymptotically 363 approached a limit with the increasing E. From this analysis the embedding dimensions was set 364 E = 4. In order to test the "predictability" of the VPD time series the S-maps method (Sugihara 365 et al., 2012) is used. We can distinguish between red noise and nonlinear deterministic behavior 366 by using S-maps as described in Sugihara et al. (2012). The S-map method suggests nonlinear 367 dynamics in the VPD data (because of the initial increase in prediction skill for θ ≥ 0, followed 368 by a gradual drop-off, Extended data Fig 2c). Therefore, the CCM method can be applied to 369 reconstruct VPD.
Equation 3 can be computed analytically if the distributions are Gaussian and numerically if they 380 are not. As discussed in Bowman et al. (2018), for the Gaussian case, an HEC can be completely 381 described by the first and second-order moments. The first moment, i.e., the mean, of the HEC is 382 defined as follows: where ρ is the correlation between z t+τ and x t ; µ xt and σ 2 xt are the mean and variance of the 384 present climate; µ z t+τ and σ 2 z t+τ are the mean and variance of the future climate, respectively, and 385 σ 2 nt is the uncertainty of the measurement y t . The second moment of [z t+τ | y t ] is 386 var(z t+τ |y t ) = σ 2 where σ 2 xt /σ 2 nt is referred to as the signal-to-noise ratio (SNR).

387
As described in Bowman et al. (2018), under Gaussian assumptions, equations (4)    The whiskers denote the standard deviation among the two observational VPD datasets (CRUv4 and ERA5). The gray shaded area indicates the CMS-Flux NBE uncertainties. b) Correlation (r) between NBE and VPD (blue bar), Partial correlation between NBE and VPD after controlling for the effect of temperature (gray bar), correlation between NBE and soil moisture (SM) (green bar, note the positive correlation between NBE and SM). c) Correlation between NBE and 2m temperature (blue bar). Partial correlation between NBE and temperature after controlling for the effect of VPD (gray bar). Significance (P = 0.00) is indicated with crosses. d) The percent variance of VPD variability explained by land-atmospheric interactions (Bowen ratio; proxy for energy partitioning). e) Partial correlation between Bowen ratio and VPD after controlling for the effect of temperature. Figure 3: Quantities used to calculate atmospheric aridity-carbon cycle feedback parameters (γ T L ). a) The projected tropical (23 • N-23 • S) mean VPD change in the prescribed CO 2 fully coupled (blue line) and biogeochemically coupled simulations (green line) and the range across 12 ESMs listed in Table 1. (b) Cumulative mean values and the range across 12 ESMs for annual atmosphere-land CO 2 fluxes from the fully (blue line) and biogeochemicaly (green line) coupled simulations of the 1pctCO2 experiment Figure 4: a) The long-term response of tropical land carbon storage to atmospheric aridity (γ T L ) versus the short-term sensitivity of tropical NBE to tropical VPD (γ N BE V P D ) for the 12 ESMs of CMIP6. The correlation between γ LT and γ N BE V P D provides an "Emergent Constraint" on the longterm response of land carbon storage to atmospheric aridity. The vertical dashed lines show the range of observed sensitivity. (b) The gray PDF is the prior PDF derived purely from the models before applying the HEC, while the red dashed PDF was derived after applying the HEC on models. Sulman, B. N., Roman, D. T., Yi, K., Wang, L., Phillips, R. P., and Novick, K. A. (2016). High 512 atmospheric demand for water can limit forest carbon uptake and transpiration as severely as