We used two satellite-based GPP models to investigate the impacts of VPD on vegetation GPP. The first model is the MODIS-GPP model, and this study used long-term global MODIS GPP dataset driven by GIMMS fPAR data (27).

The second model is the revised EC-LUE model (26), derived by (i) integrating the impact of atmospheric CO2 concentration on GPP and (ii) adding the limit of VPD to GPP. The revised EC-LUE model simulates terrestrial ecosystem GPP asGPP=PAR×fPAR×εmax×Cs×min(Ts,Ws)(10)where PAR is the incident photosynthetically active radiation (MJ m−2) per time period (e.g., day); fPAR is the fraction of PAR absorbed by the vegetation canopy calculated by the GIMMS3g NDVI dataset; εmax is the maximum LUE; Cs, Ts, and Ws represent the downward-regulation scalars for the respective effects of atmospheric CO2 concentration ([CO2]), temperature (Ta), and atmospheric water demand (VPD) on LUE; and min denotes the minimum value of Ts and Ws.

The effect of atmospheric CO2 concentration on GPP was calculated according to Farquhar et al. (44) and Collatz et al. (45)Cs=CiθCi+2θ(11)Ci=Ca×χ(12)where θ is the CO2 compensation point in the absence of dark respiration (ppm) and Ci is the CO2 concentration in the intercellular air spaces of the leaf (ppm), which is the product of atmospheric CO2 concentration (Ca) and the ratio of leaf internal to ambient CO2 (χ). χ is estimated (4648) byχ=γγ+VPD(13)γ=356.51K1.6η*(14)K=Kc(1+P0K0)(15)Kc=39.97×e79.43×(Ta298.15)298.15RTa(16)Ko=27480×e36.38×(Ta298.15)298.15RTa(17)where Kc and Ko are the Michaelis-Menten coefficient of Rubisco for carboxylation and oxygenation, respectively, expressed in partial pressure units, and Po is the partial pressure of O2 (ppm). R is the molar gas constant (8.314 J mol−1 K−1), and η* is the viscosity of water as a function of air temperature (49).

Ts and Ws were calculated using the following equationsTs=(TaTmin)×(TaTmax)(TaTmin)×(TaTmax)(TaTopt)×(TaTopt)(18)Ws=VPD0VPD+VPD0(19)where Tmin, Tmax, and Topt are the minimum, maximum, and optimum air temperature (°C) for photosynthetic activity, which were set to 0°, 40°, and 20.33°C, respectively (50). VPD0 is an empirical coefficient of the VPD constraint equation.

Parameters εmax, θ, and VPD0 were calibrated using estimated GPP at EC towers (table S7). The nonlinear regression procedure (Proc NLIN) in the Statistical Analysis System (SAS; SAS Institute Inc., Cary, NC, USA) was applied to estimate the three parameters in the revised EC-LUE model. The revised EC-LUE model was calibrated at 50 EC towers and validated at 41 different towers (table S3). The results showed good model performance of the revised EC-LUE model for simulating biweekly GPP variations (fig. S13). To estimate global GPP, EC-LUE and MODIS models used the MERRA dataset (i.e., air temperature, VPD, PAR). Because of the different model algorithm, GIMMS3g NDVI and fPAR products were used to indicate vegetation conditions for EC-LUE and MODIS, respectively.

We performed two types of experimental simulation to evaluate the relative contribution of three main driving factors: CO2 fertilization, climate change, and satellite-based NDVI/fPAR changes. The first simulation experiment (SALL) was a normal model run, and all drivers were set to change over time to examine the responses of GPP to all environmental changes, including climate, atmospheric [CO2], and NDVI/fPAR. The second type of simulation experiments (SCLI0, SNDVI0, and SCO20) allowed two driving factors to change with time while holding the third constant at an initial baseline level. For example, the SCLI0 simulation experiment allowed NDVI and atmospheric [CO2] to change with time, while climate variables were held constant at 1982 values. SNDVI0 and SCO20 simulation experiments kept NDVI and atmospheric [CO2] constant at 1982 values and varied the other two variables.

We considered the differences between simulation results of the first type (SALL) and second type (SCO20 and SNDVI0) of experiments to estimate the sensitivity of GPP to atmospheric [CO2] (βCO2) and NDVI/fPAR (βNDVI). βCO2 and βNDVI were calculated on the basis of the following equationsΔGPP(SALLSCO20)i=βCO2×ΔCO2(SALLSCO20)i+ε(20)ΔGPP(SALLSNDVI0)i=βNDVI×ΔNDVI(SALLSNDVI0)i+ε(21)where ΔGPPi, ΔCO2i, and ΔNDVIi represent the differences of GPP simulations, atmospheric [CO2], and NDVI between two model experiments from 1982 to 2015, and ε is the residual error term.

A multiple regression approach was used to estimate GPP sensitivities to three climate variables: air temperature (βTa), VPD (βVPD), and PAR (βPAR)ΔGPP(SALLSCLI0)i=βTa×ΔTa(SALLSCLI0)i+βVPD×ΔVPD(SALLSCLI0)i+βPAR×ΔPAR(SALLSCLI0)i+ε(22)where ΔTai, ΔVPDi and ΔPARi represent the differences of air temperature, VPD, and photosynthetically active radiation time series between two model experiments (SALL and SCLI0), respectively. The regression coefficient β was estimated using maximum likelihood analysis.

The EC-LUE model suggested a CO2 sensitivity (βCO2) of 19.01 ± 4.01 Pg C 100 ppm−1 (Fig. 6B and table S2), which indicates a 15.7% increase of GPP with a rise of atmospheric [CO2] of 100 ppm. Our estimate is close to CO2 sensitivity derived from ecosystem models (βCO2 = 21.92 ± 4.55 Pg C 100 ppm−1; Fig. 6B) and is comparable to the observed response of NPP (net primary production) to the increased CO2 at the FACE experiment locations (13% per 100 ppm) and estimates of other ecosytem models (5 to 20% per 100 ppm) (51).

A machine learning method (i.e., RF) was used to model the effects of VPD on NDVI. RF combines tree predictors such that each tree depends on the values of a random vector that is sampled independently, with the same distribution for all trees in the forest. We constructed RF models for simulating annual growing season mean NDVI at each pixel driven by air temperature, precipitation, radiation, wind speed, atmospheric [CO2] concentration, and VPD. The training data were the GIMMS3g NDVI dataset from 1982 to 2015. The R package “randomForest” used in the study was modified by A. Liaw and M. Wiener from the original Fortran by L. Breiman and A. Cutler (https://cran.r-project.org/web/packages/randomForest/).

The RF model was driven by all variables (climate and atmospheric [CO2]) changing over time (RFALL), and two factorial simulations of NDVI (RFCO20 and RFCLI0) were produced by holding one driving factor (climate or atmospheric [CO2]) constant at its initial level (first year of data) while allowing the other driving to change with time. The RFCLI0 simulation experiment allowed atmospheric [CO2] other than climate variables to vary since 1982. RFCO20 simulation experiments kept atmospheric [CO2] constant at 1982 values and varied the climate variables. At each pixel, we selected 33 years of NDVI observations out of the total 34 years (1982–2015) to develop the RF model, and the remaining 1 year of NDVI observations was used for cross-validation. The model was run 34 times to ensure that the data of each year can be selected to do model validation. The simulated NDVI of three model experiments (i.e., RFALL, RFCO20, and RFCLI0) are mean values of all 34 times simulations. The simulated NDVI only from the validation year constitutes the RFVLI dataset, which was used to examine the performance of random forest for reproducing NDVI. The simulated NDVI of RFVLI matched the GIMMS3g NDVI very well (fig. S7), and the correlation coefficient (R2) is larger than 0.90 at the 88% vegetated areas globally. The tropical forest showed the relative low R2. The relative predictive errors range from −1.2 to 1.04% globally and imply that the RF model can accurately simulate interannual variability and magnitude of NDVI.

On the basis of the three model experiments, we used the same method above shown at Eqs. 20 and 22 to estimate the sensitivity of NDVI to atmospheric [CO2] (δCO2) and five climate variables: air temperature (δTa), VPD (δVPD), PAR (δPAR), precipitation (δPrec), and wind speed (δWS)ΔNDVI(RFALLRFCO20)i=δCO2×ΔCO2(RFALLRFCO20)i+ε(23)ΔNDVI(RFALLRFCLI0)i=δTa×ΔTa(RFALLRFCLI0)i+δVPD×ΔVPD(RFALLRFCLI0)i+δPAR×ΔPAR(RFALLRFCLI0)i+δPrec×ΔPrec(RFALLRFCLI0)i+δWS×ΔWS(RFALLRFCLI0)i+ε(24)where Δ represents the differences of NDVI simulations, atmospheric [CO2], and climate variables between two model experiments from 1982 to 2015, and ε is the residual error term. The regression coefficient δ was estimated using maximum likelihood analysis. We quantified the contributions of atmospheric [CO2] and five climate variables to NDVI changes during the two periods (1982–1998 and 1999–2015) by multiplying the magnitude of their changes and sensitivity of NDVI (δ).

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