Analysis and prediction of global vegetation dynamics: past variations and future perspectives

Spatiotemporal dynamic vegetation changes affect global climate change, energy balances and the hydrological cycle. Predicting these dynamics over a long time series is important for the study and analysis of global environmental change. Based on leaf area index (LAI), climate, and radiation flux data of past and future scenarios, this study looked at historical dynamic changes in global vegetation LAI, and proposed a coupled multiple linear regression and improved gray model (CMLRIGM) to predict future global LAI. The results show that CMLRIGM predictions are more accurate than results predicted by the multiple linear regression (MLR) model or the improved gray model (IGM) alone. This coupled model can effectively resolve the problem posed by the underestimation of annual average of global vegetation LAI predicted by MLR and the overestimate predicted by IGM. From 1981 to 2018, the annual average of LAI in most areas covered by global vegetation (71.4%) showed an increase with a growth rate of 0.0028 a–1; of this area, significant increases occurred in 34.42% of the total area. From 2016 to 2060, the CMLRIGM model has predicted that the annual average global vegetation LAI will increase, accounting for approximately 68.5% of the global vegetation coverage, with a growth rate of 0.004 a−1. The growth rate will increase in the future scenario, and it may be related to the driving factors of the high emission scenario used in this study. This research may provide a basis for simulating spatiotemporal dynamic changes in global vegetation conditions over a long time series.


Introduction
Vegetation is the main producer of terrestrial ecosystems, which plays an important role in energy exchange, climate change, carbon-water cycle and global environmental change. (Liu et al. 2010;Gao et al. 2017). Remote sensing technology has made great achievements, and the selection of appropriate vegetation indices plays an important role in monitoring vegetation change (Piao et al. 2015). The normalized difference vegetation index (NDVI) is widely used in vegetation growth and surface greenness evaluation studies, but it is less sensitive when the vegetation cover density is high (Lin et al. 2014). The enhanced vegetation index (EVI) is commonly used in areas with high leaf area indices (LAI), i.e., dense vegetation. Because LAI directly represents the growth of vegetation, it was selected as the index for monitoring global vegetation change (Hu et al. 2021). The spatiotemporal dynamics of vegetation vary considerably from region to region because of climate change and Abstract Spatiotemporal dynamic vegetation changes affect global climate change, energy balances and the hydrological cycle. Predicting these dynamics over a long time series is important for the study and analysis of global environmental change. Based on leaf area index (LAI), climate, and radiation flux data of past and future scenarios, this study looked at historical dynamic changes in global vegetation LAI, and proposed a coupled multiple linear regression and improved gray model (CMLRIGM) to predict future global LAI. The results show that CMLRIGM predictions are more accurate than results predicted by the multiple linear regression (MLR) model or the improved gray model (IGM) alone. This coupled model can effectively resolve the problem posed by the underestimation of annual average of global vegetation LAI predicted by MLR and the overestimate predicted by IGM. From 1981 to 2018, the annual average of LAI in most areas covered by global vegetation 1 3 human activities on different vegetation types. Therefore, the monitoring and prediction of spatiotemporal dynamics of global vegetation over a long time series is of significance.
Vegetation LAI, one of the key parameters of canopy structure, is expressed as half the sum of the surface area of all leaves per unit surface area (Zhu et al. 2014;Hu et al. 2021) and is closely related to energy exchange, rainfall interception, evapotranspiration and photosynthesis (Weiss et al. 2004;Bonan 2008;Wang et al. 2020). LAI is often used as a driving factor in models of vegetation spatiotemporal dynamics, and ecosystem and terrestrial processes (Liu et al. 2012). Global LAI observation products with high spatiotemporal resolutions have become important data sources in research on vegetation spatiotemporal dynamics . For example, the Terra and Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) instruments are capable of providing global one-km resolution LAI datasets (Yang et al. 2006), the Global Land Surface Satellite (GLASS) can provide global one-km and 0.05° resolution LAI datasets (Xiao et al. 2014(Xiao et al. , 2016 and the Global Inventory Modeling and Mapping Study (GIMMS) LAI3g product can produce global 1/12-degree resolution LAI datasets (Pfeifer et al. 2014). Moreover, LAI remote sensing inversion products are more often used for vegetation change monitoring (Piao et al. 2015;Chen et al. 2020;Hu et al. 2021), and the impact mechanisms on vegetation by climate (Jiapaer et al. 2015;Liang et al. 2020), drought conditions ) and water use efficiency (Hu et al. 2008;) have been studied.
Changes in climatic factors have a significant impact on vegetation change (Schwartz and Reiter 2000), and precipitation, solar radiation and temperature play decisive roles in the growth of vegetation (Stephenson 1990;Churkina and Running 1998;Nemani et al. 2003;Chen et al. 2021a). Evapotranspiration is crucial in the global energy balance, and the carbon and water cycles, and an important component of ecohydrological processes (Birhanu et al. 2019;Niu et al. 2019). As a result, there have been predictions of future spatiotemporal changes in vegetation based on correlations between vegetation and climatic conditions, such as the NDVI, LAI, and EVI (Table 1).
All the above methods can predict vegetation indices with high accuracy, but several limitations, such as the responses by different ecosystems to climate change, make the predictive model performance subject to large uncertainties (Zhang et al. 2017;Wu et al. 2018). According to the limited, existing information, gray prediction methods can efficiently and accurately predict unknown data (Deng 1982). These models have been applied to economic forecasting and management analyses, energy and energy management analyses, agricultural and resource forecasting, and environmental and disaster forecasting (Xie and Wang 2017), but they have rarely been used for vegetation forecasting. Based on the existing traditional gray model, an improved gray model (IGM) has been constructed by solving for the initial value in the model and applying automatic weight optimization and determination methods to select the weight coefficient of the background value to maximize the model prediction accuracy. Although several combined forecasting models, for example, Huang et al. (2017) predicted NDVI data in the Yellow River Basin using a combined model of MLR and artificial neural networks, few studies have been conducted on predicting LAI. To fill this gap, this study addresses the uncertainty of the model structure by combining MLR and IGM to provide a basis for research in this field. A coupled multiple linear regression and an improved gray model (CMLRIGM) is proposed to predict future global vegetation LAI. To our knowledge, no study has been conducted to predict vegetation LAI using this model. The model can resolve the uncertainty of structure and improve prediction accuracy by combining the two models to complement each other.
The purposes of this study are to: (1) analyze the spatiotemporal changes and driving factors of global vegetation LAI from 1981 to 2018; (2) construct a coupled MLR and IGM (CMLRIGM) to predict vegetation changes and verify prediction accuracy; and, (3) use the coupled model to predict future changes in vegetation. This research provides a basis for simulating temporal and spatial dynamics of global vegetation information over a long time series in the future.

Data
Global vegetation LAI data for 1981-2018 were obtained from the National Earth System Science Data Center (http:// www. geoda ta. cn/) at a spatial resolution of 0.05° (Xiao et al. 2014). Historical climate conditions and radiation flux data were provided by the Famine Early Warning Systems Network (FEWS NET) Land Data Assimilation System (FLDAS) Products (McNally et al. 2017), with a spatial resolution of 0.1°, and the timespan of this product was from 1982 to 2018. Future climate conditions and radiant flux data were adopted from the CMIP5 climate model RCP8.5 scenario provided by the Intergovernmental Panel on Climate Change (IPCC), which suggests that the radiation intensity will increase to 8.5 W m −2 in 2100, representing a possible high emission pathway for future global development. It is commonly used in studies of future climate change. The data used are shown in Table 2. The CanMIR model parameters are the mean values of the CanESM2 and MIROC5 model parameters. The data were uniformly resampled to 0.1° using the nearest-neighbor interpolation method.
Historic dynamic changes in global vegetation LAI were studied as well as the driving factors of these changes based on trend analyses and correlation analyses. The CMLRIGM model was proposed by coupling MLR and IGM models; all three were used to predict global vegetation LAI. The accuracy of the results of each model was verified and compared. The three models were used to predict the annual average global vegetation LAI in the future, and the results compared with the annual average global vegetation LAI simulated by different CMIP5 climate models. The overall technical framework is shown in Fig. 1.

Statistical analysis
To analyze the trend of global LAI, a combination of the Sen trend and Mann-Kendal methods was used. The combination of the two methods was reduced noise interference and tested the significance of the series trend. The specific calculation formula can be found in Li et al. (2021). In addition, Pearson's correlation coefficient was used to measure the linear correlation between vegetation and drivers, and a t test was used to statistically analyze the linear correlation results.

Multiple linear regression model
To construct a model for predicting spatiotemporal changes in vegetation LAI based on climatic conditions, radiation where ET , Temp , Pre and Qair represent evapotranspiration, temperature, precipitation and specific humidity, respectively; LWdown and SWdown are the longwave radiation flux and shortwave radiation flux, respectively; b 1 , b 2 , b 3 , b 4 , b 5 , b 6 and b 7 are the coefficients and constants of the independent variables in the model.

Improved gray model
The modeling process of the IGM involves accumulating irregular original data to obtain a more regularly generated sequence, performing the modeling, and then accumulating and subtracting the data obtained from the generative model to obtain predicted original data values, finally, predictions are made (Yu et al. 2020).
Assuming that the original LAI data are listed a s X (0) = X (0) (1), X (0) (2), … , X (0) (n) , a n e w s e q u e n c e generated after first order accumulation; in this new sequence, X (1) (i) = ∑ i k=1 X (0) (k), i = 1, 2, … , n. The X (1) sequence obeys the law of exponential growth; that is, it satisfies the following first-order linear differential equation: where a is the development gray number that reflects the development trend of X (1) and the original sequence X (0) and b is the endogenous null gray number reflecting the change relationship of the data.
The equation is used to solve for a and b , and ̂=(a, b) T is the vector to be estimated. As the analyzed sequence is dis- The following equation is assumed: where Z (1) (k) is the background value of formula (2), ∈ [0, 1] , and is the weight coefficient.
( At this point, formula (2) can be discretized to obtain the following equation: Substituting = 0 into Eq. (4) and then substituting the result into Eq. (5), we can obtain the following: Based on the least squares method of solving Eq. (6), the following is obtained: where After calculating ̂= (a, b) T from Eq. (7), we continue to solve differential Eq. (2) to obtain the following: where X (1) is the predicted value of the X (1) sequence and c is the undetermined constant; Eq. (8) is discretized to obtain the following: The selection of the initial value should satisfy the minimum sum of the squared deviations between the predicted and the actual values Eq. (9) is accumulated and subtracted to obtain the estimation equation of the original sequence.
and C is substituted into Eqs. (9) and (10) to obtain the following formulas: By substituting formula (11) into the above formula, the following equation can be obtained: when dS dC = 0 , S is minimized; that is, the prediction accuracy of the model is the highest.
By substituting formula (12), the following equation can be obtained:

Spatiotemporal variation in global LAI
The spatial distribution of global LAI values and their relationships with latitude and longitude from 1981 to 2018 is shown in Fig. 2. Regions with high multiyear average LAI values (≥ 4) are mainly in South and Central America, Central Africa, and southern and southeastern Asia. Regions with low multiyear average LAI values (< 2) are distributed in southwestern South America, northern and southwestern North America, northern and southern Africa, northern and western Europe, central and western Asia, and most areas of Australia and New Zealand. The longitudinal distribution shows that the multiyear average LAI values peak at approximately − 60° W and are mainly distributed in the northern region of South America. The latitudinal distribution shows that the multiyear average LAI values peak in near the equator, in the northern part of South America, in Central Africa and in southeastern Asia.
The spatial distribution of the change trends for global annual mean LAI from 1981 to 2018 is shown in Fig. 3a. The regions with significant increases are mainly distributed in southeastern North America, Central America, most parts of South America, most of Africa, southwestern Europe, southwestern and eastern Asia, and western and northern Australia and New Zealand. The spatial distribution of annual mean LAI trends for the global and continental subregions shows that the percentage area with increasing trends is higher than the percentage area with decreasing LAI trends. Areas with an increase in global LAI account for 71.4% of the total vegetation cover, and areas with significant increases in LAI and significant decreases in LAI accounted for 34.4% and 5.9% of the total global vegetation cover, respectively. Among areas with increasing LAI trends, western Europe accounted for the smallest at 59.9%, and South Africa for the largest at 91.4%. In the proportion of areas on each continental subregion with significant increases in LAI, eastern Europe accounted for the smallest at 16.9%, southern Africa for the largest at 69.9% (Fig. 3b). Figure 4 shows the interannual changes in global annual average LAI and in all continental subregions from 1981 to 2018, with an increasing trend in both. The global multiyear average LAI was 1.4, the annual average fluctuation range was (1.4 ± 0.9), and the rate of increase was 0.0028 a −1 . The largest annual average LAI among all continental subregions is for Melanesia, with a multiyear average of 4.5 and a rate of increase of 0.0045 a −1 . The smallest annual average among all continental subregions occurred in Central Asia, with a multiyear average of 0.3 and a rate of increase of 0.0009 a −1 .

Factors influencing LAI
The spatial distribution of the t test and statistical results of the correlation between global annual average LAI and annual average climate conditions and radiation flux are shown in Fig. 5 and Table 3. Among the six drivers, specific humidity had the highest area percentage significantly correlated with LAI, and conversely, surface downward radiation had the lowest. In the correlation analysis between LAI and ET, areas with significant correlations (P < 0.05) accounted for 30.6% of the total area; areas with significant positive correlations were in central and southern North America, eastern and southern South America, central and southern Africa, western, central, and eastern Asia, and Australia and New Zealand. Significant negative correlations were in the northwestern part of South America. Areas where LAI was significantly correlated with precipitation accounted for 23.1% of the total area. The distribution of significant positive correlations was similar to that described for the correlation between LAI and evapotranspiration. Areas where LAI was negatively correlated with precipitation were more dispersed. Areas where LAI was significantly correlated with humidity accounted for 32.7% of the total area, and the distribution of significant positive correlations was similar to that described for LAI and precipitation. There were negative correlations in Central Africa. Where LAI was significantly correlated with temperature accounted for 24.0% of the total area, and were in southeastern North America, northern and central South America, central Africa and eastern Asia. Significant negative correlations were in southern and eastern South America, southern Africa, southern Asia, Australia and New Zealand. From the analysis of the correlations between LAI and radiation fluxes, areas in which LAI and downward longwave radiation were significantly correlated accounted for 23.9% of the total

Fig. 5 Spatial distribution of t test results for correlation of global LAI with climatic conditions and radiation fluxes. ET is Evapotranspiration, Temp is Temperature, Pre is Precipitation, LWdown is
Downward longwave radiation flux, SWdown is Surface downward shortwave radiation, and Qair is Specific humidity North America, northern and central South America, southern and eastern Africa, southeastern Asia, and most areas of Australia and New Zealand.

Predictive model accuracy verification
Using the annual average LAI, climatic condition, and radiation flux data from 1981 to 2015, MLR, IGM, and CML-RIGM were established. These three models were used to predict the average LAI from 2016 to 2018. The accuracy of each model was verified by a residual comparison and linear correlations between the original annual average LAI data from 2016 to 2018 and the LAI data predicted using the different models.
The spatial distribution of the residual values of the original global annual mean LAI data and the predicted LAI data using different models from 2016 to 2018 are shown in Fig. 6. Table 4 is the statistical results of Fig. 6. This paper divides them into low value areas (− 0.25-0.25), mediumvalue areas (− 0.5 to − 0.25 or 0.25-0.5) and high value areas (≤ − 0.5 or ≥ 0.5). From 2016 to 2018, the spatial distributions of the residual values by the three models revealed certain differences, and the percentage of the total area covered by low-value areas was greater than 78.0%. The percentages of areas with low residual values of CMLRIGM, IGM and MLR were 86.0%, 84.4%, and 83.4% for 2016-2018, respectively. Therefore, the accuracies of these models for predicting global vegetation LAI were ranked from high to low as CMLRIGM, IGM, and MLR. CMLRIGM predicted the average LAI residuals of global vegetation in 2016, 2017 and 2018 to be 0.0001, 0.0121, and -0.0196, respectively, IGM predicted the averages to be − 0.0121, − 0.0081 and − 0.0457, respectively, and MLR predicted the averages to be 0.0124, 0.0305, and 0.0019, respectively. The MLR predicted a low global annual mean LAI, while the IGM predicted a high LAI. By coupling MLR and IGM prediction models, the problem of the two models in predicting the annual average global LAI can be effectively solved. The MLR, IGM and CMLRIGM predicted the global average absolute vegetation LAI residual values from 2016 to 2018 to be 0.0148, 0.0219, and 0.0106, respectively. Thus, the absolute residual of the global annual average vegetation LAI predicted by CMLRCM was reduced by 28.4% and 51.6% compared with the MLR and IGM models, respectively. Figure 7 shows the raw data for global annual average LAI and linear fitting diagrams of the forecasted LAI data output by different models from 2016 to 2018. The three models are highly accurate when predicting the global annual average LAI values. Comparing Pearson's correlation coefficient (Cor), root mean square error (RMSE) and R 2 results, the prediction accuracies of the three models can be ranked as follows: CMLRIGM > IGM > MLR. Combined with the analysis of the mean annual LAI residuals described above, CMLRIGM has the highest accuracy when predicting global annual mean LAI values.

Analysis of future spatiotemporal changes in vegetation
The global vegetation LAI predicted by the three models for 2016-2018 was compared with the simulation of the CanESM2, MIROC5 and CanMIR models. Different models simulate the spatiotemporal variations of global vegetation LAI (Fig. 8). The residual differences between the average LAI from 2016 to 2018 and the average vegetation LAI from 1981 to 2000 are shown (Fig. 8 g1). Different models simulate the residuals between the average value of vegetation LAI in 2016-2018 and the average value of vegetation LAI in 1981-2000 ( Fig. 8a1-f1). The area with a residual value greater than 0 between the average value of vegetation LAI from 2016 to 2018 simulated by the CMLRIGM, IGM and MLR models and the average value of vegetation LAI from 1981 to 2000 accounted for 66.4%, 69.3%, and 66.1% of the total global area, respectively. The comparison shows that the consistency between the simulation results of CML-RIGM or IGM and the original data is higher than that of the MLR model and the original data. However, the area with a residual value greater than zero between the 2016-2018 mean LAI and the 1981-2000 mean LAI represents 63.1% of the total global area. This result shows that the simulation results of CMLRIGM are closest to the original data and further supports the conclusion that MLR-predicted global LAI data are underestimated, while the IGM-predicted data are overestimated (Table 5). The MLR model simulated areas in which the residual difference between the average The results of the CMLRIGM, IGM and MLR models predicting the mean LAI from 2041 to 2060 minus the original mean LAI from 2016 to 2018 were first analyzed. The global LAI predicted by these three models from 2041 to 2060 were then compared with the results from the CanESM2, MIROC5 and CanMIR models. Different models were used to simulate the residuals between the average vegetation LAI in 2041-2060 and the average in 2016-2018 ( Fig. 8a2-f2). The area with a residual value greater than 0 between the average value LAI from 2041 to 2060 simulated by the CMLRIGM, IGM and MLR models and the average value 2016 to 2018 accounts for 68.5%, 63.9%, and 70.1% of the total global area, respectively (Table 5). In this study, three models were used to predict future global LAI trends, and approximately 2/3 of the area showed an increasing change, with growth areas distributed in South America, Africa, and southern Asia. The area with a residual value greater than 0 between the average LAI value from 2041 to 2060 simulated by the CanESM2, MIROC5 and CanMIR models and the average from 2016 to 2018 accounted for Fig. 7 Raw data for global annual average LAI and linear fitting diagrams of the forecasted data output by different models from 2016-2018. y is the model predicted LAI value, x is the actual monitoring LAI value of satellite remote sensing, Cor is Pearson's correla-tion coefficient, RMSE is root mean square error, R 2 is coefficient of determination, MLR is multiple linear regression, IGM is improved gray model, and CMLRIGM is coupled multiple linear regression and improved gray model 50.6%, 14.7%, and 38.3% of the total global area, respectively. The simulation results by different models under the CMIP5_RCP8.5 scenario were different.
The changes for global annual average LAI simulated by different models were quite different (Fig. 9). The CMLRIGM, IGM, and MLR simulated LAI growth from 2016 to 2060 as 0.004 a −1 , 0.005 a −1 , and 0.0023 a −1 , respectively. The annual average LAI simulated by the CMLRIGM model was between those of the IGM and MLR. The longer the period used to predict the future annual average LAI, the closer the annual average LAI values simulated by the three models. The results of the different models of the CMIP5 climate model simulating annual mean LAI are highly variable. From 2006 to 2060, the CanESM2, CanMIR and MIROC5 models simulated annual average LAI growth rates of 0.003 a −1 , 0.0013 a −1 , and − 0.0004 a −1 , respectively. The global annual average LAI simulated by the MIROC5 model shows a decreasing trend. The annual average LAI values simulated by the MIROC5 and CanMIR models were both low, while the annual average LAI values simulated by the CanESM2 model were more consistent with the interannual variation trends observed in historical LAI data.

Spatiotemporal changes in vegetation LAI
During 1981-2018, regions with high global multiyear average LAI values (≥ 4) were mainly distributed in South America, Central America, Central Africa, southern Asia, and southeastern Asia. This result is consistent with the results of Liu et al. (2010), who studied the spatial distribution of average global LAI from 1981 to 2006. Different LAI is an important variable that can be used to extend leaf-level biogeophysical and biogeochemical processes to regional and global scales. These large-scale studies are of significance for predicting the future spatiotemporal characteristics of LAI (Mahowald et al. 2016). Compared with the prediction results by the CMLRIGM and IGM, the MLR predicted global vegetation LAI data were closer to the results simulated by different models under the CMIP5_RCP8.5 scenario. This finding may be related to the impact factor that arises when the input data parameter is set as CMIP5_ RCP8.5 in the MLR model predictions. Although the IGM predicted LAI data with a high degree of accuracy in this study, its accuracy decreased as the forecast time increased. Therefore, coupling IGM with the MLR model to perform year-by-year cyclic forecasting can improve the overall accuracy of the results. The CMLRIGM predicted that 68.5% of the global vegetation area will show an increase from 2016 to 2060, and the predicted spatiotemporal change obtained was smaller than those predicted in previous studies (Zhao et al. 2020). The simulation results by different models under the CMIP5_RCP8.5 scenario are very different, and the simulated LAI data also have obvious differences, especially when simulations are conducted at a small scale (Mahowald et al. 2016;Zhao et al. 2020).

Factors influencing LAI
The impact of different climatic environments on different vegetation types varies . The relationship of vegetation and climate is mainly manifested in the adaptability of vegetation to climate conditions and the feedback effects vegetation has on climate (Kong et al. 2018). Different vegetation types affect the climate by influencing material and energy exchanges between vegetation and atmosphere, and altered climate conditions affect the growth of vegetation through material and energy exchanges between the atmosphere and vegetation (Wu et al. 2015). The sensitivity of vegetation to different climates varies from region to region, with climatic conditions as the main factor influencing vegetation change (Liu et al. 2012;Niu et al. 2019), and the geographical distribution of vegetation is sensitive to small regional climatic changes (Yan et al. 2019).
The results of studies on how terrestrial plants will respond to global change are not well established. At present, numerous researchers have analyzed the driving factors affecting the dynamic changes of vegetation. Global vegetation changes occur with changes in temperature, precipitation, and other factors. These changes alter the global material and energy cycles and induce feedback effects on the climate (Liu et al. 2010). Evapotranspiration is a key indicator for quantifying and understanding the global water cycle, and changes in evapotranspiration are closely linked to changes in land cover type (Pascolini-Campbell et al. 2021). Solar radiation is one of the factors necessary for the exchange of material and energy in vegetation and can have a direct and indirect effect on vegetation growth (McKinnon et al. 2013;Liang et al. 2020;Chen et al. 2021b). In summary, the six driving factors selected in this paper all significantly interact with LAI.

Uncertainty
The limitations of the research in this study are mainly reflected in the following four points. First, although the GLASS LAI product used provides high-quality and highprecision global long-term data, there are accuracy limitations and uncertainties due to surface cover and raster accuracy impacts (Jiapaer et al. 2015). Second, the climatic conditions and radiant flux data provided by the FLDAS product and from different CMIP5_RCP8.5 models have certain limitations and errors. When the CMLRIGM model predicts future vegetation on a year-by-year cycle, the model input parameters predict vegetation LAI from only two characteristic factors: climatic conditions and radiation flux. However, carbon and nitrogen concentrations in the air, soil conditions and soil types may all affect dynamic changes in vegetation, and these influencing factors were not input into the models used in this study. Third, in addition to the uncertainty in the data and in the model input parameters, global vegetation is also subject to other uncertainties. For example, extreme weather events (Yan et al. 2019), soil respiration , human activities , and CO 2 fertilization (Piao et al. 2013(Piao et al. , 2015 can all affect the temporal and spatial dynamics of vegetation. Fourth, only two models for the CMIP5 RCP8.5 scenario were considered. In summary, research on the interaction between global vegetation change and impact factors still needs further refinement.

Conclusions
In this study, the spatiotemporal trends and driving factors of global vegetation LAI from 1981 to 2018 were analyzed, and a CMLRIGM model constructed to predict vegetation LAI and validate the model prediction accuracy. The CML-RIGM model was then to predict future spatial and temporal dynamics of vegetation. In summary: (1) The CML-RIGM predictions of future global vegetation LAI annual average are more accurate than the results predicted by the MLR model and IGM. CMLRIGM can effectively solve the problem posed by the underestimation of the annual average global LAI predicted by MLR and the overestimation predicted by IGM. (2) During the period 1981 to 2018, the annual average vegetation LAI showed increasing trends in most parts of the world (71.4%), among which significantly increasing area accounted for 34.4% of the total area, and a rate of increase in annual mean LAI of 0.0028 a −1 . (3) During the period 2016-2060, the CMLRIGM model predicted that the area in which the average annual value of global vegetation LAI would increase, would account for approximately 68.5% of the global vegetation coverage, with a growth rate of 0.004 a −1 . In addition, our research is important for future studies on the mechanisms of modeling global vegetation change over long time periods, which can provide a basis for global studies on climate change, the hydrological cycle, and the energy balance of vegetation changes.