Probabilistic assessments of the impacts of compound dry and hot events on global vegetation during growing seasons

Gridded monthly precipitation, temperature, and potential evapotranspiration data from January 1982 through December 2015 with a spatial resolution of 0.5° × 0.5°, covering the global land surface (excluding Antarctica) were used in this study. This dataset was obtained from the Climate Research Unit at the University of East Anglia. The NDVI is a remote sensing-based index to measure vegetation conditions. The biweekly NDVI data derived from NOAA Advanced Very High Resolution Radiometer instruments from 1982 to 2015 at 1/12° resolution were obtained from the Global Inventory Monitoring and Modeling System. This is a long-term record of remotely sensed-NDVI and has been widely used for the analysis of the relationships between climate and vegetation response (Wu et al 2015, Nicolai-Shaw et al 2017). To match the temporal and spatial resolution of climate data, the NDVI data were transformed to a monthly time scale through the maximum value composite method and regridded to 0.5° × 0.5° resolution. Meanwhile, we masked out the area with very low NDVI values (long-term mean NDVI in growing seasons is less than 0.1) (Zhao et al 2018). We focused on the growing season and only considered NDVI data during April–October in the area of 20° N–70° N, October–April in the area of 20° S–60° S, and January–December in the area of 20° S–20° N (Zhao et al 2018). The SPI and STI were computed based on the precipitation and temperature of the growing season. Specifically, the time scales (or accumulation periods) of SPI and STI for growing seasons of the three regions are seven months, seven months, and twelve months, respectively. The responses of vegetation to extreme events for different biomes (figure S1 (available online at stacks.iop.org/ERL/16/074055/mmedia)) were assessed based on the terrestrial ecoregions from Terrestrial Ecoregions of the World (Olson et al 2001).

The SPI and STI were employed in this study to track dry and hot conditions, respectively (Zscheischler et al 2014, Feng et al 2019). These two indicators were derived by fitting a marginal distribution (empirical Weibull distribution) to obtain the marginal probability, which was then transformed into standard variables based on the standard normal distribution. Following U.S. Drought Monitor (Svoboda et al 2002), we used the SPI value of −1.3 to represent severe drought conditions. Similarly, the threshold of 1.3 for the STI was used to define hot conditions (Feng et al 2019). The compound dry and hot condition was defined as the concurrence of low SPI and high STI (SPI ⩽ −1.3 and STI > 1.3). Other thresholds (e.g. SPI ⩽ −0.5 and STI > 0.5, SPI ⩽ −0.8 and STI > 0.8) were also used and the results were consistent (not shown). To facilitate statistical modeling, we defined the Standardized Normalized Difference Vegetation Index (SNDVI) to track the vegetation condition (i.e. SNDVI < 0 indicates a reduction of vegetation activity).

Furthermore, we used the Aridity Index (AI) (AI = MAP/MAE) to reflect the annual dry and humid conditions across the world, where MAP and MAE represent mean annual precipitation and mean annual potential evapotranspiration, respectively. We focused on the four climate regions defined based on AI (figure S2), including the arid region (0.03 ⩽ AI < 0.2), semi-arid region (0.2 ⩽ AI < 0.5), semi-humid region (0.5 ⩽ AI < 0.65), humid region (AI ⩾ 0.65) (Yuan et al 2017).

The dependence between climate indicators (SPI and STI) and vegetation (SNDVI) was evaluated based on the correlation analysis. To model the dependence among vegetation and climate indicators, multivariate and conditional distributions can be utilized to estimate the probabilistic response of vegetation under different extreme conditions from a statistical perspective (e.g. copula or vine copula models) (Feng et al 2019, Jha et al 2019, Fang et al 2019a, 2019b, Ribeiro et al 2020a). Following Feng et al (2019), the joint distribution of vegetation and climate indicators was estimated from the meta-Gaussian model, which captures dependence among multivariate variables and allows for flexible forms of marginal distributions (Kelly and Krzysztofowicz 1997, Hao et al 2018). For two continuous random variables X₁ and X₂, we can obtain two standardized normal random variables (Z₁ and Z₂) based on the Normal Quantile Transformation. As a result, the bivariate joint distribution of the meta-Gaussian model can be expressed as (Kelly and Krzysztofowicz 1997):

$$\begin{align} & P\left( {{Z_1} \le {z_1},{ }{Z_2} \le {z_2}} \right) \nonumber\\[-8pt] &\nonumber\\ & \quad = \int\limits_{ - \infty }^{{z_2}} \int\limits_{ - \infty }^{{z_1}} \frac{1}{{\left( {2\pi } \right)\sqrt {\left( {1 - {\rho ^2}} \right)} }}\nonumber\\ & \qquad \times {\text{exp}}\left\{ { - \frac{{{s^2} - 2\rho st + {t^2}}}{{2\left( {1 - {\rho ^2}} \right)}}} \right\}{\text{d}}s{\text{d}}t\end{align} \tag{ 1 }$$

where ρ is the Pearson's correlation coefficient between Z₁ and Z₂; s and t are the integral variables.

To evaluate the response of vegetation to dry and hot conditions, the conditional distribution in the trivariate case was used to estimate the probability of vegetation given different levels of dry and hot conditions. This can be obtained by extending the joint probability to the three dimensions. In this study, we were particularly interested in the vegetation decline (defined as SNDVI < 0). Thus, the conditional probability P(SNDVI < 0|SPI ⩽ −1.3), P(SNDVI < 0|STI > 1.3), and P(SNDVI < 0|SPI ⩽ −1.3, STI > 1.3) can be derived to estimate the impact of dry, hot, and compound dry-hot conditions on vegetation decline. Following Ribeiro et al (2020a), the conditional probability of vegetation decline given individual dry, individual hot, and compound dry and hot condition can be expressed as:

$$\begin{align}&{\text{P}}\left( {{\text{SNDVI}}< 0|{\text{SPI}} \le - 1.3} \right) \nonumber \\ & \quad = \frac{{{\text{P}}({\text{SNDVI}} < 0,{\text{SPI}} \le - 1.3)}}{{{\text{P}}\left( {{\text{SPI}} \le - 1.3} \right)}} \end{align} \tag{ 2 }$$

$$\begin{align} & {\text{P}}\left( {{\text{SNDVI}}< 0 |{\text{STI}}>1.3} \right) \nonumber \\ & \quad = \frac{{{\text{P}}({\text{SNDVI}} < 0) - {\text{P}}({\text{SNDVI}} < 0,{\text{STI}} \le 1.3)}}{{1 - {\text{P}}\left( {{\text{STI}} \le 1.3} \right)}}\end{align} \tag{ 3 }$$

$$\begin{equation}{\text{P}}\left( {{\text{SNDVI}}<0| {{\text{SPI}} \le - 1.3,{\text{STI}}>1.3} } \right) = \frac{{{\text{P}}({\text{SNDVI}} < 0,{\text{SPI}} \le - 1.3) - {\text{P}}({\text{SNDVI}} < 0,{\text{SPI}} \le - 1.3,{\text{STI}} \le 1.3)}}{{{\text{P}}\left( {{\text{SPI}} \le - 1.3} \right) - {\text{P}}\left( {{\text{SPI}} \le - 1.3,{\text{STI}} \le 1.3} \right)}}\end{equation} \tag{ 4 }$$

Note that if we assume statistical independence between climate extremes and vegetation, the conditional probability of the SNDVI < 0 is expected to be 0.5 (i.e. SNDVI follows the standard normal distribution). A positive (negative) impact of extremes on vegetation is expected to lead to a decreased (increased) probability of vegetation decline through comparisons with the probability of the independent case (0.5).

To show the interaction between climate conditions and vegetation during growing seasons, correlation coefficients between the SNDVI and SPI (STI) from 1982 to 2015 are shown in figure 1 (significant correlation coefficients at the 0.05 significant level are shown in figure S3). For northern high latitude regions, the correlation between the SNDVI and SPI is not significant, while that between the SNDVI and STI is mostly positive. This is consistent with previous studies showing that precipitation–vegetation correlations are relatively weak for cold regions, while positive temperature–vegetation correlations are generally present in these areas (e.g. Eurasian tundra or high latitudes regions) (Karnieli et al 2010, Wu et al 2015). A possible reason for the dependence pattern in these high latitude regions is that vegetation growth is mainly influenced by energy (or temperature) (Nemani et al 2003, Papagiannopoulou et al 2017). In tropical regions, complicated correlation patterns between climate variables and vegetation are shown. For example, positive STI-SNDVI correlations exist in certain regions, such as central Africa and northern South America, while negative STI-SNDVI correlations are shown in northeast South America. These correlation patterns may be related to different vegetation types and the critical role of radiation in the tropics (Nemani et al 2003, Zhao et al 2018, Wen et al 2019a).

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Figure 1 also shows positive correlations between SNDVI and SPI in central North America, southern South America, southern Africa, central Eurasia, and Australia, most of which are arid and semi-arid regions. In addition, a negative SNDVI-STI correlation is shown for most of these regions. These correlation patterns imply that vegetation is affected by both dry conditions and hot conditions (or their combinations) in arid and semi-arid regions, which are generally consistent with previous studies (Zeng et al 2013, Wu et al 2015, Zhao et al 2018, Xie et al 2019, Wen et al 2019a). An explanation may be that water availability is the restricted condition for vegetation activity in arid and semi-arid regions and biomes react rapidly when water deficits occur (Ichii et al 2002, Fensholt et al 2012, Vicente-Serrano et al 2013, He et al 2018, Fang et al 2019a). In these regions, warm temperatures and accompanying high evapotranspiration may result in a soil moisture deficit and further aggravate the severity of dry conditions, leading to simultaneous occurrences of dry and hot extremes that influence vegetation growth (Zscheischler et al 2015, Zscheischler and Seneviratne 2017, Hao et al 2018, Sippel et al 2018, Miralles et al 2019). Over global land areas, the concurrence of positive SNDVI-SPI and negative SNDVI-STI correlations was shown in 31.06% of all grid points (significant correlations are shown in 6.44% of all grid points). These results highlight the importance of considering the concurrent impacts of droughts and hot extremes on vegetation.

Figure 2 shows boxplots of correlation coefficients for four different climate regions (arid, semi-arid, semi-humid, and humid regions). For humid regions (including areas of tropical rainforest and high latitude of the northern hemisphere), 75.13% of grid points showed a positive relationship between the SNDVI and STI (with a median of 0.23), while the correlation coefficients between the SNDVI and SPI range from −0.73 to 0.75 (with a median of 0.02), which reflects the complex relationship between dry conditions and vegetation in these regions (Wen et al 2019a). For the arid (and semi-arid) regions, the median of the SNDVI-SPI correlation is 0.27 (0.35) and that of the SNDVI-STI correlation is −0.17 (−0.13). These results indicate that vegetation in these regions is affected by dry and hot conditions, and thus both factors need to be considered in evaluating the relationship between climate variability and vegetations. For semi-humid regions, positive SNDVI-SPI correlations are shown (with a median of 0.17) with complex correlation patterns between SNDVI and STI (i.e. with a median of 0.08).

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Based on the correlation analysis, we then employed the proposed model for the probabilistic analysis of the impact of compound dry and hot events on vegetation. We showed the results at one grid (21.25° E, 28.75° S) in southern Africa to illustrate the application of the proposed model. For the selected grid, the meta-Gaussian model was built to fit the SPI, STI, and SNDVI. The scatterplots of the simulated and observed SPI-STI, SPI-SNDVI, and STI-SNDVI correlations are shown in figures 3(a)–(c). A negative correlation exists for the SPI-STI and STI-SNDVI pairs, while a positive correlation is shown for SPI-SNDVI. Based on the proposed model, the simulated pairs of SPI, STI, and SNDVI are shown in figure 3. The consistent pattern of dependence structures for simulation and observation indicates that the proposed model generally performs well in modeling dependence among the SPI, STI, and SNDVI. Additionally, the empirical and theoretical estimations of the joint probability of SPI-STI, SPI-SNDVI, and STI-SNDVI are shown in figure S4, which confirms the overall good performance of the proposed model for this grid point. The meta-Gaussian model was then applied to assess the impacts of compound dry-hot conditions on vegetation. Following Ribeiro et al (2020a), the joint probabilities of the vegetation decline given different levels of dry and hot conditions are shown in figure 3(d). The results indicate an increase in vegetation decline with the increased severity of the compound dry-hot condition for this grid.

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The conditional probabilities of SNDVI < 0 given individual dry conditions (SPI ⩽ −1.3) and individual hot conditions (STI > 1.3) during growing seasons are shown in figures 4(a) and (b), respectively. In high latitude regions, the conditional probability of vegetation decline given dry conditions is close to the probability of the independent case. These results demonstrate that vegetation in this region is not significantly dependent on precipitation. Meanwhile, hot conditions lead to a lower probability of vegetation decline (<0.5). An explanation is that temperature is the limiting factor in biomass production in high latitude regions, and sufficient heat conditions have positive effects on vegetation during growing seasons. For certain tropical regions (such as the Amazon area), a slight increase in the conditional probability for vegetation decline given dry conditions is observed. The probability is generally higher than that of the independence case (0.5), demonstrating the effects of dry conditions on vegetation growth in tropical regions. For large regions in central North America, southern South America, southern Africa, central Eurasia, and Australia, higher conditional probabilities of vegetation decline (>0.5) given dry or hot conditions are observed. These results indicate that increased dry conditions or heat stresses induce an increased probability of vegetation decline in these regions.

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Figure 5 demonstrates, via boxplots, the conditional probability of vegetation decline over different climate regions. These probability patterns are closely related to the correlation pattern in section 3.1. Specifically, the positive (negative) correlation between SPI and SNDVI indicates a higher (lower) likelihood of vegetation reduction under dry conditions. Similarly, the positive (negative) STI-SNDVI correlation indicates a lower (higher) likelihood of vegetation decrease under high temperatures. For example, for humid regions (medians of SPI-NDVI and STI-NDVI correlations are 0.01 and 0.23), the median conditional probabilities of P(SNDVI < 0|SPI ⩽ −1.3) and P(SNDVI < 0|STI > 1.3) are 0.51 and 0.32, respectively. This indicates that the median of the probability of vegetation decline given dry conditions is close to the independent case, and that given hot condition is lower than that of the independent case. In contrast to humid regions, higher conditional probabilities of vegetation decline given dry or hot conditions are shown in arid and semi-arid regions. The median conditional probabilities of individual dry and hot conditions are 0.70 and 0.62 in arid regions (0.75 and 0.60 in semi-arid regions), which are considerably higher than those of the independent case, indicating that vegetation in these arid regions is affected by dry and hot conditions (Ji and Peters 2003, Kalisa et al 2019).

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To illustrate the impact of both dry and hot conditions on vegetation, we also computed the conditional probability of vegetation decline (SNDVI < 0) under combined water and heat stresses (i.e. SPI ⩽ −1.3 and STI > 1.3), and compared it with that from individual dry and hot conditions. The conditional probability P(SNDVI < 0|SPI⩽ −1.3, STI > 1.3) during growing seasons at the global scale is shown in figure 4(c). For high latitude regions, there is a substantial decrease in the probability of vegetation decline given compound dry and hot conditions compared with individual dry conditions. This is because, with weak SPI-NDVI correlations in these regions, hot conditions could favor vegetation growth, reducing the probability of vegetation decline. For large regions in central North America, southern South America, southern Africa, central Eurasia, and Australia, the conditional probability of vegetation decline under compound dry and hot conditions is relatively higher than that under individual dry or hot conditions (figure S5).

For the four climate divisions, the conditional probability of vegetation decline is relatively higher in arid and semi-arid regions (compared with the humid region) since the vegetation in these regions is influenced by dry conditions as well as heat stresses. Specifically, the medians of conditional probabilities of vegetation decline given SPI ⩽ −1.3 and STI > 1.3 in the arid, semi-arid, semi-humid, and humid regions are 0.77, 0.78, 0.56, and 0.34, respectively. For all grid points in arid and semi-arid regions, the average of the conditional probabilities under dry conditions, hot conditions, and compound dry-hot conditions are 0.73, 0.61, and 0.78, respectively. These results indicate that the probability of vegetation decline under compound dry-hot conditions increased by approximately around 7% and 28%, respectively, compared with that under individual dry and hot conditions, in arid and semi-arid regions.

Due to the differences in the physiological structure of vegetation, the sensitivity and vulnerability of ecosystems are expected to vary for different dry and hot conditions (Komatsu et al 2007, Liu et al 2013, He et al 2015, Zhang et al 2015, Gazol et al 2016). In this section, we discuss differences in the response of major vegetation types to extreme events, with focus on forest and grassland ecosystems. To demonstrate the relationship between climate conditions and different vegetation types during growing seasons, boxplots of correlation coefficients for SNDVI and SPI (STI) for different vegetation types are shown in figure 6(a). In addition, the conditional probabilities of vegetation decline under dry or hot conditions for different vegetation types are shown in figure 6(b).

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For the forest ecosystem, a wide range of the correlation patterns between SPI and SNDVI is shown. Slightly positive correlations between the SPI and SNDVI are observed for tropical/subtropical forests and temperate broadleaf forests (the medians of the correlation coefficients are 0.08), as shown in figure 6(a). Meanwhile, negative SPI-SNDVI correlations are shown in several areas, such as certain Amazon regions, which is likely due to the reason that high temperature and radiation during dry periods can promote photosynthesis (Hilker et al 2014, Zhao et al 2017, Zhang and Zhang 2019). The median probabilities of vegetation decline given dry conditions for the tropical and subtropical forests and temperate broadleaf forests are 0.56 (slightly higher than that of the independent case). The SPI-SNDVI correlation for the temperate coniferous forest is close to zero (with a median of −0.03), and the conditional probability under drought conditions is complex without a clear pattern. Regarding the correlations between the STI and SNDVI in forest ecosystems, we found that large portions of grid points presented positive correlations. This positive STI-SNDVI correlation in the temperate forest is generally higher than that in the tropical and subtropical forests, as shown in figure 6(a). Accordingly, a lower probability of vegetation decline (<0.5) given hot conditions is found for temperate coniferous forests and temperate broadleaf forests (e.g. probabilities are 0.33 and 0.37, respectively) (see figure 6(b)). This is consistent with previous studies that hot extreme can promote vegetation production during growing seasons for temperate forest ecosystems (Zscheischler et al 2014, Wu et al 2015, Zhang et al 2015, Papagiannopoulou et al 2017). Given compound dry and hot conditions, a large portion (59.78%) of temperate coniferous forests and temperate broadleaf forests shows a low probability of vegetation decline (<0.5), which mainly resulted from the overall positive STI-SNDVI relationship (and a weak SPI-SNDVI correlation).

Grassland ecosystems are sensitive to spatial-temporal changes in climate factors such as temperature and precipitation (Seddon et al 2016). We found that large portions of grid points presented positive correlations between the SPI and SNDVI for tropical and subtropical grasslands and temperate grasslands, as shown in figure 6(a) (e.g. medians of SPI-SNDVI correlations for the two ecosystems are 0.26 and 0.25, respectively). The SPI-SNDVI correlation for grasslands is generally much stronger than for forests. Accordingly, the probability of vegetation decline for the tropical and subtropical grasslands and temperate grasslands under dry conditions is much higher than that of the independent case (with a median of 0.69 and 0.68, respectively). A possible reason is that, compared to forests, grasslands obtain water from a shallower soil layer (thus vulnerable to water stress); while trees have greater drought adaptation abilities due to their access to water at deeper depths (Nicolai-Shaw et al 2017, Zhang and Zhang 2019). The STI-SNDVI correlation over large portions of grid points is negative for temperate grasslands, and the probability of vegetation decline given hot conditions is 0.55, which is slightly higher than that of the independent case. The relationship of STI and SNDVI for tropical and subtropical grasslands is close to the independent case. Under compound dry and hot conditions, large regions of grasslands show a higher probability of vegetation decline than that under individual dry or hot conditions. For example, the medians of conditional probabilities of vegetation decline given dry, hot, and compound dry-hot conditions are 0.68, 0.55, and 0.70, respectively, for temperate grasslands (see figure 6(b)). Furthermore, we notice the highest probability under compound dry and hot events is shown for temperate grasslands among all the vegetation types. These results indicate a high risk of vegetation loss for grassland ecosystems under compound dry and hot conditions, especially for temperate grasslands.

Following the studies by Ribeiro et al (2020a), the changes in the probability of vegetation decline from individual dry (hot) conditions to compound dry-hot conditions (SPI ⩽ −1.3 and STI > 1.3) imply the relative impact of hot (dry) conditions on vegetation. For example, the probability of vegetation decline given dry conditions, hot conditions, and compound dry-hot conditions for temperate conifer forests are 0.47, 0.33, and 0.34. Accordingly, the change of vegetation decline from dry to compound dry-hot conditions is −0.13 and from hot to compound dry-hot conditions is 0.01. This indicates that the relative impact of hot conditions on temperate conifer forests is higher than that of dry conditions. For temperate grasslands, the changes in the probability of vegetation decline from individual dry and hot conditions to compound conditions for temperate grassland are 0.02 and 0.15, respectively, implying that dry conditions have higher impacts on vegetation decline. This is consistent with previous studies showing the dominant effect of precipitation or drought on grassland productivity (Lu et al 2021).