For each grid cell, the SEDI in this study is defined as the standardized anomalies of the difference between AET and PET, as follows:
where D is the difference between AET (mm) and PET (mm), and DAVE and DSTU denote the multi-year mean and standard deviation, respectively. This approach can highlight dry and wet conditions by detecting local water storage changes, compared with direct evapotranspiration (Chattopadhyay and Hulme, 1997; Kim and Rhee, 2016; Vicente-Serrano et al., 2018). In terms of ecophysiology, the evapotranspiration deficit can explicitly account for the potential of the atmosphere (PET), but also the water actually lost from soil or vegetation (AET), which involves the physiological behavior of vegetation (Leuning, 1995). If the difference becomes large enough to lower soil moisture below wilting point, plants may die as a result of vascular damage (Anderegg et al., 2015).
Additionally, we adopted a percentile approach (Svoboda et al., 2002) to classify SEDI dry and wet conditions (Table 1). SEDI values from −0.8 to 0.8 denote dry (negative values) and wet (positive values) conditions. The larger the absolute value, the stronger the dry and wet intensity.
Drought condition Percentile chance (k) SEDI scPDSI SPEI/ SPI Extreme k ≤ 5 ≤ −0.8 ≤ −4 ≤ −2 Severe 5 < k ≤ 10 −0.8 to −0.63 −4 to −3 −2 to −1.5 Moderate 10 < k ≤ 20 −0.63 to −0.42 −3 to −2 −1.5 to −1 Slightly 20 < k ≤ 30 −0.42 to −0.26 −2 to −1 −1 to −0.5 Normal 30 < k ≤ 70 −0.26 to 0.27 −1 to 1 −0.5 to 0.5 Wet k > 70 > 0.27 > 1 > 0.5
Table 1. Categories of drought magnitude corresponding to four drought indices.
The AET data were derived from the observation-based FLUXNET-MTE (Model Tree Ensemble) and reanalysis data of ERA-Interim and CFSR (Climate Forecast System Reanalysis). The PET data were from CRU-TS3.23 (Climate Research Unit) and CFSR. These datasets were at a monthly temporal resolution and 0.5° × 0.5° spatial resolution during 1982–2011. The gridded FLUXNET-MTE dataset was taken from Jung et al. (2009), which integrated the observations from global 253 FLUXNET eddy covariance towers by a machine learning technology, the MTE algorithm. Its evapotranspiration data have been verified against observations from FLUXNET sites, estimates from 112 catchment water balances, and simulations of 16 land surface models in GSWP-2 (Global Soil Wetness Project 2), with correlation coefficients over 0.9 (Jung et al., 2010). The gridded dataset is incomplete over the Sahara Desert and Greenland, due to the lack of in-situ observations. For assessment purposes, we estimated SEDI using averaged AET from FLUXNET-MTE and ERA-Interim, which have high temporal and spatial consistency (Zhang et al., 2018), along with PET from CRU-TS3.23 (hereafter known as AVG-SEDI). The estimate based on AET and PET, both from CFSR, is referred to as CFSR-SEDI.
Three drought indices (scPDSI, SPI, and SPEI) were used to compare with SEDI. These monthly datasets for 1982–2011 are available at 0.5° spatial resolution for SPEI, and 2.5° for scPDSI and SPI. Table 1 shows the details of SEDI, scPDSI, SPI, and SPEI classifications. The scPDSI, SPI, and SPEI were obtained from NCAR’s Research Data Archive, NOAA–NCEP Climate Prediction Center, and SPEIbase v2.5, respectively. The scPDSI was derived from PDSI by calibration with local conditions (Wells et al., 2004). The calculation of SPEI was the same as that of the SPI algorithm except that SPEI used the difference between precipitation and PET instead of precipitation anomalies. The scPDSI and SPEI were calculated using the CRU high-resolution surface climate dataset of the University of East Anglia, except that the precipitation data used to calculate the scPDSI were from the Global Precipitation Climatology Project (GPCP). The SPI was calculated by gauge-satellite-merged precipitation datasets, with the difference from GPCP being less than 10% for nearly the whole land area (Janowiak and Xie, 1999). The gridded CRU and GPCP datasets are in good agreement at low–middle latitudes (Decharme and Douville, 2006), and have high temporal correlations, especially in all semi-arid regions (Los, 2015). In addition, a surface wetness index defined as the ratio of annual accumulated precipitation to PET, whose datasets are both from CRU-TS3.23, was used to determine the dry and wet climatic boundary.
The leaf area index (LAI) dataset has an 8-km spatial resolution and 15-day interval from the year 1981 onwards. The dataset was derived from GIMMS LAI3g (the third-generation Global Inventory Modeling and Mapping Studies LAI product), which is considered suitable to estimate the long-term LAI variability (Zhu et al., 2013). Here, we bilinearly interpolated the LAI data to 0.5° × 0.5° resolution. The land-use and land-cover data for the year 2011 at 500-m horizontal resolution were obtained from the Moderate Resolution Imaging Spectroradiometer (Friedl et al., 2010). Monthly soil moisture, and temperature and precipitation with 0.5°×0.5° spatial resolution during 1982–2011 were obtained from ERA-Interim and CRU-TS3.23, respectively.
Due to the lack of long-term AET observations at the global scale, we estimated AET using the latent heat flux data, according to a theoretical linear function (Jacobson, 2005; Lorenz and Kunstmann, 2012):
where AET is in units of mm, the latent heat flux λE (units: W m−2) refers to the latent heat released as water evaporates, and the latent heat of evaporation Le is the energy variation as the water phase changes, which is taken as a constant (2.501 × 106 J kg−1).
The main statistical methods used here are the Pearson correlation coefficient and least-squares linear trend estimation. We tested the significance of correlation using the Student’s t-test and that of linear trends using the F-test.
2.1. Definition of SEDI
2.3. Estimation of AET and statistical methods
It is difficult to obtain perfect datasets because of the uncertainties associated with the evapotranspiration datasets used, especially the estimate of AET, the sparse and uneven spatial distribution of AET observation (Zhang et al., 2016; Zhu et al., 2016), and the various models used for reanalysis data (Su, 2016). For this reason, we used several datasets to cross-examine the performance of SEDI in capturing dry and wet variations and climate–vegetation interactions.
We evaluated the capability of SEDI to characterize dry and wet variations at both global and regional scales. Globally, we divided the land into five regions: South America, Africa, Australia, and two areas in North America and Eurasia south of 60°N. Figure 1 shows the dynamics of SEDI and four reference indices (scPDSI, SPI, SPEI, and soil moisture) over these five regions. SEDI had consistent interannual variations and long-term trends with the reference indices, according to the Pearson’s correlation coefficient analysis (Table 2). The two SEDI estimates had a significant correlation and comparable linear trends with the reference indices (Table 3), suggesting similar skill of SEDI to the reference indices in depicting interannual variations and long-term trends. According to the long-term trends, the SEDI values in North America and Eurasia were negative, similar to the reference indices, denoting a drying climate, whereas all indices in Africa presented wetting trends. Moreover, the coefficients of CFSR-SEDI, SPI, and SPEI were positive in South America, while the AVG-SEDI, scPDSI, and soil moisture were opposite; the coefficients of AVG-SEDI, SPI, and soil moisture were negative in Australia, but the CFSR-SEDI, scPDSI, and SPEI were non-significantly positive. The highest consistency between SEDI and the reference indices was achieved in Australia, with a correlation coefficient up to 0.90. This was largely related to the uniform climate (about 70% of Australia is shared by arid and semi-arid climates). Furthermore, this suggests that SEDI is sensitive to the dry and wet variations over arid and semi-arid regions. A remarkable difference can be seen between SEDI and the reference indices as dry and wet signals weaken; for example, in the year 1999 in North America, and 1992 in South America. However, high consistency was observed for periods with strong dry and wet signals, such as 1984 in Africa and 2000 in South America. These discrepancies indicate that SEDI can comparably detect extreme dry and wet climatic fluctuations at a global scale, but also sensitively sense the effects of land processes because the contribution from land processes was enhanced during weak dry and wet periods.
Figure 1. Temporal evolutions of standardized SEDI and four reference indices (scPDSI, SPI, SPEI, and soil moisture) in (a) North America, (b) South America, (c) Africa, (d) Eurasia, and (e) Australia during 1982–2011.
Dataset North America South America Africa Eurasia Australia scPDSI AVG −0.07 0.15 0.59* 0.20 0.60* CFSR 0.70* −0.0003 0.31 0.24 0.90* SPI AVG −0.03 −0.21 0.39* 0.37* 0.62* CFSR 0.68* 0.21 0.44* 0.22 0.79* SPEI AVG 0.05 −0.29 0.46* 0.16 0.41* CFSR 0.69* 0.30 0.26 0.12 0.79* Soil moisture AVG −0.02 0.57* 0.35 0.73* 0.73* CFSR 0.41* −0.19 −0.29 0.10 0.86* Note: * represents value significant at 95% confidence level.
Table 2. Correlation coefficients between SEDI and four reference indices for five continents during 1982–2011.
North America South America Africa Eurasia Australia AVG-SEDI −0.10 −1.01* 0.04 −1.12* −1.94 CFSR-SEDI 0.21 1.87* 0.45 −0.48* 1.12 scPDSI −0.006 −0.02* 0.01 −0.002 0.006 SPI −0.001 0.003 0.001 −0.001 −0.001 SPEI −0.003 0.01 0.01* 0.001 0.01 Soil moisture (×10−3) −0.33* −0.27* −0.24* −0.24* −0.02 Note: * represents value significant at 95% confidence level.
Table 3. Linear trend coefficients (yr−1) of SEDI and four reference indices for five continents during 1982–2011.
At regional scales, we evaluated SEDI in four regions of China (Fig. 2e), which were located over transitional zones that have frequent droughts (Ma and Shao, 2006; Huang et al., 2012). The temporal evolutions of SEDI, along with the four reference indices, in these four regions (Figs. 2a–d) show the significantly positive correlations between CFSR-SEDI and reference indices, especially in Northeast China, where the coefficient reached 0.74 (Table 4). Both the AVG-based and CFSR-based SEDI datasets had consistent annual variations and long-term trends, but with different significances of the trend coefficients; for example, only the AVG-SEDI and scPDSI in North China were significant at the 95% level (Table 5). Similar to that at the global scale, the consistency of SEDI and the reference indices was lower during periods of weak dry and wet signals, such as the year 1984 in eastern Northwest China, in comparison to that of strong signals such as 2001 in North China. This variation is largely attributable to effects exerted by land processes, such as vegetation.
Figure 2. As in Fig. 1 but for (a) eastern northwest China, (b) North China, (c) Northeast China, and (d) Southwest China. The rectangles in (e) denote the four regions, and the contours represent the spatial distribution of the mean annual precipitation during 1982–2011.
Dataset Eastern Northwest North Northeast Southwest scPDSI AVG 0.31 0.32 0.32 0.36 CFSR 0.73* 0.65* 0.74* 0.68* SPI AVG 0.23 0.06 0.51* 0.26 CFSR 0.42* 0.32 0.43* 0.23 SPEI AVG 0.27 0.13 0.25 0.15 CFSR 0.60* 0.67* 0.65* 0.08 Soil moisture AVG 0.07 0.46* 0.25 0.17 CFSR 0.54* 0.41* 0.64* 0.41* Note: * represents value significant at 95% confidence level.
Table 4. As in Table 2 but for four typical regions of China.
Eastern Northwest North Northeast Southwest AVG-SEDI 0.01 −1.93* −0.81 −1.24* CFSR-SEDI 0.67 −0.59 −1.9* −1.45* scPDSI 0.01 −0.06* −0.06* −0.11* SPI 0.01* 0.01 0.0001 −0.01* SPEI 0.01 −0.003 −0.03* 0.01 Soil moisture (×10−3) 0.52* −0.24 −0.75* −0.07 Note: * represents value significant at 95% confidence level.
Table 5. As in Table 3 but for four typical regions of China.
This analysis aimed to confirm that the evapotranspiration-based SEDI is more closely related to the physiological response of vegetation to the evolution of drought than commonly used indices based on factors other than evapotranspiration. We compared the performance of each drought index in describing drought impacts on vegetation growth, using LAI. In addition, because of their similar skill in drought detection, we averaged the CFSR-SEDI and AVG-SEDI into one index, known as FNL-SEDI hereafter.
On the global scale, we evaluated the sensitivity of vegetation growth to dry and wet variations in each index. Figure 3 shows the spatial patterns of correlation coefficients between the five indices and LAI in the growing season (spring, summer, and autumn). The correlation coefficients between SEDI and LAI in most areas were over 0.4 (p < 0.05). In contrast, the correlations between the reference indices and LAI were substantially lower with fewer significant grid cells (p < 0.05). The spatial pattern of correlation between SEDI and LAI was largely the same as that between soil moisture and LAI, which indicates that SEDI can detect stronger signals from land processes as they respond to dry and wet climatic variations. Furthermore, the correlation patterns between SEDI and LAI showed seasonality. In spring and autumn, negative correlations occurred in areas north of 30°N and south of 30°S, but positive correlations were found in low latitudes; in summer, as temperature increased, positive correlations occurred in most areas of the world. A potential reason for this contrast is the different response times of various vegetation types to dry and wet variations (Braswell et al., 1997; Adams et al., 2009).
Figure 3. Global spatial patterns of correlation coefficients between LAI and (a) SEDI, (b) soil moisture, (c) SPEI, (d) SPI, and (e) scPDSI in spring (MAM), summer (JJA), and autumn (SON) during 1982–2011. Hatched areas denote the 95% confidence level. Black curves (surface wetness index equal to 0.5) denote the arid and semi-arid boundary.
From the perspective of vegetation type, we further quantified the sensitivity of the vegetation response to droughts detected by the four indices in forest, cropland, and grassland regions (Fig. 4a). Table 6 shows the correlation coefficients of the drought indices (CFSR-SEDI, AVG-SEDI, FNL-SEDI, scPDSI, SPEI, SPI, and soil moisture) and LAI in spring, summer, and autumn from 1982 to 2011. In forest, SEDI and LAI in spring, summer, and autumn had significant negative correlations, especially spring and autumn, with most coefficients more than −0.7. The maximal correlation coefficients occurred in the spring (−0.83). In contrast, the reference indices showed smaller correlation coefficients. In cropland, SEDI was significantly correlated with LAI throughout the growing season, with coefficients over 0.65, whereas the reference indices had weak correlation coefficients with LAI, with a maximum of 0.22. In grassland, the correlation showed a clear seasonality (negative correlations in spring and autumn, and positive correlations in summer). The correlation coefficients were over 0.75 between SEDI and LAI, whereas a significant correlation between the reference indices and LAI was only observed in summer. Similarly, soil moisture and LAI were significantly correlated and with a spatial pattern similar to that of SEDI. As a result, from a global perspective, SEDI can more sensitively detect the response of vegetation growth to dry and wet variations than the reference indices, but the sensitivity varies with vegetation types.
Figure 4. Spatial distribution of global land use/land cover for the (a) global scale and (b) regional scale. The rectangles denote three selected typical vegetation cover areas.
Spring (MAM) Summer (JJA) Autumn (SON) Forest Cropland Grassland Forest Cropland Grassland Forest Cropland Grassland CFSR-SEDI −0.83* 0.80* −0.80* −0.47* 0.71* 0.44* −0.66* 0.74* −0.90* AVG-SEDI −0.76* 0.81* −0.75* −0.05 0.65* 0.04 −0.74* 0.43* −0.91* FNL-SEDI −0.83* 0.82* −0.83* −0.23* 0.68* 0.17 −0.80* 0.6* −0.93* scPDSI −0.14 0.06 −0.04 −0.36* −0.08 0.40* −0.13 0.22* −0.09 SPI 0.02 −0.05 −0.07 −0.35* 0.06 0.19 −0.08 0.03 −0.05 SPEI −0.02 0.12 0.02 −0.24* 0.07 0.52* −0.09 0.20 0.03 Soil moisture −0.89* −0.13 −0.67* −0.44* 0.66* 0.21 −0.59* 0.71* −0.61* Note: * represents value significant at 95% confidence level.
Table 6. Correlation coefficients between LAI and drought indices (CFSR-SEDI, AVG-SEDI, FNL-SEDI, SPEI, SPI, scPDSI, and soil moisture) for forest, cropland, and grassland at a global scale in spring, summer, and autumn during 1982–2011.
We further evaluated the performance of SEDI at regional scales. Figure 5 shows the spatial pattern of correlation of the drought indices versus LAI across China in the growing seasons. SEDI had a significant correlation with LAI in most areas of China, but much less correlation passing the 95% confidence level between the references and LAI. The correlation of SEDI versus LAI also showed clear seasonality; negative (positive) correlations occurred in areas north (south) of 33°N in spring and autumn, whereas many more positive correlation coefficients occurred in summer. The difference stemmed from SEDI and soil moisture becoming more distinct compared with those at the global scale. The humid and semi-humid areas in spring and summer presented positive correlations between SEDI and LAI, but negative for soil moisture; the arid and semi-arid areas in autumn presented negative correlations for SEDI, whereas they were positive for soil moisture.
Figure 5. As in Fig. 3 but for China.
Regarding vegetation effects on regional scales, for three typical vegetation types (Fig. 4b), we compared the correlation coefficients of drought indices versus LAI in spring, summer, and autumn (Table 7). In forest, significant correlation coefficients between SEDI and LAI were found throughout the growing seasons; in cropland, significant correlation coefficients were observed in spring and summer; and significant negative values were found in grassland regions in spring and autumn, but positive values in summer. In contrast, the correlation between the reference indices and LAI was non-significant in all regions and seasons.
Spring (MAM) Summer (JJA) Autumn (SON) Forest Cropland Grassland Forest Cropland Grassland Forest Cropland Grassland CFSR-SEDI 0.51* −0.24* −0.77* −0.01 0.73* 0.71* 0.41* 0.3* −0.53* AVG-SEDI 0.54* 0.04 −0.89* 0.28* 0.76* 0.81* 0.61* 0.58* −0.66* FNL-SEDI 0.64* −0.1 −0.9* 0.27* 0.80* 0.82* 0.66* 0.55* −0.67* scPDSI −0.1 0.05 0.05 −0.1 −0.03 −0.02 −0.09 −0.05 −0.02 SPI −0.01 0.03 0.002 −0.18 0.03 0.15 −0.12 −0.04 0.03 SPEI −0.01 −0.01 0.04 0.09 −0.02 0.17 0.04 −0.01 0.06 Soil moisture 0.22* −0.01 −0.52* −0.26* 0.58* 0.57* 0.15 0.35* 0.42* Note: * represents value significant at 95% confidence level.
Table 7. As in Table 4 but for forest, cropland, and grassland in China at a regional scale.
We classified SEDI using a percentile approach (section 2.3). The dry and wet classifications were then used in Southwest China to examine the performance of SEDI in describing the heavy drought process and vegetation responses. The annual temporal evolution of SEDI is shown in Fig. 6. The SEDI values in 2006 and 2010 were −0.42 and −0.64, respectively, and in the dry and wet classifications (Table 1) they fell into moderate and severe droughts. Figures 7a and b show the spatial distributions of the SEDI and LAI anomalies during the 2010 severe drought. The SEDI values in the southwest increased gradually, indicating expansion in both the range and intensity of severe drought, as shown in previous studies (Li et al., 2009; Qian et al., 2011; Huang et al., 2012). The LAI sensitively followed the spatiotemporal evolution of drought detected by SEDI. The range and intensity of vegetation browning correspondingly increased, up to the autumn of 2010, and then the relief of the drought stress accelerated the recovery of vegetation from drought disturbance. The monthly time series (Fig. 7c) illustrates that SEDI presented a downward trend after September 2009, and by January to April of 2010 the drought signal occurred when the SEDI values were less than −0.26. In particular, the value in May was −0.82, denoting an extreme drought. Accordingly, vegetation browning occurred from mid-February to July of 2010 when the LAI values presented negative anomalies. The minimum LAI negative value of −0.51 occurred in March, and it corresponded to the minimum SEDI. As such, SEDI was able to regenerate the entire drought evolution process at the monthly scale, and clearly characterize the response of vegetation growth to dry and wet variations.
Figure 6. Temporal evolution of SEDI over Southwest China (21°–30°N, 95°–110°E) during 1982–2011. The y-axis is the dry and wet classification of SEDI (Table 1). The black dotted line denotes a −0.26 threshold for drought events.
Figure 7. Spatial distributions for standardized seasonal values of (a) SEDI and (b) LAI with the annual cycle removed during 2009–10. The rectangles denote Southwest China. (c) intra-annual time series of SEDI and LAI with the annual cycle removed during 2009–10. The red dotted line denotes the −0.26 threshold for drought events, and the blue dotted line denotes vegetation growth, with below or above zero indicating poor or good growth, respectively.