The impact of droughts on vegetation is essentially manifested as the transition of water shortage from the meteorological to ecological stages. Therefore, understanding the mechanism of drought propagation from meteorological to ecological drought is crucial for ecological conservation. This study proposes a method for calculating the probability of meteorological drought to trigger ecological drought at different magnitudes in northwestern China. In this approach, meteorological and ecological drought events during 1982–2020 are identified using the three-dimensional identification method; the propagated drought events are extracted according to a certain spatiotemporal overlap rule, and propagation probability is calculated by coupling the machine learning model and C-vine copula. The results indicate that (1) 46 drought events are successfully paired with 130 meteorological and 184 ecological drought events during 1982–2020, and ecological drought exhibits a longer duration but smaller affected area and severity than meteorological drought; (2) a quadratic discriminant analysis (QDA) classifier performs the best among the 11 commonly used machine learning models which are combined with four-dimensional C-vine copula to construct the drought propagation probability model; and (3) the hybrid method considers more drought characteristics and a more detailed propagation process which addresses the limited applicability of the traditional method to regions with large spatial extent.
Drought is a multivariable and complex natural hazard with the characteristics of slow evolution, wide impact, and spatial extent (Feng et al., 2021; Wu et al., 2021; Zhang et al., 2021a, b). Conventionally, drought can be classified into meteorological drought, hydrological drought, agricultural drought, and socioeconomic drought. It is commonly accepted that all types of drought originate from meteorological drought (Mishra and Singh, 2010). Crausbay et al. (2017) argued that existing drought types are described through a “human-centric” lens to characterize a range of effects generated by meteorological drought. This implies that the response of the ecosystem to drought is generally ignored in policy development, which in turn elicits water use conflicts between humans and ecosystems (J. Zhang et al., 2021). The Ecological Drought working group of Science for Nature and People Partnership (SNAPP) proposed a framework of ecological drought from an “ecology-centric” lens, which incorporates ecological, meteorological, and hydrological information (Crausbay et al., 2017). Ecological drought was thus defined as an episodic deficit in water availability that drives ecosystems beyond thresholds of resilience into a vulnerable state, impacts ecosystem services, and triggers feedback in natural and/or human systems (Bradford et al., 2020; Crausbay et al., 2017; McEvoy et al., 2018; Munson et al., 2021; Raheem et al., 2019).
Vegetation is among the most important components in terrestrial ecosystems, and the distribution and growth of vegetation are largely influenced by meteorological factors (Wang et al., 2021; Zeng et al., 2020; Z. Zhang et al., 2021). Developments in remote sensing technology have facilitated the application of vegetation indices to reflect the response of vegetation to climate change (Lawal et al., 2021). For example, a simple linear relationship was found between the standardized precipitation evapotranspiration index (SPEI) and normalized difference vegetation index (NDVI) at a global scale (Vicente-Serrano et al., 2012). The correlation between SPEI and NDVI showed a positive relationship in most regions of northwestern China (NWC), with the exception of a few regions such as the western parts of the Tarim Basin, Qaidam Basin, and southeastern part of the area (Jiang et al., 2018). Actually, the impact of drought on vegetation is manifested as the transition of water shortage from the meteorological stage to the ecological stage. Therefore, this impact should be analyzed by quantifying the effect of decreasing precipitation on the variation of available ecological water, i.e., from the perspective of drought propagation.
Drought propagation refers to the transition of one drought type to another, and it is vital for drought monitoring and prediction (Fang et al., 2020; Warter et al., 2021). Accordingly, drought propagation has become a hot topic in meteorology and hydrology fields (Apurv et al., 2017; Guo et al., 2020). Approaches to drought propagation analysis are broadly divided into model simulations and statistical methods (Han et al., 2019). In the former approach, hydrological responses to meteorological drought are analyzed by using physical-based models that are considered to be effective in representing relevant hydrological processes. Nevertheless, this approach involves labor-intensive calibration processes and is not suitable at large spatial scales (Huang et al., 2017). In contrast, statistical methods with fewer assumptions are easier to use at different spatial scales (Huang et al., 2017). However, in such methods, the propagation process was analyzed using the time series of an average value of drought index in a region or subregion (explained in the Discussion section). In other words, the temporal connection between two drought types is only considered in the traditional statistical methods, but their spatial overlap is ignored, which may result in the miscalculation of drought propagation in regions with large spatial extent.
The probability information of one type of successive drought events is contained in another type of associated drought (Wu et al., 2021). Therefore, a number of studies have attempted to assess the propagation relationships between the two drought types based on the probabilistic method. A Bayesian network is a probabilistic model that acquires probabilistic inferences over interacting variables of interest based on a graphical structure. Therefore, this method has been proven to be suitable for quantifying the probability relationship between different drought types (Ayantobo et al., 2018; Chang et al., 2016; Das et al., 2020). For example, Guo et al. (2020) calculated the occurrence probability of hydrological drought based on different intervals of duration and severities of meteorological drought. Sattar et al. (2019) identified the occurrence probability of different classes and lag times of hydrological drought according to the intensity of meteorological drought. Xu et al. (2021) found that the probability of agricultural drought severity increased synchronously with meteorological drought in different regions of China. Jehanzaib et al. (2020) concluded that in the Korean Peninsula, the probability of meteorological drought propagating into hydrological drought increased significantly under climate change. In general, these studies primarily focused on the relationship between duration and severity between the two drought types but ignored the relationships among affected areas. Xu et al. (2015a) found that the probability of drought occurrence would be underestimated if drought-affected areas are not considered. Therefore, the traditional probabilistic model of drought propagation can be improved by introducing the three-dimensional clustering method, which would provide more drought information (Liu et al., 2019).
Taking a typically ecologically fragile region, northwestern China (NWC), as an example, the motivation of this study is to identify meteorological drought and ecological drought during 1982–2020 in NWC from a three-dimensional perspective, and propose a novel method to investigate the response probability of ecological drought to meteorological drought. The remainder of the current paper is organized as follows: Sect. 2 briefly overviews the geographic information of NWC and describes the datasets used in this paper, and the procedure for estimating propagation probability from meteorological to ecological drought. The results and the comprehensive analysis of the proposed approach are presented in Sects. 3 and 4, respectively. Finally, the conclusions are given in Sect. 5.
Elevation and four divisions of northwestern China.
Northwestern China (NWC; 31
Monthly meteorological data, including surface reflectance, temperature,
relative humidity, atmospheric pressure, downward shortwave radiation, wind
speed, and longwave radiation, were obtained from the ERA5-Land reanalysis
dataset (
Previous studies have found that the standardized precipitation evaporation index (SPEI) overestimated the meteorological drought in NWC where actual
atmospheric water demand is determined by precipitation variation (Ayantobo
and Wei, 2019; B. Zhang et al., 2019; J. Zhang et al., 2019). Additionally,
precipitation is the main water resource for vegetation growth in most
regions of NWC due to the great depth to groundwater (Cao et al., 2021).
A standardized precipitation index (SPI) is thus used in the current study to
represent meteorological drought. SPI at different time scales was calculated by aggregating
A schematic diagram illustrating the procedure of the drought propagation identification method.
Commonly used drought indices indirectly reflect the influence of drought on ecosystems, and they do not comprehensively reflect the homeostasis between ecological water consumption and requirement in drought evolution (Jiang et al., 2021). Additionally, decreases in vegetation coverage are not only caused by a persistent deficit in available water for ecosystems but also other aspects, such as wildfire, hail, flood, and human activities (Bento et al., 2020). This limited the ability of vegetation indices to reflect drought conditions. Therefore, a new drought index, the standardized ecological water deficit index (SEWDI), was constructed to monitor terrestrial ecological drought in our previous study (Jiang et al., 2021). SEWDI follows a similar procedure as SPI, which includes the calculation of ecological water deficit (EWD), the selection of an optimal distribution for fitting monthly EWD series, and the inverse normal transformation of the cumulative density distribution of EWD. EWD is the difference between ecological water requirement (EWR) and ecological water consumption (EWC) (Chi et al., 2018; Jiang et al., 2021). Among them, EWR was calculated using the single crop coefficient method recommended by the Food and Agriculture Organization (FAO). EWC equals the actual evapotranspiration, which is derived from latent heat fluxes calculated by the surface energy balance system (SEBS) algorithm. Therefore, SEWDI can reflect the dynamics of energy and water balance under human activities and climate change. Additionally, the standardization method facilitates the same threshold and evaluation criteria in monitoring two drought types (Peng et al., 2019; Zang et al., 2020), which reduces the influence of other algorithms on final results and guarantees spatiotemporal comparability (Liu et al., 2017). The procedure for calculating the SEWDI calculation is detailed in Jiang et al. (2021).
Since a reliable understanding of the drought propagation process is beneficial for drought forecasting, research interest in the probability of drought propagation from meteorological droughts to other types of droughts has been increasing (Zhou et al., 2021). The current study thus proposes a novel method coupling spatial and temporal connection methods of two drought types with a machine learning model and C-vine copula to investigate the relationship between meteorological and ecological drought. A flow diagram of the method is depicted in Fig. 2.
Investigating the relationship between the characteristics of the two
drought types is key to constructing a probability model. The approach is
summarized in three steps as follows:
According to Andreadis et al. (2005), the evolution of a drought event should be viewed as a spatiotemporal continuum (longitude, latitude, and time). Different from the traditional one- or two-dimensional drought identification method, the three-dimensional array of SPI-3 and SEWDI-3 were extracted to characterize the degree of meteorological and ecological droughts. The extraction procedure involves two steps (Fig. 2) (Andreadis et al., 2005; Xu et al., 2015a, b): firstly, the clustering method was used to identify drought patches in each month; secondly, the drought continuum was constructed by selecting the overlapping areas of drought patches between two adjacent months, which was greater than 1.6 % of the total area (see Sect. 3.1 for the reason).
For each drought event, three drought characteristics were extracted as follows: (1) affected area was calculated by cumulating the area affected by drought in each month during the entire drought period. (2) Duration denotes the time that a drought event persisted. (3) Severity is a cumulative value of SEWDI-3 or SPI-3 for the entire drought duration and areal extent and equals the volume of the three-dimensional continuum.
Sensitivity test of overlapping areas of drought patches between two adjacent months.
Liu et al. (2019) developed a new method for identifying the propagation between two related drought types based on the drought identification method from a three-dimensional perspective. The current study employs this method to identify the propagation from meteorological to ecological drought. The key to this method is the determination of the temporal and spatial connection between two drought types. The specific steps are as follows.
Firstly, the identified meteorological and ecological drought events are
sorted in chronological order. Secondly, whether the two drought types
overlap in time is judged according to Eqs. (1)–(2):
Thirdly, whether the meteorological and ecological drought patches
connecting at a spatial scale is judged according to Eqs. (3) and (4)
Fourthly, successfully matched drought events are encoded following chronological order. Cells in Fig. 2 represent the relationship between preliminarily identified events of the two drought types. The propagation type from meteorological to ecological drought can be classified into four categories: one ecological drought event induced by one meteorological drought event (one-to-one), multiple ecological drought events induced by one meteorological drought event (one-to-many), one ecological drought event induced by multiple meteorological drought events (many-to-one), and multiple ecological drought events induced by multiple meteorological drought events (many-to-many). The codes of cells are identical if the propagation type belongs to one-to-many, many-to-one, and many-to-many.
Finally, the characteristics of meteorological and ecological drought events that belong to the same paired drought event are integrated. Among them, total duration is the difference between the latest-ending and earliest-starting drought events, total affected area is the projected area of all individual drought events, and total severity is the sum of severities of individual drought events.
Identification results of paired meteorological and ecological drought events.
The purpose of this part is to identify whether a meteorological drought
event has the potential to trigger ecological drought. Eleven commonly used
machine learning classification models, including the K-neighbors (KN) classifier (Parzen, 1962), support vector machine (SVM) classifier (Ben-Hur et al., 2000), Gaussian process (GP) classifier (Chen et al., 2020), decision
tree (DT) classifier (Quinlan, 1986), multi-layer perceptron (MP) classifier
(Cybenko, 1989), AdaBoost (AB) classifier (Freund and Schapire, 1997), Gaussian Naïve Bayes (GNB) (Chan et al., 1982), quadratic discriminant
analysis (QDA) (Cover, 1965), gradient boosting (GB) classifier (Friedman,
2001), XGBoost (XGB) classifier (Chen and Guestrin, 2016), and random forest
(RF) classifier (Pal, 2005), were employed for propagation judgment. Drought
duration, severity, and affected area of meteorological drought were set as
the model inputs (Fig. 2). One and zero were set as model target which represents propagation occurrence and non-occurrence, respectively. In this study, each binary classifier was constructed using a Python package called PyCaret, which wraps several machine learning libraries, including scikit-learn, XGBoost, LightGBM, CatBoost, spaCy, Optuna, and Hyperopt (Ali, 2020). The tune_model() function in the PyCaret package offers simple selection of optimal hyperparameters of each model. A five-fold cross-validation was used to train and validate the classifiers in each model by setting “fold
Five univariate distributions, including Johnson S_B (Soukissian, 2013), gamma (Thom, 1958), exponential (Marshall and Olkin, 1967), Pearson III (Wallis and Wood, 1985), and Weibull distributions (Thoman et al., 1969), were used to fit affected area, duration, and severity of meteorological drought and severity of ecological drought. The optimal distribution was selected according to the goodness of fit (GOF), which was estimated with the Kolmogorov–Smirnov (KS) test (Marsaglia et al., 2003) and root mean square error (RMSE).
Commonly used copulas, including an elliptical copula (Gaussian) and four Archimedean copulas (Clayton, Gumbel, Frank, and Joe), were used to join two marginal distributions (Chang et al., 2016). The GOF of these copulas was estimated with RMSE and the Cramer-von Mises (CvM) test (Genest et al., 2009).
The vine copula function is an effective tool for integrating different
bivariate distributions and calculating the conditional probability of
multiple variables (Ni et al., 2020). In a vine copula, an
A box plot showing the intensity, duration, and affected area of paired meteorological–ecological drought among different types.
Sensitivity test of parameter
Top 10 meteorological drought events according to severity.
Spatiotemporal continuums of
Determining overlapping areas of drought patches between two adjacent months
is critical in the identification of drought events from a three-dimensional
perspective. Sheffield et al. (2009) used 500 000 km
Similarly, the sensitivity of
Top 10 ecological drought events according to the severity.
A total of 130 meteorological drought events were identified based on SPI-3 from a three-dimensional perspective. The first 10 meteorological drought events in terms of severity in NWC during 1982–2020 are shown in Table 2. Meteorological drought events with longer duration exhibited a relatively larger affected area and were mainly concentrated between 1982 and 2000. Zou et al. (2005) estimated meteorological droughts with the Palmer drought severity index (PDSI) from 1951 to 2003 in China and found that most parts of NWC experienced severe droughts during 1997–2003, which is similar to the results of this study. As shown in Table 2, 2 of 10 meteorological drought events occurred during this period. Moreover, according to the historical record, Xinjiang and Gansu experienced severe meteorological drought during 1985–1986 (J. Zhang et al., 2019). The three-dimensional identification method could sensitively capture these events. Event No. 9 started from southern Gansu in August 1985 and ended in May 1987, and ranked first.
Temporal evolution of severity and area of
Cumulative SPI/SEWDI and migration trajectory of
A total of 184 ecological drought events during 1982–2020 were identified using the three-dimensional identification method. Table 3 lists the top 10 ecological drought events in terms of severity. The most severe ecological drought event started in April 1982 and originated from central Gansu, which was induced by the persistent meteorological drought Nos. 0 and 3. Compared with the characteristics of meteorological droughts, ecological droughts showed a longer duration and a smaller affected area. This reveals that a longer recovery time is required for the mitigation of ecological droughts.
A total of 46 paired drought events were successfully matched based on the spatiotemporal connection criterion. As shown in Fig. 4, points representing paired drought events were mainly distributed along a diagonal line, illustrating a relatively high consistency between the two types of droughts on the temporal scale. The number of one-to-one, many-to-one, one-to-many, and many-to-many were 8, 8, 4, and 26, accounting for 17.4 %, 17.4 %, 8.7 %, and 56.5 % of the total number of paired drought events, respectively. Meteorological drought of type one-to-many showed a longer duration, a larger affected area, and a greater severity than ecological drought. However, this is contrary to type many-to-one. Simultaneously, ecological drought of type many-to-one showed a longer duration, a larger affected area, and a greater severity than those of type one-to-many (Fig. 5).
Estimations of 11 machine learning models in identifying the potential of meteorological drought to trigger ecological drought. Bold formatting represents the machine learning model with the highest accuracy.
Paired drought event No. 36, comprising meteorological drought event No. 87 and ecological drought event No. 127, was taken as an example to show their spatiotemporal continuums (Fig. 6). The affected area of meteorological and ecological drought in each month was extracted to show their temporal variation. Meteorological drought No. 87 (Fig. 6a) started two months ahead of ecological drought (Fig. 6b), and its effects lasted for two months. It is noteworthy that the most severe meteorological and ecological droughts mainly occurred in central Xinjiang. The affected area and severity of meteorological drought event No. 87 and ecological drought event No. 127 maintained a similar trend of increase–decrease (Fig. 7). Among them, the peaks of the meteorological drought event appeared 2 months ahead (December 2007) of that of the ecological drought (February 2008). In terms of drought trajectory (Fig. 8), they all originated from the Yili basins and showed a counterclockwise shift.
Three-dimensional diagram showing characteristics of meteorological drought events. Larger circles indicate greater severity.
Goodness of fit of the marginal distribution.
Goodness of fit of the bivariate distribution.
To estimate the propagated potential of meteorological drought, 11 commonly used machine learning models were trained based on the characteristics of 81 integrated meteorological drought events. As can be seen in Fig. 9, propagated meteorological droughts have greater severity, larger affected area, and longer duration than non-propagated droughts. Table 4 lists the evaluation results of five-fold cross-validations, including accuracy, precision, recall, F1 score, and MCC metrics. The closer these values are to 1, the higher the precision of the model. Therefore, the five metrics were summed to compare the performances of the 11 models. Most models showed a good performance except for Gaussian process and multi-layer perceptron. The QDA classifier with maximum total value was chosen as the best model to identify the propagation potential of meteorological drought.
Goodness of fit of the multivariate distribution.
The reliability of the copula function is highly dependent on the dependence
between two variables, which was measured by Kendall's
Conditional probability of ecological drought at
E_DS with polynomial functions based on meteorological drought characteristics.
Conditional probability is helpful in providing valuable information for the
effective allocation of water resources under a certain drought level (Guo
et al., 2020). In the current study, the occurrence probabilities of
ecological drought at different levels were determined according to the
characteristics of meteorological drought (Fig. 10). For example, the occurrence probabilities of moderate, severe, and extreme ecological drought events were 80 %, 63 %, 14.7 %, respectively, when M_DA
For comparison, ternary linear and ternary quadratic models were constructed
based on 46 pairs of meteorological–ecological drought events
(Table 8). The comparisons were made in terms of
three independent variables, M_DS, M_DD, and
M_DA, and one dependent variable, E_DS. As
shown in Table 8, the
Conceptual graph depicting
Many studies have linked meteorological drought to hydrological drought at different time scales (Ding et al., 2021; Fang et al., 2020; Feng and Su, 2020; Han et al., 2019; Huang et al., 2017; Ma et al., 2019). In these studies, propagated drought events were identified on the basis of the time series between two drought types, and they focused on their lagging, attenuation, lengthening, and pooling (Fig. 11a). The spatial and temporal drought propagation identification method used in the current study not only preserved the characteristics identified by the low dimensional method but also considered the spatial overlap of two drought types (Fig. 11b). Using this method, two types of drought events without spatial connection would be excluded (only 103 out of 184 ecological drought events were induced by 81 out of 108 meteorological drought events), and more drought characteristics, such as affected area, and migration path could be extracted. This addresses the limited applicability of the traditional method to regions with large spatial extent and provides more reliable information for quantifying the relationship between characteristics of meteorological drought and ecological drought. Additionally, we improved the method for calculating the affected area and duration of paired drought events developed by Liu et al. (2019), represented by a simple sum of characteristics of multiple drought events. However, this method overestimates the duration and affected area of some paired drought events, which is inconsistent with the real situation. In this study, the enhanced method could reflect the characteristics of paired drought during the propagation process more accurately.
The conditional probability model was constructed based on paired
meteorological and ecological drought events; it is not suitable for
calculating the probability of ecological drought at different levels
according to meteorological drought events without propagation potential.
For example, the probability of moderate ecological drought was 63.3 % if
the characteristics of meteorological drought event No. 122 (
The QDA model could simulate the propagation potential of most meteorological drought events well (Table 4). However, some errors occurred in humid southern Shaanxi. For example, meteorological drought event No. 22 showed the potential to trigger ecological droughts, which were incorrectly classified as propagation occurrence. This could be attributed to the compensation of rich water resources for short-term ecological water deficit. Additionally, this paper provides a method for estimating the occurrence probability of ecological drought under the condition of a certain precipitation deficit. The effects of human activities and climate change on ecological drought were not distinguished in the current study. The proposed method may not be accurate for regions with complex water supply systems and strong anthropogenic impacts on vegetation growth.
To improve the accuracy of the method, future studies should consider the non-consistence of ecological drought to quantify the impacts of human activities on drought propagation. Moreover, SPI can be replaced by PDSI or scPDSI to represent meteorological drought through which multiple water balance processes are considered to analyze their relationship with ecological drought (Altunkaynak and Jalilzadnezamabad, 2021). However, such modification may lead to new problems associated with spatiotemporal incomparability. Nevertheless, this approach is worth applying in ecological drought warning. For example, when a meteorological drought event occurs, its characteristics can be applied as input to the tuned model to estimate propagation probability from meteorological to ecological drought in different degrees.
This study proposes a method in identifying the propagation probability of meteorological drought events to trigger ecological drought in different magnitudes. Taking NWC as an example, 130 meteorological drought and 185 ecological drought events during 1982–2020 were extracted using the three-dimensional identification method. Compared with meteorological drought, ecological drought events exhibited longer duration but smaller affected area and severity, suggesting that a longer recovery time is required for mitigating ecological drought.
A total of 46 drought events were successfully matched according to a certain spatiotemporal connection principle. The paired drought events were divided into four categories, including one-to-one, many-to-one, one-to-many, and many-to-many. The four categories accounted for 17.4 %, 17.4 %, 8.7 %, and 56.5 % of the total number of paired drought events, respectively. Then, a drought propagation probability model was constructed by coupling QDA and C-vine copula. Compared with the traditional propagation probability model, the proposed model intuitively provides more objective probabilities of ecological drought at different magnitudes.
The current study certainly provides a more robust method for estimating propagation probability from meteorological to ecological drought in similar ecologically fragile regions.
Monthly meteorological data, including surface reflectance, temperature, relative humidity, atmospheric pressure, downward shortwave radiation, wind speed, and longwave radiation, were obtained from the ERA5-Land reanalysis dataset (
TJ: conceptualization, methodology, software, visualization, writing – original draft. XS: data curation, validation, investigation, funding acquisition, supervision, formal analysis. GZ: writing – review and editing, supervision. TZ: formal analysis, investigation. HW: data curation, investigation.
The contact author has declared that none of the authors has any competing interests.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The authors would like to thank two anonymous reviewers, and the editor (Lelys Bravo de Guenni) for their constructive comments and suggestions which contributed to improving the quality of the paper. The study was supported by the National Natural Science Foundation of China (grant nos. 52079111 and 51879222).
This research has been supported by the National Natural Science Foundation of China (grant nos. 52079111 and 51879222).
This paper was edited by Lelys Bravo de Guenni and reviewed by two anonymous referees.