Drought is an economically and ecologically disruptive natural hazard that profoundly impacts water resources, agriculture, ecosystems, and basic human welfare (Dai, 2011). In recent years, extreme drought events have had disastrous impacts worldwide. The 2011 eastern African drought led to famine and severe food crises in several countries, affecting over 9 million people (Funk, 2011). As part of the 2011–2014 California Drought, the drought in 2014 alone cost California USD 2.2 billion in damages and 17 000 agricultural jobs (Howitt et al., 2014). China has also suffered from extreme drought events, such as the 2009–2010 severe drought in southwestern China (Yang et al., 2012), 2011 spring drought in the Yangtze River basin (Lu et al., 2014), and 2014 summer drought in northern China (Wang and He, 2015). Because drought is a costly and disruptive natural hazard, reliable drought prediction is fundamental for water resource managers to develop and implement feasible drought mitigation measures. In the present study, drought prediction is restricted to relatively long-term drought, which is associated with season-scale precipitation deficits.

Drought is generally predicted using two types of methods: model-based dynamical forecasting and statistical prediction. Dynamical forecasting primarily relies on computed drought indicators, such as the standardized precipitation index (SPI; McKee and Kleist, 1993), based on forecast precipitation retrieved from seasonal climate forecast systems (Dutra et al., 2013, 2014; Mo and Lyon, 2015; Yoon et al., 2012). Although dynamically predicted precipitation is useful information for drought situations, especially for short-term forecasting 1 month ahead, it also contains high levels of uncertainty and limited skill with respect to long lead times (Wood et al., 2015; Yoon et al., 2012; Yuan et al., 2013). In contrast, statistical drought prediction is an additional source of prospective drought information (Behrangi et al., 2015; Hao et al., 2014). Different from the physical, complex processes in coupled atmosphere–ocean models used for dynamical prediction, statistical drought prediction models are relatively simple but also perform well. They consist of input variables, methodology, and prediction targets (Mishra and Singh, 2011).

Reasons for good and effective performance of statistical models include methodology improvements and drought-related climate indices used as input variables. To date, much attention has been paid to methodology improvements. Taking advantage of probabilistic and temporal-evolution features of input variables, statistical drought prediction models are primarily forced with probability or machine-learning methods, such as the ensemble streamflow prediction (ESP) method (AghaKouchak, 2014), Markov chain- and Bayesian network-based models (Aviles et al., 2015, 2016; Shin et al., 2016), neural network, and support vector models (Belayneh et al., 2014). In addition to method improvement, climate indices represent large-scale atmospheric or oceanic drivers of precipitation, partly responsible for effective model performance. These climate indices include typical atmospheric and oceanic circulation patterns, such as the North Atlantic Oscillation (NAO; Hurrell, 1995) and El Niño–Southern Oscillation (ENSO; Ropelewski and Halpert, 1987), which have been widely used for drought prediction in different seasons and regions (Behrangi et al., 2015; Bonaccorso et al., 2015; Chen et al., 2013; Mehr et al., 2014; Moreira et al., 2016).

Climate indices, such as the NAO index and NINO 3.4 index, are simple, explicit, and widely used. Therefore, they are the primary indices used for drought prediction. Additionally, based on the relationship between drought indices and potential atmospheric or oceanic circulation patterns, some researchers have also discovered large-scale circulation patterns closely related to regional droughts or have structured new drought predictors (Funk et al., 2014; Kingston et al., 2015). For instance, after discovering the two dominant modes of the eastern African boreal spring rainfall variability that are tied to SST fluctuations, Funk et al. (2014) further determined that the first- and second-mode SST correlation structures were related to two SST indices that could be used to predict eastern African spring droughts.

Similarly, potential atmospheric and oceanic circulation patterns, which are closely related to regional droughts, are also used to construct drought predictors in the present study. Considering that the development of drought processes is closely related to the spatial–temporal evolution of large-scale circulation patterns, we constructed predictors based on anomalous spatial patterns. Because precipitation-inducing circulation patterns usually occur in the troposphere, predictors can be built based on sea surface temperature (SST) and 200 and 500 hPa geopotential height (HGT), reflecting information from different levels of the troposphere. Subsequently, all these predictors from different drought processes and the 3-month SPI, updated daily (hereafter, SPI3), were used to calibrate a synchronous stepwise-regression relationship. The model can be forced with dynamically forecast SST and 200 and 500 hPa HGT conditions, indicating that the lead time depends on that of the climate forecast models. Based on predicted prospective 90-day SPI3 curves, we developed angle-based rules for the drought outlook, which can make the drought outlook easily accessible to water resource managers.

Overall, the objective of this study is to build a conceptual prediction model of seasonal drought processes. The essential and important steps are to (1) structure predictors on the basis of drought-related atmospheric and oceanic circulation patterns, (2) build the synchronous statistical predictor-SPI3 relationship forced with reanalysis and operationally forecast datasets, (3) simulate and predict four severe seasonal drought processes in China to investigate model performance, and (4) propose an objective angle-based method for drought outlook.

Considering the proposed conceptual model consists of several important parts, a brief but general introduction with sequential procedures is presented (Fig. 1), prior to specific descriptions in Sects. 3–8. In Sect. 3, historical extreme and severe drought processes are identified with SPI3. These drought processes usually go through one or several dry and wet spells, in which precipitation deficit characteristics and circulation patterns vary. Therefore, process-split rules, according to dry and wet spells, are designed to assign drought process segments to different dry and wet spells in Sect. 4. Gridded values in the fields of 200 and 500 hPa HGT and SST are transformed into gridded values of standardized anomalies (SAs) in Sect. 5. Maps of atmospheric–oceanic SAs during drought process segments within the same dry and wet spells are important inputs to the construction of the predictors. After empirical orthogonal function (EOF) analyses are conducted on these SA-based maps, the first leading EOF modes are used to generate predictors (Sect. 5). Further, synchronous statistical relationships between SA-based predictors and SPI3 are calibrated with the stepwise regression method in Sect. 6. The National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) reanalysis datasets and the NCEP Climate Forecast System Version 2 (CFSv2) operational forecast datasets are used to force the synchronous statistical relationship. Simulated and predicted 90-day prospective SPI3 time series are presented in Sect. 7. With the aid of angle-based rules for seasonal drought outlook, simulated and predicted SPI3 time series are transformed to five types of drought outlooks (Sect. 8), which are easily accessible to water resource managers.

In particular, although drought process predictions in northern, eastern, and southwestern China are all the targets in the present study, only the historical drought processes in northern China are used to introduce the model construction and calibration in Sect. 3–6. Similar procedures were also applied to drought processes in eastern and southwestern China. However, for the sake of conciseness, these procedures, together with intermediate results, are not shown in this study.

The precipitation data used were the second-version Dataset of Observed Daily Precipitation Amounts at each 0.5∘ × 0.5∘ grid point in China for 1961–2014 (http://data.cma.cn/data/detail/dataCode/SURF_CLI_CHN_PRE_DAY_GRID_0.5.html), which was kindly provided by the Climate Data Centre (CDC) of the National Meteorological Information Centre, China Meteorological Administration (CMA). It was initially used to calculate area-averaged precipitation over northern China, eastern China, and southwestern China (Fig. 2), which are the three Chinese drought regions investigated in this study. They cover areas of approximately 0.69, 0.91, and 1.12 million km2, respectively. Atmospheric anomalies were diagnosed with respect to the NCEP/NCAR reanalysis datasets, which has a resolution of 2.5∘ × 2.5∘ at 17 pressure levels, extending from January 1948 to the present (Kalnay et al., 1996). The National Oceanic and Atmospheric Administration (NOAA) high-resolution SST dataset, with a spatial resolution of 0.25∘ × 0.25∘ and extending from September 1981 to present (Reynolds et al., 2007), was used for SST anomaly analysis.

The NCEP Climate Forecast System Version 2 (CFSv2; Saha et al., 2014) was used to verify operational performance of the proposed conceptual model. Since CFSv2 began on 1 April 2011, some drought processes that occurred before this date were forced with the CFS reforecast output. All the relevant reforecast and forecast datasets are accessible on the website (https://nomads.ncdc.noaa.gov/modeldata/). In particular, we focus on the prospective 90-day seasonal drought process prediction during four severe drought processes in this study. To achieve this, prospective 90-day forecast data subsets for 200 and 500 hPa HGT and SST are retrieved from CFSv2 and CFS products, which are used for the predictor calculation. Details can be found in Sect. S1 in the Supplement.

Identified drought processes usually go through one or several dry and wet spells. Different dry and wet spells usually correspond to various precipitation deficit characteristics and atmospheric–oceanic circulation patterns. Therefore, we divided drought processes into different segments according to dry and wet spells, in order to further analyze atmospheric–oceanic anomalies during drought segments within the same dry and wet spells. Additionally, SPI3 on the start date of an identified drought process indicates that SPI3 is initially less than -0.5 and a severe drought process indeed follows, which actually reflects drought-inducing precipitation information for the previous 90 days. Therefore, the start date of the drought process is advanced to the past 90th day, preceding the drought process division. This measure can contribute to introducing early drought-inducing information to predictor construction.

Using northern China as an example, the specified procedures for the division process are as follows. Similar to general seasonal classification, we divided the annual period into four dry and wet spells (Table 3) according to the temporal evolution of the daily precipitation rate in northern China (Fig. 5). It is evident that the wet spell (one-fourth of the annual duration) accounts for over 50 % of total precipitation, while the dry spell (one-third of the annual duration) accounts for about 6 %.

Based on these dry and wet spells, process-split rules (Fig. 6) are constructed using the intersection proportion (IP) and critical proportion (P, set as 40 %). Herein, IP is the proportion of initial segments accounting for relevant dry and wet spells, and the initial segments (e.g., D1, D3, and D4 in Fig. 6) refer to parts of one drought process split with dry and wet spells. As shown in Fig. 6, one complete process is first transformed into several initial segments according to dry and wet spells. Second, “IP[0]” and “IP[-1]” are calculated, which express IP at the start and end segments, respectively. Third, based on a comparison of IP and P results, these initial segments can be assigned to different dry and wet spells.

Following the process-split rules shown in Fig. 6, we divided these drought processes according to dry and wet spells in northern China (Table 3). Detailed procedures of relevant IP calculations and comparisons can be found in Fig. S1 in the Supplement, while final assignments of initial drought segments are shown in Table 4. In addition, to highlight the importance of extreme droughts, severe and extreme drought segments are considered in turn.

Considering that the development of drought processes is closely related to the spatial–temporal evolution of atmospheric and oceanic anomalies, a conceptual prediction model of seasonal drought processes is proposed in our study. Despite its weakness in predicting drought severity, the model performs well in simulating and predicting drought development. Because the proposed model is a new attempt, several associated discussion issues are as follows.

First, process prediction and outlook of seasonal drought are the focus of our study. To date, a considerable number of studies have focused on predicting discrete drought classes (Aviles et al., 2016; Bonaccorso et al., 2015; Chen et al., 2013; Moreira et al., 2016) and the probability of drought occurrence within certain classes (AghaKouchak, 2014, 2015; Hao et al., 2014). Compared with these studies, prediction of regional drought processes is another valuable attempt, which is beneficial from the moving window of SPI3 extended from 1 month to 1 day. It performs relatively well in predicting the development of seasonal drought processes (Fig. 12). In addition, it can indicate drought occurrence, persistence, and relief relatively well (Tables 8 and 9), which is meaningful for seasonal water resource management.

Second, the proposed model is essentially one stepwise-regression equation. Despite its simplicity, it incorporates drought-related spatial and temporal information as integrally as possible. Because precipitation-related synoptic systems appear in the troposphere, SST, 500 hPa HGT, and 200 hPa HGT are chosen as representatives of the low, middle, and upper levels of the troposphere, respectively. Furthermore, all drought process segments assigned to different dry and wet spells are used for EOF analysis within the same dry and wet spells (shown in Sect. 5.2). Therefore, adequate drought-related spatial–temporal information has been included in these drought predictors.

Third, the reasons for acceptable performance of operationally predicted results need to be illustrated. Compared with those forced with the NCEP/NCAR reanalysis datasets (green curves in Fig. 12), the predicted developments of drought processes forced with CFSv2 or CFS datasets (red curves in Fig. 12) are relatively similar, especially with respect to the former segment of every predicted prospective 90-day SPI3 curve. Essentially, the 90-day-accumulated SA-based predictors strengthen the good performance of operational use. This indicates that observed information from atmospheric and oceanic anomalies are involved to different degrees (Fig. 10). With the incorporation of observed data, its operational application provides relatively accurate and valuable information. However, it is also worthwhile to investigate how changing the length of the predicted period can make predicted drought processes relatively accurate and acceptable, such as the prospective 1–30-day or the prospective 1–60-day periods. The relevant comparison results with different predicted periods are shown in Fig. 14. It appears that the 2009–2010 drought in southwestern China and 2014 drought in northern China can be predicted and simulated well even for the prospective 1–75-day period. In contrast, the prospective 1–45-day period may be a feasible and acceptable lead time for simulation and prediction of the 2011 droughts in southwestern China and eastern China, after which the simulated and predicted developments clearly change.

Fourth, the weak performance in predicting the severity of drought, including drought peak and drought relief, is an important issue. Similar to the concluding remarks regarding a probabilistic drought prediction model, the weak performance in predicting the severity of the drought peak is due to the typical problem of an inherent averaging effect depressing the extremes (Behrangi et al., 2015). With the help of real-time correction from operational application, the prediction of drought peaks can be improved. In addition, the prediction of drought relief should also be considered. As listed in both Tables 8 and 9, the simulated and predicted results for drought relief are unsatisfying. This weak performance may be associated with precipitation-causing weather patterns during drought relief. They are unsteady and change dramatically compared with those features during drought persistence. Because the period of drought relief is a relatively short phase of the drought process, the relevant information may not be involved in the first EOF modes (Sect. 5.2). Generally, three measures for potential improvement are as follows. (1) More secondary EOF modes, including precipitation-causing circulation patterns during drought relief, can be incorporated when building initial predictors. (2) The rapid change index (Otkin et al., 2015) could be introduced to describe temporal changes during drought relief on subseasonal timescales. (3) The empirical factor can be introduced to improve drought-relief prediction. The predicted SPI3 during the phase of drought relief could be multiplied by empirical factors to strengthen drought relief development.

Fifth, it is necessary to explain the method of predictor construction. The predictor-structured method in our study is similar to the definition of teleconnection indices (Wallace and Gutzler, 1981). It is more goal-directed, because these structured predictors are directly related to synchronous atmospheric–oceanic anomalous circulation patterns during different drought segments within the same dry and wet spells. However, to design geographical ranges of anomalous areas and combine them is subjective, which leads to considerable uncertainties. Accordingly, an objective anomaly-recognized method with explicit critical values needs to be developed. This will contribute to auto-run feasibility of this conceptual prediction model without artificial interaction.

The sixth issue to illustrate is synchronous SST anomalies used in EOF analysis and model construction. Traditionally, SST anomalies a few months ahead influence the subsequent regional droughts. However, it is also feasible and common that synchronous SST anomalies are used in the investigation of regional drought events in southwestern China (Feng et al., 2014), the Yangtze River basin (Lu et al., 2014), and northern China (Wang and He, 2015), which may shape synchronous drought-related circulation patterns. In addition, this is convenient for operational application, while forecast SST and 200 and 500 hPa HGT can be retrieved together from CFSv2 products simultaneously.

Finally, the timescale of the drought index needs to be explained. SPI3 is the index used for drought identification and prediction in the study, which provides a seasonal estimation of precipitation and tends to be a good indication of soil moisture conditions as the growing season begins in some primary agricultural regions worldwide (WMO, 2012). However, to meet operational requirements of seasonal hydrological forecasting, the indices such as 6-month up to 24-month SPI can be also used for hydrological drought analyses and applications (WMO, 2012). With the increasing timescale of SPI, its lead time with given accuracy requirements might be longer, together with the smoother temporal evolution. Accordingly, atmospheric and oceanic anomalies used for model calibration need to be changed from 90-day accumulated to 6- or 24-month accumulated.

Drought prediction is fundamental for seasonal water management. In this study, we constructed a conceptual prediction model of seasonal drought processes based on synchronous standardized anomalies of 200 and 500 hPa geopotential height and sea surface temperature; we considered that drought development is closely related to the spatial–temporal evolution of large-scale atmospheric–oceanic circulation patterns. We used northern China as an example to introduce the method and used four recent severe regional drought processes in China for model application. This model can be used for seamless drought prediction and drought outlook, forced with seasonal climate forecast models. The main process is as follows. (1) A 3-month SPI updated daily (SPI3) was used to capture severe and extreme drought processes. (2) Empirical orthogonal function analysis was applied to SA of 200 and 500 hPa HGT and SST during drought process segments within the same dry and wet spells. Subsequently, spatial patterns of the first EOF modes were used to structure SA-based predictors. (3) The synchronous stepwise-regression relationship between SPI3 and all 90-day-accumulated SA-based predictors were calibrated using the NCEP/NCAR reanalysis datasets. (4) To achieve a prospective 90-day drought outlook, we further developed an objective method based on angles of the predicted prospective 90-day SPI3 curves. (5) Finally, simulation and prediction of seasonal drought processes, together with drought outlook, were forced with the NCEP/NCAR reanalysis datasets and the NCEP Climate Forecast System Version 2 (CFSv2) operationally forecast datasets, respectively. Model application during four recent severe drought processes in China revealed that the model is good at development prediction but weak in severity prediction. These results indicate that the proposed conceptual drought prediction model is another potentially valuable addition to current research on drought prediction.