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  • View in gallery

    Locations of the Luanhe River basin and the six hydrologic stations.

  • View in gallery

    Human activity index (HI) on a 24-month time scale at six hydrologic stations in the Luanhe River basin.

  • View in gallery

    Multivariate normality between (a) SRI (k = 24 months) and climatic index (Niño-3.4) (AP = 24 months) with lead times of M months (M = 3, 6, 12); (b) HI (time scales k = 24 months) and synchronous SRI (k = 24 months); and (c) SRI (k = 24 months), HI (time scales k = 24 months), and Niño-3.4 (AP = 24 months) with lead times of M months (M = 3, 6, 12) at the Liying hydrologic station.

  • View in gallery

    Transition probabilities from different SRI values (k = 24 months, SRI0 = −0.5, −1.25, −1.75, −2.5) and Niño-3.4 values (AP = 24 months) in August to different drought classes in October at the Liying hydrologic station.

  • View in gallery

    Transition probabilities from different SRI values (k = 24 months, SRI0 = −0.5, −1.25, −1.75, −2.5) and HI values (k = 24 months) in August to different drought classes in October at the Liying hydrologic station.

  • View in gallery

    Transition probabilities for future SRI drought classes for different time horizons M considering the current SRI values, Niño-3.4 values (CI-Ci, i = 1, 3, 5), and HI values (HI-Ci, i = 1, 3, 5) at the Liying hydrologic station (current month: August, SRI/HI k = 24 months, Niño-3.4 AP = 4 months, M = 1, 2, 3). The extreme, severe, moderate, and normal drought classes are represented by E, S, M, and N, respectively.

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Hydrological Drought Forecasting Incorporating Climatic and Human-Induced Indices

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  • 1 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, China
  • | 2 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, and Aerial Survey and Remote Sensing Institute, Bei Fang Investigation, Design and Research, Co. Ltd., Tianjin, China
  • | 3 State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin, China
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Abstract

Many drought forecasting methods have been proposed, but only a few have considered the changing environment. The main purpose of this study is to improve the accuracy of drought forecasting models under changing environments by considering the influence of large-scale climate patterns and human activities on hydrological drought. To select the most significant large-scale climatic index that influences drought events in the Luanhe River basin, Spearman’s rho correlation test was applied to detect the relationship between large-scale oceanic–atmospheric circulation patterns and the standardized runoff index (SRI). We also proposed a human activity index (HI) to represent the effect of human activities on hydrological drought. Based on a multivariate normal distribution, we included the above indices in a probabilistic forecasting model, which forecasted the probabilities of transition from the current to a future SRI value. Using the Liying hydrological station as an example, the impacts of a controlled large-scale climatic index (Niño-3.4) and the HI on the transition probabilities were illustrated, and the results showed that the turning point of the Niño-3.4 effect on the transition probabilities occurred within the range from 25.91 to 26.90. Finally, a scoring method was applied to compare the forecasting model performances. The results showed that the inclusion of the large-scale climatic index and HI improved the forecasting accuracy.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ting Zhang, zhangting_hydro@tju.edu.cn

Abstract

Many drought forecasting methods have been proposed, but only a few have considered the changing environment. The main purpose of this study is to improve the accuracy of drought forecasting models under changing environments by considering the influence of large-scale climate patterns and human activities on hydrological drought. To select the most significant large-scale climatic index that influences drought events in the Luanhe River basin, Spearman’s rho correlation test was applied to detect the relationship between large-scale oceanic–atmospheric circulation patterns and the standardized runoff index (SRI). We also proposed a human activity index (HI) to represent the effect of human activities on hydrological drought. Based on a multivariate normal distribution, we included the above indices in a probabilistic forecasting model, which forecasted the probabilities of transition from the current to a future SRI value. Using the Liying hydrological station as an example, the impacts of a controlled large-scale climatic index (Niño-3.4) and the HI on the transition probabilities were illustrated, and the results showed that the turning point of the Niño-3.4 effect on the transition probabilities occurred within the range from 25.91 to 26.90. Finally, a scoring method was applied to compare the forecasting model performances. The results showed that the inclusion of the large-scale climatic index and HI improved the forecasting accuracy.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ting Zhang, zhangting_hydro@tju.edu.cn

1. Introduction

Drought disasters are major natural disasters that impact human lives, economic development, and social progress (Pritchard 2017; Lesk et al. 2016; Schwalm et al. 2017). Drought disasters have large scales and long durations and can affect large populations (United Nations Secretariat of the International Strategy for Disaster Reduction; UNISDR 2009); approximately half of Earth’s terrestrial surfaces are susceptible to drought (Mishra and Singh 2010). According to the Office of State Flood Control and Drought Relief Headquarters, drought caused an average annual reduction of 25.2 billion kg of grain from 1990 to 2016, and more than 27 million people suffer from drinking water shortages in China each year (State Flood Control and Drought Relief Headquarters 2017). Therefore, there is an urgent need to improve the level of detection and provide early drought disaster warnings to mitigate the losses caused by drought. Hydrological drought, which is an important type of drought, has a direct impact on human water use. To quantify and characterize hydrological drought, several drought indices have been developed in recent decades, including the standardized runoff index (SRI; Shukla and Wood 2008), the streamflow drought index (SDI; Nalbantis and Tsakiris 2009), the surface water supply index (SWSI; Shafer and Dezman 1982), and the standardized streamflow index (SSI; Vicente-Serrano et al. 2012). The SRI (Shukla and Wood 2008) is based on the standardized precipitation index (SPI) concept and has the same advantages as the SPI in practical applications.

Numerous studies have documented that both large-scale oceanic–atmospheric circulation patterns and human activities have significant effects on hydrological drought in China (Hao et al. 2008; Li et al. 2012; Zhan et al. 2013; Wang et al. 2009; Lin et al. 2012). Li et al. (2014) quantified the influence of land use change on runoff decreases in the Panjiakou reservoir basin (in the Luanhe River basin in North China), and the results indicated that a decrease in the water area is the main reason leading to the reduction in runoff. This finding indirectly reflects the fact that human activities significantly impact runoff in the Luanhe River basin. Li and Zhou (2016) applied the Budyko decomposition hypothesis and the geometric approach to quantify climate change and human activities on mean annual runoff in six subbasins of the Luanhe River basin. According to the geometric approach, the contributions of climate change and human activities were 7%–49% and 51%–93%, respectively. Based on the Budyko decomposition method, the impacts of climate change and human activities accounted for 15%–40% and 60%–85% of the decrease in runoff, respectively.

Drought forecasting is typically based on probability theory and statistical principles, such as principal component analysis, regression analysis, time series models, Markov processes, gray systems, and artificial neural networks (Mishra and Desai 2006; Paulo et al. 2005; Sun and Lin 2003; Zhang and Zhou 2010). For example, based on reliability analysis, Araghinejad (2011) proposed a systematic probabilistic approach for the monitoring and prediction of drought that considered the changes in the water demand and water supply in the water resource system. Sharma and Panu (2012) focused on the estimation of parameters involving discrete autoregressive moving average (DARMA) concepts in Markov chain models to reliably predict the expected lengths of hydrological drought on monthly and weekly time scales. For the annual drought lengths (i.e., the drought index on a yearly time scale), first-order Markov chains were satisfactory, and second-order Markov models were acceptable for the prediction of monthly and weekly time periods. Li et al. (2016) predicted short-term hydrological drought classes using three-dimensional log-linear regression in the Luanhe River basin and found that this log-linear model could improve the accuracy of forecast predictions. Barros and Bowden (2008) identified and selected prediction factors by means of principal component analysis, wavelet analysis, and other methods and established a conceptual model for forecast factors and precipitation to extend the lead time of operational drought forecasts in Australia. Durdu (2010) developed the autoregressive integrated moving average (ARIMA) model to predict droughts 2 months ahead in the Büyük Menderes River basin. Lohani and Loganathan (1997) used a nonlinear Markov chain method based on the monitoring results of the Palmer drought index to evaluate drought.

In recent years, the continuous changes in the climatic system and human activities have called the stationarity hypothesis in hydrological processes into question (Hejazi and Markus 2009; Zhang et al. 2012; Chang et al. 2015; Wang et al. 2013). Among drought forecasting research, only a few studies have considered the nonstationary behavior of drought in the model structure to improve drought forecasting. Jamshidi et al. (2011) used antecedent data, including SPI, precipitation, and large-scale climate patterns [North Atlantic Oscillation (NAO) and Southern Oscillation index (SOI)], as inputs and applied a multilayer perceptron (MLP) networks to forecast SPI values in Iran. The results showed that the addition of the NAO and SOI values as inputs to the MLP networks improved the prediction accuracy of their models. Chen et al. (2013) used the El Niño–Southern Oscillation (ENSO) index as input values and proposed a probabilistic drought forecasting model to forecast the probability distribution for meteorological drought one month in advance in Southern Taiwan. Bonaccorso et al. (2015) evaluated the probability of transition in the future SPI level based on the present level or SPI and NAO values and compared this probability with other probabilities given that the NAO is often neglected in the Sicilian region (Italy). The results showed that the conversion probability is affected by the NAO index, and better results are obtained when the NAO index is included. Santos et al. (2014) applied a neural network model using NAO and sea surface temperature (SST) as input values for forecasting the SPI in the spring over a 6-month time period, and the results showed that the winter NAO significantly impacted the spring SPI in Portugal. These studies considered only the climatic system to improve drought forecasting. However, both the climatic system and human activities significantly affect hydrological drought. In particular, our novel implementation takes into account the nonstationary behavior of hydrological drought forecasting by considering climate change and anthropogenic impacts on the runoff series. In addition, the turning points of the climate index and the human activity index affecting the transition probabilities were identified.

The aims of this study were to 1) identify the nonstationarity of the runoff series, 2) recognize the relationship between the climate patterns and runoff series, 3) present human activity factors to reflect the anthropogenic influences on the runoff series, and 4) extend the probabilistic drought forecasting models put forward by Bonaccorso et al. (2015) to incorporate the large-scale climatic index and human activity index as covariates in hydrological drought forecasting.

2. Study area and data

a. Study area

The Luanhe River basin is located in the northeast part of China (Fig. 1). This region extends across 39°10′–42°30′N latitude and 115°30′–119°15′E longitude, and the total drainage area is 33 700 km2. The elevation within the area ranges from 2 to 2205 m and is 766 m on average. The mountainous regions and plains account for 98% and 2% of the area, respectively, and the terrain significantly descends from northwest to southeast. The basin is located in the temperate semiarid continental monsoon climate with an average annual precipitation of 400–700 mm, an average annual temperature from −0.3° to 11°C and an annual average potential evapotranspiration of 950–1150 mm. Approximately 70%–80% of the total rainfall in the region occurs from June to September.

Fig. 1.
Fig. 1.

Locations of the Luanhe River basin and the six hydrologic stations.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

The average annual runoff decreased by 30% after 1980 given the reduction in rainfall and human impacts (Li and Feng 2007), and more frequent and severe drought events have occurred since the late 1990s (Wang et al. 2015).

b. Datasets

Monthly rainfall and runoff data from 1960 to 2011 were recorded at six rain gauges and six hydrologic stations for the selected subwatersheds and provided by the Hydrology and Water Resource Survey Bureau of Hebei Province. The locations of the selected stations are provided in Fig. 1.

Five large-scale climatic indices, including the Atlantic Multidecadal Oscillation (AMO) index, ENSO sea surface temperature in the Niño-3.4 region (Niño-3.4 SST), Pacific decadal oscillation (PDO) index, Arctic Oscillation (AO) index, and NAO index, which are teleconnected with precipitation patterns in China (Ouyang et al. 2014; Li et al. 2015; Shen 2012; Song et al. 2011; Li et al. 2017; Ren et al. 2017), were selected from 1960 to 2011 for this study to reflect the influence of climate on hydrological drought. These large-scale climatic indices were obtained from the Global Climate Observing System (GCOS) Working Group (http://www.esrl.noaa.gov/psd/gcos_wgsp/).

3. Methodology

a. Transition probabilities based on a multivariate normal distribution

Let Zυ,τ be the SRI value at month τ = 1, 2, . . . , 12 and year υ, assuming that the SRI series follows a normal distribution. Given that the conditional distribution of the normal distribution is still a normal distribution, the transition probability from the current SRI value z0 to Zυ,τ+M, which is the drought value belonging to class CM for M months in the future with the upper and lower class bounds of CMs and CMi, respectively, can be expressed as follows (Bonaccorso et al. 2015):
P[Zυ,τ+MCM|Zυ,τ=Z0]=CMiCMs12πσze1/2(xρz01ρ2)2dx=Φ(CMsρz01ρ2)Φ(CMiρz01ρ2).

In Eq. (1) (defined as Model 1), ρ is the linear correlation coefficient between the current SRI and the future SRI, and Φ is the function of the notation of the standard normal cumulative distribution.

Based on the assumption that the SRI is a normal variable, it is reasonable to assume that the conditional distribution based on the SRI value is bivariate normal. Similarly, when the conditional distribution is extended by including a large-scale climatic index (Model 2) or human activity index (Model 3) variable in the model, we generally assume the joint distribution of z0, w0, and Zυ,τ+M as multivariate normal. Thus, the conditional probability is expressed as follows (Bonaccorso et al. 2015):
P[Zυ,τ+MCM|Zυ,τ=Z0,Wυ,τ=w0]=CMiCMs12πσze1/2(xμzσz)2dx.
However, as both large-scale climatic variability and human activities have significant effects on hydrological drought, the forecasting model must be extended to four dimensions (Model 4) with the addition of both indices. Assuming that the joint distribution of z0, w0, y0, and Zυ,τ+M is multivariate normal, the mean and variance of the distribution of Zυ,τ+M conditioned on z0, w0, and y0 is expressed as follows:
μz=12(22)1[z0w0y0],
(σz)2=112(22)121.
Then, Eq. (1) is rewritten as follows (Model 4):
P[Zυ,τ+MCM|Zυ,τ=z0,Wυ,τ=w0,Yυ,τ=y0]=CMiCMs12πσze1/2(xμzσz)2dx.

b. Climatic-induced influence indices

To screen out the large-scale oceanic–atmospheric circulation patterns linked with hydrological drought in the Luanhe River basin, the correlations between large-scale climatic indices and SRI series at various time periods for six hydrologic stations were assessed. The SRI sample series and the large-scale climatic index series were standardized, and the large-scale climatic index series averaged on time scales of 3, 6, 12, and 24 months were identified by considering 3-, 6-, 12-, and 24-month lead times of the SRI. As a result, the most significant large-scale climatic index for each hydrologic station can be selected based on the correlation values.

c. Human-induced influence indices

The double mass curve of annual rainfall and runoff was applied to identify the changepoints in the runoff series in the six subwatersheds. We considered the period before the changepoint as the reference period and that after the changepoint as the impact period. The function of the cumulative value of precipitation and runoff is expressed as follows:
R=kP+b.
Based on the regression relation of the cumulative value of precipitation and runoff in the reference period, theoretical runoff volumes in the impact period can be calculated using observed rainfall data. As a result, the theoretical SRI′ and the actual SRI can be calculated by the theoretical runoff data and observed runoff data, respectively. To quantify the human-induced effect on hydrological drought, we proposed the difference between the SRI′ and SRI as the impact of human activities. Here, the HI represents the impact of human activities and can be expressed by the following formula:
HI=SRISRI.

HI > 0 indicates that human activities aggravate the degree of hydrological drought. HI < 0 indicates the opposite effect. HI = 0 indicates no effect.

4. Results

a. Climatic and anthropogenic factors at each station

1) Climatic factors at each station

The significant large-scale climatic index is different for each hydrologic station over the Luanhe River basin. For brevity’s sake, the results of the correlation between the SRI for a 24-month time period and the large-scale climatic index data from the Goutaizi and Liying hydrologic stations are presented here.

Table 1 presents the driving large-scale climatic indices at the Goutaizi and Liying stations. At the Goutaizi station, the SRI on a 24-month scale is correlated with the averaged PDO index over 24 months. At the Liying station, the SRI is correlated with the Niño-3.4 index averaged over 24 months. The Niño-3.4 index with lead times of 3, 6, and 12 months passed the correlation test at a 5% level of significance for most cases, whereas the PDO index with different lead times failed in the correlation test for most cases. Although the correlation coefficients for the PDO index seemed relatively small, it can be concluded that these two climate indices exhibit some influence on hydrologic change.

Table 1.

Correlation coefficients between large-scale climatic indices (AP: 24 months) and SRI series (time scale: 24 months) at the Goutaizi and Liying stations for lead times of 3, 6, and 12 months.

Table 1.

2) Anthropogenic factors at each station

The changepoint reflecting the influences of human activities at six hydrologic stations was identified as 1979, and this result is consistent with the results of previous studies (Wang et al. 2015, Li et al. 2014). The time before 1979 is regarded as the reference period (1960–79), and that after 1979 is regarded as the impact period (1980–2011). The relationships between cumulative rainfall and cumulative runoff at the six stations were computed for pre- and post-1979 (Table 2). As shown in Table 2, all correlation coefficients (R2) are close to 1. In addition, the slopes of the relationships between cumulative rainfall and cumulative runoff line decreased after 1979, which indicates decreased runoff.

Table 2.

Relations between cumulative rainfall P (mm) and cumulative runoff R (106 m3).

Table 2.

The results of HI are presented in Fig. 2. Generally, increasing trends were noted in the HI series at all stations. In particular, after 1995, the HI series exhibited a pronounced increasing tendency at most stations (except the Goutaizi station), which indicates that human activities have aggravated the severity of hydrological drought.

Fig. 2.
Fig. 2.

Human activity index (HI) on a 24-month time scale at six hydrologic stations in the Luanhe River basin.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

b. Transition probabilities involving exogenous variables

The combinations of different time scales k of SRI and HI, different lead times M and moving average periods (APs) of the large-scale climatic indices (denoted as CIs) were assessed at the six hydrologic stations for multivariate normality using the W test (Shapiro and Wilk 1965) to ensure that Models 2, 3, and 4 could be applied to the corresponding hydrologic stations with the given time scales and lead times.

Figure 3 presents the test results for the CIs, HI indices, and SRI samples using the combination of k = 24 months, AP = 24 months and M = 1, 2, and 3 months at the Liying hydrologic station as examples. A black block denotes significant normality under the W test with a significance level of α = 0.05, whereas a white block denotes nonsignificant normality. The multivariate normalities under three conditions, i.e., between the SRI (k = 24 months) and Niño-3.4 index (AP = 24 months) with a lead time of M months, between the HI (k = 24 months) and synchronous SRI (k = 24 months) and between the SRI (k = 24 months), HI (k = 24 months), and Niño-3.4 index (AP = 24 months) with a lead time of M months, at the Liying hydrologic station are significant in most months. The results demonstrate that the hypothesis of multivariate normality should be accepted at a 5% significance level in most cases. Specifically, the multivariate normalities between the Niño-3.4 index, HI, and SRI are significant in August, September, and October for all combinations (i.e., Figs. 3a,b,c). Considering the results of Spearman’s rho correlation test and the W normality test, the Niño-3.4 index with a lead time of 12 months and synchronous HI will be adopted as external covariates in the following analysis.

Fig. 3.
Fig. 3.

Multivariate normality between (a) SRI (k = 24 months) and climatic index (Niño-3.4) (AP = 24 months) with lead times of M months (M = 3, 6, 12); (b) HI (time scales k = 24 months) and synchronous SRI (k = 24 months); and (c) SRI (k = 24 months), HI (time scales k = 24 months), and Niño-3.4 (AP = 24 months) with lead times of M months (M = 3, 6, 12) at the Liying hydrologic station.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

The average monthly values for 1962–2011 and the corresponding standard deviations of the Niño-3.4 index and HI from January to December were calculated (Table 3). Using August as the current month, we chose −2, −1, 0, 1, and 2 as the current standard values for the Niño-3.4 index/HI representing five classes. Then, the five corresponding original Niño-3.4 index/HI values could be calculated, and the results are provided in Table 4.

Table 3.

The mean and standard deviation (SD) of the Niño-3.4 index and HI from 1962 to 2011 at the Liying hydrologic station.

Table 3.
Table 4.

Classification and standard value (SV) of the Niño-3.4 index and HI in August.

Table 4.

Figures 4 and 5 present the transition probabilities computed by Eqs. (1) and (2) from the current month of August to October at the Liying hydrologic station. The x axis (CI-Class/HI-Class) refers to the Niño-3.4 index/HI of the different classes. The abscissa value of 0 indicates no consideration of the Niño-3.4 index/HI, and the abscissa values of 1–5 indicate that the Niño-3.4 index or HI was considered and represent the five classes of the Niño-3.4 index/HI. Here, we chose −0.5, −1.25, −1.75, and −2.5 as the current SRI values (denoted as SRI0) corresponding to the normal, moderate, severe, and extreme drought classes, respectively. Furthermore, the statistical significance of the influence of the Niño-3.4 index and HI on the future SRI classes was assessed using Monte Carlo analysis. The red-filled points in Figs. 4 and 5 indicate that the transition probability lies within the 95% confidence interval based on the Monte Carlo analysis, whereas the other points lie outside the 95% confidence interval within the abscissa value range of 1–5.

Fig. 4.
Fig. 4.

Transition probabilities from different SRI values (k = 24 months, SRI0 = −0.5, −1.25, −1.75, −2.5) and Niño-3.4 values (AP = 24 months) in August to different drought classes in October at the Liying hydrologic station.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

Fig. 5.
Fig. 5.

Transition probabilities from different SRI values (k = 24 months, SRI0 = −0.5, −1.25, −1.75, −2.5) and HI values (k = 24 months) in August to different drought classes in October at the Liying hydrologic station.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

Figure 4 demonstrates that the drought conditions become less severe or nonexistent as the Niño-3.4 index class increases from 1 to 5. Furthermore, compared with CI-Class 0 (regardless of the current Niño-3.4 value), the drought conditions become more severe in the ranges of CI-Classes 1–2. However, the drought conditions become less severe in the range of CI-Classes 3–5. Table 4 shows that the corresponding Niño-3.4 index value in August is within the original value range of 24.93–25.91 for CI-Classes 1–2 and within the original value range of 26.90–28.87 for CI-Classes 3–5. Based on the above analysis, we concluded that the turning point affecting drought conditions occurs at approximately class 3 of the Niño-3.4 index compared with those where the current Niño-3.4 index value is neglected, and the corresponding original Niño-3.4 value ranges from 25.91 to 26.90.

Figure 5 shows the transitions related to persisting or worsening drought conditions as the HI class increases from 1 to 5. Compared with HI-Class 0 (regardless of the current HI value), when the HI class increases in the range of 1–3, the drought conditions become less severe or nonexistent. In contrast, the drought conditions become more severe as the HI class increases in the range of 4–5. In addition, Table 4 demonstrates that the original HI value is less than 0 in the class range of 1–3 but greater than 0 in the class range of 4–5. Based on the above findings, we conclude that the original HI value < 0 leads to a less severe drought class in the future, whereas HI > 0 leads to a worse drought condition compared with the results that did not consider the HI value. This result is consistent with the physical sense of the HI.

To illustrate the direction of the change in the transition probabilities, both the Niño-3.4 index and HI were applied to Model 4. The results of the transition probabilities to future SRI drought classes for different time horizons M (M = 1, 2, 3) at the Liying hydrologic station are presented in Fig. 6. For the sake of brevity, we present only classes 1, 3, and 5 of the Niño-3.4 index/HI (i.e., CI-Ci, i = 1, 3, 5; HI-Ci, i = 1, 3, 5) and choose SRI0 = −0.5, −1.25, −1.75, and −2.5 as the current values. As shown in Fig. 6, when considering the different current values of the Niño-3.4 index or HI, the transition probabilities changed significantly. The effect of the HI on the transition probability to future SRI drought classes is generally stronger than that of the Niño-3.4 index, which is consistent with the results of a previous study (Li and Zhou 2016). In addition, the probability values slightly varied among the different time horizons M. For the transition to a normal drought condition, the probability values increased as the lead time M increased.

Fig. 6.
Fig. 6.

Transition probabilities for future SRI drought classes for different time horizons M considering the current SRI values, Niño-3.4 values (CI-Ci, i = 1, 3, 5), and HI values (HI-Ci, i = 1, 3, 5) at the Liying hydrologic station (current month: August, SRI/HI k = 24 months, Niño-3.4 AP = 4 months, M = 1, 2, 3). The extreme, severe, moderate, and normal drought classes are represented by E, S, M, and N, respectively.

Citation: Weather and Forecasting 34, 5; 10.1175/WAF-D-19-0029.1

c. Model performance

To quantitatively evaluate the performance of the four models in forecasting the transition probabilities to different drought classes, we applied a simple scoring method proposed by Chen et al. (2013) by computing the average monthly transition probability from the SRI values M months before to the SRI classes during the validation period (2005–11). The final model score was computed as follows:
Score=112nt112s=1nps,t.

According to normality and multivariate normality tests, the SRI series were correlated with the large-scale climatic and HI indices at five hydrologic stations with good multivariate normality. Thus, these five hydrologic stations were applied to assess the probabilistic forecasting performance, and the results are presented in Table 5.

Table 5.

The probabilistic forecasting performance of four models with SRI k = 24 months.

Table 5.

As shown in Table 5, the model score increases from Models 1 to 4 for each time horizon M considered at the five hydrologic stations, confirming that the inclusion of the large-scale climatic index and human activity index (HI) improves the forecasting accuracy, mainly for short time horizons.

5. Discussion and conclusions

We demonstrated that large-scale oceanic–atmospheric patterns and human activities exert a strong influence on hydrological drought in the Luanhe River basin. In particular, we identified nonstationarity in the runoff volume series, which is consistent with the viewpoint that stationarity is dead (Milly et al. 2008).

The correlations between large-scale climatic patterns and runoff series at six hydrologic stations were investigated using the Spearman correlation test. We also analyzed the HI at each hydrologic station based on Eq. (7). The results revealed an upward trend of the HI over time at each hydrologic station, indicating that the impacts of human activity have been increasing.

The probabilistic forecasting models (Model 1) put forward by Bonaccorso et al. (2015) were applied to calculate the transition probabilities from the current SRI values to future SRI classes at the Liying hydrologic station, and these data met the assumptions of normality according to the Shapiro–Wilk test. Then, the model was extended to add the current Niño-3.4 index (Model 2), HI (Model 3), and both the Niño-3.4 index and HI (Model 4).

The models were established and analyzed under the conditions of a multivariate normal distribution of the Niño-3.4 index, HI, and SRI series. When using the Niño-3.4 index and HI as conditional variables, we first assessed whether the Niño-3.4 index and HI impacted the drought transition probabilities using a Monte Carlo analysis method. The results indicated that the drought transition probabilities were generally affected by both indices. Specifically, the transition probabilities decreased when the drought conditions transformed to an equal or worse drought condition as the Niño-3.4 index value increased. On the other hand, the probabilities increased when the drought conditions transformed to a less severe or nondrought condition as the values of the Niño-3.4 index increased for the considered SRI on a 24-month time scale; however, the HI revealed the opposite conclusion. Compared with the condition when the current Niño-3.4 index value was neglected, the turning point of the impact of the large-scale oceanic–atmospheric circulation patterns on the transition probabilities occurred at approximately class 3 of the Niño-3.4 index (within the original value range from 25.91 to 26.90). More specifically, compared with CI-Class 0 (regardless of the current Niño-3.4 index value), the drought conditions became more severe in the range of CI-Classes 1–2, whereas the drought conditions became less severe or nonexistent in the range of CI-Classes 3–5. Both the Niño-3.4 index and HI were included in Model 4, which exhibited the same influence as Models 2 and 3. A comparison between the changes in transition probabilities resulting from the Niño-3.4 index and HI revealed that the HI had a stronger influence than the Niño-3.4 index. These results indicate that human activities have the main impact on hydrological drought.

Finally, a scoring method was applied to evaluate the performance of the four models in forecasting drought class. The results indicated that the scores of Model 4, which was used to forecast the transition probabilities from the current SRI, Niño-3.4 index, and HI values to future classes, were highest among the four models for the lead time M = 1 and k = 24. In addition, Model 3, which forecasted the transition probabilities from the current SRI and HI values to a future class, exhibited progress compared with Model 2 when the Niño-3.4 index was used instead of the HI.

The probabilistic models from the current SRI, large-scale climatic index and HI values toward future classes were generated under the hypothesis of a multivariate normal distribution of the underlying joint variables. However, these models cannot be used when the data series do not follow a multivariate normal distribution; therefore, future research will focus on how to forecast the future drought classes from the current drought indices, large-scale oceanic–atmospheric circulation patterns and human activities factor values under nonmultivariate-normal conditions. From the current drought indices, large-scale factors and human activity factors to the future level of the forecast under nonmultivariate normal conditions is a further work to be carried out.

Acknowledgments

This work was supported by the National Natural Science Foundation (Grants 51479130 and 51779165). We are grateful to the Hydrology and Water Resource Survey Bureau of Hebei Province for providing hydrologic data.

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