Analysis of drought characteristics over Luanhe River basin using the joint deficit index

Drought, considered as the least understood natural hazard, affects many social activities significantly and causes large economic losses (Mishra & Singh 2010; Masud et al. 2015). Drought commonly originates from an intense and persistent deficiency in precipitation (Zargar et al. 2011), but its evaluation, which is controlled by complex physical mechanisms, has different temporal and spatial characteristics (Modarres 2007; Pasho et al. 2011).

Up to now, a variety of drought indices (such as the Palmer drought severity index (Palmer 1965), rainfall anomaly index (Van Rooy 1965), surface water supply index (Shafer & Dezman 1982), standardized precipitation index (SPI) (McKee et al. 1993, 1995), soil moisture drought index (Hollinger et al. 1993), and standardized precipitation evapotranspiration index (Vicente-Serrano et al. 2010)), which are derived from meteorological or hydrological variables, have been established for identifying and assessing droughts. The validity and reliability of the drought index have dominant influences on the effectiveness of a drought monitoring system (Marcella & Eltahir 2008; Barua et al. 2010; Hosseinzadeh Talaee et al. 2014).

Among these drought indices, the SPI proposed by McKee et al. (1993) is the most commonly used owing to its computational simplicity and flexibility. The SPI measures the accumulated precipitation deficits over a given period of time in a probabilistic manner. It not only is statistically comparable across time and space, but also can represent drought conditions at various time scales (Wu et al. 2005; Vicente-Serrano 2006; Zarch et al. 2015).

Byun & Wilhite (1999) highlighted the causes of drought, which can be divided into two kinds, soil dryness and water resource deficiencies in reservoirs or other sources. The amount of short-term precipitation directly affects soil moisture, and long-term precipitation totals mainly have an impact on water stored in other sources. It is thus obvious that drought is a result of the cumulative effects of water shortages over different periods of time; consequently its characteristics in terms of intensity, magnitude and duration vary with the time scale considered. For a drought assessment based on the SPI, a pre-specified time scale is unable to depict the entire drought condition, while inconsistent responses to different time scales will appear and cause confusion. Therefore, it is suggested that multiple SPIs with various time scales should be examined together to capture the overall drought status, combined with historical records and descriptions. Nevertheless, the final examined results are lacking in objectivity and probabilistic properties due to the subjective judgments involved.

On these grounds, Kao & Govindaraju (2010) proposed a joint deficit index (JDI) by using empirical copulas, and indicated that the JDI is capable of providing an objective description of the overall deficit status. Moreover, Mirabbasi et al. (2013) used the JDI for an evaluation of drought conditions in the northwest of Iran, further showing the robustness and flexibility of this index. The JDI serves as a probability-based drought index that can be constructed from the dependence structures of SPIs with time scales varying from 1 to 12 months. There seems to be a consensus that the SPI at a shorter time scale (1–3 months) is used for detecting meteorological or agricultural droughts, while the SPI on longer time scales (e.g. 6 and 12 months) well represents hydrological and water resources droughts (McKee et al. 1995; Vicente-Serrano & López-Moreno 2005; Mishra & Singh 2010). Hence, the JDI, which determines joint deficit status through the joint cumulative probability of SPIs, can offer an objective and overall measure of drought conditions.

The Luanhe River basin, located in north China, is of great importance for water supply to Tianjin city. Several drought-related studies have been undertaken over the basin, indicating more frequent drought events which have caused diminished water resources availability in recent decades (e.g. Li & Feng 2007; Wang et al. 2015a). Therefore, understanding and qualifying drought occurrence and its spatio-temporal characteristics is of particular importance for the development of adequate mitigation strategies. Although various drought indices have been used for drought monitoring and assessment in the Luanhe River basin, remarkable differences are observed in the results based on different indices (e.g. Ma et al. 2013; Wang et al. 2015b). The emergence of inconsistent results would lead to confusion in making informed decisions on a regional scale, and to some extent become an obstacle to establishing an effective monitoring and forecasting system. It is thus necessary to perform an objective assessment of the overall drought condition based on a statistical drought index, straightforwardly providing an overall concise picture of drought status in the region.

According to Kao & Govindaraju (2010), the computation of JDI requires only precipitation time series with a 50-year minimum recording length. Moreover the JDI, simply the standard normal values, are climatologically consistent for any location. As for the Luanhe River basin focused on in this study, 54-year monthly precipitation data (1958–2011) are available, and precipitation deficit is the main cause of drought in the area, accordingly showing the applicability of the JDI method for this area. This study aims to analyze the drought characteristics in the Luanhe River basin using the JDI approach, expecting to provide valuable information for water resources planners and policy makers.

The focus of this study is on the Luanhe River basin, which is located in the northern part of the Haihe River basin, China. The basin is between 115 °30′ and 119 °15′E longitude and 39 °10′ and 42 °30′N latitude covering an area of 33,700 km². Its northwestern and central parts consist of mountains, while the southeast area is mainly flat. The mean annual precipitation in the basin varies from less than 400 mm in the northwest, to more than 700 mm in the southeast, and 70–80% of annual precipitation occurs from June to September. The region has a typical temperate continental monsoon climate, with a mean annual temperature of −0.3 to 11 °C. The mean annual pan evaporation over this area is 950–1,150 mm, while its mean annual actual evaporation is around 350 mm.

The Luanhe River basin was planned to provide a billion cubic meters of water per year to Tianjin city, the largest coastal city open to international trade in north China. However, due to rainfall reduction and soil and water conservation, the average annual runoff of the basin decreased by 30% after 1980 (Li & Feng 2007). Additionally, in the 21st century the consecutive droughts in the basin caused a serious insufficiency of water supplying Tianjin city, consequently aggravating environmental degradation and the water crisis. With the study area serving as an important water supply source, the occurrence and evaluation of drought there play a significant role in the social and economic development of Tianjin city.

The SPI and the JDI used in this study were originally proposed by Mckee et al. (1993) and Kao & Govindaraju (2010), respectively.

For the given marginal sets {u₁^m, … , u₁₂^m}, the copula measures the cumulative joint probability and, further, the Kendall distribution function K_c can provide the cumulative probability function (Nelsen et al. 2003; Nelsen 2006).

Under the null hypothesis H₀ that x are independent and randomly ordered, when |Z| > Z_1−α/2, the H₀ is rejected and a significant trend exists in the time series. Z_1−α/2 is the critical value of Z from the standard normal table, and for 10% significance level the value of Z_1−α/2 is 1.28.

The 1- to 12-month cumulative precipitation series for each month and each station are fitted with a two-parameter Gamma (G2) distribution, using the maximum likelihood (ML) method to estimate parameters of the distribution. The Kolmogorov–Smirnov (KS) test was then applied for the goodness of fit at the 1% significance level. Results show that more than 95% of the cases passed the KS tests, indicating that the G2 distribution is an appropriate distribution for constructing the SPI and JDI in the Luanhe River basin.

According to historical records and related literature, drought events mainly occurred in 1961, 1963, 1968, 1972, 1980–1984, 1997–2007 and 2009 for the study area. Based on the series of SPI₃, SPI₆, SPI₁₂ and JDI, the parameters (including drought duration (D) and magnitude (M)) of the above drought events are reported in Table 3, taking Chengde station as an example.

It can be seen in Table 3 that both SPI and JDI have the ability to identify and assess the historical drought events, but values of the drought parameters defined by these indices are different from each other. Short-term SPI values are more sensitive to emerging droughts, while a long-term SPI value shows a strong response to a prolonged drought. For example, the mild drought starting in July 1968 cannot be captured by the long-term SPI (namely SPI₆ and SPI₁₂), while the SPI₃ indicates this drought event with a duration of 2 months, which is also suggested by the JDI. In the case of the extreme drought that occurred in 2000, the drought parameters obtained by the multiple SPIs have great differences (e.g. the D and M of SPI₁₂ are four times larger than the corresponding ones of SPI₃), but a duration of 8 months defined by the JDI is consistent with the historical record. Among the multiple SPIs, the SPI₆ shows better performance in capturing historical drought events in the study area, since the general agreement of its assessment results and historical records seems good. However, when considering the short-term drought in 1968 and the extreme droughts in 1961 and 1972, remarkable differences are exhibited especially in terms of drought magnitude. Compared with the SPI₆, the results of JDI are in better agreement with historical records for all the cases listed in Table 3 on the whole. For instance, the extreme drought event that occurred in 1972 lasted 6 months, affecting an area of 30,000 km² in Chengde city. It was reported to be the most severe drought event since 1919 and caused great damage to the eco-environment and socio-economy in this region (Gao 1998). According to the JDI, the corresponding assessment result with a duration of 6 months and a magnitude of 11.35 replicates this drought condition well. It is indicated that the JDI, which integrates the deficit status over various durations (from 1 to 12 months), can avoid the confusion caused by multiple SPIs with different time scales, and accurately define and assess overall drought conditions.

As shown in Figure 3(a), values of SPI at all time scales for June 1972 indicate severe and even extreme drought conditions due to serious precipitation deficits. The JDI that represents the joint deficit status also suggests an extreme drought for this case. In the case of July 1972 (Figure 3(b)), the SPI₁ assigned to a wet class shows sufficient precipitation in this month, while the SPIs with other time scales reflect a drought state due to precipitation deficits in prior months. The JDI takes the effect of preceding serious deficits into account, and reports a severe drought in this instance.

For December 1993 (Figure 3(c)), SPI₁ reports a severe drought since hardly any precipitation was observed. However, other SPIs with longer memory cannot capture an emerging drought in a timely manner, showing above normal conditions. The JDI indicates a mild drought condition for this instance, demonstrating that the JDI not only can reflect the emerging drought but also has temporal memory for accumulated deficit. Figure 3(d) shows a confusing case in April 2007, in which SPI with time scales from 1 to 5 months show approximately normal precipitation in the last five months, while other SPIs accounting for the preceding serious deficit report drought status with different severity. Based on the entire dependence structure of multiple SPIs, the JDI reflects a mild drought condition in this case.

Figure 5 shows that the frequencies related to severe and extreme drought classes generally tend to increase over time, especially in the most recent decade, which is consistent with previous studies (Li & Feng 2007; Wang et al. 2015a). In Figure 6, it can be seen that mild droughts observed during 1959–2011 mostly occurred in the autumn. The maximum frequencies associated with moderate, severe and extreme drought occur in summer, indicating that summer droughts seem to be more frequent and severe.

In the Luanhe River basin, the precipitation in summer and autumn (from June to November) accounts for more than 80% of annual precipitation, predominating in the water budgets of the hydrological cycle. Most of the regional agricultural production is from irrigated agriculture, and the corresponding agricultural activities are concentrated in summer and autumn. Moreover, sufficient precipitation during the flood season (from June to September) serves as a key element for an adequate reservoir storage which directly guarantees the quality of water supply for Tianjin city. Consequently, the severe and frequent droughts in summer and autumn have seriously affected river ecosystems and irrigated agriculture in the basin, resulting in crop failures, water scarcity and environmental degeneration. In the most recent decade, Tianjin city has faced a water crisis due to the inadequate supply of water, as a response to the frequent occurrence of extreme droughts in the Luanhe River basin. It is thus of great significance for the Luanhe River basin to improve drought mitigation strategies and water resources management.

In this study, the non-parametric MK trend test was used to detect the trend of the JDI series during 1959–2011, and the Z statistics of the MK test for each month and each station are listed in Table 4. Based on the Z statistics of the MK test, a positive value shows a mitigating trend of drought condition, while a negative value shows an aggravating trend. In August and September, negative Z values are observed in all the stations, and show significance at the 90% confidence level for the stations located in the southeast. It is indicated that the drought in August and September has an aggravating trend over the basin, shown to be significant in the southeastern part. Z values for July are found to be negative in about 85% of the selected stations, suggesting aggravating trends of drought condition in July. Moreover, more than 50% of the stations show significant aggravating trends in January, February and March droughts, and these stations are mostly located in the southeast. For the drought condition in May and June, positive Z values were found in more than 75% of the stations, reflecting mitigating trends.

In this paper, monthly precipitation data from 26 rain-gauge stations over the period of 1958 to 2011 were selected to calculate the JDI. The JDI series were then employed to analyze the drought characteristics in the basin. The main conclusions are summarized as follows.

As a probability-based drought index, the JDI takes the effects of water deficits at various time scales into account, objectively reflecting the overall drought status. Compared with the SPI, the JDI can not only provide a more comprehensive drought assessment, but also characterize drought conditions more accurately. Moreover, the JDI constructed in terms of the joint cumulative probability is able to capture both emerging and prolonged droughts effectively, and is shown to be a flexible and appropriate tool for drought monitoring and assessment.

During the period of 1959–2011, serious drought events mainly occurred in summer and autumn in the Luanhe River basin, and extreme droughts appeared frequently in the most recent decade, seriously hitting the river ecosystems, irrigated agriculture and water supply capacity of the basin. Compared with the northwest in the basin, more severe and frequent droughts are observed in the southeast. In addition, the drought condition over the basin tends to be aggravating in August and September, with significant aggravating trends in the southeast. The occurrence and evaluation of droughts can be objectively described by the JDI, providing valuable information and references for developing regional mitigation strategies and water resources management.

The JDI constructed in this study is purely dependent on precipitation deficits over the time scales of 1 month to 12 months. However, under a drought condition, multiple moisture deficits could be observed in many other hydrologic variables (such as streamflow, soil moisture and reservoir storage), which are also varying with the time and spatial scales considered. Therefore, future studies should detect the dependence structures of these different types of deficits in a systematic manner, so as to construct an inter-variable drought index that is more representative for the joint behavior of regional droughts. Moreover, the drought forecast and risk assessment performed based on the JDI should be the subject of further study.

This work was financially supported by the National Natural Science Foundation of China (No. 51479130). The authors thank the Hydrology and Water Resource Survey Bureau of Hebei Province for providing the observed precipitation data.