Propagation dynamics and causes of hydrological drought in response to meteorological drought at seasonal timescales

According to the widely accepted definition of drought, meteorological and hydrological droughts originally develop from rainfall and runoff deficits, respectively. Runoff deficit is mainly derived from rainfall deficit, and the propagation from meteorological drought to hydrological drought is critical for agricultural water management. Nevertheless, the characteristics and dynamics of drought propagation in the spatiotemporal scale remain unresolved. To this end, the characteristics and dynamics of drought propagation in different seasons and their linkages with key forcing factors are evaluated. In this study, meteorological and hydrological droughts are characterized by the Standardized Precipitation Index (SPI) and the Standardized Runoff Index (SRI), respectively. Propagation time is identified by the corresponding timescale of the maximum correlation coefficient between the SPI and the SRI. Then, a 20-year sliding window is adopted to explore the propagation dynamic in various seasons. Furthermore, the multiple linear regression model is established to quantitatively explore the influence of meteorological factors, underlying surface features and teleconnection factors on the propagation time variations. The Wei River Basin, a typical Loess Plateau watershed in China, is selected as a case study. Results indicate the following: (1) the propagation time from meteorological to hydrological drought is shorter in summer (2 months) and autumn (3 months), whereas it is longer in spring (8 months) and winter (13 months). Moreover, the propagation rates exhibit a decreasing trend in warm seasons, which, however, show an increasing trend in cold seasons; (2) a significant slowing propagation in autumn is mainly caused by the decreasing soil moisture and precipitation, whereas the nonsignificant tendency in summer is generally induced by the offset between insignificant increasing precipitation and significant decreasing soil moisture; (3) the replenishment from streamflow to groundwater in advance prompts the faster propagation from meteorological to hydrological drought in spring and winter and (4) teleconnection factors have strong influences on the propagation in autumn, in which Arctic Oscillation, El Niño-Southern Oscillation and Pacific Decadal Oscillation mainly affect participation, arid index and soil moisture, thereby impacting drought propagation.


INTRODUCTION
With global climate change and intensified water circulation, extreme weather and climate events have become more frequent in recent years. History has repeatedly proved that serious drought events in a given area will not only cause great mortality and economic losses, but also arouse the widespread concern of relevant scholars as well as the introspection of local government. Numerous drought and flood events have occurred in recent decades. A string of drought events occurred in recent decades, thereinto, the sandstorm drought in America of the 1930s (Brekke 1947;Wilhite & Glant 1985;Cook et al. 1999;Fye et al. 2010), which covered across two-thirds of the United States and wreaking havoc for a decade, caused 250 million people to leave. China has been subjected to drought damage repeatedly in the past years. The year of 2010 in the southwestern of China affected .67,000 km 2 of arable land and left .20 million people without drinking water. The middle and lower reaches of the Yangtze River have suffered the worst drought for a 70-year return period (Yu et al. 2014), which impacted 17 million people and the direct economic losses reached nearly 10 billion.
Drought as a natural hazard may happen in all the places (including dry and wet regions) at multiple time scales (Fang et al. 2019a(Fang et al. , 2019b. It is deemed as a complex, multifaceted phenomenon diffusely (Van Loon 2015), which has a major impact on every part of the hydrological cycle. Moreover, drought can influence wide areas and last for a long time (WMO 1997). Drought has attracted growing attention in many different fields, such as ecology, environment, hydrology and agriculture (Tallaksen & Van Lanen 2004;Mishra & Singh 2010;Zhang et al. 2012;Mohammad et al. 2014;Chen & Sun 2017). Drought is largely driven by climate changes, such as the decreases of precipitation, which develops slowly and lasts months to years (Tallaksen & Van Lanen 2004;Tallaksen et al. 2009). Depending on the deficit of different hydrologic features, drought is commonly divided into four categories, that is, meteorological drought, hydrological drought, agricultural drought and socioeconomic drought (Mishra & Singh 2010). There are some differences and connections between them. Specifically, when the precipitation is insufficient, meteorological drought occurs; the lack of runoff then causes hydrological drought; agricultural drought is triggered by the inadequacy of soil moisture; whereas the socioeconomic drought directly results from the water supply not satisfying the human water demand, which is also the embodiment of the impacts of the above three types of droughts on human society (Dracup et al. 1980;Guo et al. 2019). In general, meteorological drought begins the earliest, then agricultural and hydrological droughts happen. If the socioeconomic drought occurs finally, this water deficit event is more serious. Many researches have focused on the establishment of drought index, to identify drought events and evaluate spatial and temporal distribution characteristics of drought (Feng et al. 2014;Huang et al. 2015;Leng et al. 2015;Xu et al. 2015;Ge et al. 2016;Huang et al. 2019).
As mentioned above, there are close links between different types of drought. The transformation from one type of drought to another is called drought propagation (Huang et al. 2017). In recent years, drought propagation has become a hot topic in the field of hydrology and water resources. The analysis methods of drought propagation are mainly divided into model simulations and statistical methods. Different hydrological models reveal the propagation time between different types of droughts to a certain extent. Wang et al. (2011) and Van Loon & Van Lanen (2012) adopted a hydro-agricultural coupling model and an integrated large-scale hydrological model to study the propagation of drought. Lorenzo-Lacruz et al. (2013) used the Pearson correlation coefficient to determine the time scale of the Standardized Precipitation Index (SPI) with the best correlation with the Standardized Runoff Index (SRI) as the response time of hydrological drought to cumulative precipitation deficit. Besides, some researches discuss the forcing factors on drought propagation, for example, the process of propagation from meteorological to hydrological drought is influenced by climate characteristics (Van Loon & Van Lanen 2012). Furthermore, underlying surface features and teleconnection factors also have a great influence on the propagation process (Huang et al. 2015(Huang et al. , 2017. For the law of drought propagation, Li et al. (2018) established the relationship between hydrological drought and driving factors, which can explain this pattern to some extent.
Although multiple researches have inquired into the relationships and influences between different types of drought, the dynamic change of drought propagation and the quantitative estimation of various influencing factors on its dynamics at seasonal scale remain unsolved. Improving the understanding of the mechanisms of drought propagation can help water resource managers to design optimal water management strategies, which may be used to mitigate the impacts of droughts. However, propagation in diverse types of drought needs further and systematic research. The numerous mechanisms behind drought propagation require to be explored in depth. To fill this research gap, the study attempts to examine the propagation time from meteorological to hydrological drought in different seasons, and analyzes their dynamic changes, for evaluating the drought propagation dynamics. With the modification of precipitation deficits in drought propagation, diverse climate, different basins as well as human activities make an important contribution, leading to the diversity of drought propagation in different catchments (Van Loon 2015). Thereupon, examining the different types of drought and how drought propagates is the top priority. It can boost the acquaintance of drought, create the foundation to support the development of drought and predict the variation tendency of drought.
This study has the following three main objectives: (1) to calculate the propagation time from meteorological drought to hydrological drought at seasonal scale; (2) to examine the seasonal dynamic propagation characteristics under the backdrop of a changing environment and (3) to quantitatively explore the impacts of meteorology, underlying surface features, teleconnection factors on seasonal dynamic propagation.

Study area
The Wei River Basin (WRB) is the largest tributary of the Yellow River basin, which covers an area of 134,600 km 2 . The distribution map of the WRB is shown in Figure 1. This basin is located in the continental monsoon climate zone with abundant precipitation and high temperature in summer, little precipitation and low temperature in winter. Generally speaking, precipitation has a significant seasonal variation. During monsoon (June-September), precipitation accounts for 60% of whole year's precipitation, which always appears in the form of rainstorm or continuous rain. Owing to the uneven annual distribution and large inter-annual variation of precipitation in this area, which are mainly caused by the instable intensity of the North Pacific subtropics. The annual maximum precipitation can be 2.5 times larger than the annual minimum precipitation. Since ancient times, natural disaster events have frequently occurred in this basin (Du 2008), especially for drought events, which is the most frequent and harmful disaster. Drought has become the main factor restricting the regional development.
The Wei River is the main water source of the Guanzhong Plain, which is an area where agriculture plays a crucial role in local economic development (Huang et al. 2017). With the rapid development, this zone has also built many industrial parks, whose functioning requires water (Huang et al. 2017). The runoff in the WRB has obviously reduced in recent decades (Huang et al. 2014a(Huang et al. , 2014b, and it was often subjected to the effect of droughts (Huang et al. 2014a(Huang et al. , 2014b. Hence, the WRB is a region with extreme shortage of water. A comprehensive drought investigation integrated with the drought propagation and its influence is of great important in mitigating the drought effects.

Data
In this paper, daily precipitation data were collected from 1960 to 2010 from 21 weather stations in the WRB, which derived from the National Climate Center of the China Meteorological Administration. The runoff data were obtained from the Yellow River conservancy commission, including daily runoff sequences from 1962 to 2010 from several hydrological stations in Linjiacun, Zhangjiashan, Huaxian and Zhuangtou and others. The mean values of these stations are used as the calculated data of the WRB in this study. The El Niño-Southern Oscillation (ENSO) events are represented by the monthly Nino 3.4 Index and the monthly Arctic Oscillation (AO) series containing 1962-2010 events obtained from the National Oceanic and Atmospheric Administration (NOAA). Daily sunspot data from 1962 to 2010 supplied by the International Council for Science (ICSU) World Data System (WDS) and the long-term observational series were used in this study (http://sidc. oma.be/silso/dayssnplot). Additionally, potential evapotranspiration series of the meteorological stations were calculated through the Penman-Monteith equation (Allen et al. 1989). The soil moisture and base flow data were both simulated by the Variable Infiltration Capacity (VIC) model.

Standardized Precipitation Index
It is hard to compare changes in diverse spatial-temporal scale utilizing the precipitation data straightly due to the high fluctuation of precipitation in different times and districts. Moreover, the distribution of precipitation is a skewed distribution. On that basis, McKee et al. (1993) first brought up the conception of SPI to address a variety of time scales, which can monitor long-term precipitation conditions. The SPI can transform the skewness distribution to normal distribution, which is not only convenient for different data comparisons, but also can eliminate spatial and temporal distribution differences. At present, many studies have applied the SPI to characterize the meteorological arid conditions in the WRB and all have good results (Huang et al. 2014a(Huang et al. , 2014bCai et al. 2018).
SPI is derived from a long-term record of precipitation, which is further transformed into standard normal distribution. In the first place, the original precipitation observations are aggregated to generate a precipitation series at a timescale of interest (typically 1, 3, 6 or 12 months). Then, the gamma probability distribution function is used to fit the average precipitation sequence. At last, the cumulative probability of the gamma distribution is converted to the standard normal distribution to calculate the SPI. The detail calculation process of SPI is introduced by Fang et al.

Standardized Runoff Index
The SRI was put forward on the strength of SPI theory used by McKee et al. (1993). Also, it was first proposed by Shukla & Wood (2008). Compared to the SPI, they take the same principles to build only using the different preliminary. That is to say, the calculation of SRI substitutes the runoff series for precipitation series of SPI. The calculation of SRI is to transform the distribution of accumulated runoff on a given time scale into a standard normal distribution through equal probability transformation.

Calculation of propagation time from meteorological to hydrological drought
In fact, the propagation from meteorological drought to hydrological drought is the conversion process from precipitation to runoff. Based on the multi-scale property of SPI, the scale range of SPI is changed, the scale range of SRI is fixed and then the correlation coefficient between the SPI in a variable scale and the SRI can be calculated. The SPI is chosen at the scale of 1-24 months and the SRI at 1 month in this study. Then, the correlations of SPI sequences at different time scales and SRI sequences are all calculated, respectively. Finally, the SPI scale corresponding to the maximum correlation coefficient is regarded as the propagation time from meteorological to hydrological drought (Yu et al. 2018;Wang et al. 2019).
The greatest advantage of the SPI is that it can characterize drought conditions at different scales, which would be perfectly applied on not only short-term, but also long-term, water resource monitoring. To investigate the propagation time from meteorological to hydrological drought, the relationship between the SRI and the SPI at different time scales in the WRB is explored, and related results are displayed in Figure 2. In the figure, the x coordinate signifies various time scales of SPI (1, 2, 3, …, 24), while the y coordinate displays months. Different colors imply the correlation coefficients of SPI and SRI, where red represents the high value region and blue represents the low value region of the correlation coefficient.

The cross-wavelet
The cross-wavelet is capable of presenting the correlation between two time series in both time and frequency domains, combined with the wavelet transformation and cross-spectrum analysis (Hudgins & Huang 1996). In the figure, the red represents the peak value of energy density, and the blue represents the valley value of energy density, respectively, showing the locality and dynamic characteristics of time-sharing transformation of the dominant wave group. The dark or light color represents the relative change of energy density. The fine solid black line represents the boundary of the cone line affected by the wavelet, and its interior is an effective spectral value region. The thick black line in the region represents a 95% confidence interval with a passing significance level of A ¼ 0.05. The direction of the arrows in the figure reflects the phase relationship between the influencing factors and rainfall erosivity. The (→) from left to right indicates that the changes in the two factors are in the same phase, showing a positive correlation. The (←) from the right finger to the left represents the inverse phase, showing a negative correlation (Grinsted et al. 2004).

Multiple linear regression model
Multiple linear regression (MLR) is a statistical technique that attempts to model the relationship between two or more explanatory variables and a response variable by fitting a linear equation to observed data. Every value of the independent variable x is associated with a value of the dependent variable y. Formally, the model for MLR, given n observations, is MLR is used to determine a mathematical relationship among a number of random variables. In other terms, MLR examines how multiple independent variables are related to one dependent variable. Once each of the independent factors have been determined to predict the dependent variable, the information on the multiple variables can be used to create an accurate prediction on the level of effect they have on the outcome variable. The model creates a relationship in the form of a straight line (linear) that best approximates all the individual data points.

Propagation time from meteorological to hydrological drought in different seasons
The relationship of the SPI and the SRI between 1962 and 2010 in the WRB was explored. The outcome reflects the response time of hydrological drought to meteorological drought is roughly 3 months corresponding to the coefficient of 0.870. The propagation time is short in summer and autumn, but relatively long in spring and winter. In terms of the correlation coefficient of all months, the maximum appears in October, and the autumn has the strongest correlation.
Generally, the WRB is strongly affected by monsoon, which has abundant precipitation and high temperature in summer, dry and cold climate occurs in winter. The annual average temperature is about 6-14°C, and the annual average precipitation is 450-700 mm (Huang et al. 2015).
Summer (June-August) and autumn (September-November) are wet seasons. Temperature is relatively high in these two seasons, especially in summer. Its average temperature reaches 24°C. Precipitation is always abundant (average 161.6 mm in autumn and 286.4 mm in summer in 1962-2010) with high-intensity rainstorms (Table 1). Once precipitation occurs, it is easy to generate runoff since soil moisture is high. After precipitation replenishes the interception, infiltration and sink filling, the loss is no longer significantly increased with the continuation of precipitation, and the soil is basically saturated, resulting in the generation of runoff (Apurv et al. 2017;Joo et al. 2020). The amount and intensity of the precipitation in summer and autumn are large. Therefore, the time of drought propagation is always short in the two seasons. Table 1 shows that the amount of the precipitation in summer is more than autumn, and land surface converge, therefore, tends to be faster. As a result, the propagation time in summer is shorter than that in autumn. It is indicated in Table 1 that spring (March-May) and winter (December-February) are dry seasons with little precipitation, especially in winter (120.6 mm in spring and 18.0 mm in winter in 1962-2010), and temperature is relatively low in these two seasons, especially in winter, and its average temperature is À1 to À3°C (Jiang et al. 2012). Almost all of the runoff is supplied by groundwater discharge in the form of base flow in dry seasons, which is generally derived from long-term precipitation accumulation of early period (Apurv et al. 2017). It is found that the runoff in this region mainly depends on groundwater formed by the accumulation of precipitation in the previous 8 months in spring and 13 months in winter. The slow development of water cycle results in few runoff generation. In consequence, the process of drought propagation tends to be slow. Moreover, the propagation time in winter is longer than that in spring mainly caused by less precipitation and cold weather. The runoff in spring comes from both groundwater and direct surface runoff, thus leading to faster propagation than winter. Figure 3 shows the trends of propagation time in different seasons, which is derived from a sliding window with 20-year length between 1962 and 2010. Then, the Mann-Kendall test was used to verify the significance of these trends. Specifically, Table 2 indicates that the propagation time has a significant decreasing trend in winter and a significant increasing trend in autumn at the 99% confidence level. The propagation time has no obvious tendency in spring and summer. Results indicate that the hydrologic circle rate is intensifying in winter and reducing in autumn in the Loess Plateau watershed under the warming climate. The possible causes of the propagation dynamics are systematically investigated in the next section. Table 2 shows the correlation between influencing factors and propagation time in different seasons. The tendency of meteorological factors and underlying surface features is shown in Table 3. It can be found that the arid index also has an insignificant decreasing trend, while precipitation has an insignificant increasing trend in summer (Table 3). It indicates that the region in summer is wetter than before, which tends to make the propagation process faster. The significant decreasing trends of base flow and soil moisture require more water to replenish them first, thus making the propagation process slower. Besides, base flow and soil moisture all have better correlation with propagation time than precipitation and arid index. As a consequence, the interaction of insignificant increasing precipitation and significant decreasing soil moisture eventually results in the insignificant increasing propagation time in summer. It indicates that underlying surface features are major influencing factors. Results in Table 3 also indicated that the precipitation has a significant downtrend at the 95% confidence level, and the arid index has a significant uptrend at the 95% confidence level in autumn. These two factors lead to the basin becoming drier, and the significant decreasing precipitation causes the decrease of runoff, thus making the propagation process slower. In  addition, base flow and soil moisture significantly decrease, especially for soil moisture. The replenishment of soil moisture needs more time, and the propagation time prolongs. As a result, both significant decreasing precipitation and soil moisture eventually lead to the significant increasing propagation time in autumn. This is the reason why the propagation time is more significantly increasing in autumn than that in summer.  Similarly, as noted in Table 3, a small amount of precipitation and high evapotranspiration cause scarce runoff generation, and the basin gets drier in winter. Streamflow in winter is reliant on groundwater supply, which is closely associated with the surface streamflow condition. Decreasing soil moisture and base flow tend to make surface streamflow exhaust earlier, thus leading to earlier replenishment of groundwater. Thus, the propagation time in winter has a significant decreasing trend. With regard to spring, its runoff is mainly impacted by precipitation and groundwater, where groundwater is the dominant factor due to the long propagation. Being similar with winter, decreasing soil moisture and base flow are expected to make surface streamflow exhaust earlier, thus resulting in earlier replenishment of groundwater. This leads to the faster propagation time. However, precipitation exhibits a significant downward trend at the 95% confidence level in spring, which causes a slower propagation time in the form of direct surface streamflow. Influenced by decreasing precipitation and earlier groundwater supply, the propagation time shows an insignificant decreasing trend.

Effects of diverse influencing factors on seasonal dynamic propagation
The above results indicate that both meteorological factors and underlying surface features have a great impact of the dynamic changes of propagation time in autumn and winter. However, since the teleconnection factors can indirectly affect the propagation of drought, the study selects relatively significant influencing factors to explore the relationship between teleconnection factors and meteorological factors, as well as underlying surface features in these two seasons.
On the whole, the teleconnection factors have great influences on meteorological factors and underlying surface features. Specifically, the influence and correlation of different factors are different in autumn and winter.
The cross-wavelet analysis shown in Figure 1967-1972 and 1997-2004. It can be found from the above results that the teleconnection factors have great influences on meteorological factors and underlying surface features, and then affect the propagation time of drought.

Quantitative impacts of meteorology, underlying surface features and teleconnection factors on seasonal dynamic propagation
The above section reveals that different seasons have distinct influence factors. For better understanding the relationship between propagation and relevant factors, the MLR is built and the determination coefficient (R 2 ) is calculated, which are shown in Figure 5. Notably, three scenarios were designed to explore the contribution of meteorological factors, surface features and teleconnection factors. The maximum R 2 of this model fitting is 0.76, which has a certain reliability. The explanation of meteorological factors to the propagation time between meteorological and hydrological drought is 44, 12, 28 and 37% in spring, summer, autumn and winter. Whereas, when the underlying surface features are added, the explanation increased to 49, 27, 37 and 41%, respectively. And when the teleconnection factors were considered, the results have further improved and reached to 57, 54, 76 and 47%. From the above results, it can clearly be seen that the interpretation of propagation time response to underlying surface features is 5, 13, 9 and 4% in different seasons. And the interpretation of propagation time response to teleconnection factors is 8, 27, 39 and 6%, respectively. By comparison, the meteorological factors have the strongest impact on spring and winter, and the teleconnection factors have the strongest impact on summer and autumn. Therefore, the significant slowing drought of propagation patterns in autumn is closely linked with teleconnection factors.
It is obvious that considering the underlying surface features and teleconnection factors will have a better performance of drought propagation, especially in summer and autumn, which is in line with the results outlined in Figures 4 and 6 of section 'Effects of diverse influencing factors on seasonal dynamic propagation', further verifying the reliability of these findings. That is to say, taking the underlying surface features and teleconnection factors into account gives a more accurate interpretation of propagation time response.

CONCLUSION
In this study, the propagation dynamics from meteorological to hydrological drought and influence factors have been revealed. The following conclusions can be reached: • The propagation time from meteorological drought to hydrological drought is generally the quickest in summer (2 months), followed by autumn (3 months), then spring (8 months) and finally winter (13 months).
• The propagation time insignificantly increases in summer and decreases in spring, while significantly increasing in autumn and decreasing in winter.
• The results indicate that AO, ENSO and PDO in autumn; ENSO and PDO in winter have great impacts.
Although the paper has determined the responding time of hydrological drought to meteorological drought in seasons and dynamic changes, and the impacts on propagation process, it also found that considering the teleconnection factors will have a better performance of drought propagation. And the study has provided the basis for drought researchers and forecasters. But the further influencing mechanism has not been revealed. How other factors impact the drought propagation needs to be studied for further investigation.