Characteristics of the transmission from meteorological drought to hydrological drought in the Xiangjiang River Basin of China using Copula function

Hydrological droughts are closely related to the meteorological ones in the arid and semi-arid areas. It is of great significance to reveal the response relationship between the meteorological and hydrological droughts in drought warning and water resource management. In this study, the changing patterns of drought were determined in the Xiangjiang River Basin of western China using Copula functions. Daily precipitation data was collected from 40 meteorological stations, while the monthly runoff data was from three hydrological stations (Laobutou, Hengyang, and Xiangtan stations). The standardized precipitation index (SPI) and standardized runoff index (SRI) were adopted to describe meteorological and hydrological droughts. The Pearson correlation coefficient was used to determine the response time to drought. The run theory was used to identify, merge, and remove the drought events. The Mann-Kendall trend test and wavelet analysis were employed to reveal the trend and periodicity of drought in different seasons in the upper, middle, and lower reaches. Furthermore, seven widely used distribution functions were selected to fit the duration and severity sequences of meteorological and hydrological drought that were obtained from SPI and SRI. The optimal parameter estimation was obtained in each marginal distribution using the maximum likelihood. There were strong links between meteorological and hydrological droughts using three Archimedean Copula functions (Frank, Gumbel, and Clayton Copula) by coupling the response probability curve in a Bayesian network model. Finally, the model performance was evaluated using the Akaike information criterion (AIC) and ordinary least squares (OLS). The main results demonstrate: 1) The run theory [0.5, 0, −0.5] was achieved to better identify the drought events, with a matching rate of over 90% between meteorological and hydrological droughts. There was a two-month propagation time from the meteorological to hydrological drought in the whole watershed. The SPI and SRI effectively detected the drought events and better matched them with the historical drought statistics from the different periods (in 1963, 1986, and 2003). 2) The frequency of meteorological drought was higher than that of hydrological drought. The duration and severity of hydrological drought were greater than those of meteorological one, where the downstream area experienced the most severe hydrological drought, but the midstream is the most severely affected by meteorological drought. The difference was attributed to the higher evapotranspiration and high level of socio-economic development in the downstream. 3) There was a tendency toward wetness of the historical data in the basin, which was consistent with the remote sensing monitoring of terrestrial water storage anomaly. However, there was a distinct seasonal variation in the inter-annual wetness of the basin. The upper and middle reaches showed a drier trend in the autumn, while the middle reaches were in a trend toward dryness in the summer. Additionally, there were several outstanding oscillation periods of dry and wet, namely 3-5, 6-10, and 18-21 a. 4) The optimal joint distribution of meteorological-hydrological drought severity in the upstream and downstream area was the Gumbel Copula function, while the Frank Copula function was the optimal joint distribution for the rest. 5) The response probability of hydrological drought duration and severity increased with the increase of characteristic variables in the meteorological drought. There was a stable response probability of hydrological drought duration when the duration of meteorological drought exceeded a specific threshold. This study is of great significance in understanding the mechanism of drought in the Xiangjiang River Basin as well as guiding the drought prevention and fighting work in the region.