Analysis of the characteristics of apple later frost risks in Shaanxi Province based on Copula functions

Late frost is one of the most destructive meteorological disasters in the Loess Plateau of China. A great threat can be posed to the sustainable production of apples, leading to great economic losses in the apple industry. Thus, it is a high demand to explore the occurrence of late frost events for the prevention of apple late frost disasters in the decision-making of the local apple industry. In this study, the late frost return periods were investigated on the duration and severity of late frost events using the Coupla functions. The reliability of the model was then verified to analyze the characteristics of apple late frost. The study area was taken as the apple-producing areas of Shaanxi Province in western China. The meteorological datasets were collected from the seven weather stations from 1971-2018. The daily minimum temperature (Tmin) of 0℃ was taken as the critical temperature for the occurrence of apple late frost events, in order to extract the two characteristic variables of duration and severity of late frost events. These characteristic variables of late frost events were first fitted by seven common distribution functions, respectively. Kolmogorov Smirnov (K-S) test was then carried out to verify the model. The joint distributions of late frost characteristic variables were constructed to evaluate the goodness-of-fit using six Copula functions. The occurrence probability and return period of late frost events were analyzed with the optimized Copula functions. The results showed that the severity of late frost risks generally increased from the southeast to northwest in the study area from 1971 to 2018. The optimal marginal distribution of late frost duration was in the log-normal distribution, while there was a great difference in the optimal marginal distributions of late frost severity. A significant positive correlation was found between the duration variables and the severity of late frost at each station. The joint cumulative probability increased significantly, as the severity and duration of late frost increased, but the increasing trend was much slower than before. A much more significant increase was observed in the co-occurrence return period under the same increase of univariate value, compared with the joint. The univariate return period was always between the joint and co-occurrence return period. Once the univariate return period was small enough, the optimal range of the actual univariate return period can be estimated, according to the joint and the co-occurrence return period. In general, a low probability was found in the late frost events with long duration and high severity at the weather stations in apple-producing areas in Shaanxi Province of China. However, the stations in the Yan'an area were more susceptible to the late frost events with high severity or long duration, as well as the late frost events with both high severity and long duration. Thus, more attention can be paid to late frost risks in the Yan'an area. This finding can provide a theoretical base to deal with the late frost disaster in apple production.