Multivariate Frequency Analysis of Drought Characteristics in Finland Using Vine Copulas

Abstract

We use a multivariate analysis to study droughts in Finland using the Joint Deficit Index (JDI). Subsequently, the joint probability of occurrence of drought characteristics was analysed using Vine copulas. For this purpose, we used monthly precipitation from 22 meteorological stations across Finland in the period 1980–2021. The JDI time series showed that Finland had a normal wetness condition most of the time during the studied period. Trend analysis of the JDI time series using a modified Mann–Kendall test showed that there was no significant trend in the values of this index during the studied period. The drought characteristics, including severity, duration and inter-arrival time (IAT), were extracted from the JDI time series for each station. The trend analysis of drought characteristics showed that only the Tohmajärvi Kemie station in eastern Finland had a significant negative trend in drought duration and severity. Furthermore, of the 22 stations studied, only two stations showed a significant increasing trend in the duration and severity of drought at the 10% level. The drought characteristics at the remaining stations showed no significant trend at the 10% level of significance. For stations with non-stationary drought characteristics, generalised additive models for location, scale, and shape (GAMLSS) were used for frequency analysis. The correlation between the three characteristics of severity, duration and IAT was investigated using Kendall's Tau statistic. The results showed a high correlation between the two variables duration and severity and a moderate and acceptable correlation between drought severity and IAT as well as the pair of duration and IAT. In the following, copula functions were used to construct a trivariate distribution of the drought characteristics. Among the copulas tested, the R-vine copula and its independent mode have the best fit for the variables under study and provide a suitable tree sequence. Finally, using the aforementioned copulas and their conditional density, the frequency analysis of the three drought variables was performed. The results of this study were presented in the form of four-dimensional graphs to estimate the joint probability of occurrence of drought characteristics based on the JDI. These graphs are presented according to the precipitation conditions of each station, and by having a drought characteristic, other characteristics can be estimated with different probabilities. The proposed method is very efficient in analysing the joint frequency of drought characteristics due to the consideration of the effective parameters and the use of conditional density.