This study presents a first-of-its-kind trivariate analysis investigating the dependence structure between temperature concentration (TCI), precipitation concentration (PCI) and potential evapotranspiration (PET) over nine Finnish meteorological stations (1980–2021) using Vine copula modeling. Trend analysis using the modified Mann–Kendall test (MMK) showed that for PCI values, 7 out of 9 stations exhibited decreasing trends (slopes: − 0.04 to − 0.68 yr-1), although not significant (p > 0.05), indicating a more uniform precipitation distribution. Only HT (+ 0.28 yr-1) and KP (+ 0.05 yr-1) showed slight increases, indicating local irregularities. As for the TCI values, significant increases (p < 0.05) in HA (+ 1.50 yr-1), Kl (+ 1.54 yr-1), SR (+ 1.30 yr-1) and TK (+ 1.59 yr-1) showed increasing temperature variability. KP (− 0.06 yr-1) was the only station with a decreasing TCI, which reflects the seasonal uniformity. For PET values, all stations showed significantly increasing trends (p < 0.05), with the steepest increase at HA (+ 69.12 mm/42yr) and KP (+ 62.86 mm/42yr), indicating an increased evaporative demand. In the next step, the trivariate distribution of the mentioned variables was created by selecting the C-vine and R-vine copulas as the superior tree sequence, and the conditional probability of the variables was calculated. Trivariate analysis of PCI, TCI and PET across the Finnish stations revealed significant spatial variations in joint probabilities (5–97%), with the northern stations (KL, TK) showing stronger linkages (e.g. 97% probability for PCI = 11/TCI = 14/PET = 550 mm/year) than the southern stations (HT, KK: ≤ 60% probability). The Vine copula framework enabled prediction scenarios, such as TCI = 13.5 at the KK station, which yielded PCI = 11/PET = 431 mm/year with a 60% probability, highlighting its utility for climate adaptation. The results also show that PCI > 10 occurs with a probability of > 50% nationwide, indicating heightened flood risks—snowmelt-driven in the north (TCI-sensitive) and rainfall-driven in the south (PCI-sensitive). These results are consistent with observed hydroclimatic shifts in Finland, including increased winter flooding (north) and extreme summer precipitation (south), emphasizing the need for region-specific water management strategies to address the combined drought and flood risks under climate change.

Investigating the Dependence Structure of Temperature and Precipitation Concentration with Evapotranspiration in Finland

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发表日期：

2025年10月18日

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Rasoul Mirabbasi,
Mohammad Nazeri Tahroudi,
Alireza Sharifi,
Ali Torabi Haghighi

摘要

This study presents a first-of-its-kind trivariate analysis investigating the dependence structure between temperature concentration (TCI), precipitation concentration (PCI) and potential evapotranspiration (PET) over nine Finnish meteorological stations (1980–2021) using Vine copula modeling. Trend analysis using the modified Mann–Kendall test (MMK) showed that for PCI values, 7 out of 9 stations exhibited decreasing trends (slopes: − 0.04 to − 0.68 yr^-1), although not significant (p > 0.05), indicating a more uniform precipitation distribution. Only HT (+ 0.28 yr^-1) and KP (+ 0.05 yr^-1) showed slight increases, indicating local irregularities. As for the TCI values, significant increases (p < 0.05) in HA (+ 1.50 yr^-1), Kl (+ 1.54 yr^-1), SR (+ 1.30 yr^-1) and TK (+ 1.59 yr^-1) showed increasing temperature variability. KP (− 0.06 yr^-1) was the only station with a decreasing TCI, which reflects the seasonal uniformity. For PET values, all stations showed significantly increasing trends (p < 0.05), with the steepest increase at HA (+ 69.12 mm/42yr) and KP (+ 62.86 mm/42yr), indicating an increased evaporative demand. In the next step, the trivariate distribution of the mentioned variables was created by selecting the C-vine and R-vine copulas as the superior tree sequence, and the conditional probability of the variables was calculated. Trivariate analysis of PCI, TCI and PET across the Finnish stations revealed significant spatial variations in joint probabilities (5–97%), with the northern stations (KL, TK) showing stronger linkages (e.g. 97% probability for PCI = 11/TCI = 14/PET = 550 mm/year) than the southern stations (HT, KK: ≤ 60% probability). The Vine copula framework enabled prediction scenarios, such as TCI = 13.5 at the KK station, which yielded PCI = 11/PET = 431 mm/year with a 60% probability, highlighting its utility for climate adaptation. The results also show that PCI > 10 occurs with a probability of > 50% nationwide, indicating heightened flood risks—snowmelt-driven in the north (TCI-sensitive) and rainfall-driven in the south (PCI-sensitive). These results are consistent with observed hydroclimatic shifts in Finland, including increased winter flooding (north) and extreme summer precipitation (south), emphasizing the need for region-specific water management strategies to address the combined drought and flood risks under climate change.