The Application of Box–Cox Transformation to Determine the Standardised Precipitation Index (SPI), the Standardised Discharge Index (SDI) and to Identify Drought Events: Case Study in Eastern Kujawy (Central Poland)

Abstract

The article presents the results of research into the transformation of series of hydro-meteorological data for determining dry periods with the Standardised Precipitation Index (SPI) and the Standardised Discharge Index (SDI). Time series from eight precipitation stations and five series of river discharge data in Eastern Kujawy (central Poland) were analysed for 1951–2010. The frequency distribution of the series for their convergence with the normal distribution was tested with the Shapiro–Wilk test and homogeneity with the Bartlett's test. The transformation of the series was done with the Box–Cox technique, which made it possible to homogenise the series in terms of variance. In Poland, the technique has never been used to determine the SPI. After the transformation the distributions of virtually all series complied with the normal distribution and were homogeneous. Moreover, a statistically significant correlation between the δ transformation parameter and the skewness of the series of monthly precipitation was observed. It was similar for the series of mean monthly discharges in the winter half-year and the hydrological year. The analysis indicates an alternate occurrence of dry and wet periods both in case of precipitation and run-offs. Drought periods coincided with low flow periods. Thus, the fluctuations tend to affect the development of agriculture more than long-term ones.

Keywords

• Box–Cox transformation
• Eastern Kujawy
• Gaussian distribution
• meteorological drought
• moving trend
• SDI
• SPI
• variance homogeneity
• homogenicznosc szeregów
• Kujawy Wschodnie
• okresy suche
• przekształcenie Boxa-Coxa
• rozkład normalny
• SDI
• SPI
• trend kroczqcy