Technical note: Decomposing a time series into independent trend, seasonal and random components

Abstract. Many time series observations in hydrology and climate show large seasonal variations and it has long been common practice to separate the original data into trend, seasonal and random components. We were interested in using that decomposition approach as a basis for understanding variability in hydro-climatic time series. For that purpose, it is desirable that the trend, seasonal and random components are independent so that the variance of the original time series equals the sum of the variances of the three components. We show that the resulting decomposition with the trend component traditionally estimated either as a linear trend or a moving average does not produce components that are independent. Instead we introduce the rarely adopted two-way ANOVA model into studies of hydro-climatic variability and define the trend as equal to the annual anomaly. This traditional approach produces a decomposition with three independent components. We then use global land precipitation data to demonstrate a simple application showing how this decomposition method can be used as a basis for comparing hydro-climatic variability. We anticipate that the three-part decomposition based on the two-way ANOVA approach will prove useful for future applications that seek to understand the space-time dimensions of hydro-climatic variability.