Meaningful Trend in Climate Time Series: A Discussion Based On Linear and Smoothing Techniques for Drought Analysis in Taiwan

Abstract

Finding significant trends in hydroclimate time series has been deemed an essential task in numerous studies. Despite the existence of various trend detection methods, statistical significance is mostly examined for linear trends and related to the meaningfulness of the found trends. We wish to draw attention to a more general definition of meaningful trends by cross-referencing not only linear but also smoothing techniques. We apply linear regression (LR) and two smoothing techniques based on regularized minimal-energy tensor-product B-splines (RMTB) to the trend detection of standardized precipitation index (SPI) series over Taiwan. LR and both RMTB-based methods identify an overall upward (wetting) trend in the SPI series across the time scales in Taiwan from 1960 to 2019. However, if dividing the entire time series into the earlier (1960–1989) and later (1990–2019) sub-series, we find that some downward (drying) trends at varied time scales migrate from southcentral–southwestern to eastern regions. Among these significant trends, we have more confidence in the recent drying trend over eastern Taiwan since all the methods show trend patterns in highest similarity. We also argue that LR should be used with great caution, unless linearity in data series and independence and normality in residuals can be assured.