Uncertainty analysis of the standardized precipitation index within a non-stationary framework

An uncertainty analysis of standardized precipitation index (SPI) with respect to the length of the sample used for parameter estimation is carried by assuming non-stationary precipitation series. Sampling properties of SPI, such as bias and root mean squared error (RMSE), are analytically derived for normal distributed data. Results indicate that, in terms of RMSE, SPI values are significantly affected by the size of the sample adopted for its estimation. In particular, in the presence of a linear trend, a minimum RMSE value can be determined corresponding to a specific sample size. This suggests that an optimal sample size (in RMSE sense) can be determined, when the underlying series is affected by trend. Furthermore, Monte Carlo simulation experiments reveal that detrending procedures are not recommended for samples whose size is smaller than a given value related to the slope of the linear trend.