Calibrazione di indici per il monitoraggio delle siccità in presenza di serie stazionarie e non stazionarie

In the present study uncertainty analyses of the Standardized Precipitation Index (SPI) and the Palmer Hydrological Drought Index (PHDI) are carried out with respect to the size of the samples used for calibrating the above mentioned drought indices, either in the case of stationary or non stationary series. In particular, sampling properties of SPI and PHDI, such as bias and root mean squared error (RMSE), are analytically and numerically derived in terms of the sample size, as measures of the error of estimation. In the case of stationary series, results indicate that the bias of estimation of SPI is equal to zero (i.e. SPI estimator is unbiased), while for PHDI it decreases as the sample size increases. For both indices, RMSE tends asymptotically to zero as sample size increases, thus the estimators of the two indices are both RMSE consistent. Furthermore, the effect of the presence of a linear trend on the assessment of SPI values is investigated. In this case, the SPI estimator is biased, while the corresponding RMSE first decreases until a minimum value is reached for a specific sample size, and then increases again. This suggests that an optimal sample size (in RMSE sense) can be determined, when the underlying series is affected by trend. Finally, the effect of preliminary trend estimation and removal is investigated numerically by simulation and compared to the case when trend is neglected. Numerical 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.