Optimization-based prediction uncertainty qualification of climatic parameters

Point predictions of hydroclimatic processes through nonlinear modeling tools are associated with uncertainty. The main goal of this research was to construct Prediction Intervals (PIs) for nonlinear Artificial Neural Network (ANN)-based models of evaporation and the Standardized Precipitation Index (SPI). These are two critical indicators for climate for four stations in Iran (i.e., Tabriz, Urmia, Ardabil and Ahvaz) to qualify their predicted Uncertainty Values (UVs). We used classical techniques of Bootstrap (BS), Mean-Variance Estimation (MVE), and Delta, as well as an optimization-based method of Lower-Upper Bound Estimation (LUBE), to construct and compare the PIs. The wavelet-based denoising method was also adopted to denoise input data, enhancing the modeling performance. The obtained results indicate the ability of the BS and LUBE methods to estimate the uncertainty bound. The Delta method mostly failed to find the desired coverage due to its narrow PIs. On the other hand, the MVE method, due to its wide bound, did not convey valuable information about uncertainty. According to the obtained results, denoising the input vector could enhance the PI quality in the modeling of the SPI by up to 76%. It was more prominent than reducing the UV for evaporation models, which was observed the most at the Ardabil station, up to 30%. The inherently more random nature of drought than the evaporation process was interpreted as the cause of this reaction. From the results, Urmia station seems the riskiest regarding drought ventures.