Improving daily rainfall extremes simulation using the generalized Pareto distribution: a case study in Western Iran

Prediction of the occurrence or non-occurrence of daily rainfall plays a significant role in agricultural planning and water resource management projects. In this study, gamma distribution function (GDF), kernel, and exponential (EXP) distributions were coupled (piecewise) with a generalized Pareto distribution. Thus, the gamma-generalized Pareto (GGP), kernel-generalized Pareto (KGP), and exponential-generalized Pareto (EGP) models were used. The aim of the present study was to introduce new methods to modify the simulated generation of extreme rainfall amounts of rainy seasons based on the preserved spatial correlation. The best approach was identified using the normalized root mean square error (NRMSE) criterion. For this purpose, the 30-yr daily rainfall datasets of 21 synoptic weather stations located in different climates of West Iran were analyzed. The first, second, and third-order Markov chain (MC) models were used to describe rainfall time series frequencies. The best MC model order was detected using the Akaike information criterion and Bayesian information criterion. Based on the best identified MC model order, the best piecewise distribution models, and the Wilks approach, rainfall events were modeled with regard to the spatial correlation among the study stations. The performance of the Wilks approach was verified using the coefficient of determination. The daily rainfall simulation resulted in a good agreement between the observed and the generated rainfall data. Hence, the proposed approach is capable of helping water resource managers in different contexts of agricultural planning.

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate model over a large frequency range, spanning several orders of magnitude. We propose a strategy to overcome these instabilities, replacing an unstable global MRI surrogate with a union of stable local rational models. The partitioning of the frequency range into local frequency sub-ranges is performed automatically and adaptively, and is complemented by a (greedy) adaptive selection of the sampled frequencies over each sub-range. We verify the effectiveness of our proposed method with two numerical examples.