The Use of GAMLSS Framework for a Non-Stationary Frequency Analysis of Annual Runoff Data over a Mediterranean Area

Abstract

Climate change affects all the components of the hydrological cycle. Starting from precipitation distribution, climate alterations have direct effects on both surface water and groundwater in terms of their quantity and quality. These effects lead to modifications in water availability for agriculture, ecology and other social uses. Change in rainfall patterns also affects the runoff of natural rivers. For this reason, studying runoff data according to classical hydrological approaches, i.e., statistical inference methods that exploit stationary probability distributions, might result in missing important information relevant to climate change. From this point of view, a new approach has to be found in the study of this type of data that allows for non-stationary analysis. In this study, the statistical framework known as Generalized Additive Models for Location, Scale and Shape (GAMLSS), which can be used to carry out non-stationary statistical analyses, was applied in a non-stationary frequency analysis of runoff data collected by four gauges widely distributed across Sicily (Italy) in the period 1916–1998. A classical stationary frequency analysis of these runoff data was followed by a different non-stationary frequency analysis; while the first was made using annual rainfall as a covariate, with the aim of understanding how certain statistical parameters of runoff distribution vary with changes in rainfall, the second derived information about the temporal variability of runoff frequencies by considering time as a covariate. A comparison between stationary and non-stationary approaches was carried out using the Akaike information criterion as a performance metric. After analyzing four different probability distributions, the non-stationary model with annual rainfall as a covariate was found to be the best among all those examined, and the three-parameter lognormal the most frequently preferred distribution.

Statistical Analysis and Scenario Modeling of Non-Stationary Runoff Change in the Loess Plateau: A Novel Application of the Generalized Additive Model in Location, Scale and Shape

“…A Generalized Additive Model in Location, Scale, and Shape (GAMLSS) is a semi parametric regression model that analyzes the frequencies of stationary and non-station ary runoff and other features [17][18][19][20][21][22]29,30].…”

“…It supports a variety of random variable frequency distribution types and is extremely useful in constructing linear or nonlinear functional relationships between distribution function position parameters, scale parameters, shape parameters, and explanatory variables [18]. The GAMLSS framework has been widely applied in non-stationary frequency analysis, modeling, and forecasting in hydrology [19][20][21][22]. This GAMLSS feature also allows for cross-driving interactions between runoff and the driving elements, or between the driving elements themselves.…”

Study of Nonstationary Flood Frequency Analysis in Songhua River Basin

“…The parameter estimation results of the optimal distribution obtained are shown in Table 4 (taking the stations in the Mayi River basin as an example; the stations in the Hulan River basin and Tangwang River basin are shown in Appendices A.1 and A.2). In these tables, cs and pb denote that the µ/σ parameter was modeled as a cubic spline or P-splines of time or precipitation [16,38]. The value 1 or 2 in parentheses denotes the degree of freedom.…”

“…The bivariate time-covariate model could better describe the nonstationarity of the flood characteristics' sequence. Pietro S. et al [16] used GAMLSS with precipitation as a covariate to analyze annual runoff data and found that it was more able to capture the variability of the observed data. Recently, some researchers have started to combine the GAMLSS model with other models, algorithms, or indexes, such as copula [15], the nonstationary SRI index [17], etc., to test the stationarity of the series or to perform the calculation of the nonstationary hydrological frequency.…”

Modelling and Clustering Sea Conditions: Bivariate FiniteMixtures of Generalized Additive Models for Location, Shape, and Scale Applied to the Analysis of Meteorological Tides and Wave Heights

“…GAMLSSs have found application in health research as well as the study of floods and wildlife. For instance, Scala et al [11] conducted a regression analysis on river floods in the Sicily Region using a GAMLSS, employing both stationary and non-stationary analyses by varying the covariates and comparing the results. They emphasized that natural events could not be adequately explained by stationary distributions alone, as they fail to account for the natural variability in variables such as temperature, atmospheric pressure, precipitation, and floods that are affected by climate change.…”