Abstract
This paper concerns the use and implementation of penalized maximum likelihood procedures to fitting smoothing functions of the generalized extreme value distribution parameters to analyze spatial extreme values of ultraviolet B (UVB) radiation across the Mexico City metropolitan area in the period 2000–2018. The model was fitted using a flexible semi-parametric approach and the parameters were estimated by the penalized maximum likelihood (PML) method. In order to investigate the performance of the model as well as the estimation method in the analysis of complex nonlinear trends for UVB radiation maxima, a simulation study was conducted. The results of the simulation study showed that penalized maximum likelihood yields better regularization to the model than the maximum likelihood estimates. We estimated return levels of extreme UVB radiation events through a nonstationary extreme value model using measurements of ozone (O3), nitrogen oxides (NOx), particles of 10 μm or less in diameter (PM10), carbon monoxide (CO), relative humidity (RH) and sulfur dioxide (SO2). The deviance statistics indicated that the nonstationary generalized extreme value (GEV) model adjusted was statistically better compared to the stationary model. The estimated smoothing functions of the location parameter of the GEV distribution on the spatial plane for different periods of time reveal the existence of well-defined trends in the maxima. In the temporal plane, a presence of temporal cyclic components oscillating over a weak linear component with a negative slope is noticed, while in the spatial plane, a weak nonlinear local trend is present on a plane with a positive slope towards the west, covering the entire study area. An explicit spatial estimate of the 25-year return period revealed that the more extreme risk levels are located in the western region of the study area.
Highlights
Ultraviolet radiation can cause different effects on Earth’s life
By a simple inspection of the descriptive statistics, we observed that the distribution of the extremes is not stationary, the use of a nonstationary model of extreme values is justified for the analysis of trends
We have developed a nonstationary extreme value model for ultraviolet B (UVB) radiation maxima on the metropolitan area of Mexico City using a semi-parameterized model to obtain a spatio-temporal smoothing of the location parameter of the generalized extreme value (GEV) distribution
Summary
Ultraviolet radiation can cause different effects on Earth’s life. In living organisms, UVB radiation destroys DNA, produces protein denaturation, triggers coagulation of albumin, as well as erythemaMathematics 2020, 8, 329; doi:10.3390/math8030329 www.mdpi.com/journal/mathematicsMathematics 2020, 8, 329 and skin problems. The intensity of UVB radiation at ground level is affected by the absorption of energy required by the chemical reactions that occur in the atmosphere and by the reflection caused by particles and gases. One of the most important is ozone, which among all atmospheric gases plays an active role in the absorption of UV radiation and protection against dangerous levels of solar radiation [3]. UVB is absorbed mainly in the ozone layer. This region concentrates ninety percent of total ozone at an altitude of between 9 to 18 miles forming a protective shield against UVB radiation
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