Modelos não lineares aplicados na descrição do acúmulo da radiação global diária no nível do solo

Abstract

Solar irradiance is the flux of electromagnetic radiation from the Sun that reaches the Earth's surface. Solar radiation is a fundamental source of energy on the planet, directly influencing the development of plant species and meteorological phenomena. Additionally, it is used in drying processes, heating, and electricity generation, among other applications. The intensity of solar radiation reaching the ground varies due to the rotation of the planet, which is associated with the time of day; the tilt of the Earth's axis and its orbit around the Sun, which cause equinoxes and solstices. Another factor that affects solar irradiance is the atmosphere, which absorbs or scatters solar rays due to the presence of aerosols and clouds. The accumulation of global solar irradiance at ground level throughout the day presents a sigmoidal characteristic. This study aimed to evaluate the suitability of nonlinear models to describe the daily accumulation of global solar irradiance (kJ/m²) at ground level using data from INMET for seventeen Brazilian cities representative of five different biomes. The global irradiance data wereextractedfromtheHistoricalMeteorological Data oftheNationalInstituteofMeteorology (INMET) for Braziliancitieslocated in theAmazonbiome (Rio Branco, Manaus, Humaitá, Macapá), Cerrado (São Luís, Brasília, Campo Grande), Caatinga (Petrolina, Mossoró), Atlantic Forest (Vitória, Rio de Janeiro, São Paulo, Belo Horizonte, Curitiba, Recife), and Pampas (Santa Maria, Santa Vitória do Palmar). To fit the models to the daily accumulated global irradiance at ground level during solstices and equinoxes, the Logistic, Gompertz, von Bertalanffy, and Richards models were chosen. The R software was used for the fitting, employing the least squares method implemented by the Gauss-Newton algorithm. In the residual analysis, the Shapiro-Wilk, Breusch-Pagan, and Durbin-Watson tests were applied. The quality of the fits was evaluated by the values of the coefficient of determination (R²), residual standard deviation (RSD), and Akaike information criterion (AIC). The results indicated that the Logistic model was the best fit in 43 of the 68 datasets, followed by the Gompertz model, which performed well in 25 datasets. The von Bertalanffy model, when assumptions were met, presented inferior results in the selection criteria, and the Richards model did not converge. Therefore, the Logistic model proved to be the most suitable for the analyzed data. The abscissas of the inflection points estimated by the Logistic model showed a very strong correlation with longitude, as did the abscissas estimated by the Gompertz model. In the Atlantic Forest biome, the correlations between the asymptotic values and latitudes, as well as between the abscissas of the inflection points and longitudes, were negative and very strong, allowing for the estimation of model parameters in cities that do not have meteorological stations.