Brazil’s Daily Precipitation Concentration Index (CI) Using Alternative Fitting Equation and Ensemble Data

Abstract

In recent years, precipitation concentration indices have become popular, and the daily precipitation concentration index has been widely used worldwide. This index is based on the Lorenz curve fitting. Recently, some biases in the fitting process have been observed in some research. Therefore, this research’s objective consisted of testing the performance of one alternative equation for fitting the Lorenz curve through the analysis of the daily precipitation concentration in Brazil. Daily precipitation data from 735 time series were used to fit the Lorenz curve and calculate the concentration index. Therefore, the goodness of fit was evaluated to determine which equation better describes the empirical data. Results show that the mean value for the concentration index based on Equation (1) was 0.650 ± 0.079, while the mean value based on Equation (2) was 0.624 ± 0.070. The results of the fitting performance show a better fitting with Equation (2) compared to Equation (1) as indicated by R2, RSS, and RMSE values, R2 = 0.9959 for Equation (1) versus 0.9996 for Equation (2), RSS = 252.78 versus 22.66, and RMSE = 1.5092 versus 0.0501. Thus, Equation (2) can be considered an alternative to improve the calculation of the concentration index.