Indices for exploring information in Lorentz curve of daily precipitation and their application in natural disaster risk assessment

The concentration index (CI) based on the Lorenz curve has been widely used to analyse the temporal structure of daily precipitation. However, two different Lorenz curves may have the same CI, while indicating different distribution information of precipitation. Previous studies have proposed Lorentz asymmetry coefficient, the value of which concentrated around 0.9 without significant distinction. Additional indicators are thus in need to investigate the complete information in Lorenz curves besides CI. In this study, six geometrical indices are defined to characterize a Lorenz curve. Together with the CI, any one of the proposed indices can help determine a unique Lorenz curve. An analysis of the daily precipitation over the Qinghai-Tibet Plateau derived five groups of meteorological stations with identical CIs, but completely different Lorenz curves. The correlation analysis between the CI and proposed indices indicated that there are two parameters independent of the CI, representing the contribution of heavy rain and the position of the transaction point, respectively, thus introducing relatively new information on precipitation beyond the CI. Within the stations with high CIs, these two indices were used to further identify areas in the Qinghai-Tibet Plateau at a high risk for natural disasters, such as rainstorms, debris flows, and aridity, the derived results were consistent with the debris flow prone areas in China designated by China Meteorological Administration. The proposed indices can not only help CI to describe the Lorentz curve of daily rainfall, but can also help identify areas at a high risk for natural disasters.