Frequency Analysis of the Loire River water Total Suspended Solid and Electrical Conductivity (Orléans, France)

Abstract

In this research, different statistical probability distributions are presented to model the total suspended solids (TSS) and electrical conductivity (EC) at two monitoring stations, Along the path of the Loire River France. These monitoring stations are Jargeau and Meung-sur-Loire. For each of these station data of the two variables are measured as a monthly series during the period 2001 to 2021. The proposed fitted statistical probability distributions are the Normal, Log-normal, Weibull, Exponential and Two parameters Gamma. The Kolmogorov-Smirnov test is used for the goodness-of-fit to select the best probability distribution from among these five tried distributions for each of the stations. The data sample is divided into two sub-samples, a fitting model sub-sample as 70 % of the data, and a validation sub-sample as the remaining 30%. The results show that the TSS at Loire a Meung-sur-Loire station has two distributions with same value of the test statistics, SIG. In these cases, the t and F tests are used to select the best-fit distribution. The Log Normal (13.71, 0.95) is found to be the best fit distribution for TSS for Jargeau station with SIG value of 0.35 while the Weibull (282.911, 8.206) with SIG value of 0.877 is the best fit for EC for the same station. For the Meung-sur-Loire station the Weibull (19.49, 1.18) and (299.40, 7.50) are the best fit distributions for the TSS and EC with test SIG values 0.75, 0.99 respectively. The best fit distribution for each station is used to generate three series of data which are tested against the 30% validation data. The Kolmogorov-Smirnov test among the three generated series with the validation confirms that these fitted models can generate data that has the same frequency of occurrence of that of the observed data.