Factor Analysis of the morphometric indices and Flood modeling :A Case Study of Watersheds in Kurdistan Province

In recent years, the quantitative analysis of the morphometric characteristics of the watershed using mathematical indices has been widely performed for several purposes, especially to assess the flood risk potential of drainage basins. Morphometric studies in the field of hydrology were first initiated by Horton and Strahler in the 1940s and 1950s, respectively. Their goal was to study the important characteristics of river flow and distinguish them from other measurable characteristics of river flow. One of the first morphometric properties of the river that became quantitative was the hierarchy of different parts of the flow. Later, researchers in other parts of the world, due to the importance of this issue, performed much research in this field. This region has always suffered significant damage due to flooding. The lack of flow measurement stations on the rivers has made the need for mathematical models necessary to study the flooding status of the region. Therefore, the present study aimed to analyze the morphometric parameters and their relationship with the region's flooding, and provide mathematical models for flood study using factor analysis.

In this research, to study the flood of the watersheds of Kurdistan province and its relationship with morphometric indices, first, the boundaries of the selected watersheds were determined using topographic maps and ARC GIS 10.5 software. Morphometric indices were calculated for all studied basins. In the next step, the normality of the data was investigated. To evaluate the normal distribution of the data, the one-sample Kolmogorov-Smirnov test was used. In the third step, the return periods were determined based on the instantaneous flood peak data using probability distribution functions. In the fourth step, factor analysis of the variables was carried out.

Investigating data adequacy is the first step in factor analysis. Therefore, first, the adequacy of the data was investigated. Considering that the obtained coefficient is higher than 0.60 (0.634), the data adequacy is acceptable for factor analysis. After determining the adequacy of the data, the data sharing was investigated and the data sharing table was extracted. The area variable has the highest commonality with other variables, which is about 97%, and then the length variable of the basin. Among the variables, the branch ratio variable has the least commonality with other variables. In the next step, the variance of the data was investigated and its table was drawn. According to the obtained data, the main variables were combined and categorized into three main and important factors. In the following, because the factors explain most of the variance of the variables, they were rotated. To make it more interpretable and better separation, the factors were rotated using Varimax rotation. After the rotation, the variables have formed a new structure by being placedin one of the three specified factors. Each variable is placed in one of the three specified factors according to its factor load, in such a way that each variable is assigned to one of the three main factors according to its highest factor load.Using exploratory factor analysis, the hidden factors in the 12 studied variables were extracted and three factors underlying the 12 studied variables were identified. Based on the results of this analysis, five variables of basin area, basin length, flow length, texture ratio, and drainage density are in the first factor. Five variables of elongation coefficient, basin shape, form coefficient, circularity coefficient, and compression coefficient are placed in the second factor, and two variables of stream frequency and branch ratio are placed in the third factor. Therefore, a name is chosen for each of the extracted factors, and other analyses are performed using these three new indicators. These three indices were named according to the variables of each factor in three variables: area, shape, and stream. Examining the collinearity of the data showed that the variables have suitable collinearity for modeling. As a result, regression analysis was performed. Because the calculations were done for more than one variable, multivariate regression analysis was used. In this study, discharge with return periods above 10 to 200 years was considered as the dependent variable, factor indices were obtained from factor analysis as independent variables, and a regression model was extracted for each of the mentioned return periods. The results showed that the models presented for higher return periods have a higher coefficient of determination (R2) and can predict floods with more confidence.

As a result of factor analysis, 12 variables were placed in three main factors, whose eigenvalues are greater than 1. These three factors include 78% of the data variance. However, the highest percentage of total explained variance is related to the first component, which is named area. This factor includes 35.369% of the total variance. Among the investigated variables, area, basin length, and stream frequency are the most effective variables in flood occurrence with 0.968, 0.963, and 0.838, respectively, and the branch ratio variable has the least effect with 0.359. After extracting the indices obtained from the factor analysis (indexing) using multivariate regression analysis, correlations were performed to the indices and the return periods above 10 to 200 years. Finally, for each of the return periods, a model for flood forecast was prepared. Examining the R2 of the models showed that with the increase of the return period, the value of this coefficient increased, which shows that the models created for higher return periods are more reliable and can predict floods more accurately.