Generation of IDF Curves for the Las Abras Stream Using Multiple Linear Regression and the Talbot Method

Abstract

Precipitation is one of the most critical meteorological processes, and its temporal analysis is fundamental in hydrological studies. This analysis enables the identification of key indices and parameters for flood prediction and the development of rainfall models based on available data. In this context, Intensity-Duration-Frequency (IDF) curves are essential tools, as they apply frequency analysis to fit the data to a probability distribution, facilitating the estimation of return periods for precipitation events. These results are crucial for ensuring the proper design and sizing of civil infrastructure near the watershed.In the statistical analysis of hydrological variables, this study employs the Talbot method and Multiple Linear Regression (MLR) for the hydrological design of a sub-basin of the Chambo River. Maximum precipitation records provided by the National Institute of Meteorology and Hydrology of Ecuador (INAMHI) are used to identify and model an intensity equation that allows for the generationof IDF curves representative of rainfall behavior in the Las Abras stream, located in Guano canton, Chimborazo province. Due to the lack of a complete tabulation and the absence of daily data for the entire year, this research addresses information gaps through correlation between missing data and available records from nearby meteorological stations.The results of this study, along with recent research conducted in areas adjacent to the basin, show that the intensity equation adjusted using the Multiple Linear Regression (MLR) method yields a perfect coefficient of determination (R² = 1.00). In turn, the Talbot method produces values above 0.95, indicating a high degree of fit. Collectively, the multi-method analysis demonstrates a probabilistic consistency that closely reflects the hydrological reality of the Las Abras stream.