Average Annual Flood Estimation Based on Power Regression Equations in Mexico’s Hydrological Region No. 10

Design floods are critical in the hydrological sizing or review of all waterworks. In sites of interest without hydrometric information, their estimation is carried out with re- gional methods, whose results must be scaled or dimensioned based on the average annual flood (Qaa). In order to estimate the Qaa in an ungauged watershed, hydrolo- gists use power regression equations developed for a homogeneous region, relating the observed values of the Qaa with different physiographic characteristics of their water- sheds. The importance of estimating the Qaa justifies the search for such regressions with different approaches and techniques for obtaining the best fit parameters. In this paper, 22 records of annual maximum flows were processed, with periods ranging from 21 to 56 years. Four regression equations were analyzed and two techniques of adjustment were applied: the least–squares of the residuals in the logarithmic domain, including their bias correction, and another based on numerical optimization, using the multivariable unconstrained Rosenbrock algorithm. 28 regression equations were obtained, including four for each of the two watersheds subgroups in which the hydro- logical region was divided. Five numerical contrasts were applied in the hydrometric stations not used in deriving the regression equations. Finally, the conclusions are formulated, which emphasize the similarity of the results and recommend the applica- tion of this analysis for other regions of the country.