Abstract

CAMPOS-ARANDA, Daniel Francisco. Extension of Annual Runoff Volume Records Based on Regional Information and Ridge Regression. Tecnol. cienc. agua [online]. 2014, vol.5, n.4, pp.173-185. ISSN 2007-2422.

The planning, design and management of water infrastructure are typically based on available historical records of annual floods, runoff and rainfall. The more years covered by these records the more accurate the hydrological estimates. Therefore, it is always necessary to expand short records (Y), for example, through multiple linear regression (MLR), which uses available regional information. Establishing a MLR has several difficulties, perhaps the most important regarding the transport of hydrological information is the presence of correlation between the auxiliary or predictor variables (X_i), which gives rise to a problem of multicollinearity. In this work, the quantitative evaluation of multicollinearity is presented in detail through variance inflation factors and eigenvalues for the X' · X matrix. In addition, the biased or Ridge MLR is described extensively as a strategy to minimize the effects of multicollinearity, seeking its biasing parameter based on the Ridge trace. A numerical application is presented in detail, which expands the annual runoff volume records in the Santa Isabel gauging station in the upper Grijalva River using four broad records nearby. Lastly, several conclusions are formulated which highlight the advantages of using the Ridge MLR.

Keywords : Multicollinearity; variance inflation factors; eigenvalues; eigenvectors; upper Grijalva River.

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