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Autocorrelation Ratio as a Measure of Inertia for the Classification of Extreme Events

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  • Alfonso Gutierrez-Lopez

    (Water Research Center, International Flood Initiative, Latin-American and the Caribbean Region (IFI-LAC), Intergovernmental Hydrological Programme (IHP), Autonomous University of Queretaro, Queretaro 76010, Mexico)

  • Carlos Chávez

    (Water Research Center, Department of Irrigation and Drainage Engineering, Autonomous University of Queretaro, Queretaro 76010, Mexico)

  • Carlos Díaz-Delgado

    (Instituto Interamericano de Tecnología y Ciencias del Agua, Universidad Autónoma del Estado de México (IITCA-UAEM), Carretera Toluca-Ixtlahuaca km 14.5, Toluca 50200, Mexico)

Abstract

One of the problems in modern hydrology concerns the estimation of design events at sites with scarce or null data. This is a challenge for developing countries because they do not have monitoring networks as extensive and reliable as in developed nations. This situation has caused states in the Latin American and Caribbean region, in particular, to rely on hydrological regionalization techniques. These procedures implement clustering algorithms in combination with aggregation rules and metric distances to generate homogeneous groups from which hydrological information can be transferred. In addition, it has been proven that the analysis of spatial variables is sensitive to the magnitudes of extreme events; therefore, a mathematical formulation that adopts this fact into consideration must be included. For this purpose, the autocorrelation distance of the daily rainfall data series is proposed as an estimator of temporal variability. The fit parameters of the mixed Poisson-exponential probability distribution are operated as estimators of spatial variability. These spatio-temporal conditions are combined to obtain a mathematical relation of the autocorrelation as a measure of inertia for the classification of extreme events. This procedure is applied to Hydrologic Region 10 in northwestern Mexico from daily rainfall records. This zone has already been explored in terms of its regional homogeneity, which allows validating the results obtained.

Suggested Citation

  • Alfonso Gutierrez-Lopez & Carlos Chávez & Carlos Díaz-Delgado, 2022. "Autocorrelation Ratio as a Measure of Inertia for the Classification of Extreme Events," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2112-:d:841486
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    References listed on IDEAS

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    1. J. Gower & P. Legendre, 1986. "Metric and Euclidean properties of dissimilarity coefficients," Journal of Classification, Springer;The Classification Society, vol. 3(1), pages 5-48, March.
    2. Alfonso Gutierrez-Lopez, 2021. "A Robust Gaussian variogram estimator for cartography of hydrological extreme events," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 107(2), pages 1469-1488, June.
    3. Iwin Leenen & Iven Van Mechelen, 2001. "An Evaluation of Two Algorithms for Hierarchical Classes Analysis," Journal of Classification, Springer;The Classification Society, vol. 18(1), pages 57-80, January.
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