IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i12p2112-d841486.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/12/2112/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/12/2112/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guohuan Su & Adam Mertel & Sébastien Brosse & Justin M. Calabrese, 2023. "Species invasiveness and community invasibility of North American freshwater fish fauna revealed via trait-based analysis," Nature Communications, Nature, vol. 14(1), pages 1-12, December.
    2. la Grange, Anthony & le Roux, Niël & Gardner-Lubbe, Sugnet, 2009. "BiplotGUI: Interactive Biplots in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 30(i12).
    3. Michael Brusco & J Dennis Cradit & Douglas Steinley, 2021. "A comparison of 71 binary similarity coefficients: The effect of base rates," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-19, April.
    4. Tom Wilderjans & Eva Ceulemans & Iven Mechelen, 2008. "The CHIC Model: A Global Model for Coupled Binary Data," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 729-751, December.
    5. Balepur, Prashant Narayan, 1998. "Impacts of Computer-Mediated Communication on Travel and Communication Patterns: The Davis Community Network Study," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt6cb1f85c, Institute of Transportation Studies, UC Berkeley.
    6. Niemann, Helen & Moehrle, Martin G. & Frischkorn, Jonas, 2017. "Use of a new patent text-mining and visualization method for identifying patenting patterns over time: Concept, method and test application," Technological Forecasting and Social Change, Elsevier, vol. 115(C), pages 210-220.
    7. Michael J. Greenacre & Patrick J. F. Groenen, 2016. "Weighted Euclidean Biplots," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 442-459, October.
    8. Douglas L. Steinley & M. J. Brusco, 2019. "Using an Iterative Reallocation Partitioning Algorithm to Verify Test Multidimensionality," Journal of Classification, Springer;The Classification Society, vol. 36(3), pages 397-413, October.
    9. Matthijs Warrens, 2008. "Bounds of Resemblance Measures for Binary (Presence/Absence) Variables," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 195-208, November.
    10. Anna Maria D’Arcangelis & Giulia Rotundo, 2016. "Complex Networks in Finance," Lecture Notes in Economics and Mathematical Systems, in: Pasquale Commendatore & Mariano Matilla-García & Luis M. Varela & Jose S. Cánovas (ed.), Complex Networks and Dynamics, pages 209-235, Springer.
    11. Carla Coltharp & Rene P Kessler & Jie Xiao, 2012. "Accurate Construction of Photoactivated Localization Microscopy (PALM) Images for Quantitative Measurements," PLOS ONE, Public Library of Science, vol. 7(12), pages 1-15, December.
    12. Letizia Mencarini & Raffaella Piccarreta & Marco Le Moglie, 2022. "Life‐course perspective on personality traits and fertility with sequence analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1344-1369, July.
    13. Vines, S.K., 2015. "Predictive nonlinear biplots: Maps and trajectories," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 47-59.
    14. Rizzi, Alfredo & Vichi, Maurizio, 1995. "Representation, synthesis, variability and data preprocessing of a three-way data set," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 203-222, February.
    15. Iwin Leenen & Iven Mechelen & Andrew Gelman & Stijn Knop, 2008. "Bayesian Hierarchical Classes Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(1), pages 39-64, March.
    16. Hennig, Christian, 2008. "Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1154-1176, July.
    17. S. T. Buckland & Y. Yuan & E. Marcon, 2017. "Measuring temporal trends in biodiversity," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 101(4), pages 461-474, October.
    18. Patrick Groenen & Niël Roux & Sugnet Gardner-Lubbe, 2015. "Spline-based nonlinear biplots," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(2), pages 219-238, June.
    19. Ricotta, Carlo & Szeidl, Laszlo, 2009. "Diversity partitioning of Rao’s quadratic entropy," Theoretical Population Biology, Elsevier, vol. 76(4), pages 299-302.
    20. Kong, Xiaolin & Ma, Chaoqun & Ren, Yi-Shuai & Baltas, Konstantinos & Narayan, Seema, 2024. "A comparative analysis of the price explosiveness in Bitcoin and forked coins," Finance Research Letters, Elsevier, vol. 61(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2112-:d:841486. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.