<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0187-6236</journal-id>
<journal-title><![CDATA[Atmósfera]]></journal-title>
<abbrev-journal-title><![CDATA[Atmósfera]]></abbrev-journal-title>
<issn>0187-6236</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Instituto de Ciencias de la Atmósfera y Cambio Climático]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0187-62362019000300237</article-id>
<article-id pub-id-type="doi">10.20937/atm.2019.32.03.06</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of a new spatial interpolation weighting method to estimate missing data applied to rainfall records]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Morales Martínez]]></surname>
<given-names><![CDATA[Jorge Luis]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Horta-Rangel]]></surname>
<given-names><![CDATA[Francisco Antonio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Segovia-Domínguez]]></surname>
<given-names><![CDATA[Ignacio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Robles Morua]]></surname>
<given-names><![CDATA[Agustín]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
<xref ref-type="aff" rid="Aaf"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Hernández]]></surname>
<given-names><![CDATA[J. Horacio]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de Guanajuato Departamento de Ingeniería Geomática e Hidráulica ]]></institution>
<addr-line><![CDATA[Guanajuato Guanajuato]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de Guanajuato Departamento de Ingeniería Civil ]]></institution>
<addr-line><![CDATA[Guanajuato Guanajuato]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Centro de Investigación en Matemáticas Departamento de Matemáticas Puras y Aplicadas ]]></institution>
<addr-line><![CDATA[Guanajuato Guanajuato]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Instituto Tecnológico de Sonora  ]]></institution>
<addr-line><![CDATA[Ciudad Obregón Sonora]]></addr-line>
<country>México</country>
</aff>
<aff id="Af5">
<institution><![CDATA[,Laboratorio Nacional de Geoquímica y Mineralogía  ]]></institution>
<addr-line><![CDATA[Ciudad de México ]]></addr-line>
<country>Mexico</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>09</month>
<year>2019</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>09</month>
<year>2019</year>
</pub-date>
<volume>32</volume>
<numero>3</numero>
<fpage>237</fpage>
<lpage>259</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S0187-62362019000300237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S0187-62362019000300237&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S0187-62362019000300237&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[ABSTRACT In the present work, two new generalized weighted methods of imputation of missing data are developed and tested using a daily rainfall series. The proposed methodology allows to fully rebuild the time series while preserving its statistical properties. Rainfall records in the state of Tabasco, Mexico, during the period 1980-2012 were used to test and evaluate the proposed methodology. The imputation of missing data in a given weather station is performed by using daily data from neighboring stations with a similar rainfall behavior. The choice of optimal parameters for the proposed formulae is based on minimizing the mean absolute error (MAE) via an evolutionary strategy (CMA-ES). The K-means method was used with the Euclidean distance in order to select the adequate neighboring weather stations. Five different methods were applied to estimate the optimal number of clusters: the elbow method, gap statistics, TraceW, Hartigan and Krzanowski-Lai indices. In addition, the structural stability of the chosen clusters was evaluated in order to demonstrate that these represent the correct data structure and are not the result of an artificial internal procedure of the grouping algorithm. Results from two different statistical tests, Friedman and Nemenyi post hoc, showed that our two new methods produce significantly and statistically better estimation when compared to existing methods in the literature.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[RESUMEN En el presente trabajo se desarrollaron y probaron dos métodos generalizados ponderados de imputación de los valores de datos faltantes, utilizando para ello series diarias de precipitación. Se usaron registros de precipitación del estado de Tabasco, México, del periodo 1980-2012, para probar y evaluar la metodología propuesta. La imputación de datos faltantes en una estación meteorológica determinada se realizó utilizando información diaria de estaciones cercanas con patrones similares de precipitación. La selección de parámetros óptimos para las fórmulas propuestas se basó en la minimización del error medio absoluto mediante una estrategia evolutiva (CMA-ES). Se utilizó el método de K-medias junto con la distancia euclidiana para elegir las estaciones meteorológicas cercanas adecuadas. Se aplicaron cinco métodos diferentes para estimar el número óptimo de clústeres: el método de Elbow, la estadística de Gap y los índices TraceW, de Hartigan y de Krasnowski-Lai. Adicionalmente, se evaluó la estabilidad estructural de los clústeres seleccionados para demostrar que representan la estructura de datos correcta y no son resultado de un procedimiento interno artificial del algoritmo de agrupación. Los resultados de dos pruebas estadísticas, Friedman y Nemenyi post hoc, mostraron que los dos nuevos métodos presentados, producen estimaciones estadísticas significativamente mejores en comparación con otros métodos encontrados en la literatura.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[missing data]]></kwd>
<kwd lng="en"><![CDATA[rainfall data]]></kwd>
<kwd lng="en"><![CDATA[K-means clustering]]></kwd>
<kwd lng="en"><![CDATA[optimization]]></kwd>
<kwd lng="en"><![CDATA[deterministic interpolation methods]]></kwd>
</kwd-group>
</article-meta>
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