[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-125970-en":3,"doc-seo-125970-105":31,"detail-sidebar-cat-0-en-105":93},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":28,"seo_description":14,"update_tm":29,"read_time":30},125970,687207024478,"Liam","https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd",8,"Research & Report","Machine learning procedures for daily interpolation of rainfall in Navarre (Spain)","Kriging is the most widely used statistical method for interpolating spatial random fields because it yields the best linear unbiased predictor and can act as an exact interpolator under normality. Its robustness tolerates mild departures, but many meteorological and environmental variables show strongly asymmetric distributions, limiting Kriging’s applicability. Machine learning alternatives—neural networks, random forest, and k-nearest neighbor—avoid restrictive distributional assumptions. Using scarce auxiliary data (spatial coordinates and altitude), predictions for daily rainfall in Navarre are assessed via RRMSE-based comparisons, showing improved performance when Kriging is not usable.","Machine learning procedures for daily interpolation of rainfall in Navarre (Spain)  \nMilitino, A.F.1 , Ugarte, M.D.1 , Prez-Goya 1  \nAbstract Kriging is by far the most well known and widely used statistical method for interpolating data in spatial random fields. The main reason is that it provides the best linear unbiased predictor and it is an exact interpolator when normality is assumed. The robustness of this method allows small departures from normality, however, many meteorological, pollutant and environmental variables have extremely asymmetrical distributions and Kriging cannot be used. Machine learning techniques such as neural networks, random forest, and k-nearest neighbor can be used instead, because they do not require specific distributional assumptions. The drawback is that they do not take account of the spatial dependence, and for an optimal performance in spatial random fields more complex machine learning techniques could be considered. These techniques also require a relatively large amount of training data and they are computationally challenging to implement. For a reduced number of observations, we illustrate the performance of the aforementioned procedures using daily rainfall data of manual meteorological gauge stations in Navarre, where the only auxiliary variables available are the spatial coordinates and the altitude. The quality of the predictions is carefully checked through three versions of the relative root mean squared error (RRMSE) . The conclusion is that when we cannot use Kriging, random forest and neural networks outperform k-  \nMilitino A.F.  \nDepartment of Statistics, Computer Science and Mathematics, Public University of Navarre (Spain), and InaMat2 (Institute for Advanced Materials and Mathematics), e-mail: militino@ [unavarra.es](unavarra.es)  \nUgarte, M. D.  \nDepartment of Statistics, Computer Science and Mathematics, Public University of Navarre (Spain), and InaMat2 (Institute for Advanced Materials and Mathematics), e-mail: lola@  \n[unavarra.es](unavarra.es)[ ](unavarra.es)Prez-Goya, U.  \nDepartment of Statistics, Computer Science and Mathematics, Public University of Navarre (Spain), and InaMat2 (Institute for Advanced Materials and Mathematics), e-mail: unai .perez@ [unavarra.es](unavarra.es)  \n2 Militino, A.F., Ugarte, M.D., Prez-Goya  \nnearest neighbor technique, and provide reliable predictions of rainfall daily data with scarce auxiliary information.  \n1 Introduction  \nSpatial interpolation of daily precipitation is a necessary task in hydrology, ecology, climatology and precision agriculture where it is important to know the accumulated rainfall in any location of a particular region of interest in a given day [18] . Regardless of the specificity and climatological properties of the region of interest, rainfall can follow very dissimilar patterns and different distributions, where at least locally, only neighbor similarity can be assumed [13] . Historically, spatial interpolation of daily precipitation has been accomplished weighting and averaging close rain gauge observations with historical information and additional auxiliary variables [27] . The most well spread spatial interpolation procedure is Kriging and its derived family. See for example [17] for a regional modelling of daily precipitation where Kriging outperforms the vector generalized additive model alternative. Very frequently, a log-transformation of rainfall is also necessary for approximating normality when using the Kriging family [30], yet with an additional cost of bias when back-transforming. The use of historical information, the precipitationelevation relationship and the topographic effects contribute to improve daily predictions, for example when using the angular weighting distance method [41] . However, the strong spatial variation of the precipitation, and the sparsity and unevenly distribution of the rain gauge stations could sometimes give disappointing results [4] . Complex relationships with auxi","cbCaidDq9rNQDYHa","https://ap.wps.com/l/cbCaidDq9rNQDYHa","pdf",533850,6,1,14,"English","en",105,"# Introduction\n## Background on spatial interpolation and Kriging\n## Machine learning alternatives for interpolation\n## Study goal and evaluation approach","[{\"question\":\"Why is Kriging often unsuitable for daily rainfall interpolation in this context?\",\"answer\":\"Kriging assumes conditions that do not hold well when variables have extremely asymmetrical distributions, which is common for many meteorological and environmental quantities.\"},{\"question\":\"Which machine learning methods are considered as alternatives to Kriging?\",\"answer\":\"Neural networks, random forest, and k-nearest neighbor are proposed because they do not require specific distributional assumptions.\"},{\"question\":\"What auxiliary information is used when predicting daily rainfall in Navarre?\",\"answer\":\"Only spatial coordinates and altitude are used as auxiliary variables for the interpolation.\"}]","Machine learning procedures for daily interpolation of rainfall in Navarre (Spain) | 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is Kriging often unsuitable for daily rainfall interpolation in this context?","Question",{"text":77,"@type":78},"Kriging assumes conditions that do not hold well when variables have extremely asymmetrical distributions, which is common for many meteorological and environmental quantities.","Answer",{"name":80,"@type":75,"acceptedAnswer":81},"Which machine learning methods are considered as alternatives to Kriging?",{"text":82,"@type":78},"Neural networks, random forest, and k-nearest neighbor are proposed because they do not require specific distributional assumptions.",{"name":84,"@type":75,"acceptedAnswer":85},"What auxiliary information is used when predicting daily rainfall in Navarre?",{"text":86,"@type":78},"Only spatial coordinates and altitude are used as auxiliary variables for the 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