[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-127522-en":3,"doc-seo-127522-105":30,"detail-sidebar-cat-0-en-105":92},{"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":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},127522,13056712833777,"Logic","https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0",8,"Research & Report","Comparing Single and Multiple Imputation Approaches for Missing Values in Univariate and Multivariate Water Level Data - Article","Missing values in water level data hinder data modelling and are especially common in developing countries. Data imputation is used to improve data quality for studying extreme events such as flooding and droughts. This work assesses single and multiple imputation methods on monthly univariate and multivariate water level data from four Nigerian stations on the Benue and Niger rivers. It compares mechanisms including missing completely at random, missing at random, and missing not at random using root mean square error and mean absolute percentage error.","water   \nArticle  \nComparing Single and Multiple Imputation Approaches for Missing Values in Univariate and Multivariate Water Level Data  \nNura Umar 1,2 and Alison Gray 1, *  \nCitation: Umar, N.; Gray, A. Comparing Single and Multiple Imputation Approaches for Missing Values in Univariate and Multivariate Water Level Data. Water 2023, 15, 1519. [https://doi.org/10.3390/](https://doi.org/10.3390/)[ ](https://doi.org/10.3390/)w15081519  \nAcademic Editors: Venkatesh  \nMerwade, Adnan Rajib and Zhu Liu  \nReceived: 4 March 2023  \nRevised: 4 April 2023  \nAccepted: 11 April 2023  \nPublished: 13 April 2023  \nCopyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) .  \n1 Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK; [nura.umar@strath.ac.uk](nura.umar@strath.ac.uk)  \n2 Department of Mathematics and Statistics, Umaru Musa Yar'adua University, Katsina 820102, Nigeria  \n* Correspondence: [a.j.gray@strath.ac.uk](a.j.gray@strath.ac.uk)  \nAbstract: Missing values in water level data is a persistent problem in data modelling and especially common in developing countries. Data imputation has received considerable research attention, to raise the quality of data in the study of extreme events such as flooding and droughts. This article evaluates single and multiple imputation methods used on monthly univariate and multivariate water level data from four water stations on the rivers Benue and Niger in Nigeria. The missing completely at random, missing at random and missing not at random data mechanisms were each considered. The best imputation method is identified using two error metrics: root mean square error and mean absolute percentage error. For the univariate case, the seasonal decomposition method is best for imputing missing values at various missingness levels for all three missing mechanisms, followed by Kalman smoothing, while random imputation is much poorer. For instance, for 5% missing data for the Kainji water station, missing completely at random, the Kalman smoothing, random and seasonal decomposition methods had average root mean square errors of 13.61, 102.60 and 10.46, respectively. For the multivariate case, missForest is best, closely followed by k nearest neighbour for the missing completely at random and missing at random mechanisms, and k nearest neighbour is best, followed by missForest, for the missing not at random mechanism. The random forest and predictive mean matching methods perform poorly in terms of the two metrics considered. For example, for 10% missing data missing completely at random for the Ibi water station, the average root mean square errors for random forest, k nearest neighbour, missForest and predictive mean matching were 22.51, 17.17, 14.60 and 25.98, respectively. The results indicate that the seasonal decomposition method, and missForest or k nearest neighbour methods, can impute univariate and multivariate water level missing data, respectively, with higher accuracy than the other methods considered.  \nKeywords: data gaps; water level data; time series; univariate; multivariate; imputation  \n1. Introduction  \nWater level is a measure of water depth in rivers/basin/lakes within a given place over time. Studying water level is important as it can provide warnings for flood risk, which helps to limit the impact of flood disasters on the local population and is also crucial for effective water resources management and for policy makers [1] . The study of water level is also important for the health of a river, to determine the required level for plants and animals to survive at various times of year [2] .  \nKhalifeloo [3] states that recent extreme events globally, suc","cbCaibGjtnOMDkUr","https://ap.wps.com/l/cbCaibGjtnOMDkUr","pdf",1731506,1,21,"English","en",105,"# Introduction\n## Water level significance\n## Extreme events and climate change context\n## Data gaps and hydrological imputation approaches\n# Missingness mechanisms in water level data\n# Imputation methods and evaluation metrics\n## Error metrics used for comparison","[{\"question\":\"Why is imputing missing values in water level data important?\",\"answer\":\"Missing observations reduce information and efficiency, leading to unreliable modelling. Imputation improves data quality for analysis of flood and drought-related extreme events.\"},{\"question\":\"Which missing-data mechanisms were considered in the study?\",\"answer\":\"The study evaluates missing completely at random, missing at random, and missing not at random mechanisms.\"},{\"question\":\"How were imputation methods compared in performance?\",\"answer\":\"Methods were assessed using two error metrics: root mean square error and mean absolute percentage error.\"}]","Comparing Single and Multiple Imputation Approaches for Missing Values in Univariate and Multivariate Water Level Data - Article | PDF",1785939722,53,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":87,"head_meta":89,"extra_data":91,"updated_unix":28},"comparing-single-and-multiple-imputation-approaches-for-missing-values-in-univariate-and-multivariate-water-level-data-article","",{"@graph":36,"@context":86},[37,54,69],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/comparing-single-and-multiple-imputation-approaches-for-missing-values-in-univariate-and-multivariate-water-level-data-article/127522/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":63,"encodingFormat":61,"isAccessibleForFree":64,"interactionStatistic":65},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-23","2026-08-05",true,{"@type":66,"interactionType":67,"userInteractionCount":20},"InteractionCounter",{"@type":68},"ViewAction",{"@type":70,"mainEntity":71},"FAQPage",[72,78,82],{"name":73,"@type":74,"acceptedAnswer":75},"Why is imputing missing values in water level data important?","Question",{"text":76,"@type":77},"Missing observations reduce information and efficiency, leading to unreliable modelling. Imputation improves data quality for analysis of flood and drought-related extreme events.","Answer",{"name":79,"@type":74,"acceptedAnswer":80},"Which missing-data mechanisms were considered in the study?",{"text":81,"@type":77},"The study evaluates missing completely at random, missing at random, and missing not at random mechanisms.",{"name":83,"@type":74,"acceptedAnswer":84},"How were imputation methods compared in performance?",{"text":85,"@type":77},"Methods were assessed using two error metrics: root mean square error and mean absolute percentage error.","https://schema.org",{"og:url":52,"og:type":88,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":90,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":93},[94,98,102,106,111,116,121,124,129,132,136],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":95,"show_sort_weight":96,"slug":97},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":99,"show_sort_weight":100,"slug":101},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":103,"show_sort_weight":104,"slug":105},"Exam",70,"exam",{"id":107,"doc_module":4,"doc_module_name":46,"category_name":108,"show_sort_weight":109,"slug":110},5,"Comic",60,"comic",{"id":112,"doc_module":4,"doc_module_name":46,"category_name":113,"show_sort_weight":114,"slug":115},6,"Technology",50,"technology",{"id":117,"doc_module":4,"doc_module_name":46,"category_name":118,"show_sort_weight":119,"slug":120},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":122,"slug":123},30,"research-report",{"id":125,"doc_module":4,"doc_module_name":46,"category_name":126,"show_sort_weight":127,"slug":128},9,"Religion & Spirituality",20,"religion-spirituality",{"id":127,"doc_module":4,"doc_module_name":46,"category_name":130,"show_sort_weight":127,"slug":131},"World Cup","world-cup",{"id":133,"doc_module":4,"doc_module_name":46,"category_name":134,"show_sort_weight":133,"slug":135},10,"Lifestyle","lifestyle",{"id":137,"doc_module":4,"doc_module_name":46,"category_name":138,"show_sort_weight":107,"slug":139},19,"General","general"]