{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,10]],"date-time":"2026-01-10T02:55:23Z","timestamp":1768013723860,"version":"3.49.0"},"reference-count":59,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2021,12,4]],"date-time":"2021-12-04T00:00:00Z","timestamp":1638576000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Energy Environment Solutions (E2S-UPPA) Consortium","award":["E2S-UPPA"],"award-info":[{"award-number":["E2S-UPPA"]}]},{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["LP180101151"],"award-info":[{"award-number":["LP180101151"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJERPH"],"abstract":"<jats:p>In situ sensors that collect high-frequency data are used increasingly to monitor aquatic environments. These sensors are prone to technical errors, resulting in unrecorded observations and\/or anomalous values that are subsequently removed and create gaps in time series data. We present a framework based on generalized additive and auto-regressive models to recover these missing data. To mimic sporadically missing (i) single observations and (ii) periods of contiguous observations, we randomly removed (i) point data and (ii) day- and week-long sequences of data from a two-year time series of nitrate concentration data collected from Arikaree River, USA, where synoptically collected water temperature, turbidity, conductance, elevation, and dissolved oxygen data were available. In 72% of cases with missing point data, predicted values were within the sensor precision interval of the original value, although predictive ability declined when sequences of missing data occurred. Precision also depended on the availability of other water quality covariates. When covariates were available, even a sudden, event-based peak in nitrate concentration was reconstructed well. By providing a promising method for accurate prediction of missing data, the utility and confidence in summary statistics and statistical trends will increase, thereby assisting the effective monitoring and management of fresh waters and other at-risk ecosystems.<\/jats:p>","DOI":"10.3390\/ijerph182312803","type":"journal-article","created":{"date-parts":[[2021,12,5]],"date-time":"2021-12-05T21:01:45Z","timestamp":1638738105000},"page":"12803","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Reconstructing Missing and Anomalous Data Collected from High-Frequency In-Situ Sensors in Fresh Waters"],"prefix":"10.3390","volume":"18","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1972-8937","authenticated-orcid":false,"given":"Claire","family":"Kermorvant","sequence":"first","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et de Leurs Applications de Pau F\u00e9d\u00e9ration MIRA, UMR CNRS 5142, Universit\u00e9 de Pau et des Pays de l\u2019Adour, 64600 Anglet, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8136-2294","authenticated-orcid":false,"given":"Benoit","family":"Liquet","sequence":"additional","affiliation":[{"name":"Laboratoire de Math\u00e9matiques et de Leurs Applications de Pau F\u00e9d\u00e9ration MIRA, UMR CNRS 5142, Universit\u00e9 de Pau et des Pays de l\u2019Adour, 64600 Anglet, France"},{"name":"Department of Mathematics and Statistics, Macquarie University, Sydney, NSW 2109, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1996-7468","authenticated-orcid":false,"given":"Guy","family":"Litt","sequence":"additional","affiliation":[{"name":"National Ecological Observatory Network, Battelle Boulder, Boulder, CO 80301, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jeremy B.","family":"Jones","sequence":"additional","affiliation":[{"name":"Institute of Arctic Biology and Department of Biology and Wildlife, University of Alaska Fairbanks, Fairbanks, AK 99775, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kerrie","family":"Mengersen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Queensland University of Technology, Brisbane, QLD 4000, Australia"},{"name":"ARC Centre of Excellence for Mathematics and Statistical Frontiers, Melbourne, VIC 3000, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Erin E.","family":"Peterson","sequence":"additional","affiliation":[{"name":"ARC Centre of Excellence for Mathematics and Statistical Frontiers, Melbourne, VIC 3000, Australia"},{"name":"Peterson Consulting, Brisbane, QLD 4000, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2140-5352","authenticated-orcid":false,"given":"Rob J.","family":"Hyndman","sequence":"additional","affiliation":[{"name":"ARC Centre of Excellence for Mathematics and Statistical Frontiers, Melbourne, VIC 3000, Australia"},{"name":"Department of Econometrics and Business Statistics, Monash University, Clayton, VIC 3800, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4186-1678","authenticated-orcid":false,"given":"Catherine","family":"Leigh","sequence":"additional","affiliation":[{"name":"ARC Centre of Excellence for Mathematics and Statistical Frontiers, Melbourne, VIC 3000, Australia"},{"name":"Biosciences and Food Technology Discipline, School of Science, RMIT University, Bundoora, VIC 3083, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,12,4]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Water Quality Monitoring Using Wireless Sensor Networks","volume":"13","author":"Tapparello","year":"2017","journal-title":"ACM Trans. Sens. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Katsriku, F.A., Wilson, M., Yamoah, G.G., Abdulai, J.-D., Rahman, B.M.A., and Grattan, K.T.V. (2015). Framework for Time Relevant Water Monitoring System, Springer.","DOI":"10.1007\/978-3-319-08239-4_1"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10661-015-4594-3","article-title":"A data management and publication workflow for a large-scale, heterogeneous sensor network","volume":"187","author":"Jones","year":"2015","journal-title":"Environ. Monit. Assess."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Park, J., Kim, K.T., and Lee, W.H. (2020). Recent Advances in Information and Communications Technology (ICT) and Sensor Technology for Monitoring Water Quality. Water, 12.","DOI":"10.3390\/w12020510"},{"key":"ref_5","unstructured":"Cawley, K.M. (2018). NEON Algorithm Theoretical Basis Document (ATBD), National Ecological Observatory Network. Technical Report."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"993","DOI":"10.1111\/1752-1688.12386","article-title":"Emerging tools for continuous nutrient monitoring networks: Sensors advancing science and water resources protection","volume":"52","author":"Pellerin","year":"2016","journal-title":"J. Am. Water Resour. Assoc."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"885","DOI":"10.1016\/j.scitotenv.2019.02.085","article-title":"A framework for automated anomaly detection in high frequency water-quality data from in situ sensors","volume":"664","author":"Leigh","year":"2019","journal-title":"Sci. Total Environ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"13719","DOI":"10.1021\/acs.est.0c04069","article-title":"Detecting Technical Anomalies in High-Frequency Water-Quality Data Using Artificial Neural Networks","volume":"54","author":"Leigh","year":"2020","journal-title":"Environ. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"119145","DOI":"10.1016\/j.jclepro.2019.119145","article-title":"An integrated data-driven framework for surface water quality anomaly detection and early warning","volume":"251","author":"Liu","year":"2020","journal-title":"J. Clean. Prod."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1016\/j.scitotenv.2017.08.232","article-title":"Applying high-frequency surrogate measurements and a wavelet-ANN model to provide early warnings of rapid surface water quality anomalies","volume":"610\u2013611","author":"Shi","year":"2018","journal-title":"Sci. Total Environ."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1080\/713827181","article-title":"An analysis of four missing data treatment methods for supervised learning","volume":"17","author":"Batista","year":"2003","journal-title":"Appl. Artif. Intell."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/2193-1801-2-222","article-title":"Principled missing data methods for researchers","volume":"2","author":"Dong","year":"2013","journal-title":"SpringerPlus"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.jhydrol.2012.09.044","article-title":"Trends in seasonal river flow regimes in the UK","volume":"475","author":"Hannaford","year":"2012","journal-title":"J. Hydrol."},{"key":"ref_14","unstructured":"Helsel, D.R., and Hirsch, R.M. (1992). Statistical Methods in Water Resources, Elsevier."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3976","DOI":"10.1002\/joc.4954","article-title":"On the impact of gaps on trend detection in extreme streamflow time series","volume":"37","author":"Slater","year":"2017","journal-title":"Int. J. Clim."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1781","DOI":"10.1029\/WR015i006p01781","article-title":"An evaluation of some record reconstruction techniques","volume":"15","author":"Hirsch","year":"1979","journal-title":"Water Resour. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1657","DOI":"10.1029\/91WR00977","article-title":"A daily hydroclimatological data set for the continental United States","volume":"27","author":"Wallis","year":"1991","journal-title":"Water Resour. Res."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1080\/02626669509491422","article-title":"Models for extending streamflow data: A case study","volume":"40","author":"Raman","year":"1995","journal-title":"Hydrol. Sci. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"W05415","DOI":"10.1029\/2005WR004455","article-title":"Updated streamflow reconstructions for the Upper Colorado River Basin","volume":"42","author":"Woodhouse","year":"2006","journal-title":"Water Resour. Res."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.5194\/hess-9-209-2005","article-title":"Using a spatio-temporal dynamic state-space model with the EM algorithm to patch gaps in daily riverflow series","volume":"9","author":"Amisigo","year":"2005","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1016\/S0022-1694(00)00332-2","article-title":"Groups and neural networks based streamflow data infilling procedures","volume":"241","author":"Khalil","year":"2001","journal-title":"J. Hydrol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0022-1694(01)00513-3","article-title":"Estimation of missing streamflow data using principles of chaos theory","volume":"255","author":"Elshorbagy","year":"2002","journal-title":"J. Hydrol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"164","DOI":"10.1016\/j.jhydrol.2004.10.008","article-title":"Nonstationary hydrological time series forecasting using nonlinear dynamic methods","volume":"307","author":"Coulibaly","year":"2005","journal-title":"J. Hydrol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"618","DOI":"10.2166\/nh.2012.110","article-title":"An appraisal of the performance of data-infilling methods for application to daily mean river flow records in the UK","volume":"43","author":"Harvey","year":"2012","journal-title":"Hydrol. Res."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9447","DOI":"10.1002\/2015WR017399","article-title":"Reconstruction of missing daily streamflow data using dynamic regression models","volume":"51","author":"Tencaliec","year":"2015","journal-title":"Water Resour. Res."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Zhao, L., and Zheng, F. (2017, January 22\u201323). Missing Data Reconstruction Using Adaptively Updated Dictionary in Wireless Sensor Networks. Proceedings of the 7th International Conference on Computer Engineering and Networks\u2014PoS(CENet2017), Sissa Medialab, Shanghai, China.","DOI":"10.22323\/1.299.0040"},{"key":"ref_27","first-page":"2101","article-title":"A multiple-regression-model-based missing values imputation algorithm in wireless sensor network","volume":"46","author":"Pan","year":"2009","journal-title":"J. Comput. Res. Dev."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.comcom.2018.09.007","article-title":"Missing data recovery using reconstruction in ocean wireless sensor networks","volume":"132","author":"Wu","year":"2018","journal-title":"Comput. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"449","DOI":"10.1016\/j.neucom.2009.07.005","article-title":"Time series prediction using RBF neural networks with a nonlinear time-varying evolution PSO algorithm","volume":"73","author":"Lee","year":"2009","journal-title":"Neurocomputing"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"100991","DOI":"10.1016\/j.aei.2019.100991","article-title":"Sensor data reconstruction using bidirectional recurrent neural network with application to bridge monitoring","volume":"42","author":"Jeong","year":"2019","journal-title":"Adv. Eng. Inform."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1255","DOI":"10.1016\/j.chemosphere.2004.10.044","article-title":"Nitrate toxicity to aquatic animals: A review with new data for freshwater invertebrates","volume":"58","author":"Camargo","year":"2005","journal-title":"Chemosphere"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1029\/2009EO140001","article-title":"Nutrient Enrichment Drives Gulf of Mexico Hypoxia","volume":"90","author":"Boesch","year":"2009","journal-title":"Eos"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/j.hal.2008.08.028","article-title":"Effects of nutrient enrichment in the nation\u2019s estuaries: A decade of change","volume":"8","author":"Bricker","year":"2008","journal-title":"Harmful Algae"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3211","DOI":"10.1016\/0045-6535(95)00182-8","article-title":"Nitrate (NO3-N) toxicity to aquatic life: A proposal of safe concentrations for two species of nearctic freshwater invertebrates","volume":"31","author":"Camargo","year":"1995","journal-title":"Chemosphere"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.aquaeng.2017.08.003","article-title":"Evaluating the chronic effects of nitrate on the health and performance of post-smolt Atlantic salmon Salmo salar in freshwater recirculation aquaculture systems","volume":"79","author":"Davidson","year":"2017","journal-title":"Aquac. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"807","DOI":"10.1016\/j.envpol.2018.07.047","article-title":"Effects of nitrate on freshwater mussel glochidia attachment and metamorphosis success to the juvenile stage","volume":"242","author":"Moore","year":"2018","journal-title":"Environ. Pollut."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"780","DOI":"10.3390\/w5020780","article-title":"Science to Support Management of Receiving Waters in an Event-Driven Ecosystem: From Land to River to Sea","volume":"5","author":"Leigh","year":"2013","journal-title":"Water"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"4881","DOI":"10.5194\/hess-20-4881-2016","article-title":"Sediment and nutrient budgets are inherently dynamic: Evidence from a long-term study of two subtropical reservoirs","volume":"20","author":"Weber","year":"2016","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/s100219900003","article-title":"Material Spiraling in Stream Corridors: A Telescoping Ecosystem Model","volume":"1","author":"Fisher","year":"1998","journal-title":"Ecosystems"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Wood, S.N. (2017). Generalized Additive Models: An Introduction with R, CRC Press.","DOI":"10.1201\/9781315370279"},{"key":"ref_41","unstructured":"Sakamoto, Y., Ishiguro, M., and Kitagawa, G. (1986). Akaike Information Criterion Statistics, D. Reidel."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1509","DOI":"10.1080\/01621459.1970.10481180","article-title":"Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models","volume":"65","author":"Box","year":"1970","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_43","unstructured":"Vance, J., Nance, B., Monahan, D., Mahal, M., and Cavileer, M. (2021, December 04). NEON Preventive Maintenance Procedure: AIS Surface Water Quality Multisonde. NEON.DOC.001569 Revision: B, Technical Report, National Ecological Observatory Network 2019. Available online: http:\/\/data.neonscience.org\/documents."},{"key":"ref_44","unstructured":"Willingham, R., Cavileer, M., Csavina, J., and Monahan, D. (2021, December 04). NEON Preventive Maintenance Procedure: Submersible Ultraviolet Nitrate analyzer. NEON.DOC.002716 Revision: B, Technical Report, National Ecological Observatory Network 2019. Available online: http:\/\/data.neonscience.org\/documents."},{"key":"ref_45","unstructured":"Cawley, K.M. (2021, December 04). NEON Aquatic Sampling Strategy, Technical Report, National Ecological Observatory Network 2016. Available online: http:\/\/data.neonscience.org\/documents."},{"key":"ref_46","unstructured":"(2021, December 04). NEON, Nitrate in Surface Water (DP1.20033.001) (2021). Available online: https:\/\/data.neonscience.org\/data-products\/DP1.20033.001\/RELEASE-2021."},{"key":"ref_47","unstructured":"(2021, December 04). NEON, Water Quality (DP1.20288.001) (2021). Available online: https:\/\/data.neonscience.org\/data-products\/DP1.20288.001\/RELEASE-2021."},{"key":"ref_48","unstructured":"(2021, December 04). NEON, Temperature (PRT) in Surface Water (DP1.20053.001) (2021). Available online: https:\/\/data.neonscience.org\/data-products\/DP1.20053.001\/RELEASE-2021."},{"key":"ref_49","unstructured":"(2021, December 04). NEON, Elevation of Surface Water (DP1.20016.001) (2021). Available online: https:\/\/data.neonscience.org\/data-products\/DP1.20016.001\/RELEASE-2021."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Leigh, C., Kandanaarachchi, S., McGree, J.M., Hyndman, R.J., Alsibai, O., Mengersen, K., and Peterson, E.E. (2019). Predicting sediment and nutrient concentrations from high-frequency water-quality data. PLoS ONE, 14.","DOI":"10.1101\/599712"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1111\/j.2517-6161.1964.tb00553.x","article-title":"An Analysis of Transformations","volume":"26","author":"Box","year":"1964","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1111\/j.1471-8286.2007.01678.x","article-title":"BOLD: The Barcode of Life Data System (http:\/\/www.barcodinglife.org)","volume":"7","author":"Ratnasingham","year":"2007","journal-title":"Mol. Ecol. Notes"},{"key":"ref_53","unstructured":"Fox, J., Weisberg, S.D., Adler, D., Bates, D., Baud-Bovy, G., and Ellison, S. (2012). Package \u2018car\u2019, R Foundation for Statistical Computing."},{"key":"ref_54","unstructured":"Hastie, T. (2021, December 04). Gam: Generalized Additive Models, R Package Version 1.20. Available online: https:\/\/CRAN.R-project.org\/package=gam."},{"key":"ref_55","unstructured":"Wickham, H., and Chang, W. (2021, September 10). Ggplot2: An Implementation of the Grammar of Graphics. Available online: http:\/\/CRAN.R-project.org\/package=ggplot2."},{"key":"ref_56","unstructured":"Taylor, J., Street, S., and Sturtevant, C. (2021, December 04). NEON Algorithm Theoretical Basis Document (ATBD): QA\/QC Plausibility Testing. NEON.DOC.011081 Revision: C, Technical Report, National Ecological Observatory Network 2020. Available online: https:\/\/data.neonscience.org\/api\/v0\/documents\/NEON.DOC.011081vC."},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Langhammer, J., and \u010ces\u00e1k, J. (2016). Applicability of a Nu-Support Vector Regression Model for the Completion of Missing Data in Hydrological Time Series. Water, 8.","DOI":"10.3390\/w8120560"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Jones, T.L., and Jones, A.S. (2021). Horsburgh, toward automating post processing of aquatic sensor data. Earth Archiv. Prepr.","DOI":"10.4211\/hs.a6ea89ae20354e39b3c9f1228997e27a"},{"key":"ref_59","unstructured":"Kermorvant, B., Liquet, G., Litt, K., Mengersen, E.E., Peterson, R., Hyndman, J.B., and Jones, C. (2021). Understanding links between water-quality variables and nitrate concentration in freshwater streams using high-frequency sensor data. arXiv."}],"container-title":["International Journal of Environmental Research and Public Health"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1660-4601\/18\/23\/12803\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:39:43Z","timestamp":1760168383000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1660-4601\/18\/23\/12803"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,4]]},"references-count":59,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["ijerph182312803"],"URL":"https:\/\/doi.org\/10.3390\/ijerph182312803","relation":{},"ISSN":["1660-4601"],"issn-type":[{"value":"1660-4601","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,4]]}}}