{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,26]],"date-time":"2026-08-26T00:50:19Z","timestamp":1787705419499,"version":"build-2784847793"},"reference-count":73,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2013,4,10]],"date-time":"2013-04-10T00:00:00Z","timestamp":1365552000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>From algorithmic information theory, which connects the information content of a data set to the shortest computer program that can produce it, it is known that there are strong analogies between compression, knowledge, inference and prediction. The more we know about a data generating process, the better we can predict and compress the data. A model that is inferred from data should ideally be a compact description of those data. In theory, this means that hydrological knowledge could be incorporated into compression algorithms to more efficiently compress hydrological data and to outperform general purpose compression algorithms. In this study, we develop such a hydrological data compressor, named HydroZIP, and test in practice whether it can outperform general purpose compression algorithms on hydrological data from 431 river basins from the Model Parameter Estimation Experiment (MOPEX) data set. HydroZIP compresses using temporal dependencies and parametric distributions. Resulting file sizes are interpreted as measures of information content, complexity and model adequacy. These results are discussed to illustrate points related to learning from data, overfitting and model complexity.<\/jats:p>","DOI":"10.3390\/e15041289","type":"journal-article","created":{"date-parts":[[2013,4,10]],"date-time":"2013-04-10T11:52:27Z","timestamp":1365594747000},"page":"1289-1310","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["HydroZIP: How Hydrological Knowledge can Be Used to Improve Compression of Hydrological Data"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1311-3867","authenticated-orcid":false,"given":"Steven","family":"Weijs","sequence":"first","affiliation":[{"name":"School of Architecture, Civil and Environmental Engineering, EPFL, Station 2, Lausanne 1015,Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7200-3353","authenticated-orcid":false,"given":"Nick","family":"Van de Giesen","sequence":"additional","affiliation":[{"name":"Water Resources Management, TU Delft, Stevinweg 1, Delft 2628 CN, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marc","family":"Parlange","sequence":"additional","affiliation":[{"name":"School of Architecture, Civil and Environmental Engineering, EPFL, Station 2, Lausanne 1015,Switzerland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2013,4,10]]},"reference":[{"key":"ref_1","unstructured":"Lehning, M., Dawes, N., Bavay, M., Parlange, M., Nath, S., and Zhao, F. (2009). The Fourth Paradigm: Data-Intensive Scientific Discovery, Microsoft Research."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ryabko, B., and Astola, J. (2005, January 6\u201310). Application of Data Compression Methods to Hypothesis Testing for Ergodic and Stationary Processes. Proceedings of the International Conference on Analysis of Algorithms DMTCS Proceedings AD, Barcelona, Spain.","DOI":"10.46298\/dmtcs.3380"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1016\/j.tcs.2006.06.004","article-title":"Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series","volume":"359","author":"Ryabko","year":"2006","journal-title":"Theor. Comput. Sci."},{"key":"ref_4","unstructured":"Cilibrasi, R. (2007). Statistical inference through data compression. [Ph.D. Thesis, Universiteit van Amsterdam]."},{"key":"ref_5","first-page":"2029","article-title":"Data compression to define information content of hydrological time series","volume":"10","author":"Weijs","year":"2013","journal-title":"Hydrol. Earth Syst. Sci. Discuss."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kavetski, D., Kuczera, G., and Franks, S.W. (2006). Bayesian analysis of input uncertainty in hydrological modeling: 1. Theory. Water Resour. Res., 42.","DOI":"10.1029\/2005WR004368"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"3123","DOI":"10.5194\/hess-15-3123-2011","article-title":"On the colour and spin of epistemic error (and what we might do about it)","volume":"15","author":"Beven","year":"2011","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1016\/j.advwatres.2011.12.006","article-title":"Calibration of hydrological models on hydrologically unusual events","volume":"38","author":"Singh","year":"2012","journal-title":"Adv. Water Resour."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gong, W., Gupta, H.V., Yang, D., Sricharan, K., and Hero, A.O. (2013). Estimating epistemic & aleatory uncertainties during hydrologic modeling: An information theoretic approach. Water Resour. Res., in press.","DOI":"10.1002\/wrcr.20161"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Stedinger, J.R., Vogel, R.M., Lee, S.U., and Batchelder, R. (2008). Appraisal of the generalized likelihood uncertainty estimation (GLUE) method. Water Resour. Res., 44.","DOI":"10.1029\/2008WR006822"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Montanari, A., Shoemaker, C.A., and van de Giesen, N. (2009). Introduction to special section on Uncertainty Assessment in Surface and Subsurface Hydrology: An overview of issues and challenges. Water Resour. Res., 45.","DOI":"10.1029\/2009WR008471"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Montanari, A., and Koutsoyiannis, D. (2012). A blueprint for process-based modeling of uncertain hydrological systems. Water Resour. Res., 48.","DOI":"10.1029\/2011WR011412"},{"key":"ref_13","unstructured":"Collins English Dictionary-Complete & Unabridged 10th Edition. Available online: http:\/\/www.collinsdictionary.com\/dictionary\/english\/zip."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1145\/321356.321363","article-title":"On the length of programs for computing finite binary sequences","volume":"13","author":"Chaitin","year":"1966","journal-title":"J. ACM"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0019-9958(64)90223-2","article-title":"A formal theory of inductive inference. Part I","volume":"7","author":"Solomonoff","year":"1964","journal-title":"Inform. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1080\/00207166808803030","article-title":"Three approaches to the quantitative definition of information","volume":"2","author":"Kolmogorov","year":"1968","journal-title":"Int. J. Comput. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1145\/321892.321894","article-title":"A theory of program size formally identical to information theory","volume":"22","author":"Chaitin","year":"1975","journal-title":"J. ACM"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Rissanen, J. (2007). Information and Complexity in Statistical Modeling, Springer Verlag.","DOI":"10.1007\/978-0-387-68812-1"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Schoups, G., van de Giesen, N.C., and Savenije, H.H.G. (2008). Model complexity control for hydrologic prediction. Water Resour. Res., 44.","DOI":"10.1029\/2008WR006836"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jaynes, E.T. (2003). Probability Theory: The Logic of Science, Cambridge University Press.","DOI":"10.1017\/CBO9780511790423"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.tcs.2007.05.016","article-title":"On universal prediction and Bayesian confirmation","volume":"384","author":"Hutter","year":"2007","journal-title":"Theor. Comput. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1076","DOI":"10.3390\/e13061076","article-title":"A philosophical treatise of universal induction","volume":"13","author":"Rathmanner","year":"2011","journal-title":"Entropy"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/TIT.2005.844059","article-title":"Clustering by compression","volume":"51","author":"Cilibrasi","year":"2005","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Emmert-Streib, F., and Dehmer, M. (2009). Information Theory and Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-84816-7"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"407","DOI":"10.3390\/e15010407","article-title":"Expanding the algorithmic information theory frame for applications to earth observation","volume":"15","author":"Cerra","year":"2013","journal-title":"Entropy"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/S0309-1708(99)00021-4","article-title":"A geomorphology-based semi-distributed watershed model","volume":"23","author":"Szilagyi","year":"1999","journal-title":"Adv. Water Resour."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5194\/hess-5-1-2001","article-title":"How far can we go in distributed hydrological modelling?","volume":"5","author":"Beven","year":"2001","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Simoni, S., Padoan, S., Nadeau, D., Diebold, M., Porporato, A., Barrenetxea, G., Ingelrest, F., Vetterli, M., and Parlange, M. (2011). Hydrologic response of an alpine watershed: Application of a meteorological wireless sensor network to understand streamflow generation. Water Resour. Res., 47.","DOI":"10.1029\/2011WR010730"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1175\/1520-0442(1990)003<0005:ITACP>2.0.CO;2","article-title":"Information theory and climate prediction","volume":"3","author":"Leung","year":"1990","journal-title":"J. Clim."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2057","DOI":"10.1175\/1520-0469(2002)059<2057:MDPUUR>2.0.CO;2","article-title":"Measuring dynamical prediction utility using relative entropy","volume":"59","author":"Kleeman","year":"2002","journal-title":"J. Atmos. Sci."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2425","DOI":"10.1175\/1520-0469(2004)061<2425:PAITPI>2.0.CO;2","article-title":"Predictability and information theory. Part I: Measures of predictability","volume":"61","author":"DelSole","year":"2004","journal-title":"J. Atmos. Sci."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"DelSole, T., and Tippett, M.K. (2007). Predictability: Recent insights from information theory. Rev. Geophys., 45.","DOI":"10.1029\/2006RG000202"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1653","DOI":"10.1175\/1520-0493(2002)130<1653:EPFUIT>2.0.CO;2","article-title":"Evaluating probabilistic forecasts using information theory","volume":"130","author":"Roulston","year":"2002","journal-title":"Mon. Weather Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1175\/2009MWR2945.1","article-title":"Scoring rules for forecast verification","volume":"138","author":"Benedetti","year":"2010","journal-title":"Mon. Weather Rev."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"352","DOI":"10.1175\/2007MWR1931.1","article-title":"Information-based skill scores for probabilistic forecasts","volume":"136","author":"Ahrens","year":"2008","journal-title":"Mon. Weather Rev."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2005","DOI":"10.1175\/MWR-D-11-00266.1","article-title":"Generalization of the ignorance score: Continuous ranked version and its decomposition","volume":"140","author":"Ahrens","year":"2012","journal-title":"Mon. Weather Rev."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"3387","DOI":"10.1175\/2010MWR3229.1","article-title":"Kullback\u2013Leibler divergence as a forecast skill score with classic reliability\u2013resolution\u2013uncertainty decomposition","volume":"138","author":"Weijs","year":"2010","journal-title":"Mon. Weather Rev."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"2545","DOI":"10.5194\/hess-14-2545-2010","article-title":"Why hydrological predictions should be evaluated using information theory","volume":"14","author":"Weijs","year":"2010","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Singh, V., and Fiorentino, M. (1992). Entropy and Energy Dissipation in Water Resources, Kluwer Academic Publishers.","DOI":"10.1007\/978-94-011-2430-0"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Alfonso, L., Lobbrecht, A., and Price, R. (2010). Information theory-based approach for location of monitoring water level gauges in polders. Water Resour. Res., 46.","DOI":"10.1029\/2009WR008101"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Li, C., Singh, V., and Mishra, A. (2012). Entropy theory-based criterion for hydrometric network evaluation and design: Maximum information minimum redundancy. Water Resour. Res., 48.","DOI":"10.1029\/2011WR011251"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1002\/(SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P","article-title":"The use of entropy in hydrology and water resources","volume":"11","author":"Singh","year":"1997","journal-title":"Hydrol. Process."},{"key":"ref_43","first-page":"169","article-title":"Are ecosystems dynamical systems","volume":"3","author":"Lange","year":"1998","journal-title":"Int. J. Comput. Anticip. Syst."},{"key":"ref_44","first-page":"1","article-title":"Time series analysis of ecosystem variables with complexity measures","volume":"250","author":"Lange","year":"1999","journal-title":"Int. J. Complex Syst."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"751","DOI":"10.1029\/97WR03495","article-title":"Toward improved calibration of hydrologic models: Multiple and noncommensurable measures of information","volume":"34","author":"Gupta","year":"1998","journal-title":"Water Resour. Res."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2136\/sssaj2001.65119x","article-title":"Information content of data for identifying soil hydraulic parameters from outflow experiments","volume":"65","author":"Vrugt","year":"2001","journal-title":"Soil Sci. Soc. Am. J."},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Vrugt, J.A., Bouten, W., Gupta, H.V., and Sorooshian, S. (2002). Toward improved identifiability of hydrologic model parameters: The information content of experimental data. Water Resour. Res., 38.","DOI":"10.1029\/2001WR001118"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"1909","DOI":"10.5194\/hess-14-1909-2010","article-title":"Exploiting the information content of hydrological \u201coutliers\u201d for goodness-of-fit testing","volume":"14","author":"Laio","year":"2010","journal-title":"Hydrol. Earth Syst. Sci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"272","DOI":"10.1109\/TGRS.1984.350621","article-title":"Comparison of the information content of data from the Landsat-4 Thematic Mapper and the Multispectral Scanner","volume":"3","author":"Price","year":"1984","journal-title":"Geosci. Remote Sens. IEEE Trans."},{"key":"ref_50","unstructured":"Horvath, K., Stogner, H., Weinhandel, G., and Uhl, A. (2011, January 4\u20136). Experimental Study on Lossless Compression of Biometric Iris Data. Proceedings of the 7th International Symposium on Image and Signal Processing and Analysis (ISPA), Dubrovnik, Croatia."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"34","DOI":"10.3390\/e12010034","article-title":"Data compression concepts and algorithms and their applications to bioinformatics","volume":"12","author":"Nalbantoglu","year":"2009","journal-title":"Entropy"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Voepel, H., Ruddell, B., Schumer, R., Troch, P., Brooks, P., Neal, A., Durcik, M., and Sivapalan, M. (2011). Quantifying the role of climate and landscape characteristics on hydrologic partitioning and vegetation response. Water Resour. Res., 47.","DOI":"10.1029\/2010WR009944"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1029\/2012WR012181","article-title":"Could electrical conductivity replace water level in rating curves for alpine streams?","volume":"49","author":"Weijs","year":"2013","journal-title":"Water Resour. Res."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1098","DOI":"10.1109\/JRPROC.1952.273898","article-title":"A method for the construction of minimum-redundancy codes","volume":"40","author":"Huffman","year":"1952","journal-title":"Proc. IRE"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1109\/TIT.1977.1055714","article-title":"A universal algorithm for sequential data compression","volume":"23","author":"Ziv","year":"1977","journal-title":"IEEE Trans. Inform. Theory"},{"key":"ref_56","unstructured":"Martin, G.N.N. (1979, January 24\u201327). Range Encoding: An Algorithm for Removing Redundancy from a Digitised Message. Proceedings of the Video & Data Recording Conference, Southampton, UK."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1147\/rd.232.0149","article-title":"Arithmetic coding","volume":"23","author":"Rissanen","year":"1979","journal-title":"IBM J. Res. Dev."},{"key":"ref_58","unstructured":"Burrows, M., and Wheeler, D.J. (1994). A Block-sorting Lossless Data Compression Algorithm, Technical report, Systems Research Center."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_60","unstructured":"Akaike, H. (1973, January 2\u20138). Information Theory and an Extension of the Maximum Likelihood Principle. Proceedings of the 2nd International Symposium on Information Theory, Tsahkadsor, Armenia SSR."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1974","journal-title":"IEEE Trans. Autom. Control"},{"key":"ref_62","first-page":"33","article-title":"Statistical encoding for text and picture communication","volume":"77","author":"Michel","year":"1958","journal-title":"Am. Inst. Electr. Eng. Part I Commun. Electron. Trans."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"2335","DOI":"10.1029\/93WR00569","article-title":"Effects of an index of atmospheric circulation on stochastic properties of precipitation","volume":"29","author":"Katz","year":"1993","journal-title":"Water Resour. Res."},{"key":"ref_64","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1175\/1520-0450-39.5.610","article-title":"An extended version of the Richardson model for simulating daily weather variables","volume":"39","author":"Parlange","year":"2000","journal-title":"J. Appl. Meteorol."},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/S0309-1708(99)00017-2","article-title":"Extreme value theory for precipitation: Sensitivity analysis for climate change","volume":"23","author":"Katz","year":"1999","journal-title":"Adv. Water Resour."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1023\/A:1005432803188","article-title":"Changes in the probability of heavy precipitation: Important indicators of climatic change","volume":"42","author":"Groisman","year":"1999","journal-title":"Clim. Chang."},{"key":"ref_67","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/s00382-001-0218-4","article-title":"Secular trends in daily precipitation characteristics: Greenhouse gas simulation with a coupled AOGCM","volume":"19","author":"Semenov","year":"2002","journal-title":"Clim. Dyn."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/j.advwatres.2011.11.007","article-title":"Entropy based derivation of probability distributions: A case study to daily rainfall","volume":"45","author":"Papalexiou","year":"2011","journal-title":"Adv. Water Resour."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1061\/(ASCE)0733-9496(2001)127:6(354)","article-title":"Evapotranspiration intensifies over the conterminous United States","volume":"127","author":"Szilagyi","year":"2001","journal-title":"J. Water Resour. Plan. Manag."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1023\/A:1026054330406","article-title":"Stochastic modeling of the effects of large-scale circulation on daily weather in the southeastern US","volume":"60","author":"Katz","year":"2003","journal-title":"Clim. Chang."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"1124","DOI":"10.1890\/04-0606","article-title":"Statistics of extremes: Modeling ecological disturbances","volume":"86","author":"Katz","year":"2005","journal-title":"Ecology"},{"key":"ref_72","doi-asserted-by":"crossref","first-page":"1676","DOI":"10.1002\/hyp.7963","article-title":"On red herrings and real herrings: Disinformation and information in hydrological inference","volume":"25","author":"Beven","year":"2011","journal-title":"Hydrol. Process."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"2156","DOI":"10.1175\/2011MWR3573.1","article-title":"Accounting for observational uncertainty in forecast verification: An information\u2013theoretical view on forecasts, observations and truth","volume":"139","author":"Weijs","year":"2011","journal-title":"Mon. Weather Rev."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/4\/1289\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:46:02Z","timestamp":1760219162000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/4\/1289"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,4,10]]},"references-count":73,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2013,4]]}},"alternative-id":["e15041289"],"URL":"https:\/\/doi.org\/10.3390\/e15041289","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,4,10]]}}}