Data compression to define information content of hydrological time series

Hydrology and Earth System Sciences

Volumn 17, Issue 8, 2013, Pages 3171-3187

  Weijs, S V ^a   Van De Giesen, N ^b   Parlange, M B ^a  

^a EPFL   (Switzerland)

^b DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CATCHMENTS; INFORMATION THEORY; TIME SERIES ANALYSIS; UNCERTAINTY ANALYSIS;

ALGORITHMIC INFORMATION THEORY; COMPRESSION PERFORMANCE; EPISTEMIC UNCERTAINTIES; HYDROLOGICAL DATA; HYDROLOGICAL MODELS; HYDROLOGICAL TIME-SERIES; INFORMATION CONTENTS; THEORETICAL FRAMEWORK;

DATA COMPRESSION;

ALGORITHM; CALIBRATION; CATCHMENT; DATA MANAGEMENT; DATA SET; HYDROLOGICAL MODELING; TIME SERIES;

EID: 84897620442     PISSN: 10275606     EISSN: 16077938     Source Type: Journal    
DOI: 10.5194/hess-17-3171-2013     Document Type: Article

References (48)

1. Akaike, H.: A new look at the statistical model identification, IEEE Trans. Automatic Control, 19, 716-723, 1974.
2. Alfonso, L., Lobbrecht, A., and Price, R.: Information theory-based approach for location of monitoring water level gauges in polders, Water Resour. Res., 46, W03528, doi:10.1029/2009WR008101, 2010a.
3. Alfonso, L., Lobbrecht, A., and Price, R.: Optimization of water level monitoring network in polder systems using information theory, Water Resour. Res., 46, W12553, doi:10.1029/2009WR008953, 2010b.
4. Beven, K. andWesterberg, I.: On red herrings and real herrings: disinformation and information in hydrological inference, Hydrol. Process., 25, 1676-1680, doi:10.1002/hyp.7963, 2011.
5. Beven, K., Smith, P. J., and Wood, A.: On the colour and spin of epistemic error (and what we might do about it), Hydrol. Earth Syst. Sci., 15, 3123-3133, doi:10.5194/hess-15-3123-2011, 2011.
6. Brutsaert, W.: Hydrology: an introduction, Cambridge University Press, New York, 2005.
7. Burrows, M. and Wheeler, D. J.: A block-sorting lossless data compression algorithm, Tech. rep., Systems Research Center, Palo Alto, CA, 1994.
8. Cahill, A. T.: Significance of {AIC} differences for precipitation intensity distributions, Adv. Water Resour., 26, 457-464, doi:10.1016/S0309-1708(02)00167-7, 2003.
9. Chaitin, G. J.: On the length of programs for computing finite binary sequences, J. ACM, 13, 547-569, 1966.
10. Chaitin, G. J.: A theory of program size formally identical to information theory, J. ACM, 22, 329-340, 1975.
11. Cilibrasi, R.: Statistical inference through data compression, Ph.D. thesis, UvA, Amsterdam, 2007.
12. Cover, T. M. and Thomas, J. A.: Elements of information theory, Wiley-Interscience, New York, 2006.
13. Feynman, R.: The character of physical law, MIT Press, 1967.
14. Gong, W., H. V. Gupta, D. Yang, K. Sricharan, and A. O. Hero III Estimating epistemic and aleatory uncertainties during hydrologic modeling: An information theoretic approach, Water Resour. Res., 49, 2253-2273, doi:10.1002/wrcr.20161, 2013.
15. Huffman, D. A.: A Method for the Construction of Minimum- Redundancy Codes, Proceedings of the IRE, 40, 1098-1101, 1952.
16. Jakeman, A. J. and Hornberger, G. M.: How much complexity is warranted in a rainfall-runoff model?, Water Resour. Res., 29, 2637-2649, 1993.
17. Katz, R.: On some criteria for estimating the order of a Markovchain, Technometrics, 23, 243-249, doi:10.2307/1267787, 1981.
18. Kolmogorov, A. N.: Three approaches to the quantitative definition of information, Int. J. Comput. Math., 2, 157-168, 1968.
19. Kraft, L. G.: A device for quantizing, grouping, and coding amplitude-modulated pulses, Master's thesis, Massachusetts Institute of Technology, Dept. of Electrical Engineering, 1949.
20. Kullback, S. and Leibler, R. A.: On Information and Sufficiency, Ann. Math. Stat., 22, 79-86, 1951.
21. Laio, F., Allamano, P., and Claps, P.: Exploiting the information content of hydrological "outliers" for goodness-of-fit testing, Hydrol. Earth Syst. Sci., 14, 1909-1917, doi:10.5194/hess-14-1909-2010, 2010.
22. Li, C., Singh, V., and Mishra, A.: Entropy theory-based criterion for hydrometric network evaluation and design: Maximum information minimum redundancy, Water Resour. Res., 48, W05521, doi:10.1029/2011WR011251, 2012.
23. Li, M. and Vitanyi, P. M. B.: An introduction to Kolmogorov complexity and its applications, Springer-Verlag New York Inc, 2008.
24. Martin, G. N. N.: Range encoding: an algorithm for removing redundancy from a digitised message, in: Video & Data Recording conference, Southampton, UK, 1979.
25. McMillan, B.: Two inequalities implied by unique decipherability, IEEE Trans. Inf. Theory, 2, 115-116, 1956.
26. Mishra, A. and Coulibaly, P.: Hydrometric network evaluation for Canadian watersheds, J. Hydrol., 380, 420-437, 2010.
27. Montanari, A., Shoemaker, C. A., and van de Giesen, N.: Introduction to special section on Uncertainty Assessment in Surface and Subsurface Hydrology: An overview of issues and challenges, Water Resour. Res., 45, W00B00, doi:10.1029/2009WR008471, 2009.
28. Paluš,M.: Coarse-grained entropy rates for characterization of complex time series, Physica D, Nonlinear Phenomena, 93, 64-77, 1996.
29. Pianosi, F. and Soncini-Sessa, R.: Real-time management of a multipurpose water reservoir with a heteroscedastic inflow model, Water Resour. Res., 45, W10430, doi:10.1029/2008WR007335, 2009.
30. Rissanen, J. and Langdon, G. G.: Arithmetic coding, IBM J. Res. Develop., 23, 149-162, 1979.
31. Ruddell, B. L., Brunsell, N. A., and Stoy, P.: Applying Information Theory in the Geosciences to Quantify Process Uncertainty, Feedback, Scale, Eos, Transactions American Geophysical Union, 94, 56-56, doi:10.1002/2013EO050007, 2013.
32. Schaefli, B. and Gupta, H. V.: Do Nash values have value?, Hydrol. Process., 21, 2075-2080, 2007.
33. Schoups, G., van de Giesen, N. C., and Savenije, H. H. G.: Model complexity control for hydrologic prediction, Water Resour. Res., 44, W00B03, doi:10.1029/2008WR006836, 2008.
34. Shannon, C. E.: A mathematical theory of communication, Bell System Technical J., 27, 379-423, 1948.
35. Singh, V. P.: The use of entropy in hydrology and water resources, Hydrol. Process., 11, 587-626, 1997.
36. Singh, V. P. and Rajagopal, A. K.: Some recent advances in application of the principle of maximum entropy (POME) in hydrology, IAHS, 194, 353-364, 1987.
37. Solomonoff, R. J.: A formal theory of inductive inference, Part I, Information Control, 7, 1-22, 1964.
38. Turing, A. M.: On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, 2, 230-265, 1937.
39. Vrugt, J. A., Bouten, W., Gupta, H. V., and Sorooshian, S.: Toward improved identifiability of hydrologic model parameters: The information content of experimental data, Water Resour. Res, 38, 1312, doi:10.1029/2001WR001118, 2002.
40. Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S.: A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters,Water Resour. Res., 39, 1201, doi:10.1029/2002WR001642, 2003.
41. Vrugt, J. A., Ter Braak, C. J. F., Gupta, H. V., and Robinson, B. A.: Equifinality of formal (DREAM) and informal (GLUE) Bayesian approaches in hydrologic modeling?, Stochastic Environ. Res. Risk Assess., 23, 1011-1026, 2009.
42. Weijs, S. V. and Van de Giesen, N.: Accounting for observational uncertainty in forecast verification: an information-theoretical view on forecasts, observations and truth, Mon. Weather Rev., 139, 2156-2162, doi:10.1175/2011MWR3573.1, 2011.
43. Weijs, S. V., Schoups, G., and van de Giesen, N.: Why hydrological predictions should be evaluated using information theory, Hydrol. Earth Syst. Sci., 14, 2545-2558, doi:10.5194/hess-14-2545-2010, 2010a.
44. Weijs, S. V., Van Nooijen, R., and Van de Giesen, N.: Kullback- Leibler divergence as a forecast skill score with classic reliability-resolution-uncertainty decomposition, Mon. Weather Rev., 138, 3387-3399, 2010b.
45. Weijs, S. V., Mutzner, R., and Parlange, M. B.: Could electrical conductivity replace water level in rating curves for alpine streams?, Water Resour. Res., 49, WR012181, doi:10.1029/2012WR012181, 2013a.
46. Weijs, S. V., van de Giesen, N., and Parlange, M. B.: HydroZIP: How Hydrological Knowledge can Be Used to Improve Compression of Hydrological Data, Entropy, 15, 1289-1310, doi:10.3390/e15041289, 2013b.
47. Westerberg, I., Guerrero, J., Seibert, J., Beven, K., and Halldin, S.: Stage-discharge uncertainty derived with a non-stationary rating curve in the Choluteca River, Honduras, Hydrol. Process., 25, 603-613, doi:10.1002/hyp.7848, 2011.
48. Ziv, J. and Lempel, A.: A universal algorithm for sequential data compression, IEEE Trans. Information Theory, 23, 337-343, 1977.