Entropy-copula in hydrology and climatology

Journal of Hydrometeorology

Volumn 15, Issue 6, 2014, Pages 2176-2189

  AghaKouchak, Amir ^a  

^a University of California at Irvine   (United States)

Author keywords

Statistical techniques; Statistics; Time series

Indexed keywords

CLIMATE VARIATION; CLIMATOLOGY; FLOOD FREQUENCY; GEOSTATISTICS; HYDROLOGICAL MODELING; MULTIVARIATE ANALYSIS; PROBABILITY DENSITY FUNCTION; TIME SERIES;

EID: 84915746695     PISSN: 1525755X     EISSN: 15257541     Source Type: Journal    
DOI: 10.1175/JHM-D-13-0207.1     Document Type: Article

References (95)

1. AghaKouchak, A., and A. Mehran, 2013: Extended contingency table: Performance metrics for satellite observations and climate model simulations. Water Resour. Res., 49, 7144-7149, doi:10.1002/wrcr.20498.
2. AghaKouchak, A., A. Bárdossy, and E. Habib, 2010a: Conditional simulation of remotely sensed rainfall data using a non-Gaussian v-transformed copula. Adv. Water Resour., 33, 624-634, doi:10.1016/j.advwatres.2010.02.010.
3. AghaKouchak, A., A. Bárdossy, and E. Habib, 2010b: Copula-based uncertainty modelling: Application to multisensor precipitation estimates. Hydrol. Processes, 24, 2111-2124, doi:10.1002/hyp.7632.
4. AghaKouchak, A., E. Habib, and A. Bárdossy, 2010c: Modeling radar rainfall estimation uncertainties: Random errormodel. J.Hydrol. Eng., 15, 265-274, doi:10.1061/(ASCE)HE.1943-5584.0000185.
5. AghaKouchak, A., D. Easterling, K. Hsu, S. Schubert, and S. Sorooshian, Eds., 2012: Extremes in a Changing Climate. Springer, 423 pp. Alexander, L., and Coauthors, 2006: Global observed changes in daily climate extremes of temperature. J. Geophys. Res., 111, D05109, doi:10.1029/2005JD006290.
6. Ané, T., and C. Kharoubi, 2003: Dependence structure and risk measure. J. Bus., 76, 411-438, doi:10.1086/375253.
7. Balakrishnan, N., and C. D. Lai, 2009: Continuous Bivariate Distributions. 2nd ed. Springer, 684 pp.
8. Bárdossy, A., 2006: Copula-based geostatistical models for groundwater quality parameters. Water Resour. Res., 42, W11416, doi:10.1029/2005WR004754.
9. Bedford, T., and R. M. Cooke, 2002: Vines-A new graphical model for dependent random variables. Ann. Stat., 30, 1031- 1068, doi:10.1214/aos/1031689016.
10. Borwein, J. M., and A. S. Lewis, 2010: Convex Analysis and Nonlinear Optimization: Theory and Examples. 2nd ed. CMS Books in Mathematics, Vol. 3, Springer, 310 pp.
11. Brunsell, N. A., 2010: A multiscale information theory approach to assess spatial-temporal variability of daily precipitation. J. Hydrol., 385, 165-172, doi:10.1016/j.jhydrol.2010.02.016.
12. Chebana, F., and T. Ouarda, 2011: Multivariate quantiles in hydrological frequency analysis. Environmetrics, 22, 63-78, doi:10.1002/ env.1027.
13. Chen, C., J. O. Haerter, S. Hagemann, and C. Piani, 2011: On the contribution of statistical bias correction to the uncertainty in the projected hydrological cycle. Geophys. Res. Lett., 38, L20403, doi:10.1029/2011GL049318.
14. Chu, B., 2011: Recovering copulas from limited information and an application to asset allocation. J. Bank. Finance, 35, 1824- 1842, doi:10.1016/j.jbankfin.2010.12.011.
15. Chu, B., and S. Satchell, 2005: On the recovery of the most entropic copulas from prior knowledge of dependence. CiteSeer. [Available online at http://citeseerx.ist.psu.edu/viewdoc/summary?doi5 10.1.1.125.2326.]
16. Chui, C., and X.Wu, 2009: Exponential series estimation of empirical copulas with application to financial returns. Adv. Econom., 25, 263-290, doi:10.1108/S0731-9053(2009)0000025011.
17. Damberg, L., and A. AghaKouchak, 2014: Global trends and patterns of droughts from space. Theor. Appl. Climatol., 117, 441-448, doi:10.1007/s00704-013-1019-5.
18. Dempster, M. A. H., E. A. Medova, and S. W. Yang, 2007: Empirical copulas for CDO tranche pricing using relative entropy. Int. J. Theor. Appl. Finance, 10, 679-701, doi:10.1142/ S0219024907004391.
19. Durrett, R., 2005: Probability: Theory and Examples. Brooks/Cole Publishing, 528 pp.
20. Easterling, D., G. Meehl, C. Parmesan, S. Changnon, T. Karl, and L. Mearns, 2000: Climate extremes: Observations, modeling, and impacts. Science, 289, 2068-2074, doi:10.1126/ science.289.5487.2068.
21. Ebtehaj, A. M., and E. Foufoula-Georgiou, 2013: On variational downscaling, fusion, and assimilation of hydrometeorological states: A unified framework via regularization. Water Resour. Res., 49, 5944-5963, doi:10.1002/wrcr.20424.
22. Estrella, N., and A. Menzel, 2013: Recent and future climate extremes arising from changes to the bivariate distribution of temperature and precipitation in Bavaria, Germany. Int. J. Climatol., 33, 1687-1695, doi:10.1002/joc.3542.
23. Favre, A.-C., S. El Adlouni, L. Perreault, N. Thiémonge, and B. Bobée, 2004: Multivariate hydrological frequency analysis using copulas. Water Resour. Res., 40, W01101, doi:10.1029/2003WR002456.
24. Friedman, C. A., and J. Huang, 2010: Most entropic copulas: General form, and calibration to high-dimensional data in an important special case. Social Science Research Network, doi:10.2139/ssrn.1725517.
25. Genest, C., and A. C. Favre, 2007: Everything you always wanted to know about copula modeling but were afraid to ask. J. Hydrol. Eng., 12, 347-368, doi:10.1061/(ASCE)1084-0699(2007)12:4(347).
26. Genest, C., A.-C. Favre, J. Béliveau, and C. Jacques, 2007: Metaelliptical copulas and their use in frequency analysis of multivariate hydrological data. Water Resour. Res., 43, W09401, doi:10.1029/ 2006WR005275.
27. Grimaldi, S., and F. Serinaldi, 2006: Asymmetric copula in multivariate flood frequency analysis. Adv. Water Resour., 29, 1155- 1167, doi:10.1016/j.advwatres.2005.09.005.
28. Hagemann, S., C. Chen, J. O. Haerter, J. Heinke, D. Gerten, and C. Piani, 2011: Impact of a statistical bias correction on the projected hydrological changes obtained from three GCMs and two hydrology models. J. Hydrometeor., 12, 556-578, doi:10.1175/ 2011JHM1336.1.
29. Hansen, J., R. Ruedy, M. Sato, and K. Lo, 2010: Global surface temperature change. Rev. Geophys., 48, RG4004, doi:10.1029/ 2010RG000345.
30. Hao, Z., and V. Singh, 2011: Single-site monthly streamflow simulation using entropy theory. Water Resour. Res., 47, W09528, doi:10.1029/2010WR010208.
31. Hao, Z., and V. Singh, 2012: Entropy-copula method for single-site monthly streamflow simulation. Water Resour. Res., 48, W06604, doi:10.1029/2011WR011419.
32. Hao, Z., and A. AghaKouchak, 2013: Multivariate standardized drought index: A parametric multi-index model. Adv. Water Resour., 57, 12-18, doi:10.1016/j.advwatres.2013.03.009.
33. Hao, Z., and V. Singh, 2013: Modeling multi-site streamflow dependence with maximum entropy copula. Water Resour. Res., 49, 7139-7143, doi:10.1002/wrcr.20523.
34. Hao, Z., and A. AghaKouchak, 2014: A nonparametric multivariate multi-index drought monitoring framework. J. Hydrometeor., 15, 89-101, doi:10.1175/JHM-D-12-0160.1.
35. Hao, Z., A. AghaKouchak, and T. J. Phillips, 2013: Changes in concurrent monthly precipitation and temperature extremes. Environ. Res. Lett., 8, 034014, doi:10.1088/1748-9326/8/3/034014.
36. Jaynes, E. T., 1957a: Information theory and statistical mechanics. Phys. Rev., 106, 620-630, doi:10.1103/PhysRev.106.620.
37. Jaynes, E. T., 1957b: Information theory and statistical mechanics. II. Phys. Rev., 108, 171-190, doi:10.1103/PhysRev.108.171.
38. Joe, H., 1997: Multivariate Models and Dependence Concepts. Chapman & Hall, 424 pp.
39. Kao, S. C., and R. S. Govindaraju, 2008: Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas. Water Resour. Res., 44, W02415, doi:10.1029/ 2007WR006261.
40. Kapur, J., 1989: Maximum-Entropy Models in Science and Engineering. John Wiley & Sons, 635 pp.
41. Kesavan, H., and J. Kapur, 1992: Entropy Optimization Principles with Applications. Academic Press, 408 pp.
42. Kolesárová, A., R. Mesiar, J. Mordelová, and C. Sempi, 2006: Discrete copulas. IEEE Trans. Fuzzy Syst., 14, 698-705, doi:10.1109/TFUZZ.2006.880003.
43. Kotz, S., N. Balakrishnan, and N. L. Johnson, 2000: Continuous Multivariate Distributions: Models and Applications. Vol. 1. Wiley-Interscience, 752 pp.
44. Koutsoyiannis, D., 1994: A stochastic disaggregation method for design storm and flood synthesis. J. Hydrol., 156, 193-225, doi:10.1016/0022-1694(94)90078-7.
45. Kullback, S., and R. Leibler, 1951: On information and sufficiency. Ann. Math. Stat., 22, 79-86, doi:10.1214/aoms/1177729694.
46. Lee, T., 2012: Serial dependence properties in multivariate streamflow simulation with independent decomposition analysis. Hydrol. Processes, 26, 961-972, doi:10.1002/hyp.8177.
47. Liu, Z., A. Mehran, T. J. Phillips, and A. AghaKouchak, 2014: Seasonal and regional biases in CMIP5 precipitation simulations. Climate Res., 60, 35-50, doi:10.3354/cr01221.
48. Madani, K., and J. R. Lund, 2010: Estimated impacts of climate warming on California's high-elevation hydropower. Climatic Change, 102, 521-538, doi:10.1007/s10584-009-9750-8.
49. Mayor, G., J. Suñer, and J. Torrens, 2005: Copula-like operations on finite settings. IEEE Trans. Fuzzy Syst., 13, 468-477, doi:10.1109/TFUZZ.2004.840129.
50. McNeil, A. J., 2008: Sampling nested Archimedean copulas. J. Stat. Comput. Simul., 78, 567-581, doi:10.1080/00949650701255834.
51. McNeil, A. J., and J. Nešlehová, 2009: Multivariate Archimedean copulas, d-monotone functions and '1-norm symmetric distributions. Ann. Stat., 37, 3059-3097.
52. Mead, L., and N. Papanicolaou, 1984: Maximum entropy in the problem of moments. J. Math. Phys., 25, 2404-2417, doi:10.1063/1.526446.
53. Meeuwissen, A. M. H., and T. Bedford, 1997: Minimally informative distributions with given rank correlation for use in uncertainty analysis. J. Stat. Comput. Simul., 57, 143-174, doi:10.1080/00949659708811806.
54. Mehran, A., and A. AghaKouchak, 2014: Capabilities of satellite precipitation datasets to estimate heavy precipitation rates at different temporal accumulations. Hydrol. Processes, 28, 2262-2270, doi:10.1002/hyp.9779.
55. Mehran, A., A. AghaKouchak, and T. J. Phillips, 2014: Evaluation of CMIP5 continental precipitation simulations relative to satellite-based gauge-adjusted observations. J. Geophys. Res. Atmos., 119, 1695-1707, doi:10.1002/2013JD021152.
56. Möller, A., and Coauthors, 2012: Multivariate probabilistic forecasting using ensemble Bayesian model averaging and copulas. Quart. J. Roy. Meteor. Soc., 139, 982-991, doi:10.1002/ qj.2009.
57. Nazemi, A., and A. Elshorbagy, 2012: Application of copula modelling to the performance assessment of reconstructed watersheds. Stochastic Environ. Res. Risk Assess., 26, 189-205, doi:10.1007/s00477-011-0467-7.
58. Nelsen, R. B., 2006: An Introduction to Copulas. 2nd ed. Springer, 272 pp.
59. Phillips, S. J., R. P. Anderson, and R. E. Schapire, 2006: Maximum entropy modeling of species geographic distributions. Ecol. Modell., 190, 231-259, doi:10.1016/j.ecolmodel.2005.03.026.
60. Piani, C., and J. O. Haerter, 2012: Two dimensional bias correction of temperature and precipitation copulas in climate models. Geophys. Res. Lett., 39, L20401, doi:10.1029/2012GL053839.
61. Piantadosi, J., P. Howlett, and J. Boland, 2007:Matching the grade correlation coefficient using a copula with maximum disorder. J. Ind. Manage. Optim., 3, 305-312, doi:10.3934/ jimo.2007.3.305.
62. Piantadosi, J., P. Howlett, and J. Borwein, 2012a: Copulas with maximumentropy. Optim. Lett., 6, 99-125, doi:10.1007/s11590-010-0254-2.
63. Piantadosi, J., P. Howlett, J. Borwein, and J. Henstridge, 2012b: Maximum entropy methods for generating simulated rainfall. Numer. Algebra Control Optim., 2, 233-256, doi:10.3934/naco.2012.2.233.
64. Pougaza, D.-B., and A. Mohammad-Djafari, 2011: Maximum entropies copulas. AIP Conf. Proc., 1305, 329, doi:10.1063/ 1.3573634.
65. Pougaza, D.-B., and A. Mohammad-Djafari, 2012: New copulas obtained by maximizing Tsallis or Rényi entropies. AIP Conf. Proc., 1443, 238, doi:10.1063/ 1.3703641.
66. Pougaza, D.-B., A. Mohammad-Djafari, and J.-F. Bercher, 2010: Link between copula and tomography. Pattern Recognit. Lett., 31, 2258-2264, doi:10.1016/ j.patrec.2010.05.001.
67. Qu, L., and W. Yin, 2012: Copula density estimation by total variation penalized likelihood with linear equality constraints. Comput. Stat. Data Anal., 56, 384-398, doi:10.1016/ j.csda.2011.07.016.
68. Qu, L., H. Chen, and Y. Tu, 2011: Nonparametric copula density estimation in sensor networks. Proc. MSN 2011: Seventh Int. Conf. on Mobile Ad-Hoc and Sensor Networks, Beijing, China, IEEE, doi:10.1109/MSN.2011.50.
69. Sadri, S., and D. H. Burn, 2012: Copula-based pooled frequency analysis of droughts in the Canadian Prairies. J. Hydrol. Eng., 19, 277-289, doi:10.1061/(ASCE)HE.1943-5584.0000603.
70. Salvadori, G., and C. De Michele, 2007: On the use of copulas in hydrology: Theory and practice. J. Hydrol. Eng., 12, 369-380, doi:10.1061/(ASCE)1084-0699(2007)12:4(369).
71. Salvadori, G., C. De Michele, N. T. Kottegoda, and R. Rosso, 2007: Extremes in Nature: An Approach Using Copulas. Springer, 292 pp.
72. Schefzik, R., 2011: Ensemble copula coupling. Diploma thesis, Faculty of Mathematics and Informatics, Heidelberg University, 149 pp.
73. Schoelzel, C., and P. Friederichs, 2008: Multivariate non-normally distributed random variables in climate research-introduction to the copula approach. Nonlinear Processes Geophys., 15, 761-772, doi:10.5194/npg-15-761-2008.
74. Serinaldi, F., 2009: A multisite daily rainfall generator driven by bivariate copula-based mixed distributions. J. Geophys. Res., 114, D10103, doi:10.1029/2008JD011258.
75. Serinaldi, F., and S. Grimaldi, 2007: Fully nested 3-copula: Procedure and application on hydrological data. J. Hydrol. Eng., 12, 420-430, doi:10.1061/(ASCE)1084-0699(2007)12:4(420).
76. Shannon, C. E., 1948:Amathematical theory of communications. Bell Syst.Tech. J., 27, 379-423, doi:10.1002/j.1538-7305.1948.tb01338.x.
77. Shiau, J.-T., H.-Y. Wang, and C.-T. Tsai, 2006: Bivariate frequency analysis of floods using copulas. J. Amer. Water Resour. Assoc., 42, 1549-1564, doi:10.1111/j.1752-1688.2006.tb06020.x.
78. Singh, V. P., 1992: Elementary Hydrology. Prentice Hall, 973 pp.
79. Singh, V. P., 1997: The use of entropy in hydrology and water resources. Hydrol. Processes, 11, 587-626, doi:10.1002/ (SICI)1099-1085(199705)11:6<587::AID-HYP479>3.0.CO;2-P.
80. Singh, V. P., 2011: Hydrologic synthesis using entropy theory: Review. J. Hydrol. Eng., 16, 421-433, doi:10.1061/ (ASCE)HE.1943-5584.0000332.
81. Sklar, A., 1959: Fonctions de répartition à n dimensions et leurs marges. Publ. Inst. Stat. Univ. Paris, 8, 229-231.
82. Sorooshian, S., and Coauthors, 2011: Advanced concepts on remote sensing of precipitation at multiple scales. Bull. Amer. Meteor. Soc., 92, 1353-1357, doi:10.1175/2011BAMS3158.1.
83. Stedinger, J. R., and R. M. Vogel, 1984: Disaggregation procedures for generating serially correlated flow vectors. Water Resour. Res., 20, 47-56, doi:10.1029/WR020i001p00047.
84. Stedinger, J. R., D. P. Lettenmaier, and R. M. Vogel, 1985:Multisite ARMA (1, 1) and disaggregation models for annual streamflow generation. Water Resour. Res., 21, 497-510, doi:10.1029/ WR021i004p00497.
85. Stedinger, J. R., R. M. Vogel, and E. Foufoula-Georgiou, 1993: Frequency analysis of extreme events. Handbook of Hydrology, D. R. Maidment, Ed., McGraw-Hill, 18.1-18.66.
86. Tian, Y., and Coauthors, 2009: Component analysis of errors in satellite-based precipitation estimates. J. Geophys. Res., 114, D24101, doi:10.1029/2009JD011949.
87. Trivedi, P. K., and D. M. Zimmer, 2005: Copula modeling: An introduction for practitioners. Found. Trends Econometrics, 1, 1-111, doi:10.1561/0800000005.
88. Vapnyarskii, I. B., 2001: Lagrange multipliers. Encyclopedia of Mathematics, M. Hazewinkel, Ed., Springer, 1-8.
89. Venter, G. G., 2002: Tails of copulas. Proc. Casualty Actuarial Soc., 89, 68-113. [Available online at http://casualtyactuaries.com/ library/studynotes/Venter_Tails_of_Copulas.pdf.]
90. Westra, S., C. Brown, U. Lall, and A. Sharma, 2007: Modeling multivariable hydrological series: Principal component analysis or independent component analysis? Water Resour. Res., 43, W06429, doi:10.1029/2006WR005617.
91. Yue, S., and Coauthors, 1999: The Gumbel mixed model for flood frequency analysis. J. Hydrol., 226, 88-100, doi:10.1016/ S0022-1694(99)00168-7.
92. Zhang, L., and V. P. Singh, 2007: Bivariate rainfall frequency distributions using Archimedean copulas. J. Hydrol., 332, 93-109, doi:10.1016/j.jhydrol.2006.06.033.
93. Zhang, X., L. Alexander, G. C. Hegerl, P. Jones, A. K. Tank, T. C. Peterson, B. Trewin, and F. W. Zwiers, 2011: Indices for monitoring changes in extremes based on daily temperature and precipitation data. Wiley Interdiscip. Rev.: Climate Change, 2, 851-870, doi:10.1002/wcc.147.
94. Zhao, N., and W. T. Lin, 2011: A copula entropy approach to correlation measurement at the country level. Appl. Math. Comput., 218, 628-642, doi:10.1016/j.amc.2011.05.115.
95. Zhu, S. C., Y. N. Wu, and D. Mumford, 1997: Minimax entropy principle and its application to texture modeling. Neural Comput., 9, 1627-1660, doi:10.1162/neco.1997.9.8.1627.