Modelling and simulation of seasonal rainfall using the principle of maximum entropy

Entropy

Volumn 16, Issue 2, 2014, Pages 747-769

  Borwein, Jonathan ^a   Howlett, Phil ^b   Piantadosi, Julia ^b  

^a UNIVERSITY OF NEWCASTLE   (Australia)

^b UNIVERSITY OF SOUTH AUSTRALIA   (Australia)

Author keywords

Checkerboard copula; Maximum entropy; Rainfall modelling and simulation

Indexed keywords

EID: 84894573812     PISSN: None     EISSN: 10994300     Source Type: Journal    
DOI: 10.3390/e16020747     Document Type: Article

References (27)

1. Peel, M.C.; Finlayson, B.L.; and McMahon, T.A. Updated world map of the Köppen-Geiger climate classification, Hydrol. Earth Syst. Sci. 2007, 11, 1633-1644.
2. Jaynes, E.T. Information theory and statistical mechanics. Phys. Rev. 1957a, 106, 620-630.
3. Jaynes, E.T. Information theory and statistical mechanics II. Phys. Rev. 1957b, 108, 171-190.
4. Von Neumann, J. Mathematical Foundations of Quantum Mechanics; Princeton University Press: Princeton, NJ, USA, 1996.
5. Ziedler, E. Applied Functional Analysis, Applications to Mathematical Physics (Applied Mathematical Sciences); Springer: New York, NY, USA, 1997; Volume 108.
6. Shannon, C.E. A mathematical theory of communication Bell Syst. Tech. J. 1948, 27, 379-423, 623-656.
7. Stern, R.D.; Coe, R. A model fitting analysis of daily rainfall. J. Roy. Stat. Soc. A 1984, 147, 1-34.
8. Srikanthan, R. Stochastic Generation of Daily Rainfall at a Number of Sites; Technical Report 05/7; Cooperative Research Centre for Catchment Hydrology: Melbourne, Australia, 2005.
9. Getz, W.M. Correlative coherence analysis: Variation from intrinsic and extrinsic sources in competing populations. Theor. Popul. Biol. 2003, 64, 89-99.
10. Hasan, M.M.; Dunn, P.K. Two Tweedie distributions that are near optimal for modelling monthly rainfall in Australia. Int. J. Climatol. 2011, 31, 1389-1397.
11. Srikanthan, R.; McMahon, T.A. Stochastic generation of annual, monthly and daily climate data: A review. Hydrol. Earth Syst. Sci. 2001, 5, 633-670.
12. Wilks, D.S.; Wilby, R.L. The weather generation game: A review of stochastic weather models. Prog. Phys. Geogr. 1999, 23, 329-357.
13. Katz, R.W.; Parlange, M.B. Overdispersion phenomenon in stochastic modelling of precipitation. J. Clim. 1998, 11, 591-601.
14. Rosenberg, K.; Boland, J.; Howlett, P.G. Simulation of monthly rainfall totals. ANZIAM J. 2004, 46, E85-E104.
15. Koutsoyiannis, D. Hurst-Kolmogorov dynamics and uncertainty. J. Am. Water Resour. Assoc. 2011, 47, 481-495.
16. Borwein, J.M.; Lewis, A.S. Convex Analysis and Nonlinear Optimization, Theory and Examples, 2nd ed.; Springer-Verlag Inc.: New York, NY, USA, 2006; Volume 3.
17. Borwein, J.M.; Vanderwerff, J.D. Convex Functions: Constructions, Characterizations and Counterexamples; Cambridge University Press: Cambridge, UK, 2010; Volume 109.
18. Rissanen, J. Modeling by shortest data description. Automatica 1978, 14, 465-471.
19. Rissanen, J. A universal prior for integers and estimation by minimum description length. Ann. Stat. 1983, 11, 416-431.
20. Akaike, H. A new look at the statistical model identification. IEEE Trans. Autom. Control 1974, 19, 716-723.
21. Weijs, S.V.; van de Giesen, N.; Parlange, M.B. HydroZIP: How hydrological knowledge can be used to improve compression of hydrological data. Entropy 2013, 15, 1289-1310.
22. Bailey, D.H.; Borwein, J.M.; de Prado, M.L.; Zhu, Q. Pseudo Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on out-of-Sample Performance. Available online: http://www.carma.newcastle.edu.au/jon/backtest.pdf (accessed on 24 December 2013).
23. Kulpa, T. On approximation of copulas. Int. J. Math. Math. Sci. 1999, 22, 259-269.
24. Nelsen, R.B. An Introduction to Copulas; Lecture Notes in Statistics; Springer-Verlag: New York, NY, USA, 1999; Volume 139.
25. Piantadosi, J.; Howlett, P.G.; Borwein, J.M. Copulas of maximum entropy. Optim. Lett. 2012, 6, 99-125.
26. Piantadosi, J.; Howlett, P.G.; Borwein, J.M.; Henstridge, J. Maximum entropy methods for generating simulated rainfall. Numer. Algebra Control Optim. 2012, 2, 233-256.
27. Centre for Computer Assisted Research Mathematics and its Applications (CARMA) website. Available online: http://www.carma.newcastle.edu.au/hydro/(accessed on 7 December 2013).