On temporal stochastic modeling of precipitation, nesting models across scales

Advances in Water Resources

Volumn 63, Issue , 2014, Pages 152-166

  Paschalis, Athanasios ^a   Molnar, Peter ^a   Fatichi, Simone ^a   Burlando, Paolo ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Alternating renewal process; Markov chain; Multiplicative Random Cascade; Poisson cluster model; Stochastic rainfall models

Indexed keywords

ALTERNATING RENEWAL PROCESS; AUTOCORRELATION STRUCTURES; CLUSTER MODELS; PRECIPITATION DEPTHS; PRECIPITATION PROPERTIES; RANDOM CASCADE MODEL; RANDOM CASCADES; STOCHASTIC RAINFALLS;

CLIMATE MODELS; MARKOV PROCESSES; PROBABILITY DISTRIBUTIONS; RAIN;

STOCHASTIC MODELS;

HYDROLOGICAL MODELING; MARKOV CHAIN; POISSON RATIO; PRECIPITATION (CLIMATOLOGY); PROBABILITY; RAINFALL; STOCHASTICITY; TEMPORAL ANALYSIS;

EID: 84890934284     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2013.11.006     Document Type: Article

References (95)

1. Todorovic P, Yevjevich V. Stochastic process of precipitation. Technical report, Colo. State Univ. Fort Collins, Fort Collins, Colorado; 1969.
2. Todorovic P., Woolhiser D.A. A stochastic model of n-day precipitation. J Appl Meteorol 1975, 14:17-24. 10.1175/1520-0450(1975)014<0017:ASMODPgt;2.0.CO;2.
3. Chin E. Modeling daily precipitation occurrence process with Markov chain. Water Resour Res 1977, 13:949-956. 10.1029/WR013i006p00949.
4. Katz R. Precipitation as a chain-dependent process. J Appl Meteorol 1977, 16:671-676. 10.1175/1520-0450(1977)016<0671:PAACDP>2.0.CO;2.
5. Foufoula-Georgiou E., Lettenmaier D. A Markov renewal model for rainfall occurrences. Water Resour Res 1987, 23:875-884. 10.1029/WR023i005p00875.
6. Schmitt F., Vannitsem S., Barbosa A. Modeling of rainfall time series using two-state renewal processes and multifractals. J Geophys Res 1998, 103:23,181-23,193. 10.1029/98JD02071.
7. Ivanov V.Y., Bras R.L., Curtis D.C. A weather generator for hydrological, ecological, and agricultural applications. Water Resour Res 2007, 43. 10.1029/2006WR005364.
8. Yang C., Chandler R.E., Isham V.S., Wheater H.S. Spatial-temporal rainfall simulation using generalized linear models. Water Resour Res 2005, 41. 10.1029/2004WR003739.
9. Chandler R.E., Wheater H.S. Analysis of rainfall variability using generalized linear models: a case study from the west of Ireland. Water Resour Res 2002, 38. 10.1029/2001WR000906.
10. Richardson C. Stochastic simulation of daily precipitation, temperature, and solar radiation. Water Resour Res 1981, 17:182-190. 10.1029/WR017i001p00182.
11. Racsko P., Szeidl L., Semenov M. A serial approach to local stochastic weather models. Ecol Model 1991, 57:27-41. 10.1016/0304-3800(91)90053-4.
12. Katz R., Parlange M. Generalizations of chain-dependent processes: application to hourly precipitation. Water Resour Res 1995, 31:1331-1341. 10.1029/94WR03152.
13. Le Cam L. A stochastic description of precipitation. Proceedings of fourth berkeley symposium on mathematical statistics and probability 1961, vol. 3:165-176. Univ. of Calif. Press, Berkeley. J. Neyman (Ed.).
14. Cox D., Isham V. A simple spatial-temporal model of rainfall. Proc R Soc Lond Ser A Math Phys Sci 1988, 415:317-328. 10.1098/rspa.1988.0016.
15. Rodriguez-Iturbe I., Cox D., Isham V. Some models for rainfall based on stochastic point processes. Proc R Soc Lond Ser A Math Phys Sci 1987, 410:269-288. 10.1098/rspa.1987.0039.
16. Rodriguez-Iturbe I., Cox D., Isham V. A point process model for rainfall: further developments. Proc R Soc Lond Ser A 1988, 417:283-298. 10.1098/rspa.1988.0061.
17. Rodriguez-Iturbe I., Eagleson P.S. Mathematical models of rainstorm events in space and time. Water Resour Res 1987, 23:181-190. 10.1029/WR023i001p00181.
18. Entekhabi D., Rodriguez-Iturbe I., Eagleson P.S. Probabilistic representation of the temporal rainfall process by a modified Neyman-Scott rectangular pulses model: parameter estimation and validation. Water Resour Res 1989, 25:295-302. 10.1029/WR025i002p00295.
19. Cowpertwait P.S.P. Further developments of the Neyman-Scott clustered point process for modeling rainfall. Water Resour Res 1991, 27:1431-1438. 10.1029/91WR00479.
20. Cowpertwait P.S.P. A generalized point process model for rainfall. Proc R Soc Lond Ser A Math Phys Sci 1994, 447:23-37. 10.1098/rspa.1994.0126.
21. Cowpertwait P.S.P., O'Connell P., Metcalfe A., Mawdsley J. Stochastic point process modelling of rainfall: I. Fitting and validation. J Hydrol 1996, 175:17-46. 10.1016/S0022-1694(96)80004-7.
22. Cowpertwait P.S.P. A Poisson-cluster model of rainfall: some high-order moments and extreme values. Proc R Soc A Math Phys Eng Sci 1998, 454:885-898. 10.1098/rspa.1998.0191.
23. Onof C., Chandler E., Kakou A., Northrop P., Wheater H.S., Isham V. Rainfall modeling using Poisson-cluster processes: a review of developments. Stochastic Environ Res Risk Assess 2000, 14:384-411. 10.1007/s004770000043.
24. Burton A., Kilsby C., Fowler H., Cowpertwait P.S., O'Connell P. RainSim: a spatial-temporal stochastic rainfall modelling system. Environ Model Software 2008, 23:1356-1369. 10.1016/j.envsoft.2008.04.003.
25. Burlando P., Rosso R. Stochastic models of temporal rainfall: reproducibility, estimation and prediction of extreme events. Stochastic hydrology in its use in water resources systems simulation and optimization. Proc. of NATO-ASI workshop 1993, 137-173. Kluwer, Peñiscola, Spain. J. Salas, R. Harboe, E. Marco-Segura (Eds.).
26. Fatichi S., Ivanov V.Y., Caporali E. Simulation of future climate scenarios with a weather generator. Adv Water Resour 2011, 34:448-467. 10.1016/j.advwatres.2010.12.013.
27. Onof C., Wheater H.S. Modelling of British rainfall using a random parameter Bartlett-Lewis rectangular pulse model. J Hydrol 1993, 149:67-95. 10.1016/0022-1694(93)90100-N.
28. Sansom J. A hidden Markov model for rainfall using breakpoint data. J Clim 1998, 11:42-53. 10.1175/1520-0442(1998)011<0042:AHMMFR>2.0.CO;2.
29. Hughes J.P., Guttorp P., Charles S.P. A non-homogeneous hidden Markov model for precipitation occurrence. J R Stat Soc Ser C (Appl Stat) 1999, 48:15-30. 10.1111/1467-9876.00136.
30. Robertson A., Kirshner S., Smyth P. Downscaling of daily rainfall occurrence over northeast Brazil using a hidden Markov model. J Clim 2004, 17:4407-4424. 10.1175/JCLI-3216.1.
31. Veneziano D, Langousis A. Scaling and fractals in hydrology. In: Advances in data-based approaches for hydrologic modeling and forecasting; 2010.
32. Foufoula-Georgiou E., Krajewski W.F. Recent advances in rainfall modeling, estimation, and forecasting. Reviews of Geophysics 1995, 1125-1138. (US National Report to International Union of Geodesy and Geophysics). 10.1029/95RG00338.
33. Koutsoyiannis D., Paschalis A., Theodoratos N. Two-dimensional Hurst-Kolmogorov process and its application to rainfall fields. J Hydrol 2011, 398:91-100. 10.1016/j.jhydrol.2010.12.012.
34. Lombardo F., Volpi E., Koutsoyiannis D. Rainfall downscaling in time: theoretical and empirical comparison between multifractal and Hurst-Kolmogorov discrete random cascades. Hydrol Sci J 2012, 57:1052-1066. 10.1080/02626667.2012.695872.
35. Rebora N., Ferraris L., von Hardenberg J., Provenzale A. RainFARM: rainfall downscaling by a filtered autoregressive model. J Hydrometeorol 2006, 7:724-738. 10.1175/JHM517.1.
36. Ferraris L., Gabellani S., Rebora N. A comparison of stochastic models for spatial rainfall downscaling. Water Resour Res 2003, 39. 10.1029/2003WR002504.
37. Kolmogorov A. Wienersche Spiralen und einige andere interessante Kurven im Hilbertsche Raumitle. Acad Sci URSS 1940, 26:115-118.
38. Benzi R., Ciliberto S., Tripiccione R., Baudet C., Massaioli F., Succi S. Extended self-similarity in turbulent flows. Phys Rev E Stat Phys Plasmas Fluids Related Interdisciplinary Top 1993, 48:R29-R32. 10.1103/PhysRevE.48.R29.
39. Schertzer D., Lovejoy S. Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes. J Geophys Res 1987, 92:9693-9714. 10.1029/JD092iD08p09693.
40. Over T.M., Gupta V.K. A space-time theory of mesoscale rainfall using random cascades. J Geophys Res 1996, 101:26,319-26,331. 10.1029/96JD02033.
41. Deidda R. Rainfall downscaling in a space-time multifractal framework. Water Resour Res 2000, 36:1779-1794. 10.1029/2000WR900038.
42. Pathirana A., Herath S. Multifractal modelling and simulation of rain fields exhibiting spatial heterogeneity. Hydrol Earth Syst Sci 2002, 6:659-708. 10.5194/hess-6-695-2002.
43. Veneziano D., Furcolo P. Multifractality of rainfall and intensity-duration-frequency curves. Water Resour Res 2002, 38. 10.1029/2001WR000372.
44. Veneziano D., Langousis A., Furcolo P. Multifractality and rainfall extremes: a review. Water Resour Res 2006, 42:W06D15. 10.1029/2005WR004716.
45. Molnar P., Burlando P. Preservation of rainfall properties in stochastic disaggregation by a simple random cascade model. Atmos Res 2005, 77:137-151. 10.1016/j.atmosres.2004.10.024.
46. Gaume E., Mouhous N., Andrieu H. Rainfall stochastic disaggregation models: calibration and validation of a multiplicative cascade model. Adv Water Resour 2007, 30:1301-1319. 10.1016/j.advwatres.2006.11.007.
47. Gires A., Onof C., Maksimovic C., Schertzer D., Tchiguirinskaia I., Simoes N. Quantifying the impact of small scale unmeasured rainfall variability on urban runoff through multifractal downscaling: a case study. J Hydrol 2012, 442-443:117-128. 10.1016/j.jhydrol.2012.04.005.
48. Paulson K.S., Baxter P.D. Downscaling of rain gauge time series by multiplicative beta cascade. J Geophys Res 2007, 112. 10.1029/2006JD007333.
49. Groppelli B., Bocchiola D., Rosso R. Spatial downscaling of precipitation from GCMs for climate change projections using random cascades: a case study in Italy. Water Resour Res 2011, 47. 10.1029/2010WR009437.
50. Kang B., Ramírez J.a. A coupled stochastic space-time intermittent random cascade model for rainfall downscaling. Water Resour Res 2010, 46. 10.1029/2008WR007692.
51. Molini A., Lanza L., La Barbera P. Improving the accuracy of tipping-bucket rain records using disaggregation techniques. Atmos Res 2005, 77:203-217. 10.1016/j.atmosres.2004.12.013.
52. Fraedrich K., Larnder C. Scaling regimes of composite rainfall time series. Tellus A 1993, 45:289-298. 10.1034/j.1600-0870.1993.t01-3-00004.x.
53. Marani M. On the correlation structure of continuous and discrete point rainfall. Water Resour Res 2003, 39:1128. 10.1029/2002WR001456.
54. Veneziano D., Furcolo P., Iacobellis V. Imperfect scaling of time and space-time rainfall. J Hydrol 2006, 322:105-119. 10.1016/j.jhydrol.2005.02.044.
55. Cârsteanu A., Foufoula-Georgiou E. Assessing dependence among weights in a multiplicative cascade model of temporal rainfall. J Geophys Res D Atmos 1996, 101:26,363-26,370. 10.1029/96JD01657.
56. Paschalis A., Molnar P., Burlando P. Temporal dependence structure in weights in a multiplicative cascade model for precipitation. Water Resour Res 2012, 48. 10.1029/2011WR010679.
57. Cowpertwait P.S., Xie G., Isham V., Onof C., Walsh D.C.I. A fine-scale point process model of rainfall with dependent pulse depths within cells a fine-scale point process model of rainfall with dependent pulse depths within cells. Hydrol Sci J 2011, 56:1110-1117. 10.1080/02626667.2011.604033.
58. Molnar P., Burlando P. Variability in the scale properties of high-resolution precipitation data in the Alpine climate of Switzerland. Water Resour Res 2008, 44. 10.1029/2007WR00614.
59. Rupp D., Keim R., Ossiander M., Brugnach M., Selker J. Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation. Water Resour Res 2009, 45. 10.1029/2008WR007321.
60. Serinaldi F. Multifractality, imperfect scaling and hydrological properties of rainfall time series simulated by continuous universal multifractal and discrete random cascade models. Nonlinear Process Geophys 2010, 17:697-714. 10.5194/npg-17-697-2010.
61. Menabde M., Sivapalan M. Modeling of rainfall time series and extremes using bounded random cascades and Levy-stable distributions. Water Resour Res 2000, 36:3293-3300. 10.1029/2000WR900197.
62. Veneziano D., Iacobellis V. Multiscaling pulse representation of temporal rainfall. Water Resour Res 2002, 38:1138. 10.1029/2001WR000522.
63. Onof C., Wheater H. Improvements to the modelling of British rainfall using a modified random parameter Bartlett-Lewis rectangular pulse model. J Hydrol 1994, 157:177-195. 10.1016/0022-1694(94)90104-X.
64. Gyasi-Agyei Y., Willgoose G. A hybrid model for point rainfall modeling. Water Resour Res 1997, 33:1699-1706. 10.1029/97WR01004.
65. Koutsoyiannis D. Coupling stochastic models of different timescales. Water Resour Res 2001, 37:379-391. 10.1029/2000WR900200.
66. Frei C., Schär C. A precipitation climatology of the Alps from high-resolution rain-gauge observations. Int J Climatol 1998, 18:873-900. 10.1002/(SICI)1097-0088(19980630)18:8<873::AID-JOC255>3.0.CO;2-9.
67. Beuchat X., Schaefli B., Soutter M., Mermoud A. Toward a robust method for subdaily rainfall downscaling from daily data. Water Resour Res 2011, 47. 10.1029/2010WR010342.
68. Olsson J., Burlando P. Reproduction of temporal scaling by a rectangular pulses rainfall model. Hydrol Process 2002, 16:611-630. 10.1002/hyp.307.
69. Cowpertwait P.S., Kilsby C., O'Connell P. A space-time Neyman-Scott model of rainfall: empirical analysis of extremes. Water Resour Res 2002, 38:1131. 10.1029/2001WR000709.
70. Molini A., Katul G.G., Porporato A. Revisiting rainfall clustering and intermittency across different climatic regimes. Water Resour Res 2009, 45. 10.1029/2008WR007352.
71. Becchi I, Caporali E, Castellani L, Castelli F. Multiregressive analysis for the estimation of the spatial zero rainfall probability. In: Workshop on climate change and hydrogeological hazards in the Mediterranean area. Italy: Grafica Salvi Perugia, Colombella, Perugia; 1994. p. 133-45.
72. Goodrich D.C., Keefer T.O., Unkrich C.L., Nichols M.H., Osborn H.B., Stone J.J., Smith J.R., et al. Long-term precipitation database, Walnut Gulch Experimental Watershed, Arizona, United States. Water Resour Res 2008, 44. 10.1029/2006WR005782.
73. Roldan J., Woolhiser D.A. Stochastic daily precipitation models 1, a comparison of occurence processes. Water Resour Res 1982, 18:1451-1459. 10.1029/WR018i005p01451.
74. Buishand T. Some remarks on the use of daily rainfall models. J Hydrol 1978, 36:295-308. 10.1016/0022-1694(78)90150-6.
75. Bernardara P., De Michele C., Rosso R. A simple model of rain in time: an alternating renewal process of wet and dry states with a fractional (non-Gaussian) rain intensity. Atmos Res 2007, 84:291-301. 10.1016/j.atmosres.2006.09.001.
76. Srikanthan R., McMahon T.A. Stochastic generation of annual, monthly and daily climate data: a review. Hydrol Earth Syst Sci 2001, 5:653-670. 10.5194/hess-5-653-2001.
77. Papalexiou S., Koutsoyiannis D. Entropy based derivation of probability distributions: a case study to daily rainfall. Adv Water Resour 2011, 45:51-57. 10.1016/j.advwatres.2011.11.007.
78. Papoulis A., Unnikrishna S. Probability, random variables and stochastic processes 2002, McGraw Hill. 4th ed.
79. Haan C.T., Allen D.M., Street J.O. A Markov chain model of daily rainfall. Water Resour Res 1976, 12:443. 10.1029/WR012i003p00443.
80. Srikanthan R., Pegram G.G. A nested multisite daily rainfall stochastic generation model. J Hydrol 2009, 371:142-153. 10.1016/j.jhydrol.2009.03.025.
81. Burlando P., Rosso R. Comment on parameter estimation and sensitivity analysis for the modified Bartlett-Lewis rectangular pulses model of rainfall by S. Islam et al. J Geophys Res 1991, 96:9391-9395. 10.1029/91JD00288.
82. Paschalis A. Modelling the space time structure of precipitation and its impact on basin response. PhD thesis, ETH Zurich; 2013.
83. Gupta V.K., Waymire E. A statistical analysis of mesoscale rainfall as a random cascade. J Appl Meteorol 1993, 32:251-267. 10.1175/1520-0450(1993)032<0251:ASAOMR>2.0.CO;2.
84. Güntner A., Olsson J., Calver A., Gannon B. Cascade-based disaggregation of continuous rainfall time series: the influence of climate. Hydrol Earth Syst Sci 2001, 5:145-164. 10.5194/hess-5-145-2001.
85. Menabde M., Harris D., Seed A., Austin G., Stow D. Multiscaling properties of rainfall and bounded random cascades. Water Resour Res 1997, 33:2823-2830. 10.1029/97WR02006.
86. Schertzer D., Lovejoy S. Hard and soft multifractal processes. Phys A Stat Mech Appl 1992, 185:187-194. 10.1016/0378-4371(92)90455-Y.
87. Over TM. Modeling space-time rainfall at the mesoscale using random cascades. PhD thesis, University of Colorado; 1995.
88. Holley R., Waymire E. Multifractal dimensions and scaling exponents for strongly bounded random cascades. Ann Appl Probab 1992, 2:819-845. 10.1214/aoap/1177005577.
89. Veneziano D., Furcolo P. Marginal distribution of stationary multifractal measures and their Haar wavelet coefficients. Interdisciplinary J Fract 2003, 11:253-270. 10.1142/S0218348X03002051.
90. Bordoy R. Spatiotemporal downscaling of climate scenarios in regions of complex orography. PhD thesis, ETH Zurich; 2013.
91. Bordoy R, Burlando P. Stochastic downscaling of precipitation to high-resolution scenarios in orographically complex regions. Part 1: Model evaluation. Water Resour Res; 2013 [Submitted for publication].
92. Olsson J. Evaluation of a scaling cascade model for temporal rain-fall disaggregation. Hydrol Earth Syst Sci 1998, 2:19-30. 10.5194/hess-2-19-1998.
93. Vandenberghe S., Verhoest N.E.C., De Baets B. Fitting bivariate copulas to the dependence structure between storm characteristics: a detailed analysis based on 105year 10min rainfall. Water Resour Res 2010, 46. 10.1029/2009WR007857.
94. Li C., Singh V.P., Mishra A.K. Simulation of the entire range of daily precipitation using a hybrid probability distribution. Water Resour Res 2012, 48. 10.1029/2011WR011446.
95. Velghe T., Troch P., De Troch F., Van de Velde J. Evaluation of cluster-based rectangular pulses point process models for rainfall. Water Resour Res 1994, 30:2847-2857. 10.1029/94WR01496.