Simulation of daily rainfall scenarios with interannual and multidecadal climate cycles for South Florida

Origianl Paper

Abstract

Concerns about the potential effects of anthropogenic climate change have led to a closer examination of how climate varies in the long run, and how such variations may impact rainfall variations at daily to seasonal time scales. For South Florida in particular, the influences of the low-frequency climate phenomena, such as the El Nino Southern Oscillation (ENSO) and the Atlantic Multi-decadal Oscillation (AMO), have been identified with aggregate annual or seasonal rainfall variations. Since the combined effect of these variations is manifest as persistent multi-year variations in rainfall, the question of modeling these variations at the time and space scales relevant for use with the daily time step-driven hydrologic models in use by the South Florida Water Management District (SFWMD) has arisen. To address this problem, a general methodology for the hierarchical modeling of low- and high-frequency phenomenon at multiple rain gauge locations is developed and illustrated. The essential strategy is to use long-term proxies for regional climate to first develop stochastic scenarios for regional climate that include the low-frequency variations driving the regional rainfall process, and then to use these indicators to condition the concurrent simulation of daily rainfall at all rain gauges under consideration. A newly developed methodology, called Wavelet Autoregressive Modeling (WARM), is used in the first step after suitable climate proxies for regional rainfall are identified. These proxies typically have data available for a century to four centuries so that long-term quasi-periodic climate modes of interest can be identified more reliably. Correlation analyses with seasonal rainfall in the region are used to identify the specific proxies considered as candidates for subsequent conditioning of daily rainfall attributes using a Non-homogeneous hidden Markov model (NHMM). The combined strategy is illustrated for the May–June–July (MJJ) season. The details of the modeling methods and results for the MJJ season are presented in this study.

Keywords

Rainfall simulation Low frequency Wavelet autoregressive model Non-homogeneous hidden Markov model Climate variability 

References

  1. Box GEP, Jenkins G (1970) Time series analysis, forecasting and control. Holden-Day, San FranciscoGoogle Scholar
  2. Chen HJ, Lee KC, Murphy-Chutorian E, Triesch J (2005) Toward a unified probabilistic framework for object recognition and segmentation. Adv Visual Comput Proc 3804:108–117CrossRefGoogle Scholar
  3. Chui CK (1992) An Introduction to Wavelets, Wavelet Analysis and its Application Vol. 1. Academic Press, BostonGoogle Scholar
  4. Cook ER, Woodhouse CA, Eakin CM, Meko DM, Stahle DW (2004) Long-term aridity changes in the western United States. Science 306(5698):1015–1018CrossRefGoogle Scholar
  5. Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Royal Stat Soc B 39:1–38Google Scholar
  6. Enfield DB, Mestas-Nunez AM, Trimble PJ (2001) The Atlantic multidecadal oscillation and its relation to rainfall and river flows in the continental US. Geophys Res Lett 28(10):2077–2080CrossRefGoogle Scholar
  7. Farge M (1992) Wavelet transforms and their applications to turbulence. Ann Rev Fluid Mech 24:395–457CrossRefGoogle Scholar
  8. Foufoula-Georgiou E, Kumar P (1995) Wavelets in geophysics. Academic Press, New YorkGoogle Scholar
  9. Gelman A, Carlin J, Stern H, Rubin D (2003) Bayesian data analysis. Chapman & Hall/CRC, LondonGoogle Scholar
  10. Godsill S, Doucet A, West M (2001) Maximum a posteriori sequence estimation using Monte Carlo particle filters. Ann Inst Stat Math 53(1):82–96CrossRefGoogle Scholar
  11. Gray ST, Graumlich LJ, Betancourt JL, Pederson GT (2004) A tree-ring based reconstruction of the Atlantic Multidecadal Oscillation since 1567 AD. Geophys Res Lett, 31(12)Google Scholar
  12. Hubbard BB (1996) The World according to wavelets: the story of a mathematical technique in the making. AK Peters, MassachusettsGoogle Scholar
  13. Hue C, Le Cadre JP, Perez P (2002) Sequential Monte Carlo methods for multiple target tracking and data fusion. IEEE Trans Signal Process 50(2):309–325CrossRefGoogle Scholar
  14. Hughes JP, Guttorp P (1994) A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena. Water Resour Res 30(5):1535–1546CrossRefGoogle Scholar
  15. Hughes JP, Guttorp P, Charles SP (1999) A non-homogeneous hidden Markov model for precipitation occurrence. J R Stat Soc Ser C Appl Stat 48:15–30CrossRefGoogle Scholar
  16. Kaplan A, Cane M, Kushnir Y, Clement A, Blumenthal M, Rajagopalan B (1998) Analyses of global sea surface temperature 1856–1991. J Geophys Res 103(C9):18567–18589CrossRefGoogle Scholar
  17. Koutsoyiannis D (1994) A stochastic disaggregation method for design storm and flood synthesis. J Hydrol 156(1–4):193–225CrossRefGoogle Scholar
  18. Kulkarni JR (2000) Wavelet analysis of the association between the Southern Oscillation and the Indian Summer Monsoon. Int J Climatol 20(1):89–104CrossRefGoogle Scholar
  19. Kwon H-H, Khalil AF, Lall U (2006a) Modeling the Atlantic multi-decadal oscillation and the associated rainfall variability in S. Florida. Columbia University, New YorkGoogle Scholar
  20. Kwon H-H, Khalil AF, Lall U (2008) Non-homogeneous hidden Markov model based daily rainfall simulation using seasonal climate forcing: application to Everglades National Park, Florida. Water Resour Res (in press)Google Scholar
  21. Kwon H-H, Lall U, Khalil AF (2007) Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature. Water Resour Res, 43(W05407), doi:10.1029/2006WR005258
  22. Kwon H-H, Lall U, Moon Y-I, Khalil AF, Ahn H (2006b) Episodic interannual climate oscillations and their influence on seasonal rainfall in the Everglades National Park17. Water Resour Res, 42(W11404), doi:10.1029/2006WR0050
  23. McPherson BF, Halley R (1996) The South Florida environment: a region under stress: National Water-Quality Assessment Program, U.S. Geological Survey Circular 1134Google Scholar
  24. Park J, Mann ME (2000) Interannual temperature events and shifts in global temperature: a multiple wavelet correlation approach. Earth Interact 4:1–53CrossRefGoogle Scholar
  25. Rabiner LR (1989) A tutorial on hidden Markov-models and selected applications in speech recognition. Proc IEEE 77(2):257–286CrossRefGoogle Scholar
  26. Ridgeway G, Madigan D (2003) A sequential Monte Carlo method for Bayesian analysis of massive datasets. Data Min Knowl Discov 7(3):301–319CrossRefGoogle Scholar
  27. Robertson AW, Kirshner S, Smyth PJ (2003) Hidden Markov models for modeling daily rainfall occurrence over Brazil. Technical Report ICS-TR 03–27, Information and Computer Science. University of California, IrvineGoogle Scholar
  28. Robertson AW, Kirshner S, Smyth P (2004) Downscaling of daily rainfall occurrence over northeast Brazil using a hidden Markov model. J Clim 17(22):4407–4424CrossRefGoogle Scholar
  29. Schmidt N, Lipp EK, Rose JB, Luther ME (2001) ENSO influences on seasonal rainfall and river discharge in Florida. J Clim 14(4):615–628CrossRefGoogle Scholar
  30. Stedinger JR, Vogel RM (1984) Disaggregation procedures for generating serially correlated flow vectors. Water Resour Res 20(1):47–56CrossRefGoogle Scholar
  31. Thomas HA, Fiering MB (1962) Mathematic synthesis of streamflow sequences for analysis of river basins by simulation. In: Mass A (ed) Design of water resources systems. Harvard University press, Massachusetts, pp 459–493Google Scholar
  32. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79(1):61–78CrossRefGoogle Scholar
  33. Trimble PJ, Santee ER, Neidrauer CJ (1997) Including the effects of solar activity for more efficient water management: an application of neural networks. In: Second International Workshop on Artificial Intelligence Applications in Solar-Terrestrial Physics, SwedenGoogle Scholar
  34. Trimble PJ, Santee ER, Neidrauer CJ (1998) A refined approach to lake Okeechobee water management: An application of climate forecast, Special report. South Florida Water Management District, FloridaGoogle Scholar
  35. Trimble PJ, Trimble B (1998) Recognition and predictability of climate variability within south-central Florida. In: 23rd Annual Climate Diagnostics and Prediction Workshop, U.S. Dept. of Comm., NOAA, NWS, NCEP., Rosenstiel School of Marine and Atmospheric Science, University of Miami, MiamiGoogle Scholar
  36. Tsionas EG (2001) Bayesian multivariate Poisson regression. Commun Stat Theory Methods 30(2):243–255CrossRefGoogle Scholar
  37. Tucker A, Liu XH (2003) Learning dynamic Bayesian networks from multivariate time series with changing dependencies. Adv Intell Data Anal V 2810:100–110Google Scholar
  38. Valencia D, Schaake JC (1973) Disaggregation Processes in Stochastic Hydrology. Water Resour Res 9(3):580–585CrossRefGoogle Scholar
  39. Van Lent TJ (1993). Analysis of the historical Taylor Slough rainfall/flow relationship. University of Virginia, Environmental Sciences DepartmentGoogle Scholar
  40. Viterbi AJ (1967) Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Trans Inform Theory It13(2):260Google Scholar
  41. Wang B, Wang Y (1996) Temporal structure of the Southern Oscillation as revealed by waveform and wavelet analysis. J Clim 9(7):1586–1598CrossRefGoogle Scholar
  42. Weng HY, Lau KM (1994) Wavelets, Period-Doubling, and Time-Frequency Localization with Application to Organization of Convection over the Tropical Western Pacific. J Atmos Sci 51(17):2523–2541CrossRefGoogle Scholar
  43. Yevjevich V (1972) Stochastic processes in hydrology, Water Resources publication, Fort Collins, 30 COGoogle Scholar
  44. Zhang EY, Trimble P (1996) Predicting effects of climate fluctuations for water management by applying neural network. World Resour Rev 8(3):334Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Hyun-Han Kwon
    • 1
  • Upmanu Lall
    • 2
  • Jayantha Obeysekera
    • 3
  1. 1.Water Resources DivisionKorea Institute of Construction TechnologyKyeonggi-DoSouth Korea
  2. 2.Department of Earth and Environmental EngineeringColumbia UniversityNew YorkUSA
  3. 3.Hydrologic and Environmental Systems ModelingSouth Florida Water Management DistrictWest Palm BeachUSA

Personalised recommendations