A stochastic model of space-time variability of mesoscale rainfall: Statistics of spatial averages

Water Resources Research

Volumn 39, Issue 12, 2003, Pages

  Kundu, Prasun K ^a,b   Bell, Thomas L ^b  

^a UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

^b NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

Fractal behavior; Precipitation spectrum; Rainfall statistics; Scaling; Stochastic model; TOGA COARE data modeling

Indexed keywords

DATA REDUCTION; MATHEMATICAL MODELS; RAIN; RANDOM PROCESSES; STATISTICAL METHODS;

SPECTRAL MODELS;

WATER RESOURCES;

PRECIPITATION ASSESSMENT; RAINFALL; SPATIOTEMPORAL ANALYSIS; STOCHASTICITY;

EID: 1242322117     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2002WR001802     Document Type: Article

References (45)

1. Anderson, T. W., An Introduction to Multivariate Statistical Analysis, John Wiley, Hoboken, N. J., 1958.
2. Bell, T. L., Climate sensitivity from fluctuation dissipation: Some simple model tests, J. Atmos. Sci., 37, 1700-1707, 1980.
3. Bell, T. L., A space-time stochastic model of rainfall for satellite remote-sensing studies, J. Geophys. Res., 92, 9631-9643, 1987.
4. Bell, T. L., and P. K. Kundu, A study of the sampling error in satellite rainfall estimates using optimal averaging of data and a stochastic model, J. Clim., 9, 1251-1268, 1996.
5. Bell, T. L., and P. K. Kundu, Comparing satellite rainfall estimates with rain-gauge data: Optimal strategies suggested by a spectral model, J. Geophys. Res., 108(D3), 4121, doi:10.1029/2002JD002641, 2003.
6. Bell, T. L., and N. Reid, Detecting the diurnal cycle of rainfall using satellite observations, J. Appl. Meteorol., 32, 311-322, 1993.
7. Bell, T. L., A. Abdullah, R. L. Martin, and G. R. North, Sampling errors for satellite-derived tropical rainfall: Monte Carlo study using a space-time stochastic model, J. Geophys. Res., 95, 2195-2205, 1990.
8. Bell, T. L., P. K. Kundu, and C. D. Kummerow, Sampling errors of SSM/I and TRMM rainfall averages: Comparison with error estimates from surface data and a simple model, J. Appl. Meteorol., 40, 938-954, 2001.
9. Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert, The fractional-order governing equation of Lévy motion, Water Resour. Res., 36, 1413-1423, 2000.
10. Cox, D. R., and V. Isham, A simple spatial-temporal model of rainfall, Proc. R. Soc. London, Ser. A, 415, 317-328, 1988.
11. Deidda, R., Rainfall downscaling in a space-time multifractal framework, Water Resour. Res., 36, 1779-1794, 2000.
12. Foufoula-Georgiou, E., and W. F. Krajewski, Recent advances in rainfall modeling, estimation and forecasting, Rev. Geophys., 33, 1125-1137, 1995.
13. Gupta, V. K., and E. C. Waymire, A stochastic kinematic study of subsynoptic space-time rainfall, Water Resour. Res., 15, 637-644, 1979.
14. Gupta, V. K., and E. C. Waymire, Multiscaling properties of spatial rainfall and river flow distributions, J. Geophys. Res., 95, 1999-2009, 1990.
15. Ha, E., G. R. North, C. Yoo, and K.-J. Ha, Evaluation of some ground truth designs for satellite estimates of rain rate, J. Atmos. Oceanic Technol., 19, 65-73, 2002.
16. Jenkins, G. M., and D. G. Watts, Spectral Analysis and Its Applications, Holden-Day, Boca Raton, Fla., 1968.
17. Kedem, B., L. S. Chiu, and G. R. North, Estimation of mean rain rate: Application to satellite observations, J. Geophys. Res., 95, 1965-1972, 1990.
18. Lau, K.-M., and P. H. Chan, Aspects of the 40-50-day oscillation in the tropics, Mon. Weather. Rev., 113, 1889-1909, 1985.
19. Laughlin, C. R., On the effect of temporal sampling on the observation of mean rainfall, in Precipitation Measurements from Space, Workshop Report, edited by D. Atlas and O. W. Thiele, pp. D59-D66, NASA Goddard Space Flight Center, Greenbelt, Md., 1981.
20. Le Cam, L., A stochastic description of precipitation, in IV Berkeley Symposium in Mathematical Statistics and Probability, vol. 3, pp. 165-186, Univ. of Calif. Press, Berkeley, 1961.
21. Lovejoy, S., Area-perimeter relations for rain and cloud areas, Science, 216, 185-187, 1982.
22. Lovejoy, S., and B. Mandelbrot, Fractal properties of rain and a fractal model, Tellus, Ser. A, 37, 209-232, 1985.
23. Madden, R. A., Seasonal variations of the 40-50-day oscillation in the tropics, J. Atmos. Sci., 43, 3138-3158, 1986.
24. Marsan, D., D. Schertzer, and S. Lovejoy, Causal space-time multifractal processes: Predictability and forecasting of rain fields, J. Geophys. Res., 101, 26,333-26,346, 1996.
25. Marshak, A., A. Davis, R. Cahalan, and W. Wiscombe, Bounded cascade models as nonstationary fractals, Phys. Rev. A, 49, 55-69, 1994.
26. McConnell, A., and G. R. North, Sampling errors in satellite estimates of tropical rain, J. Geophys. Res., 92, 9567-9570, 1987.
27. Menabde, M., D. Harris, A. W. Seed, G. Austin, and D. Stow, Multiscaling properties of rainfall and bounded random cascades, Water Resour. Res., 33, 2823-2830, 1997.
28. Nakazawa, T., Intraseasonal oscillations during the TOGA COARE IOP, J. Meteorol. Soc. Jpn., 73, 305-319, 1995.
29. North, G. R., and S. Nakamoto, Formalism for comparing rain estimation designs, J. Atmos. Oceanic Technol., 6, 985-992, 1989.
30. Over, T. M., and V. K. Gupta, A space-time theory of mesoscale rainfall using random cascades, J. Geophys. Res., 101, 26,319-26,331, 1996.
31. Schertzer, D., and S. Lovejoy, Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes, J. Geophys. Res., 92, 9693-9714, 1987.
32. Schertzer, D., S. Lovejoy, F. Schmitt, Y. Chigirinskaya, and D. Marsan, Multifractal cascade dynamics and turbulent intermittency, Fractals, 5(3), 421-471, 1997.
33. Seed, A. W., R. Srikanthan, and M. Menabde, A space-time model for design storm rainfall, J. Geophys. Res., 104, 31,623-31,630, 1999.
34. Short, D. A., D. B. Wolff, D. Rosenfeld, and D. Atlas, A study of the threshold method utilizing raingage data, J. Appl. Meteorol., 32, 1379-1387, 1993.
35. Short, D. A., P. A. Kucera, B. S. Ferrier, J. A. Gerlach, S. A. Rutledge, and O. W. Thiele, Shipborne radar rainfall patterns within the TOGA COARE IFA, Bull. Am. Meteorol. Soc., 78, 2817-2836, 1997.
36. Smith, J. A., and W. F. Krajewski, Statistical modeling of space-time rainfall using radar and rain gage observations, Water Resour. Res., 23, 1893-1900, 1987.
37. Takayabu, Y. N., Large-scale cloud disturbances associated with equatorial waves. part II: Westward propagating inertio-gravity waves, J. Meteorol. Soc. Jpn., 72, 451-465, 1994.
38. Takayabu, Y. N., K.-M. Lau, and C.-H. Sui, Two-day variation in cloud-atmosphere coupled system observed in TOGA COARE IOP, Mon. Weather Rev., 124, 1892-1913, 1996.
39. Venugopal, V., E. Foufoula-Georgiou, and V. Sapozhnikov, Evidence of dynamic scaling in space-time rainfall, J. Geophys. Res., 104, 31,599-31,610, 1999.
40. Waymire, E., Scaling limits and self-similarity in precipitation fields, Water Resour. Res., 21, 1271-1281, 1985.
41. Waymire, E., V. K. Gupta, and I. Rodriguez-Iturbe, A spectral theory of rainfall intensity at the meso-β scale, Water Resour. Res., 20, 1453-1465, 1984.
42. Webster, P. J., and R. Lukas, TOGA COARE: The Coupled Ocean-Atmosphere Experiment, Bull. Am. Meteorol. Soc., 73, 1377-1416, 1992.
43. Wheater, H. S., V. S. Isham, D. R. Cox, R. E. Chandler, A. Kakou, P. J. Northrop, L. Oh, C. Onof, and I. Rodríguez-Iturbe, Spatial-temporal rainfall fields: Modelling and statistical aspects, Hydrol. Earth Syst. Sci., 4, 581-601, 2000.
44. Wolfram, S., The Mathematica Book, 4th ed., Wolfram Media, Chapman, Ill., 1999.
45. Yoo, C., J. B. Valdés, and G. R. North, Stochastic modeling of multidimensional precipitation fields considering spectral structure, Water Resour. Res., 32, 2175-2187, 1996.