A coupled stochastic space‐time intermittent random cascade model for rainfall downscaling

[1] Analysis of Next Generation Weather Radar rainfall data indicates that for the central United States, rainfall exhibits a composite behavior with respect to its spatial and temporal scaling characteristics. Our data analysis shows that rainfall fluctuations at spatial scales smaller than a reference scale exhibit self-similarity and that at scales larger than the reference scale, rainfall fluctuations are scale dependent. Accordingly, we present a new methodology for downscaling large-scale rainfall consistent with this composite character of rainfall variability. The new downscaling model is a composite of a stochastic space-time submodel that preserves the spatial and temporal dependency characteristics at scales larger than the reference scale and an intermittent random cascade submodel that preserves the statistical self-similarity and spatial intermittency at scales smaller than the reference scale. The new model is applied to downscale summer daily rainfall for the central United States from a scale of 256 km to a scale of 2 km. We show that the new model reproduces quite well the intermittency and self-similarity features and the interscale and across-scale correlation structures of observed rainfall with a relatively low computational burden.

[1]  Praveen Kumar,et al.  A multicomponent decomposition of spatial rainfall fields: 2. Self‐similarity in fluctuations , 1993 .

[2]  R. Valencia,et al.  Disaggregation processes in stochastic hydrology , 1973 .

[3]  Joel B. Smith.  The Potential Impacts of Climate Change on the Great Lakes , 1991 .

[4]  V. Gupta,et al.  MODELING SPACE-TIME RAINFALL AT THE MESOSCALE USING RANDOM CASCADES , 2004 .

[5]  Keith Beven,et al.  Effects of spatial variability and scale with implications to hydrologic modeling , 1988 .

[6]  E. Foufoula‐Georgiou,et al.  Linkage of scaling and thermodynamic parameters of rainfall: Results from midlatitude mesoscale convective systems , 1996 .

[7]  Praveen Kumar,et al.  A multicomponent decomposition of spatial rainfall fields: 1. Segregation of large‐ and small‐scale features using wavelet transforms , 1993 .

[8]  Wilson H. Tang,et al.  Probability concepts in engineering planning and design , 1984 .

[9]  R. Pielke,et al.  Influence of landscape structure on local and regional climate , 1990, Landscape Ecology.

[10]  R. Pielke,et al.  A comprehensive meteorological modeling system—RAMS , 1992 .

[11]  J. Ramirez,et al.  A Statistical–Dynamical Parameterization of Interception and Land Surface–Atmosphere Interactions , 2000 .

[12]  Jorge A. Ramírez,et al.  Precipitation and Water-Table Effects on Agricultural Production and Economics , 1996 .

[13]  Shaun Lovejoy,et al.  Universal Multifractals: Theory and Observations for Rain and Clouds , 1993 .

[14]  T. Wigley,et al.  Obtaining sub-grid-scale information from coarse-resolution general circulation model output , 1990 .

[15]  D. Wilks,et al.  The Statistical Problem of Climate Inversion: Determination of the Relationship between Local and Large-Scale Climate , 1984 .

[16]  J. M. Mejía,et al.  Disaggregation models in hydrology revisited , 1976 .

[17]  James M. Murphy,et al.  An Evaluation of Statistical and Dynamical Techniques for Downscaling Local Climate , 1999 .

[18]  Dennis P. Lettenmaier,et al.  Hydrologic sensitivities of the Sacramento‐San Joaquin River Basin, California, to global warming , 1990 .

[19]  She,et al.  Quantized energy cascade and log-Poisson statistics in fully developed turbulence. , 1995, Physical review letters.

[20]  D. Wilks.  Statistical specification of local surface weather elements from large-scale information , 1989 .

[21]  M. Seyfried,et al.  Scale and the Nature of Spatial Variability: Field Examples Having Implications for Hydrologic Modeling , 1995 .

[22]  Shaun Lovejoy,et al.  Atmospheric complexity or scale by scale simplicity? , 2009 .

[23]  Thomas P. Minka,et al.  Gates , 2008, NIPS.

[24]  C. Bretherton,et al.  Statistical Precipitation Downscaling over the Northwestern United States Using Numerically Simulated Precipitation as a Predictor , 2003 .

[25]  Murugesu Sivapalan,et al.  Tests of a space‐time model of daily rainfall in southwestern Australia based on nonhomogeneous random cascades , 2000 .

[26]  Roger A. Pielke,et al.  Coupled Atmosphere–Biophysics–Hydrology Models for Environmental Modeling , 2000 .

[27]  Jorge A. Ramírez,et al.  CO2 AND TEMPERATURE EFFECTS ON EVAPOTRANSPIRATION AND IRRIGATED AGRICULTURE , 1996 .

[28]  Event-specific multiplicative cascade models and an application to rainfall , 1999 .

[29]  M. Schlesinger,et al.  A Method of Relating General Circulation Model Simulated Climate to the Observed Local Climate. Part I: Seasonal Statistics , 1990 .

[30]  Jonas Olsson,et al.  Evaluation of a scaling cascade model for temporal rain- fall disaggregation , 1998 .

[31]  C. Frei,et al.  Downscaling from GCM precipitation: a benchmark for dynamical and statistical downscaling methods , 2006 .

[32]  The Potential Impacts of a Scenario of C02-Induced Climatic Change on Ontafio, Canada , 1988 .

[33]  Edward C. Waymire,et al.  A statistical analysis of mesoscale rainfall as a random cascade , 1993 .

[34]  K. Paulson,et al.  Downscaling of rain gauge time series by multiplicative beta cascade , 2007 .

[35]  D. Lettenmaier,et al.  Hydrologic Implications of Dynamical and Statistical Approaches to Downscaling Climate Model Outputs , 2004 .

[36]  G. McCabe,et al.  Use of weather types to disaggregate general circulation model predictions , 1992 .

[37]  Thomas M. Over,et al.  A space‐time theory of mesoscale rainfall using random cascades , 1996 .

[38]  B. Kang,et al.  Response of Streamflow to Weather Variability under Climate Change in the Colorado Rockies , 2007 .

[39]  J. Ramirez,et al.  Spatial Disaggregation for Studies of Climatic Hydrologic Sensitivity , 1994 .

[40]  D. Schertzer,et al.  Physical modeling and analysis of rain and clouds by anisotropic scaling multiplicative processes , 1987 .

[41]  D. Rupp,et al.  Time scale and intensity dependency in multiplicative cascades for temporal rainfall disaggregation , 2009 .