Evaluating spatio-temporal representations in daily rainfall sequences from three stochastic multi-site weather generation approaches

Abstract Many hydrological and agricultural studies require simulations of weather variables reflecting observed spatial and temporal dependence at multiple point locations. This paper assesses three multi-site daily rainfall generators for their ability to model different spatio-temporal rainfall attributes over the study area. The approaches considered consist of a multi-site modified Markov model (MMM), a reordering method for reconstructing space–time variability, and a nonparametric k -nearest neighbour (KNN) model. Our results indicate that all the approaches reproduce adequately the observed spatio-temporal pattern of the multi-site daily rainfall. However, different techniques used to signify longer time scale observed temporal and spatial dependences in the simulated sequences, reproduce these characteristics with varying successes. While each approach comes with its own advantages and disadvantages, the MMM has an overall advantage in offering a mechanism for modelling varying orders of serial dependence at each point location, while still maintaining the observed spatial dependence with sufficient accuracy. The reordering method is simple and intuitive and produces good results. However, it is primarily driven by the reshuffling of the simulated values across realisations and therefore may not be suited in applications where data length is limited or in situations where the simulation process is governed by exogenous conditioning variables. For example, in downscaling studies where KNN and MMM can be used with confidence.

[1]  Edward C. Waymire,et al.  A Spectral Theory of Rainfall Intensity at the Meso‐β Scale , 1984 .

[2]  Upmanu Lall,et al.  A Nearest Neighbor Bootstrap For Resampling Hydrologic Time Series , 1996 .

[3]  P. Guttorp.  Stochastic modeling of scientific data , 1995 .

[4]  R. Mehrotra,et al.  A nonparametric nonhomogeneous hidden Markov model for downscaling of multisite daily rainfall occurrences , 2005 .

[5]  M. Parlange,et al.  Effects of an index of atmospheric circulation on stochastic properties of precipitation , 1993 .

[6]  G. McCabe,et al.  Simulation of precipitation by weather type analysis , 1991 .

[7]  Ashish Sharma,et al.  A nonparametric stochastic downscaling framework for daily rainfall at multiple locations , 2006 .

[8]  Dennis P. Lettenmaier,et al.  A hierarchical stochastic model of large‐scale atmospheric circulation patterns and multiple station daily precipitation , 1992 .

[9]  M. Clark,et al.  The Schaake Shuffle: A Method for Reconstructing Space–Time Variability in Forecasted Precipitation and Temperature Fields , 2004 .

[10]  M. Parlange,et al.  Overdispersion phenomenon in stochastic modeling of precipitation , 1998 .

[11]  Katharine Hayhoe,et al.  Statistical downscaling of precipitation through nonhomogeneous stochastic weather typing , 2007 .

[12]  Budong Qian,et al.  Multisite stochastic weather models for impact studies , 2002 .

[13]  T. A. Buishand,et al.  Simulation of extreme precipitation in the Rhine basin by nearest-neighbour resampling , 1998 .

[14]  A. Bárdossy,et al.  SPACE-TIME MODEL FOR DAILY RAINFALL USING ATMOSPHERIC CIRCULATION PATTERNS , 1992 .

[15]  Theo Brandsma,et al.  Multisite simulation of daily precipitation and temperature in the Rhine Basin by nearest‐neighbor resampling , 2001 .

[16]  R. Srikanthan,et al.  A comparison of three stochastic multi-site precipitation occurrence generators , 2006 .

[17]  R. Mehrotra,et al.  Comparison of two approaches for downscaling synoptic atmospheric patterns to multisite precipitation occurrence , 2004 .

[18]  Marc B. Parlange,et al.  Stochastic Modeling of the Effects of Large-Scale Circulation on Daily Weather in the Southeastern U.S. , 2003 .

[19]  Ashish Sharma,et al.  Seasonal to interannual rainfall probabilistic forecasts for improved water supply management: Part 3 — A nonparametric probabilistic forecast model , 2000 .

[20]  T. A. Buishand,et al.  Some remarks on the use of daily rainfall models , 1978 .

[21]  James P. Hughes,et al.  A class of stochastic models for relating synoptic atmospheric patterns to regional hydrologic phenomena , 1994 .

[22]  Ignacio Rodriguez-Iturbe,et al.  Rainfall generation: A nonstationary time‐varying multidimensional model , 1976 .

[23]  Ashish Sharma,et al.  A nonparametric approach for representing interannual dependence in monthly streamflow sequences , 2002 .

[24]  J. Beersma,et al.  Multi-site simulation of daily precipitation and temperature conditional on the atmospheric circulation , 2003 .

[25]  Upmanu Lall,et al.  A k‐nearest‐neighbor simulator for daily precipitation and other weather variables , 1999 .

[26]  Daniel S. Wilks,et al.  Simultaneous stochastic simulation of daily precipitation, temperature and solar radiation at multiple sites in complex terrain , 1999 .

[27]  Ashish Sharma,et al.  A nonparametric model for stochastic generation of daily rainfall occurrence , 2003 .

[28]  D. Lettenmaier.  Stochastic Modeling of Precipitation with Applications to Climate Model Downscaling , 1995 .

[29]  J. Porter,et al.  Climatic variability and the modelling of crop yields , 1995 .

[30]  James P. Hughes,et al.  A stochastic approach for assessing the effect of changes in synoptic circulation patterns on gauge precipitation , 1993 .

[31]  R. Mehrotra,et al.  A semi-parametric model for stochastic generation of multi-site daily rainfall exhibiting low-frequency variability , 2007 .

[32]  D. Wilks.  Multisite downscaling of daily precipitation with a stochastic weather generator , 1999 .

[33]  P. Guttorp,et al.  A non‐homogeneous hidden Markov model for precipitation occurrence , 1999 .

[34]  R. Mehrotra,et al.  Preserving low-frequency variability in generated daily rainfall sequences , 2007 .

[35]  Balaji Rajagopalan,et al.  A resampling procedure for generating conditioned daily weather sequences , 2004 .

[36]  A. Bárdossy,et al.  Multivariate stochastic downscaling model for generating daily precipitation series based on atmospheric circulation , 2002 .

[37]  Mikhail A. Semenov,et al.  A serial approach to local stochastic weather models , 1991 .

[38]  Ashish Sharma,et al.  A nonparametric model for stochastic generation of daily rainfall amounts , 2003 .

[39]  D. Wilks.  Multisite generalization of a daily stochastic precipitation generation model , 1998 .