Development of statistical downscaling methods for the daily precipitation process at a local site

Over the past decade, statistical procedures have been employed to downscale the outputs from global climate models (GCM) to assess the potential impacts of climate change and variability on the hydrological regime. These procedures are based on the empirical relationships between large-scale atmospheric predictor variables and local surface parameters such as precipitation and temperature. This research is motivated by the recognized lack of a comprehensive yet physically and statistically significant downscaling methodology for daily precipitation at a local site. The primary objectives are to move beyond the 'black box' approaches currently employed within the downscaling community, and develop improved statistical downscaling models that could outperform both raw GCM output and the current standard: the SDSM method. In addition, the downscaling methods could provide a more robust physical interpretation of the relationships between large-scale predictor climate variables and the daily precipitation characteristics at a local site. The first component of this thesis consists of developing linear regression based downscaling models to predict both the occurrence and intensity of daily precipitation at a local site using stepwise, weighted least squares, and robust regression methods. The performance of these models was assessed using daily precipitation and NCEP re-analysis climate data available at Dorval Airport in Quebec for the 1961-1990 period. It was found that the proposed models could describe more accurately the statistical and physical properties of the local daily precipitation process as compared to the CGCM1 model. Further, the stepwise model outperforms the SDSM model for seven months of the year and produces markedly fewer outliers than the latter, particularly for the winter and spring months. These results highlight the necessity of downscaling precipitation for a local site because of the unreliability of the large-scale raw CGCM1 output, and demonstrate the comparative performance of the proposed stepwise model as compared with the SDSM model in reproducing both the statistical and physical properties of the observed daily rainfall series at Dorval. In the second part of the thesis, a new downscaling methodology based on the principal component regression is developed to predict both the occurrence and amounts of the daily precipitation series at a local site. The principal component analysis created statistically and physically meaningful groupings of the NCEP predictor variables which explained 90% of the total variance. All models formulated outperformed the SDSM model in the description of the statistical properties of the precipitation series, as well as reproduced 4 out of 6 physical indices more accurately than the SDSM model, except for the summer season. Most importantly, this analysis yields a single, parismonious model; a non-redundant model, not stratified by month or season, with a single set of parameters that can predict both precipitation occurrence and intensity for any season of the year. The third component of the research uses covariance structural modeling to ascertain the best predictors within the principal components that were developed previously. Best fit models with significant paths are generated for the winter and summer seasons via an iterative process. The direct and indirect effects of the variables left in the final models indicate that for either season, three main predictors exhibit direct effects on the daily precipitation amounts: the meridional velocity at the 850 HPa level, the vorticity at the 500 HPa level, and the specific humidity at the 500 HPa level. Each of these variables is heavily loaded onto the first three principal components respectively. Further, a key fact emerges: From season to season, the same seven significant large-scale NCEP predictors exhibit a similar model structure when the daily precipitation amounts at Dorval Airport were used as a dependent variable. This fact indicated that the covariance structural model was physically more consistent than the stepwise regression one since different model structures with different sets of significant variables could be identified when a stepwise procedure is employed.

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