Evaluation of statistical downscaling models using pattern and dependence structure in the monsoon-dominated region of Pakistan

Khan, Firdos ; Ali, Shaukat ; Pilz, Jürgen

The uphill topography and sudden spatial variation in the climate of the monsoon‐dominated region of Pakistan render it difficult to make predictions with dynamical climate models. This study evaluates the use of two statistical models for the downscaling of climate variables: the Multivariate Multiple Linear Regression Model (MMLRM) and the Multisite Multivariate Statistical Downscaling Model (MMSDSM). A randomisation technique was implemented to establish the extreme values and spatial dependence structure for a number of variables by adding correlated noise to the predictand data for multiple sites, generated from a multivariate normal distribution. In the case of precipitation, probability mapping techniques were used to make adjustments based on a gamma distribution. To cope with the dimensionality and multicollinearity problems of the input data (predictors), empirical orthogonal functions were used. The models were calibrated using the National Centers for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) predictors for the period 1960-1990 and validated for 1990-2000. To investigate the efficacy of the proposed models, different statistical measures - such as root mean square error, mean bias error and analysis of how closely the observed variability was reproduced - were used. The results show mixed support for both models: MMLRM underestimates the variability, and MMSDSM has the ability to predict the extreme values and spatial dependence structure. The results of logistic regression analysis show that the precipitation probability values generated by the logistic model closely reproduced the patterns of observed precipitation - there is an increase in the occurrence of precipitation events during the monsoon season over the target area.

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