Statistical downscaling daily rainfall statistics from seasonal forecasts using canonical correlation analysis or a hidden Markov model?

Here we downscale retrospective seasonal forecasts of precipitation to a network of rainfall stations over central Chile, to predict daily rainfall statistics pertinent to dry-land management; the targeted statistics include winter season rainfall total, rainfall frequency; the drought indices including the number of heavy rainfall days, and the (daily) accumulated precipitation deficit. Two contrasting approaches are taken: In the first, a canonical correlation analysis (CCA) is employed to the time series of the targeted seasonal statistic, calculated from daily station rainfall observations, together with the GCM (here CFS) retrospective forecasts of gridded seasonal-mean precipitation. In the second approach, a non-homogeneous hidden Markov model (NHMM) is trained on the daily station observations, using the GCM's seasonal-mean precipitation as a predictor; the targeted seasonal statistic is then computed from a large ensemble of stochastic daily rainfall sequences generated by the NHMM. We assess the pros and cons of each method. Both methods are shown to perform quite similarly under cross-validation. Although more complex, the NHMM is able to provide probabilistic information and the daily rainfall sequences required for water balance modeling directly.