Uncertainties of statistical downscaling from predictor selection: Equifinality and transferability

The nonhomogeneous hidden Markov model (NHMM) statistical downscaling model, 38 catchments in southeast Australia and 19 general circulation models (GCMs) were used in this study to demonstrate statistical downscaling uncertainties caused by equifinality to and transferability. That is to say, there could be multiple sets of predictors that give similar daily rainfall simulation results for both calibration and validation periods, but project different amounts (or even directions of change) of rainfall changing in the future. Results indicated that two sets of predictors (Set 1 with predictors of sea level pressure north-south gradient, u-wind at 700 hPa, v-wind at 700 hPa, and specific humidity at 700 hPa and Set 2 with predictors of sea level pressure north-south gradient, u-wind at 700 hPa, v-wind at 700 hPa, and dewpoint temperature depression at 850 hPa) as inputs to the NHMM produced satisfactory results of seasonal rainfall in comparison with observations. For example, during the model calibration period, the relative errors across the 38 catchments ranged from 0.48 to 1.76% with a mean value of 1.09% for the predictor Set 1, and from 0.22 to 2.24% with a mean value of 1.16% for the predictor Set 2. However, the changes of future rainfall from NHMM projections based on 19 GCMs produced projections with a different sign for these two different sets of predictors: Set 1 predictors project an increase of future rainfall with magnitudes depending on future time periods and emission scenarios, but Set 2 predictors project a decline of future rainfall. Such divergent projections may present a significant challenge for applications of statistical downscaling as well as climate change impact studies, and could potentially imply caveats in many existing studies in the literature.