Downscaled Climate Projections by Katharine Hayhoe
A Modified Statistical Asynchronous Regression Downscaling Method
Anne Stoner, Katharine Hayhoe, and Xiaohui Yang
This approach uses daily predictor fields from AOGCMs to statistically downscale maximum and minimum temperature and 24h cumulative precipitation. The AOGCM simulations are first re-gridded to the scale of the observations (whether for stations or grids) using bilinear interpolation. For training, the method requires a minimum of 20 years of observations with less than 5% missing data over that time period in order to produce robust results. Where data is available, at most the method uses the entire observational record from 1960 to present for training purposes.
The downscaling approach is based on a highly generalizable statistical approach, quantile regression. This approach has two key advantages: first, it does not require temporal correspondence between AOGCM simulations and observations; and second, it is capable of incorporating AOGCM-simulated changes in the shape of the distribution (including shifts in the mean, skewedness, and variance) into future projections.
Model predictor values and observed predictand values are ranked and a function (here, a piecewise linear regression) is fitted to the datasets by month, including two weeks of overlapping data on either side. This additional refinement was added to account for shifting seasons in future projections that may produce conditions outside the range of a typical historical month in the future, and allows the method to utilize each data point twice rather than once during the training process.
Optimal placements and number of break points (up to six) in the piecewise linear regressions are identified automatically as locations with higher curvature on a plot of ranked modeled vs. observed values. The slopes of the regression segments are checked to ensure no negative slopes are present, and if there is a negative slope a break point is removed to force a positive slope.
Temperature. Based on tests during the development stage of this method, it was determined that the most reliable predictor for daily maximum and minimum 2m temperature were those same fields as simulated by the AOGCMs. Improved performance on temperature downscaling is obtained by filtering the AOGCM fields using an EOF analysis and retaining only 97% of the original variance. As the linear regressions at the tails are based on a much lower number of data points than those in the center of the distribution, the low and high tail of the distributions undergo further scrutiny by performing bias correction at the tails, ensuring that values are within 30% of the observations.
Precipitation. The downscaling model for precipitation is similar to that for temperature in many aspects, but with some key differences. First, for practical reasons an AOGCM predictor had to be chosen that was commonly archived at the daily scale. Although upper-level humidity and geopotential height have shown promise in downscaling precipitation, few AOGCMs have preserved daily outputs. Thus, 24h cumulative precipitation was selected as the predictor for precipitation, with the additional refinement of incorporating convective and large-scale precipitation if both predictors were available. For models with these variables, the downscaling approach selects from three possible predictors the one best suited to each month: convective, large-scale, or total. This refinement significantly improved the method’s ability to simulate precipitation over arid and semi-tropical regions. Second, EOF filtering of the GCM output is not performed since we found that to degrade the results along with introducing negative values for precipitation. Finally, the logarithm of precipitation values is used instead of raw precipitation amount. This was found to decrease the residuals of the regression.
The resulting outputs have been statistically estimated to be accurate to the 99.6th percentile of the distribution (i.e., to 1-2 days per year). This is likely a fairly conservative estimate as it does not incorporate the effects of bias correction in the tails of the distribution. Analyses of biases in the quantiles of the distribution and in key thresholds such as wet days show good correspondence with historical observations (see below).
Figure 1. The bias in (a) the 99th quantile of the distribution of maximum temperature as simulated by downscaling GFDL CM2.1, and (b) the number of wet days per year (pr>0.1”) in downscaled simulations compared to observations for the period 1960-2000, as simulated by downscaling HadCM3.