Downscaling station temperatures to glacier locations using empirical orthogonal functions and Bayesian model averaging

Glaciers are important reservoirs of freshwater and their recession has major implications for agriculture, forestry, fisheries and power generation. Quantification of glacier mass balance requires seasonal temperatures and precipitation. We present a method for reconstructing past temperatures at glacier locations in northwest North America. Meteorological measurements and proxy data are usually collected far from glaciers, at lower elevations, and under the influence of strong local boundary-layer effects (BLE). Alternatively, reanalysis data (e.g., NARR) provide a dynamically consistent representation of the atmosphere. We demonstrate a procedure to extract typical monthly mean temperature patterns from 1979-2007 NARR output and fit these to station observations from 1901-1978. We use CRU TS 2.1 gridded station monthly mean 2-m temperatures on a 0.5° latitude-longitude grid from 1901-2002. To compare CRU 2-m temperatures with NARR pressure-level temperatures requires removal of BLE from CRU 2-m temperatures and calculation of surface pressures. Boundary-layer effects and surface pressures are calculated for the years of overlap between NARR and CRU, 1979-2002, and regressed against the observations contained in the CRU data set: temperature, daily temperature range, precipitation, vapor pressure, cloud cover, number of frost days, and number of wet days. With the regression results, CRU 2-m temperatures from 1901-1978 are converted to pressure-level temperatures. Finally we determine 3-D empirical orthogonal functions (EOF) of NARR mean monthly temperature fields from 1979-2007. These are interpreted as representations of typical temperature patterns and are used as regression predictors to fit the converted 1901-1978 CRU temperatures. All regressions are carried out using Bayesian model averaging, essentially summing over the posterior distributions of all regression models, each distribution weighted by the model's Bayesian probability. This creates mixture models beyond the regression model space and can therefore outperform any individual regression model. Furthermore, Bayesian model averaging avoids over fitting and provides more robust confidence intervals and posterior predictive distributions. This procedure eliminates the need for vertical extrapolation from low-lying CRU observations to typically higher located glaciers without lapse rate information at these elevations. Moreover, unlike a simple spatial extrapolation, the procedure presented here yields the associated uncertainties. Another advantage is the characterization of climate in discrete units, i.e. EOF. This allows further research into the role of various climate indices and the relationship between global climate change and BLE. With some modifications the method can be extended further back in time using proxy data or can be used to downscale global climate model output.