What is the uncertainty in degree day projections due to different 2 calibration methodologies?

Degree-days are a temperature index used for understanding the impact of climate change. Different methods to deal with climate model biases, termed bias correction or more generally calibration, yield different projections of such indices, something not widely understood for temperature indices in many impact sectors. An analytical expression is derived for the expected value of degree-days given parameters of the underlying statistical distribution (assumed to be Gaussian). It is demonstrated that the uncertainty introduced by calibration methodology is driven by the magnitude of the nonlinearity in this expression. In a climate where mean temperature is, and remains, far from (approximately three standard deviations) the threshold used in defining the index, the equation is approximately linear, and methodological choice makes little difference relative to the absolute number of degree-days. However, case studies for U.K. cities London and Glasgow for heating and cooling degree-days (HDD and CDD; these are degree-day indices used in the estimation of energy use for heating and cooling buildings) demonstrate that, when temperatures are close to the threshold, unrealistic results may arise if appropriate calibration is not performed. Seasonally varying temperature biases in the 11-member perturbed parameter ensemble HadRM3 are discussed, and different calibration strategies are applied to this ensemble. For projections of U.K. HDD, the difference between results from simple and advanced methodologies is relatively small, as the expression for HDD is approximately linear in many months and locations. For U.K. CDD, an inappropriate method has a large relative impact on projections because of the proximity to the threshold. In both cases, the uncertainty caused by methodology is comparable to that caused by ensemble spread.