A General Bayesian approach is developed and applied to the detection and attribution of climate change signal. The conditional probability of a certain model given the obervations (a-posteriori) is evaluated from the marginal probability of the model itself (a-priori) and the conditional probability of the data given the model (likelihood). The a-priori includes the description of the model's internal variability and a subjective measure of the overall probability of the model. The likelihood contains the description of the observational uncertainty. The decision rule to attribute the data into one of the two possible cases (control and a climate change scenario) is based on the log ratio of the two a-posteriori values. This approach reduces in case of Gaussian probability density functions and identical covariance matrices for the two model cases and the data to a standard linear discriminant function analysis.

NCEP/NCAR reanalysis data from 1958 to 1999 are used as observation and ECHAM3/LSG scenario runs utilizing the IS92a emission scenario data for the period 1880 to 2049 provide the model data. Spatially averaged near surface temperature and 70 hPa temperature for the Northern hemisphere extratropics are selected as detection variables because these combination provides the most reliable yet still simplest observational data. The two model cases are defined from an ensemble of 4 realizations of ECHAM3/LSG namely control as all simulation for the 100 year period 1880-1979 and the climate change scenario as the mean for all model realization in model year 2000 but the covariance matrix derived from (the trend reduced) anomalies 1980 till 2049.

Result shows that the observations (monthly and area mean of 2 m temperature and 70 hPa for the Northern hemisphere extratropics) are classified into the climate change scenario with an increasing frequency since the mid 1990's. Even if the subjectively selected a-priori probability for the climate change scenario is as low as 25%, the classification of the observations of the late 1990's into the climate change scenario is still present.