Model Error-Induced Biases of Greenhouse Gas Contribution to Global Warming: A Piecewise Integration Approach

Many of the observed changes of the climate system since the 1950s are unprecedented, and there is a high level of confidence in the conclusion that greenhouse gases (GHGs) caused a substantial part of the observed global warming. We need to consider the model errors, that usually accumulate in long-term integration as a result of imperfect physical and numerical representations, to attribute climate changes using model simulations. Here, we present a new method of the piecewise integration (PWI) with simulation corrected by the observation at each step, to identify model error-induced bias of global warming in the Community Earth System Model (CESM). To confirm the hypothesis of constant model-observation bias under different external forcing, we disturb the original CESM into a less low-cloud version and take its historical and GHGs-fixed simulations as our “observations”. In the PWI historical and GHGs-fixed runs of original CESM from 1958 to 2005, we use the difference between “historical observation” and PWI historical run to correct both PWI runs at the end of each 1-day step. The results show that the PWI can effectively reduce model’s cumulative error and presents a GHGs-induced global warming trend of 0.688℃ (48yr) -1 , which is very close to the “observational” trend of 0.683℃ (48yr) -1 , confirming the hypothesis of constant model bias under different external forcing. The continuous runs, as usually done by the Coupled Model Intercomparison Project (CMIP) models, present a much higher GHGs-induced global warming trend of 0.887℃ (48yr) -1 , which means that the model overestimates the GHGs’s role in global warming trend by 32.3% compared to our “observations”. Global distribution of this model bias is also discussed. The PWI method provides a new way to correct model biases in analyzing relative contribution of anthropogenic and natural forcing to global warming.