A kernel method for calculating effective radiative forcing in transient climate simulations

Effective radiative forcing (ERF) is calculated as the flux change at the top of the atmosphere, after allowing fast adjustments, due to a forcing agent such as greenhouse gasses or volcanic events. Accurate estimates of the ERF are necessary in order to understand the drivers of climate change. ERF cannot be observed directly and is difficult to estimate from indirect observations due to the complexity of climate responses to individual forcing factors. We present a new method of calculating ERF using a kernel populated from a time series of a model variable (e.g. global mean surface temperature) in a CO2 step change experiment. The top of atmosphere (TOA) radiative imbalance has the best noise tolerance for retrieving the ERF of the model variables we tested. We compare the kernel method with the energy balance method for estimating ERF in the CMIP5 models. The energy balance method uses the regression between the TOA imbalance and temperature change in a CO2 step change experiment to estimate the climate feedback parameter. It then assumes the feedback parameter is constant to calculate the forcing time series. This method is sensitive to the number of years chosen for the regression and the nonlinearity in the regression leads to a bias. We quantify the sensitivities and biases of these methods and compare their estimates of forcing. The kernel method is more accurate for models in which a linear fit is a poor approximation for the relationship between temperature change and TOA imbalance.