Abstract
Abstract. Reliable estimates of historical effective radiative forcing (ERF) are important for understanding the causes of past climate change and for constraining predictions of future warming. This study proposes a new linear-filtering method for estimating historical radiative forcing from time series of global mean surface temperature (GMST), using energy-balance models (EBMs) fitted to GMST from CO2-quadrupling general circulation model (GCM) experiments. We show that the response of any k-box EBM can be represented as an ARMA(k, k−1) (autoregressive moving-average) filter. We show how, by inverting an EBM's ARMA filter representation, time series of surface temperature may be converted into radiative forcing. The method is illustrated using three-box EBM fits to two recent Earth system models from CMIP5 and CMIP6 (Coupled Model Intercomparison Project). A comparison with published results obtained using the established ERF_trans method, a purely GCM-based approach, shows that our new method gives an ERF time series that closely matches the GCM-based series (correlation of 0.83). Time series of estimated historical ERF are obtained by applying the method to a dataset of historical temperature observations. The results show that there is clear evidence of a significant increase over the historical period with an estimated forcing in 2018 of 1.45±0.504 W m−2 when derived using the two Earth system models. This method could be used in the future to attribute past climate changes to anthropogenic and natural factors and to help constrain estimates of climate sensitivity.
Highlights
The estimation of historical radiative forcing, a measure of the net change in the energy balance of the climate system in response to an external perturbation, is a matter of strong scientific interest, as evidenced by the dedication of a whole chapter to this topic in the most recent assessment report from the Intergovernmental Panel on Climate Change (IPCC) (Myhre et al, 2013)
In this paper we develop a new method for estimating radiative forcing by inverting simple climate models, a method that can be of benefit to the detection and attribution of climate change
This paper is a proof-of-concept study in which we develop a method for performing the proposed deconvolution of temperature time series using k-box energy-balance models (EBMs)
Summary
The estimation of historical radiative forcing, a measure of the net change in the energy balance of the climate system in response to an external perturbation, is a matter of strong scientific interest, as evidenced by the dedication of a whole chapter to this topic in the most recent assessment report from the Intergovernmental Panel on Climate Change (IPCC) (Myhre et al, 2013). We propose that detection and attribution of changes in GMST using simple climate models could be improved by first deconvolving temperature observations to obtain series of estimated radiative forcing and by performing the traditional regression step on radiative-forcing time series. We use the fact that a system of k first-order linear ODEs has a discrete-time representation as an ARMA(k, k − 1) filter (Spolia and Chander, 1974; Chang et al, 1982) This correspondence has been used before in the context of three-box EBMs by Grieser and Schönwiese (2001) as a convenient means of integrating the continuoustime model over a time series of discrete forcing inputs and by Stern (2005) as a way to enforce energy-balance constraints on estimated parameters of an ARMA model. In this paper we show how the k-box model’s equivalent ARMA filter representation may be derived, and we describe how, by inverting the ARMA filter, radiative forcing may be obtained from a temperature time series
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