SSM projection results

1. The State Space Model (SSM) is used as a simplified surrogate model to assess future climate change uncertainty using several key physical parameters. The SSM parametric form is based on common two-layer Earth energy balance equations, with the modeling of surface air and deep ocean temperature. The SSM includes a state transition function which models the latent variables (in this case latent surface temperature and deep ocean temperature); and a measurement function which models the measurements of surface temperature and deep ocean temperature. The SSM parametric form integrates six different physical parameters, i.e., ECS, C1, C2, Beta, Gamma1, Gamma2; and as well as four parameters for the noise terms of latent and measurement variables of surface and deep ocean temperature.

2. The methodology follows a common Bayesian inference approach. The GCM simulations of global average temperature are used as the input of the SSM (along with provided SSP forcing time series) to obtain parameter posteriors unique to each GCM. These parameter posteriors represent the information obtained from the GCMs. Subsequently, these parameter posteriors were processed and combined as GCM-informed priors to further process observations.

3. Both pseudo observations and historical observations are used to obtain parameter posteriors and to obtain final future projections of global average temperature. Different amounts of observations are assumed and used, leading to analysis results on ECS and TCR posterior distributions based on different amounts of historical observations and as well as projection results for the pseudo observation series when different amounts of such observations are used. Projections from using historical observations up to 2022 are also provided.