Efficient Estimation of Climate State and Its Uncertainty Using Kalman Filtering with Application to Policy Thresholds and Volcanism

ABSTRACT
We present the Energy Balance Model – Kalman Filter (EBM-KF), a hybrid model of the global mean surface temperature (GMST) and ocean heat content anomaly (OHCA). It combines an energy balance model with parameters drawn from the literature and a statistical Extended Kalman Filter assimilating observed and/or earth system model-simulated GMST and OHCA. Our motivation is to create an efficient and natural estimator of the climate state and its uncertainty. Our climate emulator has the physical rationale of an annual energy budget, and is compatible with an Extended Kalman Filter both because it forms a set of difference equations (involving 17 constants) and because climate models and historical records of GMST and OHCA follow nearly Gaussian distributions about their relevant means. We illustrate four applications: 1) EBM-KF generates a similar estimate to the 30-year time-averaged climate state 15 years sooner. 2) EBM-KF conveniently assesses annually the likelihood of crossing a policy threshold, e.g., 2°C over preindustrial. 3) The EBM-KF also approximates the behavior of an entire climate model large ensemble using only one or a few ensemble members. 4) The EBM-KF is sufficiently fast to allow thorough sampling from non-Gaussian probabilistic futures, e.g., the impact of rare but significant volcanic eruptions. Indeed, volcanic eruptions dominate the future uncertainty over the slowly growing GMST climate state uncertainty. This sampling with the EBM-KF better determines how future volcanism may affect when policy thresholds will be crossed and what a larger-than-large ensemble including future intermittent volcanism would reveal.

SIGNIFICANCE STATEMENT
The global average of the Earth's historical climate over the past 150 years can be explained by a thermal/radiation physics equation involving a small number of constants (17), atmospheric CO2, human-produced cloud-seeding aerosols, and dust from volcanic eruptions. Global mean surface temperature measurements vary around this climate state within a consistent normal distribution. This physics equation and statistical depiction allowed us to construct a simple model that can rapidly estimate the uncertainty in Earth’s current climate, aid in policy discussions, and reduce ensemble modeling costs.