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

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John Matthew Nicklas , Baylor Fox-Kemper, Charles E Lawrence


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 annual energy balance model (difference equations) with 17 parameters drawn from the literature and a statistical Extended Kalman Filter assimilating GMST and OHCA, either observed timeseries or simulated by earth system models. Our motivation is to create an efficient and natural estimator of the climate state and its uncertainty, which we believe to be Gaussian at a global scale. We illustrate four applications: 1) EBM-KF generates a similar estimate to the 30-year time-averaged climate state 15 years sooner, or a model-simulated hindcasts’ annual ensemble average, depending on the preparation of volcanic forcing. 2) EBM-KF conveniently assesses annually likelihoods of crossing a policy threshold, e.g., based on temperature records up to the end of 2023, p=0.0017 that the climate state was 1.5°C over preindustrial, but a 16% likelihood that the GMST in 2023 itself could have been over that threshold. 3) The EBM-KF also approximates the spread 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. This sampling with the EBM-KF better determines how future volcanism may affect when policy thresholds will be crossed and what an ensemble with thousands of members exploring future intermittent volcanism reveals.




Longitudinal Data Analysis and Time Series, Non-linear Dynamics, Planetary Sciences, Statistical Models


Kalman filters, time series, uncertainty, temperature, climate models, Ensembles, interannual variability


Published: 2022-10-19 01:50

Last Updated: 2024-04-05 20:47

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CC BY Attribution 4.0 International