Parameter inference and uncertainty quantification for an intermediate complexity climate model

Well-adapted parameters in climate models are essential to make accurate predictions
for future projections. In climate science, the record of precise and comprehensive obser-
vational data is rather short and parameters of climate models are often hand-tuned or
learned from artificially generated data. Due to limited and noisy data, one wants to use
Bayesian models to have access to uncertainties of the inferred parameters. Most popu-
lar algorithms for learning parameters from observational data like the Kalman inversion
approach only provide point estimates of parameters.
In this work, we compare two Bayesian parameter inference approaches applied to the
intermediate complexity model for the El Niño-Southern Oscillation by Zebiak & Cane. i)
The "Calibrate, Emulate, Sample" (CES) approach, an extension of the ensemble Kalman
inversion which allows posterior inference by emulating the model via Gaussian Processes
and thereby enables efficient sampling. ii) The simulation-based inference (SBI) approach
where the approximate posterior distribution is learned from simulated model data and
observational data using neural networks.
We evaluate the performance of both approaches by comparing their run times and the
number of required model evaluations, assess the scalability with respect to the number
of inference parameters, and examine their posterior distributions.