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\begin{document}

\title{Bayesian History Matching applied to the calibration of a gravity wave
parameterization}



\author[1]{Robert C King}%
\author[1]{Laura A Mansfield}%
\author[1]{Aditi Sheshadri}%
\affil[1]{Stanford University}%


\vspace{-1em}



  
  \date{May 23, 2024}


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\begin{abstract}
Breaking atmospheric gravity waves in the tropical stratosphere are
essential in driving the roughly two year oscillation of zonal winds in
this region known as the Quasi-Biennial Oscillation (QBO). As Global
Climate Models (GCM)s are not typically able to directly resolve the
spectrum of waves required to drive the QBO, parameterizations are
necessary. Such parameterizations often require knowledge of poorly
constrained physical parameters. In the case of the spectral gravity
parameterization used in this work, these parameters are the total
equatorial gravity wave stress and the half width of phase speed
distribution. Radiosonde observations are used to obtain the period and
amplitude of the QBO, which are compared against values obtained from a
GCM. We utilize two established calibration techniques to obtain
estimates of the range of plausible parameter values: History Matching
\& Ensemble Kalman Inversion (EKI). History Matching is found to reduce
the size of the initial range of plausible parameters by a factor of
98\%, requiring only 60 model integrations. EKI cannot natively provide
any uncertainty quantification but is able to produce a single best
estimate of the calibrated values in 25 integrations. When directly
comparing the approaches using the Calibrate, Emulate, Sample method to
produce a posterior estimate from EKI, History Matching produces more
compact posteriors with fewer model integrations at lower ensemble sizes
compared to EKI; however, these differences become less apparent at
higher ensemble sizes.%
\end{abstract}%



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