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\begin{document}

\title{Decomposition of the horizontal wind divergence associated with the
Rossby, inertia-gravity, mixed Rossby-gravity and Kelvin waves on the
sphere}



\author[1]{Valentino Neduhal}%
\author[1]{Nedjeljka Žagar}%
\author[1]{Frank Lunkeit}%
\author[2]{Inna Polichtchouk}%
\author[3]{Žiga Zaplotnik}%
\affil[1]{Meteorological Institute, Center for Earth System Research and Sustainability, Universität Hamburg}%
\affil[2]{European Centre for Medium-Range Weather Forecasts}%
\affil[3]{Faculty of Mathematics and Physics, University of Ljubljana}%


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  \date{May 26, 2024}


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\begin{abstract}
The paper presents a new method for the decomposition of the horizontal
wind divergence among the linear wave solutions on the sphere:
inertia-gravity (IG), mixed Rossby-gravity (MRG), Kelvin and Rossby
waves. The work is motivated by the need to quantify the vertical
velocity and momentum fluxes in the tropics where the distinction
between the Rossby and gravity regime, present in the extratropics,
becomes obliterated. The new method decomposes divergence and its power
spectra as a function of latitude and pressure level. Its application on
ERA5 data in August 2018 reveals that the Kelvin and MRG waves made
about 6\% of the total divergence power in the upper troposphere within
10S-10N, that is about 25\% of divergence. Their contribution at
individual zonal wavenumbers k can be much larger; for example, Kelvin
waves made up to 24\% of divergence power at synoptic k in August 2018.
The relatively small roles of the Kelvin and MRG waves in tropical
divergence power are explained by decomposing their kinetic energies
into rotational and divergent parts. The Rossby wave divergence power is
0.3-0.4\% at most, implying up to 6\% of global divergence due to the
beta effect. The remaining divergence is about equipartitioned between
the eastward- and westward-propagating IG modes in the upper
troposphere, whereas the stratospheric partitioning depends on the
background zonal flow. This work is a step towards a unified
decomposition of the momentum fluxes that supports the coexistence of
different wave species in the tropics in the same frequency and
wavenumber bands.~%
\end{abstract}%



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