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\begin{document}

\title{What is the neutral wind in height-integrated ionospheric
electrodynamics?}



\author[1]{Spencer Mark Hatch}%
\author[2]{Johnathan K. Burchill}%
\author[3]{Heikki Vanhamäki}%
\author[4]{Rafael Luiz Araujo de Mesquita}%
\author[5]{Karl Laundal}%
\author[2]{David J. Knudsen}%
\affil[1]{Birkeland Centre for Space Science}%
\affil[2]{University of Calgary}%
\affil[3]{University of Oulu}%
\affil[4]{Johns Hopkins University Applied Physics Laboratory}%
\affil[5]{University in Bergen}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
In most large-scale MHD models of Earth's space environment, coupling
between the magnetosphere and the ionosphere-thermosphere (IT) is
addressed by representing the latter as a two-dimensional spherical
shell. Similarly, most empirical models of IT electrodynamics are based
on solving the height-integrated ionospheric Ohm's law on a spherical
shell. We show that there is in general no single suitable definition of
the neutral wind term in high-latitude, height-integrated IT
electrodynamics. Instead, two neutral wind terms weighted by Hall and
Pedersen conductivities appear. We show that a commonly used expression
for Joule heating in terms of height-integrated quantities is a lower
bound of the actual Joule heating. Using neutral wind profiles derived
from sounding rocket chemical release experiments near Poker Flat,
Alaska, and Poker Flat Incoherent Scatter Radar (PFISR) measurements, we
find differences of order 10--100 m/s between the two neutral wind
terms.%
\end{abstract}%



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