\chapter{ARTS Units and Conversion Factors}
 \label{app:arts_units}


\starthistory
  2001-21-05 & Created by Thomas Kuhn. \\
\stophistory

 This appendix gives an overview of the arts physical units 
 and how they can be converted to other common unit systems.
 The internal physical units of arts for frequencies is $[$Hz$]$,
 for pressure $[$Pa$]$ and for the absorption coefficient $[$1/m$]$.
 Table \ref{tab:app_arts_units} gives some common conversion
 coefficients to arts units.

\begin{table}[!thb]
  \begin{center}
  \begin{tabular}{lllllllllll}
   \hline
   $x$ & g/cm$^3$ & = & $y$ & kg/m$^3$ & $\Leftrightarrow$ & $y$ & = &
   $x$ & $\times$ & $10^{3}$ \\
   $x$ & g/m$^3$  & = & $y$ & kg/m$^3$ & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{-3}$ \\
   $x$ & GHz      & = & $y$ & Hz       & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $ 10^{9}$ \\
   $x$ & 1/GHz    & = & $y$ & 1/Hz     & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{-9}$ \\
   $x$ & hPa      & = & $y$ & Pa       & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{2}$ \\
   $x$ & 1/hPa    & = & $y$ & 1/Pa     & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{-2}$ \\
   $x$ & 1/cm     & = & $y$ & 1/m      & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{2}$ \\
   $x$ & 1/km     & = & $y$ & 1/m      & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{-3}$ \\
   $x$ & dB       & = & $y$ & Np       & $\Leftrightarrow$ & $y$ & = & $x$ & / & $[10\cdot\log{(e)}]$ \\
   $x$ & dB/km    & = & $y$ & 1/m      & $\Leftrightarrow$ & $y$ & = &
   $x$ & $\times$ & $10^{-3} / [10\cdot\log{(e)}]$ \\
   $x$ & Np/km    & = & $y$ & 1/m      & $\Leftrightarrow$ & $y$ & = & $x$ & $\times$ & $10^{-3}$ \\
   \hline
 \end{tabular}
 \end{center}
 \caption{Conversion factors for the physical units used in arts.}
 \label{tab:app_arts_units}
\end{table}

Especially for the MPM model versions
\citep{liebeandlayton:87,liebe:89,liebeetal:93} 
we get for the pre-factor:
\begin{eqnarray}
   \frac{4\cdot\pi}{c} \cdot 10 \cdot \log(e) &=& 0.1820 \cdot 10^{6}~\mbox{dB/km/GHz}\\
                                              &=& 0.1820 \cdot 10^{-6}~\mbox{dB/m/Hz}
\end{eqnarray}
where $c$ is the speed of light ($c=2.9979\cdot 10^{8}$m/s).



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