\documentstyle{article}
\begin{document}

{\Large{\center Spurious Moisture Source \\}}

\vspace{5mm}

In the polar latitudes, one expects precipitation to be uniform as
most of it is the direct result of propagating synoptic-scale
disturbances.  However, the Reanalysis precipitation has many 
quasi-stationary small-scale features whose relationship to
orography seems quite obvious.  Prevailing wisdom was that this
precipitation was the so called ``spectral rain'', an artifact of
the Gibb's phenomenon in spectral models.

In August 1996, R. Kistler, M. Iredell and H. Pan decided to
to figure out the reason for this ``spectral rain''.  They found
that by shutting off the horizontal diffusion of moisture in the
boundary layer, the ``spectral rain'' can be reduced or eliminated.
That is when S. Moorthi pointed out, what he had discovered a few
months earlier while applying horizontal diffusion in his
semi-Lagrangian model (MWR, Moorthi 1997), that the culprit is
not the diffusion itself, but the approximation of the correction
term and that the resulting rain is not ``spectral rain'' but
``spurious rain''.  He also showed that the observation made by 
Kistler, Iredell and Pan can be easily explained.  Subsequently,
it was confirmed that by eliminating the correction term,
this ``spurious rain'' indeed disappeared.

All models have diffusion of quantities such as vorticity, humidity and 
temperature.  One would expect the diffusion to be anisotropic; different
diffusion constants/parameterizations for the vertical and horizontal 
directions.  Ocean modelers have long considered that diffusion takes
place more easily on isentropic surfaces than for other directions.
As a result, they parameterize diffusion along the the isentropic surface
differently than the diffusion in the direction perpendicular to that
surface.  Originally the MRF considered two types of diffusion,
vertical diffusion and diffusion along the sigma surfaces.  Later the
diffusion was divided into vertical diffusion and diffusion along the
pressure surfaces.  Since the exact evaluation of diffusion on 
pressure surfaces is a costly operation, an approximation was made,

\begin{equation}
\nabla ^2_p q \approx \nabla^2_\sigma q - \frac{\partial \overline{q}}
   {\partial \ln \sigma} \nabla^2_\sigma \ln P_s
\end{equation}
where $P_s$ is the surface pressure and $\overline{q}$ is the global
average of $q$, the specific humidity.

This approximation (1) is very cheap as both terms can be evaluated spectrally.
This is very important as one does not want to use a large number of CPU 
cycles on a small term such as diffusion.  This change was found to improve 
the model in regions of strong orography.  

At high latitudes and elevations, $q$, the specific humidity, is much 
smaller than 
the global average of specific humidity, $\overline{q}$. As a result, 
the horizontal diffusion is dominated by the second term; i.e.,

\begin{equation}
 \nabla ^2_p q \approx - \frac{\partial \overline{q}} 
          {\partial \ln \sigma} \nabla^2_\sigma \ln P_s
\end{equation}

The above equation (2) shows that the first approximation (1) 
can lead to unreasonable errors in the specific-humidity diffusion.  
This spurious moisture source/sink can cause unrealistically
large or small amounts of precipitation.

A more accurate approximation of the moisture diffusion is planned for
the next Reanalysis; however, no change will be made
to the current Reanalysis.  The operational forecast model was
``fixed'' by removal of last term in equation 1 (NWS Office of
Meteorology, Technical Procedures Bulletin 443, 
http://www.nws.noaa.gov/om/tpb/443.htm, note equation 1 of the 
bulletin is incorrect).  A post-processing correction may be done.
In this case, the some of the excess precipitation associated with
this spurious moisture source may be removed.  Of course, this correction
will be crude as it is impossible to recover the precipitation that
would have occurred if a better moisture diffusion were used.  Other
terms such as precipitable water, 2 meter relative humidity, latent heat 
release, were also affected by the spurious moisture source/sink but 
the no bias removal is planned.

As always, the Reanalysis precipitation is based on the model physics and
is not based not rain gauge, radar or satellite estimates of precipitation.
In general, model parameterizations of clouds and precipitation are often
considered to be two of the weakest areas in atmospheric modeling.  
(This situation may change with high-resolution models which can use ``micro-physics''.)
For people who need the actual precipitation, rain gauge data
is the most accurate, followed by radar and then satellite estimates of
precipitation.  The Party line is that the anomalies in the Reanalysis
precipitation are more similar to the observed anomalies than the
Reanalysis precipitation is to the total rainfall.


\end{document}
