Doppler radar analysis techniques - Severe Convective Storms and Tornadoes: Observations and Dynamics - page 432

technique requires a relatively long dwell time and averaging in space, so that the
spatial and temporal resolutions are degraded. However, one does not need to
worry about having the target storm appear only in a very limited volume.
It is also possible to estimate the wind field using only one Doppler radar
by making use of the tracking of reflectivity elements. The equation for the con-
servation of radar reflectivity is
@ =@

t ¼ u

@ =@

x v @

=@

y w

@ =@

z þð source and sink terms Þ A

:

6 Þ R R R R

If we ignore the source and sink terms and if the local time derivative term and
advection terms are known from the radar reflectivity field, then (A.1), (A.6), and
the equation of continuity are three independent equations in three unknowns.
Again, the time-dependent vorticity equation or mass continuity may be used as
constraints to solve for the three-dimensional wind field, and terminal fall velocity
must be accounted for.
The two-dimensional wind field has also been estimated using TREC (tracking
radar echoes by correlation), in which the horizontal wind direction and speed are
estimated from the highest correlation between the radar reflectivity field for two
successive scans of a limited area, one scan lagged with respect to the other. This
procedure and the previous one fail when vertical motions are significant, when
condensation or evaporation/sublimation is significant, when the radar reflectivity
field is very noisy, or when the radar reflectivity field is perfectly uniform.
A retrieval technique for estimating thermodynamic variables based on the
wind field derived from Doppler radar wind data is discussed in the main body of
the text in Section 2.5.2. This technique may be improved upon by using a
thermodynamic equation as a weak constraint. The retrieval of thermodynamic
fields from wind data is sensitive to the vertical velocity field and its time
derivative, which are not estimated very well.
More recently, researchers have incorporated Doppler radar data into
numerical models using data assimilation techniques to estimate thermodynamic
variables, which are not measured directly by Doppler radars, and to obtain esti-
mates of the three-dimensional wind field when multiple-Doppler analyses are not
possible. It has been found that when data from radars at different locations are
assimilated, the accuracy of retrieved variables is increased. If a good fit of obser-
vational data to model ''data'' (i.e., to numerically simulated variables) can be
obtained, then one can do diagnostic studies of the model data, which contain
thermodynamic information in addition to the wind field. How to assimilate data
into models is an area of current research and it is somewhat of an art to deter-
mine the best way to process the data. Ideally, one would expect the model, if left
alone, to make a relatively ''good'' prediction of future events in order for one to
trust retrieved variables enough to make diagnostic computations based on them,
relevant to testing hypotheses.
When a best fit in the least square sense (i.e., through a variational analysis,
involving cost functions) is found between wind data and their temporal evolution,
the technique is referred to as 4DVAR, or four-dimensional variational analysis.
An alternative to 4DVAR is the ensemble Kalman filter (EnKF) approach, in