Geoscience Reference
In-Depth Information
weighting function
R
H
of 3 km and a variable vertical radius of influence
R
V
that matches
the beamwidth of ARAMIS radars.
Term
B
is given by:
2
u
v
1
w
Buvw
,,
(4)
1
xy
z
where is the air density and
1
is a normalized weighting parameter that controls the
relative importance of this term with respect to term A.
This term
represents the least-squares adjustment with respect to mass continuity. It is
formulated for each individual grid box in terms of mass flux throughout the faces of the
considered box, which allows solving the wind field over both flat and complex terrains
(Chong and Cosma 2000). In this formalism the wind components estimated at the
previously investigated plane are used as input values to solve the wind at the current level.
In order to initialize the wind synthesis, horizontal components are assumed constant
between the surface and the first plane for which the solution for the wind components is
searched.
Term C
is given by:
2
C uvw
,,
Ju
()
Jv
()
Jw
( )
(5)
2
where
J
is a differential operator based on 2
nd
and 3
rd
derivatives of the wind components
[see Bousquet and Chong (1998) for the detailed expression of this term].
It is a constraint that acts as a low pass filter. Term C allows decreasing small-scale wind
variations through the minimization of the second- and third order derivatives. It is
controlled by a weighting factor
2
, which is a function of the cutoff wavelength of the filter.
In addition to provide more regular fields, this term is also essential to obtain an objective
solution in regions of ill-conditioned analysis through realizing a regular extrapolation in
these regions from surrounding properly conditioned areas.
Finally, D is given by:
2
2
2
2
(
u
sin
v
sin
cos
)
(
u
sin
cos
v
cos
)
i
i
i
i
i
i
Du v
(,)
(6)
3
x
y
where
3
is given by:
4
cos
(7)
3
m
and
m
defines the angle between the horizontal projection of the two radar beam axes.
Term D is a constraint that is applied in regions covered by only 2 radars. It allows
minimizing the variation of the cross-baseline component of the wind. Its effect is maximum
close to the radar baseline and weak in properly conditioned areas (the reader is referred to
Bousquet et al. 2008b for more details about this specific term).
