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Méso-NH
Méso-NH Documentation
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a7aa3901
Commit
a7aa3901
authored
7 years ago
by
CHABOUREAU Jean-Pierre
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Jean-Pierre 29/01/2018: updating SLEVE coordinate
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ScieDoc/1-3-CoordinateSystems.tex
+11
-4
11 additions, 4 deletions
ScieDoc/1-3-CoordinateSystems.tex
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11 additions
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4 deletions
ScieDoc/1-3-CoordinateSystems.tex
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a7aa3901
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% March 2008, J.-P. Chaboureau, editorial corrections
% June 2008, E. Richard, adding the SLEVE coordinate part
% January 2018, J.-P. Chaboureau, fixing the SLEVE formulation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\chapter
{
Coordinate Systems
}
...
...
@@ -33,7 +34,8 @@ We use a system of curvilinear coordinates $\widehat{x},\widehat{y},
The vertical coordinate
$
\hat
z
$
is a height-based
terrain-following coordinate which can be alternatively selected as
the classical Gal-Chen and Sommerville (1975) coordinate or as the
SLEVE coordinate more recently proposed by Sch
\"
ar et al. (2002).
SLEVE coordinate proposed by Sch
\"
ar et al. (2002)
and modified by Leuenberger et al. (2010).
The Gal-Chen and Sommerville coordinate is defined by
\begin{equation}
\hat
z = H
\frac
{
z-z
_
s
}{
H-z
_
s
}
,
...
...
@@ -62,10 +64,11 @@ respectively. In practice, the large-scale contribution is obtained from the
full topography by an appropriate smoothing operation. The SLEVE coordinate
is then defined by the relationship
\begin{equation}
\label
{
slevecoord
}
z=
\hat
z
+ z
_{
s1
}
\frac
{
\sinh
[(H
-
\hat
z
)
/s
_
1]
}
{
\sinh
[(H/s
_
1)]
}
+ z
_{
s2
}
\frac
{
\sinh
[(H
-
\hat
z
)
/s
_
2]
}
{
\sinh
[(H/s
_
2)]
}
z=
\hat
z
+ z
_{
s1
}
\frac
{
\sinh
[(H
/s
_
1)
^
n-(
\hat
z/s
_
1
)
^
n
]
}
{
\sinh
[(H/s
_
1)
^
n
]
}
+ z
_{
s2
}
\frac
{
\sinh
[(H
/s
_
2)
^
n-(
\hat
z/s
_
2
)
^
n
]
}
{
\sinh
[(H/s
_
2)
^
n
]
}
\end{equation}
where
$
n
$
is a real number, set to 1.15.
The second and the third terms in the right-hand side of (
\ref
{
slevecoord
}
)
govern the decay with height of large- and small-scale terrain features
with the scale heights
$
s
_
1
$
and
$
s
_
2
$
, respectively.
...
...
@@ -680,6 +683,10 @@ Phillips, N. A., 1966:
The equations of motion for a shallow rotating atmosphere and the "traditional approximation".
{
\it
J. Atmos. Sci
}
,
{
\bf
23
}
, 626-628
\decrefname
Leuenberger, D., M. Koller, O. Fuhrer, and C. Sch
\"
ar, 2010:
A Generalization of the SLEVE Vertical Coordinate.
{
\it
Mon. Wea. Rev.,
}
,
{
\bf
138,
}
3683–3689, https://doi.org/10.1175/2010MWR3307.1
\decrefname
Sch
\"
ar, C., D. Leuenberger, O. Fuhrer, D. L
\"
uthi, and C. Girard, 2003:
A new terrain-following vertical coordinate formulation
for atmospheric prediction models.
...
...
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