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ATMOSPHERIC SCIENCE LETTERS
Atmos. Sci. Let. 6: 152–159 (2005)
Published online 27 September 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asl.109
Comparison of four non-hydrostatic models for flow over
the Isle of Arran
Juma Al-Maskari* and Alan M. Gadian
School of the Environment, University of Leeds, Leeds, UK
*Correspondence to:
Juma Al-Maskari, School of the
Environment, Leeds University,
Leeds, LS2 9JT, UK.
E-mail: juma@env.leeds.ac.uk
Received: 28 October 2004
Revised: 23 May 2005
Accepted: 10 June 2005
Abstract
Four non-hydrostatic atmospheric models were compared for a case study of southerly
airflow over the Isle of Arran in Scotland. The model results are contrasted with each other
and aircraft wind observations. All resolve qualitatively similar the background gravity
wave flow, despite different formulations. Copyright  2005 Royal Meteorological Society
Keywords: numerical atmospheric non-hydrostatic model inter-comparison; flow over
steep slopes
1. Introduction
One of the challenges that faces small-scale nonhydrostatic models is the simulation of flow over steep
terrain, i.e. where gradients exceed 45◦ , including the
generation of gravity waves. Gravity waves generated
by flow over hills propagate downstream, depending
on the background winds and stratification. They
can break or dissipate, allowing the deposition of
momentum at higher altitudes. It is impossible to
quantitatively evaluate different aspects of a model
from an individual study such as this, but intercomparison studies do provide useful tools in the
modelling community (Doyle et al., 2000) to analyse
characteristics of the equation sets and numerical
methods. Comparison with observed fields provides
an estimate of their accuracy.
Four meso-scale non-hydrostatic models are applied
to the flow over the island. For brevity, the vertical
velocity fields are compared with each other and
aircraft observations. The models’ characteristics are
summarised in the next section, and the set-up and
the synoptic situations are described in Section 3.
Analyses of the results are covered in Section 4,
followed by the conclusions in Section 5.
2. Description of the models
The four meso-scale models used in the comparison
are the Clark, Smolarkiewicz, BLASIUS (Boundary
Layer Above Stationary Inhomogeneous Uneven Surfaces), and the UK Met Office Unified Model (V5.3
‘New Dynamics’). The characteristics of the model
options employed in this study, selected purposely to
maximize the range of numerical designs, are summarised in Table 1.
The Clark and Hall model (Clark, 1977, 1979),
which uses the anelastic equation set (Lipps and
Copyright  2005 Royal Meteorological Society
Hemler, 1982), has been applied to a wide range
of meso-scale atmospheric processes including flow
over complex terrain (Thielen et al., 2002; Clark et al.,
1997). The model is non-hydrostatic time-dependent,
with a regular Cartesian grid in the horizontal and a
terrain following vertical coordinate (Gal Chen and
Somerville, 1975).
The same anelastic equation set is used in the
Smolarkiewicz model. It has both semi-Lagrangian
(Smolarkiewicz and Pudykiewicz, 1992) and Eulerian
(used here) schemes, (Smolarkiewicz and Margolin,
1993). It has been used for a variety of problems
including small and large-amplitude internal gravity
wave problems and orographic precipitating clouds.
This model is run (here) in an inviscid mode, and,
as with the Clark model, assumes a free slip lower
boundary condition and terrain following coordinates.
The BLASIUS model (Mason, 1987; Wood and
Mason, 1991) employs the same terrain following
coordinate system and selectively solves Boussinesq
or anelastic equations. The leapfrog numerical scheme
used in the model is the same as the Clark model, but
with the option of carrying turbulent kinetic energy
as a prognostic variable. The model normally uses a
boundary layer mixing length proportional to height
near the ground and approaches a constant value (40 m
in this study) with increasing height. Stratification
effects are taken into account via a Richardson number
dependency of the eddy viscosity. Above a critical
value (0.3 in this study) the eddy viscosity is set to
zero.
The UK Met Office Unified Model differs, as it
is a fully compressible model and has hybrid Gal
Chen terrain following vertical coordinates but is used
here in the same form as the other models. A SemiLagrangian advection scheme with semi-implicit time
stepping, but no horizontal diffusion, is applied. The
boundary layer scheme is turned off and there is no
turbulence closure even in the boundary layer. The
Comparison of four non-hydrostatic models for flow over the Isle of Arran
153
Table I. Summary of the main set-up of the four models in this case study
Description
Clark
Smolarkiewicz
Anelastic/Lipps and
Hemler (1982)
Gal Chen and Somerville
(1975) terrain following
coordinates
Staggered Arakawa
(1966) C-grid
Anelastic/Lipps & Hemler
Anelastic/Boussinesq
Fully compressible(Cullen, 1993)
Gal Chen terrain
following coordinates
Gal Chen terrain
following coordinates
Gal Chen terrain following up to
an arbitrary height
Non-staggered Arakawa
A-grid
Staggered Arakawa
C-grid
Advection scheme and
time stepping
Turbulence closure
Explicit second-order
accurate leapfrog scheme
Smagorinsky (1963)
scheme and free slip
Semi-implicit & NFT
Eulerian
Free slip inviscid
Model
Explicit second-order
accurate leapfrog scheme
Linear mixing length
and no slip lower b.c.
(also a run with free slip)
Arakawa C-grid staggering in the
horizontal and Charney–Phillips
in the vertical
Semi-implicit semi-Lagrangian
Lateral boundary
relaxation
1 km
12 km
4.5 km
Equations
Coordinate system
Grid structure
UM is designed as an operational model as well as
a research model. In this research mode, small time
steps are used to satisfy the Courant Friedrich and
Lewy (CFL) condition. The fully compressible set
of equations is better for large-scale GCMs when
modelling deep atmospheres, but not considered of a
great advantage for shallow flows.
The models use different grid structures. The Smolarkiewicz model has an A-grid which is generally fast,
but not considered as accurate for modelling flows
as the C-grid used in the other three models (Durran, 1998). The Charney–Phillips staggering grid in
the vertical in the UM reduces spurious gravity wave
generation. (Cullen, 1993).
The Clark and BLASIUS models both use an
explicit second-order accurate leapfrog scheme compared to the semi-implicit time integration used in the
UM and Smolarkiewicz models. The leapfrog requires
only one function evolution per unit time step, but
the weakness is that undamped computational modes
can slowly amplify and can, but not seen here, generate a time-splitting instability (Durran, 1998). The
UM model uses a semi-Lagrangian scheme, which,
when combined with a semi-implicit time stepping,
brings greater stability (Cullen, 1993) and can be
more efficient than Eulerian methods (Durran, 1998).
Ritchie et al., 1995, show that the semi-implicit semiLagrangian method, with a 15-min time step, has
equivalent accuracy and is more efficient than the
semi-implicit Eulerian method, with a 3-min time step.
However, small time steps are used in the UM simulation so that gravity wave modes can be accurately
approximated and the CFL condition is satisfied. None
of the four models uses time filters; they were all run
with a 4-s time step.
For all models, a Helmholtz or Poisson equation for
the pressure must be solved at every time step. Both
Smolarkiewicz and the UM use an iterative generalized conjugate residual (GCR) technique, accelerated
by an Alternating Direction Implicity (ADI) preconditioner (Thomas et al., 2003), for improving efficiency.
Copyright  2005 Royal Meteorological Society
BLASIUS
UM
No turbulence closure
1 km
No turbulence closure is used in the UM model,
implicit diffusion being provided by the semi-implicit
Semi-Lagrangian scheme. The BLASIUS uses a mixing length closure of 40 m, whereas the Clark model
uses a first-order closure scheme of Smagorinsky
(1963). The use of an inviscid model does not produce significantly different results from the viscous
model for this type of gravity wave simulations, (Thielen et al., 2002). Smagorinsky (1963), proposed that
the effective Laplacian viscosity due to unresolved
scales should be proportional to the resolved horizontal
deformation rate multiplied by the squared grid spacing. This scheme parameterises the effects of three
dimensional isotropic turbulence and is defined by
νT = (Cs g )2 (2 Sij Sij )1/2
Where, νT is the eddy viscosity, and Cs is the
Smagorinsky coefficient, and g is the grid spacing
and Ŝij is the resolved strain rate tensor. In the
BLASIUS scheme, the first bracket is approximated
by the mixing length l.
3. Setting up the case study
The four models are initialised with a profile (see
Table 2) based on a combination of the radiosonde
ascent and aircraft data for 1200 UTC, 4 April 1996.
The model domain is approximately 74 by 54 km with
266 by 196 grid points in the horizontal and 45 levels
in the vertical, a grid spacing of 280 m, a smoothed
topography field derived from a 50-m data set.
Figure 1(a) shows a height contour map of the
orography of the domain used with the axis being
in model grid points. The solid line AB shows the
approximate aircraft track from A (upwind) to B
(downwind). The synoptic map, Figure 1(b), shows a
blocking high pressure system over Denmark and the
eastern North Sea and a stationary low pressure system
situated in the mid-Atlantic west of the Bay of Biscay
with a second low pressure to the south of Iceland.
Atmos. Sci. Let. 6: 152–159 (2005)
154
J. Al-Maskari and A. M. Gadian
Table II. The profile used to initialise the models
Pressure
(mb)
T
(C)
Wind direction
(degrees)
Wind speed
(m/s)
Vapour
(g/kg)
1026.3
1022.6
1015.4
1004.6
991.5
975.1
956.1
936
915
892.9
869.8
845.1
816.8
783.2
744.4
700.4
651.1
596.6
539.5
482.4
422.7
360.6
304
252.6
201.4
150.4
99.5
56.9
6.2
5.9
5.4
4.6
3.6
2.4
1.4
1.1
0.3
0.5
0.4
0
−0.8
−2
−3.6
−6.8
−9.9
−14.6
−20
−24.1
−30.2
−38.1
−48.3
−59.9
−68.6
−62.8
−61.4
−62.6
187.8
187.7
187.4
187.1
187.4
187.1
186.2
182.7
178.2
173.9
169.5
165.4
163.9
158.5
155.8
162.2
164.1
158.1
158.4
159.6
163.1
154
139.4
112.8
103.9
94.1
73.9
63.8
11.2
12.7
13.6
14.5
15.3
16.5
16.7
16.6
16.4
16.1
15.8
15.6
15.6
14.7
14.2
12.7
14
15.1
13.6
15
15.3
16.3
13.6
12.8
12
10.8
16
25.2
3.3
3.3
3.3
3.2
3.1
2.6
1.3
0.7
0.7
0.2
0.7
0.6
0.8
0.7
1.4
0.6
1.9
0.9
0.2
0.1
0.5
0.3
0.1
0
0
0
0
0
Consequently, the surface wind at Prestwick airport
was around 10 m/s south-south-easterly midday on
4th April, veering to a fairly steady 15 m/s southerly
wind between 1000 m and 3000 m. The boundary
layer was capped with a 5 ◦ C inversion at around
1600 m. Convection was suppressed in regions of
downward wave motion and enhanced in the upward
wave, resulting in a banded cloud field extending to
the boundary layer inversion.
The UMIST Cessna aircraft flew in upwind/downwind direction as in Figure 1(a). Boundary layer cloud
into ‘bands’ roughly perpendicular to the wind direction indicated that the direction of wave propagation was close to the direction of the wind. The
path of the aircraft was chosen so as to sample as
much of the downwind orographically disturbed air
motion as possible. The aircraft flew at several levels in the vertical, but, for brevity, only one height is
shown, while others are briefly commented on. The
aircraft data was recorded with spatial resolution of
∼5 m.
4. Analysis of the results
The four models are run for 50 min, outputing every
minute. The model spin appears to take less than
30 min, but only values from 40 to 50 min are shown
in the analysis. The Smolarkiewicz model was also
run for up to 90 min (not shown here) and gave no
significant change.
Copyright  2005 Royal Meteorological Society
Figure 2 are still images from animation of the last
11 min of the models run for the vertical velocity
field at 1400 m for the four models. The Clark model
(upper right, Figure 2b) has clear evidence of a low
amplitude southern boundary induced mode, but all
four models are similar. The unfiltered profile was
used to enable an unbiased comparison. All produce
similar patterns and with close agreement in terms of
the magnitude of the vertical velocity and phase, as
described below. Figure 3 shows a vertical velocity
cross-section at 1400 m.
However, the BLASIUS model results differ in
terms of vertical velocity wavelength and amplitude
in the downstream region. The reasons are not clear.
When the lower boundary scheme in the BLASIUS
model is changed to a free slip condition (not shown
here), a similar wavelength pattern is produced, with
approximately a 10% increase in amplitude of vertical
velocity.
Additional sensitivity tests performed with the Smolarkiewiz model (e.g. testing solution dependence on
the domain size or vertical and temporal resolution) do
not provide a conclusive insight. The four models have
different outflow boundary relaxation lengths (see
Table 1), the Smolarkiewicz has the largest (12 km).
Increasing the domain size gave no effect on the interior flow. Therefore, it is unlikely that the smaller
relaxation length (4.5 km) in the BLASIUS model is
the cause of the larger downwind vertical velocity.
With both the BLASIUS and the Clark models having the same advection scheme, it is plausible that the
influence of the outflow boundary could be a factor,
but there is a need for further tests to investigate this.
Comparison between models and aircraft observations, Figure 3, shows differences in the fine details.
The reasons for this are partly the inability for the
models to resolve fine scale structures that are evident
in the aircraft observations and, therefore, there is a
need for higher model resolution grid spacing. Repeating the comparison for level 1960 m produces the
same conclusion. Table 3 shows a correlation between
the four models and aircraft observation. Further, close
agreement is reliant on an ‘accurate’ initial profile. One
sounding is unlikely to produce a good profile, and this
is reflected in the model results. Meso-scale models,
e.g. Thielen et al., 2002, are known to be sensitive to
initial profiles.
Both the UM and the Smolarkiewicz are significantly better correlated with each other and the observations, as shown in Table 3, than the other two models. The only significant similarity between these two
models is the pressure solver.
A power spectrum analysis (Bendat and Piersol,
1986) for vertical velocity at 1400 m of frequency versus spectral energy is given in Figure 4. A resolution
of 280 m used in the models is unable to resolve
the observed 400-m feature evident from the aircraft.
However, the power spectrum analysis shows that all
models are able to reproduce observed low-resolution
feature of wavelength ∼5 km.
Atmos. Sci. Let. 6: 152–159 (2005)
Comparison of four non-hydrostatic models for flow over the Isle of Arran
155
(a)
B
250
700
600
200
150
400
100
Height (m)
Y-index
500
300
A
200
50
100
20
40
60
80
100
120
140
160
180
X-index
(b)
Figure 1. (a) Height contour map of the orography of the domain used in the models and the line AB represents the approximate
aircraft track starting from point A. (b) Mean sea level synoptic chart analysis at 1200 UTC for 4 April 1996 (Crown copyright
1996 Published by the Met Office)
Table III. Correlation coefficient between models and aircraft
observation at t + 40 min at 1400 m
Clark
BLASIUS
Smolark.
UM
Aircraft
0.77
BLASIUS
0.87
0.64
Smolark.
0.74
0.62
0.90
UM
0.20
0.22
0.37
0.29
Copyright  2005 Royal Meteorological Society
Figure 5 is a wavelet power spectrum for vertical velocity at 1400 m for (A) aircraft observation,
(B) Smolarkiewicz model and (C) the UM model. The
Clark and BLASIUS models give similar wavelets
to the UM. Wavelet analysis (Torrence and Compo,
1998)) can be used to obtain the dominant wavelength
of a spatial, but equally spaced, data set. The black
triangle represents the cone of influence, which distinguishes between the area where the spectrum is
affected by the padding. The right side of Figure 5
gives the global wavelet spectrum. The solid line
Atmos. Sci. Let. 6: 152–159 (2005)
156
J. Al-Maskari and A. M. Gadian
Smolarkiewicz Model. Orography contours on top of w
at 1400m. 4/4/ 1996, t+40min
Clark Model. Orography contours on top of w
at 1400m. 4/4/ 1996, t+40min
250
250
200
100
50
0
50
100
100
50
0
150
0
50
X-Index
Blasius Model. Orography contours on top of w
at 1400m. 4/4/ 1996, t+40min
200
200
5.0
4.0
3.0
2.0
1.0
0.0
−1.0
−2.0
−3.0
−4.0
−5.0
150
100
50
0
100
150
Y-Index
250
ms−1
Y-Index
250
50
150
X-Index
UM Model. Orography contours on top of w
at 1400m. 4/4/ 1996, t+40min
0
100
ms−1
5
4
3
2
1
0
−1
−2
−3
−4
−5
150
5.0
4.0
3.0
2.0
1.0
0.0
−1.0
−2.0
−3.0
−4.0
−5.0
150
100
50
0
0
50
100
ms−1
0
Y-Index
150
ms−1
Y-Index
200
5.0
4.0
3.0
2.0
1.0
0.0
−1.0
−2.0
−3.0
−4.0
−5.0
150
X-Index
X-Index
Figure 2. Orography contours on top of vertical velocity (m/s2 ) at 1400 m for t + 40 min for the four models. (Upper left — a)
(Smolarkiewicz), (upper right — b) (Clark), (lower left — c) (UM), (lower right — d) (BLASIUS). The animation files can be found
on the supplementary materials page
shows the normalized wavelet spectrum, and the
dashed line is the mean red-noise spectrum. As with
the power spectrum, the model wavelet energy diagram reproduces the dominant wavelength pattern for
the observations. However, the models overestimate
the wavelet power. At approximately 2 km, there is a
second peak in the global wavelet energy spectrum,
which is poorly resolved by the models. The patterns
are similar in all diagrams, confirming that the models are replicating the observed energy spectra and the
ability of the models to simulate the important wave
features.
Semi-Lagrangian schemes are considered by some
to be at a disadvantage to Eulerian schemes because
the accuracy considerations often require that both
methods use similar time steps (Durran, 1998). In
the case of flow over steep orography, forcing that
is stationary in the Eulerian system is Doppler shifted
to a higher frequency in the Lagrangian coordinate
system (Pinty et al., 1995; Hereil and Laprise, 1996).
Any spurious orographic resonance can be treated with
a space and time average of the forcing term, together
Copyright  2005 Royal Meteorological Society
with a modification of the surface pressure equation as
given in Ritchie and Tanguay, 1996. However, Salerno
and Balsamo (2003) argue that in some cases this
treatment can be unsuccessful, especially at very high
resolution (<10 km), unless a small time step is used.
They show that a smoothing filter partially overcomes
this problem, but reduces the representation of the
orographic waves. The UM results show no evidence
of spurious resonances for the semi-Lagrangian semiimplicit scheme and these problems are probably
avoided by using a small time step of 4 s. Table 2
suggests the UM is better than the Clark and BLASIUS
models, and that none of these concerns are apparent.
5. Conclusion
An inter-comparison of vertical velocity of four mesoscale non-hydrostatic models and aircraft observations
is completed.
Model results are compatible with each other. The
overall gravity wave structure is well simulated in
Atmos. Sci. Let. 6: 152–159 (2005)
Comparison of four non-hydrostatic models for flow over the Isle of Arran
157
5.0
4.0
3.0
2.0
W (m/s)
1.0
UM_1400
Clark_1400
0.0
Smol_1400
Aircraft
−1.0
BLA_1400
−2.0
−3.0
0.8
km
0.6
Orography underneath flight path from left to right
0.4
0.2
0.0
Figure 3. Vertical velocity cross section at 1400 m for the 4 models and the aircraft observation (yellow). As in line AB Figure 1(a)
Power Spectrum for w at 1400 m
102
Aircraft
UM
Smola.
Clark
Blasius
100
Spectral energy
10−2
10−4
10−6
10−8
10−10
10−12
10−4
10−3
10−2
10−1
100
101
500 m
50 m
5m
Frequency
50 km
5 km
Figure 4. Vertical velocity power spectrum at 1400 m for the four models along the line AB (see Figure 1a), and aircraft
observation (blue)
Copyright  2005 Royal Meteorological Society
Atmos. Sci. Let. 6: 152–159 (2005)
158
J. Al-Maskari and A. M. Gadian
b) Global wavelet spectrum
a) Vertical velocity wavelet power spectrum
30
16
20
8
10
4
2
1
0
10
20
30
40
50
60
0
Wavelet power spectrum (m2 S2)
Horizontal wavelength (km)
(a)
0
20
Distance (km)
a) Vertical velocity wavelet power spectrum
b) Global wavelet spectrum
30
16
20
8
10
4
2
1
0
10
20
30
40
50
60
0
Wavelet power spectrum (m2 S2)
Horizontal wavelength (km)
(b)
0
Distance (km)
a) Vertical velocity wavelet power spectrum
b) Global wavelet spectrum
16
20
8
10
0
10
20
30
Distance (km)
40
Power
30
4
2
1
20
40
50
60
0
Wavelet power spectrum (m2 S2)
Horizontal wavelength (km)
(c)
40
Power
0
20
Power
40
Figure 5. Vertical velocity wavelet power spectrum for 1400 m. (A) Aircraft observation. (B) Smolarkiewicz model. (C) UM
model. The cone of influence is marked by the black triangle. The left side of the image shows the normalized global wavelet
spectrum (solid line), and the mean red-noise spectrum (dashed line)
all models. The inter-comparison with aircraft data
is consistent, and the Smolarkiewicz and the UM
model results correlate with a factor of 0.9, although
using different equation sets. The initial profile taken
from radiosonde and aircraft soundings introduces
uncertainties. The profile is not necessarily truly representative of the actual state of the atmosphere at
the time of the flights, 2 h later. This asks to what
degree we can hope to accurately model trapped
lee waves with a fixed single upwind profile. Finer
scale modelling is required to resolve the smaller
scale features, but with ever increasing computer
resources, higher resolution should improve the model
results.
Acknowledgements
The authors would like to thank the UK Met Office for allowing
them to use the new version of the New Dynamics and for the
Copyright  2005 Royal Meteorological Society
support given to set up the model. Special thanks should be
given to Richard Forbes and Simon Vosper. Also, we would
like to thank Chang-Gui Wang from UWERN support team
for the help with Jview, and to Terry Davies for his useful
comments. The authors are very grateful for the help and
assistance provided by Piotr Smolarkiewicz and for the aircraft
observations made by Ian Stromberg and Robert Wood.
References
Arakawa A. 1966. Computational design for long-term numerical
integration of the equations of fluid motion: two-dimensional
incompressible flow. Part I. Journal of Computational Physics 1:
119–143.
Bendat JS, Piersol AG. 1986. Random Data: Analysis and Measurement Procedures, 2nd edn. John Wiley & Sons: New York; 566.
Clark TL. 1977. A small-scale dynamic model using a terrainfollowing transformation. Journal of Comparative Physiology B 24:
186–215.
Atmos. Sci. Let. 6: 152–159 (2005)
Comparison of four non-hydrostatic models for flow over the Isle of Arran
Clark TL. 1979. Numerical simulations with a three dimensional cloud
model: lateral boundary condition experiments and multicellular
severe storm simulations. Journal of the Atmospheric Sciences 36:
2191–2215.
Clark TL, Keller T, Coen J, Neilley P, Hsu H, Hall WD. 1997. Terrain
induced turbulent over Lantau Island. Journal of the Atmospheric
Sciences 54: 1795–1814.
Cullen M. 1993. The unified forecast model. Meteorological Magazine
8: 279–286.
Doyle JD, Durran DR, Chen C, Colle BA, Georgelin M, Grubisic V,
Hsu WR, Huang CY, Landau D, Lin YL, Pulos GS, Sun WY,
Weber DB, Wurtele MG, Xue M. 2000. An intercomparison of
mode-predicted wave breaking for the 11 January 1972 Boulder
windstorm. Monthly Weather Review 128: 901–914.
Durran DR. 1998. Numerical Methods for Wave Equations in
Geophysical Fluid Dynamics. Springer-Verlag: New York; 464.
Gal Chen T, Somerville RJC. 1975. On the use of a coordinate
transformation for the solution of the Navier-Stokes equations.
Journal of Comparative Physiology B 17: 209–228.
Hereil P, Laprise R. 1996. Sensitivity of internal gravity wave
solutions to the time step of a semi-implicit semi-Lagrangian
nonhydrostatic model. Monthly Weather Review 124: 972–999.
Lipps FB, Hemler RS. 1982. A scale analysis of deep moist convection
and some related numerical calculations. Journal of Atmospheric
Sciences 39: 2192–2210.
Mason PJ. 1987. Diurnal variations in flow over a succession of ridges
and valleys. Quarterly Journal of the Royal Meteorological Society
113: 1117–1140.
Pinty J, Benoit R, Richard E, Laprise R. 1995. Simple test of a semiimplicit semi-Lagrangian model on 2D mountain wave problem.
Monthly Weather Review 123: 3042–3058.
Copyright  2005 Royal Meteorological Society
159
Ritchie H, Tanguay M. 1996. A comparison of spatially averaged
eulerian and semi-Lagrangian treatment of mountains. Monthly
Weather Review 124: 167–181.
Ritchie H, Temperton C, Simmons A, Hortal M, Davis T, Dent D,
Hamrud M. 1995. Implementation of the semi-Lagrangian method
in a high-resolution version of the ECMWF forecast model. Monthly
Weather Review 123: 489–514.
Salerno R, Balsamo C. 2003. Influence of Nonhydrostatic Effects and
Time-Integration Schemes on Numerical Simulations in a Complex
Orography Environment. ICAM/MAP2003 Programe.
Smagorinsky J. 1963. General circulation experiments with the
primitive equations. Part I: the basic experiment. Monthly Weather
Review 91: 99–164.
Smolarkiewicz PK, Pudykiewicz JA. 1992. A class of semi-Lagrangian
approximations for fluids. Journal Atmospheric Sciences 49:
2082–2096.
Smolarkiewicz PK, Margolin LG. 1993. On forward-in-time
differencing for fluids: extension to a curvilinear framework.
Monthly Weather Review 121: 1847–1859.
Thielen J, Gadian A, Vosper S, Mobbs S. 2002. Air flow modeling
studies over the Isle of Arran. Journal of Wind Engineers 5:
115–126.
Thomas S, Hacker J, Smolarkiewicz P, Stull R. 2003. Spectral
preconditioners fo non-hydrostatic models. Monthly Weather Review
131: 345–357.
Torrence C, Compo GP. 1998. A practical guide to wavelet analysis.
Bulletin of the American Meteorological Society 79(1): 61–78,
http://paos.colorado.edu/research/wavelets/.
Wood N, Mason P. 1991. The influence of static stability on the
effective roughness length for momentum and heat transfer.
Quarterly Journal of the Royal Meteorological Society 117:
1025–1056.
Atmos. Sci. Let. 6: 152–159 (2005)
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