AN INTERCOMPARISON OF LARGE-EDDY
SIMULATIONS OF THE STABLE BOUNDARY
LAYER
ROBERT J. BEARE
1†
, MALCOLM K. MACVEAN
1
, ALBERT A.
M. HOLTSLAG
2
, JOAN CUXART
3
, IGOR ESAU
4
,
JEAN-CHRISTOPHE GOLAZ
5
, MARIA A. JIMENEZ
3
, MARAT
KHAIROUTDINOV
6
, BRANKO KOSOVIC
7
, DAVID LEWELLEN
8
,
THOMAS S. LUND
9
, JULIE K. LUNDQUIST
7
, ANNE MCCABE
1
,
ARNOLD F. MOENE
2
, YIGN NOH
10
, SIEGFRIED RAASCH
11
and
PETER SULLIVAN
12
1
Met Office, UK;
2
Wageningen University, The Netherlands;
3
Universitat de les
Illes Balears, Spain;
4
Nansen Environmental and Remote Sensing Center, Norway;
5
National Research Council, Naval Research Laboratory, Monterey, CA, USA;
6
Colorado State University, USA;
7
Lawrence Livermore National Laboratory, USA;
8
West Virginia University, USA;
9
Colorado Research Associates, USA;
10
Yonsei
University, South Korea;
11
University of Hannover, Germany;
12
National Center
for Atmospheric Research, USA.
Abstract. Results are presented from the first intercomparison of Large-eddy
simulation (LES) models for the stable boundary layer (SBL), as part of the GABLS
(Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study)
initiative. A moderately stable case is used, based on Arctic observations. All models
produce successful simulations, inasmuch as they reflect many of the results from
local scaling theory and observations. Simulations performed at 1 m and 2 m resolu-
tion show only small changes in the mean profiles compared to coarser resolutions.
Also, sensitivity to sub-grid models for individual models highlights their importance
in SBL simulation at moderate resolution (6.25 m). Stability functions are derived
from the LES using typical mixing lengths used in Numerical Weather Prediction
(NWP) and climate models. The functions have smaller values than those used in
NWP. There is also support for the use of K-profile similarity in parametrizations.
Thus, the results provide improved understanding and motivate future developments
of the parametrization of the SBL.
Keywords: Stable boundary layer, Large-eddy simulation, Resolution, Sub-grid
model, Parametrization
1. Introduction
The large-eddy simulation of the stably stratified atmospheric bound-
ary layer is a very challenging task. Whilst much progress has been
made in simulating the convective cloudy boundary layer over the last
†
Email:bob.beare@metoffice.com
c
! 2004 Kluwer Academic Publishers. Printed in the Netherlands.
gabls_pap.tex; 13/07/2004; 10:53; p.1
2
decade (see Moeng et al., 1996 and Brown et al., 2002 for recent in-
tercomparison studies), progress with modelling the stable boundary
layer has been slower. One source of difficulty with the stable bound-
ary layer LES is that the characteristic eddies are much smaller than
in the convective boundary layer, and thus require significantly more
resolution and computer power for a reliable simulation. The small size
of the eddies makes it much more difficult for the model to maintain
resolved turbulence. When the resolution is coarse relative to the size of
the eddies, or the sub-grid model excessively dissipative, the sub-grid
fluxes dominate over the total and the resolved turbulence vanishes
in scenarios where the forcings imply continuous turbulence. Although
the sub-grid model may still provide a reasonable model of the fluxes in
these instances, the simulation is no longer a true LES. Those papers
which have reported successful simulations (i.e. with resolved turbu-
lence) are mainly for the weakly/moderately stable boundary layer:
Mason and Derbyshire (1990), Brown et al. (1994), Andren (1995),
Galmarini et al. (1998), Kosovic and Curry (2000) and Saiki et al.
(2000). Most of these are reviewed by Beare and MacVean (2004).
Whilst the SBL is difficult for LES, the parametrization of SBLs
in large-scale models is important for various aspects of Numerical
Weather Prediction and Climate modelling (Louis, 1979; Beljaars and
Holtslag, 1991; King et al., 2001). Examples include: surface tempera-
ture forecasting over land at night, fog prediction, the timing of convec-
tion, and polar climate. Given the need to improve and understand the
parametrization of SBLs in large-scale models, the GABLS initiative
was launched in 2002 (Holtslag, 2003). One question motivating this
study was: why do climate models require more mixing in their SBL
schemes relative to Monin-Obukhov theory and observations? Since
LES has proved a useful guide for other physical parametrizations in the
past, one component of the initiative was to perform the first intercom-
parison of large-eddy models for the SBL. This paper describes results
from this component. The role of the intercomparison study was to
assess the reliability and sensitivity of different models for an SBL case
based on observations. This mirrored the approach of intercomparisons
of the convective boundary layer, for example Moeng et al. (1996). Also,
the results would provide further guidance for SBL parametrization.
In order to provide a useful test-case for intercomparison, the situa-
tion studied by Kosovic and Curry (2000) was chosen. This was adopted
because it used initial conditions consistent with the BASE (Beaufort
Sea Arctic Stratus Experiment) observations, was moderately stable
(
h
L
∼ 2, where h is the SBL height and L is the surface Obukhov length)
and thus likely to be mainly continuously turbulent, and had previously
been successfully simulated. The case, described more in section 2, rep-
gabls_pap.tex; 13/07/2004; 10:53; p.2
3
resents a typical quasi-equilibrium moderately stable boundary layer,
akin to those commonly observed over polar regions and equilibrium
nighttime conditions over land in middle latitudes. Given that it was
mainly a continuously turbulent case, it was then possible to compare
this case against scalings derived from observations of other continu-
ously turbulent SBLs, for example the results of Nieuwstadt (1984).
It was appreciated from the outset that this was only one regime
of the SBL, and others, such as the very stable nocturnal boundary
layer, were also very important to understand for the parametrization
problem. However, given the difficulty of LES of SBLs in the past, it
was decided that the moderately stable case gave the best chance of
success. Modelling the turbulence of the very stable boundary layer is
a useful ultimate goal, but is beyond the scope of this work.
Using the moderately stable case (outlined in section 2), this paper
provides an overview of the output of different LES models (section 3),
assesses the sensitivity to resolution and sub-grid scale model (section
4), and compares the results with observations (section 5), and typical
first-order parametrizations used in NWP and climate models (section
6). Finally, the results are discussed in section 7, and conclusions made
in section 8.
2. Case description
The case used here is also described by Kosovic and Curry (2000). In
a similar way to other intercomparisons (e.g. Moeng et al., 1996 and
Brown et al., 2002), an initial state and forcings were used which are
broadly based on an observational data set, in this case the BASE
Arctic observations.
The initial potential temperature profile consisted of a mixed layer
(with potential temperature 265K) up to 100m with an overlying in-
version of strength 0.01 Km
−1
. A prescribed surface cooling of 0.25
Kh
−1
was applied for 9 hours so that a quasi-equilibrium state was
approached. Timescales quoted for adjustment to quasi-equilibrium for
this case differ: Beare and MacVean (2004) give 9 hours, but Kosovic
and Curry (2000) state a full inertial period of 12 hours. Also, achieve-
ment of quasi-equilibrium depends on the quantity being examined.
For the purposes of this work, it was defined as the time when the
hour averaged mean wind reached a quasi-steady state. An assessment
of how well this was achieved for the different models will be given in
section 4.
The geostrophic wind was set to 8 ms
−1
in the East-West direc-
tion, with a Coriolis parameter of 1.39 × 10
−4
s
−1
(corresp onding to
gabls_pap.tex; 13/07/2004; 10:53; p.3
4
latitude 73
◦
N). The initial wind profile was geostrophic except at the
bottom grid point where it was zero. In order to stimulate turbulence,
a random potential temperature perturbation of amplitude 0.1K and
zero mean was applied below height 50m. For models with a turbulent
kinetic energy (TKE) sub-grid closure, the TKE field was initialised as
0.4
!
1 −
z
250
"
3
m
2
s
−2
, below a height (z) of 250m.
The vertical velocity was set to zero at the surface and upper lid of
the domain, and the upper boundary condition was free slip. To limit
gravity-wave reflection at the top of the domain, most models applied
gravity wave damping above 300m. Monin-Obukhov similarity was ap-
plied at the bottom boundary (with recommended constants β
m
= 4.8
and β
h
= 7.8) using a surface roughness length of 0.1 m for momentum
and heat, and a von Karman constant (κ) of 0.4. The reference surface
potential temperature was 263.5K, density 1.3223 kgm
−3
, gravity 9.81
ms
−2
. The domain size was set to 400m x 400m x 400m; Beare and
MacVean (2004) found that doubling the horizontal domain size had
a negligible effect for this case. However, it is acknowledged that the
domain size was still too small to permit the majority of gravity waves
that might be stimulated (domains significantly larger than 1km would
be required). Nevertheless, since the motivation of the study was to
model SBL turbulence, this was not a severe restriction in this instance.
An isotropic grid was used, and simulations were performed at grid
lengths of 12.5 m, 6.25 m, 3.125 m, 2 m, and 1 m, depending on the
computer power and time available to the contributors. Profiles av-
eraged over the horizontal domain and over the final and penultimate
hours of the simulation were calculated; in general, the mean profile will
refer to averages over the final hour, except when specified otherwise.
Time series data were provided for the entire simulation. The boundary
layer depth (h) calculation involved first determining the height where
the mean stress fell to 5% of its surface value (h
0.05
) followed by linear
extrapolation: h = h
0.05
/0.95. This was the same method as used by
Kosovic and Curry (2000), who gave a justification for calculating SBL
height from the stress instead of heat flux.
Table I lists the participants and Table II summarises the mod-
els, giving the minimum grid length used and distinguishing the types
of sub-grid model and scalar advection scheme. This summary omits
much of the detail of the formulations. For more detail, the reader
should consult the references listed in Table III. As is evident, the
configurations of the models do not permit a clean test of sensitivity
to individual model components. However, some sensitivity tests were
performed, varying the configuration constants for the individual sub-
grid models at moderate resolution. Whilst many participants were able
to perform simulations down to a grid length of 3.125 m, only two were
gabls_pap.tex; 13/07/2004; 10:53; p.4
5
able to perform an LES at 1 m. This was because it required well over
a month of state-of-the-art parallel supercomputer time to perform the
calculation.
3. Overview
A large amount of data was made available by the participants, not all
of which it is possible to include here. Comprehensive details of the case
and results are available online at www.gabls.org. Table IV gives a
summary of the mean SBL heights for all simulations performed. Even
simulations at 12.5 m resolution were successful, supported by fact that
the boundary layer depths were within 40% of the very high resolution
(1m) simulations. In the remainder of the section, an overview of the
results is presented by showing plots at resolutions between 2 m and
6.25 m, thus covering data from all participants and spanning a range
of resolutions.
Mean profiles of the potential temperature, wind speed, buoyancy
and momentum flux are shown in Figures 2, 3, 4 and 5 respectively. The
profiles exhibit a positive curvature in the potential temperature near
the top of the SBL, a pronounced super-geostrophic jet peaking near
the top of the boundary layer, and linear buoyancy flux profiles. These
features are consistent with the theoretical 1D model of Nieuwstadt
(1985). The model assumes equilibrium conditions with a constant
Richardson number closure and predicts a supergeostrophic jet with a
momentum balance between the Coriolis force and vertical divergence
of momentum flux. The spread in Figures 2-5 is not surprising given
the sensitivity of previous SBL simulations to model configuration (see,
for example, Brown et al., 1994). Given the difficulty of SBL LES in
the past, a notable success here is that the spread was not any larger.
The main differences in the mean potential temperature and wind
profiles occur towards the top of the boundary layer (Figures 2 and
3). There are fewer differences lower down due to the fact that the
surface boundary condition prescribes both the surface temperature
and the wind. However, the behaviour of the LLNL simulation at 6.25
m resolution is quite different at the surface suggesting differences in the
application of the surface boundary conditions. In addition to boundary
layer depth, there are differences in the potential temperature profiles
at the top of the SBL where they blend with the overlying inversion.
In the wind speed, a spread can be seen in both the magnitude and
height of the nocturnal jet. Even at 2 m resolution, there is a range
of results, with the NCAR and CORA models favouring deeper, more
turbulent SBLs relative to IMUK and MO, and UIB in the middle. The
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