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Atmos. Sci. Let. 6: 140–144 (2005)
Published online in Wiley InterScience ( DOI: 10.1002/asl.106
Idealized modelling of the northern annular mode:
orographic and thermal impacts
Mario Sempf,1 * Klaus Dethloff,1 Dörthe Handorf1 and Michael V. Kurgansky2†
1 Alfred Wegener Institute for Polar and Marine Research, Telegrafenberg, Potsdam, Germany
2 Department of Geophysics, Faculty of Physics and Mathematics, University of Concepcion, Concepcion,
*Correspondence to:
Mario Sempf, Alfred Wegener
Institute for Polar and Marine
Research, Telegrafenberg A43,
D-14473 Potsdam, Germany.
† On
leave from A. M. Obukhov
Institute of Atmospheric Physics,
Moscow, Russia.
In an idealized model of northern hemisphere’s wintertime atmospheric circulation, it is
shown that the Northern Annular Mode arises from an annular pattern on a rotating aquaplanet and is modified to a zonally asymmetric pattern by land–sea contrasts and orography,
connected with the localization of transient baroclinic activity. Copyright  2005 Royal
Meteorological Society
Keywords: northern annular mode; arctic oscillation; quasi-geostrophic model; internal
climate variability
Received: 28 October 2004
Revised: 6 April 2005
Accepted: 6 April 2005
1. Introduction
The leading variability mode of northern hemispheric
sea level pressure consists of perturbations in the
Arctic region and, of opposite sign, over the North
Atlantic and the North Pacific. These variations are
well known as the Northern Annular Mode (NAM),
or Arctic Oscillation (AO) (Wallace and Thompson,
2002; Thompson and Wallace, 1998). This structure,
existing over the entire year, extends upward into the
whole troposphere and, during boreal winter, even
into the stratosphere, where it gains stronger zonal
symmetry and is associated with modulations in the
strength of the polar night jet.
In this study, we investigate the influence of orographic and non-zonal thermal forcing on the structure
of the NAM. In particular, it will be examined whether
either of these two forcing components is a necessary or sufficient ingredient for the generation of the
observed NAM pattern and its upward extension. To
this end, we employ a hemispheric, perpetual winter
version of the idealized three-level quasi-geostrophic
model, which has been used by Weisheimer et al.
(2003) for an assessment of the influence of the horizontal resolution on decadal-scale variability. Here,
horizontal T21 resolution and improved orographic
and thermal forcing (zonal and non-zonal) is used.
We show the model being capable of simulating the
NAM with reasonable accuracy. Furthermore, the simple model setup allows for switching off individual
forcing components. The impact of orography and
non-zonal heating contrasts on the formation of the
Copyright  2005 Royal Meteorological Society
NAM is examined by means of three sensitivity experiments, including an aqua-planet setup. In the latter,
only the zonally symmetric part of thermal forcing
is acting and no orography is used. The relationships
between the centres of action of low-frequency variability patterns and the regions of increased transient
eddy activity are investigated.
2. Model description
The model, described in detail by Weisheimer et al.
(2003), simulates the quasi-geostrophic evolution of
northern hemispheric streamfunctions at the three vertical levels 167 hPa, 500 hPa, and 833 hPa, under
perpetual winter conditions. This three-level model
has a minimum needed vertical resolution to reproduce interactions between the troposphere and the
lower stratosphere. Whereas in reality the stratospheric
polar night jet is situated above about 20 km altitude, our model simulates only the lowermost part
of that jet. Northern hemisphere’s T21 topography
(Figure 1(a)) acts as orographic forcing. Diabatic heating is established by thermal relaxation towards predefined radiative equilibrium temperature fields at the
auxiliary model pressure levels 333 hPa and 667 hPa.
The relaxation timescale is 22.7 days. An additional
surface friction/momentum forcing mechanism damps
the 833 hPa streamfunction towards a predefined zonally symmetric surface forcing function (Houtekamer,
1991) with a timescale of 1.4 days. A non-zero surface forcing proves to be necessary in this simplified
model setup. The forcing acts as a substitute for the
Idealized modelling of the northern annular mode: orographic and thermal impacts
Figure 1. (a) T21 topography of the northern hemisphere. Contour interval is 500 m. (b) Non-zonal part of wintertime (DJF)
extra-tropical diabatic heating at 700 hPa derived from NCEP-NCAR reanalysis data and used in the QG three-level model.
Contour interval is 0.5 K/day, negative contours are dashed, zero contour omitted. (c) The same as in the middle, but for 300 hPa
Copyright  2005 Royal Meteorological Society
167 hPa model
167 hPa obs.
500 hPa model
500 hPa obs.
833 hPa model
833 hPa obs.
zonal velocity [m/s]
absent baroclinicity within the lowermost layer and
helps to enforce low-level westerlies, which would be
too weak otherwise. A horizontal scale-selective ∇ 6 hyperdiffusion attenuates particularly the short waves;
e.g. those with total wavenumber 21 are damped with
an e-folding time of 12.9 h. The vertical temperature
lapse rate has been fixed to 3.0 K/km at 333 hPa and
6.5 K/km at 667 hPa.
The goal of this study is to investigate the influence
of orographic forcing and of zonal asymmetries in
extra-tropical diabatic heating. Therefore, the nonzonal components of the above-mentioned radiative
equilibrium temperature fields have been adjusted in
a way that, on the time mean, realistic patterns of
non-zonal extra-tropical diabatic heating are acting
in the model, while the zonal components of the
equilibrium temperature fields and the surface forcing
have been tuned to produce a zonal climatology
as realistic as possible, in order to ensure adequate
westerly flow against orography and appropriate flow
instability conditions. However, it should be noted that
the diabatic heating in this simplified model is not
interactive with the variability in the same way as it is
in reality. For example, latent heat release associated
with travelling cyclones is accounted for only on the
time mean.
The adjustments of forcings are made by an automatic iterative procedure, working as follows. For a
given forcing, a test run is performed, and the model’s
time-mean zonal wind profiles for the three model
levels are compared with observed wintertime (DJF)
zonal winds taken from NCEP-NCAR reanalysis data
( According to arising differences, moderate changes of the zonally symmetric
portions of the forcing fields are computed. Additionally, the model’s time-mean non-zonal diabatic heating
at 333 hPa and 667 hPa is diagnosed a posteriori and
compared with the non-zonal parts of wintertime heating fields derived from observations by Nigam et al.
(2000) at 300 hPa and 700 hPa. The latter fields have
been attenuated near the equator and are shown in
Figure 1(b,c). Corrections of the non-zonal portions of
the model’s equilibrium temperature fields are derived
from the differences between modelled and observed
heating patterns. After the corrections of forcing, the
latitude [°N]
Figure 2. Modelled and observed time-mean zonal wind
profiles for the three model levels and corresponding vertical
layers, respectively
model is run again, repeating the procedure, until a
convergence criterion is satisfied. This forcing adjustment procedure follows a similar principle as used by
Lunkeit et al. (1998), but with discrete forcing updates
at the end of medium-term test runs instead of a continuous adaptation of the forcing during a longer run.
3. Model results
The time-mean zonal wind profiles taken from a 100year perpetual winter model simulation are presented
in Figure 2, together with observed wintertime zonal
winds. The latter have been computed after averaging the NCEP-NCAR reanalysis data over three vertical layers of approximately equal mass, respectively,
instead of using individual pressure level data, in order
to capture the contribution of the stratospheric polar
vortex. As visible, the agreement between the modelled and the observed wind profiles is almost perfect,
showing the effectiveness of the tuning procedure. The
wind speed maximum situated at about 30 ◦ N in the
middle and upper level corresponds to the subtropical jet. The bump in the upper level profile at high
latitudes is due to the polar vortex.
Atmos. Sci. Let. 6: 140–144 (2005)
In order to facilitate further comparisons between
model results and observations, the daily streamfunction output for each level has been converted into a
time series of geopotential height fields by means of
a non-linear balance equation (cf. Kurgansky, 2002).
The model’s geopotential height data have been 10day low-pass filtered, as well as the reanalysis data
averaged over the three vertical layers, as mentioned
above, and EOF analyses have been performed for
the whole hemispheric domain, using area weighting.
EOFs are normalized so that the corresponding principal components have unit variance.
The first EOF of the model’s 833-hPa geopotential
height is shown in Figure 3(a), while Figure 3(b)
displays the first EOF of wintertime geopotential
height taken from the reanalysis data averaged over
the lowest vertical layer, ranging from 700 hPa to
1000 hPa. The latter structure is virtually identical to
the AO pattern (Thompson and Wallace, 1998), and
the pattern generated by the model strongly resembles
it (spatial correlation 0.89). The Arctic centre of
action has maximum amplitude over Greenland in the
model as well as in the reanalysis. The Pacific and
Atlantic centres are shifted westward compared to the
observations, and the latter centre is somewhat weaker
than observed, as well as the Arctic centre. The slight
lack of AO variability in the model might, at least
in parts, be attributed to the absence of changes in
the external forcing of the model atmosphere, such as
anomalies of sea surface temperatures.
In order to establish an additional measure of the
annular nature of the variability, rotated EOFs have
been computed. The first rotated EOF at 833 hPa,
shown in Figure 3(c), exhibits no substantial change of
the pattern. Although rotated EOFs generally tend to
exhibit more localized structures than unrotated ones,
the first rotated EOF possesses an annular structure
similar to the first unrotated EOF. However, there is
stronger emphasis on the Atlantic and Icelandic sector
after rotation, while the Pacific centre of action is more
pronounced in the unrotated pattern. The robustness
of the NAM versus more regional patterns like North
Atlantic Oscillation (NAO) and the Pacific–North
America pattern is still a matter of ongoing discussions
(e.g. Ambaum et al., 2001).
M. Sempf et al.
The model simulates the extension of the AO into
the upper troposphere/lower stratosphere with accuracy. At 500 hPa as well as at 167 hPa, the model’s
first EOF also possesses an annular structure and
resembles an observed pattern for the corresponding
layer, namely, the first EOF (at 167 hPa, correlation
0.72) and the second EOF (at 500 hPa, correlation
0.76, figures not shown), respectively. The upper level
pattern represents a strengthening/weakening of the
polar vortex. Upward extension of the AO signal is
confirmed by the fact that the first principal component (PC) at 833 hPa has a correlation of 0.93 with
the first PC at 500 hPa, and a correlation of 0.67 with
the first PC at 167 hPa.
4. Orographic and thermal effects
In order to estimate the impact of the orographic and
non-zonal thermal forcing, respectively, and of their
combined effects on the model’s annular mode, three
additional 100-year experiments have been performed.
In the experiment named ORO, stationary waves are
forced by orography only, i.e. the non-zonal parts of
the radiative equilibrium temperature fields at 333 hPa
and 667 hPa are set to zero. The THERMAL experiment, in turn, uses the non-zonal thermal forcing,
while orography is switched off. In the third experiment, called AQUA, both orography and non-zonal
thermal forcing are disabled. In all the experiments,
the zonal thermal and surface forcing is the same as
in the full model run (CONTROL). For the AQUA
integration, it is important to set up an initial state
with non-zero wave amplitudes.
EOFs have been computed again based on 10-day
low-pass-filtered geopotential height data. The first
EOF for 833 hPa is shown in Figure 4 for the three
experiments. The patterns for ORO and THERMAL
are similar to each other in magnitude, but weaker
than the CONTROL pattern (Figure 3(a); note that in
Figure 4 the contour interval has been halved in comparison to Figure 3). Both patterns possess a notable
zonal (annular) component. ORO exhibits an AO-like
structure similar to CONTROL. However, the midlatitude centres, in particular the Atlantic one, are slightly
Figure 3. (a) First EOF of geopotential height of the 833 hPa model level. (b) First EOF of observed wintertime geopotential
height in the lowest vertical layer. (c) First rotated EOF of geopotential height of the 833 hPa model level. Contour interval is
10 m, negative contours are dashed, zero contour omitted
Copyright  2005 Royal Meteorological Society
Atmos. Sci. Let. 6: 140–144 (2005)
Idealized modelling of the northern annular mode: orographic and thermal impacts
shifted to the southwest, and the Arctic counterpart is
somewhat elongated. In contrast, the THERMAL pattern has stronger zonal symmetry, at least over North
America. Still, some concentration on the Atlantic and
Pacific sector is also evident here. The AQUA pattern shows almost perfect annular symmetry (the slight
deviations are due to the limited integration length),
and has considerably weaker amplitude than the ORO
and THERMAL pattern. The AQUA result shows that
annular mode variability can be established solely by
the interactions between transient baroclinic waves and
the zonal flow. This is in qualitative agreement with
the simplified primitive equation model studies by
James and James (1989) and James and James (1992).
ORO and THERMAL, however, indicate the annular variability being greatly enhanced and localized
over both oceanic regions by the presence of stationary waves due to forcing by orography and thermal
land-sea contrasts.
The degree to which the annular mode signal
extends upward differs between the experiments. In
THERMAL, EOF 1 at 500 hPa (not shown) is similar
to EOF 1 at 833 hPa, but with stronger emphasis
on the Atlantic sector, reminiscent of the NAO. The
correlation between PC 1 at 833 hPa and PC 1 at
500 hPa is 0.84. ORO and AQUA, in turn, reveal
no annular structure at all in any of the first 20
EOFs at 500 hPa. On the other hand, structures
corresponding to fluctuations in polar vortex strength
can be discovered for all three experiments when
analyzing the upper level. However, these variations
are comparatively weak as the corresponding patterns
are represented only by EOF number 5 or higher. The
weak variability of the vortex is accompanied by great
vortex strength. A zonal wind maximum of roughly
30 m/s at 75 ◦ N develops at the upper model level,
except for AQUA, where the wind speed even reaches
40 m/s.
In order to analyze how the localization in longitude of the annular mode variability arises in the
CONTROL run and in the experiments, time-averaged
patterns of kinetic energy at 833 hPa, derived from 6day high-pass filtered streamfunction fields, have been
computed for all four runs. These fields, displayed
in Figure 5 for CONTROL, ORO, and THERMAL,
are a measure of baroclinic eddy activity. It is well
known that transient eddies are playing a key role in
the forcing and maintenance of annular modes (e.g.
Limpasuvan and Hartmann, 2000). For CONTROL, a
prominent maximum of the high-pass transient kinetic
energy (TKE) is visible over the Pacific and Atlantic
region, respectively. The positions of these maxima
coincide with jet streams of the time-mean flow (not
shown), and also with the centres of heating over
the oceans, as visible in Figure 1. There is reasonable agreement with the positions of the observed
storm tracks (not shown), which are, however, located
slightly farther to the east. The model possesses a third
storm track over Eurasia, which is much less pronounced in the observations. Obviously, the oceanic
centres of the modelled AO pattern (Figure 3) coincide with the downstream ends of the storm tracks over
the oceans, and the existence of the third, continental
storm track does not seriously affect the structure of
Figure 4. First EOF of 833 hPa geopotential height for the experiments ORO (a), THERMAL (b), and AQUA (c). Contour interval
is 5 m, negative contours are dashed, zero contour omitted
Figure 5. Six-day high-pass kinetic energy at the 833 hPa model level for CONTROL (a), ORO (b), and THERMAL (c). Contour
interval is 5 m2 s−2
Copyright  2005 Royal Meteorological Society
Atmos. Sci. Let. 6: 140–144 (2005)
the AO pattern. For ORO, the TKE is considerably
weaker. The Pacific centre is almost at the same place
as in the CONTROL run, but the Atlantic centre has
shifted towards North America. Both centres coincide
with pronounced jet streams of the mean flow (not
shown). The shift of the Atlantic TKE maximum is
reflected by the shift of the Atlantic centre of action
in the first EOF (Figure 4). THERMAL exhibits a
localized maximum of TKE in the Atlantic sector, at
the same position as in CONTROL. A second area of
high TKE stretches across the entire Eurasian continent. The mean flow (not shown) has stronger zonal
symmetry than in the CONTROL and ORO runs and
does not have pronounced jets. In the case of THERMAL, the localization of eddy activity in the Atlantic
region coincides with the Atlantic centre of action of
the first EOF. Such a pronounced connection is not visible over the Pacific. The TKE field for AQUA (not
shown) consists of a zonally symmetric belt centred
at 31 ◦ N, consistent with the structure of the first EOF
for AQUA (Figure 4).
5. Summary
A quasi-geostrophic three-level model using the T21
orography of the northern hemisphere has been
adapted to NCEP-NCAR reanalysis data using an automated iterative procedure, so that it possesses a realistic zonal wind structure and time-mean non-zonal
extra-tropical diabatic heating virtually identical to
observations. On the basis of a 100-year perpetual
winter integration, the model has shown to reproduce
the AO signature in the troposphere and the upward
extension of the AO. This is in agreement with the
comprehensive study by Limpasuvan and Hartmann
(2000), who showed similarities in the structure of
annular modes derived from NCEP-NCAR data and
the output from a realistic atmospheric general circulation model with the bottom boundary specified by
realistic orography and the sea surface temperatures
fixed to the climatological annual cycle.
The influence of orographic and non-zonal thermal
forcing on the emergence of the annular mode and
its upward extension has been investigated by means
of three sensitivity experiments over 100 years. With
both forcings switched off, a zonally symmetric annular mode with comparatively weak amplitude emerges
at the lowest model level, but without upward extension into the middle level. With orography switched
on, the model is able to reproduce roughly the zonal
asymmetries associated with the AO structure at the
lowest model level. But still, the AO signal does not
extend upward into the middle level. However, it does
so when using non-zonal thermal forcing instead of
orography. On the other hand, in the latter case, the
zonal asymmetries visible in the AO pattern are reproduced in a weaker fashion. Apparently, the effect of
Copyright  2005 Royal Meteorological Society
M. Sempf et al.
non-zonal thermal forcing is more barotropic than the
orographic influence, which is mostly confined to the
lowest model level. Presumably this is because thermal forcing is acting in the interfaces at 333 hPa and
667 hPa and therefore affecting all three model levels
directly, whereas orography has immediate influence
on the lowest level only.
In the full model run as well as when using
orographic forcing only, the pronounced midlatitude
oceanic centres of annular mode variability are associated with centres of baroclinic eddy activity. With thermal forcing instead of orography, such a pronounced
connection is visible only over the Atlantic and not
over the Pacific region.
It has been shown that the NAM is modified from
an annular pattern on a rotating aqua-planet to a
zonally asymmetric, strengthened pattern by thermal
land–sea contrasts and orography, accompanied by the
localization of transient baroclinic activity.
We are very grateful to two anonymous referees, whose
comments helped to improve the article. Furthermore, we
highly appreciate Eric DeWeaver and Sumant Nigam who sent
us the diabatic heating data. We also thank Franco Molteni
for kindly providing us the orographic dataset. At last, we are
very grateful to Antje Weisheimer for support in the model’s
handling and many useful hints.
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Atmos. Sci. Let. 6: 140–144 (2005)
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