Modeling the barotropic response of the global ocean to atmospheric
wind and pressure forcing - comparisons with observations
Loren Carre`re and Florent Lyard
Laboratoire d’Etudes en Ge´ophysique et Oce´anographie Spatiale, Toulouse, France
Received 17 October 2002; accepted 10 February 2003; published 19 March 2003.
[1] A global simulation of the ocean response to
atm ospheric wind and pressure forcing has been run
during the Topex/Poseidon (T/P) period (1992–2002),
using a new hydrodynamic finite element (FE) model,
MOG2D-G. Model outputs are compared to in situ
observations with tide gauge data (TG) and bottom
pressure gauge data (BPR), and also with T/P altimetric
cross over points (noted CO). Intercomparisons were
performed over the 1993–1999 period. The model
correction reduces the sea level variance by more than
50% at TG locations, and by more than 15% at T/P CO,
when compared to the classical inverse barometer correction
(IB). The model impact differs between high and low
latitudes: in the very energetic high latitudes areas,
MOG2D-G is efficient in reducing the variance, while at
low latitudes, the results are similar to the IB static response.
In shallow water, the model shows an oceanic response very
different from the IB response. In conclusion, MOG2D-G
models the high frequency (HF) atmospheric forced
variability of the global ocean with unprecedented
accuracy.
INDEX TERMS: 4255 Oceanography: General:
Numerical modeling; 4 504 Oceanography: Physical: Air/sea
interactions (0312); 4560 Oceanography: Physical: Surface waves
and tides (1255); 4564 Oceanography: Physical: Tsunamis and
storm surges. Citation: Carre`re, L., and F. Lyard, Modeling the
barotropic response of the global ocean to atmospheric wind and
pressure forcing - comparisons with observations, Geophys. Res.
Lett., 30(6), 1275, doi:10.1029/2002GL016473, 2003.
1. Introduction
[2] The T/P and Jason altimeters deliver very accurate
data sets (within 2 centimeter global error for T/P). How-
ever for mesoscale circulation applica tions and satellite
calibration campaigns, the HF ocean signal (periods less
than 20 days for T/P), is aliased into the low frequency band
(LF; periods larger than 20 days for T/P), and needs to be
corrected from independent models at centimetric accuracy.
The present HF tidal corrections have mainly reached this
requirement, through the high resolution hydrodynamic
model FES [Lefe`vre et al., 2002] or the assimilated model
GOT [Ray, 1999]. In contrast, the ocean response to
meteorological forcing is still poorly accounted for by
simply applying the inverted barometer correction (IB,
[Wunsch and Stammer, 1997]).
[
3] The classical IB approximation formulates the static
response of the ocean to atmospheric pressure forcing, and
wind effects are totally ignored . The validity of this IB
assumption depends on the time and space scales consid-
ered: the ocean response to atmospheric pressure generally
differs from the IB at periods <3 days and at high latitudes.
Wind effects also prevail particularly around the 10 day
period.
[
4] Earlier barotropic ocean models have been developed
by Ponte [1991], and Mathers [2000], characterised by a
finite difference space discretisation on fairly large grids of
1° by 1°. They include very strong dissipation processes,
either via a strong linear and uniform bottom friction or a
large horizontal eddy viscosity.
[
5] The aim of our work is to model the HF oceanic
response to me teorological forcing with a new realistic
hydrodynamic model, with the best possible accuracy. We
have performed a global simulation over the 10 year T/P
period (1992– 2002). We also estimate the relevance of
applying such a numerical model correction to in-situ (TG
and BPR) and altimeter (T/P) observations.
2. Methodology-Hydrodynamic Model
MOG2D-G
2.1. Description
[
6] MOG2D-G (2D Gravity Waves model) is a baro-
tropic, non linear and time stepping model, derived from
(Lynch and Gray [1979]; Greenberg and Lyard, personal
communication). The model governing equations are the
classical shallow water continuity and momentum equa-
tions. The model can include tides and its main originality is
a finite element space discretisation (FE), which allows us
to increase the resolution in strong topographic gradient
areas or in shallow seas.
[
7] The FE mesh is shown in Figure 1. The grid size
ranges from 400 km in deep ocean to 20 km in coastal,
shallow areas. This medium resolution is a good compro-
mise to resolve the physics and minimise the computational
costs. The global simulation domain includes shallow water
areas and marginal seas, which are generally neglected by
other studies; including continental shelves, the Mediterra-
nean Sea, Hudson Bay, Bering Strait, the Arctic Ocean and
the Weddell and the Ross Seas, whose distinctive feature is
to be partly covered with a permanent ice field. The ice
cover impact is taken into account through the diminution
of the water column height, due to the submerged ice
thickness [Lyard, 1997]. The bottom friction is parameter-
ised by a quadratic law. A new dissipation process is
introduced to take into account the barotropic to baroclinic
energy transfer via internal wave (IW) generation over
topographic features. This term is well known to dissipate
around 1/3rd of the global barotropic energy [Egbert and
Ray, 2000]. CL
N
~
rH
~
u
~
rH is the internal wave gen-
GEOPHYSICAL RESEARCH LETTERS, VOL. 30, NO. 6, 1275, doi:10.1029/2002GL016473, 2003
Copyright 2003 by the American Geophysical Union.
0094-8276/03/2002GL016473
8
--
1
eration parameterisation. L is a tidal incursion scale;
N is
equivalent to a depth-averaged Bru¨nt-Va¨ssa¨la¨ frequency
[Baines, 1982]; H is the depth; u is the barotropic current;
C is a tuning parameter. This parameterisation of the impact
of an oscillating current on a sloping topography, has been
deduced by analogy with the formulation of the effect of a
permanent current flowing over an oscillating bathymetry
[Gill, 1982].
[
8] This formulation is complementary to those of Jayne
and St. Laurent [2001] who dealt with roughness effects. A
Smagorinsky viscosity scheme [Smagorinsky, 1963] takes
into account the varying FE grid cells size; the mean
viscosity coefficient is only 90 m
2
/s.
[
9] The semi-implicit numerical scheme combined with a
new sub-step time process allows us to maintain a larger
time step for most calculations, while preserving model
stability. At the present time, the model is running with a 3
min time step.
2.2. Validation
[
10] For validation purposes, tides were simulated with
MOG2D-G, as an example of HF gravity waves, with
similar dynamics to our atmospheric forced ocean waves.
Oceanic tides are also well-known on the global ocean
through observations (TG) and high precision numerical
models (FES 99, GOT ). MOG2D-G computed tides are of
state of the art quality for non assimilating models. Tide
gauge performances are given in Table 1; they are better
than the FES 99 hydrodynamic model for the HF (M2 and
K1); and equivalent to the FES 99 assimilated model
performances for the LF waves (Mm, Mf ). Note that
including the IW generation parameterisation allows us to
divide the bias/rms of the high frequency waves, M2 and
K1, by a factor of 2.
[
11] The ocean response to an idealised forcing by a
Rossby-Haurwitz westward propagating pressure wave at a
period of 5 days (RH5) was also investigated. Comparing
results with those of Ponte [1997] and Mathers [2000],
shows very similar 5 days structures, which are far from a
purely IB oceanic response. Given these tidal and RH5
computation results, we consider that the MOG2D-G model
has been validated for both high and low frequencies.
2.3. Forcing
[
12] Pressure and wind speeds (at the altitude of 10 m)
are taken from the ECMWF analysis fields [ECMWF,
1991]. These forcing fields have been interpolated onto a
regular 1° by 1° grid. The temporal resolution is 6 hours, so
frequencies lower than 12 hours are misrepresented. The
forcing fields are linearly interpolated to the model time
step.
[
13] At each time step, the spatial averag e over the global
ocean is removed from the atmospheric pressure, to make it
consistent with the IB correction.
[
14] The wind stress is deduced from wind speed with the
classical formula of Hellereman and Rosenstein [1983]; the
heat flux between ocean and the atmosphere is taken equal
to zero. In essence, our barotropic model does not include
any 3D dissipation; some unrealistically strong deep ocean
circulation can appear when the annual mean wind stress is
kept in the forcing. An additional dissipation term is thus
introduced, giving a local increase in the quadratic friction
coefficient, in order to parameterise the baroclinic dissipa-
tion between different ocean layers. Only the atmospheric
induced currents are taken into account in this formulation.
[
15] Initially, the ocean is at rest, then the forcing is
established linearly during 3 days to prevent shocks. The
simulation was performed over the T/P period November
1992–2002, including both atmospheric pressure and wind
forcing. Since the model spin up takes less than 2 months,
comparisons with tidal gauges and satellites observations
have been performed on the 1993– 1999 period. The pres-
sure-only forcing configuration has been tested on the year
1995.
3. Comparison to Tidal Gauges
[16] The MOG2D-G solutions are compared to a data set
of 142 TG (Figure 2), from the WOCE and MEDGLOSS
databases [Ponchaut et al., 2001] , to evaluate the quality of
the model in coastal areas. The model correction is applied
to the observed signal and, we measure the improvements
with respect to a classical IB correction. We quantify the
reduction of the residual variance for both the aliased
frequency band (0.5 days to 20 days for T/P, referred to
Figure 1. Mid-resolution finite element mesh used.
Table 1. Mean Bias/Rms for 95 Tidal Gauges From the WOCE
and IAPSO Data Sets, for Mog2d and Fes99 Models, in cm; IW:
Internal Wave Generation is Included; Assim.: Assimilated Model
M
2
K
1
Mm Mf
Mog2d 4.7/8.4 0.4/2.1 0.3/0.4 0.1/0.2
Fes99 4.6/13.1 0.4/2.3 – –
Mog2d + IW 1.3/6 0/1.4 – –
Fes99 + assim. 0.1/1.3 0/1.1 0.3/0.4 0.1/0.2
Figure 2. Localisation of all tidal gauges (circles) and
bottom pressure gauges (stars) considered in this study.
8 - 2 CARRE
`
RE AND LYARD: GLOBAL OCEAN RESPONSE TO METEO FORCING
as HF). Table 2 shows the percentage of variance reduction
after the MOG2D-G correction has been applied. The model
allows us to reduce the variance of the corrected signal by a
significantly higher percentage than the IB correction alone,
although the results depend strongly on location and fre-
quency band.
[17] The pressure-only simulation allows to reduce the
TG variance by 7.3% when compared with the IB correction
alone, while the variance reduction reaches more than 50%
when wind stress is included in the forcing. The dynamical
character of the ocean response to atmospheric pressure and,
the importance of the wind forcing are clearly illustrated.
[
18] As expected, t he model correction i s the most
effective at high latitudes : the variance reduction reaches
50.4% to 56.7% poleward of 30°S and 30°N, over the
period studied. For the equatorial band (between 30°S and
30°N), the reduc tion remains ar ound 17.2%– 26.5%.
Indeed, the high latitudes are very energetic areas where
the ocean dynamics have smaller space and time scales, and
thus the ocean response to atmospheric forcing is farther
from a classical IB response.
[
19] Model performances are also better for coastal tide
gauges rather than island gauges, which underscores the
efficiency of MOG2D-G in shallow water, due to small
scales processes and our smaller FE spacing. The effect of
the model correction varies depending on the oceanic basin
considered, the Atlantic Ocean being the best improved with
more than 60% variance reduction.
[
20] Another striking result is the obvious temporal
stability of these results (Table 2), during the period
1993–1999. We also notice a clear improvement of the
MOG2D-G statistics over time, which is probably explained
by improvements in the ECMWF model over the same
period. Note that 1996–1999 gives better variance reduc-
tion than 1993–1995.
4. Comparison to Bottom Pressure Records
[21] The MOG2D-G solutions are also compared to 5
bottom pressure records from the GLOUP database (cf.
Figure 2), in order to evaluate the model in the deeper
ocean. The observed time series of bottom pressure are
compared with the model sea level minus IB. Table 3 gives
the MOG2D-G performances at these sites for the year
1995. For the HF, the pressure forced model induces a 5.2%
reduction of the residual variance compared to the non
corrected signal, while the model forced by pressure and
wind induces a greater reduction of 29.1%. The model
efficiency as well as the strong wind effects are thus
highlighted here for the open ocean.
5. Comparison to Altimetry
[22] MOG2D-G elevations are used to correct the alti-
metric sea level data. This approach allows us to evaluate
the interest of such a correction for altimetry. The T/P cross-
overs (CO) were used, with the classical geophysical and
instrumental corrections. We removed tides from the CO
time series, by simple harmonic analysis of the 19 main
tidal frequencies (M2, S2, N2, K2, K1, O1, P1, 2N2, MU2,
NU2, L2, T2, M4, MS4, S1, Q1, OO1, J1, N4). The map
given in Figure 3 shows the global variance reduction,
obtained when applying the model to correct CO data,
compared to the simple IB correction. As expected, the
greater variance reductions (yellow and red colours) are
mainly located in some high latitudes deep ocean areas
(south-east and north of Pacific, south-west of Australia,
south Atlantic) and on continental shelves. The deep ocean
red spots on Figure 3 correspond to the areas where the
ocean dynamic response to atmospheric forcing has a strong
variability, which is induced by a resonant phenomena due
Table 2. Ratio of the Variance Reduction at Tide Gauges [Var
(TG-IB)-Var(TG-model)]/Var(TG-IB), as a Percentage, for HF
1993
P+W
1994
P+W
1995
P+W
1995
P only
1996
P+W
1997
P+W
1998
P+W
1999
P+W
93 – 99
P+W
GO 45.1 43.2 43.9 6.9 45.6 43.2 44.8 51.8 45.4
HL 53.6 51 50.4 7.3 52.8 52.3 53.8 56.7 52.9
LL 17.2 20.2 22.6 5.7 22.1 17.4 16.3 26.5 20.3
Co 54.1 50.7 51.2 7.5 53.4 51.8 53.3 56.7 53
Is 28.8 26.7 31.5 5.8 31.5 28.8 31.3 40.9 31.4
HLCo 59.9 55.6 55.2 8.9 57.1 57.6 57.4 58.8 57.4
HLIs 37.7 35.9 39.3 3.5 41.3 40 45.5 50.6 41.5
LLCo 20.7 25.1 29.2 0.1 29.6 24.4 27.5 37.5 27.7
LLIs 14.9 14.4 17.7 9.9 17.8 12.3 10.2 18.5 15.1
Atl 60.4 62.6 61.2 7.2 61.6 60.7 62 68 62.4
Pac 21 20.8 25.4 2.9 23.6 19.9 19.4 29.9 22.9
Ind 35 30.4 37.5 4.8 38.2 34.8 37.3 34.6 35.4
The values are averaged over each year named in the column, and over
all TG in the spatial region named in each row, for all frequencies. Var(x) is
the variance of x. P + W: simulation forced by pressure and wind; P only:
simulation forced only by atmospheric pressure. GO: Global Ocean; HL:
High Latitudes; LL: low latitudes; Co: Coastal TG; Is: Island TG;
Atl: Atlantic Ocean; Pac: Pacific Ocean; Ind: Indian Ocean.
Table 3. Residual Signal Variance at BPR Sites for HF (cm
2
)
longitude latitude Obs. Obs-IB
Obs-model
P only
Obs-model
P+W
57.502 56.837 108.44 6.55 6.43 4.02
36.012 31.998 27.54 6.57 6.5 5.52
54.715 60.85 86.1 3.97 3.13 1.73
56.355 58.363 90.63 6.35 6 4.64
58.392 54.943 93.34 3.93 4.06 3.63
Variance reduction compared to
IB correction:
5.25% 29.11%
Obs: total variance; Obs-IB: residual variance after IB correction; Obs-
model P only: residual variance after pressure-alone for ced model
correction; Obs-model P + W: residual variance after pressure and wind
forced model correction.
Figure 3. Var(CO-IB)-Var(CO-model) for the year 1999 in
cm
2
, with the model MOG2D-G forced by atmospheric
pressure and wind.
CARRE
`
RE AND LYARD: GLOBAL OCEAN RESPONSE TO METEO FORCING 8 - 3
to closed contours of f/h in the southern ocean [Fukumori et
al., 1998].
[
23] Table 4 summarises the means of these variance
reduction over the period 1993 to 1999 and for different
geographic areas. The striking pattern is again the difference
between the high and low latitude response: the low
latitudes band (between 30°S and 30°N) has a lower energy
level and the model correction remains very closed to the IB
one. At high latitudes ( poleward of 30°N and 30°S), the
signal is m ore energetic and has smaller characteristic
scales; here the model correction is the most relevant. In
this last area, the pressure only forcing simulation induces a
global variance reduction of only 1.7% for the year 1995,
while the pressure plus wind forcing reduces the variance by
15–16% over the 1993 –1999 period. The dominant effects
of wind forcing are thus corroborated here.
[
24] Once again, the model performs extremely well in
shallow waters (depths less than 1000 m), with a variance
reduction of 34 –39% compared with 6–11% in the deep
ocean. This result points out the efficiency of the refined
finite element grid in shallow seas. Note that the MOG2D-G
performances at T/P CO remain very stable over the 7 years
studied, with a clear improvement after 1995.
6. Conclusion
[25] The relevance of our model is to predict the HF
global barotropic response to fast and large scale atmos-
pheric forcing, and thus to correct this aliased signal in both
the altimetric data and the in situ measurements.
[
26] Our results are coherent with earlier studies ([Stam-
mer et al., 2000], [Tierney et al., 2000] and [Hirose et al.,
2002]); MOG2D-G induces large variance reductions when
applied to observations (TG, BPR, T/P CO). The model
correction allows to reduce the variance of the corrected
signal by 52.9% at tidal gauges and nearly 16% at high
latitudes for T/P C O. This variance reduction depends
strongly on the frequency band and the locations: high
latitudes, continental shelf areas and shallow waters are
the best improved. As expected, the low energy equatorial
band remains weakly affected b y the barotropic model
correction. The dominant influence of the wind forcing
appears clearly in this study (year 1995 in Tables 2, 3,
and 4).
[
27] For altimetric purposes, we suggest that only the
aliased HF model correction be used (to preserve the wind
forced barotropic motions with periods longer than a few
days). Various model parameters (including better dissipa-
tion processes, and a higher resolution mesh) are still being
developed to improve the model.
References
ECMWF, European Centre for Medium-Range Forecasts Model, ECMWF
research manual, 1991.
Egbert, G. D., and R. D. Ray, Significant dissipation of tidal energy in the
deep ocean inferred from satellite altimeter data, Nature, 405, 2000.
Fukumori, I., et al., Nature of global large-scale sea level variability in
relation to atmospheric forcing: A modeling study, JGR, 103, 5493 –
5512, 1998.
Gill, A. E., Atmosphere-Ocean Dynamics, vol. 30, 1982.
Hellereman, S., and Rosenstein, Normal wind stress over the world ocean
with error estimates, JPO, 13, 1093 – 1105, 1983.
Hirose, N., et al., High frequency barotropic response to atmospheric dis-
turbances: Sensitivity to forcing, topography, and friction, JGR, 106(C12),
2002.
Jayne, S. R., and L. C. St. Laurent, Parameterizing Tidal Dissipation over
Rough Topography, GRL, 28(5), 811, 2001.
Lefe`vre, F., et al., FES99: A Global Tide Finite Element Solution Assim-
ilating Tide Gauge and Altimetric Information, JAO Tech., 19, 2002.
Lyard, F., The Tides in the Arctic Ocean from a Finite Element Model, JGR,
102(C7), 15,611 – 15,638, 1997.
Lynch, D. R., and W. G. Gray, A wave equation model for finite element
tidal computations, Computers and fluids, 7, 207 – 228, 1979.
Mathers, E. L., Sea level response o atmospheric pressure and wind forcing
in the global deep ocean, PhD Thesis, University of Liverpool, 2000.
Ponchaut, F., et al., An analysis of the tidal signal in the WOCE sea level
dataset, JAOT, 18, 2001.
Ponte, R. M., et al., Sea level response to pressure forcing in a barotropic
numerical model, JPO, 1043 – 1057, 1991.
Ponte, R. M., Non equilibrium response of the global ocean to the 5-day
Rossby-Haurwitz wave in atmospheric surface pressure, 1997.
Ray, R. D., A global ocean tide model from Topex/Poseidon altimetry:
GOT99.2, NASA Technical Memo. 209478, Goddard Space Flight Cen-
ter, Greenbelt, 58 pp., 1999.
Smagorinsky, J., General circulation experiments with the primitive equa-
tions, Monthly Weather Review, 1963.
Stammer, D., et al., De-aliasing of global high frequency barotropic mo-
tions in altimeter observations, GRL, 27(8), 1175, 2000.
Tierney, C., et al., Short-period oceanic circulation: implications for satellite
altimetry, GRL, 27(9), 1255 –1258, 2000.
Wunsch, C., and D. Stammer, Atmospheric loading and the oceanic in-
verted barometer effect, Reviews of Geophysics, 35, 1997.
L. Carre`re and F. Lyard, LEGOS, 18 av. Ed. Belin 31401, Toulouse,
France. (carrere@notos.cst.cnes.fr; florent.lyard@cnes.fr)
Table 4. Ratio of the Variance Reduction at CO [Var (CO-IB)-
Var(CO-model)]/Var(CO-IB), as a Percentage
1993
P+W
1994
P+W
1995
P+W
1995
P only
1996
P+W
1997
P+W
1998
P+W
1999
P+W
93 – 99
P+W
GO 9.5 11.2 12.1 1.5 14.8 13.9 14.5 13.5 12.8
HL 10.9 12.4 13.7 1.7 16.6 16 16.9 15.1 15.5
LL 2.2 3.2 2.3 0.2 3.4 3.1 1.5 3.6 2.8
Sh. 35.1 38.3 34.4 4.6 39 38.3 39.7 34.9 37.1
D 5.9 7.3 8.8 1 11 10.4 10.7 10.7 9.3
HLSh 36.3 39.6 35.2 4.9 40.6 39.9 41.7 35.9 38.5
HLD 7 8.3 10.3 1.1 12.7 12.3 12.8 12.2 10.8
LLSh 22.9 26.2 27.5 1.2 23.3 24.3 20 26.1 24.3
LLD 0.5 1 0.1 0.2 1.4 1.1 0.1 1.3 0.7
Atl 9.9 12.4 13.6 2.2 14.2 15.3 15.5 14.5 13.6
Pac 10.4 10.8 10.8 0.6 16.2 13.1 17.5 15.1 13.4
Ind 7 8 11.8 1.4 13.6 12.3 9 11.1 10.4
The values are averaged over all years named in the column, and over all
CO in the spatial region named in each row. Var(x) is the variance of x. P +
W: simulation forced by pressure and wind; P only: simulation forced only
by atmospheric pressure. GO: Global Ocean; HL: High Latitudes; LL: low
latitudes; Sh: shallow waters, depth less than 1000 m; D: Deep ocean,
deeper than 1000 m.
8 - 4 CARRE
`
RE AND LYARD: GLOBAL OCEAN RESPONSE TO METEO FORCING
![Table 2. Ratio of the Variance Reduction at Tide Gauges [Var (TG-IB)-Var(TG-model)]/Var(TG-IB), as a Percentage, for HF](/figures/table-2-ratio-of-the-variance-reduction-at-tide-gauges-var-2e33ekld.webp)
