James Rennell Division for Ocean Circulation and Climate
Southampton Oceanography Centre
European Way
Southampton
SO14 3ZH
UK

Tel: 023 8059 6405
Fax: 023 8059 6400
 
 

ABSTRACT

This report presents work in progress on the use of ocean models to investigate Rossby wave propagation. The original motivation for this was to make some preliminary investigations of the role of wind forcing in driving such waves. Following a brief discussion of what Rossby waves are, the first part of the report describes a 3-1/2 layer reduced gravity model that could be used for such studies. Three sets of monthly climatological windsets are presented ó ECMWF, SOC and ERS scatterometry ó and initial results discussed.

In the second main part of the report, we compare output from a high-resolution (1/3^o) numerical model based on the Miami Isopycnic Coordinate Ocean Model (MICOM) with satellite observations of Rossby waves in the North-East Atlantic.

KEYWORDS

Altimetry; MICOM, North Atlantic, ocean general circulation model, reduced gravity model; Rossby waves, sea surface height, sea surface temperature.

CONTENTS
 

ABSTRACT *

1. INTRODUCTION *

3 OCEAN GENERAL CIRCULATION MODELLING *

ACKNOWLEDGEMENTS *

ACRONYMS *

FIGURES : MICOM VS. SATELLITE *
 
 

1. INTRODUCTION

1.1 General remarks on ocean modelling

The development of realistic ocean models will help our understanding of the circulation of the oceans and enable more accurate predictions of the ocean's response to changes in environmental conditions. As well as accurately reproducing the known mean circulation and seasonal variation, it is clearly important that models contain a good representation of Rossby waves, since these transmit information from one side of an ocean basin to the other and introduce a significant time lag into the response of the system. Thus the generation, propagation and speed of Rossby waves in models is an important indication of their ability to respond to remote forcing and the time taken to reach a new equilibrium. Indeed when models are "spun up" from initial conditions, there are usually a whole fleet of strong signals propagating throughout the basins, as they evolve towards model equilibrium. However such Rossby waves are for anomalous conditions; instead we examine the properties of Rossby waves in models in which the current field and background density structure are in quasi-equilibrium with the atmospheric forcing. Semi-realistic models also give us the ability to evaluate the importance of various features, e.g. currents and bathymetric relief, through the opportunity to experiment with different runs of the model. This would be a useful topic for further work.

Rossby waves are not explicitly coded into these models; they are simply a series of solutions to the equations of motion on a rotating surface with varying surface forcing. Therefore the comparison of Rossby waves from models with observations makes a good test of how well the model dynamics are reproducing reality. Where models and reality disagree, the model code does not require specific adjustment of "Rossby wave parameters", but an effort to address the underlying problems. For example, weak vertical mixing or too few model layers will lead to a poor representation of the stratification and hence the vertical shear, whilst errors in the parameterisation of the bottom drag will affect the bottom few layers and thus the depth structure of baroclinic modes. Weak signals are probably indicative of over-smoothed forcing fields or a weakened response to them, whereas slow propagation may be due to an inability to represent adequately the vertical velocity and density structures.

1.2 What are Rossby waves?

Before we embark on model and satellite studies of propagating Rossby waves, it is instructive to consider what they are; in particular, how waves arise in a stratified ocean on a rotating surface.

Physical and mathematical descriptions of Rossby waves can be found in the fluid dynamics literature: see, for example, Gill (1982). The essential features are as follows. The Earth rotates around its axis with constant angular velocity W. At any locality on the Earthís surface, the component of the angular velocity around a local normal to the surface (which by convention is indicated as f/2) is

     [2]

Equation [2] basically says that, because f varies with latitude on the spherical Earth, when a parcel of water is displaced latitudinally it is subject to a restoring force in order that potential vorticity is conserved. The resultant effect of the restoring force, the inertia of the fluid parcel and the initial disturbance (which may be due to atmospheric forcing or a change in ocean currents) is a propagating Rossby wave. (In Section 2, which describes reduced gravity ocean modelling, we present model equations in terms of the prognostic variables, layer dynamic height and velocity.)

Solutions of [2], representing the different modes of propagating Rossby waves, take the form

where (k,l) are the zonal (east-west) and meridional (north-south) wavenumbers, respectively, and wis the wave frequency. The dispersion relation for zero background mean flow is:

where a is the local deformation radius, which varies with latitude, the local density stratification, and the mode number. Each of the baroclinic modes has an associated deformation radius:

which can be called the nth baroclinic Rossby radius, cn being equal to the wave speed of the nth mode in a nonrotating system; c_n=gH_n, where H_n is the equivalent depth for the nth baroclinic mode. The baroclinic Rossby radius is a natural length scale often associated with boundary currents, fronts and eddies. A recent study by Chelton et al. [1998] presents and discusses the geographical variability of the first baroclinic deformation radius due to variation in equivalent depth and the Coriolis parameter.

The minus sign on the right-hand side of Equation [4] indicates that Rossby waves have westward phase velocity. In the long wavelength limit, , Rossby waves are non-dispersive. It is worth noting from Equation [4] that Rossby waves have a maximum or cut-off frequency , which occurs when l = 0 and k = a^-1. Alternatively, Rossby waves have a turning latitude, a poleward latitude limit beyond which Rossby wave solutions become evanescent, i.e. no propagation exists (see Gill, 1982, pp. 440-443 for further details).

Several mechanisms have been proposed for the generation of propagating baroclinic Rossby waves. They typically involve a disturbance of the ocean: a local anomaly in wind stress curl, local buoyancy forcing, triggering by coastally-trapped waves, or reversals in coastal currents. In the eastern North Atlantic, the most likely forcing mechanism is wind stress fluctuation at the eastern boundary (Polito and Cornillon, 1997). In a study of assimilation of altimetric data into an eddy-permitting model of the North Atlantic, it was observed that wave propagation is even visible in model runs without wind forcing (both with and without assimilation), suggesting that buoyancy effects, perhaps at coasts, are generating much of the wave signal (Peter Killworth, pers. comm., 2000).

2 REDUCED GRAVITY MODELLING

2.1 Model physics

Here we describe an ocean model based on a N 1/2 -layer reduced gravity model, i.e. a model with N dynamically active layers, and an infinitely deep passive abyssal layer. The prognostic equations of the model are the equations of motion and the equation of continuity, written for each layer k, in standard notation (e.g. Gill, 1982), as follows:
 
 

                                                                                        divergence     Ekman pumping     diffusion
 
 

                                                                                        pressure       forcing       viscosity    nonlinear advection   drag

and gí_k, the reduced gravity for layer k is given by:

The prognostic equations above are expressed in (x,y) notation. However, the model is now running with proper spherical geometry, as appropriate to the large latitudinal range in the model (see below). At present, our runs of the reduced gravity model are purely wind-driven, i.e. the Ekman pumping term in equation [6] is set to zero. Layers are numbered from 0 at the bottom (the passive abyssal layer) to N at the top (surface layer). In the present study, we use a 3.5-layer ocean: 3 active layers overlying the passive layer. It is assumed that all layers have a positive thickness everywhere for all time, implying that layers do not rise to the surface or outcrop. Because the lowest layer is infinitely deep, there is no barotropic mode and the influence of bottom topography is removed. Furthermore, assuming that the pressure gradient vanishes in the lowest layer implies that the velocity is zero in the deep ocean. The free surface height is given by:
 
 

where the values of H_k represent the unperturbed (initial) values of layer thickness.

2.2 Numerical Formulation

The model run presented below covers the Atlantic Ocean from 20^oS to 65^oN, and 80^oW to 10^oE at a resolution of 0.5^o x 0.5^o . (The wide longitude range facilitates a "realistic" model equstor). All boundaries are closed and a no-slip condition is applied. A linear drag is applied to u and v fields near the southern boundary to suppress the coastally trapped waves arising from the artificial boundary there. In order to achieve this, the drag coefficient K (last term on RHS of Equations [7] and [8]) falls off linearly with northward distance, and is zero over most of the basin, including the area where Rossby waves are to be studied. The region south of the equator in the model is essentially a passive sink of equatorial wave activity, with the linear drag coefficient K sufficient to attenuate waves prpagating along the artificial southern boundary. The stepping coast line follows the 200 m isobath of the ETOPO5 dataset, with some simplification.

The model is coded in Fortran-77, fully optimised to run on Unix workstations. The model equations [6]-[9] are discretised in space on an Arakawa C-grid (Arakawa and Lamb, 1977). The leap-frog time integration scheme uses a 20-minute timestep with 72 timesteps per day (In the present leap-frog scheme, the computational mode is suppressed by mixing states every 31 timesteps).

Density and initial layer thickness values were selected on the basis of those used in MICOM runs in the North Atlantic (Jia, pers. comm., 2000), as follows:
 
 

r₃ = 1026.0 kg m^-3 ; H₃ = 200 m

r₂ = 1026.8 kg m^-3 ; H₂ = 300 m

r₁ = 1027.4 kg m^-3 ; H₁ = 500 m

r_abyssal = 1027.8 kg m^-3 ; H_abyssal = infinity

2.3 Wind fields

In order to run the reduced gravity model, we must obtain a suitable wind field. Three monthly climatological datasets were prepared for this purpose:

1. ECMWF reanalysis wind fields (Barnier et al., 1995).
2. SOC climatology (Josey et al., 1998).
3. ERS scatterometer data (available via ftp from CERSAT web site: http://www.ifremer.fr/cersat, from which we prepared a monthly climatology.

 Windstress fields for January.

 Windstress fields for February

 Windstress fields for March

 Windstress fields for April.

 Windstress fields for May.

 Windstress fields for June.

 Windstress fields for July

 Windstress fields for August.

 Windstress fields for September

 Windstress fields for October

 Windstress fields for November

 Windstress fields for December

2.4 Provisional results

In the results to date, model runs have collapsed after less than 2 model years as a consequence of the surface layer thickness (layer 3) reducing to zero. Investigations are continuing into why this occurs. This was not a problem when the model was run at a resolution of 1^o x 1^o in the Indian Ocean by Bulusu (1998). He observed, however, that 1^o resolution runs did not adequately reproduce the observed variability; hence the motivation to move to 0.5^o resolution here. Varying the model viscosity and diffusion coefficients alleviates the problem of the model tripping over to some extent, as does increasing the lengthscale over which linear drag is applied at the southern boundary. However, the underlying problem may relate to the numerical coding of the nonlinear advection term on the RHS of equations [7] and [8]; what was appropriate at 1^o resolution may no longer be adequate at 0.5^o resolution. Some earlier models (e.g. Jensen, 1993) apply a "fix" to limit the minimum allowed thickness of the uppermost layer, though it is often claimed that it is "seldom" required.
 
 

FIGURES: OUTPUT FROM REDUCED GRAVITY MODELLING

There follow snapshots of layer thickness (left panel) and velocity (right panel) for each of the 3 active layers at time increments of 0.2 years (15 pages).

Note:

C.I. = contour interval.

Solid contours represent positive values; dashed contours represent negative values.
 

 Layer 3 at 0.2 years      Layer 2 at 0.2 years      Layer 1 at 0.2 years      SSH at 0.2 years

 Layer 3 at 0.4 years      Layer 2 at 0.4 years      Layer 1 at 0.4 years      SSH at 0.4 years

 Layer 3 at 0.6 years      Layer 2 at 0.6 years      Layer 1 at 0.6 years      SSH at 0.6 years

 Layer 3 at 0.8 years      Layer 2 at 0.8 years      Layer 1 at 0.8 years      SSH at 0.8 years

 Layer 3 at 1.0 years      Layer 2 at 1.0 years      Layer 1 at 1.0 years      SSH at 1.0 years

3 OCEAN GENERAL CIRCULATION MODELLING

3.1 Introduction

In this section we examine output from AIM (the Atlantic Isopycnic Model), whose grid covers the whole of the Atlantic north of 20°S at a resolution of 1/3° in longitude by 1/3° cos(latitude) in latitude using 19 constant density layers (isopycnals) and a surface layer. This model was developed and integrated under the DYNAMO (Dynamics of North Atlantic Models) project. This was an extensive intercomparison exercise involving three types of model. A detailed account can be found in DYNAMO Group (1997). After 20 years of "spin up" AIM exhibits strong gyral circulation, with branching of the North Atlantic Current to produce an eastward-flowing Azores Current. The model current is a broad feature occupying 32°-35°N, with a mean transport of 10.6 Sv at 30°W (New et al., 1999) which is in good agreement with hydrographic observations (Gould, 1985).
 

3.2 The eastern North Atlantic subtropical gyre

High-resolution ocean general circulation models (OGCMs) are able to reproduce many features of the world ocean circulation at large- and meso-scales. Validation of OGCMs has often focussed on comparisons of model and observed root-mean-square variability in sea surface height and eddy kinetic energy (EKE) [e.g. Beckmann et al., 1994a; Spall, 1990]. We propose here an additional validation tool. Recent advances in space-based observations of propagating baroclinic Rossby waves [e.g. Chelton and Schlax, 1996; Cipollini et al., 1997b] suggest that this would provide a powerful validation tool for ocean models. Rossby waves are an important dynamic element of ocean circulation. They play a fundamental role in the maintenance of western boundary currents, the transfer of energy from eastern margins of basins to western margins and from low to mid- and high-latitudes, and in the adjustment of the ocean to atmospheric forcing [e.g. Gill , 1982]. Therefore, one yardstick to judge the capability of a model to reproduce the real ocean is how well the model reproduces observed features of Rossby wave propagation. This requires not only that a realistic model faithfully represent sea surface height signatures, but also in situ stratification since this determines the internal Rossby radius and, in turn, influences the velocity of baroclinic Rossby waves. In other words, such a validation tool will provide a check on both ocean surface signatures and subsurface structure. Although the amplitude of any OGCM Rossby waves may well depend on the nature of the applied wind stress field, the propagation speed should not.

The eastern North Atlantic subtropical gyre is especially interesting as it exhibits complex dynamics [e.g. Käse et al., 1985; Pingree, 1997] and thereby offers a stringent testbed for ocean model realism. Ocean signals at many length scales and timescales are observed in the region: meandering of the Azores Current and its associated front [Käse and Siedler, 1982; Gould, 1985]; strong currents and transport changes [Siedler et al., 1985; Siedler and Finke, 1993]; and propagation of eddies [Pingree and Sinha, 1998] and baroclinic Rossby waves [Tokmakian and Challenor, 1993; Le Traon and De Mey, 1994; Cipollini et al., 1997a,b]. There are persistent westward recirculations of the main Azores Current [Cromwell et al., 1996; Pingree, 1997; Tychensky et al., 1998], generated through a rectification process effected by turbulent mesoscale features (Alves, 1996).

The SEMAPHORE (Structure of the Sea/Atmosphere Exchanges, Ocean Properties and Heterogeneities, Experimental Research) programme, in particular, was a concerted effort to improve understanding of this dynamically important region of ocean circulation using a multitude of satellite, meteorological, hydrographic and modelling datasets [Eymard, 1998].

Pingree and Sinha [1998] proposed that large (diameter ~300 km), westward-travelling cyclonic eddies previously observed, for example, by Gould [1985] and Pingree et al. [1996], propagate in a zonal ëcorridorí in the eastern basin of the North Atlantic between ~32^o-34^oN, at a frequency of ~2 per year. These eddies were termed ëSTORMsí (SubTropical Oceanic Rings of Magnitude) by Pingree et al. [1996] and are formed by meanders pinching off at the southern edge of the Azores Front. The region ~32^o-34^oN in the North Atlantic is therefore the ëSTORM corridorí [Pingree and Sinha, 1998]. We also note that this region is almost coincident with a ëwavebandí of enhanced energy in propagating baroclinic Rossby waves observed at ~33^o-34^oN in both altimeter and sea surface temperature data [Cipollini et al., 1997a]. The reason for this enhancement is unknown but is presumably related to the presence of the strong zonal Azores Current. Cromwell et al. [2000] examined the STORM corridor further by combining along-track ERS altimeter measurements with hydrography and derived a refined estimate of the STORM period as ~7.5 months. They also showed that the Rossby wave waveguide reported by Cipollini et al. [1997a] is distinct from the STORM corridor, the former clearly lying further north of the latter. It is beyond the scope of this paper to explain the clearly complex interaction between the Azores Current, the westward-propagating STORM eddies, and the amplified propagation of westward-travelling Rossby waves.

Several mechanisms have been proposed for the generation of propagating baroclinic Rossby waves. They typically involve a disturbance of the ocean at, or near, the eastern boundary of a basin since this is where most waves originate: a local anomaly in wind stress curl, local buoyancy forcing, triggering by coastally-trapped waves, or reversals in coastal currents. In the eastern North Atlantic, the most likely forcing mechanism is wind stress fluctuation at the eastern boundary [e.g. Polito and Cornillon , 1997]. In a study of assimilation of altimetric data into an eddy-permitting model of the North Atlantic, Killworth et al. [1999] observe that wave propagation is even visible in model runs without wind forcing (both with and without assimilation). The authors suggest that buoyancy effects, perhaps at coasts, are generating much of the wave signal. The main thrust of the present paper is the analysis of propagating Rossby waves in SSH datasets from both a high-resolution version of the Miami Isopycnic Coordinate Ocean Model (MICOM) and TOPEX/POSEIDON, though we also consider SST datasets (in the case of the model, the mixed layer temperature is taken as a proxy for SST). The comparison is indicative rather than actual, in the sense that the model does not attempt to simulate the same time period as the satellite observations. The aim is to determine whether the model is capable of reproducing observed properties of Rossby waves (speed, frequency, period), rather than actual occurrences of specific Rossby wave events.

In Section 3.3 we describe the ocean model, then we present the satellite datasets, with details of their processing, in Section 3.4. In Section 3.5 we undertake a quantitative comparison of satellite and model behaviour in terms of root-meanósquare SSH and SST variability, and then Rossby wave propagation. Section 3.6 is a short note on low-resolution vs high-resolution MICOM results. We conclude with a summary and discussion of the results in Section 4.

3.3 Description of MICOM

The model used in this report is based on the Miami Isopycnic Coordinate Ocean Model in which the vertical coordinate is the surface-referenced potential density, s_{o. Details of MICOM numerics can be found in Bleck et al. [1992]. The model domain covers the Atlantic basin from approximately 20^o S to 70^o N, and from 100^o W to 20^o E. The horizontal resolution is 1/3^o in longitude by 1/3^o cos(}f) in latitude (where f is latitude), thus yielding an isotropic horizontal grid. There are 20 vertical layers (see Table 1). The top layer is a mixed layer of Kraus-Turner formulation where density and other model variables are allowed to vary with time and in space. The 19 layers below the mixed layer are isopycnic where potential density is maintained as a constant. Model bathymetry is taken from ETOPO5, resolution 1/12^o, database (National Geophysical Data Center, 1988).

The wind stress, friction velocity (used in computing turbulent kinetic energy for mixed layer forcing) and the heat flux used to force the model are taken from a three-year monthly climatology derived from the European Centre for Medium-range Weather Forecasting analysis (1986-1988). The full surface heat flux consists of the ECMWF climatology plus a restoring term towards an equivalent sea surface temperature with a variable time scale as described in Barnier et al. [1995]. The surface salinity is restored towards the Levitus [1982] climatology with a time scale identical to that used in the heat flux formulation.

The model was developed and integrated under the DYNAMO (Dynamics of North Atlantic Models) project funded by the European Union. This was an extensive modelling intercomparison exercise involving three types of model. A detailed account can be found in DYNAMO Group [1997].

The model boundaries are closed in the north, south and at the strait of Gibraltar. Connection with the ocean exterior to the model domain is parameterised by means of buffer zones in which the model variables of layer interface depth and salinity are restored towards observed values. The inclusion of salinity restoring on the density layers does not influence the dynamics, but provides the layers with the appropriate water mass characteristics (temperature and salinity). In the version of MICOM used in this study, salinity is the active thermodynamic variable in the density layers, which is advected and diffused. Layer temperature is derived from layer density and salinity.

The model was integrated for 20 years and the last five years have been used in this study. The model data output used here are instantaneous fields of SSH and mixed layer temperature (as a proxy for SST) at 3-day intervals. A DYNAMO intercomparison study has been performed by Willebrand et al., [1999].

3.4 Satellite observations

3.4.1 TOPEX/POSEIDON altimeter data

The TOPEX/POSEIDON (hereafter, T/P) data used in this study were extracted from the geophysical data records (GDRs) provided on CD-ROMs by Aviso Altimetrie [AVISO, 1996]. The data extracted from the GDRs consist of geo-located, approximately one-second average SSH estimates in the North Atlantic Ocean, covering the approximate 4-year period December 1992 to January 1997 (cycles 8 to 159). [Clearly, more data has since become available, but the present intercomparison between model and satellite data was carried out when this dataset was relatively recent].

A standard set of geophysical corrections is applied [Fu et al., 1994] to the SSH values at each along-track location. An inverse barometer calculation is adopted and the four-parameter model of Gaspar et al. [1996] is used to correct for sea state bias. The CSR3.0 [Eanes and Bettadpur, 1995] tidal model is used to remove the effects of tides, and the dual-frequency ionospheric correction is smoothed with a 21-second moving average before applying it. After correction, the SSH data are collocated onto a set of reference latitudes and longitudes corresponding to cycle 18 (this being a cycle close to the nominal ground track position). Collocation is by a perpendicular bisector approach [e.g. Jones et al., 1998] whereby the effects of across-track mean sea surface gradients are removed. At each point on the reference cycle, the collocated SSH data are used to generate a time-mean SSH for the three-year period 1993-1995. (Using a non-integral number of years would introduce a seasonal bias in the mean SSH). This time-mean is then subtracted from individual SSH cycles to obtain the SSH anomaly for each cycle. Finally, the SSH anomalies are gridded onto a regular 1^o by 1^o grid by means of Gaussian interpolation using a full-width half-maximum (FWHM) of 150 km and a search radius of 200 km. These parameters were selected after experimentation with several different parameters and study of the resulting gridded fields. Propagating signals are evident in the longitude-time plots of SSH anomalies at different latitudes [Cipollini et al., 1999]. In this study we actually use the zonal gradient of SSH [Hughes 1995, 1996; Cipollini et al., 1997a]. This highlights the presence of dynamical features of order hundreds of kmís, such as Rossby waves, and filters out unwanted larger-scale signals, including the large-scale seasonal steric effect.

3.4.2 Along-Track Scanning Radiometer data

We use data from the Along-Track Scanning Radiometer (ATSR), flown on the satellite ERS-1, in particular, the spatially averaged (0.5^o in latitude and longitude) SST data (ASST), provided by the UK Rutherford Appleton Laboratory (RAL). The ASST data are obtained by averaging the 1 km resolution brightness temperatures into 10 arcminute cells, and then obtaining a SST measurement for each cell. The ASST is the average of the SSTs of the 10 arcminute cells. We used the 4-year dataset January, 1992 ó December 1995 as this was readily available from RAL at the time of the present study.

The ATSR instrument has several design improvements over the AVHRR instruments which allow a more accurate point measurement of SST to be made. These improvements result in (1) more accurate calibration, (2) lower detector noise, and (3) a more accurate atmospheric correction [e.g. Závody et al., 1995]. Validation studies have shown that the ATSR can measure SST to a point relative accuracy of 0.3 K [e.g. Forrester and Challenor, 1995; Mutlow et al., 1994], twice the accuracy of the AVHRR [McClain et al., 1985].

Infrared measurements of SST are not possible in the presence of cloud and hence cloudy data must be identified and removed. A series of tests based on the work of Saunders and Kriebel [1988] are used at RAL to identify cloud contaminated data. Jones et al. [1996] identify the presence of residual cloud contamination (caused by fog, low stratus, and stratocumulus cloud types) in the ASST data and describe a filtering algorithm to reduce this contamination. We use their filtering algorithm to reduce this error source. In brief, the algorithm involves fitting an annual and semi-annual model to the daytime ASST data at each location, and rejecting data that differs from the model by more than three times the standard deviation of the daytime residuals. Since infrared measurements are not possible in the presence of cloud, it is impossible to achieve gap-free SST fields over a 10-day averaging period in many regions. Since this study focuses on long period (several hundred days) Rossby waves we use monthly averages to reduce the need for interpolation (although during the time of the ERS-1 3-day repeat orbit phase some locations are never sampled due to the track spacing being larger than the 512 km swath width of ATSR). To reduce the effect of residual data spikes we use the median SST within each month. Typically, 3-4 SST values contribute to each monthly average within the North Atlantic region. We then obtain SST anomalies from the mean over the 4-year time period of the dataset. These are spatially averaged into 1û bins to give monthly 1û SST anomaly maps comparable to the SSH anomaly fields.

Baroclinic Rossby waves are observable in SSH fields because the propagating waves perturb the density structure of the ocean, and hence produce a SSH signature: a positive height anomaly if the vertical integral of the density perturbation is negative (less dense); a negative anomaly if the vertical integral is positive (more dense). There is global evidence for their propagation in SST fields, notwithstanding the surface skin effect (e.g. Schluessel et al., 1990) where the amplitude of Rossby waves in temperature can exceed 1K (Hill et al. 1999). The gradient of the resulting SSH signature is related to the surface speed in the wave through geostrophy. If the SST gradient can be regarded as a proxy for the surface density gradient, and if this surface density gradient is correlated with the density gradient at depth, then perturbations in the density field should also be visible as perturbations in the SST field. Indeed, Cipollini et al. [1997a] showed that it is possible to observe propagating baroclinic Rossby waves in the North-East Atlantic by analysis of the zonal gradient of the SST anomaly fields. Using the zonal gradient of SST anomalies also has the advantage (analogous to that observed for the SSH field) that the large scale seasonal steric signal is filtered out (this is the dominant SST signal in many regions) thus highlighting any Rossby waves.

3.5 Comparison of model and satellite data

3.5.1 RMS variability in sea surface height and temperature

As a first-look comparison, in Figure 1 we present the root-mean-square SSH variability in both the 5-year model (a) and 4-year T/P (b) datasets in the North Atlantic region bounded by 10^o ó 60^o N, 75^o ó 5^o W. In geographical terms, the patterns correspond quite well, with high rms values in the Gulf Stream region though the region of maximum rms variability in the model is rather tighter than in satellite observations and hugs the North American coastline too far to the north. Typical peak values of SSH variability in the T/P data are ~25 cm, around 250% larger than peak values in the model data. DYNAMO Group [1997] shows that MICOM SSH variability is low compared to other models, probably because of higher viscosity in the model. However, in general, model variability in SSH is typically lower than that observed, which is typically attributed to the need for yet higher spatial resolution in models [e.g. Beckmann et al., 1994b] and/or higher temporal resolution in wind forcing [ e.g. Milliff et al., 1996].

Figure 2 displays the rms SST variability for the 5-year model (a) and 4-year satellite (b) datasets. The same broad features are seen in both with once again high values in the Gulf Stream region. Peak rms SST values are comparable at ~5^o C. Given that the mixed layer temperature of the model is relaxed to the Levitus climatology, it is to be expected that the model and observed SST values would be broadly consistent and, therefore, that the peak rms in model and observed SST values would be in better agreement than the respective rms SSH values. It is worth noting that model SSH and EKE variability values exhibit peaks near the latitude of the observed Azores Front [Jia, 1999.].

3.5.2 Properties of propagating baroclinic Rossby waves

It is known from earlier observations [e.g. Tokmakian and Challenor, 1993; Cipollini et al., 1997b] that baroclinic Rossby wave propagation velocity can be significantly affected when crossing the Mid-Atlantic Ridge. For reasons of simplicity we restrict the comparison in this section to the mid-latitude ocean basin east of the Mid-Atlantic Ridge. Let us consider the latitude range 25^o ó 45^oN. Due to the existence of a poleward turning latitude (refer back to page 9), there is in any case, little Rossby wave propagation north of 45^oN in the North Atlantic, as confirmed by the ray-tracing experiments of Killworth and Blundell (1999). No clear signal of propagating baroclinic Rossby waves is seen in the model in the latitude range 40^o-45^oN, although they do exist here in the satellite data. South of 30^oN, which we briefly consider later, there are westward propagating features in the model, but they do not correspond to observed Rossby waves. As we wish to make an intercomparison at latitudes where Rossby waves exist in both model data and observations we focus for the moment on 30^o -38^oN.

Figures 3-7 show pairs of longitude-time diagrams of the zonal gradient in SSH from (a) 5-year model data and (b) 4-year T/P observations at latitudes 30^oN - 38^oN in steps of 2^o. At each latitude, the longitude range is chosen to extend east of the Mid-Atlantic Range to the eastern edge of the basin. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ (equivalent to a SSH difference of 10 cm over 100 km; or a geostrophic velocity at 35^oN of ~12 cm s^-1). By taking the 2D Fourier Transform (not shown) of each longitude-time diagram, the frequency, zonal wavelength and zonal speed of the observed propagating baroclinic Rossby waves can be determined. The resolution in frequency and wavenumber space is determined by the length of the time series and the longitude span selected, respectively. Cipollini et al., [1997a] presented evidence from SSH and SST data which suggested that at 34^oN, not only the first baroclinic mode could be observed, but (weaker) second and third order modes too. In what follows, we present results for the first baroclinic mode observed in satellite and model data. [A fruitful topic for future research would be to determine where, and why, higher order modes can be observed.] As an example of the results, at 34^oN baroclinic Rossby wave characteristics in the satellite (model) data are: period of ~200 days (~1 year), wavelength of ~510 (~690) km, and a zonal speed of ~2.2 (~1.6) cm/s (see Figure 5). The complete results, including error estimates, are provided in Table 2 and are discussed further in what follows.

We also examined the energy of the propagating modes in both model data and observations. Whereas remotely-sensed data indicate strongest propagation at ~34^oN (Figure 5b), MICOM surface dynamic topography shows strongest propagation at ~38^oN (Figure 7a). In satellite observations, the Azores Current (AC) may act to concentrate Rossby wave energy just to the north of its flow, i.e. at ~34^oN, as was suggested in Cipollini et al. [1997b]. In the model, as pointed out in the study of Jia [1999], the AC is induced by a "restoring condition" in the Gulf of Cadiz, applied in an area between 11^o-6^oW, and between 33.5^o-38^oN. The southern edge of the restoring area coincides with the mean position of the model AC (see Figure 9) where there is eastward propagation west of 25^oW. It is possible that model Rossby waves are excited by the restoring condition in the Gulf of Cadiz.

At 32^o-34^oN in the model, but not in the satellite data, there is a convergence of eastward and westward propagating structures at ~30^o-25^oW (Figures 4a and 5a). The eastward propagation signal west of the convergence region is very likely the eastward propagation of meanders in the AC and eddies. As shown by Jia [1999], in the region between 32^o - 35^o N and 50^o - 25^o W, the model AC is characterised by large meanders and eddies which propagate eastward. Siedler et al. [1985] reported both eastward and westward propagation of meanders and suggested that the large-scale flow field is sometimes strong enough to lead to an eastward phase propagation by overriding the westward propagation of Rossby waves. It is not clear why there is no clear evidence of a convergence zone of eastward and westward propagation in the satellite observations (Figures 4b and 5b) although a Fourier analysis (not shown) does reveal the presence of weaker eastward propagating energy at these latitudes.

At most latitudes in the MICOM data there is a clear annual signal, related to the annual forcing of the model. At locations south of 30^oN, however, there are striking westward propagating features which persist over several years: see Figure 8 for an example at 25^oN. These slow features have no analogue in the observations and we do not consider these model artefacts further.

Sea surface temperature data were also examined for propagating Rossby waves. The strongest evidence for propagation was seen near 34^oN. As these structures have already been reported in Cipollini et al. [1997b], we do not reproduce the results here.In MICOM SST data, it is difficult to unambiguously identify propagating Rossby waves. The only clear signal is a large-scale annual one near wavenumber, k = 0.0 (i.e. infinite wavelength), which is probably a residual steric effect not completely removed by taking zonal gradients. In the real ocean, observing Rossby waves in SST data is more difficult than in SSH data for a variety of reasons such as decoupling of surface temperatures from subsurface structure, and cloud cover.

On average, the Rossby wave zonal speeds seen in model SSH data are ~40% slower than the speeds observed in T/P SSH (Table 2). The error bars in the speeds are somewhat conservative. We believe that the difference in observed and model speeds is statistically significant. This analysis is consistent with observations [Chelton and Schlax, 1996] and a revised theory of mid-latitude Rossby waves showing a factor of ~2 increase in speed over the standard linear theory when the effect of background baroclinic mean flows are accounted for [Killworth et al., 1997]. As shown by Cipollini et al [1997b], there is no significant meridional propagation here, so that the zonal speeds are close to the magnitudes of the Rossby wave velocities.

3.6 MICOM: low-resolution vs. high-resolution

The above discussion relates to the high-resolution version of MICOM. The right hand panel of Figure 10 shows output from another run of the isopycnic model at 36°N, with a resolution of 4/3° in longitude by 4/3° cos(latitude), but otherwise identical conditions as before. This too contains an eastward-flowing Azores Current at 33°-35°N. However the variability in the model dynamic heights is much less than in its finer resolution counterpart and the Rossby waves are also much weaker. In this case, the strength of Rossby waves again increases as one moves northward from 32°N to 36°N, but with dominant eastward-propagating signals at 38°N. In Figure 10, the Rossby waves are weaker in the coarser resolution run, but the propagation speeds are slightly greater (but still lower than T/P-observed speeds), and show a slight acceleration on crossing the Mid-Atlantic Ridge (MAR) at ~40°W. On the other hand, the finer resolution run shows a marked reduction in the propagation speed on crossing the MAR; this is not consistent with observations, and may be due to strong eastward flow advecting the Rossby waves. The monthly climatological forcing generates very regular seasonal cycles in the output of the coarse run, whereas the finer resolution run is able to generate interannual variations from the same forcing fields, perhaps because the model resolves and "remembers" features at finer scales.

4. SUMMARY AND CONCLUSIONS

In Section 2, we presented a reduced gravity model that we are currently developing for the study of wind forcing of Rossby waves, and possibly other ocean dynamic effects also. Currently, we are working on various ways of improving the robustness of the model so that it does not collapse after just 2 years of model time. Improvements include adjustments to the model viscosity and diffusivity coefficients; sinusoidal ramping up of the applied wind stress field from zero to the climatology values over a number of years; and investigation of improved parameterisation of the nonlinear advection term (see Equations [7] and [8]), which may well be of importance with the enhancement of the model resolution from 1 degree to 0.5 degree.

In Section 3, we showed that analysis of propagating baroclinic Rossby waves provides a powerful and novel method of validating ocean general circulation models. We compare propagation characteristics in the North-East Atlantic as observed in satellite and ocean model sea surface height (SSH) and temperature (SST) data. We use 5 years of output from a high-resolution (1/3^o) numerical model based on the Miami Isopycnic Coordinate Ocean Model. The satellite dataset comprises TOPEX/POSEIDON SSH observations from January 1992 ó January 1997, and ERS-1 Along-Track Scanning Radiometer SST data from January 1992 ó December 1995.

Over the latitude range examined in detail (30^o-38^oN), Rossby wave speeds are around 40% lower in the model compared to T/P SSH observations, on the basis of SSH signatures. At most latitudes in the model there is a clear annual cycle in Rossby wave propagation related to the annual wind forcing in the model. The Rossby waves have shorter periods and wavelengths in the satellite observations compared to model data. Whereas satellite data indicate strongest propagation east of the Mid-Atlantic Ridge near 34^oN, MICOM data show strongest propagation further north near 38^oN. At 32^o-34^oN in the model, but not in the satellite data, there is a convergence of eastward and westward propagating structures at ~30^o-25^oW.

Jacobson and Spiesberger [1998] studied bathythermometric observations of Rossby waves in the northeast Pacific apparently induced by El Niño-Southern Oscillation events. They compared the observed phase speeds with those in a 1/8^o resolution nonlinear primitive equation hydrodynamic model. The model was isopycnic, but with only six constant-density layers. At midlatitudes, the authors report that observed phase speeds are more than 1.5 times faster than theory, but that the model phase speeds exceed standard linear theory by only 0.1 cm/s. This intriguing result is surprising since it is claimed that the model reproduces realistic in situ wind forcing, bathymetry, and baroclinic currents ó all of which have been proposed as possible mechanisms that could account for the observed speed of baroclinic Rossby waves.

In closing, we note that, as a litmus test of model realism, MICOM performs reasonably well in reproducing observed features of baroclinic Rossby wave propagation. We suggest that the underestimate of Rossby wave propagation speed in MICOM data relates to unrealistically low values of thermal wind shear in the model which, in turn, could arise from use of s_o(surface-referenced density) as the model vertical coordinate. Investigating this should be the subject of another report.
 

ACKNOWLEDGEMENTS

The authors thank NASA and CERSAT-IFREMER for providing altimeter data, ESA and RAL for ATSR data, and the DYNAMO group for providing model data. Grateful thanks to Paolo Cipollini and Graham Quartly for contributing to research which has been included here. Thanks also to Yanli Jia and the large-scale modelling team for provision of MICOM output. We are grateful to Matthew Jones for his work on the ATSR data and to Helen Snaith for support of the altimeter processing software. The description of the reduced gravity model is taken from Bulusu Subrahmanyamís PhD thesis (University of Southampton, 1998). He also supplied ERS scatterometer data, originally provided by IFREMER, which enabled us to construct a monthly climatology. We had useful discussions with Peter Challenor and Adrian New.

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ACRONYMS

ADEOS ADvanced Earth Observation System

ASST Average Sea Surface Temperature

ATSR Along-Track Scanning Radiometer (instrument on board ERS-1/2)

AVHRR Advanced Very High Resolution Radiometer

BFC Brazil-Falklands Confluence

EOS Earth Observation System (NASA satellite series)

ERS European Remote Sensing satellite

ESA European Space Agency

IRS Indian Remote Sensing satellite

MERIS Medium Resolution Imaging Spectrometer (on board Envisat)

MODIS Moderate Resolution Imaging Spectrometer (on board EOS)

MOS Modular Optoelectronic Scanner (ocean colour sensor on board IRS)

NASA National Aeronautics and Space Administration

OCTS Ocean Colour and Temperature Scanner (on board ADEOS)

OPC Optical Plankton Counter

SeaWiFS Sea-viewing Wide Field-of-view Sensor (US ocean colour satellite)

SOC Southampton Oceanography Centre

SSH Sea Surface Height

SSHA SSH anomaly

SST Sea Surface Temperature

T/P TOPEX/POSEIDON

WOCE World Ocean Circulation Experiment
 

FIGURES : MICOM VS. SATELLITE
 

Figure 1. Root-mean-square variability in sea surface height data from (a) 1/3^o MICOM ocean model data, years 16-21; the contour interval is 1 cm ; (b) TOPEX/POSEIDON altimeter observations from Jan 1993 ó Dec 1997; contour interval is 5 cm.
 
 

Figure 2. Root-mean-square variability in sea surface temperature data from (a) 1/3^o MICOM ocean model data, years 16-21; the contour interval is 0.5K ; (b) ERS-1 Along-Track Scanning Radiometer observations from Jan 1992 ó Dec 1995; contour interval is 0.5 K.
 
 

Figure 3. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 30^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-1.0:0.2:1.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 
 

Figure 4. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 32^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-1.0:0.2:1.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 

Figure 5. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 34^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 106 for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-2.0:0.4:2.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 
 

Figure 6. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 36^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-1.0:0.2:1.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 
 

Figure 7. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 38^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-1.0:0.2:1.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 
 

Figure 8. Longitude-time diagrams of zonal gradient in sea surface height anomaly at 25^oN east of the Mid-Atlantic Ridge. SSH gradients have been converted to units of microradians, i.e. slope of 1 in 10⁶ for (a) MICOM ocean model data; contour range [-0.2:0.05:0.2]; and (b) TOPEX/POSEIDON altimeter observations; contour range [-1.0:0.2:1.0]. Solid contours and dark grey shading represent positive values and dashed contours and light grey shading represent negative values.
 
 

Figure 9. The mean velocity at 110m depth of the 1/3^o MICOM ocean model.
 
 

Figure 10. Longitude-time plots of zonal height anomalies at 36^oN from MICOM: 1/3^o model (left hand panel); 4/3^o model (right hand panel). Both datasets were interpolated to : 1^o x 1^o resolution prior to analysis and plotting.

Table 1. The surface-referenced potential density anomaly (s₀) of the 20 layers defining the discretised vertical coordinate of the model. Layer 1 is the model mixed layer which has a variable density distribution.

TABLE 2
 

		ocean model data			TOPEX/POSEIDON altimeter observations
Latitude (oN)	Longitude (oW)	l (km)	T (days)	v (cm/s)	l (km)	T (days)	v (cm/s)
30	42 - 14
32	40 - 10
34	38 - 8
36	34 - 8
38	30 - 10

Table 2. Characteristics of propagating baroclinic Rossby waves in 5-year datasets of both ocean model data and TOPEX/POSEIDON altimeter observations. Error bars are derived on the basis of spectral resolution in the frequency and wavenumber domains.
 

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