Turbulent viscosity optimized by data assimilation

As an alternative approach to classical turbulence modelling using a first or second order closure, the data assimilation method of optimal control is applied to estimate a time and space-dependent turbulent viscosity in a three-dimensional oceanic circulation model. The optimal control method, described for a 3-D primitive equation model, involves the minimization of a cost function that quantifies the discrepancies between the simulations and the observations. An iterative algorithm is obtained via the adjoint model resolution. In a first experiment, a k ± L model is used to simulate the one-dimensional development of inertial oscillations resulting from a wind stress at the sea surface and with the presence of a halocline. These results are used as synthetic observations to be assimilated. The turbulent viscosity is then recovered without the k + L closure, even with sparse and noisy observations. The problems of controllability and of the dimensions of the control are then discussed. A second experiment consists of a two-dimensional schematic simulation. A 2-D turbulent viscosity field is estimated from data on the initial and final states of a coastal upwelling event.     

A three-dimensional model study of warm core ring interaction with continental shelf and slope

The interaction of warm core rings with a western wall and shelf/slope is examined with a three-dimensional primitive-equation model. The model ring is initialized with an axisymmetric Gaussian-type anticyclonic eddy placing far from the coastal boundary to allow the ring to freely propagate towards the wall and shelf/slope. The ring initially propagates steadily to the southwest at about 3 km/day under the combined planetary β and nonlinear effects. When colliding with a wall, the ring adjusts into a ‘D’ shape and moves poleward under primarily the image effect. When colliding with a shelf and slope, the ring however becomes stalled and bounces on and off the shelf/slope with little net movement. Small cyclones marked by strong upwelling are generated near the shelfbreak. Cyclones and anticyclones also are spawned at the periphery of the ring. Satellite SST images and concurrent ADCP transects are used to illustrate the strong interaction of a Gulf Stream warm ring (99B) with the Middle Atlantic Bight.     

Barotropic wind-driven circulation patterns in a closed rectangular basin of variable depth influenced by a peninsula or an island

We study how a coastal obstruction (peninsula or coastal island) affects the three-dimensional barotropic currents in an oblong rectangular basin with variable bathymetry across the basin width. The transverse depth profile is asymmetric and the peninsula or island lies in the middle of the long side of the rectangle. A semi-spectral model for the Boussinesq-approximated shallow water equations, developed in Haidvogel et al. and altered for semi-implicit numerical integration in time in Wang and Hutter, is used to find the steady barotropic state circulation pattern to external winds. The structural (qualitative) rearrangements and quanti2tative features of the current pattern are studied under four principal wind directions and different lengths of the peninsula and its inclination relative to the shore. The essentially non-linear relationships of the water flux between the two sub-basins (formed by the obstructing peninsula) and the corresponding cross-sectional area left open are found and analysed. It is further analysed whether the depth-integrated model, usually adopted by others, is meaningful when applied to the water exchange problems. The flow through the channel narrowing is quantitatively estimated and compared with the three-dimensional results. The dynamics of the vortex structure and the identification of the up-welling/down-welling zones around the obstruction are discussed in detail. The influence of the transformation of the peninsula into a coastal island on the global basin circulation is considered as are the currents in the channel. The geometric and physical reasons for the anisotropy of the current structure which prevail through all obtained solutions are also discussed.Dedicated to Professor L.A. Mysak on the occasion of his sixtieth birthday.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part I: hypothetical boundaries

A baroclinic shallow-water model is developed to investigate the effect of the orientation of the eastern ocean boundary on the behavior of equatorial Kelvin waves. The model is formulated in a spherical polar coordinate system and includes dissipation and non-linear terms, effects which have not been previously included in analytical approaches to the problem. Both equatorial and middle latitude response are considered given the large latitudinal extent used in the model. Baroclinic equatorial Kelvin waves of intraseasonal, seasonal and annual periods are introduced into the domain as pulses of finite width. Their subsequent reflection, transmission and dissipation are investigated. It is found that dissipation is very important for the transmission of wave energy along the boundary and for reflections from the boundary. The dissipation was found to be dependent not only on the presence of the coastal Kelvin waves in the domain, but also on the period of these coastal waves. In particular the dissipation increases with wave period. It is also shown that the equatorial β-plane approximation can allow an anomalous generation of Rossby waves at higher latitudes. Nonlinearities generally have a small effect on the solutions, within the confines of this model.     

Intercomparison of oceanic and atmospheric forced and coupled mesoscale simulations. Part I: Surface fluxes

A mesoscale non-hydrostatic atmospheric model has been coupled with a mesoscale oceanic model. The case study is a four-day simulation of a strong storm event observed during the SEMAPHORE experiment over a 500 × 500 km² domain. This domain encompasses a thermohaline front associated with the Azores current. In order to analyze the effect of mesoscale coupling, three simulations are compared: the first one with the atmospheric model forced by realistic sea surface temperature analyses; the second one with the ocean model forced by atmospheric fields, derived from weather forecast re-analyses; the third one with the models being coupled. For these three simulations the surface fluxes were computed with the same bulk parametrization. All three simulations succeed well in representing the main oceanic or atmospheric features observed during the storm. Comparison of surface fields with in situ observations reveals that the winds of the fine mesh atmospheric model are more realistic than those of the weather forecast re-analyses. The low-level winds simulated with the atmospheric model in the forced and coupled simulations are appreciably stronger than the re-analyzed winds. They also generate stronger fluxes. The coupled simulation has the strongest surface heat fluxes: the difference in the net heat budget with the oceanic forced simulation reaches on average 50 Wm⁻² over the simulation period. Sea surface-temperature cooling is too weak in both simulations, but is improved in the coupled run and matches better the cooling observed with drifters. The spatial distributions of sea surface-temperature cooling and surface fluxes are strongly inhomogeneous over the simulation domain. The amplitude of the flux variation is maximum in the coupled run. Moreover the weak correlation between the cooling and heat flux patterns indicates that the surface fluxes are not responsible for the whole cooling and suggests that the response of the ocean mixed layer to the atmosphere is highly non-local and enhanced in the coupled simulation.     

Reflection of equatorial Kelvin waves at eastern ocean boundaries Part II: Pacific and Atlantic Oceans

The effect of viscosity, non linearities, incident wave period and realistic eastern coastline geometry on energy fluxes are investigated using a shallow water model with a spatial resolution of 1/4 degree in both meridional and zonal directions. Equatorial and mid-latitude responses are considered. It is found that (1) the influence of the coastline geometry and the incident wave period is more important for the westward energy flux than for the poleward flux, and (2) the effect of the inclination of the eastern ocean boundary on the poleward energy flux, for the Pacific and Atlantic Oceans, decline as the period of the incident wave increases. Furthermore, the model simulations suggest that the poleward energy fluxes from meridional boundaries give plausible results for motions of seasonal and annual periods. For comparatively shorter periods, a realistic coastline geometry has to be included for more accurate results. It is recommended that any numerical model involving the reflection of baroclinic Rossby waves (of intraseasonal, seasonal or annual periods) on the eastern Pacific or Atlantic Oceans, should consider the effect of the coastline geometry in order to improve the accuracy of the results.     

Passive tracers in a general circulation model of the Southern Ocean

Passive tracers are used in an off-line version of the United Kingdom Fine Resolution Antarctic Model (FRAM) to highlight features of the circulation and provide information on the inter-ocean exchange of water masses. The use of passive tracers allows a picture to be built up of the deep circulation which is not readily apparent from examination of the veloCity or density fields. Comparison of observations with FRAM results gives good agreement for many features of the Southern Ocean circulation. Tracer distributions are consistent with the concept of a global “conveyor belt” with a return path via the Agulhas retroflection region for the replenishment of North Atlantic Deep Water.     

The evolution of an internal bore at the Malin shelf break

Observations of internal waves were made at the Malin shelf edge during SESAME (Shelf Edge Studies Acoustic Measurement Experiment), a part of the NERC LOIS-SES experiment, in August-September 1996. These measurements provide a high resolution dataset demonstrating internal wave generation and propagation. This note presents observations of the evolution of an internal bore. The process is shown clearly in a sequence of thermistor chain tows across the shelf break covering a complete tidal cycle, as the double-sided bore transforms into a group of undulations and eventually into more distinct solitary waveforms. Current structures associated with the bore and waves were also observed by ship-mounted ADCP. Analysis of the waveforms in terms of the linear modes and empirical orthogonal functions (EOFs) indicate the dominance of the first mode, which is typical of a shallow water seasonal thermocline environment. Determination of the phase speed of the waves from the consecutive ship surveys enabled the Doppler shift in the towed data to be removed, allowing analysis of the real length scales of the waves. The bore evolution has been modelled using a first order non-linear KdV model for the first mode, initialised with the waveform in the first survey. Comparison of the model and the observations show close agreement in the amplitudes, length scales, phase speeds and separations of the leading internal waves as they evolve. Finally, analysis of the observed internal wave shapes indicates that, within the uncertainties of measurement, the wave-lengths lie between those predicted by first and second order soliton theory.     

Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

A dynamically consistent analysis of circulation and transports in the southwestern Weddell Sea

An inverse model is applied for the analysis of hydrographic and current meter data collected on the repeat WOCE section SR4 in the Weddell Sea in 1989–1992. The section crosses the Weddell Sea cyclonic gyre from Kapp Norvegia to the northern end of the Antarctic Peninsula. The concepts of geostrophy, conservation of planetary vorticity and hydrostatics are combined with advective balances of active and passive properties to provide a dynamically consistent circulation pattern. Our variational assimilation scheme allows the calculation of three-dimensional velocities in the section plane. Current speeds are small except along the coasts where they reach up to 12 cm/s. We diagnose a gyre transport of 34 Sverdrup which is associated with a poleward heat transport of 28 × 10¹² W corresponding to an average heat flux of 15 Wm^–2 in the Weddell Sea south of the transect. This exceeds the estimated local flux on the transect of 2 Wm^–2. As the transect is located mostly in the open ocean, we conclude that the shelf areas contribute significantly to the ocean-atmosphere exchange and are consequently key areas for the contribution of the Weddell Sea to global ocean ventilation. Conversion of water masses occuring south of the section transform 6.6 ± 1.1 Sv of the inflowing warm deep water into approximately equal amounts of Weddell Sea deep water and Weddell Sea bottom water. The volume transport of surface water equals in the in-and outflow. This means that almost all newly formed surface water is involved in the deep and bottom water formation. Comparison with the results obtained by pure velocity interpolation combined with a hydrographic data subset indicates major differences in the derived salt transports and the water mass conversion of the surface water. The differences can be explained by deviations in the structure of the upper ocean currents to which shelf areas contribute significantly. Additionally a rigorous variance analysis is performed. When only hydrographic data are used for the inversion both the gyre transport and the poleward heat transport are substantially lower. They amount to less than 40% of our best estimate while the standard deviations of both quantities are 6.5 Sv and 37 × 10¹² W, respectively. With the help of long-term current meter measurements these errors can be reduced to 2 Sv and 8 × 10¹² W. Our result underlines the importance of velocity data or equivalent information that helps to estimate the absolute velocities.     

The effect of coastal upwelling on the sea-breeze circulation at Cabo Frio, Brazil: a numerical experiment

The effect of coastal upwelling on sea-breeze circulation in Cabo Frio (Brazil) and the feedback of sea-breeze on the upwelling signal in this region are investigated. In order to study the effect of coastal upwelling on sea-breeze a non-linear, three-dimensional, primitive equation atmospheric model is employed. The model considers only dry air and employs boundary layer formulation. The surface temperature is determined by a forcing function applied to the Earths surface. In order to investigate the seasonal variations of the circulation, numerical experiments considering three-month means are conducted: January-February-March (JFM), April-May-June (AMJ), July-August-September (JAS) and October-November-December (OND). The model results show that the sea-breeze is most intense near the coast at all the seasons. The sea-breeze is stronger in OND and JFM, when the upwelling occurs, and weaker in AMJ and JAS, when there is no upwelling. Numerical simulations also show that when the upwelling occurs the sea-breeze develops and attains maximum intensity earlier than when it does not occur. Observations show a similar behavior. In order to verify the effect of the sea-breeze surface wind on the upwelling, a two-layer finite element ocean model is also implemented. The results of simulations using this model, forced by the wind generated in the sea-breeze model, show that the sea-breeze effectively enhances the upwelling signal.     

Combining T/P altimetric data with hydrographic data to estimate the mean dynamic topography of the North Atlantic and improve the geoid

The mean dynamic topography of the surface of the North Atlantic is estimated using an inverse model of the ocean circulation constrained by hydro-graphic and altimetric observations. In the North Atlantic, altimetric observations have no significant impact on the topography estimate because of the limited precision of available geoid height models. They have a significant impact, however, when uncertainties in the density field are increased to simulate interpolation errors in regions where hydrographic data are scarce. This result, which moderates the conclusion drawn by Ganachaud and co-workers of no significant contribution of altimetric observations to the determination of the large-scale steady circulation, reflects the simple idea that altimetric data are most useful near the surface of the ocean and in areas where the hydrography is poorly determined. One application of the present inverse estimate of the mean dynamic topography is to compute a geoid height correction over the North Atlantic which reduces the uncertainty in the geoid height expanded to spherical harmonic 40 down to a level of about 5 cm.     

Water mass distribution in Fram Strait and over the Yermak Plateau in summer 1997

The water mass distribution in northern Fram Strait and over the Yermak Plateau in summer 1997 is described using CTD data from two cruises in the area. The West Spitsbergen Current was found to split, one part recirculated towards the west, while the other part, on entering the Arctic Ocean separated into two branches. The main inflow of Atlantic Water followed the Svalbard continental slope eastward, while a second, narrower, branch stayed west and north of the Yermak Plateau. The water column above the southeastern flank of the Yermak Plateau was distinctly colder and less saline than the two inflow branches. Immediately west of the outer inflow branch comparatively high temperatures in the Atlantic Layer suggested that a part of the extraordinarily warm Atlantic Water, observed in the boundary current in the Eurasian Basin in the early 1990s, was now returning, within the Eurasian Basin, toward Fram Strait. The upper layer west of the Yermak Plateau was cold, deep and comparably saline, similar to what has recently been observed in the interior Eurasian Basin. Closer to the Greenland continental slope the salinity of the upper layer became much lower, and the temperature maximum of the Atlantic Layer was occasionally below 0.5 °C, indicating water masses mainly derived from the Canadian Basin. This implies that the warm pulse of Atlantic Water had not yet made a complete circuit around the Arctic Ocean. The Atlantic Water of the West Spitsbergen Current recirculating within the strait did not extend as far towards Greenland as in the 1980s, leaving a broader passage for waters from the Atlantic and intermediate layers, exiting the Arctic Ocean. A possible interpretation is that the circulation pattern alternates between a strong recirculation of the West Spitsbergen Current in the strait, and a larger exchange of Atlantic Water between the Nordic Seas and the inner parts of the Arctic Ocean.     

Wind-induced baroclinic response of Lake Constance

We present results of various circulation scenarios for the wind-induced three-dimensional currents in Lake Constance, obtained with the aid of a semi-spectral semi-implicit finite difference code developed in Haidvogel et al. and Wang and Hutter. Internal Kelvin and Poincaré-type oscillations are demonstrated in the numerical results, whose periods depend upon the stratification and the geometry of the basin and agree well with measured data. By solving the eigenvalue problem of the linearized shallow water equations in the two-layered stratified Lake Constance, the interpretation of the oscillations as Kelvin and Poincaré-type waves is corroborated.     

The beneficial role of rubble mound coastal structures on seawater oxygenation

The beneficial role of rubble mound coastal structures on oxygenation under the effect of waves is discussed, based on analytical considerations and experimental data from laboratory experiments with permeable and impermeable structures. Significant oxygenation of the wave-protected area was observed as a result of horizontal transport through the permeable structure. A two-cell model describing the transport of dissolved oxygen (DO) near a rubble mound breakwater structure was developed and used for the determination of the oxygen transfer coefficients from the experimental data. Oxygen transfer through the air-water interface is considered a source term in the transport equation and the oxygen flux through the structure is taken into account. The mass transport equations for both sides of the structure are solved analytically in terms of time evolution of DO concentration. The behaviour of the solution is illustrated for three different characteristic cases of initial conditions. The oxygen transfer through the air-water interface in the wave-influenced area increases the DO content in the area; the resulting oxygen flux through the structure is discussed. The analytical results depend on the initial conditions, the oxygen transfer coefficient and the exchange flow rate through the structure. Experiments with impermeable structures show that air water oxygen transfer in the harbour area is negligible in the absence of waves. In addition the ratio of the horizontal DO flux to the vertical flux into the seaward side tends towards a constant value, independent of the initial conditions.     

Climatic features of the Mediterranean Sea detected by the analysis of the longwave radiative bulk formulae

Some important climatic features of the Mediterranean Sea stand out from an analysis of the systematic discrepancies between direct measurements of longwave radiation budget and predictions obtained by the most widely used bulk formulae. In particular, under clear-sky conditions the results show that the surface values of both air temperature and humidity over the Mediterranean Sea are larger than those expected over an open ocean with the same amount of net longwave radiation. Furthermore, the twofold climatic regime of the Mediterranean region strongly affects the downwelling clear-sky radiation. This study suggests that a single bulk formula with constant numerical coefficients is unable to reproduce the fluxes at the surface for all the seasons.     

Multi-instrument observations of the electric and magnetic field structure of omega bands

High time resolution data from the CUTLASS Finland radar during the interval 01:30–03:30 UT on 11 May, 1998, are employed to characterise the ionospheric electric field due to a series of omega bands extending 5° in latitude at a resolution of 45 km in the meridional direction and 50 km in the azimuthal direction. E-region observations from the STARE Norway VHF radar operating at a resolution of 15 km over a comparable region are also incorporated. These data are combined with ground magnetometer observations from several stations. This allows the study of the ionospheric equivalent current signatures and height integrated ionospheric conductances associated with omega bands as they propagate through the field-of-view of the CUTLASS and STARE radars. The high-time resolution and multi-point nature of the observations leads to a refinement of the previous models of omega band structure. The omega bands observed during this interval have scale sizes 500 km and an eastward propagation velocity 0.75 km s^–1. They occur in the morning sector (05 MLT), simultaneously with the onset/intensification of a substorm to the west during the recovery phase of a previous substorm in the Scandinavian sector. A possible mechanism for omega band formation and their relationship to the substorm phase is discussed.     

Meridian-scanning photometer, coherent HF radar, and magnetometer observations of the cusp: a case study

The dynamics of the cusp region and post-noon sector for an interval of predominantly IMF B_y, B_z < 0 nT are studied with the CUTLASS Finland coherent HF radar, a meridian-scanning photometer located at Ny Ålesund, Svalbard, and a meridional network of magnetometers. The scanning mode of the radar is such that one beam is sampled every 14 s, and a 30° azimuthal sweep is completed every 2 minutes, all at 15 km range resolution. Both the radar backscatter and red line (630 nm) optical observations are closely co-located, especially at their equatorward boundary. The optical and radar aurora reveal three different behaviours which can interchange on the scale of minutes, and which are believed to be related to the dynamic nature of energy and momentum transfer from the solar wind to the magnetosphere through transient dayside reconnection. Two interpretations of the observations are presented, based upon the assumed location of the open/closed field line boundary (OCFLB). In the first, the OCFLB is co-located with equatorward boundary of the optical and radar aurora, placing most of the observations on open field lines. In the second, the observed aurora are interpreted as the ionospheric footprint of the region 1 current system, and the OCFLB is placed near the poleward edge of the radar backscatter and visible aurora; in this interpretation, most of the observations are placed on closed field lines, though transient brightenings of the optical aurora occur on open field lines. The observations reveal several transient features, including poleward and equatorward steps in the observed boundaries, braiding of the backscatter power, and 2 minute quasi-periodic enhancements of the plasma drift and optical intensity, predominantly on closed field lines.     

Effects of substorms on the stormtime ring current index Dst

There has been some discussion in recent times regarding whether or not substorm expansive phase activity plays any role of importance in the formation of the stormtime ring current. I explore this question using the K_p index as a proxy for substorm expansive phase activity and the D_st index as a proxy for symmetric ring current strength. I find that increases in D_st are mildly related to the strength of substorm expansive phase activity during the development of the storm main phase. More surprisingly, I find that the strength of D_st during the storm recovery phase is positively correlated with the strength of substorm expansive phase activity. This result has an important bearing on the question of how much the Dst index reflects activity other than that of the stormtime symmetric ring current strength for which it is supposed to be a proxy.     

Validation of the stream function method used for reconstruction of experimental ionospheric convection patterns

In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary) for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM) recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s) of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region) is compared with the original IZMEM/DMSP electric potential distribution(s), as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modeled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.