## 1. Introduction

Climate interannual variability on a global scale seems closely related to processes such as deep convection, occuring on much smaller scales in some specific areas. It is important to evaluate the heat and salt fluxes in such areas and to document the link between these small-scale events and the general circulation. Reliable overall budgets of deep convection are difficult to obtain from in situ observations since convective processes are localized and intermittent, thus covering a wide range of time and space scales.

The Gulf of Lion in the Western Mediterranean is one of the few spots in the world where “deep convection” occurs. This area exhibits some geographical similarities with higher latitude convection areas. It is exposed during the winter to dry and cold continental winds (mistral and tramontane) and the North Mediterranean Current, which follows the continental slope from the Ligurian Sea to the Catalan sea, induces a cyclonic circulation. Moreover, the bottom topography associated to the Deep Sea Fan of the Rhone River may enhance the localization of this cyclonic circulation.

The description of the mechanisms for deep convection, exposed bellow, was pionered by the MEDOC Group who performed cruises from 1969 to 1975 (MEDOC Group 1970; Stommel 1972). Deep convection is controlled by thermodynamical instability (Chu 1991) and leads to vertical mixing, which may reach the ocean bottom. The basic forcing to deep convection is an intense surface cooling produced by strong cold and dry winds. Additional factors, grouped under the term “preconditioning,” favor the occurrence of deep convection (Hogg 1973; Killworth 1976). A week basic stratification reduces the cooling necessary to produce surface waters denser than the deep waters. A local cyclonic circulation contributes to decrease the surface water stratification in two ways: first it produces a doming of the isopycnals, bringing weakly stratified water from below closer to the surface; second, the closed coherent circulation increases the time of exposure to the local surface cooling. As in the subpolar areas, deep convection in the Gulf of Lion exhibits large interannual variability in relation with the variability of the surface forcing (Mertens and Schott 1998). Convection may reach full depth (2000–2500 m) in some years but only 1000 m or even less in other instances.

The range of scales covered by the process of deep convection is summarized by Marshall and Schott (1999). They identify three categories of scales, each attached to a particular process. The *mixed patch* is defined as the area influenced directly by deep convection in contrast with the surrounding stratified areas. The size of this area is of the order of 100 km and corresponds to the geometry overlapping both the preconditioned and the forced area. Inside the mixed patch the *plumes,* columns with *O*(1 km) diameter and high downward velocities, are encountered. Vertical velocities within the plumes were first measured by Stommel et al. (1971), but a more complete description was obtained by Schott and Leaman (1991), who have measured *O*(10 cm s^{−1}) vertical downward velocities with acoustic Doppler current profilers (ADCPs) during the winter 1986/87. Understanding of the small scale processes leading to the plumes and their overall effect as mixing agent has been improved by numerical nonhydrostatic modeling (Jones and Marshall 1993; Send and Marshall 1996). At last, intermediate scales associated to eddies have been observed within the mixed patch. Gascard and Clarke (1983) have detected such structure with floats in both the Mediterranean and Labrador Seas. They are generally considered as resulting from the baroclinic instability of the boundary current surrounding the mixed patch. However, recent works by Legg et al. (1998) show that eddies can act as preconditionners, making the implicit assumption that eddies are preexistent.

Deep convection is often decomposed in three phases (The MEDOC Group 1970). During the *preconditioning period,* the surface forcing erodes the upper-layer stratification. Then occurs the *violent mixing phase.* This period is characterized by the creation of plumes, which lead to the homogenization of the mixed patch. During this time, vertical motion dominates. The last phase, described by Stommel (1972) as the *spreading phase,* occurs mainly when the forcing stops. Vertical transfers give way to horizontal transfers associated with the formation of eddies on geostrophic scales. The best data coverage of the Gulf of Lion, provided by Thetis 1 in terms of velocity measurements, is obtained during this last phase, and we will restrict the analysis to this period.

Killworth (1976) invokes baroclinic instability as the most efficient mechanism for the spreading, which occurs during the “postconvection.” Killworth’s conclusions were confirmed by later numerical studies. Barnier et al. (1989), using a quasigeostrophic model, and later Madec et al. (1991) and Hermann and Owens (1993) using a primitive equation model, have studied the response of the Gulf of Lion to a buoyancy forcing. In their works, the rim current associated with the mixed patch meanders and breaks into eddies of diameter 15 to 25 km. The three-dimensional effects associated with baroclinic instability tend to slow down the convective process by inducing horizontal exchanges of water and contributing to the restratification at the end of the forcing period. In all these simulations, the eddies generated by the instability at the edge of the mixed patch are strongly baroclinic although they exhibit in some cases a weak barotropic transport.

Thermohaline forcing, which removes surface buoyancy, is obviously the main agent for deep-water formation (DWF), but the occurrence of convection in very specific areas, with scales smaller than the air–sea heat flux, suggests that other factors should be taken into account. The numerical experiment of Madec et al. (1996) suggests that, besides the thermohaline forcing, the wind stress and the bottom topography can affect the DWF. The wind stress is shown to generate a strong cyclonic barotropic circulation, with transport close to 18 Sv. This wind induced barotropic response is not significantly modified by thermohaline forcing which induces a baroclinic circulation of a few centimeters per second in the upper 100 m. A second effect of the wind is to stabilize the flow and delay baroclinic instability. Finally, bottom topography imposes a constraint on the wind-induced barotropic circulation through conservation of potential vorticity. The Madec et al. (1996) study, performed in a more realistic configuration than previous process studies based on thermal forcing alone, leads to a revised image of convection and emphasizes the key role played by the barotropic circulation.

We present here a dynamical analysis of the time evolution of the full three-dimensional fields of temperature and advection in a convective area. The work is based on a dataset collected in the Gulf of Lion during the winter of 1991/92 (the Thetis 1 experiment). Our main objective is to present a methodology and to evaluate the efficiency and added value of such a method in comparison to more classical approaches. A second objective is to extract quantitative informations on the time and space scale variability, on the heat transport and on the most salient dynamical features for the time period following the convection phase in the Gulf of Lion.

We take advantage of the complementarity of different types of in situ measurements to evaluate global quantities related to the heat and energy budget. Despite the rather high density of data collected during Thetis 1, the ocean spectrum is so rich in time and space that we cannot obviously pretend to cover the full range of scales, and the problem is a priori strongly underdetermined. Nevertheless, by combining the information provided by different systems that have filtered the ocean spectrum through their own transfer function, we expect to be able to improve the global transfer function and provide a valid estimate for a significant part of the spectral band. Three main types of data time series are available. Eulerian measurements contain the full ocean spectrum, but measured at isolated points. Lagrangian measurements sample mainly the mesoscale band. Integral tomographic data, on the other hand, give access to the largest scales contained in the observed area. This approach is a natural extension to the detailed analysis performed on individual datasets by Send et al. (1995) and Schott et al. (1996). It is also preliminary to more advanced methods such as data assimilation in numerical models. A first analysis by Gaillard et al. (1997, hereafter GDSS) used a monitoring approach to estimate the time evolution of the full temperature field over the duration of the experiment, based on a combination of local and integral measurements. Morawitz et al. (1996) have performed a similar analysis with data collected in the Greenland Sea and were able to compute heat and salt budgets and estimate the amount of deep water formed.

We extend here the analysis of the thermal structure presented in GDSS to a dynamical analysis by including velocity measurements from moored current meters, deep floats, and reciprocal tomography. The simultaneous estimation of the temperature and velocity field will give access to the advective terms of the heat transport equation.

## 2. The Thetis 1 experiment

The Thetis 1 experiment was designed to observe the development of deep convection in the Gulf of Lion. It was conducted by the Thetis group, formed in 1990 within the european MAST-I program. Thetis 1 relied on the combination of CTD casts and a moored array equiped with current meters, temperature/salinity sensors, Doppler profilers, and acoustic tomography. Such a combination of in situ measurement techniques was deployed to cover the wide range of scales involved.

The measurements performed during the winter 1991–92 were organized as follows.

A small-scale array of three moorings was set at the central point of the convection area (42°N, 5°E). It was designed to study the plumes and was equiped with ADCPs and thermistor chains.

Acoustic tomography was the core of a monitoring array set to observe the mixed patch. Moorings equipped with current meters, temperature sensors, and tomographic instruments were deployed in November at the positions shown on Fig. 1. The moorings were retrieved in February in order to repair a malfunction of the new tomography controller; they were immediately redeployed.

Five hydrographic cruises performed during the course of the experiment provided a fine description of the vertical structure of temperature and salinity and of its time evolution from fall to the end of winter.

In addition to the Thetis 1 measurements, three floats from the French ConvHiv experiment had been operating from March to April 1992.

A first analysis of the Thetis 1 dataset (Send et al. 1995) focused on the thermal structure analysis and validated the tomographic measurements by comparing section averages with temperature profiles and time series. They evidenced the complementarity of the local and integral measurements and were able to perform deep convection volume estimates based on the tomographic data horizontal averages. This paper was followed by a more detailed description of the convection process by Schott at al. (1996). The vertical penetration of the mixing was analyzed through the water mass properties. The central triangle, meant to describe the plume scales, revealed that the plume horizontal scale was below the 2-km spacing of the array and probably close to 500 m. The maximum velocities observed within the plume were 5 cm s^{−1}, slower than during the winter 1986/87. These measurements confirmed the role of mixing agent played by the plumes, with no net mean vertical transport over the 2-km array, as predicted by the nonhydrostatic modeling (Send and Marshall 1996). The analysis of the current meter time series showed a wide variety of behavior among the different mooring sites regarding the relative importance of the baroclinic component or a change in mesoscale kinetic energy during the course of the experiment. One clear conclusion of the paper is that the mesoscale activity existed before convection, indicating that baroclinic instability of the boundary current is not the only possible source for the eddies generation in this basin. The four-dimensional (4D) analysis by Gaillard et al. (1997) has synthesized the temperature data from the various Thetis 1 measurements and provided a description of the spatial extent of deep convection. By comparing the heat content time series to the atmospheric forcing, they deduced that horizontal advection was providing 45 W m^{−2} to the convection area, compensating in part for the surface heat losses.

## 3. Merging the datasets

### a. The datasets

The best spatial coverage with current measurements was obtained during the second deployment period when the floats were operating, that is, from 6 March to 10 April. Although we had performed the temperature analysis over the whole experiment (Nov–Apr), we will restrict the dynamical analysis to the period covered by the floats. Convection had started around 20 February and reached its maximum extent around 2 March, which means that the period analyzed in this study covers mostly the post-convection period, mentioned in the introduction.

The Thetis 1 and ConvHiv datasets used in this analysis can be dispatched into four categories: vertical profiles localized in time and space, Eulerian time series (at a fixed point), Lagrangian time series (at a moving point), and time series of integral measurements along sections. The temperature database and corresponding processing are the same as in the previous analysis (GDSS 1997). Although only a few vertical profiles from CTDs and XBTs are available during the period of analysis, the large CTD dataset collected between 18 February and 9 March is important to consider since it will be the main dataset during the setup period of the analysis. The processing of the current related data will be described with more details.

Current meter data exist for all the mooring points displayed in Fig. 1 and the levels sampled are summarized in Table 1. They are grouped by layers, defined according to the description of the hydrography by Millot (1987): a surface layer (0–200 m), influenced by its Atlantic origin, a Levantine Intermediate Water layer (200–700 m) formed by convection in the eastern basin, and a deep layer found below 700 m, renewed by the deep winter convection known to occur in the Gulf of Lion. The time series of the horizontal components of velocity measured by the current meters are low-passed filtered in order to remove fluctuations at periods shorter than a day. They are subsequently resampled at the time step chosen for the analysis (0.5 day).

The Lagrangian experiment during ConvHiv consisted in deploying floats [RAFOS Vertical Current Meter (VCM)] in February 1992 at two different levels (depth 300 and 1000 m) and three acoustic beacons for tracking over a 50-day period the neutrally buoyant floats measuring in situ pressure, temperature, and vertical velocity. Three floats were launched: float 6 was ballasted for 300 m and went to 280–290 m during the whole period of 40 days. Float 10, ballasted for 1000 m, went to its nominal depth, which is quite remarkable in contrast with float 9, ballasted for 1000 m too but stabilizing around 1180 m. The temperature series collected revealed the following structures: float 6 indicated temperatures varying from 12.90°C, typical of newly formed deep water in ventilated regions, to 13.20°C, typical of unaltered intermediate water. In particular, an abrupt change in temperature from low to high temperatures did occur on 20 March, indicative of a quick transition from a ventilated region to a stratified one. Float 10 indicated a fairly stable temperature around 13°C, typical of deep water in situ temperatures at 1000-m depth. Float 9 temperatures were not measured properly. Since RAFOS VCM floats were operated during a postconvection stage, vertical velocities will not be considered in this paper.

Floats trajectories, sampled 10 times per day, have been calculated to an accuracy of better than 1 km after taking into account clock drifts for both floats and sound sources over a period of 40 days and applying a linear correction. Time series for both float latitude and longitude were filtered independently and reassembled to produce smooth trajectories reported on Fig. 1. The time series of Lagrangian velocities and temperature are converted to Eulerian series at a moving point. Horizontal velocities are computed as finite differences along the trajectory: *u* = *dx*/*dt, υ* = *dy*/*dt.* Then, position, horizontal velocity and temperature are interpolated at the basic rate of 0.5 day. The error of the 12-h averaged velocity is mostly due to positioning accuracy; it is estimated to be smaller than 0.2 cm s^{−1}.

*C*

*z*), and the sound speed perturbations

*δC*(

*x, y, z*). We apply Fermat’s principal to compute the travel time integrals over the unperturbed ray path Γ leading to the linear relations:

**u**is the horizontal velocity and

**n**is a unit vector tangent to the raypath, oriented positively for the direct path.

Equation (1) relates the mean travel time perturbation to the sound speed anomaly. The previous analysis by GDSS showed that a depth-dependent correlation *α*(*z*) relates temperature and sound speed anomalies in the Gulf of Lion: *δT*(*x, y, z*) = *α*(*z*)*δC*(*x, y, z*); this allows a simple formulation of the tomographic thermometry data. Equation (2) relates the differential travel time to the current component along the section.

While the impact of the temperature signal on the travel time anomaly is of the order of 20–100 ms, the impact of the velocity signal is at least one order of magnitude smaller. A mean current of 15 cm s^{−1} over 150 km produces a differencial travel time Δ*t* of only 10 ms. We may wonder whether the reciprocal travel times will be distinguishable from the noise in areas dominated by eddy activity at scales smaller than the pair length, as is the case in the Gulf of Lion. The error on reciprocal travel times comes from the clock accuracy, from imperfect reciprocity (the transmissions are not simultaneous) and from ray arrival misidentifications. A first linear estimate of the clock drift is given by pre- and postdeployement comparison with GPS time, a second estimate is done by inverting the travel times, and fitting a third-order polynomial through this estimated drift. This correction is then applied to the data before the final inversion. The effect of imperfect reciprocity is expected to average out over a day. The misidentifications producing large differences in travel times have been manually eliminated. We estimate the global error on reciprocal travel times to be of the order of 2 milliseconds. In such case, we expect that, at least during the periods when the mean current is larger than 3 cm s^{−1}, the reciprocal tomography is an efficient constraint. We will see in the following that the noise level is probably lower than our estimate, due to the averaging effect, and that the reciprocal data contribute significantly to the estimation of the barotropic component of the field.

### b. Method for data merging (the Kalman filter)

The method for extracting a single solution from the dataset is described in detail in previous papers: Gaillard (1992) for the stationary case and Gaillard et al. (1997) for the introduction of the time evolution. In this last paper, the temperature field was reconstructed from temperature and tomography measurements. We intend here to estimate a new variable, the horizontal velocity (*u, υ*), and to improve the previously reconstructed temperature field (*T*). The new data are current point measurements (Eulerian and Lagrangian) and reciprocal tomography. Salinity will not be explicitely estimated because the relevant data are too sparse to expect a reliable estimation, but it will appear through the geostrophic velocity.

For each type of measurement we write the relation between the data and the parameter, as given by Eqs. (1) and (2) for the tomography data. Complementary information extracted from our theoretical and statistical knowledge of the ocean is introduced either as statistical information or as additional relations between parameters. The estimation produced at each time step uses the previous estimation and associated statistical error as a starting point. This combination of updating the field with data, then carrying information in time, defines a Kalman filter.

**y**

_{n}

*G*

_{n}

**x**

_{n}

**x**

_{n}is the set of parameters describing the field we wish to estimate at time

*t*

_{n}, and

**y**

_{n}is the vector of the data available for this time step.

**x**

^{0}

_{n}

*H*

_{n}to the innovation vector (

**y**

_{n}−

*G*

_{n}

**x**

^{0}

_{n}

*C*

^{x′}

_{n}

*C*

^{e}

_{n}

*C*

^{ϵ}

_{n}

**x**

_{n}

*P*

_{n−1}

**x**

_{n−1}

**r**

_{n}

*r*

_{n}is the prediction error. A forecast step predicts the a priori estimate

*x*

^{0}

_{n}

*C*

_{x}

_{′}

_{n+1}

**x**

_{c}= 0, and

*t*

_{m}is the memory time.

The prediction error is assumed random, as is the a priori covariance at the initial time. The memory time is set to 8 days and the prediction error is taken as 17% of the climatological rms over the 12-h forecast step. A priori information are introduced by specifying the relative weight of the different vertical modes, based on the CTD statistics. The horizontal scales are controled by introducing gaussian shaped horizontal covariances. Table 2 summarizes the values chosen for these parameters.

### c. Defining the state vector

The unknown variable that appears in the data–parameter relation is in the form *f*(*x, y, z, t*), with *f* = [*u, υ, T*], where (*x, y, z, t*) can be any point in space and time (within the area and during the period studied). To solve the problem we represent the parameters by a discrete and finite state vector and adjust its characteristics to the resolution of the dataset. We choose to represent the unknown fields by a set of normal modes in the vertical direction and Fourier components in the horizontal directions.

*T*and

*S*through a state equation. The density anomaly, relative to a mean density profile, is approximated by a linear function of the temperature and salinity anomalies:

*δρ*

*x, y, z*

*a*

*z*

*δT*

*x, y, z*

*b*

*z*

*δS*

*x, y, z*

*δS*

*x, y, z*

*β*

*z*

*δT*

*x, y, z*

*δS*

*x, y, z*

*a*(

*z*),

*b*(

*z*) and

*β*(

*z*). More than 200 full depth profiles were collected between November 1991 and April 1992. A least squares fit of the

*T*and

*S*data to relations (12) and (13) has been computed at each depth. We found that the coefficients of the density anomaly are approximately linear, and nearly constant. Here

*a*(

*z*) ranges from −0.21 at surface to −0.25 kg m

^{−3}(°C)

^{−1}at 2500 m and

*b*(

*z*) from 0.775 to 0.760 kg m

^{−3}(psu)

^{−1}over the same range;

*β*(

*z*) is a depth dependent

*T–S*relationship. The part of the salinity anomaly independent of the temperature anomaly is far from negligeable. Between 400 and 1200 m, the rms value of

*δS*′ is less than 25% of the rms value of

*δS,*but at levels shallower than 300 m, or deeper than 1700 m, it exceeds 50%. The failure of a unique

*T–S*relation at the surface is real and corresponds to the variety of water masses. At depth it is more likely due to the reduced number of data and smaller variance, which increases the relative anomalies.

*δT*is projected on

*n*

_{1}vertical empirical orthogonal functions (EOF), [

*H*

^{T}

_{k}

*z*),

*k*= 1,

*n*

_{1}]. These EOFs are computed as the eigenvectors of the temperature anomaly covariance matrix built from the CTD data. The modes for

*δS*′ ([

*H*

^{S}

_{k}

*z*),

*k*= 1,

*n*

_{2}]) are computed in a similar way on the remainder obtained after projecting the salinity anomaly on the previous set of modes [weighted by

*β*(

*z*)]. We finally write the density anomaly as a sum over temperature and salinity modes:

*F*

_{k}for the streamfunction by vertically integrating the density modes

*f*

_{0}is the coriolis parameter,

*ρ*

_{0}a mean constant density and

*L*

_{k}=

*L*

^{T}

_{k}

*L*

^{S}

_{k}

*z*

_{0}is such that

^{0}

_{−h}

*F*

_{k}

*dz*= 0, where

*h*is the ocean depth. For the following analysis, we take

*n*

_{1}= 5, as in GDSS, and

*n*

_{2}= 3, which makes a total of eight baroclinic modes. A barotropic constant mode, independent of the density signal, is added to the streamfunction basis. As will be shown in the next section, most of the estimated signal is captured by modes

*F*

^{T}

_{1}

*F*

^{T}

_{2}

*F*

^{T}

_{3}

*F*

^{S}

_{1}

*μ*coefficients are continuous functions in space. They are converted to a discrete and finite vector in wavenumber space by truncated Fourier transform. The minimum and maximum wavelengths are 36.6 and 256.0 km, respectively. The length scale

*L*associated with the cutoff wavelength 2 ×

*πL*is 5.8 km. It is close to the first Rossby radius, which will only be marginally resolved. However, the purpose of this study is to assess the mesoscale dynamics, so this resolution, although limited, should allow us to get a first estimate of this dynamics.

The linearized relations used to link the data to the parameters and the simplified representation of the temperature and velocity fields introduce errors, generally called “model” errors. In the inversion formalism, these errors play the same role as the measurement errors both in the estimate and its corresponding covariance. They are taken into account as an additional measurement error.

### d. Initialization and diagnostics

The Kalman filter is started from rest with a temperature field horizontally homogeneous and defined by the reference stratification. The incoming data progressively builds up the currents and horizontal variations of temperature and the quality of the estimation increases with time. To avoid performing the analysis during the setting up of the filter, the model is run for an initialization period from 21 February to 6 March. During this period we had very scarce velocity data, but a large CTD dataset was available; so at the end of the setup period the temperature field and streamfunction first baroclinic mode are well defined.

The relations we have defined to relate the measurements to the model parameters assume a number of simplifications regarding the horizontal scales (truncation of high wavenumber), the vertical scales (limited number of vertical modes), and the small perturbation hypothesis (particularly for tomography data). We also have included a priori information in the form of statistics (amplitudes and horizontal covariances), or structure (the persistence of the field over 12 hours). The method used to solve the problem produces a solution which is the best compromise, in a least squares sense, among the data, the model, and the a priori information. The degree of compatibility of the datasets, for the prescribed model is expressed in the residuals, or data misfit. Figure 3 presents the time evolution of the rms value of the residuals normalized by the measurement error, for each category of data. The figure also gives the number of data over which the rms is computed. The residuals for each type of data are in agreement with the measurement and model error statistics as indicated by the normalized residuals which remain close to 1. The slight variations in the mean value from dataset to dataset is likely due to the evaluation of the measurement or model errors.

A detailed look at the float series quantifies the agreement between the estimated field and the data and document the nature of the residuals. Figure 4 shows the time series of temperature and (*u, υ*) components following one of the floats trajectory. On the same graph we have superimposed the corresponding time series extracted from the estimated field. The temperature curves and current vector plots relative to float data and inversion estimates are similar. The differences occur on timescales of one to two days. The time series of the estimated variables are smoother than the corresponding measurement series. Although this smoothing appears in the time domain, it includes the space smoothing induced by the limited resolution of the observing array, the imposed cutoff wavelength of the Fourier representation and penalization by the a priori horizontal covariances of the scales shorter than the covariance length.

We can conclude that the solution found is compatible with all datasets and the model approximations. In particular, the set of vertical modes seems sufficient to represent the data. The model can be considered valid, given our database. This of course does not mean that we have found the exact ocean state. Up to now, the problem of ocean observation remains a severely underdetermined one because of the strong undersampling of the various ocean scales due to the lack of data. With our statistic-based formalism, the degree of indeterminacy cannot be simply expressed as the ratio: number of unknown/number of data, or even as the rank of a matrix (which is well known to depends on the noise level), but the stochastic method gives an estimate for the a posteriori error which contains the equivalent information. We will now examine both the amplitudes of the estimated field and the corresponding errors to evaluate the vertical and horizontal resolution.

The temperature and advection fields are reconstructed as the sum of vertical modes (five modes are allowed for temperature, nine for the streamfunction). The distribution of the amplitude of the estimated parameters over these modes, gives a first idea of the vertical scales resolved by the data. The rms amplitude of each mode, computed over the days of analysis, are shown Fig. 3. The barotropic mode clearly dominates the estimated field. Among the baroclinic modes, the most important are the first baroclinic modes *F*^{T}_{1}*F*^{S}_{1}*F*^{T}_{1}*F*^{S}_{1}*T–S* relation but determined only from the velocity measurements. The importance of this salinity mode indicate that the vertical shear is not totally explained by the temperature structure alone, salinity effects, independant from temperature are detected. Temperature modes *F*^{T}_{2}*F*^{T}_{3}

The error maps in physical space give an idea of the quality of the estimated field. These maps, deduced from the covariance matrix of the a posteriori error, computed at each step of the Kalman analysis, represents the progress made in the evaluation of the field, starting from the a priori covariance as a first guess. Figure 5 shows the time mean of the relative error for temperature and streamfunction at two levels. The first level, 300 m, is above the zero crossing of the first baroclinic mode, while the second level shown (1000 m) is located below. The major part of the dataset provides constraints on temperature, and consequently this field is well estimated inside the array. The tomography constraints, in particular, produce lines of relative minima in the error maps. The quality of the estimation of temperature degrades in the deep layer. At this level the higher modes are expected to become important but are not well resolved. The streamfunction error is higher than the temperature error because it has more degrees of freedom:the barotropic mode, vertical mode *F*^{S}_{1}

## 4. Results from the 4D analysis

### a. Relative influence of the different datasets

In the previous section we have shown that the 4D analysis has found an ocean state compatible with the different datasets and our a priori knowledge. We will now try to evaluate the contribution of each data type to the solution by analyzing the results of three additional test runs. The first analysis obtained with all datasets available is called the reference, in the sense that it is the best estimation we can do. The three test runs have been performed by removing successively one dataset. In run 1 we have removed only the float data, in run 2 we have removed only the tomography data, and in run 3 we have removed both datasets. In this last case only two types of datasets are used, the CTD profiles performed just before and during the first days of the period of analysis and the fixed temperature sensors and current meters, which provide time series for the duration of the period.

The contribution of each dataset in the wavenumber domain can be evaluated by comparing the average energy spectrum of the streamfunction for the different runs presented above. In Fig. 6 we have isolated the contribution of the barotropic mode and of the dominant baroclinic modes. The main contribution to the baroclinic modes comes from the CTD dataset (run 3) which provide a good description of the initial state for the baroclinic part. Since the large-scale structure of the field does not evolve drastically during the 35 days of the analysis, this information remains pertinent. The Lagrangian (float) dataset increases slightly (10%) the energy in the *k* = 1 band. The contribution of the integral (tomography) measurements covers a wider spectral band, inducing a 30% increase for *k* = 1, 2, and 4 (wavelength 256, 128, and 64 km) and 60% increase in the mesoscale band for *k* = 3 (wavelength 85 km). Tomography data improve the baroclinic mode mostly by providing the time evolving part of the temperature field not captured by the CTD.

Reciprocal tomography data contribute significantly to the estimate of the barotropic component over a wide range of scales. Energy is multiplied by more than 5 at *k* = 1, by almost 3 at *k* = 2, and by 2 at *k* = 3 and 4. The impact of Lagrangian data is weaker but still important on this mode. These data raise the energy level by more than 100% at *k* = 1 and nearly 60% at *k* = 2. The weaker contribution from the float data is explained by the low number of instruments: only three float trajectories and two float temperature series were available. A float trajectory provides velocity at a single level, and cannot discriminate between baroclinic and barotropic component of the flow.

The maximum of the spectrum at *k* = 1 and 2 for the streamfunction shifts to *k* = 3 for the kinetic energy spectrum and to *k* = 4 for the enstrophy spectrum, that is a well-known behavior from mesoscale turbulence studies (Rhines 1979). The wavenumbers higher than 5 (wavelength smaller than 50 km, or length scales smaller than 10 km) are not resolved. This limitation is not imposed by the model (since wavenumbers up to 8 are allowed), but by the datasets.

The distribution over the horizontal space of the information carried by the in situ datasets is illustrated by the mean amplitude of the current (Fig. 7). In the estimate obtained with mooring data only (run 3), significant currents are detected only in the vicinity of the moorings. From this first map, the contrast in current intensity between the central area and its surrounding is evident: low current amplitudes are estimated around T5 and T6 (see Fig. 1 for the location). When the float data are added (run 2), the current is now estimated along the float trajectories. Tomography data (run 1) extend the area where currents can be estimated to the sections defined by mooring pairs. The change is particularly obvious along the T1–T6 and T2–T6 section. When all data are used (reference run), the spatial extension of the observed area is maximum and only a few spots inside the array remain in the shadow zone.

To study the impact of the different datasets in the resolution of horizontal scales, we will now examine the temperature and velocity fields at particular instants. The 4D analysis provides the temperature and velocity profiles at all grid points within the modeled area. We will restrict the discussion to the part of the array located east of T5, where the error maps indicate that the estimation is reliable. Figure 8 shows the maps of temperature and current for 26 March as given by the reference and test runs 1 to 3 at the 300-m level. The estimate produced by run 3 (no floats or tomography) shows a strong current at T1 and T2 (east of the convection area), and we observe a temperature dipole around T1, although no temperature data are provided in the vicinity of this point. This dipole effect will be explained later. The trace of the convective mixed patch appears in the western part of the map as a cold temperature anomaly centered on mooring T5 and as a slightly cold one around T6. When tomography data are used (run 1), the temperature structure is strongly modified, a warm water patch appears in the eastern part. The cold anomaly intensifies north of T6 and the dipole on T1 is reduced. The current structure is no longer confined to the moorings vicinity, a link is now established between all moorings, except may be along T5–T3 section.

An example of cross-validation of datasets appears when comparing runs 1 and 2 (Fig. 8). The float data (run 2), which provide current and temperature along the trajectories, have sampled a cold cyclonic eddy in the middle of the triangle defined by T1–T5–T6. In the velocity field produced by run 1 with tomography data, a strong northeastward current relates T6 to T1, and a return current exists between T1 and T5. The current associated with this mesoscale structure detected by the float is in agreement with the large scale current detected by tomography. The best estimate is obtained by combining all datasets (the reference run): float data bring their estimate of the local structure with exact amplitude and position: tomography adds a number of large-scale features in the temperature and velocity field that escaped the local measurements.

The vertical structure of the temperature field is captured differently by the datasets. The temperature section along section T1–T6, as obtained with run 1 and the reference run, is shown on Fig. 9. This section extends from the center of the convection area to the limit with the North Mediterranean Current. The depth of the 13°C isotherm, for example, is modified when tomography is used. When only mooring data are provided (run 3), the estimate is constructed with temperature measurements at different levels at the end points. This defines the temperature profile at each end. Between these end points, temperature returns to the mean value with the scale specified by the horizontal covariance, a well-known behavior in objective analysis. Near T1 (6°N), the 13°C isotherm defines a column of cold water. It corresponds to the cold anomaly seen south of T1 on the horizontal maps for run 3, which we described as a dipole effect. It occurs where the current meters detect a vertical shear, which is translated into a horizontal density and hence temperature gradient. The current meter data impose no limit on the amplitude away from the mooring point. The size of the dipole is only determined by the covariance scale. Adding tomography data (reference) reduces the dipole effect and only a surface anomaly is kept. The heat content revealed by the vertical section differs significantly in the two runs, that is, with and without tomography. Again, we see that the mesoscale signal is present in all estimates with variable resolution, but only tomography data provide a strong constraint on the large scale component of the spectrum.

The dramatic changes observed when withholding any of the datasets emphasizes their complementary characteristic. As could be expected from the very nature of the data, point and integral measurements provide information on different spectral components of the field. CTD data give access to the baroclinic modes, with no time coverage (unless profile are repeated). Point measurements, either fixed or moving, capture the small- to mesoscale part of the spectrum with vertical resolution between modes depending on the number of levels measured. Tomography extends the resolution toward larger scales of the spectrum.

### b. The time evolution of the fields

In the runs including only local measurements some structures appear and disappear suddenly from one day to the next. This scintillation effect occurs with the small-scale structures, which are visible when they are illuminated by the moorings or floats, and then lost as soon as they leave the measurement point. In the reference run tomography improves the estimate of the large-scale features and this scintillation effect is strongly reduced. Some shadow zones still remain, as seen in the error maps, and only full data assimilation with a model including a more complete dynamics can carry over in space and time the properties estimated by the array. Nevertheless, the combination of data has greatly improved the continuity of the currents, and we can follow the displacement of some structures without any prediction on the advective field.

In the first diagnostics of section 3d, we have noticed, in the mode amplitude, the strong weight of the barotropic mode. The time series of the barotropic and baroclinic components of the kinetic energy for the Thetis 1 area during the postconvection period is shown Fig. 10. On average the barotropic component represents 85% of the total kinetic energy. The barotropic character of the circulation in the Gulf of Lion was already a conclusion by Madec et al. (1996) who found in their numerical simulation that the wind forcing induced a large-scale barotropic cyclone with a transport of 18 Sv (Sv ≡ 10^{6} m^{3} s^{−1}). The consequence of this energy distribution is that, except for the surface layers where the baroclinic modes contribution become important, the currents at all levels are very similar. We then choose to present the fields at a depth of 300 m, a level located within the Levantine Intermediate Water (LIW). The temperature structure as reconstructed by our estimation is not always correlated with the velocity field. The explanation is that temperature at this level is captured by the highest baroclinic modes while currents are strongly dominated by the barotropic component.

An overview of the field evolution in the Gulf of Lion is provided by the maps (Fig. 11) showing the velocity vectors overlayed on the corresponding temperature field. Mooring sites and instantaneous float positions are drawn on the same maps. The general impression is that of a rapidly changing field, dominated by mesoscale structures involving strong axisymetric vortices. No mean circulation can be defined over this time period, although a large-scale temperature field emerges with warmer waters at the eastern boundary.

The situation at the beginning of the time series corresponds to the postconvection period: the strongest convective event had occurred about 15 days earlier. At 300-m depth the effect of convection is a depletion of warm LIW by mixing with the cold water of the surface and deep layers. Horizontal advection of the cold water out of the array occurs mainly after 15 March, following an increase in the currents. In the time series of maps we observe the displacement of a cyclone that moves westward and cross isobath from the center of the array between 7 and 15 March and is expelled between 19 and 23 March. A westward current crossed the convection area, allowing cold waters to move away. This current event seems to have its source in the northeast corner, in the area of the North Mediterranean Current. The warm water enters mostly from the eastern open boundary, although some is seen to come from the southern boundary.

The dominant horizontal scale corresponds to structures with diameter 30 to 40 km. This scale is small compared to those of eddies found outside the Gulf of Lion in the Western Mediterranean [*O*(100–150 km)] according to Millot et al. (1990); however, it is larger than the 10-km eddy scale observed during Medoc 75 (Gascard 1978). It must be stressed that our array cannot resolve such small scales, but the three float trajectories do not indicate that such structures were encountered. The convection observed during Thetis 1 differs from the convection observed during the Medoc 69 winter, on which many of the schemes relative to deep-water formation were built. Medoc 69 was a year with strong full-depth early convection: the mixed patch was large and rather homogeneous horizontally, and the observed eddy could result from the baroclinic instability of the boundary current. On the other hand, Thetis 1 corresponds to a year of partial and late convection (Mertens and Schott 1998). The deepest mixed layer depth observed here is 1500 m and the mixed patched had always been discontinuous, as if convection only occured over the area preconditioned by the mesoscale eddy field following the mechanism proposed by Legg et al. (1998).

In order to describe the displacement of the main mesoscale structures we have computed the relative vorticity and sorted out the strongest vortices. Only structures with a relative vorticity higher than 10^{−5} s^{−1} and lifetimes greater than 4 days have been kept. Over the 35 days of the analysis, four positive and three negative vortices have been tracked (Fig. 12). The cyclones (positive vortices) are found in the central area (close to 5°E) and have low temperature (13.0°C), indicating their convective origin. They move westward, mostly cross isobath, with slight southward component. Their speed is significant and reaches a mean value of 2.5 cm s^{−1}. The anticyclones are found in the eastern part where they carry warm water (13.3°C) influenced by the LIW. They have much slower or no significant mean displacements.

### c. Horizontal advection and heat fluxes

^{−2}had to be provided to the observed volume by horizontal advection.

In the present analysis we have in hand estimates of the variables that contribute to the net heat budget due to horizontal advection, so we can compute directly the advective term. We have evaluated this quantity over a box centered on the best estimated area. The size of the box is varied over a few grid points to test for the robustness of this estimate. The mean values over time of the advective heat flux obtained for different sizes of the box are plotted Fig. 13 with the corresponding rms over the time period analyzed. For the smallest boxes the rms are much larger than the estimated mean, they decrease when the size of the box is increased. The large variability is due to the time variability associated with the mesoscale structures: the transport is operated by eddies that enter or leave the box. The area over which the mean is computed is to small and the duration of the computation too short for containing a sufficient number of eddies. Despite these large errors (which are in fact a time variability), most estimates indicate a heat gain by horizontal advection of 50 W m^{−2}. Another estimate of the error is obtained by combining the “a posteriori error” provided by the method used on the streamfunction and the temperature, which is seen on the error maps of Fig. 5. On the average over the central area, the error in the product, *T***u**, is close to 80%, similar to the error deduced from the rms.

The contribution of horizontal advection to the heat budget has then been estimated by two methods: GDSS deduced it from the difference between heat content variation and surface heat flux, while in this study it is computed directly. The two methods of computation are independent since in none of the analysis the equation of conservation has been imposed. The two estimates agree on a gain of heat at the rate of 50 W m^{−2}, by horizontal advection in the observed area. Horizontal advection of heat is obtained by advecting in and out waters with different temperature and no net volume transport. The resulting heat flux of 50 W m^{−2} over an area 100 × 100 km^{2} is equivalent to the advection of 0.4 Sv of waters with 0.4°C difference.

### d. The vorticity balance

The mesoscale flow field observed during the postconvection period is characterized by strongly barotropic vortices with a size of the order of 30–40 km. It is difficult from the available datasets to infer the mechanisms responsible for their formation. However we can address the question about the mechanisms that govern their evolution. The absence of permanent forcing in this area, such as wind stress forcing or a mean vertical current shear, suggests that these barotropic vortices are freely evolving. Then, the only parameters that could affect their evolution are the planetary vorticity gradient and the closeness of the topographic slope. Within the geostrophic approximation a topographic slope acts as a *β* effect (Pedlosky 1987). In the Thetis area the “topographic *β*” is |*β*_{t}| = *f*|**∇***h*|/*h* ≈ *O*(10^{−9}–10^{−10}), that is, much larger than the “planetary *β*” [≈*O*(10^{−11})]. Thus the topographic slope should affect the evolution of the vortices. Within this context the examination of the vorticity balance can help to better identify the characteristics of their evolution.

**u**= (

*u, υ*) and

*ζ*the relative vorticity. The second term represents the nonlinear wave–wave interactions. It controls the inverse energy cascade that leads to growing vortices. The third term is related to the dispersion of the topographic waves, a mechanism leading to the decay of large vortices. In

*forced geostrophic turbulence,*the second and third terms are large and statistically in equilibrium, which leads to the emergence of energetic vortices with a size close to the topographic arrest scale (Rhines 1979):

*u*〉 an estimate of the rms mesoscale velocity. However, in

*unforced turbulence,*vortices whose initial scale is close to

*L*

_{eq}can be ultimately destroyed by the wave dispersion, but this depends strongly on their shape. If their shape is asymmetric, nonlinear interactions as well as the wave dispersion effects are large. After some times the vortices are ultimately destroyed by the wave dispersion and the equilibrium flow is dominated by large-scale waves. On the other hand, if their shape is axisymmetric (which means that the axisymmetric processes have had time to work before their size attains

*L*

_{eq}), nonlinear interactions and wave dispersion effects are quite weak. Indeed such vortices are often described as axisymmetric monopoles that verify

**u**·

**∇***ζ*≈ 0. Furthermore the axisymmetric processes make these vortices stronger and more resistent to dispersive decay by the topographic waves for a very long time (Morel 1998). Such coherent vortices that keep their typical size close to

*L*

_{eq}can persist for a long time and travel in areas of smaller

*β*_{t}.

*L*

_{eq}in the Thetis area using 〈

*u*〉 ≈ 10

^{−1}m s

^{−1}and |

*β*_{t}| ≈ 10

^{−9}m

^{−1}s

^{−1}. This leads to

*L*

_{eq}≈

*O*(30–40 km), that is, of the order of the observed barotropic vortices size, which means that these vortices could be affected by the wave dispersion effects induced by the topographic slope. Since they appear to be freely evolving, we have attempted to discriminate which equilibrium flow should emerge through the estimation of

**u**·

**∇***ζ*and

**u**·

*β*_{i}for the energetic mesoscale structures. These terms can be rewritten as

**u**

**∇**

*ζ*

**u**

**∇***ζ*

*α*

_{n}

**u**

*β*_{t}

**u**

*β*_{t}

*α*

_{t}

*α*

_{n}the angle between

**u**and

**∇***ζ*and

*α*

_{t}the one between

**u**and

*β*_{t}. When the vortices are energetic, |

**u**| and |

**∇***ζ*| are large and the nonlinear term is close to zero only if

*α*

_{n}is close to

*π*/2. The probability density function (PDF) of

*α*

_{n}, computed over all space and time points with velocity over 4 cm s

^{−1}(which includes 4500 points), displays a quite narrow peak around

*π*/2 (Fig. 14), indicating that the observed energetic vortices should be mostly nonlinear axisymmetric monopoles. This peak seems to be meaningful since its magnitude increases when only velocities over 5 cm s

^{−1}are considered. The area corresponding to |

*β*_{t}| ≥ 5 × 10

^{−10}m

^{−1}s

^{−1}amounts to less than 20% of the domain and is mainly located on the Rhone Deep Sea Fan. The PDF of

*α*

_{t}computed in this area with velocity over 2 cm s

^{−1}(≈1000 points) displays poor alignment of the streamlines with the isobaths (Fig. 14). This means that small radiation due to the topographic waves is acting, which should make the axisymmetric vortices propagate up- or downgradient, depending on the vortex parity (Morel 1998). Therefore, these PDFs indicate that the observed vortices should be mostly persistent and coherent and that those on the topographic slope could be affected (although weakly) by the radiation of topographic waves.

These results sustain that the scenario, involving coherent axisymmetric vortices, is the most plausible one and that the nearby topographic slope may control the evolution of the barotropic vortices. The relevance of these results certainly has to be strongly moderated because of the coarse resolution of the experimental data, which produce errors that should spread the PDF. However, the sharp shape of the PDF of Fig. 14, and the order of magnitude produced by *L*_{eq}, close to the estimated size of the vortices are encouraging. Furthermore, the computation of vortex trajectories indicate that some cyclonic vortices are moving cross-isobaths towards shallower water. This supports the preceding findings about the coherence and axisymmetric nature of the vortices.

## 5. Conclusions

The combination of multiple localized datasets such as hydrography, Eulerian, and Lagrangian measurements with an integral dataset provided by tomographic measurements has allowed us to estimate the full four-dimensional fields of temperature and horizontal velocity over 35 days of the postconvection period in the Gulf of Lion. The model used for relating the parameters is simple geostrophy, and persistence is assumed for controlling the time evolution. In that respect, this analysis is a demonstration of the possibilities offered by data combination. A real assimilation procedure with a more complex model would extend in time and space the influence of the data and permit more detailed estimates of the different terms involved in the heat or vorticity equation.

The advantage of combining different types of data over multiplying a single type of data, for accessing the whole ocean spectrum, relies on their complementariness. The ocean spectrum covers a wide range of scales, in time and space, and each dataset of a single type captures it through its specific filter. So, unless one is interested only in that part of the spectrum captured by a single dataset, it is more efficient, for accessing the whole ocean spectrum, to merge data types with different filtering characteristics, rather than multiplying the number of sensors of the same type. In our experiment, CTD data have provided the initial temperature field. The time evolution of this field and access to the current was provided by the time series. Current meters give good estimates of barotropic and baroclinic modes but at a limited number of points, which are difficult to relate since most of the energy is distributed over spatial scales much smaller than the mooring spacing. Underwater floats can be merged with moored data; they illuminate the temperature and barotropic current field along their trajectory. Acoustic tomography, by controlling the mean temperature and current along sections, provides the link between these points, reduces the scintillation effect and allows one to follow the displacement of eddies. Regarding the wavenumber spectrum, hydrography and Eulerian measurements provide a first estimate of the baroclinic mode spectrum, but tomography improves the estimated amplitudes at all horizontal scales. Float data provide information on the barotropic mode but the major contribution for this mode comes from the reciprocal tomography data, particularly at the largest scales. On the other hand, floats contribute efficiently to a better identification of the mesoscale and submesoscale structures.

The distribution of kinetic energy obtained by combining all datasets indicates that the barotropic mode is dominant, representing 85% of the total energy. This was not the case in modeling results on convection based only on heat flux forcing alone. But our results confirms the numerical modeling work of Madec et al. (1996), which included wind forcing and bottom topography. Horizontal advection transfers heat toward the central area at a mean rate of 50 W m^{−2}, compensating for the heat losses through the surface.

In the estimated field at 300 m, we observe cold cyclones, resulting from earlier convection. The mass transfer from the Gulf of Lion in the western direction toward the basin circulation is not a continuous process, but occurs mostly as strong intermittent events separated by periods of weak activity. One of these events has been captured by our array. It may be related to the behavior of the North Mediterranean Current or to a surface forcing event, but the size of the observed area is too limited to establish such a connection. The southwestward advection of structures is confirmed by the census of vortices trajectories. Strong cyclones are found in the convection area and are advected toward the southwest while anticyclones are weaker, mostly found outside the convection area and move more slowly.

The vortices observed during the postconvection period are strongly barotropic with estimated scales of the order of 30–40 km. This scale appears to be close to the topographic arrest scale. The horizontal velocities in the mesoscale field are mostly orthogonal to the relative vorticity gradient, indicating that the vortices are mostly nonlinear axisymmetric monopoles. This property is corroborated by the vortex trajectories, which reveal that some of them are moving cross isobaths. This means that weak radiation due to the topographic waves is acting and that these vortices are coherent, can persist for a long time, and travel away from their generation area.

Although the method of combining point measurements and integral data has been proven to give a more complete description of the field, the interpretation of the results is limited by the time and space availability of the data. For describing convection and studying how the convected water is transferred toward the basin interior, it is important to include the western part of the Gulf of Lion. In order to understand how some events are triggered, the North Mediterrranean Current, which is an important source of energy, must be monitored simultaneously and modeled. Our estimation was restricted to the deep ocean part and did not represent this boundary current. Finally, convection has a large interannual variability, as does the atmospheric forcing, and monitoring of the area must be planned over several years to reach some representativeness.

## Acknowledgments

The Thetis 1 experiment and project was made possible by funding from the European Community MAST program (Contract MAST 0008-C), the German Ministry of Science and Technology (BMFT, Contract 03F0542A), IFREMER, and the Programme Atmosphère Météorologique et Océan Superficiel (CNRS). ConvHiv was supported by CNRS (Contract 520349), IFREMER (Contract 901430016), and DRET (Contract 91/1203). The authors acknowledge the valuable comments and suggestions of both reviewers, which led to substantial improvement in the manuscript.

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Vertical modes for the streamfunction: (a) modes *F*^{T}_{1}*F*^{T}_{2}*F*^{T}_{3}*F*^{S}_{1}

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vertical modes for the streamfunction: (a) modes *F*^{T}_{1}*F*^{T}_{2}*F*^{T}_{3}*F*^{S}_{1}

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vertical modes for the streamfunction: (a) modes *F*^{T}_{1}*F*^{T}_{2}*F*^{T}_{3}*F*^{S}_{1}

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Global diagnostics of the analysis. (a) Number of available data for each type of measurement. 1: tomographic temperature data, 2: tomographic current data, 3: temperature sensors, 4: current data (Eulerian + Lagrangian), and asterisk: CTD data. (b) Rms residual to noise ratio for each category of data; a ratio of 1 means that the estimation fits the data within the a priori error bars. Curve numbering is the same as for (a). (c) Rms of estimated amplitude of the vertical modes

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Global diagnostics of the analysis. (a) Number of available data for each type of measurement. 1: tomographic temperature data, 2: tomographic current data, 3: temperature sensors, 4: current data (Eulerian + Lagrangian), and asterisk: CTD data. (b) Rms residual to noise ratio for each category of data; a ratio of 1 means that the estimation fits the data within the a priori error bars. Curve numbering is the same as for (a). (c) Rms of estimated amplitude of the vertical modes

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Global diagnostics of the analysis. (a) Number of available data for each type of measurement. 1: tomographic temperature data, 2: tomographic current data, 3: temperature sensors, 4: current data (Eulerian + Lagrangian), and asterisk: CTD data. (b) Rms residual to noise ratio for each category of data; a ratio of 1 means that the estimation fits the data within the a priori error bars. Curve numbering is the same as for (a). (c) Rms of estimated amplitude of the vertical modes

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and horizontal velocity time series along float 10 (1000 m) trajectory. The data from the float are in grey, the results from the analysis in black. (a) Temperature from the float and estimated by the model. (b) Current vectors deduced from the float. (c) Current vectors estimated by the model

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and horizontal velocity time series along float 10 (1000 m) trajectory. The data from the float are in grey, the results from the analysis in black. (a) Temperature from the float and estimated by the model. (b) Current vectors deduced from the float. (c) Current vectors estimated by the model

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and horizontal velocity time series along float 10 (1000 m) trajectory. The data from the float are in grey, the results from the analysis in black. (a) Temperature from the float and estimated by the model. (b) Current vectors deduced from the float. (c) Current vectors estimated by the model

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Maps of the error expressed as percent of a priori error, averaged over the period of analysis at 300 m (level 1) and 1000 m (level 2). Left: temperature error; right: streamfunction error

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Maps of the error expressed as percent of a priori error, averaged over the period of analysis at 300 m (level 1) and 1000 m (level 2). Left: temperature error; right: streamfunction error

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Maps of the error expressed as percent of a priori error, averaged over the period of analysis at 300 m (level 1) and 1000 m (level 2). Left: temperature error; right: streamfunction error

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Wavenumber spectrum of the streamfunction for the different runs. Run 3 includes initial CTDs and Eulerian measurements, run 2 includes run 3 data and Lagrangian data, run 1 includes run 3 data and integral tomography data. The reference run uses all datasets. The spectrum is an average over the 35 days of analysis

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Wavenumber spectrum of the streamfunction for the different runs. Run 3 includes initial CTDs and Eulerian measurements, run 2 includes run 3 data and Lagrangian data, run 1 includes run 3 data and integral tomography data. The reference run uses all datasets. The spectrum is an average over the 35 days of analysis

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Wavenumber spectrum of the streamfunction for the different runs. Run 3 includes initial CTDs and Eulerian measurements, run 2 includes run 3 data and Lagrangian data, run 1 includes run 3 data and integral tomography data. The reference run uses all datasets. The spectrum is an average over the 35 days of analysis

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Horizontal distribution of the rms current amplitude in the different test and reference runs

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Horizontal distribution of the rms current amplitude in the different test and reference runs

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Horizontal distribution of the rms current amplitude in the different test and reference runs

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and current at 300 m on 26 Mar as estimated by the test and reference runs. Run 3: current meters only, run 2: current meters + floats, run 1: current meters + tomography, and reference: all data. The floats and mooring positions are drawn on the same figure. Section T1T6 is shown as an orange line

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and current at 300 m on 26 Mar as estimated by the test and reference runs. Run 3: current meters only, run 2: current meters + floats, run 1: current meters + tomography, and reference: all data. The floats and mooring positions are drawn on the same figure. Section T1T6 is shown as an orange line

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Temperature and current at 300 m on 26 Mar as estimated by the test and reference runs. Run 3: current meters only, run 2: current meters + floats, run 1: current meters + tomography, and reference: all data. The floats and mooring positions are drawn on the same figure. Section T1T6 is shown as an orange line

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vertical temperature section along T1T6 on 26 Mar. Top: run 3 (current meters only), bottom: reference run (all data)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vertical temperature section along T1T6 on 26 Mar. Top: run 3 (current meters only), bottom: reference run (all data)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vertical temperature section along T1T6 on 26 Mar. Top: run 3 (current meters only), bottom: reference run (all data)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Barotropic (heavy line) and baroclinic (light line) component of the kinetic energy in the Thetis 1 area during postconvection

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Barotropic (heavy line) and baroclinic (light line) component of the kinetic energy in the Thetis 1 area during postconvection

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Barotropic (heavy line) and baroclinic (light line) component of the kinetic energy in the Thetis 1 area during postconvection

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Time series of velocity vectors and temperature field at 300 m. Color scale is given above for temperature. Velocity scale is given by the 10 cm s^{−1} vector on the bottom right corner of each image

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Time series of velocity vectors and temperature field at 300 m. Color scale is given above for temperature. Velocity scale is given by the 10 cm s^{−1} vector on the bottom right corner of each image

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Time series of velocity vectors and temperature field at 300 m. Color scale is given above for temperature. Velocity scale is given by the 10 cm s^{−1} vector on the bottom right corner of each image

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Trajectories of vorticies detected by the array during more than 5 days. Black: positive vortices, gray: negative vortices

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Trajectories of vorticies detected by the array during more than 5 days. Black: positive vortices, gray: negative vortices

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Trajectories of vorticies detected by the array during more than 5 days. Black: positive vortices, gray: negative vortices

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Advective heat flux in the central area as a function of surface (squares). Rms over time (plus sign) is high for areas under (100 km)^{2}, it becomes of the order of the flux for larger surfaces

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Advective heat flux in the central area as a function of surface (squares). Rms over time (plus sign) is high for areas under (100 km)^{2}, it becomes of the order of the flux for larger surfaces

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Advective heat flux in the central area as a function of surface (squares). Rms over time (plus sign) is high for areas under (100 km)^{2}, it becomes of the order of the flux for larger surfaces

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vorticity balance. Top left: Location of points with topographic terms above the threshold *β*_{t}. Middle: Probability density function of the angle (**U**, **∇***q*) (with **∇***q* = **∇***ζ* + *β*_{t}) expressing conservation of the absolute vorticity. Bottom: Probability density function for the nonlinear term angle *α*_{n} (curve) and for the topographic term angle *α*_{t} (bars)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vorticity balance. Top left: Location of points with topographic terms above the threshold *β*_{t}. Middle: Probability density function of the angle (**U**, **∇***q*) (with **∇***q* = **∇***ζ* + *β*_{t}) expressing conservation of the absolute vorticity. Bottom: Probability density function for the nonlinear term angle *α*_{n} (curve) and for the topographic term angle *α*_{t} (bars)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Vorticity balance. Top left: Location of points with topographic terms above the threshold *β*_{t}. Middle: Probability density function of the angle (**U**, **∇***q*) (with **∇***q* = **∇***ζ* + *β*_{t}) expressing conservation of the absolute vorticity. Bottom: Probability density function for the nonlinear term angle *α*_{n} (curve) and for the topographic term angle *α*_{t} (bars)

Citation: Journal of Physical Oceanography 30, 12; 10.1175/1520-0485(2000)030<3113:AMFATP>2.0.CO;2

Depth in meters of the current meter series used in our analysis. They cover approximately the three typical layers, S: surface, I: intermediate, and D: deep

Parameters of the run. Column 1: Vertical mode number (mode 0 is the barotropic mode; modes 1–5 are temperature modes;modes 6–8 are salinity modes. Column 2: Horizontal scale in kilometers. Column 3: relative weight of the mode