Feature-Oriented Coastal Acoustic Tomography: Upwelling at Cabo

Feature-oriented acoustic tomography: Upwelling at Cabo Frio (Brazil)

Olivier Carriere` ∗, Jean-Pierre Hermand∗, Leandro Calado†, Ana ClaudiadePaula´ †, and Ilson Carlos Almeida da Silveira‡ ∗Environmental Hydroacoustics Lab., Universite´ libre de Bruxelles (U.L.B.) Avenue Franklin D. Roosevelt, 50 - B-1050 Brussels, Belgium Email: [email protected] †Marinha do Brasil - Instituto de Estudos do Mar Almirante Paulo Moreira Rua Kioto 253 - Arraial do Cabo - RJ 28930-000 Brazil ‡Instituto Oceanografico´ da Universidade de Sao˜ Paulo Praça do Oceanografico´ 191 - Sao˜ Paulo - SP 05508-120 Brazil

Abstract— The Cabo Frio region (Brazil) presents a unique coastal-oceanic system. Among several interesting oceanic phe- nomena that occur in this region, the coastal upwelling is the most important coastal feature and is mainly forced by persistent winds northeast. An oceanic feature model which specifically describes the Cabo Frio upwelling process is used as a parameterization scheme to track the time evolution of the sound-speed field of a vertical slice of the coastal waters. The tracker processes the repeated measurements of broad-band, multi-frequency (220–880 Hz), full-field acoustic field on a vertical receiver array. The acoustic data are assimilated in the feature model to continuously correct the prediction of the upwelling slope of the temperature field. To cope with the nonlinearity between the environmental parameters and the acoustic propagation data, advanced nonlinear extensions of Kalman filters are necessary. It is shown that an ensemble Kalman filter (EnKF) continuously tracks the upwelling conditions, outperforming the extended Kalman filter (EKF). Fig. 1. AVHRR image from 10th of January, 2001 exemplifying the coastal I. INTRODUCTION upwelling in Cabo Frio region. The blueish-yellow colors are associated with the cooler and fresher Coastal Water on the shelf, and the reddish colors mark The principles of ocean acoustic tomography were intro- the presence of the warmer and saltier Tropical Water. Image courtesy of W. Lins de Mello, Brazilian Navy. duced at the end of the 1970s by Munk and Wunsch [1]. Since, number of theoretical, numerical and experimental studies proved the efficiency of acoustic measurements to assess or monitor ocean environments. However, the coupling of ocean the surface winds rotate counter-clockwise and blow for a few modeling, acoustic inversion and data assimilation remains a days from the southern quadrant, inhibiting the upwelling [3]. complex problem, particularly in coastal environments. This The coastal upwelling in Cabo Frio occurs when the work investigates the use of an oceanic feature model for the South Atlantic Central Water, carried by Brazil Current (BC), ◦ acoustic monitoring of coastal upwelling in Cabo Frio (23 S) “climbs” the shelf break, and the isotherms (as well as in Brazil (Fig. 1). isopycnals) bend upwards in the vicinity of the continental The Brazilian coast at Cabo Frio region develops a unique slope. The main forcing of coastal upwelling in Cabo Frio is coastal-oceanic system when the coast orientation changes and the persistent winds northeast, that typically blow for several shelf break topography reinforces the interaction between the days, producing strong upwelling. On the other site, the surface oceanic and coastal systems [2]. The most important coastal layers of the shelf break region are normally occupied by feature in Cabo Frio region is the upwelling (Fig. 1). the Brazil Current (BC) waters, with high temperatures and During the summer months, when coastal upwelling is more salinities. The BC surface temperatures may range from 25◦C frequent and sustained due to favourable wind conditions over to 27◦C during the summer and from 22◦Cto24◦C during the the Cabo Frio area, the surface temperature difference between winter. Surface salinities normally vary from 36.5 to 37.0 [4], the Brazil Current front and upwelled waters near the coast [5]. As shown in [6], the interaction of these two systems (BC is most of the time greater than 10◦C. On the synoptic time and coastal upwelling) can create an environment that impacts scale of 6–11 days, as cold fronts pass through the region, the density field. Oceanic forecasts require the best possible

0-933957-38-1 ©2009 MTS specifications of density initial conditions. Therefore, precise models provide significant improvements on the prediction of knowledge or monitoring of the synopticity of these coastal transmission loss with respect to range-independent models. and oceanic systems are fundamental for the initialization of In this paper, the feature model imposes a strong apriori oceanic numerical forecasting model. constraint on the oceanic feature that we want to invert. A The traditional acoustic tomography, which consists essen- previous work showed that the acoustic monitoring of the tially in the inversion of the range-integrated sound-speed central position of a seasonal thermal front was feasible by profile, is often not meaningful in coastal environments where coupling a basic feature model and appropriate inversion large inhomogeneities can occur rapidly and frequently at techniques involving broad-band and full-field acoustic propa- small- and meso-scales. For the same reason, common inver- gation modeling [17]. Here, the same technique is applied to a sion methods based on the linearization around a reference en- different feature model which describes the coastal upwelling vironment can fail because of the strong change of the environ- that occurs on the southeastern coast of Brazil and in particular mental conditions between successive time frames of acoustic the Cabo Frio area. probing. Therefore, range-resolving inversion schemes are be- In this work, the feature-oriented acoustic inversion is fo- ing developed to obtain accurate estimates of range-dependent cused on only one transect of the coastal environment. Further features of the environment, suitable for data assimilation in works will consider the inversion of several transects that cross oceanic model. Several works have shown that the inversion the upwelling front, thereby enabling the reconstruction of of range-dependent environments was possible to achieve the subsurface conditions over the whole zone by introducing using multiple pairs of source and receivers, with travel-time appropriate correlation functions. based methods [7], [8] or matched-field processing [9], [10]. The paper is organized as follow: Section II is dedicated However, the problem of recovering a range-dependent sound- to the basic principles of oceanic feature models and their speed field using a single pair of source-receiver is a more application to the particular case of the Cabo Frio upwelling. complicated problem, mainly because of the co-existence of After introducing some typical properties of the acoustic multiple solutions to the inverse problem. Different works propagation in the transect of interest, Section III develops proposed appropriate schemes to estimate the range-dependent the concept of acoustic monitoring of the upwelling using sound-speed field in a single vertical slice. To cope with an ad hoc feature model. Simulation results are presented in the existence of multiple solutions (sometimes non-physical), Section IV. Finally, the paper is concluded in Section V. different strategies are developed, basically to constrain the inverse problem by introducing aprioriknowledge of the II. FEATURE MODELS environment. Most of works use empirical orthogonal func- The philosophy of the feature modeling approach is to tions (EOF) to parameterize the temperature (or sound-speed) develop a first-order system for a very complex nonlinear profiles. In [11], the range-dependent sound-speed field of system such as a regional ocean where most processes strongly a deep water environment was inverted by introducing cor- interact and where processes cannot be studied separately. relation lengths in the inversion scheme. The tracking of Once the first-order structures are placed within a numeri- a cold filament was proposed in [12], for a shallow water cal models dynamical framework, the nonlinearity stimulates environment, by including the known position of the local further interaction among features and should create realistic perturbation. In [13], smoothness conditions on the solution four-dimensional complex fields. Thus, changing the parame- are imposed and the final estimate is given by averaging over ter values of the feature models, it could be possible to study the best solutions of the inversion algorithm. More recently, the interaction between features and the different dominant it was shown that the tracking of the fine hourly variations (and possibly candidate) processes in isolation [2], [18]. of a range-dependent sound-speed field in a vertical slice was In this framework, a single feature model is first developed possible by using an ensemble Kalman filter (EnKF) to invert to describe the upwelling feature near Cabo Frio region. full-field acoustic measurements on a vertical array [14]. In a The feature model approach enables the representation of shallow water environment, the acoustic propagation is highly the coastal feature in a low-dimensional scheme. Sensitivity dependent on the geoacoustic properties. Therefore, a precise studies can be done by varying the upwelling parameters to knowledge of the bottom and subbottom properties is essential generate different scenarios which can then be studied for to invert for the water column properties. All cited works made further understanding of the complex relationship between the assumption of known bottom and subbottom properties. acoustic propagation and upwelling characteristics. In a second As proposed in [15], when tracking a specific range- step, the feature model is used as a parameterization scheme dependent oceanic feature, the integration of the apriori to perform acoustic inversion of the environment and estimate knowledge can be done through the use of a feature model the values of feature parameters that describe the best the for the parameterization of the environment. Feature models upwelling. consist of simple mathematical expressions that are commonly used to mimic the typical oceanic features. The feature models A. The Synoptic Data-based Feature Models were initially developed for oceanic modeling and forecasting The temperature and salinity structures for the upwelling purposes. As proposed in [16], feature models can also be used feature model at Cabo Frio are derived on the basis of the for acoustic forecasting purposes. It was shown that the feature Project Dinamicaˆ do Ecossistema de Plataforma da Regiao˜ 22oS

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−2000 −500 24oS −1000 Radial 1 −1500 Radial 2 30’ Radial 3 −2000 −2500 Radial 4 Fig. 4. A schematic representation of the coastal upwelling feature model 25oS structure. (Adapted from [2]) 43oW 30’ 42oW 30’ 41oW 30’ 40oW

Fig. 2. DEPROAS Summer 2001 transect hydrographic stations. (from [19]) in Fig. 4. It is derived from the continental shelf-slope front feature model developed by [18] and updated by [20] and [2]. Its general formulation is given by

T (η,z)=To(z)+[Ti(z) − To(z)]m(η,z), (1) where η − θz m(η,z)=0.5+0.5 tanh χ (2) is a meld function, η is the cross-frontal distance from the axis of the front, and z is positive vertically upward. T (η,z) is the upwelling frontal temperature distribution, Ti(z) is the inshore temperature profile, and To(z) is the offshore temperature θ = (h/x) χ Fig. 3. Temperature field of the DEPROAS summer 2001 sections, on the profile. atan is the slope of the front, and is 10th and 11th of february, 2001. (from [19]) the e-folding half-width of the front (= L/2) (Fig. 4). In this preliminary study, this model is simplified to reduce the parameterization of the upwelling feature to a single Oeste do Atlanticoˆ Sul (DEPROAS) synoptic data set from variable. The meld function m(η,z) is rewritten as the austral summer of 2001. m(η,z)=f(γ), B. The DEPROAS Data Set where the parameter γ varies between 0 (no upwelling, i.e. hor- This work applies a subset of the DEPROAS hydrographic izontally stratified environment) and 1 (maximal upwelling). (CTD) data set collected by the University of Sao˜ Paulo, Further works will consider the joint tracking of several aboard the R/V Prof. W. Besnard. This subset consists of the parameters, including the extremal temperature profiles. measurements taken during the summer season, when coastal Note that the setup of this formulation (1) is bathymetry- upwelling is more likely to occur. independent. If Ti is defined only over the first 100 m over The DEPROAS summer 2001 cruise (6–12th of January, the shelf, the bottommost available temperature is used for Ti 2001) consisted of four realizations of a transect normal to below this level. The meld function introduces the effect of the tip of Cabo Frio. Stations were about 25–35 km apart bathymetry. (Fig. 2). Fig. 3 presents a temperature section for the second realization of the Cabo Frio transect focused on the upwelling III. ACOUSTIC MONITORING OF THE UPWELLING FRONT front near the coast. The data from the DEPROAS summer A. Acoustic Propagation through the Upwelling Front 2001 sections were used for the calibration of the upwelling feature model [2]. Coastal environments show specific features also from the acoustic propagation viewpoint. First, mesoscale features C. The Coastal Upwelling Feature Model present often a high dynamics. Second, the shallow depths A schematic representation of the proposed feature model imply strong acoustic interactions with the range-dependent structure for the upwelling region near Cabo Frio is shown seafloor and subseafloor. It is well established that in such where w(tk) and v(tk) are zero-mean Gaussian random vectors of covariance Rww and Rvv, respectively. As pointed in [21] the joint estimation of oceanic and acoustic variables should enhance forecast or estimation results of both disciplines. Instead of assimilating inverted acoustic measurements, the state vector contains both the oceanic and acoustic variables, and the measurement model links the different types of data to this state vector. In the present case of a simplified oceanic model, the state vector contains the upwelling parameter γ and no oceanic model is assumed for its time evolution. Therefore this parameter is supposed to follow a random walk which is characterized by its second- Fig. 5. Synthetic acoustic configuration for a vertical slice of the Cabo Frio coastal area. The temperature field (in ◦C) depicts a typical upwelling feature. order statistics. The mapping of the upwelling parameter on the sound-speed field and the normal mode acoustic solution is embedded in the measurement function (4), which is therefore situations, travel-time based tomography is difficult to use with nonlinear. In this work, the measurement function is modified real measurements because of the lack of resolvable indepen- to enable the use of a cost function based on the Bartlett dent arrivals. A full-field based tomography method must thus processor on the N transmitted frequencies, defined as [22] be envisioned. In this work, the assimilated measurements are 1 N p†(γ,ω )R(ω )p(γ,ω ) a broad-band multi-frequency complex acoustic field on a ver- φ(γ)= n n n N ||p(γ,ω )||2||d(ω )||2 (5) tical array of hydrophones. In the present case of an upwelling n=1 n n front in a coastal area, the environment is characterized by where γ is the model vector (here, the single upwelling rapid variations of the temperature and the bathymetry along parameter), p(γ,ω) is the predicted (replica) field vector of the range. Therefore, no adiabatic assumptions can be made the acoustic-pressure observations across the vertical array at with regard to modal propagation. the frequency ω, and d(ω) is the vector of acoustic-pressure For this preliminary study, the acoustic source is placed at measurements across the vertical array at the frequency ω. 20-m depth near the coast and a 16-element vertical array is R(ω) is the corresponding spatial correlation matrix of the placed at 40-km away from the source, between 60- and 90-m complex acoustic data at the frequency ω, defined as depth. This geometry is depicted in Fig. 5. The modal prop- † agation takes into account the range-dependent bathymetry R(ω)=d(ω)d (ω). (6) and the acoustic bottom properties. The geoacoustic model † is derived from a set of multibeam, seismic and sediment core The symbol denotes the conjugate transpose. data being obtained in the framework of the EC FP7 Ocean The Kalman filter operates as a predictor-corrector algo- xˆ(t |t ) Acoustic Exploration project. The bottom is modeled with the rithm. In a first step, the new state estimate k k−1 P˜(t |t ) following parameters: compression speed: 1600 m/s, density: [and its associated error covariance k k−1 ] is predicted 1.8 g/cm3, attenuation: 0.2 dB/λ. using the state-space model (3). In the second phase, when Fig. 6 shows typical transmission losses through a sound- measurements are available, the state estimate is corrected by speed field generated by the upwelling feature model with the difference between the measurement predictions and the two extreme values of the upwelling parameter γ representing actual measurements, weighted by the so-called Kalman gain K respectively the absence of upwelling and a strong upwelling . Extensions of the Kalman filter are required to process in the section of interest. The upwelling feature modifies the nonlinearity introduced by the measurement function. the acoustic propagation along the range with a stronger The basic algorithm of the extended Kalman filter (EKF) modification of the acoustic field for higher frequencies also is shown in Fig. 7. More details about the Kalman filtering due to mode coupling. can be found in [23]. The more recent ensemble Kalman filter (EnKF) represents the underlying distributions with a B. Kalman-based Tracking large ensemble of model realizations, as in the Monte-Carlo The dynamics of the environment and the resulting acoustic methods. Each member is propagated through the state tran- measurements are embedded in a Gauss-Markov state-space sition and measurement functions and the statistics of the model. Denoting the environment by a state vector x with estimates are propagated without the use of any linearisation a formal oceanic model A which describes the evolution of step. Theoretical considerations and details about the EnKF the parameters, and the acoustic measurements y related to can be found in [24]. the state vector through a general function C, we express the IV. RESULTS discrete state-space model as In this feasibility study, the tracking of the upwelling is x(t )=A[x(t )] + w(t ) k k−1 k (3) tested in a twin experiment, i.e., a synthetic test for which y(tk)=C[x(tk)] + v(tk) (4) the environmental model is the same for the data synthesis (a) (b)

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Fig. 6. Example of coherent transmission losses (in dB) in absence of upwelling (left column) and with a strong upwelling (right column) for three frequencies [220 Hz (c,d), 440 Hz (e,f), and 880 Hz (g,h)]. The corresponding temperature ﬁelds of the vertical slice are shown respectively in (a) and (b). the upwelling parameter. Fig. 9 shows the evolution of the cost function based on seven third-octave frequencies between 220 Hz and 880 Hz with a 16-element vertical array, placed at 40-km away from the source, between 60- and 90-m depth. No additive noise on the hydrophones is assumed for this test. This ﬁgure can be understood as the ambiguity surface “seen” by the optimization algorithm during the tracking. At every time step, the cost function is multimodal. The simulations show that the higher frequencies show typically more and higher local peaks in the objective function. However, the peaks are more sharp and it reduces therefore the uncertainty around estimates. For this reason, the use of multiple frequencies allows us to realize the trade-off between these two opposite features. Fig. 7. Diagram of the EKF algorithm in a predictor-corrector form. The matrices A and C are the Jacobians of the transition and the measurement As shown in Fig. 9, the use of seven frequencies enables function, respectively. The EnKF algorithm shows a similar structure, but the reduction of the local peaks in the underlying ambiguity covariance matrices and Jacobians are replaced by stochastic ensemble of function while keeping a sharp peak in correspondence to the realizations. global maximum of the objective function.

0 C. Tracking Results −2

m/s An EKF and EnKF are applied on synthetic acoustic data set −4 generated from the wind-driven upwelling scenario. The same −6 noise realization on the acoustic pressure on the hydrophones −10 0 10 20 30 40 50 60 time (h) is used to compare the performances of both filter. Fig. 10 (a) shows that the EKF cannot track the upwelling parameter when the variations are too fast, resulting in a diverging esti- 1 mate after the first few iterations. The second result shows that 440 γ 0.5 the filtering of the single frequency Hz is not sufficient to track the variations of γ along the whole period. The estimate

0 −10 0 10 20 30 40 50 60 errors made by the EnKF can be reduced by increasing the time (h) ensemble size. However, the value of 50 ensemble members (b) was kept to ensure a sufficiently fast computation time. Fig. 11 compares the reconstruction of the temperature field using the Fig. 8. (a) Wind force and direction during 51 hours. (b) Upwelling parameter deduced from the wind data. true values of the γ parameter and the seven-frequency EnKF result, corresponding to the red curve in Fig. 10. and the tracking procedure. This allows us to verify if the V. C ONCLUSION acoustic observations and the associated state-space model are In this paper, it was shown that the tracking of the main sufficient for efficient inversion and tracking of the strongly feature of a coastal upwelling can be carried out by using a range-dependent environments occuring during the upwelling upwelling feature model as a parameterization scheme. Acous- periods. tic measurements at seven third-octave frequencies between A. Wind-driven Scenario 220 Hz and 880 Hz on a 16-hydrophone vertical array are inverted through a Bartlett processor. For this first study, the As shown in [25], [26], the upwelling in Cabo Frio is upwelling feature was reduced to a unique parameter that strongly correlated to the wind force and direction. For this quantifies the upwelling between the two extremal tempera- preliminary study, the simulation scenario for the variation of ture profiles. The time-evolution of this parameter is placed the upwelling parameter γ is based on real wind data from in a state-space model which allows the application of a NCEP database, during the period of January to February Kalman filter to perform the tracking by filtering the acoustic 2001 (Fig. 8). These typical wind variations were found to measurements. It was also shown that the ensemble Kalman initiate the upwelling feature and increase gradually its force. filter (EnKF) outperforms the standard extended Kalman filter The DEPROAS summer 2001 data were used to calibrate the (EKF). upwelling parameter γ based on these real wind data. B. Bartlett Representation ACKNOWLEDGMENT The sensitivity of the observables to the upwelling param- The authors acknowledge the support of the Fonds pour la eter variations can be represented through the evolution of formation a` la Recherche dans l’Industrie et dans l’Agriculture the Bartlett cost function over a typical range of values of (FRIA), Belgium, European Seas Observatory Network (a) (b)

Fig. 9. Evolution of the Bartlett cost function for the wind-driven scenario. The cost function is computed for (a) a single frequency (440 Hz) and (b) seven frequencies [220.0 Hz 277.2 Hz 349.2 Hz 440.0 Hz 554.4 Hz 698.5 Hz 880.0 Hz] on the 16-element vertical array. The gray line indicates the location of the tracked value (global maximum).

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