1 Ocean Modelling Archimer J anuary 2015, Volume 85, Pages 56-67 http://archimer.ifremer.fr http://dx.doi.org/10.1016/j.ocemod.2014.11.004 http://archimer.ifremer.fr/doc/00238/34910/ © 2014 Elsevier Ltd. All rights reserved. Lagrangian water mass tracing from pseudo-Argo, model- derived salinity, tracer and velocity data: An application to Antarctic Intermediate Water in the South Atlantic Ocean Blanke Bruno 2, 3, * , Speich Sabrina 1, 3, Rusciano Emanuela 1, 2 1 Laboratoire de Physique des Océans, UMR 6523 CNRS-Ifremer-IRD-UBO, UFR Sciences et Techniques, 6 avenue Le Gorgeu, CS 93837, 29238 Brest CEDEX 03, France 2 Laboratoire de Météorologie Dynamique, UMR 8359 CNRS-École Polytechnique-ENS-UPMC, 24 rue Lhomond, 75231 Paris CEDEX 05, France 3 Ifremer, France *Corresponding author : Bruno Blanke, tel.: +33 2 98 01 67 02 ; email address : [email protected] Abstract : We use the tracer and velocity fields of a climatological ocean model to investigate the ability of Argo- like data to estimate accurately water mass movements and transformations, in the style of analyses commonly applied to the output of ocean general circulation model. To this end, we introduce an algorithm for the reconstruction of a fully non-divergent three-dimensional velocity field from the simple knowledge of the model vertical density profiles and 1000-m horizontal velocity components. The validation of the technique consists in comparing the resulting pathways for Antarctic Intermediate Water in the South Atlantic Ocean to equivalent reference results based on the full model information available for velocity and tracers. We show that the inclusion of a wind-induced Ekman pumping and of a well-thought-out expression for vertical velocity at the level of the intermediate waters is essential for the reliable reproduction of quantitative Lagrangian analyses. Neglecting the seasonal variability of the velocity and tracer fields is not a significant source of errors, at least well below the permanent thermocline. These results give us confidence in the success of the adaptation of the algorithm to true gridded Argo data for investigating the dynamics of flows in the ocean interior. Keywords : Ocean circulation, Conservation equations, Mathematical models, Density field, Subsurface drifters, Intermediate water masses Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive publisher-authenticated version is available on the publisher Web site. 24   25   1. Introduction 26   Argo data provide invaluable and remarkable information about the ocean structure over the 27   first 2000 m of the water column, especially in basins that were, until recently, poorly sampled by 28   field experiments (Roemmich et al., 2009). The standard lifestyle of an Argo float is the following: 29   it drifts passively for 8-9 days at depth 1000 m, it dives down to 2000 m and then samples the water 30   column up to the surface where it can emit data to satellites, before it returns to its parking level. 31   Since the early results proposed by Wong and Johnson (2003), many efforts have been made in 32   using Argo temperature and salinity measurements over the vertical, especially in basins that 33   remained poorly observed until the intensive deployment of Argo floats. Among the recent studies 34   that deal with the South Atlantic (the regional focus of our work) Dong et al. (2011) analysed the 35   performance of a coupled general circulation model with respect to the reproduction of the 36   meridional overturning circulation and meridional heat transport, with and without assimilation of 37   Argo data. Garzoli et al. (2013) combined cruise data and Argo profiles to infer the variability these 38   two quantities over 2002-2011. Wu et al. (2011) could relate the spatial distribution of turbulent 39   diapycnal mixing at depths 300 to 1800 m to the interaction of the Antarctic Circumpolar Current 40   with the topography by making full use of high-resolution vertical profiles. Sato and Polito (2014) 41   focused on the identification and formation of South Atlantic subtropical mode waters. They 42   showed that most of the eddies sampled by an Argo profile and with marks of these mode waters 43   were anticyclonic. 44   Probably more marginally because more complicated, some other studies have attempted to 45   make the most of the displacements of autonomous floats at depth, knowing that only the 46   successive positions of the instruments at the sea surface are trackable (e.g., Davis, 2005, Park et 47   al., 2005, Lebedev et al., 2007, Katsumata and Yoshinari, 2010, Menna and Poulain, 2010). In each 48   study, the extrapolation of the start and end of the deep displacement from the successive surface 49   positions is an essential step. Recently, Gray and Riser (2014) used a velocity analysis at the Argo 50   parking depth to produce a reference velocity field for geostrophic calculations at other depths. A   3 51   few years ago, the Laboratoire de Physique des Océans in Brest (France) undertook a 52   comprehensive processing of the Argo data collected over the world ocean to produce an atlas 53   (named ANDRO, for Argo New Displacements Rannou and Ollitrault) of deep displacements based 54   on Argos-tracked surface locations, and fully checked and corrected for possible errors found in the 55   public Argo data files because of wrong decoding or instrumental failure (Ollitrault and Ranou, 56   2012). 57   It is tempting to blend absolute velocity information from a dataset like ANDRO and 58   geostrophic velocity profiles obtained over the vertical with the thermal wind equation, as done for 59   instance successfully by Gray and Riser (2004) in their global analysis of the Sverdrup balance. 60   Then, the resulting gridded absolute geostrophic velocity field might be a good candidate for the 61   investigation of water mass displacements and conversions, in the style of the analyses performed 62   on the output of an ocean general circulation models (OGCM), by combining Lagrangian 63   trajectories and the knowledge of in situ temperature and salinity (e.g., Blanke et al., 2006). 64   Unfortunately, the ocean interior is not purely geostrophic, and oceanic variability develops at time 65   scales ranging from a few hours (i.e., internal waves) to several years (i.e., decadal variability) 66   (Ferrari and Wunsch, 2010). Gridded climatologies of temperature and salinity and of the mean 67   absolute geostrophic velocity field correspond to independent calculations, which may result in the 68   poor rendering of the genuine temperature and salinity modifications along three-dimensional 69   movements. The physical reality of the modifications is however essential because they relate to the 70   sudden or progressive conversion of a water mass into another. The study of such water mass 71   transformations refers essentially to the close combination of tracer and velocity information, and a 72   Lagrangian analysis of gridded mass and velocity annual fields may not be so accurate unless 73   special care is brought to the calculations and to the interpretation of the results. 74   We will not discuss the process of gridding scattered velocity and tracer information though 75   this is of course a crucial step when working with genuine Argo data, and we take the availability of 76   gridded datasets for granted. Our paper aims at testing the successful derivation of a fully non-   4 77   divergent three-dimensional velocity field by using here, for convenience, synthetic velocity and 78   tracer data calculated and gridded by an OGCM. Our methodology uses only model data that mimic 79   the gridded information that can be retrieved from the profiles and displacements of the Argo 80   profilers. Therefore, we are confident that it will be easily transposable to true, gridded Argo data, 81   while beneficiating from the present results inferred from equivalent and thorough model-based 82   calculations. For instance, the sensitivity of water mass tracing experiments to the inclusion or 83   exclusion of seasonal variability in the gridded dataset can be investigated in the model, knowing 84   that Argo-derived gridded products consist predominantly of annual mean climatologies that 85   disregard the seasonal scales of ocean variability. Section 2 presents the model simulation that 86   provides pseudo-like Argo information, i.e., the horizontal velocity field at 1000 m and the vertical 87   profiles of temperature and salinity. Section 3 introduces a retrieval algorithm for the full three- 88   dimensional velocity and tracer fields, and discusses some key hypotheses in the light of known 89   patterns of the circulation of intermediate waters. Section 4 details the validation of the Lagrangian 90   experiments that can be carried out with these fields, with reference to results obtained with the 91   original velocity and tracer model data. Our concluding remarks follow in section 5. 92   93   2. Model and method 94   The numerical simulation we choose for our study is a somewhat realistic description of the 95   world ocean circulation (see detailed description in Blanke et al., 2002). The model that generated it 96   (the OPA model, Madec et al. (1998)) was used mostly as a dynamic interpolator of the mass field 97   derived from an observational climatology of salinity and temperature (Levitus ,1982). The domain 98   simulation extends from 78°S to 90°N with a 2° zonal resolution at the equator and a meridional 99   grid interval that varies from 0.5° at the equator to a maximum of 2° in the tropics. There are 31 100   levels in the vertical with the highest resolution (10 m) in the upper 150 m. The simulation is forced 101   by a daily climatology obtained from the European Centre for Medium-Range Weather Forecasts 102   (ECMWF) 15-year (1979-1993) reanalyses, and smoothed by an 11-day running mean. The   5 103   restoring term to the Levitus climatology appears as a Newtonian damping in the temperature and 104   salinity equations of the OGCM. The intensity of the restoring is given by the inverse of a 105   characteristic time scale that varies with depth and with the distances from the surface, the coast, 106   and the equator (Madec and Imbard, 1996). The simulation is equilibrated (there is no substantial 107   drift in the tracer and velocity fields after ten years of integration) and the internal sources and sinks 108   of heat and salt introduced by the Newtonian damping balance exactly the surface heat and 109   evaporation-minus-precipitation fluxes that are almost zero when integrated over the global domain. 110   The restoring (together with the climatological atmospheric forcing) is here an essential ingredient 111   to allow useful comparisons with circulation schemes deduced from observations (e.g., Blanke et 112   al., 2001, Friocourt et al., 2005). It does not interact directly with the model turbulent mixing and 113   bottom boundary layer schemes since it is not applied near the coastlines or within the mixed layer. 114   The restoring can still be considered as part of the model physics (at it intends to mimic the effects 115   of poorly performing subgrid scale parameterizations), with a non-local redistribution of heat and 116   salt (unlike lateral and vertical mixing that do conserve heat and salinity through exchanges 117   between adjacent grid cells). 118   The model horizontal resolution and the time scales kept for variability (monthly averages) 119   compare favourably with the resolution of the gridded atlases one can calculate from in situ Argo 120   data (e.g., Hosoda et al., 2008, Roemmich and Gilson, 2009, von Schuckmann et al., 2010). Of 121   course, at this resolution, the model does not sample the full spectrum of variability of the real 122   ocean: submonthly and subgrid scale movements are only parameterized with physical schemes that 123   account for the mean effect of turbulent lateral and vertical mixing. By comparison, the gridded 124   atlases calculated with Argo data average all the scales of variability truly experienced by the 125   drifters. 126   One model level for tracers and horizontal velocities lies at 1033 m and matches appropriately 127   the parking depth of most Argo drifters. Therefore, in this study, we use the annual mean currents 128   modelled at this depth in the South Atlantic Ocean as a reference absolute velocity field. The annual   6 129   mean values of temperature and salinity are combined to define an average mass field on which the 130   thermal wind equations are applied to derive geostrophic velocity components. The surface wind 131   stress that forced the model is used to estimate the annual mean Ekman circulation that can be 132   added on the total horizontal velocity field. These three stages represent a set of operations that can 133   be applied to true Argo-derived gridded datasets and available wind stress climatologies. The full 134   monthly varying model velocity and tracer fields are kept for reference Lagrangian experiments, to 135   which all comparisons will be made. 136   The focus is here on the South Atlantic Ocean because the northward spreading of Antarctic 137   Intermediate Water (AAIW) from the Subantarctic Front to the North Atlantic has long been a 138   subject of intense interest (Wüst, 1935; Talley 1996) and has been addressed in the recent years by 139   major research projects, e.g., GoodHope (Ansorge et al., 2005, Speich et al., 2007) and SAMOC 140   (Garzoli et al., 2007). Our study builds especially on the results obtained by Rusciano et al. (2012) 141   on the spreading of AAIW south of Africa, based on a thorough Eulerian analysis of Argo 142   hydrographic profiles and reference displacements at 1000 m. Evidence for AAIW penetration into 143   the South Atlantic north of the Subantarctic Front is a major result of their study, which 144   complements and updates the description of the AAIW circulation in the South Atlantic provided 145   by Suga and Talley (1995). This will be the focus of the model-based water mass tracing 146   experiments developed in section 4. 147   148   3. Retrieval algorithm for a fully non-divergent 3D velocity field 149   On seasonal time scales, the OGCM tracer field is in balance with the velocity field and 150   model physics (which includes here the vertical penetration of the solar radiation, as well as the 151   sources and sinks of tracers induced by the internal restoring of temperature and salinity on 152   climatological values). Water mass tracing requires the knowledge of the three components of the 153   velocity. The vertical velocity is usually several orders of magnitude smaller than the zonal and 154   meridional velocities, but the large-scale volume fluxes are of equivalent magnitude in the three   7 155   directions because of the depth-to-width aspect ratio of an ocean basin. Volume conservation (no 156   source or sink of volume within the active ocean domain) is a main property to be satisfied, before 157   addressing tracer conservation. 158   One major difficulty when dealing with absolute geostrophic velocity is the lack of control on 159   2D divergence. The implications are huge, since the vertical velocity is mostly a diagnostic field. It 160   can be computed by integrating upward or downward the 2D convergence of the horizontal 161   circulation, noting that it will accumulate all the errors and inaccuracies of the horizontal velocity 162   estimate. Three main issues exist here. First, geostrophy defines horizontal velocity components 163   that are only 2D non-divergent once multiplied by the Coriolis parameter (f); since f varies with the 164   sine of latitude, the deep and open ocean is usually characterized by a balance between the 165   advection of planetary vorticity (the beta effect) and divergence. Second, the absolute velocity field 166   at 1000 m has no reason for being itself exactly 2D non-divergent; being added at each depth, any 167   local divergence has repercussions on the whole water column and can translate into a linear growth 168   rate (with depth) of the calculated vertical velocity. Finally, the geostrophic relations cannot be 169   applied with confidence near continents or continental slopes where the ocean currents can be 170   highly turbulent or show full three-dimensionality (with for instance topography-induced vertical 171   movements), which adds uncertainty on the vertical velocity. 172   In this study we propose the following procedure for determining a three-dimensional (3D) 173   velocity field plausibly suitable for trajectory calculations in the ocean interior and eventually for 174   interrelation with tracer or salinity variability. The first guess 3D velocity field consists of the 175   addition of the geostrophic, Ekman and 1000-m absolute components of the horizontal velocity 176   field, as calculated from the annual mean model outputs and forcing fields. Then, a control surface 177   defined at the level of the intermediate waters is used with simple geometric and kinematic 178   considerations to infer the value of vertical velocity at that depth. Finally, a minimization technique 179   finds the optimal barotropic velocity corrections to add to the first guess so that the depth-integrated 180   circulation from the ocean surface to the control surface is compatible with this vertical velocity.   8 181   The resulting 3D velocity field will be used as a test bed for Lagrangian experiments: numerical 182   particles will be transported by the zonal, meridional and vertical components of the velocity field 183   across the South Atlantic Ocean, with special insight into water mass modification, in conjunction 184   with the original model tracers. 185   186   3.1. Horizontal interpolation of the model salinity and temperature values 187   As already specified, Argo temperature and salinity data are commonly gathered, and possibly 188   merged with other available measurements, to produce gridded fields. The temporal (monthly to 189   annual) and horizontal (0.5° to 2°) resolution of these Argo-based fields varies according to the 190   period of analysis and to the amount of independent data. For the Southern Ocean, because of more 191   recent systematic deployments of Argo profilers, the definition of robust monthly fields continues 192   to be a challenge. Therefore, the annual mean values of temperature and salinity from the model 193   simulation are good candidates for use as pseudo gridded Argo data. 194   The equations of the OGCM are discretized on a staggered C-grid (Arakawa, 1972). The 195   horizontal interpolation of the tracer values onto the "F" points of the grid is a necessary step to 196   calculate easily the horizontal density gradients that provide the zonal and meridional geostrophic 197   components of the flow, on the "U" and "V" points of the C-grid, respectively (Fig. 1). The 198   interpolation is made by averaging the ocean tracer grid points available in the immediate 199   neighbourhood of each "F" grid point. In the absence of any neighbouring tracer information, the 200   "F" grid point remains masked and is considered inland. Then, in the situ density is calculated at the 201   "F" grid points with the formulation that was used in the OGCM (Jackett and McDougall, 1995). 202   203   3.2. Geostrophic velocity components   9 204   At each level of the original model grid, the geostrophic u and v components are calculated g g 205   at the "U" and "V" points of the grid with the thermal wind equations, assuming a zero horizontal 206   velocity at 1000 m, or at the ocean bottom if it is locally shallower than 1000 m. ⎧∂u g ∂ρ g = ⎪ ⎪ ∂z ρ f ∂y 207   ⎨ 0 (1) ∂v g ∂ρ ⎪ g =− ⎪ ∂z ρ f ∂x ⎩ 0 208   The horizontal density gradients are first computed, and then the vertical integration is 209   performed upward. 210   211   3.3. Account for a surface wind-induced Ekman spiral 212   An analytical Ekman spiral is added from the knowledge on the mean value of the surface 213   wind stress used in the OGCM (a seasonal climatology obtained from the ECMWF reanalyses), 214   with a coefficient of eddy viscosity (A ) arbitrarily set to a constant: v 1 ( )( ) ⎧⎪ f ( ) ⎫⎪ 215   u +iv = 1+i τx +iτy exp⎨ 1−i z⎬ (2) e e ρ0 2 f Av ⎩⎪ 2Av ⎭⎪ 216   The formulation was first introduced by Ekman (1905). It is given here in complex variable 217   form and is valid for the Southern Hemisphere (f < 0), with z negative and increasing upward (z = 0 218   at the sea surface). The actual existence of such a spiral in the real ocean is debatable, especially 219   because the viscosity coefficient actually varies in the vertical (see for instance Ralph and Niiler 220   (1999)), but this is by far the simplest way to account fully for the wind stress forcing in a gridded 221   velocity field. The value of A is chosen here equal to 10-2 m2 s-1 to match the order of magnitude v 222   derived by Chereskin (1995) from the observation with moored instruments of a wind-driven flow 223   in Ekman balance, knowing that the recent results obtained from an underway acoustic Doppler 224   current profiler in Drake Passage suggest eddy coefficients values about 10 times greater (Polton et 225   al., 2013). However, it is worth noting that the value of A will not interfere much with our v   10 226   Lagrangian calculations since we will focus on movements well below the vertical extent of the 227   theoretical Ekman layer. What matters most is the algebraic divergence of the Ekman transport, 228   which is a function only of the surface wind stress (and of the Coriolis parameter): ( ) ∇× τx,τy 229   ∇i(U ,V )=− (3)   e e ρ f 0 230   where, for H much larger than the depth of the surface Ekman layer, % 0 τy 'U = ∫ u dz=− ' e e ρ f 231   & −H 0 (4) 'V = ∫0 v dz= τx (' e e ρ f −H 0 232   233   3.4. Addition of a reference velocity field at 1000 m 234   Wherever the ocean floor is deeper than 1000 m, the annual mean reference velocity field 235   (u , v ) modelled at 1000 m is added at each depth. The total velocity fields then reads: a a ( ) ( ) ( ) ( ) ⎧u x,y,z =u x,y,z +u x,y,z +u x,y ⎪ g e a 236   ⎨ ( ) ( ) ( ) ( ) (5) v x,y,z =v x,y,z +v x,y,z +v x,y ⎩⎪ g e a 237   238   3.5. Expression of the vertical velocity at intermediate depth 239   Most Argo profilers have a parking depth at 1000 m, which strengthens the reliability of the 240   circulation calculated at AAIW depth range. We choose to introduce an additional constraint on the 241   velocity field based on a priori knowledge of the behaviour of this water mass. In this step, we 242   determine on each vertical the depth of minimum salinity, z , and we estimate the vertical velocity ctrl 243   as w = U ⋅ ∇z ctrl ctrl ctrl   11