A Lagrangian-trajectory study of a gradually mixed ... - Kristofer DÃ¶Ã¶s

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1812 B.F. Jönsson et al. / Continental Shelf Research 31 (2011) 1811–1817 62°N 61°N 60°N 59°N Stockholm >6.5 Hanko 6.0 3.0 2.5 2.0 Helsinki 5.0 4.5 4.0 3.5 5.5 Tallin 2> Neva St Petersburg Moshnyi Island Hiiuma 58°N 18°E 21°E 24°E 27°E 30°E 33°E Fig. 1. Map of the Gulf of Finland where the thin black line represents the model coastline. The heavy grey line indicates where the ‘‘Baltic’’ trajectories are released to the Gulf and the heavy black line where all trajectories are removed. Also included are observed surface isohalines as adapted from Jurva (1951). 0.0 -25.0 -50.0 -75.0 -100.0 -125.0 -150.0 22.0 23.0 24.0 25.0 27.0 28.0 29.0 30.0 Fig. 2. Salinity sections along the central axis of the Gulf of Finland. Colour-coded contours show a long-term average of the RCO-modelled salinity field. The green lines represent observations as adapted from Jurva (1951). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) models tend to be somewhat deficient in reproducing the salt dynamics of the system under consideration. The present investigation will instead approach the problem from a Lagrangian standpoint, i.e. using trajectory analysis. In next section the technical details of this procedure are outlined, whereafter the subsequent section deals with the results concerning mixing and water-mass composition obtained for the Gulf of Finland. Hereafter, a discussion is undertaken of the large-scale circulation in the Gulf based on a Lagrangian decomposition of the overturning stream-function, this in order to estimate the contributions of the waters originating from the river Neva and the Baltic, respectively. The study is concluded by a review of the overall outcome of the analysis. 2. Methods Classical trajectory analysis, as primarily applied to the atmosphere, mainly relied upon graphical techniques used in conjunction with meteorological good sense and experience. Modern-day trajectory methods are, however, based on numerical circulation models. In the present study, velocity fields from the Rossby Centre Ocean (RCO) model (Meier et al., 2003) serve as the basis for the further investigations. This well-proven (Meier and Kauker, 2003) finite-difference model has 41 depth levels (at intervals ranging from 3 m in the surface region to 12 m at greater depths) and a horizontal resolution of 2 4 nautical miles. It is based on an Arakawa B-grid and is capable of resolving the meso-scale
B.F. Jönsson et al. / Continental Shelf Research 31 (2011) 1811–1817 1813 eddies of importance for the dynamics of the Baltic. For the present investigation with focus on the north-eastern Baltic, the remotely applied boundary conditions at the border to the North Sea do not give rise to any spurious effects. Given 0.21 0.21 gridded standard meteorological forcing (sea-level pressure, geostrophic 10 m wind components, 2 m air temperature and relative humidity, precipitation, and cloud cover) provided by the Swedish Meteorological and Hydrological Institute (SMHI) at 3-hour intervals, the circulation model yields the evolution in time of the velocity, temperature and salinity fields. As an example of what can be achieved within the RCO framework, Fig. 2 also includes a long-term average of the modeled salinity along the central axis of the Gulf of Finland. The two data sets show a high degree of resemblance to one another, with the exception of a more pronounced Neva-river plume in the observations. This discrepancy indicates that the RCO model may have too large a diffusion (which in turn affects the distribution of tracers). In the present study, a trajectory scheme based on results due to Döös (1995) as well as Blanke and Raynaud (1997) was used to compute Lagrangian paths from the three-dimensional velocity fields in the Gulf of Finland provided by the RCO model. The trajectory algorithm is based on analytical calculations using a prescribed velocity field which is five-fold more highly resolved in time than the circulation-model data, from which it is generated by linear interpolation. This permits analyses of the water-parcel motion over smaller scales than the model grid by interpolation of the zonal, meridional, and vertical velocities defined in the corners of the grid cell. It should be noted that true Lagrangian trajectories are only affected indirectly by the sub-grid parameterisation of viscosity and diffusion implemented within the circulation model. (An alternative method of water-mass analysis is based on the tracer equation, which includes diffusion in contrast to what is the case for true Lagrangian trajectories. However, this diffusion is not only physical, but also numerical due to, e.g. finite-difference truncation error.) Following Döös and Engqvist (2007), sub-grid turbulence affecting the trajectories has thus been parameterized by adding a random turbulent velocity at each ‘‘high-resolution’’ time step, this in order to include a measure of turbulent diffusion in the analysis of the present study. It should furthermore be underlined that the trajectory calculations can be run in an autonomous fashion with regard to the circulation model, i.e. off-line. This makes it possible to carry through the analysis without having to take recourse to excessive computer resources. Convection has not been taken into account in the present study, but the effects of this process have been examined in the course of a previous investigation (Döös, 1995) by assigning a water parcel a random depth whenever it enters a convectively unstable water column. (Like the velocities used to calculate the trajectories, these convective events also originate from the circulation model.) This study showed, however, that the effects of convection did not affect the results to any significant degree. To examine the behavior of the system, all water parcels entering the Gulf of Finland from the Baltic and the river Neva were ‘‘tagged’’ with the aim of determining the origin of the water masses characterizing the system in ‘‘steady state’’. This refers to when the number of water parcels released into the system equals that exiting and when a ‘‘saturated’’ ratio between the number of trajectories originating from the two sources is established over a meridional transect half-way into the Gulf. These criteria were found to be amply satisfied for numerical experiments of an approximately 5000-day duration, well above the estimated turnover time of the system (Andrejev et al., 2004b) being 1–2 years. Every 6 h trajectories were seeded over the exit from the river Neva as well as over the entire breadth and depth of the Hanko–Hiumaa transect delimiting the Gulf of Finland from the Baltic proper. Each trajectory was specified as representing a volume flux of 100 m 3 s 1 , which, based on a transport of 7–8000 m 3 s 1 entering the Gulf, yielded a sufficient number of trajectories, in this case around 80 each 6th hour. The sensitivity was tested by stepwise increasing the volume flux associated with each trajectory, corresponding to a decrease of the trajectory ‘‘density’’. The threshold when a further decrease of this density had a degrading effect on the outcome was found to be around 50, i.e. considerably below the value of 80 trajectories ‘‘seeded’’ every 6 h during our numerical simulations. All trajectories leaving the system were removed from the model run at a meridional transect located 5 grid-points west of the Baltic Proper boundary where source water originally was tagged (cf. Fig. 1). The rationale behind this procedure was to reduce the computational costs and to, as far as possible, prevent trajectories from recirculating, which would have entailed the risk of multiple tagging of water parcels. When the trajectory integrations had attained a steady state in the sense described above, the results were analyzed using techniques to be outlined in what follows. 3. Mixing and water mass composition Before proceeding with a discussion of the overall results from the numerical experiments, we examine some specific features in order to judge whether the model can be regarded as performing in an adequate fashion. The underlying rationale is that even if a circulation model yields more-or-less correct overall results, considerable local irregularities may arise, in particular adjacent to the boundaries of the system. In the larger Baltic perspective, the Gulf of Finland can be looked upon as a marginal area, and thus the modelers in the course of developing the RCO formalism did not focus specifically on this region, even though the discharge from the river Neva potentially could create anomalies here. The model results were thus verified by collating the timeaveraged RCO-generated velocity fields with the results from earlier studies. One interesting area for comparisons of this type is located close to Moshnyi Island in the inner part of the Gulf, where Andrejev et al. (2004b) reported exceptionally long residence times of the water. This state of affairs also manifests itself in the present circulation-model results, assuming the form of a prevalence of stable, highly persistent eddies in the area. In general, the time-averaged RCO velocity fields employed for calculating the trajectories proved to be in agreement with well-known transport patterns (Palmén, 1930) characterizing the Gulf of Finland. Thus high-saline water from the Baltic Proper enters the Gulf as a deep boundary current adjacent to the Estonian coast, whereas transports associated with the river Neva discharge tends to take place on the Finnish side of the Gulf. Once each experiment had been concluded, analysis of the trajectory behavior was undertaken by calculating a mixing ratio R defined as the number of trajectories from Neva divided by the total number of trajectories within each grid-box. This was done for each cell in the Gulf of Finland modeling domain, the value R¼1 representing a situation where all water originated from the river Neva, the value R¼0 indicating the presence of only Baltic water. To investigate the relative water-mass composition along the main axis of the Gulf of Finland, this distribution was averaged across the Gulf. By also carrying through a vertical integration, it proved feasible to construct a Hovmøller diagram representing the evolution of this water-mass distribution along a section in the Gulf of Finland as a function of time, cf. Fig. 3. From this diagram it can be concluded that a saturated ratio between the number of trajectories originating from the two sources was
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A Lagrangian-trajectory study of a gradually mixed ... - Kristofer DÃ¶Ã¶s

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