Inhomogeneous Turbulent Dispersion across the Nearshore Induced by Surfzone Eddies

In various oceanic regions, drifter-derived diffusivities reach a temporal maximum and subsequently decrease. Often, these are regions of inhomogeneous eddies, however, the effect of inhomogeneous turbulence on dispersion is poorly understood. The nearshore region (spanning from the surfzone to the inner shelf) also has strong cross-shore inhomogeneous turbulence. Nearshore Lagrangian statistics are estimated from drifter trajectories simulated with a wave-resolving two-dimensional Boussinesq model with random, normally incident, and directionally spread waves. The simulation is idealized and does not include other (wind, tidal, Coriolis) processes. The eddy field cross-shore inhomogeneity affects both the mean cross-shore drift and cross- and alongshore diffusivities. Short-time diffusivities are locally ballistic, and the mean drift is toward the eddy velocity variance maximum. The diffusivities reach a maximum and subsequently decrease, that is, are subdiffusive. The diffusivity maximum and time to maximum are parameterized taking into account the eddy field inhomogeneity. At long times, the cross- and alongshore diffusivities scale as t−1/2 and t−1/4, respectively, which is related to the offshore decay of the eddy intensity. A diffusion equation, with a space-dependent Fickian diffusivity related to the eddy velocity variance, reproduced the short-, intermediate-, and long-time behavior of the mean drift and cross-shore diffusivity. The small Middleton parameter, indicating fixed float dispersion, suggests the Eulerian time scale can parameterize the Lagrangian time scale in this region. Although this idealized simulation had no mean currents, and thus no shear dispersion or mixing suppression, inhomogeneous turbulence effects may be relevant in other regions such as the Antarctic Circumpolar Current (ACC) and western boundary current extensions.

Diagnosing Isopycnal Diffusivity in an Eddying, Idealized Midlatitude Ocean Basin via Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT)

Isopycnal diffusivity due to stirring by mesoscale eddies in an idealized, wind-forced, eddying, midlatitude ocean basin is computed using Lagrangian, in Situ, Global, High-Performance Particle Tracking (LIGHT). Simulation is performed via LIGHT within the Model for Prediction across Scales Ocean (MPAS-O). Simulations are performed at 4-, 8-, 16-, and 32-km resolution, where the first Rossby radius of deformation (RRD) is approximately 30 km. Scalar and tensor diffusivities are estimated at each resolution based on 30 ensemble members using particle cluster statistics. Each ensemble member is composed of 303 665 particles distributed across five potential density surfaces. Diffusivity dependence upon model resolution, velocity spatial scale, and buoyancy surface is quantified and compared with mixing length theory. The spatial structure of diffusivity ranges over approximately two orders of magnitude with values of O(105) m2 s−1 in the region of western boundary current separation to O(103) m2 s−1 in the eastern region of the basin. Dominant mixing occurs at scales twice the size of the first RRD. Model resolution at scales finer than the RRD is necessary to obtain sufficient model fidelity at scales between one and four RRD to accurately represent mixing. Mixing length scaling with eddy kinetic energy and the Lagrangian time scale yield mixing efficiencies that typically range between 0.4 and 0.8. A reduced mixing length in the eastern region of the domain relative to the west suggests there are different mixing regimes outside the baroclinic jet region.

Lagrangian Time Scales and Eddy Diffusivity at 1000 m Compared to the Surface in the South Pacific and Indian Oceans

Argo floats cannot be regarded as true Lagrangian drifters because they periodically rise to the surface. Hence, previous estimates of eddy diffusivity at depth using single-particle statistics have been limited to one submerged cycle. However, unless the Lagrangian time scale is significantly shorter than the Argo cycle time, this single-particle calculation can have a large bias. Here, eddy diffusivity computed from single-particle statistics using Argo data is compared to that computed by assuming that Eulerian scales at depth are the same as at the surface, and that the relationship between Lagrangian and Eulerian time scales derived by Middleton is valid. If the methods provide the same answer, one can have confidence in both methods. Eddy diffusivity calculated from the single-particle statistics shows the same spatial structure as that computed from inferred time scale, but is smaller by a factor of about 2. It is suggested that this is because the deep Lagrangian time scale over much of the region is comparable to, or longer than, the 10-day Argo submergence cycle.

Comparing Lagrangian and Eulerian models for CO₂ transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.

Comparing Lagrangian and Eulerian models for CO2 transport – a step towards Bayesian inverse modeling using WRF/STILT-VPRM

We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the Eulerian-based Weather Research Forecasting (WRF) model and the Lagrangian-based Stochastic Time-Inverted Lagrangian Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (Eulerian vs. Lagrangian) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and Lagrangian time-scale in STILT is needed to achieve a better match between the Eulerian and the Lagrangian transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.

The effect of a non-zero Lagrangian time scale on bounded shear dispersion

Previous studies of shear dispersion in bounded velocity fields have assumed random velocities with zero Lagrangian time scale (i.e. velocities are$\delta $-function correlated in time). However, many turbulent (geophysical and engineering) flows with mean velocity shear exist where the Lagrangian time scale is non-zero. Here, the longitudinal (along-flow) shear-induced diffusivity in a two-dimensional bounded velocity field is derived for random velocities with non-zero Lagrangian time scale${\tau }_{L} $. A non-zero${\tau }_{L} $results in two-time transverse (across-flow) displacements that are correlated even for large (relative to the diffusive time scale${\tau }_{D} $) times. The longitudinal (along-flow) shear-induced diffusivity${D}_{S} $is derived, accurate for all${\tau }_{L} $, using a Lagrangian method where the velocity field is periodically extended to infinity so that unbounded transverse particle spreading statistics can be used to determine${D}_{S} $. The non-dimensionalized${D}_{S} $depends on time and two parameters: the ratio of Lagrangian to diffusive time scales${\tau }_{L} / {\tau }_{D} $and the release location. Using a parabolic velocity profile, these dependencies are explored numerically and through asymptotic analysis. The large-time${D}_{S} $is enhanced relative to the classic Taylor diffusivity, and this enhancement increases with$ \sqrt{{\tau }_{L} } $. At moderate${\tau }_{L} / {\tau }_{D} = 0. 1$this enhancement is approximately a factor of 3. For classic shear dispersion with${\tau }_{L} = 0$, the diffusive time scale${\tau }_{D} $determines the time dependence and large-time limit of the shear-induced diffusivity. In contrast, for sufficiently large${\tau }_{L} $, a shear time scale${\tau }_{S} = \mathop{ ({\tau }_{L} {\tau }_{D} )}\nolimits ^{1/ 2} $, anticipated by a simple analysis of the particle’s domain-crossing time, determines both the${D}_{S} $time dependence and the large-time limit. In addition, the scalings for turbulent shear dispersion are recovered from the large-time${D}_{S} $using properties of wall-bounded turbulence.

Lagrangian Data Assimilation in Multilayer Primitive Equation Ocean Models

Because of the increases in the realism of OGCMs and in the coverage of Lagrangian datasets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications, such as environmental pollutant transport, biological, and naval-related problems. In this study, a Lagrangian data assimilation method, which was introduced in prior studies in the context of single-layer quasigeostrophic and primitive equation models, is extended for use in multilayer OGCMs using statistical correlation coefficients between velocity fields in order to project the information from the data-containing layer to the other model layers. The efficiency of the assimilation scheme is tested using a set of twin experiments with a three-layer model, as a function of the layer in which the floats are launched and of the assimilation sampling period normalized by the Lagrangian time scale of motion. It is found that the assimilation scheme is effective provided that the correlation coefficient between the layer that contains the data and the others is high, and the data sampling period Δt is smaller than the Lagrangian time scale TL. When the assimilated data are taken in the first layer, which is the most energetic and is characterized by the fastest time scale, the assimilation is very efficient and gives relatively low errors also in the other layers (≈ 40% in the first 120 days) provided that Δt is small enough, Δt << TL. The assimilation is also efficient for data released in the third layer (errors < 60%), while the dependence on Δt is distinctively less marked for the same range of values, since the time scales of the deeper layer are significantly longer. Results for the intermediate layer show a similar insensitivity to Δt, but the errors are higher (exceeding 70%), because of the lower correlation with the other layers. These results suggest that the assimilation of deep-layer data with low energetics can be very effective, but it is strongly dependent on layer correlation. The methodology also remains quite robust to large deviations from geostrophy.