Lagrangian Diagnostics Research Articles

A Lagrangian analysis of a developing and non-developing disturbance observed during the PREDICT experiment

Abstract. The problem of tropical cyclone formation requires among other things an improved understanding of recirculating flow regions on sub-synoptic scales in a time evolving flow with typically sparse real-time data. This recirculation problem has previously been approached assuming as a first approximation both a layer-wise two-dimensional and nearly steady flow in a co-moving frame with the parent tropical wave or disturbance. This paper provides an introduction of Lagrangian techniques for locating flow boundaries that encompass regions of recirculation in time-dependent flows that relax the steady flow approximation. Lagrangian methods detect recirculating regions from time-dependent data and offer a more complete methodology than the approximate steady framework. The Lagrangian reference frame follows particle trajectories so that flow boundaries which constrain particle transport can be viewed in a frame-independent setting. Finite-time Lagrangian scalar field methods from dynamical systems theory offer a way to compute boundaries from grids of particles seeded in and near a disturbance. The methods are applied to both a developing and non-developing disturbance observed during the recent pre-depression investigation of cloud systems in the tropics (PREDICT) experiment. The data for this analysis is derived from global forecast model output that assimilated the dropsonde observations as they were being collected by research aircraft. Since Lagrangian methods require trajectory integrations, we address some practical issues of using Lagrangian methods in the tropical cyclogenesis problem. Lagrangian diagnostics are used to evaluate the previously hypothesized import of dry air into ex-Gaston, which did not re-develop into a tropical cyclone, and the exclusion of dry air from pre-Karl, which did become a tropical cyclone and later a major hurricane.

Diagnosing Lateral Mixing in the Upper Ocean with Virtual Tracers: Spatial and Temporal Resolution Dependence

Abstract Several recent studies diagnose lateral stirring and mixing in the upper ocean using altimetry-derived velocity fields to advect “virtual” particles and fields offline. However, the limited spatiotemporal resolution of altimetric maps leads to errors in the inferred diagnostics, because unresolved scales are necessarily imperfectly modeled. The authors examine a range of tracer diagnostics in two models of baroclinic turbulence: the standard Phillips model, in which dispersion is controlled by large-scale eddies, and the Eady model, where dispersion is determined by local scales of motion. These models serve as a useful best- and worst-case comparison and a valuable test of the resolution sensitivity of tracer diagnostics. The effect of unresolved scales is studied by advecting tracers using model velocity fields subsampled in space and time and comparing the derived tracer diagnostics with their “true” value obtained from the fully resolved flow. The authors find that eddy diffusivity and absolute dispersion, which are governed by large-scale dynamics, are insensitive to spatial sampling error in either flow. Measures that depend strongly on small scales, such as relative dispersion and finite-time Lyapunov exponents, are highly sensitive to spatial sampling in the Eady model. Temporal sampling error is found to have a more complicated behavior because of the onset of particle overshoot leading to scrambling of Lagrangian diagnostics. This leads to a potential restriction on the utility of raw altimetry maps for studying mixing in the upper ocean. The authors conclude that offline diagnostics of mixing in ocean flows with an energized submesoscale should be viewed with some caution.

Episodic upwelling and dust deposition as bloom triggers in low-nutrient, low-chlorophyll regions

[1] Summertime phytoplankton blooms in the oligotrophic North Pacific Ocean are supported by N2-fixing organisms that relieve the system of nitrate limitation. Phosphate and iron, however, limit their growth and need to be supplied for these organisms to thrive. We analyze two recent blooms in the region whose differences provide insight into their possible formation mechanisms. In 2008, a typical late summer bloom, with sporadic patches of higher-chlorophyll concentration, occurred near the island chain and the subtropical front. In 2010, an unusually large, contiguous bloom was observed in the western oligotrophic North Pacific, a region where blooms seldom, if ever, occur. Streaks of high chlorophyll in 2008 coincide with surface temperature fronts and regions of large horizontal stretching, as detected by Lagrangian diagnostics. Such regions are prone to the generation of vertical velocities via frontogenesis. Horizontal transport from upwelling regions or iron-rich island sediments is also important for the redistribution of nutrients. In the case of the 2010 bloom, we use a global aerosol transport model as well as space-borne lidar observations to argue that atmospheric dust deposition events prior to the bloom provided the necessary nutrient conditions for the growth of N2-fixing organisms. As sea surface temperature increased in the region, chlorophyll values increased significantly, showing that this bloom was likely a consequence of prior enrichment and that temperature is a key factor in bloom development in this important biome.

Water masses as a unifying framework for understanding the Southern Ocean Carbon Cycle

Abstract. The scientific motivation for this study is to understand the processes in the ocean interior controlling carbon transfer across 30° S. To address this, we have developed a unified framework for understanding the interplay between physical drivers such as buoyancy fluxes and ocean mixing, and carbon-specific processes such as biology, gas exchange and carbon mixing. Given the importance of density in determining the ocean interior structure and circulation, the framework is one that is organized by density and water masses, and it makes combined use of Eulerian and Lagrangian diagnostics. This is achieved through application to a global ice-ocean circulation model and an ocean biogeochemistry model, with both components being part of the widely-used IPSL coupled ocean/atmosphere/carbon cycle model. Our main new result is the dominance of the overturning circulation (identified by water masses) in setting the vertical distribution of carbon transport from the Southern Ocean towards the global ocean. A net contrast emerges between the role of Subantarctic Mode Water (SAMW), associated with large northward transport and ingassing, and Antarctic Intermediate Water (AAIW), associated with a much smaller export and outgassing. The differences in their export rate reflects differences in their water mass formation processes. For SAMW, two-thirds of the surface waters are provided as a result of the densification of thermocline water (TW), and upon densification this water carries with it a substantial diapycnal flux of dissolved inorganic carbon (DIC). For AAIW, principal formatin processes include buoyancy forcing and mixing, with these serving to lighten CDW. An additional important formation pathway of AAIW is through the effect of interior processing (mixing, including cabelling) that serve to densify SAMW. A quantitative evaluation of the contribution of mixing, biology and gas exchange to the DIC evolution per water mass reveals that mixing and, secondarily, gas exchange, effectively nearly balance biology on annual scales (while the latter process can be dominant at seasonal scale). The distribution of DIC in the northward flowing water at 30° S is thus primarily set by the DIC values of the water masses that are involved in the formation processes.

A comparison of the present and last interglacial periods in six Antarctic ice cores

Abstract. We compare the present and last interglacial periods as recorded in Antarctic water stable isotope records now available at various temporal resolutions from six East Antarctic ice cores: Vostok, Taylor Dome, EPICA Dome C (EDC), EPICA Dronning Maud Land (EDML), Dome Fuji and the recent TALDICE ice core from Talos Dome. We first review the different modern site characteristics in terms of ice flow, meteorological conditions, precipitation intermittency and moisture origin, as depicted by meteorological data, atmospheric reanalyses and Lagrangian moisture source diagnostics. These different factors can indeed alter the relationships between temperature and water stable isotopes. Using five records with sufficient resolution on the EDC3 age scale, common features are quantified through principal component analyses. Consistent with instrumental records and atmospheric model results, the ice core data depict rather coherent and homogenous patterns in East Antarctica during the last two interglacials. Across the East Antarctic plateau, regional differences, with respect to the common East Antarctic signal, appear to have similar patterns during the current and last interglacials. We identify two abrupt shifts in isotopic records during the glacial inception at TALDICE and EDML, likely caused by regional sea ice expansion. These regional differences are discussed in terms of moisture origin and in terms of past changes in local elevation histories, which are compared to ice sheet model results. Our results suggest that elevation changes may contribute significantly to inter-site differences. These elevation changes may be underestimated by current ice sheet models.

Contributions of the wall boundary layer to the formation of the counter-rotating vortex pair in transverse jets

Using high-resolution 3-D vortex simulations, this study seeks a mechanistic understanding of vorticity dynamics in transverse jets at a finite Reynolds number. A full no-slip boundary condition, rigorously formulated in terms of vorticity generation along the channel wall, captures unsteady interactions between the wall boundary layer and the jet – in particular, the separation of the wall boundary layer and its transport into the interior. For comparison, we also implement a reduced boundary condition that suppresses the separation of the wall boundary layer away from the jet nozzle. By contrasting results obtained with these two boundary conditions, we characterize near-field vortical structures formed as the wall boundary layer separates on the backside of the jet. Using various Eulerian and Lagrangian diagnostics, it is demonstrated that several near-wall vortical structures are formed as the wall boundary layer separates. The counter-rotating vortex pair, manifested by the presence of vortices aligned with the jet trajectory, is initiated closer to the jet exit. Moreover tornado-like wall-normal vortices originate from the separation of spanwise vorticity in the wall boundary layer at the side of the jet and from the entrainment of streamwise wall vortices in the recirculation zone on the lee side. These tornado-like vortices are absent in the case where separation is suppressed. Tornado-like vortices merge with counter-rotating vorticity originating in the jet shear layer, significantly increasing wall-normal circulation and causing deeper jet penetration into the crossflow stream.

Lagrangian Coherent Structure Analysis of Terminal Winds Detected by Lidar. Part I: Turbulence Structures

Abstract The accurate real-time detection of turbulent airflow patterns near airports is important for safety and comfort in commercial aviation. In this paper, a method is developed to identify Lagrangian coherent structures (LCS) from horizontal lidar scans at Hong Kong International Airport (HKIA) in China. LCS are distinguished frame-independent material structures that create localized attraction, repulsion, or high shear of nearby trajectories in the flow. As such, they are the fundamental structures behind airflow patterns such as updrafts, downdrafts, and wind shear. Based on a recently developed finite-domain–finite-time Lyapunov exponent (FDFTLE) algorithm from Tang et al. and on new Lagrangian diagnostics presented in this paper that are pertinent to the extracted FDFTLE ridges, the authors differentiate LCS extracted from lidar data. It is found that these LCS derived from horizontal lidar scans compare well to convergence and divergence suggested by vertical slice scans. At HKIA, horizontal scans are predominant: they cover much bigger azimuthal ranges as compared with only two azimuthal angles from the vertical scans. LCS extracted from horizontal scans are thus advantageous in providing organizing turbulence structures over the entire observational domain as compared with a single line along the vertical scan direction. In Part II of this study, the authors will analyze the evolution of LCS and their impacts on landing aircraft based on recorded flight data.

Impact of nearshore wind stress curl on coastal circulation and primary productivity in the Peru upwelling system

Coastal upwelling dynamics are strongly affected by alongshore wind stress and nearshore wind stress curl. A coupled physical‐biogeochemical regional model and lagrangian diagnostics are used in the Peru current system to determine how the upwelling of nutrients and the primary productivity are impacted by the spatial structure of the nearshore wind stress. Three wind stress products derived from the ERS and QuikSCAT scatterometers and a smoothed QuikSCAT field, mainly differing in nearshore wind stress curl patterns, were used. Simulations are found to produce significantly different mean surface chlorophyll distributions and show that strong upwelling‐favorable nearshore wind stress curl may locally induce a wide coastal productive zone through upwelling of nutrient‐replete waters brought by a shoaling coastal undercurrent. Using wind stress products with realistic nearshore patterns is therefore crucial for the modeling of coupled physical‐biogeochemical coastal processes.

Fluid dynamical niches of phytoplankton types.

The biogeochemical role of phytoplanktonic organisms strongly varies from one plankton type to another, and their relative abundance and distribution have fundamental consequences at the global and climatological scales. In situ observations find dominant types often associated to specific physical and chemical water properties. However, the mechanisms and spatiotemporal scales by which marine ecosystems are organized are largely not known. Here we investigate the spatiotemporal organization of phytoplankton communities by combining multisatellite data, notably high-resolution ocean-color maps of dominant types and altimetry-derived Lagrangian diagnostics of the surface transport. We find that the phytoplanktonic landscape is organized in (sub-)mesoscale patches (10-100 km) of dominant types separated by physical fronts induced by horizontal stirring. These physical fronts delimit niches supported by water masses of similar history and whose lifetimes are comparable with the timescale of the bloom onset (few weeks). The resonance between biological activity and physical processes suggest that the spatiotemporal (sub-)mesoscales associated to stirring are determinant in the observation and modeling of marine ecosystems.

On the pathways of the equatorial subsurface currents in the eastern equatorial Pacific and their contributions to the Peru‐Chile Undercurrent

The connections between the Equatorial Current System and the Peru Current System in the eastern tropical Pacific (ETP) are examined with a primitive equations eddy‐resolving regional model. The quasi‐equilibrium solutions reproduce three eastward equatorial subsurface currents of interest: the Equatorial Undercurrent (EUC, located between 1°N and 1°S), the primary Southern Subsurface Countercurrent (pSSCC, between 3° and 4°S) and, farther south the secondary Southern Subsurface Countercurrent (sSSCC, between 7° and 8 °S). Using a Lagrangian tracking procedure, the fate of these currents in the ETP and their contribution to the Peru‐Chile Undercurrent (PCUC) are studied. Lagrangian diagnostics show that for the most part the EUC water contributes to westward flows, including the South Equatorial Current and deeper flows below it, and strikingly only a very little fraction feeds the PCUC, while a significant part of both SSCCs contribute substantially. Mesoscale eddies are shown to exert an effect on these connections. In addition, about 30% of the PCUC is fed by the three subsurface equatorial flows (EUC, pSSCC, sSSCC). The remaining part of the PCUC comes from an alongshore recirculation associated with flows below it, and from the southern part of the domain (south of ∼9°S).

Asymmetries in the moisture origin of Antarctic precipitation

The seasonality of moisture sources for precipitation in Antarctica is studied with a Lagrangian moisture source diagnostic. Moisture origin for precipitation in Antarctica has strongly asymmetric properties, which are related to the Antarctic topography, seasonal sea ice coverage, and the land/ocean contrasts in the mid‐latitudes of the southern hemisphere. The highest altitudes of the East Antarctic ice shield, where major ice cores have been drilled, have mean source latitudes of 45–40°S year‐round. This finding contrasts to results from previous Lagrangian studies which detected a more southerly moisture origin due to too short trajectories. Now, results from Lagrangian moisture source diagnostics are consistent with findings from general circulation models with tagged tracers. Thus, both approaches can serve as a common benchmark for the interpretation of moisture source indicators based on stable isotopes, such as deuterium excess, in Antarctic ice cores.

Impact of submesoscale variability in estimating the air‐sea CO2 exchange: Results from a model study of the POMME experiment

A high‐resolution ocean biogeochemical model is used to estimate oceanic pCO2 and air‐sea CO2 flux in the NE Atlantic. The model is validated against shipboard and Carioca drifting float data acquired during the POMME experiment. Between winter and spring, the seasonal variability is characterized by a rapid drawdown of pCO2 of ∼20 μatm associated with the phytoplankton bloom driving CO2 uptake by the ocean. The model reveals that this uptake propagates northward in response to the northward propagation of the bloom. More remarkably, this study demonstrates intense variability of the carbon system at the submesoscale. Our model predicts filamentary structures of pCO2 that show gradients of 25 μatm over 20 km, consistent with observations from Carioca drifting floats. This submesoscale variability is similar in magnitude to the mean seasonal drawdown. Lagrangian diagnostics suggest that pCO2 small‐scale structures are shaped by horizontal stirring of large‐scale gradients created by the bloom northward propagation. We compared air‐sea flux derived from model pCO2 and from observed pCO2 and estimated the error due to data undersampling to ∼15 to 30%. Results from a simulation at coarser resolution showed that the impact of model resolution on air‐sea CO2 flux is only ∼5%. This suggests that the submesoscale variability of pCO2, although large in amplitude, accounts for small modulation of the net air‐sea CO2 flux in this region.

Chaotic advection and separatrix branching in the Lagrangian diagnostics of flows

Chaotic advection and separatrix branching in the Lagrangian diagnostics of flows

Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin

Transport and mixing properties of surface currents can be detected from altimetric data by both Eulerian and Lagrangian diagnostics. In contrast with Eulerian diagnostics, Lagrangian tools like the local Lyapunov exponents have the advantage of exploiting both spatial and temporal variability of the velocity field and are in principle able to unveil subgrid filaments generated by chaotic stirring. However, one may wonder whether this theoretical advantage is of practical interest in real-data, mesoscale and sub-mesoscale analysis, because of the uncertainties and resolution of altimetric products, and the non-passive nature of biogeochemical tracers. Here we compare the ability of standard Eulerian diagnostics and the finite-size Lyapunov exponent in detecting instantaneous and climatological transport and mixing properties in the south-western Mediterranean. By comparing with sea-surface temperature patterns, we find that the two approaches provide similar results for slowly evolving eddies like the first Alboran gyre. However, the Lyapunov exponent is also able to predict the (sub-)mesoscale filamentary processes occurring along the Algerian current and above the Balearic Abyssal Plain. Such filaments are also observed, with some mismatch, in sea-surface temperature patterns. Climatologies of Lyapunov exponents do not show any compact relation with other Eulerian diagnostics, unveiling a different structure even at the basin scale. We conclude that filamentation dynamics can be detected by reprocessing available altimetric data with Lagrangian tools, giving insight into (sub-)mesoscale stirring processes relevant to tracer observations and complementing traditional Eulerian diagnostics.

The Global Conveyor Belt from a Southern Ocean Perspective

Abstract Recent studies have proposed the Southern Ocean as the site of large water-mass transformations; other studies propose that this basin is among the main drivers for North Atlantic Deep Water (NADW) circulation. A modeling contribution toward understanding the role of this basin in the global thermohaline circulation can thus be of interest. In particular, key pathways and transformations associated with the thermohaline circulation in the Southern Ocean of an ice–ocean coupled model have been identified here through the extensive use of quantitative Lagrangian diagnostics. The model Southern Ocean is characterized by a shallow overturning circulation transforming 20 Sv (1 Sv ≡ 106 m3 s−1) of thermocline waters into mode waters and a deep overturning related to the formation of Antarctic Bottom Water. Mode and intermediate waters contribute to 80% of the upper branch of the overturning in the Atlantic Ocean north of 30°S. A net upwelling of 11.5 Sv of Circumpolar Deep Waters is simulated in the Southern Ocean. Antarctic Bottom Water upwells into deep layers in the Pacific basin, forming Circumpolar Deep Water and subsurface thermocline water. The Southern Ocean is a powerful consumer of NADW: about 40% of NADW net export was found to upwell in the Southern Ocean, and 40% is transformed into Antarctic Bottom Water. The upwelling occurs south of the Polar Front and mainly in the Indian and Pacific Ocean sectors. The transformation of NADW to lighter water occurs in two steps: vertical mixing at the base of the mixed layer first decreases the salinity of the deep water upwelling south of the Antarctic Circumpolar Current, followed by heat input by air–sea and diffusive fluxes to complete the transformation to mode and intermediate waters.

Lagrangian Diagnostics of Tropical Deep Convection and Its Effect upon Upper-Tropospheric Humidity

AbstractThis study combines geostationary water vapor imagery with optical cloud property retrievals and microwave sea surface observations in order to investigate, in a Lagrangian framework, (i) the importance of cirrus anvil sublimation on tropical upper-tropospheric humidity and (ii) the sea surface temperature dependence of deep convective development. Although an Eulerian analysis shows a strong spatial correlation of ∼0.8 between monthly mean cirrus ice water path and upper-tropospheric humidity, the Lagrangian analysis indicates no causal link between these quantities. The maximum upper-tropospheric humidity occurs ∼5 h after peak convection, closely synchronized with the maximum cirrus ice water path, and lagging behind it by no more than 1.0 h. Considering that the characteristic e-folding decay time of cirrus ice water is determined to be ∼4 h, this short time lag does not allow for significant sublimative moistening. Furthermore, a tendency analysis reveals that cirrus decay and growth, in terms of both cloud cover and integrated ice content, is accompanied by the drying and moistening of the upper troposphere, respectively, a result opposite that expected if cirrus ice were a primary water vapor source. In addition, it is found that an ∼2°C rise in sea surface temperature results in a measurable increase in the frequency, spatial extent, and water content of deep convective cores. The larger storms over warmer oceans are also associated with slightly larger anvils than their counterparts over colder oceans; however, anvil area per unit cumulus area, that is, cirrus detrainment efficiency, decreases as SST increases.

Lagrangian Study of Tropical Instability Vortices in the Atlantic

Abstract Tropical instability waves and tropical instability vortices (TIVs) exert major controls on ocean dynamics, thermodynamics, and biology on intraseasonal to seasonal time scales. To understand the fundamental mechanisms at play, a Lagrangian analysis of the 3D circulation of westward-propagating TIVs was performed in a high-resolution Atlantic Ocean simulation. The model reproduces the main temperature and velocity features of the tropical Atlantic mean state and the TIVs. Lagrangian diagnostics were used to track the water masses transported in vortices and exchanged with surrounding waters. The 3D circulation within vortices is consistent with previous observations and dominated by anticyclonic rotation with downwelling and upwelling near the leading and trailing edges of the vortex, respectively. This convergent flow creates sharp gradients at the TIV southwestern edge, where vertical mixing is most efficient. While TIVs remain highly dynamically coherent throughout their lifetime, significant exchanges occur with their surroundings, with 50% of their water being renewed over one rotation cycle. A detailed investigation of the eddies’ sources and sinks reveals that they mostly transport southern water zonally, while northern waters are mostly passing through or fluxed southward in their lee. A notable source of entrained water is the Equatorial Undercurrent.

Leaking method approach to surface transport in the Mediterranean Sea from a numerical ocean model

We use Lagrangian diagnostics (the leaking and the exchange methods) to characterize surface transport out of and between selected regions in the Western Mediterranean. Velocity fields are obtained from a numerical model. Residence times of water of Atlantic origin in the Algerian subbasin, with a strong seasonal dependence, are calculated. Exchange rates between these waters and the ones occupying the northern basin are also evaluated. At surface, northward transport is dominant, and involves filamental features and eddy structures that can be identified with the Algerian eddies. The impact on these results of the presence of small scale turbulent motions is evaluated by adding Lagrangian diffusion.

Eastern Mediterranean Transient studied with Lagrangian diagnostics applied to a Mediterranean OGCM forced by satellite SST and ECMWF wind stress for the years 1988–1993

In this work, we estimate deep and intermediate water mass dispersal in the different phases of the Eastern Mediterranean Transient by means of the Lagrangian analysis of a Mediterranean ocean general circulation model (OGCM) run, forced by daily European Centre for Medium‐Range Weather Forecasts (ECMWF) wind stress and satellite sea surface temperature (SST) over the years from 1988 to 1993. While in a first phase (1989–1991) major modifications of the intermediate salty waters path are observed, during 1992 and 1993 the general mechanism of the transient is reproduced in the deep Ionian basin, where the Cretan overflow replaces Adriatic deep water that uplifting of several hundred meters freshens in the intermediate layers. Analysis of the water mass formation rates shows that dense water production during 1993 is twice the climatological values in the eastern subbasins of the Mediterranean and that the densest water is formed in the Cretan Sea. From 1988 to 1993, about 1.3 × 1014 m3 of water flows over the Cretan Arcs (see the caption of Figure 1 for a definition of the Cretan Arcs) to sink deeper than 600 m in the eastern Mediterranean, which is roughly half of the value estimated by Roether et al. [1996]. About 60% of this deep outflow (∼0.8 × 1014 m3) occurs in a few months, during the cold winters of 1992 and 1993, when the overflow of Cretan dense water in the Antikithera Strait reaches 1.5 Sv and rapidly propagates in the deep Ionian basin, developing very energetic coherent structures. We study the characteristic times of the relaxation of the system toward the climatology, and finally, we estimate the rate and the geographical distribution of the upwelling in the intermediate and subsurface layers.

Diagnosing and Picturing the North Atlantic Segment of the Global Conveyor Belt by Means of an Ocean General Circulation Model

The monthly mean velocity, salinity, and temperature fields of a numerical simulation of the World Ocean climatological circulation are used to study the intensity and pathways associated with the meridional overturning in the North Atlantic. Lagrangian diagnostics based on the computation of several hundreds of thousands of individual three-dimensional trajectories are combined with an appropriate study of water mass potential densities in order to describe the warm and cold limbs of the so-called conveyor belt. Circulation schemes are established for both limbs of the overturning, and can be easily compared with schemes or transport estimates deduced from direct measurements, as the model temperature and salinity fields are constrained to remain close to the observed climatology. Diagnostics emphasize most typical pathways as well as main mass transfers that lead to the establishment of such numerical circulation schemes.