Lagrangian Estimator Research Articles

Lagrangian Versus Eulerian Spectral Estimates of Surface Kinetic Energy Over the Global Ocean

AbstractIn this study, we conducted a novel massive Lagrangian simulation experiment based on a global 1/48° tide‐resolving numerical simulation of the ocean circulation. This first‐time twin experiment enables a comparison between Eulerian (fixed‐point) and Lagrangian (along‐flow) estimates of kinetic energy (KE) across the global ocean, and the quantification of systematic differences between both types of estimations. This comparison represents an important step forward for the mapping of upper ocean high‐frequency variability from Lagrangian observations of the Global Drifter Program. Eulerian KE rotary frequency spectra and band‐integrated energy levels (e.g., tidal and near‐inertial) serve as references and are compared to Lagrangian estimates. Our analysis reveals that, except for the near‐inertial band, Lagrangian velocity spectra are systematically smoother, for example, with wider and lower spectral peaks compared to Eulerian counterparts. On average, Lagrangian KE levels derived from spectral band integrations tend to underestimate Eulerian KE levels at low‐frequency and tidal bands, especially in regions with strong low‐frequency KE. Better agreement between Lagrangian and Eulerian low‐frequency and tidal KE levels is generally found in regions with weak low‐frequency KE and/or convergent surface circulation, where Lagrangian particles tend to accumulate. Conversely, Lagrangian and Eulerian near‐inertial spectra and energy levels are comparable. Our results demonstrate that Lagrangian estimates may provide a distorted view of low‐frequency and tidal variance. To accurately map near‐surface velocity climatology at these frequencies from drifter database, conversion methods accounting for the Lagrangian bias need to be developed.

A Lagrangian Estimate of the Mediterranean Outflow's Origin

AbstractThe origin of the Mediterranean Outflow is investigated by deploying six millions virtual Lagrangian parcels at the Strait of Gibraltar, and tracing them backward in time using velocity estimates from an eddy‐permitting reanalysis. The Lagrangian parcels are followed until they intercept one of three sections. The hypothesis is that each section is associated with distinct water masses: the Gulf of Lions, related to Western Mediterranean Deep Water and Western Intermediate Water, carries 86% of the Outflow's transport; the Northern Tyrrhenian, related to Tyrrhenian Deep and Intermediate Waters, carries 1% of the transport; the Strait of Sicily, related to Levantine Intermediate Waters, carries 13% of the transport. The median transit times from the sections to the Strait of Gibraltar range from 5 years (Gulf of Lions) to 8 years (Strait of Sicily).

Traction open boundary condition for incompressible, turbulent, single- or multi-phase flows, and surface wave simulations

In simulations, artificial boundaries need to be introduced to limit the size of computational domains and thereby lower computational cost. At these boundaries, flow variables need to be calculated in a way that will not induce any perturbation of the interior solution, which poses a great challenge in incompressible flows. In this paper, we demonstrate the potential of a new traction open boundary condition to address the classical problems encountered in simulations with open boundary conditions: backflow instability, wave reflections, and confinement caused by the proximity of the outlet. This novel boundary treatment, based on a Lagrangian estimation of the traction in the outlet section coupled to a stabilization term, is shown to provide accuracy and stability for turbulent, single- or multi-phase flows, test cases. Using a simulation of surface gravity waves, we show that if special care is given to the computation of the estimated traction, it is possible to get a fully non-reflective open boundary condition.

A Lagrangian Multiplier Method for TDOA and FDOA Positioning of Multiple Disjoint Sources with Distance and Velocity Correlation Constraints

This paper considers the source localization problem using time differences of arrival (TDOA) and frequency differences of arrival (FDOA) for multiple disjoint sources moving together with constraints on their distances and velocity correlation. To make full use of the synergistic improvement of multiple source localization, the constraints on all sources are combined together to obtain the optimal result. Unlike the existing methods that can achieve the normal Cramér-Rao lower bound (CRLB), our object is to further improve the accuracy of the estimation with constraints. On the basis of maximum likelihood criteria, a Lagrangian estimator is developed to solve the constrained optimization problem by iterative algorithm. Specifically, by transforming the inequality constraints into exponential functions, Lagrangian multipliers can be used to determine the source locations via Newton’s method. In addition, the constrained CRLB for source localization with distance and velocity correlation constraints is also derived. The estimated accuracy of the source positions and velocities is shown to achieve the constrained CRLB. Simulations are included to confirm the advantages of the proposed method over the existing methods.

Does perspective matter? A case study comparing Eulerian and Lagrangian estimates of common murre (Uria aalge) distributions.

Studies estimating species' distributions require information about animal locations in space and time. Location data can be collected using surveys within a predetermined frame of reference (i.e., Eulerian sampling) or from animal‐borne tracking devices (i.e., Lagrangian sampling). Integration of observations obtained from Eulerian and Lagrangian perspectives can provide insights into animal movement and habitat use. However, contemporaneous data from both perspectives are rarely available, making examination of biases associated with each sampling approach difficult. We compared distributions of a mobile seabird observed concurrently from ship, aerial, and satellite tag surveys during May, June, and July 2012 in the northern California Current. We calculated utilization distributions to quantify and compare variability in common murre (Uria aalge) space use and examine how sampling perspective and platform influence observed patterns. Spatial distributions of murres were similar in May, regardless of sampling perspective. Greatest densities occurred in coastal waters off southern Washington and northern Oregon, near large murre colonies and the mouth of the Columbia River. Density distributions of murres estimated from ship and aerial surveys in June and July were similar to those observed in May, whereas distributions of satellite‐tagged murres in June and July indicated northward movement into British Columbia, Canada, resulting in different patterns observed from Eulerian and Lagrangian perspectives. These results suggest that the population of murres observed in the northern California Current during spring and summer includes relatively stationary individuals attending breeding colonies and nonstationary, vagile adults and subadults. Given the expected growth of telemetry studies and advances in survey technology (e.g., unmanned aerial systems), these results highlight the importance of considering methodological approaches, spatial extent, and synopticity of distribution data sets prior to integrating data from different sampling perspectives.

Measuring Area-Averaged Vertical Motions with Dropsondes

Abstract Measurements of vertical profiles of areal-mean mass divergence, vorticity, and vertical velocity, based on dropsondes distributed over an area of 25 000 km2, are presented. The dropsondes were released with high frequency along circular flight patterns during an airborne field campaign taking place over the tropical Atlantic near Barbados. Vertical profiles of the area-averaged mass divergence and vorticity were computed from the horizontal wind profiles, and the area-averaged vertical velocity was then inferred from the divergence. The consistency of measurements over pairs of circles flown within the same air mass demonstrated the reproducibility of the measurements, and showed that they characterize the environmental conditions on the scale of the measurement, rather than being dominated by measurement error or small-scale wind variability. The estimates from dropsondes were found to be consistent with the observed cloud field, with Lagrangian estimates of the mean vertical velocity inferred from the free-tropospheric humidity field, and with the mean vertical velocity derived from simulations using an atmospheric model representing kilometer-scale motions and initialized with meteorological analyses. In trade wind–like conditions, the divergence and vorticity profiles exhibit a rich vertical structure and a significant variability in space and time. Yet a few features appear to be robust, such as the presence of layers of mass convergence at the top of moist layers, extrema of the area-averaged vertical velocity at the top of the subcloud layer and in the midtroposphere, and minima around the trade inversion near 2 km. The analysis of spatial and temporal autocorrelation scales suggests that the divergent mass field measured from dropsondes is representative of the environment of shallow clouds.

Mesoscale and Submesoscale Processes in the Southeast Atlantic and Their Impact on the Regional Thermohaline Structure

AbstractThe turbulent processes in the Cape Basin, the southeasternmost gate of the Atlantic Ocean, play a key role in the transport and mixing of upper to intermediate water masses entering the area from the Indian Ocean, making them especially relevant for the Indo‐Atlantic transfer of heat and salt. In this paper, two numerical simulations at different horizontal resolutions are used to study mesoscale and submesoscale dynamics, their phenomenology, their evolution, and their impact on the local water masses. Submesoscale processes seasonally affect both, the upper and intermediate layers, but there are clear dynamical differences between the two layers. Several types of instabilities underline this spatial and temporal variability. Near the surface, mixed layer instabilities occur during winter, while mesoscale‐driven instabilities, as the symmetric type, prevail in summer. The connection between these two seasonal regimes is ensured, in anticyclonic eddies and within the mixed layers, by Charney baroclinic instabilities, involved in the local formation and subduction of mode water, that we have dubbed as Agulhas Rings mode water. Intermediate depths are instead characterized by mesoscale mechanisms of density compensation and lateral stirring of the tracer variance, triggering a significant filamentogenesis whose vertical scales are comparable to those mentioned in previous studies. This leads to a particularly efficient mixing of Antarctic Intermediate Waters of Indian and Atlantic origins. Lagrangian estimates highlight the new and significant role of fine scale structures in setting the water masses properties of upper and lower thermocline waters materializing the Indo‐Atlantic exchange and therefore potentially affecting the global ocean circulation.

Using Conical Regularization in Calculating Lagrangian Estimates in Quadratic Optimization Problems

For nonconvex quadratic optimization problems, the authors consider calculation of global extreme value estimates on the basis of Lagrangian relaxation of the original problems. On the boundary of the feasible region of the estimate problem, functions of the problem are discontinuous, ill-conditioned, which imposes certain requirements on the computational algorithms. The paper presents a new approach taking into account these features, based on the use of conical regularizations of convex optimization problems. It makes it possible to construct an equivalent unconditional optimization problem whose objective function is defined on the entire space of problem variables and satisfies the Lipschitz condition.

Robust Differential Received Signal Strength-Based Localization

Source localization based on signal strength measurements has become very popular due to its practical simplicity. However, the severe nonlinearity and non-convexity make the related optimization problem mathematically difficult to solve, especially when the transmit power or the path-loss exponent (PLE) is unknown. Moreover, even if the PLE is known but not perfectly estimated or the anchor location information is not accurate, the constructed data model will become uncertain, making the problem again hard to solve. This paper particularly focuses on differential received signal strength (DRSS)-based localization with model uncertainties in case of unknown transmit power and PLE. A new whitened model for DRSS-based localization with unknown transmit powers is first presented and investigated. When assuming the PLE is known, we introduce two estimators based on an exact data model, an advanced best linear unbiased estimator (A-BLUE) and a Lagrangian estimator (LE), and then we present a robust semidefinite programming (SDP)-based estimator (RSDPE), which can cope with model uncertainties (imperfect PLE and inaccurate anchor location information). The three proposed estimators have their own advantages from different perspectives: the A-BLUE has the lowest complexity; the LE holds the best accuracy for a small measurement noise; and the RSDPE yields the best performance under a large measurement noise and possesses a very good robustness against model uncertainties. Finally, we propose a robust SDP-based block coordinate descent estimator (RSDP-BCDE) to deal with a completely unknown PLE and its performance converges to that of the RSDPE using a perfectly known PLE.

Small‐scale fluctuations in barium drifts at high latitudes and associated Joule heating effects

AbstractMost previous estimates of Joule heating rates, especially the contribution of small‐scale structure in the high‐latitude ionosphere, have been based on incoherent scatter or coherent scatter radar measurements. An alternative estimate can be found from the plasma drifts obtained from ionized barium clouds released from sounding rockets. We have used barium drift data from three experiments to estimate Joule heating rates in the high‐latitude E region for different magnetic activity levels. In particular, we are interested in the contribution of small‐scale plasma drift fluctuations, corresponding to equivalent electric field fluctuations, to the local Joule heating rate on scales smaller than those typically resolved by radar or other measurements. Since Joule heating is a Lagrangian quantity, the inherently Lagrangian estimates provided by the chemical tracer measurements are a full description of the effects of electric field variance and neutral winds on the heating, differing from the Eulerian estimates of the type provided by ground‐based measurements. Results suggest that the small‐scale contributions to the heating can be more than a factor of 2 greater than the mean field contribution regardless of geomagnetic conditions, and at times the small‐scale contribution is even larger. The high‐resolution barium drift measurements, moreover, show that the fine structure in the electric field can be more variable than previous studies have reported for similar conditions. The neutral winds also affect the heating, altering the height‐integrated Joule heating rates by as much as 12%, for the cases studied here, and modifying the height distribution of the heating profile as well.

Evaluation of the utility of xanthophyll cycle pigment dynamics for assessing upper ocean mixing processes at Station ALOHA

ments was collected from the sea-surface in order to quantify the time-dependent rate of change in the ratio of XCP to chlorophyll a (XCP/CHLA). In situ XCP/CHLA values were measured by rapid collection of cells in the mixed layer using a diaphragm pumping system and the xanthophyll cycle activity inhibitor dithiothreitol. Turbulent transfer velocity (TTV) was estimated as the quotient of the XCP/CHLA photoadaptation rate and the XCP/CHLA gradient in the mixed layer. TTVs ranged from 0.3 to 0.5 cm s 21 , and agreed to within a factor of 2 of the Lagrangian floatderived estimate of vertical mixing at a comparable friction velocity. Coincident measurements of dissolved gases suggest that XCP dynamics may be useful for the interpretation of trace gases species distributions, such as hydrogen and carbon monoxide, in the upper ocean.

Deuterium excess as a proxy for continental moisture recycling and plant transpiration

Abstract. Studying the evaporation process and its link to the atmospheric circulation is central for a better understanding of the feedbacks between the surface water components and the atmosphere. In this study, we use 5 months of deuterium excess (d) measurements at the hourly to daily timescale from a cavity ring-down laser spectrometer to characterise the evaporation source of low-level continental water vapour at the long-term hydrometeorological monitoring site Rietholzbach in northeastern Switzerland. To reconstruct the phase change history of the air masses in which we measure the d signature and to diagnose its area of surface evaporation we apply a Lagrangian moisture source diagnostic. With the help of a correlation analysis we investigate the strength of the relation between d measurements and the moisture source conditions. Temporal episodes with a duration of a few days of strong anticorrelation between d and relative humidity as well as temperature are identified. The role of plant transpiration, the large-scale advection of remotely evaporated moisture, the local boundary layer dynamics at the measurement site and recent precipitation at the site of evaporation are discussed as reasons for the existence of these modes of strong anticorrelation between d and moisture source conditions. We show that the importance of continental moisture recycling and the contribution of plant transpiration to the continental evaporation flux may be deduced from the d–relative humidity relation at the seasonal timescale as well as for individual events. The methodology and uncertainties associated with these estimates of the transpiration fraction of evapotranspiration are presented and the proposed novel framework is applied to individual events from our data set. Over the whole analysis period (August to December 2011) a transpiration fraction of the evapotranspiration flux over the continental part of the moisture source region of 62% is found albeit with a large event-to-event variability (0% to 89%) for continental Europe. During days of strong local moisture recycling a higher overall transpiration fraction of 76% (varying between 65% and 86%) is found. These estimates are affected by uncertainties in the assumptions involved in our method as well as by parameter uncertainties. An average uncertainty of 11% results from the strong dependency of the transpiration estimates on the choice of the non-equilibrium fractionation factor. Other uncertainty sources like the influence of boundary layer dynamics are probably large but more difficult to quantify. Nevertheless, such Lagrangian estimates of the transpiration part of continental evaporation could potentially be useful for the verification of model estimates of this important land–atmosphere coupling parameter.

Network-Wide Traffic State Estimation Using Loop Detector and Floating Car Data

In real-time traffic management and intelligent transportation systems (ITS) applications, an accurate picture of the prevailing traffic state in terms of speeds and densities is critical, for which traffic state estimation methods are needed. The most popular and effective techniques used are so-called model-based traffic state estimators, which consist of a dynamic traffic flow model to predict the evolution of the state variables; a set of observation equations relating sensor observations to the system state; and data-assimilation techniques to combine the model predictions with the sensor observations. Commonly, both process and observation models are formulated in Eulerian (space–time) coordinates. However, recent studies show that (first-order) macroscopic traffic flow models can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number–time) coordinates (which move with traffic stream) than in Eulerian coordinates (which are fixed in space). In this article such a Lagrangian system model for state estimation is used. The approach uses the extended Kalman filtering technique, in which the discretized Lagrangian kinematic wave model with an extension (node models) for network discontinuities is used as the process equation and the average relation between vehicle spacing and speed (the fundamental diagram) is used as the observation equation. The Lagrangian state estimator is validated and compared with its Eulerian counterpart based on ground-truth data from a microscopic simulation environment. The results demonstrate that network-wide Lagrangian state estimation is possible and provide evidence that the Lagrangian estimator outperforms the Eulerian approach.

Real-Time Lagrangian Traffic State Estimator for Freeways

Freeway traffic state estimation and prediction are central components in real-time traffic management and information applications. Model-based traffic state estimators consist of a dynamic model for the state variables (e.g., a first- or second-order macroscopic traffic flow model), a set of observation equations relating sensor observations to the system state (e.g., the fundamental diagrams), and a data-assimilation technique to combine the model predictions with the sensor observations [e.g., the extended Kalman filter (EKF)]. Commonly, both process and observation models are formulated in Eulerian (space-time) coordinates. Recent studies have shown that this model can be formulated and solved more efficiently and accurately in Lagrangian (vehicle number-time) coordinates. In this paper, we propose a new model-based state estimator based on the EKF technique, in which the discretized Lagrangian Lighthill-Whitham and Richards (LWR) model is used as the process equation, and in which observation models for both Eulerian and Lagrangian sensor data (from loop detectors and vehicle trajectories, respectively) are incorporated. This Lagrangian state estimator is validated and compared with a Eulerian state estimator based on the same LWR model using an empirical microscopic traffic data set from the U.K. The results indicate that the Lagrangian estimator is significantly more accurate and offers computational and theoretical benefits over the Eulerian approach.

Lagrangian and Eulerian lateral diffusivities in zonal jets

Meridional diffusivities from Lagrangian particle dispersion and Eulerian diffusivities from a flux-gradient relationship are estimated in an idealized primitive equation channel model featuring eddy-driven zonal jets. The Eulerian estimate shows an increase with depth and clear minima of meridional diffusivities within the zonal jets, indicating mixing barriers. The Lagrangian estimates agree with the Eulerian method on the vertical variation and also show indications of meridional mimima, although meridional variations are poorly resolved. We found early maxima in the particle spreading rates which should not be related to diffusivities since they are caused by the meandering zonal jets. The meanders also produce rotational eddy fluxes, which can obscure the Eulerian diffusivity estimates. Zonal particle dispersion rates do not converge within the chosen lag interval, because of shear dispersion by the mean flow, i.e. it is not possible to estimate Lagrangian zonal diffusivities representative for regions of similar size of the zonal jet spacing. Removing the zonal mean flow, zonal and meridional dispersion rates converge and show much higher zonal than meridional diffusivities. Further, the pronounced vertical increase and indications of meridional minima in the Lagrangian meridional diffusivities disappear, pointing towards the importance of shear dispersion by the mean flow for the suppression of meridional mixing by zonal jets.

A Comparison of Lagrangian Model Estimates to Light Detection and Ranging (LIDAR) Measurements of Dust Plumes from Field Tilling

A Lagrangian particle model has been adapted to examine human exposures to particulate matter ≤ 10 µm (PM10) in agricultural settings. This paper reports the performance of the model in comparison to extensive measurements by elastic LIDAR (light detection and ranging). For the first time, the LIDAR measurements allowed spatially distributed and time dynamic measurements to be used to test the predictions of a field-scale model. The model outputs, which are three-dimensional concentration distribution maps from an agricultural disking operation, were compared with the LIDAR-scanned images. The peak cross-correlation coefficient and the offset distance of the measured and simulated plumes were used to quantify both the intensity and location accuracy. The appropriate time averaging and changes in accuracy with height of the plume were examined. Inputs of friction velocity, Monin–Obukhov length, and wind direction (1 sec) were measured with a three-axis sonic anemometer at a single point in the field (at 1.5-m height). The Lagrangian model of Wang et al. predicted the near-field concentrations of dust plumes emitted from a field disking operation with an overall accuracy of approximately 0.67 at 3-m height. Its average offset distance when compared with LIDAR measurements was approximately 38 m, which was 6% of the average plume moving distance during the simulation periods. The model is driven by weather measurements, and its near-field accuracy is highest when input time averages approach the turbulent flow time scale (3–70 sec). The model accuracy decreases with height because of smoothing and errors in the input wind field, which is modeled rather than measured at heights greater than the measurement anemometer. The wind steadiness parameter (S) can be used to quantify the combined effects of wind speed and direction on model accuracy.

Continuous measurements of net production over a shallow reef community using a modified Eulerian approach

We made continuous measurements of the flux of dissolved oxygen over an algal‐dominated reef flat community on the Kaneohe Bay Barrier Reef, Hawaii as a proxy for the net production (NP) of organic carbon. Fluxes were calculated from measurements of dissolved oxygen and current profiles taken from moored oxygen sensors and acoustic Doppler current profilers (ADCPs) located at points defining the vertices of a triangular control volume 250 m in length on each side. Surface cruciform drifters as well as dye patches were tracked across the control volume to get independent measurements of Lagrangian currents. While the dye patch speeds were highly correlated with the depth‐averaged current speeds calculated from ADCP data on a 1:1 basis (r2 = 0.86, n = 24), drifter speeds exceeded both dye and calculated current speeds by 30–100% on average. Measurements of dissolved oxygen sampled within the dye patches as it propagated across the study site were used to calculate NP following a Lagrangian approach. Lagrangian estimates of NP were highly correlated with Eulerian estimates of NP on a 1:1 basis (r2 = 0.81, n = 7). Ratios of community production and community respiration varied from 0.7 to 1.4 on a daily basis, but approached a value of 1.0 when integrated over the entire data record.

On the Potential of the Lagrangian Estimator for Endovascular Ultrasound Elastography: In Vivo Human Coronary Artery Study

Diagnosis and prognosis of coronary artery atherosclerosis evolution currently rely on plaque morphology and vessel stenosis degree. Such information can accurately be assessed with intravascular ultrasound (IVUS) imaging. A severe complication of coronary artery atherosclerosis is thrombosis, a consequence of plaque rupture or fissure, which might lead to myocardial infarction and sudden ischemic death. Plaque rupture is a complicated mechanical process, correlated with the plaque morphology, composition, mechanical properties and with the blood pressure. Extracting information on the plaque local mechanical properties may reveal relevant features about plaque vulnerability. Accordingly, endovascular elastography (EVE) was introduced to complement IVUS for investigating coronary artery diseases. In this article, in vivo elastographic data are reported for three patients (patient 1, patient 2 and patient 3) who were diagnosed with severe coronary artery stenoses. Time-sequence radio-frequency (RF) data were acquired, in the minutes preceding angioplasty, using an ultrasound scanner working with a 30 MHz mechanical rotating single-element transducer. The elastograms of the radial strain and radial shear distributions within the vessel wall were computed from pairs of successive RF images using the Lagrangian estimator (LE). A hard atherosclerotic plaque (low radial strain and shear) was identified in patient 1. High radial strain and shear values in the plaque areas for patient 2 and patient 3 suggested the presence of lipid cores (soft materials), known to be prone-to-rupture sites when located close to the lumen. To conclude, EVE allowing radial strain and shear images is an improvement over existing EVE methods that may assist IVUS in preoperative vessel lesion assessments and in endovascular therapy planning. (E-mail: guy.cloutier@umontreal.ca)

Lagrangian Estimates of Diapycnal Mixing in a Simulated K–H Instability

Abstract The Lagrangian properties of a high-resolution, three-dimensional, direct numerical simulation of Kelvin– Helmholtz (K–H) instability are examined with the goal of assessing the ability of Lagrangian measurements to determine rates and properties of ocean mixing events. The size and rotation rates of the two-dimensional K–H vortices are easily determined even by individual trajectories. Changes in density along individual trajectories unambiguously show diapycnal mixing. These changes are highly structured during the early phases of the instability but become more random once the flow becomes turbulent. Only 36 particles were tracked, which is not enough to usefully estimate volume-averaged fluxes from the average rates of temperature change. Similarly, time-and volume-averaged vertical advective flux can be estimated to only 20% accuracy. Despite the relatively low Reynolds number of the flow, Rλ ≈ 100, the dissipation rates of energy e and density variance χ are correlated with the spectral lev...

Lagrangian estimations of ozone loss in the core and edge region of the Arctic polar vortex 1995/1996: Model results and observations

Ozone evolution and diabatic descent in the Arctic polar vortex in winter 1995/1996 was studied with a newly developed diabatic trajectory–chemistry model (DTCM). To study the chemical and dynamic evolution of the species in the polar vortex, 400 diabatic trajectories were calculated in the vortex core and edge region by using three-dimensional (3-D) wind data provided by the European Centre for Medium-Range Weather Forecasts (ECMWF). The averaged diabatic descending motion and ozone behavior were obtained for particles started from the core and from the edge region of the vortex. The difference in ozone-loss rates as well as the difference in descending rates between the vortex core and the vortex-edge region was not statistically significant. The average cumulative ozone loss of 65 ± 16% in the vortex core obtained from the model calculations was consistent with the estimates obtained with a different method (Match experiment). The model results for the vortex core were compared with those obtained using trajectories with the vertical winds calculated on the basis of radiative cooling rates as used by the SLIMCAT 3-D chemical transport model. Although the trajectories based on cooling rates exhibited lower descending rates than those based on 3-D analyzed wind data, the ozone behavior was similar for both types of trajectory. Ozonesonde data from two stations (Ny-Alesund in the vortex core and Yakutsk in the vortex edge) were compared with the model results. For Lagrangian estimation of the ozone loss at these stations, the descending rates obtained by the diabatic trajectory calculations were used. Good agreements were obtained between the model results and observations for both the vortex core and edge region. These results suggest that strong ozone depletion occurred not only in the core, but also in the edge region of the vortex, and that air masses from the mid-latitudes did not appreciably affect the degree of ozone depletion in this winter–spring period. The sensitivity of the model to different descending rates and to the presence of large nitric acid trihydrate (NAT) particles was also examined.