Lagrangian Circulation Research Articles

Extraction of persistent lagrangian coherent structures for the pollutant transport prediction in the Bay of Bengal

Lagrangian Coherent Structures (LCS) are the hidden fluid flow skeletons that provide meaningful information about the Lagrangian circulation. In this study, we computed the monthly climatological LCSs (cLCS) maps utilizing 24 years (1994–2017) of HYbrid Coordinate Ocean Model (HYCOM) currents and ECMWF re-analysis winds in the Bay of Bengal (BoB). The seasonal reversal of winds and associated reversal of currents makes the BoB dynamic. Therefore, we primarily aim to reveal the cLCSs associated with seasonal monsoon currents and mesoscale (eddies) processes over BoB. The simulated cLCS were augmented with the complex empirical orthogonal functions to confirm the dominant lagrangian transport pattern features better. The constructed cLCS patterns show a seasonal accumulation zone and the transport pattern of freshwater plumes along the coastal region of the BoB. We further validated with the satellite imagery of real-time oil spill dispersion and modelled oil spill trajectories that match well with the LCS patterns. In addition, the application of cLCSs to study the transport of hypothetical oil spills occurring at one of the active oil exploration sites (Krishna-Godavari basin) was described. Thus, demonstrated the accumulation zones in the BoB and confirmed that the persistent monthly cLCS maps are reasonably performing well for the trajectory prediction of pollutants such as oil spills. These maps will help to initiate mitigation measures in case of any occurrence of oil spills in the future.

Cross‐Shore Distribution of the Wave‐Induced Circulation Over a Dissipative Beach Under Storm Wave Conditions

AbstractThis study explores the spatial distribution and the driving mechanisms of the wave‐induced cross‐shore flow within the shoreface and surf zone of a dissipative beach. Unpublished results from a field campaign carried out in early 2021 under storm wave conditions are presented and compared with the predictions from a state‐of‐the‐art phase‐averaged three‐dimensional circulation modeling system based on the vortex force formalism. Under storm wave conditions, the cross‐shore flow is dominated by a strong seaward‐directed current in the lower part of the water column. The largest current velocities of this return current are located in the surf zone, where the dissipation by depth‐induced breaking is most intense, but offshore‐directed velocities up to 0.25 m/s are observed as far as 4 km from the shoreline (≃12 m‐depth). Numerical experiments further highlight the key control exerted by non‐conservative wave forces and wave‐enhanced mixing on the cross‐shore flow across a transition zone, where depth‐induced breaking, whitecapping, and bottom friction all significantly contribute to the wave energy dissipation. Under storm conditions, this transition zone extended almost 6 km offshore and the cross‐shore Lagrangian circulation shows a strong seaward‐directed jet in the lower part of the water column, whose intensity progressively decreases offshore. In contrast, the surf zone edge appears clearly delimited under fair weather conditions and the seaward‐directed current is weakened by a near bottom shoreward‐directed current associated with wave bottom streaming in the shoaling region, such that the clockwise Lagrangian overturning circulation is constrained by an additional anti‐clockwise overturning cell at the surf zone edge.

Ocean surface hidden structures in the Lofoten area of the Norwegian Sea

We investigate the structure of surface lateral mixing in the Lofoten area in the Norwegian Sea using surface velocity field derived from a 1/12o reanalysis data. We compute a Lagrangian diagnostic based on the evolution of Finite Time Lyapunov Exponents (FTLEs) by advecting (backward in time) a large number of particles to quantify the hidden skeleton of different dynamical regions in the study area. By constructing maps of deterministic Lagrangian Coherent Structures (LCSs), four dynamical regions are generally identified: (i) regions of maximal dynamical attraction along the west coast of Norway and Barents Sea Opening; (ii) area of quasi-prominent anticyclonic eddy located at the centre of Lofoten Basin (LB); (iii) mid-ocean system of the Mohn Ridge which separates the Atlantic and Arctic waters: (iv) areas expanded between shallow continental shelf and deep basins populated with multiscale structures. We further construct a climatology of LCSs and FTLE statistical distributions with 11-year of reanalysis data to investigate the seasonal variability of Lagrangian circulations and to classify further their dynamical properties. The FTLE and LCS analyses in the present study can contribute to better understand the key transport barriers to the fate of larval dispersion and ocean contaminants, and marine population connectivity.

Lagrangian Geography of the Deep Gulf of Mexico

AbstractUsing trajectories from acoustically tracked (RAFOS) floats in the Gulf of Mexico, we construct a geography of its Lagrangian circulation within the 1500–2500-m layer. This is done by building a Markov-chain representation of the Lagrangian dynamics. The geography is composed of weakly interacting provinces that constrain the connectivity at depth. The main geography includes two provinces of near-equal areas separated by a roughly meridional boundary. The residence time is about 4.5 (3.5) years in the western (eastern) province. The exchange between these provinces is effected through a slow cyclonic circulation, which is well constrained in the western basin by preservation of f/H, where f is the Coriolis parameter and H is depth. Secondary provinces of varied shapes covering smaller areas are identified with residence times ranging from about 0.4 to 1.2 years or so. Except for the main provinces, the deep Lagrangian geography does not resemble the surface Lagrangian geography recently inferred from satellite-tracked drifter trajectories. This implies disparate connectivity characteristics with potential implications for pollutant (e.g., oil) dispersal at the surface and at depth. Support for our results is provided by a Markov-chain analysis of satellite-tracked profiling (Argo) floats, which, while forming a smaller dataset and having seemingly different water-following characteristics than the RAFOS floats, replicate the main aspects of the Lagrangian geography. Our results find further validation in independent results from a chemical tracer release experiment.

Connectivity of Pulley Ridge With Remote Locations as Inferred From Satellite‐Tracked Drifter Trajectories

AbstractUsing historical (1994–2017) satellite‐tracked surface drifter trajectory data, we conduct a probabilistic Lagrangian circulation study which sheds light on the connectivity of Pulley Ridge with other locations in the Gulf of Mexico and adjacent areas. The analysis reveals that Pulley Ridge is connected with the North Atlantic, the Caribbean Sea, and most of the Gulf of Mexico. Preferred connecting pathways are identified and arrival times to potential reef sites computed. The study demonstrates the importance of Pulley Ridge as a source for neighboring regions like the Dry Tortugasa, the Florida Keys, Campeche Bank, and the east Florida coast as well as a self‐recruitment area for species with short competence time. The study further suggests that the reefs in the Caribbean Sea, the Dry Tortugas, the western Florida Keys, and the West Florida Shelf can act as sources for Pulley Ridge, indicating the importance of Pulley Ridge as a central refugium for species in the Gulf of Mexico.

Extracting quasi-steady Lagrangian transport patterns from the ocean circulation: An application to the Gulf of Mexico

We construct a climatology of Lagrangian coherent structures (LCSs)—the concealed skeleton that shapes transport—with a twelve-year-long data-assimilative simulation of the sea-surface circulation in the Gulf of Mexico (GoM). Computed as time-mean Cauchy–Green strain tensorlines of the climatological velocity, the climatological LCSs (cLCSs) unveil recurrent Lagrangian circulation patterns. The cLCSs strongly constrain the ensemble-mean Lagrangian circulation of the instantaneous model velocity, showing that a climatological velocity can preserve meaningful transport information. The quasi-steady transport patterns revealed by the cLCSs agree well with aspects of the GoM circulation described in several previous observational and numerical studies. For example, the cLCSs identify regions of persistent isolation, and suggest that coastal regions previously identified as high-risk for pollution impact are regions of maximal attraction. We also show that cLCSs are remarkably accurate at identifying transport patterns observed during the Deepwater Horizon and Ixtoc oil spills, and during the Grand LAgrangian Deployment (GLAD) experiment. Thus it is shown that computing cLCSs is an efficient and meaningful way of synthesizing vast amounts of Lagrangian information. The cLCS method confirms previous GoM studies, and contributes to our understanding by revealing the persistent nature of the dynamics and kinematics treated therein.

Assessing the impact of tidal stream energy extraction on the Lagrangian circulation

Whereas numerous numerical modelling have been conducted to gain further insights about the hydrodynamic characteristics of tidal stream energy sites, the long-term transport of water particles has been routinely ignored. However, a refined evaluation of circulation pathways is fundamental to assess water-quality changes induced by tidal energy converters. The present study investigates the tide-induced Lagrangian circulation in north-western coastal waters of Brittany (France, western Europe), including numerous islands, shoals and straits with strong potential for turbine farm implementation. Particular attention is dedicated to the hydrodynamic impact of tidal stream power extraction from a series of horizontal-axis turbines. An original approach, based on the coupling of the Lagrangian barycentric method with predictions from a model at high spatial resolution, is considered to assess circulation pathways in a single synoptic view. Spatial results reveal a complex Lagrangian circulation highly controlled by bathymetry and islands geometry. The residual flow in the Fromveur Strait, separating Ushant island from Molène archipelago, displays thus a strong asymmetry, between a prominent north-eastern pathway with residual currents up to 0.45ms-1 and a southward circulation. The positions of cyclonic and anti-cyclonic recirculations, both upstream and downstream the Strait, are furthermore precisely defined. The north eddy is found closely located to the sand bank of the Four. The extraction of tidal stream power impacts mainly the residual Lagrangian circulation along the current stream emerging from the Strait, with a tendency for surrounding eddies to get closer to the tidal stream energy site. The displacements of the south and north recirculations may thus exceed 1.5km with possible implications on the evolution of surrounding seabed features.

The Effect of Stokes Drift and Transient Rip Currents on the Inner Shelf. Part II: With Stratification

AbstractThis is Part II of a two-part study focused on Stokes drift and transient rip current (TRC) effects on the unstratified (Part I) and stratified (this paper) inner shelf. Part I focuses on funwaveC–Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST) coupling and TRC effects on mixing and exchange on an unstratified inner shelf. Here, two simulations (R3 and R4) are performed on a stratified inner shelf and surfzone with typical bathymetry, stratification, and wave conditions. R3 is a COAWST-only simulation (no TRCs), while R4 has funwaveC–COAWST coupling (with TRCs). In R4, TRCs lead to patchy, near-surface cooling, vertical isotherm displacement, and increased water column mixing. For both R3 and R4, the mean Lagrangian circulation has two nearly isolated surfzones and inner-shelf overturning circulation cells, with a stronger, R4, inner-shelf circulation cell. The R4, inner-shelf, vertical velocity variability is 2–3 times stronger than a simulation with TRCs and no stratification. Relative to R3, R4 eddy diffusivity is strongly elevated out to three surfzone widths offshore due to TRCs and TRC-induced density overturns. The R4 inner-shelf stratification is reduced nearshore, and mean isotherms slope more strongly than R3 because of the TRC-enhanced irreversible mixing. At six surfzone widths offshore, both R3 and R4 are in geostrophic balance, explaining the stratified (summertime) observed deviation from Stokes–Coriolis balance. In this region, baroclinic pressure gradients induced by sloping isotherms induce an alongshore geostrophic jet offshore, strongest in R4. In R4, TRCs result in an enhanced (2–10 times) cross-shore exchange velocity across the entire inner shelf, relative to R3. Accurate, stratified, inner-shelf simulations of pollution, larval, or sediment transport must include transient rip currents.

The Effect of Stokes Drift and Transient Rip Currents on the Inner Shelf. Part I: No Stratification

AbstractThis is part one of a two-part study focused on Stokes drift and transient rip current (TRC) effects on the unstratified (this paper) and stratified (see Part II) inner shelf. A TRC-generating, wave-resolving model funwaveC is coupled to the 3D, wave-averaged wave and circulation model Coupled Ocean–Atmosphere–Wave–Sediment Transport (COAWST). Two simulations (R1 and R2) are performed on an unstratified inner shelf and surfzone with typical bathymetry and wave conditions. R1 is a COAWST-only simulation (no TRCs), while R2 has funwaveC–COAWST coupling (with TRCs). R2 and funwaveC vertical vorticity (eddy) statistics are similar, indicating that the model coupling accurately generates TRCs, with TRC-induced eddies out to four surfzone widths offshore. R1 has a two-layered, inner-shelf-to-surfzone-connected, mean Lagrangian circulation, while R2 has separate inner shelf and surfzone circulation cells. The R2, TRC-induced, cross-shore and vertical eddy velocities are stronger than the R1 or R2 mean Lagrangian velocity out to four surfzone widths offshore. The R2, inner-shelf, mean, vertical eddy diffusivity is an order of magnitude larger than R1 out to four surfzone widths offshore. Both R1 and R2 are in a Stokes–Coriolis balance at six surfzone widths offshore, as is R1 at three surfzone widths offshore. For R2, TRC-induced horizontal advection and vertical mixing dominate the cross-shore momentum dynamics at three surfzone widths offshore. The R2 surfzone and inner-shelf cross-shore exchange velocity is 2–10 times larger for R1 because of the TRC-induced stirring. Accurate, unstratified, inner-shelf simulations of pollution, larval, or sediment transport must include transient rip currents. In Part II, the effects of Stokes drift and TRCs on the stratified inner shelf are examined.

How can operational oceanography products contribute to the European Marine Strategy Framework Directive? The Italian case

ABSTRACTOperational oceanography products have been used to define the Marine Strategy Framework Directive (MSFD) good environmental status (GES) relative to the Italian marine ecosystem subregions. Observations include sea surface temperature (SST), winds and chlorophyll Mediterranean Sea satellite products and Italian national tide gauge network winds. These were used to obtain SST seasonal climatology data and trends, 90th percentile of chlorophyll climatology data and SST and wind coastal upwelling indices. Also, Eulerian and Lagrangian circulation models have been used to map the residence time (RT) of Lagrangian particles in the marine subregions, which mimics pollutant dispersion capability at a given location and time.

Genesis of Tropical Storm Debby (2006) within an African Easterly Wave: Roles of the Bottom-Up and Midlevel Pouch Processes

Abstract The “bottom up” generation of low-level vortices (LVs) and midlevel vortices (MVs) during the genesis of Tropical Storm Debby (2006) and the roles of a midlevel “marsupial pouch” associated with an African easterly wave (AEW) are examined using an 84-h simulation with the finest grid size of 1.33 km. Results show that several MVs are generated in leading convective bands and then advected rearward into stratiform regions by front-to-rear ascending flows. Because of different Lagrangian storm-scale circulations, MVs and LVs are displaced along different paths during the early genesis stages. MVs propagate cyclonically inward within the AEW pouch while experiencing slow intensification and merging under the influence of converging flows. The MVs’ merging into a mesovortex is accelerated as they come closer to each other in the core region. In contrast, the low-level Lagrangian circulation is opened as a wave trough prior to tropical depression (TD) stage, so the LVs tend to “escape” from the pouch region. Only after the low-level flows become closed do some LVs congregate and contribute directly to Debby’s genesis. The TD stage is reached when the midlevel mesovortex and an LV are collocated with a convective zone having intense low-level convergence. Results also show the roles of upper-level warming in hydrostatically maintaining the midlevel pouch and producing mesoscale surface pressure falls. It is found that the vertically tilted AEW with a cold dome below is transformed to a deep warm-core TD vortex by subsiding motion. A conceptual model describing the key elements in the genesis of Debby is also provided.

The Genesis of Mesovortices within a Real-Data Simulation of a Bow Echo System

Abstract The genesis of two mesovortices (MVs) within a real-data, convection-resolving simulation of the 8 May 2009 central U.S. bow echo system is studied. Both MVs form near the bow apex but differ distinctively in intensity, lifetime, and damage potential. The stronger and longer-lived mesovortex, MVa, stays near the bow apex where the system-scale rear-inflow jet (RIJ) is present. The descending RIJ produces strong downdrafts and surface convergence, which in turn induce strong vertical stretching and intensification of MVa into an intense mesovortex. In contrast, the weaker and shorter-lived mesovortex, MVb, gradually moves away from the bow apex, accompanied by localized convective-scale downdrafts. Lagrangian circulation and vorticity budget analyses reveal that the vertical vorticity of MVs in general originate from the tilting of near-surface horizontal vorticity, which is mainly created via surface friction. The circulation of the material circuit that ends up to be a horizontal circuit at the foot of the MVs increases as the frictionally generated horizontal vortex tubes pass through the tilted material circuit (tilted following backward trajectories defining the material circuit) surface, especially in the final few minutes prior to mesovortex genesis. The tilted material circuit becomes horizontal at the MV foot, turning associated horizontal vorticity into vertical. The results show at least qualitatively that, in addition to baroclinicity, surface friction can also have significant contributions to the generation of low-level MVs, which was not considered in previous MV studies.

Some Numerical Simulations of Circulation in the East China Sea

By using the self-adaptive numerical model, 3-dimensional bar clinic Lagrangian circulation in the East China Sea (the Bohai Sea, Huanghai Sea (Yellow Sea) and East China Sea) (ECS) in winter and summer is computed, the results reflect well the features of the circulation in the ECS. The conclusion that “the Huanghai Sea Warm Current in winter is the mixing water of the Tsushima Warm Current and the continental shelf water, it is not a direct branch of the Tsushima Warm Current” is inconsistent with the traditional viewpoint, but agrees well with the actual observations.

A Numerical Model of Circulation in the East China Sea

The coastal circulation is one of the focuses in environmental protection. A self-adaptive numerical model of the circulation in the East China Sea (the Bohai Sea, Huanghai Sea (Yellow Sea) and East China Sea) (ECS) is established for the first time. By using a self-adaptive grid system, the grids are denser at the continental slope of the ECS. Thus, the difficult problem of applying a 3-dimensional (3D) baroclinic model with coordinate transformation at continental slope is solved. This model can be used to simulate 3D baroclinic current fields and to obtain wind-driven, thermohaline and tide-induced Lagrangian circulation.

Field observations of wave‐driven circulation over spur and groove formations on a coral reef

AbstractSpur and groove (SAG) formations are found on the forereefs of many coral reefs worldwide. Modeling results have shown that SAG formations together with shoaling waves induce a nearshore Lagrangian circulation pattern of counter‐rotating circulation cells, but these have never been observed in the field. We present results from two separate field studies of SAG formations on Palmyra Atoll which show their effect on waves to be small, but reveal a persistent order 1 cm/s depth‐averaged Lagrangian offshore flow over the spur and onshore flow over the grooves. This circulation was stronger for larger, directly incident waves and low alongshore flow conditions, consistent with predictions from modeling. Favorable forcing conditions must be maintained on the order of 1 h to accelerate and develop the SAG circulation cells. The primary cross and alongshore depth‐averaged momentum balances were between the pressure gradient, radiation stress gradient, and nonlinear convective terms, and the bottom drag was similar to values found on other reefs. The vertical structure of these circulation cells was previously unknown and the results show a complex horizontal offshore Lagrangian flow over the spurs near the surface driven by alongshore variability in radiation stress gradients. Vertical flow was downward over the spur and upward over the groove, likely driven by alongshore differences in bottom stress and not by vortex forcing.

A new circulation type classification based upon Lagrangian air trajectories

A new classification method of the large-scale circulation characteristic for a specific target area (NW Iberian Peninsula) is presented, based on the analysis of 90-h backward trajectories arriving in this area calculated with the 3-D Lagrangian particle dispersion model FLEXPART. A cluster analysis is applied to separate the backward trajectories in up to five representative air streams for each day. Specific measures are then used to characterise the distinct air streams (e.g., curvature of the trajectories, cyclonic or anticyclonic flow, moisture evolution, origin and length of the trajectories). The robustness of the presented method is demonstrated in comparison with the Eulerian Lamb weather type classification. A case study of the 2003 heatwave is discussed in terms of the new Lagrangian circulation and the Lamb weather type classifications. It is shown that the new classification method adds valuable information about the pertinent meteorological conditions, which are missing in an Eulerian approach. The new method is climatologically evaluated for the five-year time period from December 1999 to November 2004. The ability of the method to capture the inter-seasonal circulation variability in the target region is shown. Furthermore, the multi-dimensional character of the classification is shortly discussed, in particular with respect to inter-seasonal differences. Finally, the relationship between the new Lagrangian classification and the precipitation in the target area is studied.

Statistical clustering of drifting buoy trajectories to identify Lagrangian circulation features around Japan and off Fukushima

Abstract A simple statistical clustering method is demonstrated to aid the identification of spatially repeating or persistent Lagrangian circulation patterns inherent in ensembles of drifting buoy trajectories. The technique is applied to the regional oceanic circulation about Japan and to the mesoscale circulation off Fukushima on Japan’s east coast. The drifter trajectories form a highly irregular data set in both space and time, with very different locations, configurations, cumulative travel distances (tens of metres to thousands of km), travel times (hours to years), and start and end positions. The interpolation technique of Kim, Kim, Ho, and Chu, Journal of Climate 24 (2) (2011), is found suitable to transform the spatially complex buoy data into a form suitable for statistical clustering. To resolve and give context to the very different spatial scales encountered in oceanic circulations the methods are applied in a hierarchical fashion to progressively smaller areas (120–180°E, 20–50°N; 140–160°E, 32–44°N; 140–145°E, 35–40°N). A winding number method is devised to identify and distinguish between clockwise and anti-clockwise sense of circulation. The analysis techniques provide what can be regarded as a spatial decomposition of Lagrangian flow fields. The methods do not require curve fitting or modelling, feature analysis, curve alignment, or spatial gridding, binning, and averaging, and are not dependent on density of observations. The methodology forms a useful data exploration technique for examination of trajectory data in general.

Hydrodynamics of spur and groove formations on a coral reef

Spur and groove (SAG) formations are found on the fore reefs of many coral reefs worldwide. Although these formations are primarily present in wave‐dominated environments, their effect on wave‐driven hydrodynamics is not well understood. A two‐dimensional, depth‐averaged, phase‐resolving nonlinear Boussinesq model (funwaveC) was used to model hydrodynamics on a simplified SAG system. The modeling results show that the SAG formations together with shoaling waves induce a nearshore Lagrangian circulation pattern of counter‐rotating circulation cells. The mechanism driving the modeled flow is an alongshore imbalance between the pressure gradient (PG) and nonlinear wave (NLW) terms in the momentum balance. Variations in model parameters suggest the strongest factors affecting circulation include spur‐normal waves, increased wave height, weak alongshore currents, increased spur height, and decreased bottom drag. The modeled circulation is consistent with a simple scaling analysis based on the dynamical balance of NLW, PG, and bottom stress terms. Model results indicate that the SAG formations efficiently drive circulation cells when the alongshore SAG wavelength allows for the effects of diffraction to create alongshore differences in wave height without changing the mean wave angle.

Comparison between Dual-Doppler and EnKF Storm-Scale Wind Analyses: The 29–30 May 2004 Geary, Oklahoma, Supercell Thunderstorm

Abstract Kinematical analyses of storm-scale mobile radar observations are critical to advancing our understanding of supercell thunderstorms. Maximizing the accuracy of these analyses, and characterizing the uncertainty in ensuing conclusions about storm structure and processes, requires knowledge of the error characteristics of different retrieval techniques under different observational scenarios. Using storm-scale mobile radar observations of a tornadic supercell, this study examines the impacts on ensemble Kalman filter (EnKF) wind analyses of the number of available radars (one versus two), uncertainty in the model-initialization sounding, the sophistication of the microphysical parameterization scheme (double versus single moment), and assimilating reflectivity observations. The relative accuracy of three-dimensional variational data assimilation (3DVAR) dual-Doppler wind retrievals and single- and dual-radar EnKF wind analyses of the supercell is also explored. The results generally reinforce the findings of a previous study that used observing system simulation experiments to explore the same issues. Both studies suggest that single-radar EnKF wind analyses can be very useful once enough data have been assimilated, but that subsequent analyses that operate on the retrieved wind field gradients should be interpreted with caution. In the present study, severe errors appear to occur in computed Lagrangian circulation time series, imperiling interpretation of the underlying dynamics. This result strongly suggests that dual- and multiple-Doppler radar deployment strategies continue to be used in mobile field campaigns.

Spatial Heterogeneity of Artificial Reefs Functioning according to Wind-Induced Lagrangian Circulation

In the scope of the program “Récifs Prado” for artificial reef immersion in the bay of Marseilles (southern France), we adapted the fine resolution (100 m) of the 3D numerical model POM (Princeton Ocean Model) to compute the typical patterns of the wind induced circulation within the bay. In addition, we derived from those results the Lagrangian trajectories of planktonic particles drifting over periods of 3 days, both from natural habitats to colonize the reefs, and inversely from the reefs to enrich peripheral ecosystems. Results emphasized the high spatial heterogeneity of the reefs functioning at short scales. First, reefs were submitted to a general southward particle flux, being colonized from the northern bay and then impacting the southern bay 50% and 40% of the time, respectively. Second, adjacent reefs frequently showed contrasted impacts, with fluxes simultaneously oriented offshore or inshore, in opposite directions. Third, at the top of reefs particles were released both southward and northward 32% and 8.6% of the time, respectively; when at the bottom of reefs particles were only released southward 40% of the time.