Three-dimensional Circulation Model Research Articles

Influences of tides on shelf circulation in the northeastern South China Sea during summer

Tides have significant effects on material and energy transports over the continental shelf. A mooring system located in the shelf region of the northeastern South China Sea observed strong and weak mean currents during the spring and neap tides in summer, respectively. The mechanism leading to this difference is investigated by using a three-dimensional circulation model. We find that the impact of tides (TI) on currents exhibited as current components opposing wind-driven circulation play an important role. The TI current components are stronger than the tidal residual currents in summer when vertical stratification enhances the tidal rectification. Tides can affect pressure gradient by modifying sea surface height on the shelf, while in shallow and shelf break regions, the non-linear advection and vertical diffusion become significant in momentum equations attributable to the interactions of tidal currents, bottom topography and water column stratification. Consequently, the along-shelf volume transport is reduced by about 21.6% due to the TI current components and only by about 6.1% due to the tidal residual currents. This study highlights the importance of both tidal mixing and tidal rectification in regulating shelf circulation in the northeastern South China Sea.

The Influence of Freshwater Discharge and Wind Forcing on the Dispersal of River Plumes Using a Three-Dimensional Circulation Model

Tidal estuaries provide crucial pathways for contaminant transport. The salinity levels in estuaries and coasts are conserved substances that function as natural tracers to easily understand the offshore transport of substances that are subject to environmental factors. A three-dimensional (3D) circulation and mass transport model were utilized to delineate the salinity plume in a tidal estuary and continental shelf. The numerical modeling results were compared with the tidal amplitudes and phases, velocities, and salinities at different gauging stations in 2017. Quantitatively, the simulation and measurement results are in reasonably good agreement. Furthermore, the validated model was adopted to estimate the recovery times in tidal estuaries that are subjected to extreme freshwater discharges that come from the upstream reaches during typhoon events and to analyze the influences of freshwater discharge and wind stress on the river plume around the continental shelf. The simulated results revealed that the salinity recovery time at the river mouth due to Typhoon Saola in 2012 was less than 8 days. Increased inputs from freshwater discharge resulted in changes in the distances and areas of the river plumes. Linear regression relationships between the plume distance/plume area and the total freshwater discharge inputs were established. Neap and high slack tides were associated with the maximum plume distances and areas. Excluding tidal forcing resulted in larger plume distances and areas compared to the case in which tidal forcing was considered. The southward-favorable and northward-favorable plumes were controlled by northeasterly winds and southwesterly winds, respectively. The relative importance of freshwater discharges and wind forcing was explored. The results indicate that freshwater discharges frequently dominated the river plume, except when strong southwesterly or northeasterly winds prevailed.

Modelling Internal Tides in the Strait of Canso

ABSTRACT A three-dimensional regional circulation model is used to investigate the internal M2 tide structure in the Strait of Canso located in eastern Nova Scotia, Canada. The embayment, an active shipping port, was found to have M2 baroclinic velocities occasionally reaching 0.15 m s−1 and typically faster than the barotropic tide. An internal tide spatial structure develops, characterized by the first vertical mode, and highly sensitive to the details of stratification. A region near the mouth of the Strait, with a strong cross-bathymetry barotropic flow was identified as the main generating site. The regular “canyon-like” features of the Strait concentrate the energy towards the bottom and head and, under favourable conditions, reflect energy from the head, forming a standing wave. The modelling study found that, although some internal tide is generated year-round, only summer stratification conditions were favourable for standing wave development because of both increased internal energy levels and longer wavelengths capable of transporting the energy farther up the Strait. A balanced internal energy budget for the area highlights a tendency towards local dissipation and enhanced mixing rates. Persistent convection cells and upwelling zones suggest possible impacts on biological activity, sediment, and oil spill dynamics in the region. The findings are validated with current meter and water level observations.

Characteristics of the East Sea (Japan Sea) circulation depending on surface heat flux and its effect on branching of the Tsushima Warm Current

The effects of the surface heat flux and wind forcing on the East Sea (Japan Sea) circulation and the branching of the Tsushima Warm Current were investigated using a three-dimensional circulation model (RIAMOM). For the numerical experiments with surface heat flux, regardless of wind forcing, the Tsushima Warm Current, the Nearshore Branch, and the East Korea Warm Current were well simulated in the southern part of the East Sea. Furthermore, the cold water mass of 1–2 °C was formed at a depth of 200–250 m because of the convection of the upper layer and ventilation that actively occurs in the northern part of the East Sea. However, in the experiments without surface heat flux, the East Korea Warm Current was not simulated. The Tsushima Warm Current through the Korea/Tsushima Strait flows mostly northeastward along the Japanese coast as the Nearshore Branch. Moreover, the cold water mass was not formed at the northern part of the East Sea, thus the 1–2 °C cold water was distributed below 300–400 m depth with weak ventilation. The upper layer in the southern part of the East Sea, ranging from the surface to the bottom of the pycnocline, was thicker than the case of the surface heat flux forcing. Since the Tsushima Warm Current flowing through the Korea/Tsushima Strait is dominantly affected by the continental slope of the Japanese coast, the current does not lead to formation of the East Korea Warm Current as a western boundary current. If the effect of the continental slope of the Japanese coast is not applied, the Tsushima Warm Current flows only along the Korean coast as a western boundary current. The numerical experiments reveal that the surface heat flux serves as a critical external forcing which controls the topographic and planetary beta effects on the upper layer circulation in the southern part of the East Sea.Therefore, if the surface heat flux is changed due to global warming in the future, the distribution of surface currents is also expected to change in the southern part of the East Sea.

Estimating habitat volume of living resources using three-dimensional circulation and biogeochemical models

Coupled three-dimensional circulation and biogeochemical models predict changes in water properties that can be used to define fish habitat, including physiologically important parameters such as temperature, salinity, and dissolved oxygen. However, methods for calculating the volume of habitat defined by the intersection of multiple water properties are not well established for coupled three-dimensional models. The objectives of this research were to examine multiple methods for calculating habitat volume from three-dimensional model predictions, select the most robust approach, and provide an example application of the technique. Three methods were assessed: the “Step,” “Ruled Surface”, and “Pentahedron” methods, the latter of which was developed as part of this research. Results indicate that the analytical Pentahedron method is exact, computationally efficient, and preserves continuity in water properties between adjacent grid cells. As an example application, the Pentahedron method was implemented within the Habitat Volume Model (HabVol) using output from a circulation model with an Arakawa C-grid and physiological tolerances of juvenile striped bass (Morone saxatilis). This application demonstrates that the analytical Pentahedron method can be successfully applied to calculate habitat volume using output from coupled three-dimensional circulation and biogeochemical models, and it indicates that the Pentahedron method has wide application to aquatic and marine systems for which these models exist and physiological tolerances of organisms are known.

A Coupled Circulation–Wave Model for Numerical Simulation of Storm Tides and Waves

AbstractThe Stevens Institute of Technology Estuarine and Coastal Ocean Model (sECOM) is coupled here with the Mellor–Donelan–Oey (MDO) wave model to simulate coastal flooding due to storm tides and waves. sECOM is the three-dimensional (3D) circulation model used in the New York Harbor Observing and Prediction System (NYHOPS). The MDO wave model is a computationally cost-effective spectral wave model suitable for coupling with 3D circulation models. The coupled sECOM–MDO model takes into account wave–current interactions through wave-enhanced water surface roughness and wind stress, wave–current bottom stress, and depth-dependent wave radiation stress. The model results are compared with existing laboratory measurements and the field data collected in New York–New Jersey (NY–NJ) harbor during Hurricane Sandy. Comparisons between the model results and laboratory measurements demonstrate the capabilities of the model to accurately simulate wave characteristics, wave-induced water elevation, and undertow current. The model results for Hurricane Sandy reveal the successful performance of sECOM–MDO in situations where high waves and storm tides coexist. The results indicate that the temporal maximum wave setup in NY–NJ harbor was 0.26 m. On the other hand, the contribution of wave setup to the peak storm tide was 0.13 m, a contribution of only 3.8%. It is found that the inclusion of wave radiation stress and wave-enhanced bottom friction in the circulation model can reduce the errors in the calculated storm tides. At the Battery (New York), for example, the root-mean-square error reduced from 0.17 to 0.12 m.

Direct Observations and Modeling of Summertime Coastal Circulation Patterns in the Western Bohai Sea

ABSTRACT Xing, C.; Zhao, Q.; Hu, Z., and Liu, Y., 2018. Direct observations and modeling of summertime coastal circulation patterns in the western Bohai Sea. Eutrophication of the coastal waters in the western Bohai Sea results in serious environmental problems. In summer, severe brown tide frequently happens in the Qinhuangdao coastal areas, causing enormous losses to the local fishery. A survey array with four sets of seabed-based current observation systems equipped with acoustic Doppler current profilers was deployed in September 2013 to investigate the hydrodynamic background of the brown tide. The observations suggest that the shore currents flow generally northward and offshore currents flow southward during the survey period. The coastal circulation system and its formation mechanisms are studied with a three-dimensional nested-grid ocean circulation model. The model results suggest that coastal currents form a clockwise eddy-shaped circulation system with a diameter of 65 km. Numerical sensitivit...

Coastal flooding: impact of waves on storm surge during extremes – a case study for the German Bight

Abstract. This study addresses the impact of wind, waves, tidal forcing and baroclinicity on the sea level of the German Bight during extreme storm events. The role of wave-induced processes, tides and baroclinicity is quantified, and the results are compared with in situ measurements and satellite data. A coupled high-resolution modelling system is used to simulate wind waves, the water level and the three-dimensional hydrodynamics. The models used are the wave model WAM and the circulation model GETM. The two-way coupling is performed via the OASIS3-MCT coupler. The effects of wind waves on sea level variability are studied, accounting for wave-dependent stress, wave-breaking parameterization and wave-induced effects on vertical mixing. The analyses of the coupled model results reveal a closer match with observations than for the stand-alone circulation model, especially during the extreme storm Xaver in December 2013. The predicted surge of the coupled model is significantly enhanced during extreme storm events when considering wave–current interaction processes. This wave-dependent approach yields a contribution of more than 30 % in some coastal areas during extreme storm events. The contribution of a fully three-dimensional model compared with a two-dimensional barotropic model showed up to 20 % differences in the water level of the coastal areas of the German Bight during Xaver. The improved skill resulting from the new developments justifies further use of the coupled-wave and three-dimensional circulation models in coastal flooding predictions.

Water age in the Columbia River estuary

The concept of water age is applied to the Columbia River estuary to investigate water renewing time scales. Water age tracers were implemented in a three-dimensional circulation model. The model was run for a nine month period in 2012, covering both high and low flow conditions. In the lower estuary renewing water age ranges from roughly 20 h during high flow season (typically April–June) to 70 h during lowest river discharge (typically September–October). The age of riverine water is strongly dependent on river discharge. Dense oceanic waters, in contrast, are always relatively young in the estuary (roughly 20 h) although their age does vary with tidal range and river discharge. Compared to the main channels, water age tends to be larger in the lateral bays throughout the simulation period; this is especially true under low flow and neap tides conditions when water age can exceed 120 h in the bays. During low flow conditions a strong lateral circulation pattern emerges and leads to higher water age near Grays Bay. The maximal water age in the main channels is associated with mixed water mass (around 6–12 psu) located in front and above the salt wedge. The circulation model results are used to derive simple regression models that can be used to predict renewing water time scales without the need of a circulation model.

The effect of clam grazing on phytoplankton spring blooms in the low-salinity zone of the San Francisco Estuary: A modelling approach

Benthic grazing by estuarine bivalves can be an important top-down process impacting pelagic food webs. In the low-salinity zone of the San Francisco Estuary mass balance calculations and models have reported that clams (especially the invasive Potamocorbula amurensis) suppress phytoplankton blooms. However, spring blooms frequently occur. We aimed to understand this clam paradox using a biogeochemical modelling approach to evaluate the effects of clam grazing and excretion on phytoplankton production and nutrient uptake. The conceptual framework combines both the reduction of phytoplankton biomass by grazing and the role of ammonium (from clam excretion, wastewater plant discharge and sediment efflux) in minimizing chlorophyll accumulation, since phytoplankton cannot access nitrate (the major form of available nitrogen) for growth, due to ammonium suppression of nitrate uptake. We constructed the CLAMFLOW model by adding a clam module (with pathways of nitrogen for clam grazing, clam excretion and sediment efflux) to an existing phytoplankton-nitrogen-flow model. Whatever the parameter that was varied in the model (clam abundance, grazing, excretion, sediment efflux or flow) it decreased the peak nitrate uptake by the phytoplankton and shifted the time to reach peak uptake so delaying the likelihood of bloom initiation.Outcomes of the CLAMFLOW model were to demonstrate how clams can indirectly impact phytoplankton growth through excretion of ammonium, and to illustrate how most published laboratory filtration rates are likely too high for application in the field. There are management implications from using too high a clam grazing rate in models that may overestimate their impact on trophic estuarine and wetland productivity. We suggest that improved prediction of bloom occurrences requires the use of lower filtration rates combined with observed clam abundances, and a suitable combination of flow and ammonium source concentrations. This simple modular model (CLAMFLOW) offers portability to other ecosystems and is designed to connect with estuary scale three-dimensional circulation or numerical biogeochemical models. Our model and results are applicable to other situations, including aquaculture development and bivalve restoration efforts, where the biogeochemical effects of bivalves on phytoplankton productivity need to be quantitatively understood.

Water exchanges between a multi-inlet lagoon and the ocean: the role of forcing mechanisms

Understanding the influence of the main drivers controlling the circulation and the transport in coastal lagoons is a necessary step towards the description of the dynamics of their ecosystems. Thus, the influence of the main physical drivers on the water exchanges in a multi-inlet barrier island (western sector of the Ria Formosa coastal lagoon, Portugal) was investigated. Several scenarios of tide, wind, bathymetry and point source discharges were simulated using a three-dimensional circulation model and a particle-tracking model. The circulation is adequately reproduced by the hydrodynamic model, with root mean square errors of about 5–8 cm for the water levels and 5–10 cm/s for the cross-sectional averaged velocities in the western inlets and main channels. Wind has a negligible effect on the modelled water levels and cross-sectional velocities, with differences smaller than 1 % between the simulations with and without wind. However, results show that wind influences significantly the transport by affecting the residual circulation, with distinct effects depending on the wind direction. Upwelling favourable winds (with west component) increase the landward transport through the Faro-Olhao inlet and promote a larger dispersion of the water-borne material inside the lagoon. The residual circulation between the three inlets of the western sector of the lagoon is also significantly affected by the bathymetry. Results show a decrease of about 50 % of the tidal prism of the Ancao inlet between 2002 and 2011, which reduces its capacity to export waterborne material to the adjacent coastal area and increases the residence times in some areas of the lagoon, with potentially adverse effects on the ecosystems’ health. The dispersion of potential contaminants from point sources inside the lagoon to the coastal area depends on the combined effect of the tidal phase and amplitude and the location of the source. Mean residence times for the discharges from the wastewater treatment plants of the western sector ranged from 7 to 18 days. These findings improve the understanding of the influence of the physical forcings in the circulation and transport dynamics of multi-inlet coastal systems.

Establishment of ocean dumping area capacity assessment model

Dumping area capacity is mainly affected by the hydrodynamic process (tidal sediment, storm surge and wave, etc.) as well as the size and depth of dumping area. Based on three-dimensional ocean circulation model known as FVCOM (Finite Volume Coast and Ocean Model) and the stochastic dynamic statistical analysis model, taking advantage of dumping ground topography evolution and dumping quantity, the author aims to discuss the influence of hydrodynamic processes and dumping activity so as to built a new model of ocean dumping area capacity. With the data of depth and dumped amount in the dumping area, the changes of bottom topographic which caused by tidal current under the natural condition based on the FVCOM hydrodynamic and sediment module, the author strive to analyze the statistical relation of the changes for dumping amount, tidal current and bottom topographic. Through real data to fit revision coefficient values, which will be regarded as topographic changes reference value affected by wave and storm surges. Thus taking this evaluation as the long-term changes in the dumping capacity. In the premise of setting up the threshold of bottom topographic changes, the dumping area capacity is calculated. Take Yangtze Estuary No. 1 dumping area as an example, As the water depth reduces by 0.5 m annually, the dumping area capacity is about 6.7 million m3/a, the model results are in reasonable agreement with the actual amount. Then the model is validated in Luoyuan Bay dumping area, Shengsishangchuan Mountain dumping area, Dongding dumping area, Dongshan dumping area, and Wenzhou Port dumping area, it is turns out the results are similar to that of the actual observations.

Modeling the Effect of Waves on the Diurnal Temperature Stratification of a Shallow Lake

In this paper a three-dimensional circulation model has been applied to determine the spatial distribution of the temperature and mixed-layer depth (MLD) of a medium-sized shallow lake. In order to reproduce the vertical thermal structure of the lake, the impact of waves has been incorporated using several recently published schemes. These schemes approximate the additional mixing due to the orbital motion of waves, the turbulent kinetic energy produced by waves, or both. The reference solver is the Reynolds-Averaged Navier-Stokes equations with two-equation Mellor-Yamada 2.5 turbulence closure. The wave field is characterized by bulk parameters, e.g. significant wave height. The sensitivity to the choice of the wave mixing scheme is analyzed by means of an academic test case. The accuracy of the scheme is explored through data collected in Lake Balaton. The modeled temperature profiles and MLDs match measurements much better when the effect of non-breaking surface waves is included.

Large-Scale Atmospheric and Oceanic Control on Krill Transport into the St. Lawrence Estuary Evidenced with Three-Dimensional Numerical Modelling

ABSTRACTA three-dimensional circulation model, coupled to a Lagrangian particle drift model, is used to understand the processes leading to krill transport from the northwest Gulf of St. Lawrence (nwGSL) towards the head of the Lower St. Lawrence Estuary (LSLE), a well-known site of krill accumulation. An analysis of the circulation at the scale of the Gulf of St. Lawrence (GSL) over five years (2006 to 2010) evidenced four major findings. (i) There are two main seasonal circulation patterns, one in winter–spring and one in summer–fall, driven by local wind forcing and transport at Cabot Strait and at the Strait of Belle Isle. (ii) The freshwater runoff variability does not control the observed inflow events at the mouth of the LSLE. (iii) Extratropical storms passing over the GSL are important for the transport of krill into the LSLE through the generation of inflow events at Pointe-des-Monts. (iv) The contribution of the transport in the surface layer (where krill are found at night) during these inflow events is also important in modulating the variability of the transport of krill into the LSLE. The inflow events, combined with the presence or absence of high krill densities in the nwGSL, partly control the interannual variability of the transport of krill into the LSLE.

Three-Dimensional Structure of Optimal Nonlinear Excitation for Decadal Variability of the Thermohaline Circulation

AbstractThe decadal variability of the North Atlantic thermohaline circulation (THC) is investigated within a three-dimensional ocean circulation model using the conditional nonlinear optimal perturbation method. The results show that the optimal initial perturbations of temperature and salinity exciting the strongest decadal THC variations have similar structures: the perturbations are mainly in the northwestern basin at a depth ranging from −1500 to −3000 m. These temperature and salinity perturbations act as the optimal precursors for future modifications of the THC, highlighting the importance of observations in the northwestern basin to monitor the variations of temperature and salinity at depth. The decadal THC variation in the nonlinear model initialized by the optimal salinity perturbations is much stronger than that caused by the optimal temperature perturbations, indicating that salinity variations might play a relatively important role in exciting the decadal THC variability. Moreover, the deca...

A modeling study of physical controls on hypoxia generation in the northern Gulf of Mexico

The Louisiana shelf (LA shelf) in the northern Gulf of Mexico experiences hypoxic conditions every summer due to the combination of eutrophication and strong water column stratification. Here we use a three-dimensional circulation model coupled with a simple oxygen model to examine the physical controls on hypoxia generation on the LA shelf. The model assumes a constant oxygen utilization rate in the water column and a sediment oxygen consumption rate that depends on the bottom water oxygen concentration and temperature. Despite its simplicity, the model reproduces the observed variability of dissolved oxygen and hypoxia on the LA shelf, highlighting the importance of physical processes. Model results demonstrate that both river discharge and wind forcing have a strong effect on the distribution of the river plume and stratification, and thereby on bottom dissolved oxygen concentrations and hypoxia formation on the LA shelf. The seasonal cycle of hypoxia is relatively insensitive to the seasonal variability in river discharge, but the time-integrated hypoxic area is very sensitive to the overall magnitude of river discharge. Changes in wind speed have the greatest effect on the simulated seasonal cycle of hypoxia and hypoxic duration, while changes in wind direction strongly influence the geographic distribution of hypoxia. Given that our simple oxygen model essentially reproduces the evolution of hypoxia simulated with a full biogeochemical model and that physical processes largely determine the magnitude and distribution of hypoxia, a full biogeochemical model might not be necessary for short-term hypoxia forecasting.

Physical controls of hypoxia in waters adjacent to the Yangtze Estuary: A numerical modeling study

A three-dimensional circulation model (the Environmental Fluid Dynamic Code) was used to examine the role that physical forcing (river discharge, wind speed and direction) plays in controlling hypoxia in waters adjacent to the Yangtze Estuary. The model assumes that the biological consumption of oxygen is constant in both time and space, which allows the role of physical forcing in modulating the oxygen dynamics to be isolated. Despite of the simplicity of this model, the simulation results showed that it can reproduce the observed variability of dissolved oxygen in waters adjacent to the Yangtze Estuary, thereby highlighting the important role of changes in physical forcing in the variation of hypoxia. The scenarios tested revealed appreciable changes in the areal extent of hypoxia as a function of wind speed and wind direction. Interestingly, well-developed hypoxia was insensitive to river discharge.

A Comparison of Bulk Estuarine Turnover Timescales to Particle Tracking Timescales Using a Model of the Yaquina Bay Estuary

The ability to determine a bulk estuarine turnover timescale that is well defined under realistic conditions is in high demand for estuarine research and management. We compare how turnover timescales vary with tidal and river forcing from idealized forcing scenarios using a three-dimensional circulation model of the Yaquina Bay estuary in order to understand the limitations and benefits of different timescale methods for future application. Using model results, we compare bulk formula approaches—the tidal prism method, freshwater fraction method, and a relatively new estuarine timescale calculation method based on the total exchange flow (TEF)—to directly calculated timescales from particle tracking in order to assess the utility of the bulk formula timescales. All of the timescales calculated had similar magnitudes during high river discharge but varied significantly at low discharge and had different dependences on tidal amplitude. Even in the application of a single estuary-averaged timescale, we did not find that any of the bulk timescales described the estuary over a realistic range of tidal and river discharge forcing. During high discharge, the Yaquina Bay timescale is on the order of 2–5 tidal cycles based on the particle tracking analysis, but during low discharge, the turnover time varies across methods and spatial considerations appear to be more important.

Hydrodynamic response of a fringing coral reef to a rise in mean sea level

Ningaloo Reef, located along the northwest coast of Australia, is one of the longest fringing coral reefs in the world extending ~300 km. Similar to other fringing reefs, it consists of a barrier reef ~1–6 km offshore with occasional gaps, backed by a shallow lagoon. Wave breaking on the reef generates radiation stress gradients that produces wave setup across the reef and lagoon and mean currents across the reef. A section of Ningaloo Reef at Sandy Bay was chosen as the focus of an intense 6-week field experiment and numerical simulation using the wave model SWAN coupled to the three-dimensional circulation model ROMS. The physics of nearshore processes such as wave breaking, wave setup and mean flow across the reef was investigated in detail by examining the various momentum balances established in the system. The magnitude of the terms and the distance of their peaks from reef edge in the momentum balance were sensitive to the changes in mean sea level, e.g. the wave forces decreased as the mean water depth increased (and hence, wave breaking dissipation was reduced). This led to an increase in the wave power at the shoreline, a slight shift of the surf zone to the lee side of the reef and changes in the intensity of the circulation. The predicted hydrodynamic fields were input into a Lagrangian particle tracking model to estimate the transport time scale of the reef-lagoon system. Flushing time of the lagoon with the open ocean was computed using two definitions in renewal of semi-enclosed water basins and revealed the sensitivity of such a transport time scale to methods. An increase in the lagoon exchange rate at smaller mean sea-level rise and the decrease at higher mean sea-level rise was predicted through flushing time computed using both methods.

Estimating ventilation time scales using overturning stream functions

A simple method for estimating ventilation time scales from overturning stream functions is proposed. The stream function may be computed using either geometric coordinates or a generalized vertical coordinate, such as potential density (salinity in our study). The method is tested with a three-dimensional circulation model describing an idealized semi-enclosed ocean basin ventilated through a narrow strait over a sill, and the result is compared to age estimates obtained from a passive numerical age tracer. The best result is obtained when using the stream function in salinity coordinates. In this case, the reservoir-averaged advection time obtained from the overturning stream function in salinity coordinates agrees rather well with the mean age of the age tracer, and the corresponding maximum ages agree very well.