Mixed Layer Properties Research Articles

Seasonal evolution of the mixed layer in the Subantarctic zone south of Australia

The circumpolar Subantarctic Zone (SAZ) is a globally significant region of water mass formation and carbon dioxide uptake from the atmosphere. Here we synthesize the results of nine voyages over 8 years to describe the seasonal variation in mixed layer properties in the SAZ south of Australia for comparison with biogeochemical process studies carried out in late summer (March 1998) as part of the SAZ Project. Winter mixing extends to depths >400 m, resulting in the formation of Subantarctic Mode Water. In summer the mixed layer shoals to 75–100 m, depths which are still sufficiently deep that phytoplankton growth may be light limited. Nitrate and phosphate concentrations are reduced in summer (e.g., nitrate decreases from >15 to <5 μmol kg−1) but remain well above limiting levels. Silicate, in contrast, is low throughout the year (4 μmol kg−1 in winter and <2 μmol kg−1 in summer). Water mass properties along a north‐south hydrographic section in March 1998 suggest that near‐surface waters spread from south to north across the Subantarctic Front (SAF), supplying cool, fresh, nutrient‐rich water to the SAZ. As a consequence, the properties of the southern SAZ differ from those farther north: the mixed layer in the south is cooler, fresher, deeper, higher in nutrients, and bounded below by a halocline (rather than by a seasonal thermocline, as in the northern SAZ). The contrast between the northern and southern SAZ persists throughout the year, suggesting the cross‐front exchange occurs year‐round and likely contributes to the differences in seasonal thermal amplitude and algal biomass accumulation seen in satellite images. Density‐compensated horizontal gradients of temperature and salinity are common in the mixed layer of the SAZ and the northern SAF, consistent with the hypothesis that the vigor of lateral mixing in the mixed layer is a strong function of the magnitude of the lateral density gradient.

Importance of solar subsurface heating in ocean general circulation models

The importance of subsurface heating on surface mixed layer properties in an ocean general circulation model (OGCM) is examined using attenuation of solar irradiance with depth below the ocean surface. The depth‐dependent attenuation of subsurface heating is given by global monthly mean fields for the attenuation of photosynthetically available radiation (PAR), kPAR. These global fields of kPAR are derived from Sea‐viewing Wide Field‐of‐view Sensor (SeaWiFS) data on the spectral diffuse attenuation coefficient at 490 nm (k490), and have been processed to have the smoothly varying and continuous coverage necessary for use in OGCM applications. These monthly fields provide the first complete global data sets of subsurface optical fields that can be used for OGCM applications of subsurface heating and bio‐optical processes. The effect on global OGCM prediction of sea surface temperature (SST) and surface mixed layer depth (MLD) is examined when solar heating, as given by monthly mean kPAR and PAR fields, is included in the model. It is found that subsurface heating yields a marked increase in the SST predictive skill of the OGCM at low latitudes. No significant improvement in MLD predictive skill is obtained when including subsurface heating. Use of the monthly mean kPAR produces an SST decrease of up to 0.8°C and a MLD increase of up to only 4–5 m for climatological surface forcing, with this primarily confined to the equatorial regions. Remarkably, a constant kPAR value of 0.06 m−1, which is indicative of optically clear open ocean conditions, is found to serve very well for OGCM prediction of SST and MLD over most of the global ocean.

Annual and Interannual Changes in the North Atlantic STMW Layer Properties

Subtropical mode waters (STWMs) are water masses formed in winter by convective mixing on the equatorward side of western boundary currents in the subtropical gyres. After the return of the seasonal stratification in spring, it is found at the stratification minimum between the seasonal and main pycnoclines. By characterizing STMW primarily at the density gradient minimum, previous studies were limited in their ability to describe STMW properties over large temporal and spatial scales. Rather than using a density-based characterization, the North Atlantic STMW layer was identified here by its much smaller temperature gradient relative to the more stratified seasonal and main thermocline, its temperature, and its large thickness. By using this temperature-based characterization, this study was able to develop a climatology using the large number of XBTs deployed between 1968 and 1988 and contained in the World Ocean Atlas 1994 historical hydrographic database and to use this climatology to examine STMW properties on large spatial and long temporal scales. Three different characterizations were used to assess the degree of convective renewal of the STMW layer during the 1968–88 winters. Two characterizations were based on comparing the winter mixed layer properties to the STMW layer properties in the previous fall, while the third characterization involved comparing the temperature gradient through the STMW layer in the spring to the STMW layer temperature gradient in the previous fall. Based on these characterizations, there was considerable spatial and temporal variability in the renewal of the STMW layer's vertical homogeneity from 1968 to 1988. Basinwide renewal occurred in 1969, 1970, 1977, 1978, 1981, and 1985, with more localized renewal, usually east of 55°W, in the other years. While STMW is nearly vertically homogeneous immediately after renewal, the temperature gradient through the layer increases with time following renewal. The annual rate of increase in the temperature gradient in the year following renewal is ∼5–6 (× 10−4°C per 100 m per day), while the interannual rate of increase is ∼2.0 × 10−4°C per 100 m per day following winters with no renewal of the STMW layer.

One-year observation of urban mixed layer characteristics at Tsukuba, Japan using a micro pulse lidar

One-year characteristics of the urban mixed layer is observed by an eye-safe, compact micro pulse lidar (MPL). Retrieval method of the mixed layer height (MLH) and the encroachment model of the mixed layer growing are presented. Two case studies are carried out using summer and late winter data. Comparisons are made between the aerosol optical thickness, the rawinsonde data and the model calculation. The development of the mixed layer exhibits temporal behavior similar to that of the aerosol optical thickness, but with a time difference of about 1– 2 h . The growth rate of the MLH agrees well with the encroachment model only in the morning, with considerate deviation during the daytime because of the wind effect. One-year growth rate and the maximum MLH are estimated from the MPL measurement between May 1999 and May 2000. The results show that the properties of mixed layer are strongly correlated with the seasonal meteorological conditions. This work also demonstrates that an automated, compact lidar system such as a MPL is quite useful for long-term monitoring of the mixed layer.

Where Does Dense Water Sink? A Subpolar Gyre Example*

It is proposed that a dominant component of the downwelling limb of the thermohaline circulation takes place in regions where convective mixing is found adjacent to steep topography. A simple theoretical estimate of the overturning forced by such boundary convection is derived that depends only on the properties of the oceanic mixed layer along the boundary. Scaling estimates indicate that sinking forced by boundary convection is an order of magnitude greater than sinking in the open ocean resulting from large-scale dynamics or baroclinic instability of deep convective sites. Recent hydrographic observations in the Labrador Sea are used to estimate the downwelling due to these different mechanisms and support the notion that boundary sinking dominates. The theory compares well with the overturning rates diagnosed in a noneddy-resolving general circulation model over a wide range of parameters. As a direct consequence of these dynamics, the high-latitude hydrography and overturning circulation in the model are very sensitive to the presence of cyclonic rim currents. Lateral density advection by the rim currents in the subpolar gyre increases the stratification and limits the mixing near the boundaries, thus reducing the maximum downwelling. As a result, most of the high-latitude meridional heat transport is carried by the horizontal circulation instead of the overturning circulation. Such rim currents are found in different configurations of the model, including 1) a continental slope and standard diffusion parameters and 2) zero horizontal diffusion and a flat bottom.

A singular evolutive extended Kalman filter to assimilate ocean color data in a coupled physical–biochemical model of the North Atlantic ocean

Within the European DIADEM project, a data assimilation system for coupled ocean circulation and marine ecosystem models has been implemented for the North Atlantic and the Nordic Seas. One objective of this project is to demonstrate the relevance of sophisticated methods to assimilate satellite data such as altimetry, surface temperature and ocean color, into realistic ocean models. In this paper, the singular evolutive extended Kalman (SEEK) filter, which is an advanced assimilation scheme where three-dimensional, multivariate error statistics are taken into account, is used to assimilate ocean color data into the biological component of the coupled system. The marine ecosystem model, derived from the FDM model [J. Mar. Res. 48 (1990) 591], includes 11 nitrogen and carbon compartments and describes the synthesis of organic matter in the euphotic zone, its consumption by animals of upper trophic levels, and the recycling of detritic material in the deep ocean. The circulation model coupled to the ecosystem is the Miami isopycnic coordinate ocean model (MICOM), which covers the Atlantic and the Arctic Oceans with an enhanced resolution in the North Atlantic basin. The model is forced with realistic ECMWF ocean/atmosphere fluxes, which permits to resolve the seasonal variability of the circulation and mixed layer properties. In the twin assimimation experiments reported here, the predictions of the coupled model are corrected every 10 days using pseudo-measurements of surface phytoplankton as a substitute to chlorophyll concentrations measured from space. The diagnostics of these experiments indicate that the assimilation is feasible with a reduced-order Kalman filter of small rank (of order 10) as long as a sufficiently good identification of the error structure is available. In addition, the control of non-observed quantities such as zooplankton and nitrate concentrations is made possible, owing to the multivariate nature of the analysis scheme. However, a too severe truncation of the error sub-space downgrades the propagation of surface information below the mixed layer. The reduction of the actual state vector to the surface layers is therefore investigated to improve the estimation process in the perspective of sea-viewing wide field-of-view sensor (SeaWiFS) data assimilation experiments.

The role of the annual cycles for the air–sea exchange of CO2

Abstract The annually integrated air–sea flux of CO 2 is governed by two quantities: the basic state of the ocean (e.g., the properties of the winter mixed layer) and the signal from the annual cycles. In this study, I focus on the role of the annual cycles in mixing, sea-surface temperature and biological production. By integrating these cycles, it is shown that the annually integrated flux of CO 2 can be written as F = α ( C T W − C Eq ), where F is the mean annual air–sea flux of CO 2 , α is an equilibrium rate constant (m/year), C T W is the total dissolved inorganic carbon concentration in the winter mixed layers and C Eq is the dynamic equilibrium concentration for C T W . In the formula, α and C Eq capture the influence of the annual cycles as well as the spatial variations in, for example, the alkalinity. I analyze data from the Ocean Weather Stations (OWS) in the North Atlantic and some results from the MIT biogeochemical ocean model to find adequate descriptions of α and C Eq . According to these model/data estimates, the influence of the annual cycles in sea-surface temperature and biological production on the dynamic equilibrium concentration is on the order of −5 to −20 and 0–30 μmol/kg, respectively. These numbers are not negligible showing that the annual cycles must be considered when analyzing the oceanic carbon cycle. The spatial distribution of the quantities C T W , α , and C Eq are estimated for the North Atlantic using data from the TTO/NAS expedition and a combination of model and data analyses. The air–sea flux is calculated according to the above formula, and the seawards flux is estimated to be 0.4 Gt C/year for the area north of 30°N.

Interannual variability of Si and N cycles at the time-series station KERFIX between 1990 and 1995 – a 1-D modelling study

Interannual variability of nutrients and plankton cycles were studied at the time-series station KERFIX (50°40′S, 68°25′E) using a 1-D coupled physical-biogeochemical model that is descended from that of Pondaven et al. (1998). At KERFIX, a high half saturation constant for silicic acid uptake ( K Si ) and a high Si/ N uptake ratio are required to reproduce the Si and N cycles. Although very high in comparison with most data from temperate systems, these values are consistent with K Si and Si/ N uptake ratios measured in the Indian sector of the Southern Ocean. Past and recent finding on the role of light and iron limitation on nutrient consumption ratios might explain these “unusual” silicon uptake kinetic parameters. Comparison of model results with observations show that the model correctly reproduces the observed interannual variability of nutrients and plankton cycles at KERFIX between 1992 and 1995. Characteristic features of this region are a spring phytoplankton bloom of 1.0–1.5 mg Chlorophyll a m −3 and a net excess of silicic acid utilisation over that of nitrate. This high silicic acid utilisation leads to low Si concentrations in late summer and subsequent Si limitation of diatom growth. The interannual variability of production of silicon and nitrogen predicted by the model is 1.93±0.04 mol Si m −2 yr −1 and 1.35±0.07 mol N m −2 yr −1 (±SD). In parallel, the predicted export is 1.12±0.04 mol Si m −2 yr −1 and 0.06±0.01 mol N m −2 yr −1. It is shown that diatoms may contribute significantly to export if diatom sinking is taken into account. An interannual variability of the predicted Si and N cycles is detected. This variability is associated with changes in the mixed layer properties, which have been documented to be linked to the Pacific El Niño Southern Oscillation or displacement of the Polar Front.

Estimation of Surface Heat Fluxes at Field Scale Using Surface Layer Versus Mixed-Layer Atmospheric Variables with Radiometric Temperature Observations

Radiometric surface temperature observations TR(f), near-surface meteorological/surface energy flux (METFLUX), and atmospheric boundary layer (ABL) data were collected during the Washita ’94 Experiment conducted in the Little Washita Experimental Watershed near Chickasha, Oklahoma. The TR(f) measurements were made from ground and aircraft platforms near the METFLUX stations located over vegetated surfaces of varying amounts of cover and over bare soil. Continuous, half-hourly averaged ground-based TR(f) measurements essentially at the point scale were calibrated with periodic ground transect and aircraft-based TR(f) observations at coarser resolutions so that the continuous TR(f) measurements would be representative of surface temperatures at the field scale (i.e., on the order of 104 m2). The METFLUX data were collected nominally at 2 m above the surface, while ABL measurements were made in the lower 8‐10 km of the atmosphere. The ‘‘local’’ wind speed, u, and air temperature, TA, from the METFLUX stations, as well as the mixed-layer wind speed, UM, and potential temperature, QM, were used in a two-source energy balance model for computing fluxes with continuous TR(f) measurements from the various surfaces. Standard Monin‐ Obukhov surface layer similarity was used with the ‘‘local’’ u and TA data from the METFLUX stations. Bulk similarity approaches were used with the UM and QM data referenced either to ABL height or the top of the surface layer. This latter approach of using mixed-layer data to drive model computations for the different sites is similar to the so-called flux-aggregation schemes or methods proposed to account for subgrid variability in atmospheric models, such as the ‘‘tile’’ or ‘‘mosaic’’ approach. There was less agreement between modeled and measured fluxes when using mixedlayer versus local meteorological variables data for driving the model, and the type of bulk formulation used (i.e., whether local or regional surface roughness was used) also had a significant impact on the results. Differences between the flux observations and model predictions using surface layer similarity with local u and TA data were about 25% on average, while using the bulk formulations with UM and QM differences averaged about 30%. This larger difference was caused by an increase in biases and scatter between modeled and measured fluxes for some sites. Therefore, computing spatially distributed local-scale fluxes with ABL observations of mixed-layer properties will probably yield less reliable flux predictions than using local meteorological data, if available. Given the uncertainty in flux observations is about 20%, these estimates are still considered reasonable and moreover permit the mapping of spatially distributed surface fluxes at regional scales using a single observation of UM and QM with high resolution TR(f) data. Such TR(f) observations with a 90-m pixel resolution will be available from the Advanced Spaceborne Thermal Emission and Reflection Radiometer to be launched on NASA’s Earth Observing System.

Seasonal and interannual variability of the mixed layer properties and steric height at station KERFIX, southwest of Kerguelen

Monthly hydrographic data collected from May 1991 to December 1994 at station KERFIX (50°40′S, 68°25′E) were analysed to describe and understand the seasonal and interannual variability of the mixed layer properties and steric height for the first 500-m water column. The monthly mean mixed layer depth (determined from the density difference criterion of 0.02 σ θ ) varies from 60 m in January to 185 m in August, with corresponding temperature and salinity varying within a limited annual range of 2.3°C (around 4.1°C in March and 1.8°C in September) and 0.06 (around 33.825 in June and 33.886 in October). A noticeable interannual change in mixed layer properties has been detected: warm and low-salinity anomalies in 1992 and cold and high-salinity anomalies in 1994; the mixed layer depth was significantly deeper in more recent years. A possible linkage of these low-frequency variations to the Pacific El Niño Southern Oscillation (ENSO) is suspected. The 3 years' (1992–1994) mean monthly steric height varies from +2.2 cm in March to −2.3 cm in September, with the appearance of a secondary maximum in July and a secondary minimum in June. Consistent with the mixed layer properties, the steric sea level of the site reveals an important interannual change, with a positive anomaly (+1.3 cm) in 1992 and a negative anomaly (−1.3 cm) in 1994. Superimposed on this low-frequency drift are quasi-semiannual (5–6 months) variations, due to the halocline-layer salinity anomalies having the same periodicity. The commonly observed mesoscale eddy activity in the Kerguelen region seems to be the major cause. Finally, the monthly mixed layer salinity of the site is determined largely by the competing effects of evaporation–precipitation and horizontal advection. On an annual basis, however, the entrainment of saltier deep water mostly compensates the eventual freshening of the mixed layer which might otherwise be caused by the excess of precipitation over evaporation in this region.

Using 234Th disequilibria to estimate the vertical removal rates of polycyclic aromatic hydrocarbons from the surface ocean

Abstract A novel 234 Th-coupled approach was employed to deduce the vertical fluxes of polycyclic aromatic hydrocarbons (PAHs) through surface waters of harbor, coastal, shelf, and pelagic regimes. We found reasonable agreement between these surface ocean fluxes, based on direct measurements of mixed-layer properties, and fluxes deduced from underlying sediments. Fluxes decreased exponentially away from the northeastern U.S.A. Source-diagnostic molecular ratios indicate that atmospheric fall-out of combustion-derived PAHs from the continents is the dominant source. Despite higher unit area fluxes inshore, the open ocean represents a large integral sink for PAHs. For example, of the 60 metric tonnes of pyrene that we estimate to annually become sequestered in the western North Atlantic, only ~ 10% is deposited in coastal waters while the remaining 90% is exported farther offshore on the continental shelf and to pelagic regimes.

An Apparent Surface Buoyancy Flux Associated with the Nonlinearity of the Equation of State

Abstract The temperature dependence of the expansion coefficient of seawater can lead to a nonzero annual-average surface buoyancy flux even if the annual-average heat flux is zero. In the Mediterranean Sea, for example, this effect apparently gives the same buoyancy flux into the sea as a heat flux of 6 W m−2. This does not, however, lead to an increase in the surface layer buoyancy over the course of a year; compensating cabbeling occurs mainly in the winter and spring when there is intensive mixing. The magnitude of the apparent buoyancy flux is proportional to the area inside the hysteresis loop of the seasonal cycle of the sea surface temperature versus the total heat content of the ocean. The output of a simple mixed layer model, however, shows only a weak sensitivity of mixed layer properties, such as depth, to inclusion of the nonlinearity in the equation of state.

A model of the effects of horizontal density gradients on mixing processes in the oceanic surface layer

A diurnal Eulerian model of the upper mixed layer incorporating the effects of horizontal density gradients is developed based on that of Janowitz and Kamykowski [1991] and is utilized to study the effects of wind‐driven cross‐isopycnal transport on mixing processes in the layer. Four runs of the model are conducted for a constant horizontal density gradient of 2.5 × 10−5 kg m−4 with wind directions at 0°, 90°, 180°, and 270° to this gradient. Two runs are conducted with half this density gradient and wind directions 90° to the left and right of the gradient and one run with no density gradient. In all cases the model is first run with a constant heat loss rate of 150 W m−2 through the sea surface for 11 hours to simulate nighttime cooling and to provide initial conditions for daytime runs. The model is then run for 24 hours with a constant wind speed of 7 m s−1 and a maximum solar radiation of 900 W m−2 during the first 13 hours of the 24‐hour simulation. The results show that the shallowest mixed layer occurs when the wind direction is 90° to the left of the density gradient and the deepest layer occurs with the wind direction 90° to the right of the gradient. After 24 hours, the ratio of the deepest to the shallowest mixed layer depth is 2.35 for the stronger gradient and 1.83 for the weaker gradient. These results are explained by the effect of vertical shear of the wind‐driven advection of horizontal density variations, which changes the vertical density gradient and can destabilize or stabilize the mixed layer. The results indicate that wind‐driven, cross‐isopycnal transport can have significant effects on mixing processes in the layer. Dimensionless parameters are developed to estimate the relative importance of cross‐isopycnal, wind‐driven transport on mixed layer properties.

Stationary Shock Fronts in a Continuously Stratified Thermocline Model

Fronts are ubiquitous in the ocean. Recent work by Dewar has considered the formation of oceanic fronts in a simple layered model. In this contribution, the position and structure of similar fronts within a coupled mixed layer-thermocline model are studied. A subtropical gyre is considered. The mixed layer is chosen to be warm and light along the southern boundary of this gyre but cooler and denser to the east and north. This contrast in mixed layer properties drives the formation of a front within the southern flank of the subtropical gyre. For the model dynamics require the mixed layer to be deeper where it is dense and shallower where it is less dense. The more rapid northward Ekman drift due to the concentration of the Ekman transport within the thinner mixed layer to the south tries to override the weaker drift associated with the thicker mixed layer to the north. There are sharp jumps in mixed layer thickness and isopycnal depths over this front. It also carries substantial transports. This front is of particular interest because it is a site of anomalously strong subduction driven by the buoyancy yielded up by the northward Ekman drift as it moves across the front into cooler, denser waters.

On the Thermodynamics of Subduction

Abstract The thermodynamic processes attendant on the transfer of fluid between a surface mixed layer and a stratified thermocline beneath are discussed. For a parcel of fluid in the mixed layer to pass into the stratified thermocline—to subduct—it must be stratified by buoyancy input; this buoyancy can be supplied by local air–sea exchange and/or by lateral advective processes. A series of experiments is described in which a mixed layer, coupled to an ideal-fluid thermocline, undergoes differing seasonal cycles: in one limit the mixed layer is held fixed in a steady, winter configuration; in the other the mixed layer is, more realistically, shallow over most of the year and deepens briefly in late winter. It is shown that the annual subduction rate Sann depends, to first order, only on late winter mixed layer properties. However the annual-mean air–sea buoyancy exchange is sensitive to the details of the seasonal cycle and becomes vanishingly small as the effective subduction period shortens. In this lim...

Mixing and transport

Imberger and Parker1 reported observations of the formation of frontal structures in a lake. Winds and their spatial variability were important in determining the horizontal variability of surface mixed layer properties. Fine-scale measurements of temperature in the mixed layer of a reservoir were reported by Imberger;2 the observations covered periods governed by various mixing mechanisms. A one-dimensional model that was used to assess the importance of each mechanism worked well, but showed the need to incorporate the energetics of billowing. A one-dimensional model was also used by Rahm3 to study stratification in a small, ice-covered lake. It was shown that the sediment heat flux gave rise to a stable stratification and an organized circulation pattern. An investigation of detailed water properties in the Dead Sea indicated that the sea had turned over, ending a long period of stratification, following a lowering of the water surface.4 Effler and Owens5 studied the effect of acidification on the thermal stratification of lakes by using a mixed-layer model. The acidification increases light transparency and can exert a large effect on stratification. Solutions to the response of a rectangular, n-layered, stratified lake to an unsteady wind stress were presented by Monismith.6 The case n = 3 was studied in detail, and the predictions compared with field measurements. The design of an instrument for measuring small bottom lake currents between 0.3 and 3 cm/s with an accuracy of ?5% for speed and ?15? for direction was given by Lemmin et al.7 Deployments in Swiss lakes were discussed.

Modeling the effects of buoyancy on the evolution of geophysical boundary layers

A simple modeling based on the Imperial College k‐ε turbulence description is shown to be capable of describing the highly anisotropic phenomena associated with the strong buoyancy effects encountered in upper ocean (and atmospheric boundary layer) environments. Both diurnal stratification and transition to buoyant mixing (from that driven by wind shear) are described in considerable detail, provided that the modeling of the turbulent Prandtl number and of the buoyant generation term in the ε model equation are evaluated in a suitably realistic and consistent way. The resulting model equations are suitable for simulating the evolution of the ensemble‐averaged properties of the oceanic mixed layer in response to a specified history of interfacial shear stress and heat flux. The model is tested by comparing the predicted mixed layer evolution with the dissipation rate measurements of Shay and Gregg.

Measured and calculated optical property profiles in the mixed layer and free troposphere

Nearly simultaneous measurements of the physical and optical properties of mixed layer and free tropospheric aerosols near Boulder, Colorado, were made on several occasions using aircraft, balloon, and ground‐based sensors. This effort (Front Range Lidar, Aircraft, and Balloon experiment (FRLAB)) was conducted with the purpose of obtaining a diverse, self‐consistent data set that could be used for testing optical model calculations based on measured physical characteristics such as apparent size distribution, composition, and shape. It was found that even with the uncertainties involved, the model predictions are in good agreement with the measurements in the visible and near infrared wavelength regions. At CO2 lidar wavelengths there is considerably more uncertainty in both the calculated and measured values; however, within the estimated errors there appears to be satisfactory agreement except for the highest free tropospheric layer studied. The results also indicate that during FRLAB the aerosol in the boundary layer and free troposphere behaved as spherical particles for optical modeling purposes. The utility of the observations for determining the extinction‐to‐backscatter ratio relevant to aerosols in the boundary layer and free troposphere is described with typical measured values being in the 20 to 30 sr range.

Spanwise averaging of plane mixing layer properties

An attempt is made to demonstrate the effects of streamwise vorticity on such mixing layer global properties as layer thickness and peak Reynolds stresses. Attention is given to differences between results obtained from spanwise averaging over a number of velocity profiles and those given by the more conventional approach of analyzing a single profile measured along the test section centerline. It is found that the growth rate and streamwise development of peak Reynolds stresses in the near field can be significantly affected by spanwise variations in the mixing layer.

A two‐dimensional thermodynamic model for sea ice advance and retreat in the Newfoundland marginal ice zone

A time dependent two‐dimensional ice‐ocean coupled thermodynamic model is developed to study the ice edge advance and retreat, development of the oceanic mixed layer, and oceanic response to ice movement, ice melt, and heat balance in the Newfoundland marginal ice zone. The model domain is a vertical section of the ocean along the direction of the ice velocity. Initially, the ocean is free of ice and has a deep mixed layer formed by winter surface cooling. An ice sheet then moves into the domain from the upstream boundary at constant velocity. It melts from the bottom and a shallow mixed layer beneath the ice is developed. Heat and buoyancy fluxes at the air‐sea and ice‐water interfaces and at the bottom of the mixed layer determine the melt rate and change of the mixed layer properties. The ice edge reaches a maximum distance and starts to retreat when the ice is being melted by the warm water faster than it is being advected into the area. The oceanic properties change with the ice movement. During the advancing phase of the ice movement, the heat loss to the ice bottom from ice melting exceeds the heat gain by surface heating and entrainment, causing the mixed layer temperature to drop. But since the buoyancy created by the melting is not sufficient to overcome the effect of wind mixing, the mixed layer deepens rapidly. During the retreating phase, the mixed layer becomes shallower and warmer because of the increasing surface heating and buoyance production by ice melting. The most important factors controlling the melt rate and the excursion distance are the air temperature and the ambient water temperature. Higher wind speeds increase the mixed layer depth but do not have a strong effect on the melt rate.