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International audience; Midlevel Cloud-base Turbulence (MCT) caused by ice/snow precipitation from midlevel clouds falling into dry air below the cloud base and sublimating is investigated. MCT phenomena in the lower troposphere as revealed by the Middle and Upper atmosphere (MU) radar in Shigaraki, Japan, during the Shigaraki unmanned aerial vehicle and radar Experiment campaigns in the spring-summer of 2015 and 2016 are described. The MU radar was operated in a high-resolution ( 20-m) range imaging mode and hence revealed the structure of these MCTs in great detail. These MCT layers grew to hundreds of meters in thickness, often reaching nearly 2,000 m in depth, lasting often for as much as 24 hr. A simple analytical model and a second-moment closure-based turbulent mixing model are used to estimate the levels of turbulence kinetic energy and its dissipation rate in the MCT layer and compare them to those measured by the MU radar. The study shows that MCT can give rise to moderate levels of turbulence of potential interest to aviation, confirming conclusions reached by earlier pioneering studies. However, to our knowledge, this important process has not received the attention it deserves by the atmospheric community so far, and therefore, it is the principal goal of this paper to not only present some observations and preliminary modeling results, but also redraw the attention of atmospheric scientists to this important process.

Our knowledge of the spatio-temporal variability of the dissipation rates of turbulence kinetic energy (TKE) in the free atmosphere is severely limited because of the difficulty and expense of making these measurements globally. A few MST/ST radar facilities that are still in operation around the globe have provided us with valuable data on temporal variability of the dissipation rate in the atmospheric column above the radars but the data covers an extremely tiny fraction of the global free atmosphere. Moreover, there are limitations to these data also, since restrictive hypotheses are necessary for making these measurements. It appears that simple radiosondes launched from the existing global sonde network might be able to provide a much wider coverage, provided the technique for deducing the dissipation rates from overturns detected by the sondes can be calibrated and validated against existing techniques. An intensive field campaign conducted over the Harrow ST radar site located in western Ontario, Canada, during the summer of 2007 provided precisely such an opportunity. In this paper, we report on the comparison of the TKE dissipation rates derived from the PTU measurements made by ozonesondes launched during the campaign with those obtained from direct ST radar measurements. We find encouraging agreement between the two, which suggests that routine measurements of TKE dissipation rates by radiosondes in the global free atmosphere might indeed be feasible.

Though ubiquitous in the global oceans, double diffusive mixing has been largely ignored or poorly represented in the models of turbulent mixing in the ocean and in 3-D ocean models, until recently. Salt fingers occur in the interior of many marginal seas and ocean basins, the Tyrrhenian Sea and the subtropical Atlantic being two examples. Diffusive convection type of double diffusion occurs in the upper layers of many sub-polar seas and polar oceans due to cold melt water from sea ice. Consequently, it is important to be able to properly parameterize double diffusive mixing in basin scale and global ocean models, so that the water mass structure in the interior of the ocean can be properly simulated. This note describes a model for double diffusive mixing in the presence of background shear, based on Mellor–Yamada type second moment closure, more specifically Kantha, 2003 , Kantha and Clayson, 2004 second moment closure models of resulting turbulence, following Canuto et al. (2008a) but employing a different strategy for modeling the pertinent terms in the second moment equations. The resulting model is suitable for inclusion in ocean general circulation models.

In this note, we examine the extraction of energy from waves by the turbulence in the upper ocean as one possible physical mechanism for the attenuation of swell as it propagates across an ocean basin. We derive a simple expression for the swell attenuation rate that is of potential use in wave forecast models.

We present here a 1/4° resolution near-global barotropic tidal model designed specifically to provide more accurate tides in shallow water. The model assimilates tides derived from 4 years of TOPEX/Poseidon (T/P) altimetric data. Procedures are used that tend to preserve the small spatial scales in the tidal structure in shallow water. Data from coastal tide gauges are also assimilated into the model. The result is a tidal model that is useful in most of the shallow and deep areas of the global oceans. Some problems exist in regions where no data are available for assimilation, such as the Southern Ocean. Pelagic tide gauge comparisons show that in deep water the new model is comparable in accuracy to the best of the existing T/P-based global tidal models. Comparisons to crossover differences in shallow water suggest improved performance. We found that more accurate accounting of the load tides in the ocean tide model using an iterative technique based on the Green's function formalism does not yield ocean tides that are significantly different from the simpler approaches used thus far by ocean tide modelers when data are assimilated. It is our hope that this tidal model will not only help advance our understanding of shallow water tidal processes around the globe but also extend the utility of altimetry to waters shallower than 1000 m.

We describe here a nowcast/forecast system for the entire Mediterranean Sea, designed for real-time forecasts and closely resembling operational numerical weather prediction systems. The core of the system is a high-resolution (10 km) three-dimensional primitive equation-based, sigma-coordinate numerical circulation model, assimilating remotely sensed multi-channel sea surface temperature and in situ expendable bathythermograph/conductivity-temperature-depth observational data, using an optimal-interpolational scheme. We present results for 1993 and 1994 from this data-assimilation model, focusing principally on the mesoscale features prevalent in the western and eastern Mediterranean Sea. We show that the model exhibits considerable skill in simulating both the permanent and transient mesoscale features in the Mediterranean. In particular, hitherto less well-known and less well-studied circulation features in the Adriatic and Aegean Seas are carefully examined and presented. Particular care is given to discussing the circulation in the entire Mediterranean, with particular attention to flows through various straits and their variability.

We describe the application of a nowcast/forecast system for three-dimensional currents, temperature, and salinity to the Red Sea. The modeling system is constructed around a high-resolution (6×7 km) primitive-equation numerical circulation model with complete thermodynamics and an imbedded turbulence closure submodel. It is coupled to near-real-time databases containing meteorological forecasts and remotely sensed and in situ temperature and salinity data. The temperature and salinity data are ingested into the model daily using a nudged objective analysis technique. Because the Red Sea is a relatively narrow basin bounded by typically high and complex orography, a single-layer atmospheric boundary layer submodel has been used to increase the effective resolution of the original 40-km resolution meteorological fields by taking into account orographic steering of the low-level winds. In order to validate the modeling system, two very complete hydrographic surveys of the Red Sea were undertaken, and their results are described. Both the surveys and the modeling system nowcasts demonstrate that the circulation pattern of the Red Sea is variable and often composed of a series of eddies or subgyres, mainly anticyclones. Immediately before one survey, the winds tended to be along axis, while just before the second, they tended to be cross axis. The Red Sea circulation was much more eddy-like when the winds were cross-axis. By forcing the modeling system with and without orographically steered winds we were able to establish that the complex eddy structure is a response to a wind field which can be highly structured and vorticity rich because of interaction with the high and variable adjacent orography. When the winds are more along axis, there is less interaction with the adjacent orography, and consequently, there are fewer eddies in the Red Sea.

A one-dimensional numerical model has been applied to simulate the evolution of the temperature and CO2 stratification in Lake Nyos since the 1986 disaster. It incorporates a second-moment turbulence closure scheme for mixing and heating and cooling in the upper layers of the lake. The effects of inflowing stream water and input of the CO2, heat, and dissolved solids at the bottom of the lake are taken into account. The model is initialized by conditions observed immediately after the disastrous outgassing event in 1986 and integrated forward for 10 years, forced by seasonally modulated diurnal heating and nocturnal cooling and heavy summer time precipitation at the surface. Four possible conditions are investigated. The first simulation considers the normal seasonal heating/cooling cycle and steady input of heat, dissolved solids, and CO2 at the bottom. It shows that the upper layers of the lake are quite stable under normal seasonal forcing but the bottom layers reach high CO2 concentrations in less than a decade. The second simulation considers a brief introduction at the bottom of the lake of cooler waters that contain less CO2 and temporarily destabilize the bottom layers. The third and fourth simulations consider anomalous surface forcing conditions that can produce anomalous mixed layer deepening during the cooling seasons, capable of releasing the CO2 stored immediately below the normal mixed layer. These results suggest that a destabilization of the bottom layers is more likely to lead to massive and catastrophic degassing. The results also demonstrate the utility of a numerical model in investigations of caldera/crater lakes such as Lake Nyos.

[1] The turbulent Reynolds stresses in the upper layers of the ocean interact with the vertical shear of the Stokes drift velocity of the wave field to extract energy from the surface waves. The resulting rate of dissipation of wind waves in the global ocean is about 2.5 TW on the average but can reach values as high as 3.7 TW, making it as important as the dissipation of wave energy in the surf zones around the ocean margins. More importantly, the effect of Stokes dissipation is felt throughout the mixed layer. It also contributes to Langmuir circulations. Unfortunately, this wave dissipation mechanism has hitherto been largely ignored. In this note, we present a preliminary estimate of the Stokes dissipation rate in the global oceans based on the results of the WAVEWATCH III model for the year 2007 to point out its potential importance. Seasonal and regional variations are also described.

[1] A microstructure profiler was deployed to make turbulence measurements in the upper layers of the southern Adriatic Sea in the Mediterranean during the Naval Research Laboratory (NRL) DART06A (Dynamics of the Adriatic in Real Time) winter cruise in March 2006. Measurements in the Po river plume along the Italian coast near the Gargano promontory displayed classic double-diffusive layers and staircase structures resulting from the relatively colder and fresher wintertime Po river outflow water masses overlying warmer and more saline water masses from the Adriatic Sea. We report here on the water mass and turbulence structure measurements made both in the double-diffusive interfaces and the adjoining mixed layers in the water columns undergoing double-diffusive convection (DDC). This dataset augments the relatively sparse observations available hitherto on the diffusive layer type of DDC. Measured turbulence diffusivities are consistent with those from earlier theoretical and experimental formulations, suggesting that the wintertime Po river plume is a convenient and easily accessible place to study double diffusive convective processes of importance to mixing in the interior of many regions of the global oceans.

[1] A Lagrangian analysis of the transport and dispersal of plumes observed in satellite-derived ocean color images was conducted using a data-assimilating model of the Gulf of Mexico. The interaction between pervasive cyclonic and anticyclonic eddies in the Gulf generated advective paths that connect remote shelf regions. These paths aligned remarkably well with the plume events recorded with the chlorophyll-a ocean color product from SeaWiFS. Two such events were studied. In one event material was transported in a thin strip between the northern wall of the Loop Current and an adjacent cyclone, connecting the eastern Campheche shelf (off the Yucatan Peninsula) and South Florida shelves. The other event began off the Louisiana shelf break as a small plume traced by chlorophyll and then developed into a long and thin feature which meandered to the shelf break off the northern Yucatan Peninsula, moving between a large anticyclone and several adjacent cyclones. These results indicate that inter-eddy advection plays a crucial role in developing the ocean color patterns observed in the satellite ocean color data.

[1] Ocean predictability skill is investigated using a Gulf of Mexico nowcast/forecast model. Power law scaling is found in the mean square error of displacement between drifting buoy and model trajectories (both at 50 m depth). The probability density function of the model valid prediction period (VPP) is asymmetric with a long and broad tail on the higher value side, which suggests long-term predictability. The calculations demonstrate that the long-term (extreme long such as 50–60 day) predictability is not an "outlier" and shares the same statistical properties as the short-term predictions.

In this first part of a two-part paper we present results from a high-resolution, data-assimilative, fully nonlinear barotropic tidal model of the global oceans that excludes the Arctic. The model assimilates, in waters deeper than 1000 m, altimetric tides derived from the analysis of 2 years of TOPEX altimetric data. It also assimilates tide gage data from coastal tide gages. The model domain includes that covered by the altimeter and extends to the Antarctic. In the first part we present tidal results for the primary semidiurnal (M2, S2, N2, and K2) and diurnal (K1, O1, P1, and Q1) constituents. The second part deals with applications (Kantha, et al., this issue). The model results are compared with observational data from pelagic gages. These comparisons show that overall in the open ocean, in deep waters away from the margins of the primary basins, the model performance is comparable to other tidal models derived using TOPEX data, except for M2 and S2. However, one advantage of this model compared with those based solely on the analysis of altimetric data is that the altimetry-derived tides are subjected to dynamical constraints by the model. This results in reduction of subtidal variability often folded into tidal signals by TOPEX data analysis. It is also shown that in shallow waters along the margins, especially in east Asian marginal seas, the model differs substantially from these other models. In addition to sea surface heights, we also present dynamically consistent barotropic currents in the form of tidal ellipses for M2 and K1 constituents. Since the goal of this research is a global tidal model uniformly valid in both deep and shallow waters, we finally present tidal elevations and currents on two well-known shallow water areas, the northwest European shelf and the northeast American shelf, and a semienclosed western Pacific marginal sea, the Bering Sea. The model results are compared with independent observations and, where possible, with results from other numerical models. The results highlight the importance of bottom topography; on the northwest European shelf, where accurate bottom topography was included in the model, the results are much better than on the northeast American shelf, where the Digital Bathymetric Data Base 5 (DBDB5) topographic database has significant errors. Results from the Bering Sea, where the topography is more accurate than the DBDB5, compare well with known tides in the region.

In this second part, we explore the implications of the tides derived from the high-resolution, data-assimilative, nonlinear barotropic global ocean tidal model described by Kantha (this issue) in altimetric analysis and geophysical applications. It is shown that when applied to the task of removing tidal sea surface height from TOPEX altimetric records, the model performance is comparable to other global tidal models in the open ocean as measured by the reduction in crossover variances. The performance is slightly better than that of the only other high-resolution global tidal model from Grenoble (Le Provost et al., 1994). The results are however mixed in regions shallower than 1000 m and in semienclosed seas such as the Bering Sea, with the model performance slightly worse overall than the Grenoble model. Computations of total power input (and hence total tidal dissipation rate) are shown to be in excellent agreement with recent analyses of TOPEX data and geophysical observations. In addition, distributions of the tidal power input, tidal dissipation, and the power fluxes in the global oceans are shown for the two primary constituents, M2 and K1. Load tides in solid Earth due to ocean tidal loading fluctuations are also computed for the major semidiurnal and diurnal constituents. The load tides are shown to be large in the shallow seas adjacent to the coasts with high tides such as the Patagonian shelf, because of the higher resolution of this global tide model. This has potential implications in geophysical applications.

Arctic leads are thought to play an important role in the air-sea heat exchange at high latitudes. The evolution of the local ice-ocean-atmosphere coupled system, when a lead opens up and immediately begins to refreeze, is of considerable interest in terms of the heat exchanged by the ocean to the atmosphere, as well as the amount of salt extruded into the oceanic mixed layer. Here we will present a coupled model of the ice-ocean system that provides a quantitative description of a refreezing lead, especially the evolution of the ice cover and the mixed layer below. The model is applied and compared with what has been learned from the Lead Experiment (LEADEX) observations in the April of 1992 in the Beaufort Sea. The results suggest that Arctic leads, especially during winter, are, in general, close to a state of free convection. Strong convection driven by the extruded brine in a refreezing lead drives vigorous mixing in the mixed layer immediately below, irrespective of the advective velocity of ice. Turbulence intensities reach quite high values during the initial phases of refreezing but weaken gradually with a half-life time of about 2 days. Inertial oscillations are superimposed on the resulting currents and are especially vigorous below the mixed layer. The ice builds up to a thickness of over 12 cm in the first 24 hours in a refreezing lead, in accordance with LEADEX observations, with a significant contribution coming from frazil ice formation in the supercooled water below. Not surprisingly, since the water below is at or close to freezing, advection of water masses past the lead due to ice motion or prevailing currents does not alter the refreezing rate substantially, even though the frazil ice contribution shows a significant increase. Advection does affect the local properties in the mixed layer immediately below and downstream of the lead. For example, the increase in salinity, an indicator of the intensity of the refreezing process in a lead, depends very much on the motion of ice cover relative to the underlying water. For large advective velocities the salinity increase is an order of magnitude smaller than the purely convective situation and the turbulence is dominated by that generated by shear underneath the rough ice, upstream of the lead which tends to mask that generated by convection in the lead itself. For a stationary lead, refreezing gives rise to an inward jet underneath the ice and outward flow at the base of the mixed layer. Vertical motion is in the form of convective cells centered at the lead edges.

An improved mixed layer model, based on second-moment closure of turbulence and suitable for application to oceanic and atmospheric mixed layers, is described. The model is tested against observational data from different locations in the global oceans, including high latitudes and tropics. The model belongs to the Mellor-Yamada hierarchy but incorporates recent findings from research on large eddy simulations and second-moment closure. The modified expansion of Galperin, Kantha, Hassid and Rosati (1988) that leads to a much simpler and more robust quasi-equilibrium turbulence model is employed instead of the original Mellor and Yamada (1974) model. Findings from ongoing research at the National Center for Atmospheric Research on large eddy simulations of the atmospheric boundary layer are utilized to improve parameterizations of pressure covariance terms in the second-moment closure. Shortwave solar radiation penetration is given careful treatment in the model so that the model is applicable to investigations of biological and photochemical processes in the upper ocean. But by far the major improvement is in the inclusion of the shear instability-induced mixing in the strongly stratified region below the oceanic mixed layer that leads to a more realistic and reliable mixed layer model that is suitable for application to a variety of geophysical mixed layers and circulation problems. The model appears to predict the mixing in the upper ocean well on a variety of time scales, from event scale storm-induced deepening and diurnal scale variability to seasonal time scales. With proper attention to the heat and salt balances in the upper ocean, it should be possible to use it for simulations of interannual variability as well. While the model validation has been primarily against oceanic mixed layer data sets, it is believed that the improvements can be readily incorporated into a model of the atmospheric boundary layer as well.

The decade of the 1980s might well have been designated “The Decade for Marginal Ice Zone (MIZ) Research.” These highly energetic regions where air, ice, and water intermingle and interact thermodynamically and dynamically have undergone an unprecedented amount of study during this past decade. Relevant major programs have included the Office of Naval Research-sponsored Marginal Ice Zone Experiment (MIZEX) West and East experiments, the Coordinated Eastern Arctic Experiment (CEAREX) in the Arctic, and the National Science Foundation-sponsored Antarctic Marine Ecosystem Research in the Ice Edge Zone (AMERIEZ) program in the Antarctic. There have been a host of smaller experiments as well.

The influence of streamline curvature on small-scale turbulence and vertical mixing in stratified fluids is the subject of this study. The roles of curvature and stratification in enhancing and suppressing turbulent mixing are explored using second-moment closure for turbulence. Governing equations for second moments are expressed in generalized orthogonal curvilinear coordinates, from which, through a series of approximations, simplified expressions are derived for second moments in the limit of small streamline curvature. The governing equations are then used to obtain a quasi-equilibrium turbulence model suited for application to atmospheric and oceanic mixed layers. A typical model application is illustrated by simulation of stratified flows over two-dimensional, idealized mountains and valleys. The limit of local equilibrium is further invoked to derive semi-analytical results for the enhancement and suppression of vertical turbulent mixing under the combined influence of stratification and curvature. It is shown that stabilizing curvature can drastically suppress turbulence even when the stratification is strongly destabilizing. Conversely, under strong stable stratification that would otherwise lead to total suppression of turbulence, destabilizing curvature can keep turbulence alive. Streamline curvature is also shown to significantly modify the Monin-Obukhov similarity laws for momentum and heat fluxes in the constant flux region of the atmospheric boundary layer. Finally, the need for observational data on curvature effects on mixing in stratified flows either in the laboratory or in flows over topography in the oceans and the atmosphere is highlighted.

The maximum heat transfer possible from a sphere of magma ascending through a viscous lithosphere is estimated using a Nusselt number formulation. An upper bound is found for the Nusselt number by using the characteristics of a potential flow which, it is argued, is similar in the limit to a non-isothermal Stokes-flow in which the fluid (wall rock) viscosity is sensitive to temperature. A set of cooling curves are calculated for a magma ascending at a constant velocity beneath an island arc. If the magma is to arrive at the surface without solidifying its ascent velocity must be greater than about 5.8 × 10−3 cm s−1, for a magma radius of 1 km, and greater than about 2.7 × 10−5 cm s−1, for a magma radius of 6 km. If the magma begins its ascent crystal free it will generally become superheated over most of its ascent. Using essentially the same formulation as for heat transfer the mass transfer to or from a spherical body of magma ascending at these velocities is given approximately by ΔC ⋍ ΔW/10, where ΔC is the change in weight percent of a component in the magma during ascent and ΔW is the compositional contrast of that component between the magma and its wall rock.

Turbulent fluctuations in active mixed layers can excite internal waves in stably stratified fluid regions adjoining them. Expressions are derived for the energy and momentum fluxes radiated away by internal waves from an oceanic mixed layer, in terms of the spectrum of the static pressure fluctuations imposed at the base of the mixed layer by the turbulent eddies. The role of these internal wave fluxes in questions such as the determination of the rate of deepening of the layer due to an applied surface stress and the origin of internal waves in the deep ocean is discussed.

Reflection of propagating inertial and internal waves at a rigid boundary gives rise to oscillatory fluid motions parallel to it. The interaction of these motions with the boundary induces a small steady drift current at the boundary. An expression is derived for the magnitude of such induced currents at a sloping boundary, with possible application to the generation of weak currents often observed in the benthic boundary layers of the deep ocean.

When the fluid below a buoyancy interface such as the seasonal thermocline in the ocean is stably stratified as it is often, energy radiation by internal waves into regions deep below is possible. In this paper, the dispersion relation for a sharp thermocline separating a well-mixed layer from a weakly but stably stratified fluid below is derived and examined for such energy leakage into the fluid below. It is found that the interfacial waves running along such a buoyancy interface leak their energy to radiating internal waves and are rapidly attenuated, if their frequency is less than the buoyancy frequency of the fluid below. The implications the leaky nature of the modes have on resonant excitation of internal waves in the ocean by atmospheric pressure fluctuations and turbulence in the mixed layer are also examined. It is found that efficient resonant build up of interfacial waves is possible only for nonleaky modes and even then their growth rate is modified slightly by the presence of stratified fluid below the interface.

Combined effects of stratification and rotation on vertical mixing and the characteristics of associated small-scale turbulence are explored using second-moment closure methodology; the rotational terms in the equations for Reynolds stresses and turbulent heat fluxes are retained, not ignored as in earlier works. Semianalytical results valid for arbitrary values of rotation and stratification are derived by further invoking the local equilibrium limit of closure. Two cases are considered: nonzero vertical rotation and nonzero meridional rotation; the latter case is of more general interest in geophysics because of its potential application to equatorial mixed layers. In both cases the influence of rotation on mixing coefficients and Monin-Obukhov constant flux layer similarity relations is investigated for arbitrary values of rotation and stratification. In both cases, turbulent mixing coefficients assume tensorial properties. However, meridional rotation appears to have a stronger influence on vertical mixing and turbulence characteristics than does vertical rotation. These results, along with perturbation expansions for weak rotation, suggest that for geophysical flows, in most cases, the direct effect of rotation on vertical turbulent mixing itself is but a small correction, a few tens of percent at best. It is seldom large, although it might not be negligible in some particular cases. Nevertheless, the study of rotational effects on small-scale turbulence provides a fascinating insight into the direct impact of rotation on the characteristics of small-scale turbulence and mixing in stratified fluids; the results are also of interest in other fields such as engineering.

A two-dimensional coupled ice-ocean model has been formulated and applied to the wintertime Bering Sea marginal ice zone. The oceanic component is a multilevel model that incorporates second-moment closure for turbulent mixing in the water column. The ice cover is modeled as a viscous-plastic continuum. Melting at the ice-ocean interface is computed using well-known lawof-the-wall concepts in a turbulent boundary layer, with particular attention to the disparate momentum and scalar transfer resistance coefficients over rough walls. The thermodynamic and dynamical interactions between the ocean and the ice cover and the energy balances at the air-ice and air-sea interfaces are modeled according to the companion paper (Mellor and Kantha, this issue). The model incorporates barotropic tides, both diurnal and semidiurnal, for application to the Bering Shelf. Double-diffusive fluxes across the interface between the colder, fresher layer beneath the melting ice and the warmer, more saline water underneath are prescribed from laboratory data on double-diffusive convection. During winter, sea ice in the central Bering Sea is transported toward the shelf break by off-ice winds, where it encounters northward flowing warmer north Pacific waters and melts. It is this situation to which the two-dimensional model has been applied by neglecting all variations in the along-ice-edge direction. The water conditions downstream of the ice edge, the ice conditions upstream, and the wind stress are the primary inputs to the model. The model simulates transition from ice-covered to open ocean conditions and the associated ice edge front and the two-layer circulation underneath the ice cover. Sensitivity studies indicate that the density structure and the circulation beneath the ice and the position of the ice edge are rather sensitive to the parameters affecting the dynamics and the thermodynamics of the coupled ice-ocean system. Even small changes in the relevant parameters can cause a substantial retreat or advance of the ice edge, which may help explain why marginal ice zones are such dynamically active regions.

An ice model, an ocean model, and a method of coupling the models are described. The ice model is a synthesis, with variations and extensions, of previous modeling ideas. Ice thickness, concentration, velocity, and internal energy are prognostic variables. The ice thermodynamics are represented by temperatures at the snow surface, ice surface, the interior, and the bottom surface. Melting and freezing rates are calculated at the ice-atmosphere, ice-ocean, and atmosphere-ocean interfaces. A prescribed portion of summer meltwater can be stored on the surface and refrozen in the fall. The ocean model includes a second moment, turbulence closure submodel and enables one to solve for oceanic heat flux, the interfacial stress, and subsurface properties. In this paper the model is applied to one-dimensional simulations, but the equations are cited in a form for implementation by two- and three-dimensional models. In a companion paper (Kantha and Mellor, this issue) the model is used for two-dimensional (vertical plane) simulations in the Bering Sea. Several one-dimensional sensitivity studies are performed in the case where the ice model is decoupled from the ocean; here the oceanic heat flux and sea surface temperature are prescribed constants. The studies reveal the role and sensitivity of surface trapped meltwater, ice concentration, and ice divergence. With the coupled ice-ocean model, the seasonally varying oceanic heat flux and mixed layer properties are determined by the model. Some comparisons with observations in the central Arctic ocean are possible. The role of the molecular sublayer immediately adjacent to the ice is examined; frazi! ice production is related to the large disparity in the molecular diffusivities for temperature and salinity. The mixed layer model contains empirical constants which are known from turbulence data. The molecular sublayer parameterization requires one empirical parameter b, which is uncertain but, from this study, is assuredly greater than zero, the value implicit in previous models. The ice model requires the empirical parameters cI) F and cI)u to quantitatively account for freezing or melting processes in open leads; their values are also uncertain, but we present reasoning and sensitivity studies to suggest specific values. Finally, an empirical parameter G is introduced; it is the ratio of the value of the ice thickness used to represent average ice volume in the dynamic and thermodynamic equations to the value of the thickness needed in the heat conduction equation. Estimates of G are made from observed thickness distribution functions; sensitivity studies show it to be an important parameter.

A two-dimensional, multilevel model for simulating changes in the atmospheric boundary layer across a marginal ice zone is described and applied to off-ice, on-ice, and along-ice edge wind conditions. The model incorporates a second-moment closure for parameterizing the intensification and suppression of turbulent mixing in the boundary layer due to stratification effects. For off-ice winds, as the atmospheric boundary layer passes from cold smooth ice onto warm open water, the onset of intense convection raises the inversion. Over the transition zone of rough rafted ice with open leads, the shear stress on the ice cover increases significantly before dropping down to the downstream values over water. Such nonmonotonic surface stress could be the cause of divergence of sea ice near the ice edge in a marginal ice zone. These results are in agreement with the one-layer model simulations of off-ice winds by Overland et al. (1983). For on-ice wind conditions, as the warm flow in the boundary layer encounters the cold ice conditions, the resulting stable stratification could rapidly suppress the turbulence in the boundary layer, leading to the development of a shallow inversion and an associated jet. When the wind is predominantly along the ice edge, the temperature contrast between the open water and the ice could produce a thermal front at the ice edge in the boundary layer with strong associated turbulence. More observations are needed to verify these model predictions. Nevertheless, these model results suggest that it is important to account for the changes in the characteristics of the atmospheric boundary layer across the marginal ice zone in our attempts to understand the behavior of the ice cover in these regions.