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.

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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; frazil 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 ΦF and ΦM 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.

Mixing in the free atmosphere above the planetary boundary layer is of great importance to the fate of trace gases and pollutants. However, direct measurements of the turbulent dissipation rate by in situ probes are very scarce and radar measurements are fraught with uncertainties. In this paper, turbulence scaling concepts, developed over the past decades for application to oceanic mixing, are used to suggest an alternative technique for retrieving turbulence properties in the free atmosphere from high-resolution soundings. This technique enables high-resolution radiosondes, which have become quite standard in the past few years, to be used not only to monitor turbulence in the free atmosphere in near-real time, but also to study its spatiotemporal characteristics from the abundant archives of high-resolution soundings from around the world. Examples from several locations are shown, as well as comparisons with radar-based estimations and a typical Richardson number-based parameterization.

In this study, a coupled atmosphere-ocean wave modeling system is used to simulate air-sea interaction under high wind conditions. This coupled modeling system is made of three well-tested model components: The Pennsylvania State University-National Center for Atmospheric Research regional atmospheric Mesoscale Model, the University of Colorado version of the Princeton Ocean Model, and the ocean surface gravity wave model developed by the Wave Model Development and Implementation Group. The ocean model is initialized using a 9-month spinup simulation forced by 6-hourly wind stresses and with assimilation of satellite sea surface temperature (SST) and altimetric data into the model. The wave model is initialized using a zero wave state. The scenario in which the study is carried out is the intensification of a simulated hurricane passing over the Gulf of Mexico. The focus of the study is to evaluate the impact of sea spray, mixing in the upper ocean, warm-core oceanic eddies shed by the Gulf Loop Current, and the sea surface wave field on hurricane development, especially the intensity. The results from the experiments with and without sea spray show that the inclusion of sea spray evaporation can significantly increase hurricane intensity in a coupled air-sea model when the part of the spray that evaporates is only a small fraction of the total spray mass. In this case the heat required for spray evaporation comes from the ocean. When the fraction of sea spray that evaporates increases, so that the evaporation extracts heat from the atmosphere and cools the lower atmospheric boundary layer, the impact of sea spray evaporation on increasing hurricane intensity diminishes. It is shown that the development of the simulated hurricane is dependent on the location and size of a warm-core anticyclonic eddy shed by the Loop Current. The eddy affects the timing, rate, and duration of hurricane intensification. This dependence occurs in part due to changes in the translation speed of the hurricane, with a slower-moving hurricane being more sensitive to a warm-core eddy. The feedback from the SST change in the wake of the simulated hurricane is negative so that a reduction of SST results in a weaker-simulated hurricane than that produced when SST is held unchanged during the simulation. The degree of surface cooling is strongly dependent on the initial oceanic mixed layer (OML) depth. It is also found in this study that in order to obtain a realistic thermodynamic state of the upper ocean and not distort the evolution of the OML structure during data assimilation, care must be taken in the data assimilation procedure so as not to interfere with the turbulent dynamics of the OML. Compared with the sensitivity to the initial OML depth and the location and intensity of the warm eddy associated with the loop current, the model is found to be less sensitive to the wave-age-dependent roughness length.

Turbulent entrainment at the density interface of a stable two-layer stratified fluid is studied in the laboratory, a constant surface stress being applied at the free surface. Conservation of mass requires that the overall Richardson number Ri = Dgδρ/ρu*2 is constant in each experiment, where D is the depth of the mixed layer, gδρ/ρ the buoyancy difference and u* the friction velocity. If the entrainment rate E = ue/u* is a function only of Ri, it is therefore constant in each experiment and can be measured with a greater accuracy than has previously been attained. The functional dependence of ue/u* on Ri is established over the range 30 < Ri < 1000; it is found not to follow any simple power law. The entrainment rates are considerably higher than those measured by Kato & Phillips (1969), for which the fluid below the mixed layer was linearly stratified. Such a condition allows internal gravity waves to be radiated downwards and the reduction in entrainment rate is consistent with that found by Linden (1975).

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