Entrainment Parameterization Research Articles

The role of the deep mixing in the Storfjorden shelf water plume

Hydrographic observations in deep Fram Strait evidence a plume of Storfjorden Brine-enriched Shelf Water in 1986, 1988 and 2002. The plume spreads along the continental slope over 600 km away from its formation area and reaches 2000 m depth. The plume is 30 to 80 m thick in the deep layer of Fram Strait; it is almost 0.4 °C warmer and 0.06 more saline than the ambient water. The velocity of the plume, observed by a moored current meter in Fram Strait, is 12.60±4.70 cm s −1 .The hydrographic properties of the plume are used to study entrainment. A streamtube model with four entrainment parameterizations is applied. Two Froude-number dependent parameterizations lead to mixing mostly happening over the shelf break, where the Froude number is large. This is in agreement with the traditional view, but is inconsistent with the observed temperature and salinity of the Storfjorden plume. Therefore further entrainment assumptions (a constant and a volume-dependent entrainment) are tested. The volume-dependent entrainment scheme yields the best representation of entrainment in the Storfjorden plume. Our results emphasize the necessity of strong mixing in the deep layers in Fram Strait to achieve an agreement with observed properties of the plume.

A Higher-Order Closure Model with an Explicit PBL Top

Abstract In 2001, the authors presented a higher-order mass-flux model called “assumed distributions with higher-order closure” (ADHOC 1), which represents the large eddies of the planetary boundary layer (PBL) in terms of an assumed joint distribution of the vertical velocity and scalars. In a subsequent version (ADHOC 2) the authors incorporated vertical momentum fluxes and second moments involving pressure perturbations into the framework. These versions of ADHOC, as well as all other higher-order closure models, are not suitable for use in large-scale models because of the high vertical and temporal resolution that is required. This high resolution is needed mainly because higher-order closure (HOC) models must resolve discontinuities at the PBL top, which can occur anywhere on a model’s Eulerian vertical grid. This paper reports the development of ADHOC 3, in which the computational cost of the model is reduced by introducing the PBL depth as an explicit prognostic variable. ADHOC 3 uses a stretched vertical coordinate that is attached to the PBL top. The discontinuous jumps at the PBL top are “hidden” in the layer edge that represents the PBL top. This new HOC model can use much coarser vertical resolution and a longer time step and is thus suitable for use in large-scale models. To predict the PBL depth, an entrainment parameterization is needed. In the development of the model, the authors have been led to a new view of the old problem of entrainment parameterization. The relatively detailed information available in the HOC model is used to parameterize the entrainment rate. The present approach thus borrows ideas from mixed-layer modeling to create a new, more economical type of HOC model that is better suited for use as a parameterization in large-scale models.

Impact of entrainment from overshooting thermals on land–atmosphere interactions during summer 1999

The depth of the planetary boundary layer (PBL) or mixed layer is important for carbon dioxide source/sink estimation because the response of atmospheric carbon dioxide concentration to a given amount of surface flux is inversely proportional to this depth. The PBL depth is affected by entrainment from overshooting thermals that is often underestimated in mesoscale meteorological models. An experiment was performed for the late summer of 1999 that includes a parameterization of PBL top entrainment that is based on a downward buoyancy flux at the top of the PBL. Simulations with this parameterization produce a warmer, drier and deeper boundary layer than a control simulation. The monthly mean diurnal cycle of PBL depth at a location in northernWisconsin is better simulated with this enhanced entrainment when compared to observations. The altered atmospheric conditions cause the vegetation’s stomata to respond and possibly close in an evolved response to limit water loss, thus reducing transpiration and shifting the Bowen ratio. The stomatal closing also reduces carbon assimilation, consequently altering horizontal and vertical carbon gradients. The overall effect of enhanced PBL entrainment is to alter time–mean regional gradients in CO2 mixing ratio by as much as 7 ppmv over 1000 km.

On the parameterization of convective entrainment: Inherent relationships among entrainment parameters in bulk models

In this paper, the equilibrium entrainment into a shear-free, linearly stratified atmosphere is discussed under the framework of bulk models, namely, the zero-order jump model (ZOM) and the first-order jump model (FOM). The parameterizations for the dimensionless entrainment rate versus the convective Richardson number in the two models are compared. Based on the assumption that the parameterized entrainment rates in ZOM and FOM should be the same, the inherent relationships among the entrainment parameters in the bulk models are revealed. These relationships are supported by tank experiments and large-eddy simulations. The validity of these inherent relationships indicates that, for a convective boundary layer growing into a linearly stratified free atmosphere, the only dominant factors of the growth rate are the turbulent buoyancy in the mixed layer and the stratification in the free atmosphere. In the point of the similarity view, the former is characterized by turbulent temperature and mixing length scales (mixed layer depth), and the latter is characterized by the lapse rate of potential temperature in the free atmosphere. Thus, the commonly-used Richardson number scheme for the parameterization of the entrainment rate is just as an equivalent description. The variability of the total entrainment flux ratio in FOM, which is connected with the entrainment zone thickness, can implicitly describe the effect of the stratification in the free atmosphere, but the entrainment zone thickness is not an independent parameter. These results demonstrate the validity of the hypothesis that there exists a similarity limit in which the mixed layer depth is the only lengthscale.

Sensitivity of Land‐Atmosphere Exchanges to Overshooting PBL Thermals in an Idealized Coupled Model

The response of atmospheric carbon dioxide to a given amount of surface flux is inversely proportional to the depth of the planetary boundary layer (PBL). Overshooting thermals that entrain free tropospheric air down into the boundary layer modify the characteristics and depth of the mixed layer through the insertion of energy and mass. In addition, entrainment “dilutes” the effects of surface fluxes on scalar quantities (temperature, water vapor, carbon dioxide, etc.) in the PBL. Therefore, incorrect simulation of PBL depth can lead to linear errors in estimates of carbon dioxide fluxes in inverse models. Dilution by entrainment directly alters the surface‐air gradients in scalar properties, which serve as the “driving force” for surface fluxes. In addition, changes in near‐surface temperature and water vapor affect surface fluxes through physiological processes in plant canopies (e.g. stomatal conductance). Although overshooting thermals are important in the physical world, their effects are unresolved in most regional models. We explore the sensitivity of surface fluxes and PBL scalars to the intensity of PBL top entrainment by manipulating its strength in an idealized version of the coupled SiB‐RAMS model. An entrainment parameterization based on the virtual potential temperature flux at the surface is implemented into SiB‐RAMS to produce a warmer and drier mixed layer, to alter the surface fluxes, and to increase the depth of the PBL. These variations produce modified CO2 concentrations and vary with the strength of the parameterized entrainment.

On the rise of turbulent plumes: Quantitative effects of variable entrainment for submarine hydrothermal vents, terrestrial and extra terrestrial explosive volcanism

The maximum height reached by a turbulent plume rising in a stratified environment is a key tool to estimate the flux released at its source, particularly for large‐scale flows because flux can often be very hard to measure directly. This height is known to be mainly controlled by the stratification of the ambient fluid, source buoyancy flux, and the efficiency of turbulent mixing between the plume and the external fluid. The latter effect has been only superficially explored in spite of its fundamental control on the dynamics. Here we show that commonly used one‐dimensional models incorporating a constant entrainment coefficient do not provide satisfying predictions. We propose a new model allowing for variable entrainment which gives excellent predictions of maximum heights reached by laboratory plumes in stratified environments. We then apply our formalism to natural plumes produced by explosive volcanic eruptions under terrestrial, paleo‐Martian, and Venusian conditions and by submarine hydrothermal activity at mid‐ocean ridges. Source mass discharge rates deduced from maximum volcanic column heights for terrestrial eruptions are found to be greater than those estimated with the commonly used constant entrainment parameterization by a factor of 2. In the paleo‐Martian atmosphere, existing models overestimate plume heights by 14–27%. In the current atmosphere of Venus, the maximum height reached by a volcanic plume is also found to be smaller than previously estimated for large eruption rates. The source heat flux released by the TAG field (Atlantic Ocean) deduced from several submarine hydrothermal plumes is found greater by a factor 3 with our model.

Implementation of a windblown dust parameterization into MODELS-3/CMAQ: Application to episodic PM events in the US/Mexico border

Windblown dust is known to impede visibility, deteriorate air quality and modify the radiation budget. Arid and semiarid areas with unpaved and unvegetated land cover are particularly prone to windblown dust, which is often attributed to high particulate matter (PM) pollution in such areas. Yet, windblown dust is poorly represented in existing regulatory air quality models. In a study by the authors on modeling episodic high PM events along the US/Mexico border using the state-of-the-art CMAQ/MM5/SMOKE air quality modeling system [Choi, Y.-J., Hyde, P., Fernando, H.J.S., 2006. Modeling of episodic particulate matter events using a 3D air quality model with fine grid: applications to a pair of cities in the US/Mexico border. Atmospheric Environment 40, 5181–5201], some of the observed PM 10 NAAQS exceedances were inferred as due to windblown dust, but the modeling system was incapable of dealing with time-dependent episodic dust entrainment during high wind periods. In this paper, a time-dependent entrainment parameterization for windblown dust is implemented in the CMAQ/MM5/SMOKE modeling system with the hope of improving PM predictions. An approach for realizing windblown dust emission flux for each grid cell over the study domain on an hourly basis, which accounts for the influence of factors such as soil moisture content, atmospheric stability and wind speed, is presented in detail. Comparison of model predictions with observational data taken at a pair of US/Mexico border towns shows a clear improvement of model performance upon implementation of the dust emission flux parameterization.

Numerical Simulation of the Red Sea Outflow Using HYCOM and Comparison with REDSOX Observations

Abstract The outflow of warm, salty, and dense water from the Red Sea into the western Gulf of Aden is numerically simulated using the Hybrid Coordinate Ocean Model (HYCOM). The pathways of the modeled overflow, temperature, salinity, velocity profiles from stations and across sections, and transport estimates are compared to those observed during the 2001 Red Sea Outflow Experiment. As in nature, the simulated outflow is funneled into two narrow channels along the seafloor. The results from the three-dimensional simulations show a favorable agreement with the observed temperature and salinity profiles along the channels. The volume transport of the modeled overflow increases with the increasing distance from the southern exit of the Bab el Mandeb Strait due to entrainment of ambient fluid, such that the modeled transport shows a reasonable agreement with that estimated from the observations. The initial propagation speed of the outflow is found to be smaller than the estimated interfacial wave speed. The slow propagation is shown to result from the roughness of the bottom topography characterized by a number of depressions that take time to be filled with outflow water. Sensitivities of the results to the horizontal grid spacing, different entrainment parameterizations, and forcing at the source location are investigated. Because of the narrow widths of the approximately 5 km of the outflow channels, a horizontal grid spacing of 1 km or less is required for model simulations to achieve a reasonable agreement with the observations. Comparison of two entrainment parameterizations, namely, TPX and K-profile parameterization (KPP), show that similar results are obtained at 1-km resolution. Overall, the simulation of the Red Sea outflow appears to be more strongly affected by the details of bottom topography and grid spacing needed to adequately resolve them than by parameterizations of diapycnal mixing.

A regional modeling study of the entraining Mediterranean outflow

We have evaluated a regional‐scale simulation of the Mediterranean outflow by comparison with field data obtained in the 1988 Gulf of Cádiz Expedition. Our ocean model is based upon the Hybrid Coordinate Ocean Model (HYCOM) and includes the Richardson number–dependent entrainment parameterization of Xu et al. (2006). Given realistic topography and sufficient resolution, the model reproduces naturally the major, observed features of the Mediterranean outflow in the Gulf of Cádiz: the downstream evolution of temperature, salinity, and velocity profiles, the mean path and the spreading of the outflow plume, and most importantly, the localized, strong entrainment that has been observed to occur just west of the Strait of Gibraltar. As in all numerical solutions, there is some sensitivity to horizontal and vertical resolution. When the resolution is made coarser, the simulated currents are less vigorous and there is consequently less entrainment. Our Richardson number–dependent entrainment parameterization is therefore not recommended for direct application in coarse‐resolution climate models. We have used the high‐resolution regional model to investigate the response of the Mediterranean outflow to a change in the freshwater balance over the Mediterranean basin. The results are found in close agreement with the marginal sea boundary condition (MSBC): A more saline and dense Mediterranean deep water generates a significantly greater volume transport of the Mediterranean product water having only very slightly greater salinity.

Parameterization of Entrainment in a Sheared Convective Boundary Layer Using a First-order Jump Model

Basic entrainment equations applicable to the sheared convective boundary layer (CBL) are derived by assuming an inversion layer with a finite depth, i.e., the first-order jump model. Large-eddy simulation data are used to determine the constants involved in the parameterizations of the entrainment equations. Based on the integrated turbulent kinetic energy budget from surface to the top of the CBL, the resulting entrainment heat flux normalized by surface heat flux is a function of the inversion layer depth, the velocity jumps across the inversion layer, the friction velocity, and the convection velocity. The developed first-order jump model is tested against large-eddy simulation data of two independent cases with different inversion strengths. In both cases, the model reproduces quite reasonably the evolution of the CBL height, virtual potential temperature, and velocity components in the mixed layer and in the inversion layer.

Dynamics of Sheared Convective Boundary Layer Entrainment. Part II: Evaluation of Bulk Model Predictions of Entrainment Flux

Abstract Several bulk model–based entrainment parameterizations for the atmospheric convective boundary layer (CBL) with wind shear are reviewed and tested against large-eddy simulation (LES) data to evaluate their ability to model one of the basic integral parameters of convective entrainment—the entrainment flux ratio. Test results indicate that many of these parameterizations fail to correctly reproduce entrainment flux in the presence of strong shear because they underestimate the dissipation of turbulence kinetic energy (TKE) produced by shear in the entrainment zone. It is also found that surface shear generation of TKE may be neglected in the entrainment parameterization because it is largely balanced by dissipation. However, the surface friction has an indirect effect on the entrainment through the modification of momentum distribution in the mixed layer and regulation of shear across the entrainment zone. Because of this effect, parameterizations that take into account the surface friction velocity but exclude entrainment zone shear may sufficiently describe entrainment when wind shear in the free atmosphere above the CBL is small. In this case, the surface shear acts as a proxy for the entrainment zone shear. Such parameterizations can be most useful if applied in situations where atmospheric data are insufficient for calculating entrainment zone shear. The importance of modeling a Richardson-number-limited, finite-depth entrainment zone is evidenced by the relatively accurate entrainment flux predictions by models that explicitly account for effects of entrainment zone shear, but predictions by these models are often adversely affected by the underestimation of TKE dissipation in the entrainment zone.

The route to self-similarity in turbulent jets and plumes

The description of entrainment in turbulent free jets is at the heart of physical models of some major flows in environmental science, from volcanic plumes to the dispersal of pollutant wastes. The classical approach relies on the assumption of complete self-similarity in the flows, which allows a simple parameterization of the dynamical variables in terms of constant scaling factors, but this hypothesis remains under debate. We use in this paper an original parameterization of entrainment and an extensive review of published experimental data to interpret the discrepancy between laboratory results in terms of the systematic evolution of the dynamic similarity of the flow as a function of downstream distance from the source. We show that both jets and plumes show a variety of local states of partial self-similarity in accordance with the theoretical analysis of George (1989), but that their global evolution tends to complete self-similarity via a universal route. Plumes reach this asymptotic regime faster than jets which suggests that buoyancy plays a role in more efficiently exciting large-scale modes of turbulence.

Turbulent entrainment in jets with arbitrary buoyancy

Explosive volcanic jets present an unusual dynamic situation of reversing buoyancy. Their initially negative buoyancy with respect to ambient fluid first opposes the motion, but can change sign to drive a convective plume if a sufficient amount of entrainment occurs. The key unknown is the entrainment behaviour for the initial flow regime in which buoyancy acts against the momentum jet. To describe and constrain this regime, we present an experimental study of entrainment into turbulent jets of negative and reversing buoyancy. Using an original technique based on the influence of the injection radius on the threshold between buoyant convection and partial collapse, we show that entrainment is significantly reduced by negative buoyancy. We develop a new theoretical parameterization of entrainment as a function of the local (negative) Richardson number that (i) predicts the observed reduction of entrainment and (ii) introduces a similarity drift in the velocity and buoyancy profiles as a function of distance from source. This similarity drift allows us to reconcile the different estimates found in the literature for entrainment in plumes.

Comparison of entrainment in overflows simulated by z-coordinate, isopycnal and non-hydrostatic models

A series of idealised numerical simulations of dense water flowing down a broad uniform slope are presented, employing both a z-coordinate model (the MIT general circulation model) and an isopycnal coordinate model (the Hallberg Isopycnal Model). Calculations are carried out at several different horizontal and vertical resolutions, and for a range of physical parameters. A subset of calculations are carried out at very high resolution using the non-hydrostatic variant of the MITgcm. In all calculations dense water descends the slope while entraining and mixing with ambient fluid. The dependence of entrainment, mixing and down-slope descent on resolution and vertical coordinate are assessed. At very coarse resolutions the z-coordinate model generates excessive spurious mixing, and dense water has difficulty descending the slope. However, at intermediate resolutions the mixing in the z-coordinate model is less than found in the high-resolution non-hydrostatic simulations, and dense water descends further down the slope. Isopycnal calculations show less resolution dependence, although entrainment and mixing are both reduced slightly at coarser resolution. At intermediate resolutions the z-coordinate and isopycnal models produce similar levels of mixing and entrainment. These results provide a benchmark against which future developments in overflow entrainment parameterizations in both z-coordinate and isopycnal models may be compared.

Comparison of gravity current mixing parameterizations and calibration using a high-resolution 3D nonhydrostatic spectral element model

In light of the pressing need for development and testing of reliable parameterizations of gravity current entrainment in ocean general circulation models, two existing entrainment parameterization schemes, K-profile parameterization (KPP) and one based on Turner’s work (TP), are compared using idealized experiments of dense water flow over a constant-slope wedge using the HYbrid Coordinate Ocean Model (HYCOM). It is found that the gravity current entrainment resulting from KPP and TP differ significantly from one another. Parameters of KPP and TP are then calibrated using results from the high-order nonhydrostatic spectral element model Nek5000. It is shown that a very good agreement can be reached between the HYCOM simulations with KPP and TP, even though these schemes are quite different from each other.

A model for the spreading and sinking of the Deep Ice Shelf Water in the Ross Sea

Spreading and sinking of the Deep Ice Shelf Water (DISW) in the Ross Sea are analysed using in situ observations and the results of a nonlinear, reduced gravity, layered numerical model, which is able to simulate the motion of a bottom trapped current over realistic topography. The model is forced by prescribing thickness and density of the DISW layer at the southern model boundary as well as ambient density stratification above the DISW layer. This density structure is imposed using hydrographic data acquired by the Italian PNRA-CLIMA project. In the model water of the quiescent ambient ocean is allowed to entrain in the active deep layer due to a simple entrainment parameterization. The importance of forcing the model with a realistic ambient density is demonstrated by carrying out a numerical simulation using an idealized ambient density. In a more realistic simulation the path and the density structure of the DISW vein flowing over the Challenger Basin are obtained and are found to be in good agreement with data. It is found that entrainment, which is particularly active in regions of strong topographic variation, significantly influences the pattern followed by the DISW layer. The evolution of the DISW layer beyond the continental shelf, i.e., in a region where the paucity of experimental data does not allow for a detailed description of the deep ocean dynamics, is also investigated.

Numerical simulations of the Mediterranean sea outflow: impact of the entrainment parameterization in an isopycnic coordinate ocean model

Gravity current entrainment is essential in determining the properties of the interior ocean water masses that result from marginal sea overflows. Although the individual entraining billows will be unresolvable in large-scale ocean models for the foreseeable future, some large-scale simulations are now being carried out that do resolve the intermediate scale environment which may control the rate of entrainment. Hallberg [Mon. Wea. Rev. 128 (2000) 1402] has recently developed an implicit diapycnal mixing scheme for isopycnic coordinate ocean models that includes the Richardson number dependent entrainment parameterization of Turner [J. Fluid Mech. 173 (1986) 431], and which may be capable of representing the gravity current evolution in large-scale ocean models. The present work uses realistic regional simulations with the Miami Isopycnic Coordinate Ocean Model (MICOM) to evaluate ability of this scheme to simulate the entrainment that is observed to occur in the bottom boundary currents downstream of the Mediterranean outflow. These simulations are strikingly similar to the observations, indicating that this scheme does produce realistic mixing between the Mediterranean outflow and the North Atlantic Central Water. Sensitivity studies identify the critical Richardson number below which vigorous entrainment occurs as a particularly important parameter. Some of these experiments also show meddies detaching from the Mediterranean undercurrent at locations that appear to be highly influenced by topographic features.

A New Boundary Layer Mixing Scheme. Part I: Scheme Description and Single-Column Model Tests

A new boundary layer turbulent mixing scheme has been developed for use in the UKMO weather forecasting and climate prediction models. This includes a representation of nonlocal mixing (driven by both surface fluxes and cloud-top processes) in unstable layers, either coupled to or decoupled from the surface, and an explicit entrainment parameterization. The scheme is formulated in moist conserved variables so that it can treat both dry and cloudy layers. Details of the scheme and examples of its performance in single-column model tests are presented.

Entrainment Parameterization in Convective Boundary Layers

Abstract Various runs were performed with a large eddy simulation (LES) model to evaluate different types of entrainment parametrizations. For this evaluation, three types of boundary layers were simulated: a clear convective boundary layer (CBL), a boundary layer containing a smoke concentration, and a cloud-topped boundary layer. It is shown that the assumption that the entrainment flux equals the product of the entrainment rate and the jump over a discontinuous inversion is not valid in CBLs simulated by an LES model. A finite inversion thickness (i.e., a first-order jump model) is needed to define an entrainment flux for which this approximation of the flux is valid. This entrainment flux includes not only the buoyancy flux at the inversion, but also the surface heat flux. The parameterization of the buoyancy flux at the inversion is evaluated for different closures, as suggested in the literature (i.e., Eulerian partitioning, process partitioning, and a closure developed by Deardorff), and where need...

A study of the seasonal cycle of sea surface temperature in the tropical Pacific Ocean using reduced gravity models

A simple model of the upper ocean is used to simulate the seasonal cycle of sea surface temperature (SST) in the tropical Pacific Ocean. The model is an extension of the conventional 1½‐layer reduced gravity system that includes the physics of the surface mixed layer and allows prediction of the sea surface temperature. Two types of mixed layer models, a constant depth mixed layer model of Cane and Zebiak and a variable depth mixed layer model of Kraus and Turner, are examined. The numerical simulations indicate that the simple models are capable of capturing the essential seasonal SST variability in the tropical Pacific when forced with climatological surface forcing. The sensitivity study of model SST response to changes in the surface forcing demonstrates that although the response to surface heat flux forcing dominates the seasonal cycle of SST in most areas of the tropical Pacific, the dynamical response of the ocean to changes in the wind also makes a significant contribution to the seasonal variation of SST in the eastern equatorial Pacific. The seasonal variation of the winds is particularly important in maintaining the phase structure of the annual SST signal along the equator. Moreover, the sensitivity of the SST response depends on the form of vertical entrainment parameterization in the model. It is shown that the Cane‐Zebiak type of model has a bias toward the dynamical response of the ocean to the winds, whereas the Kraus‐Turner type of model has bias toward the surface heat flux variations. The simple model results are also compared with those from an ocean general circulation model.