On the entrainment assumption in Schatzmann's integral plume model

The behaviour of stationary, non-passive plumes can be simulated in a reasonably simple and accurate way by integral models. One of the key requirements of these models, but also one of their less well-founded aspects, is the entrainment assumption, which parameterizes turbulent mixing between the plume and the environment. The entrainment assumption developed by Schatzmann and adjusted to a set of experimental results requires four constants and an ad hoc hypothesis to eliminate undesirable terms. With this assumption, Schatzmann’s model exhibits numerical instability for certain cases of plumes with small velocity excesses, due to very fast radius growth. The purpose of this paper is to present an alternative entrainment assumption based on a first-order turbulence closure, which only requires two adjustable constants and seems to solve this problem. The asymptotic behaviour of the new formulation is studied and compared to previous ones. The validation tests presented by Schatzmann are repeated and it is found that the new formulation not only eliminates numerical instability but also predicts more plausible growth rates for jets in co-flowing streams.

Effect of shear rupture on aggregate scale formation in sea ice

A discrete element model is used to study shear rupture of sea ice under convergent wind stresses. The model includes compressive, tensile, and shear rupture of viscous elastic joints connecting floes that move under the action of the wind stresses. The adopted shear rupture is governed by Coulomb’s criterion. The ice pack is a 400 km long square domain consisting of 4 km size floes. In the standard case with tensile strength 10 times smaller than the compressive strength, under uniaxial compression the failure regime is mainly shear rupture with the most probable scenario corresponding to that with the minimum failure work. The orientation of cracks delineating formed aggregates is bimodal with the peaks around the angles given by the wing crack theory determining diamond-shaped blocks. The ice block (floe aggregate) size decreases as the wind stress gradient increases since the elastic strain energy grows faster leading to a higher speed of crack propagation. As the tensile strength grows, shear rupture becomes harder to attain and compressive failure becomes equally important leading to elongation of blocks perpendicular to the compression direction and the blocks grow larger. In the standard case, as the wind stress confinement ratio increases the failure mode changes at a confinement ratio within 0.2–0.4, which corresponds to the analytical critical confinement ratio of 0.32. Below this value, the cracks are bimodal delineating diamond shape aggregates, while above this value failure becomes isotropic and is determined by small-scale stress anomalies due to irregularities in floe shape.

Influence of the Antarctic ozone hole on the polar mesopause region as simulated by the Canadian Middle Atmosphere Model

It is well established that variations in polar stratospheric winds can affect mesospheric temperatures through changes in the filtering of gravity wave fluxes, which drive a residual circulation in the mesosphere. The Canadian Middle Atmosphere Model(CMAM) is used to examine this vertical coupling mechanism in the context of the mesospheric response to the Antarctic ozone hole. It is found that the response differs significantly between late spring and early summer, because of a changing balance between the competing effects of parametrised gravity wavedrag (GWD)and changes in resolved wave drag local to the mesosphere. In late spring, the strengthened stratospheric westerlies arising from the ozone hole lead to reduced eastward GWD in the mesosphere and a warming of the polar mesosphere, just as in the well known mesospheric response to sudden stratospheric warmings, but with an opposite sign.In early summer, with easterly flow revailing over most of the polar stratosphere,the strengthened easterly wind shear within the mesosphere arising from the west ward GWD anomaly induces a positive resolved wave drag anomaly through baroclinic instability. The polar cooling induced by this process completely dominates the upper mesospheric response to the ozone hole in early summer. Consequences for the past and future evolution of noctilucent clouds are discussed

On the potential of assimilating meteorological analyses in a global climate model for the purpose of model validation

A simple four-dimensional assimilation technique, called Newtonian relaxation, has been applied to the Hamburg climate model (ECHAM), to enable comparison of model output with observations for short periods of time. The prognostic model variables vorticity, divergence, temperature, and surface pressure have been relaxed toward European Center for Medium-Range Weather Forecasts (ECMWF) global meteorological analyses. Several experiments have been carried out, in which the values of the relaxation coefficients have been varied to find out which values are most usable for our purpose. To be able to use the method for validation of model physics or chemistry, good agreement of the model simulated mass and wind field is required. In addition, the model physics should not be disturbed too strongly by the relaxation forcing itself. Both aspects have been investigated. Good agreement with basic observed quantities, like wind, temperature, and pressure is obtained for most simulations in the extratropics. Derived variables, like precipitation and evaporation, have been compared with ECMWF forecasts and observations. Agreement for these variables is smaller than for the basic observed quantities. Nevertheless, considerable improvement is obtained relative to a control run without assimilation. Differences between tropics and extratropics are smaller than for the basic observed quantities. Results also show that precipitation and evaporation are affected by a sort of continuous spin-up which is introduced by the relaxation: the bias (ECMWF-ECHAM) is increasing with increasing relaxation forcing. In agreement with this result we found that with increasing relaxation forcing the vertical exchange of tracers by turbulent boundary layer mixing and, in a lesser extent, by convection, is reduced.

A Lagrangian model of air-mass photochemistry and mixing using a trajectory ensemble: the Cambridge Tropospheric Trajectory model of Chemistry And Transport (CiTTyCAT) version 4.2

A Lagrangian model of photochemistry and mixing is described (CiTTyCAT, stemming from the Cambridge Tropospheric Trajectory model of Chemistry And Transport), which is suitable for transport and chemistry studies throughout the troposphere. Over the last five years, the model has been developed in parallel at several different institutions and here those developments have been incorporated into one "community" model and documented for the first time. The key photochemical developments include a new scheme for biogenic volatile organic compounds and updated emissions schemes. The key physical development is to evolve composition following an ensemble of trajectories within neighbouring air-masses, including a simple scheme for mixing between them via an evolving "background profile", both within the boundary layer and free troposphere. The model runs along trajectories pre-calculated using winds and temperature from meteorological analyses. In addition, boundary layer height and precipitation rates, output from the analysis model, are interpolated to trajectory points and used as inputs to the mixing and wet deposition schemes. The model is most suitable in regimes when the effects of small-scale turbulent mixing are slow relative to advection by the resolved winds so that coherent air-masses form with distinct composition and strong gradients between them. Such air-masses can persist for many days while stretching, folding and thinning. Lagrangian models offer a useful framework for picking apart the processes of air-mass evolution over inter-continental distances, without being hindered by the numerical diffusion inherent to global Eulerian models. The model, including different box and trajectory modes, is described and some output for each of the modes is presented for evaluation. The model is available for download from a Subversion-controlled repository by contacting the corresponding authors.

Heat and moisture budgets from airborne measurements and high-resolution model simulations

High-resolution simulations with a mesoscale model are performed to estimate heat and moisture budgets of a well-mixed boundary layer. The model budgets are validated against energy budgets obtained from airborne measurements over heterogeneous terrain in Western Germany. Time rate of change, vertical divergence, and horizontal advection for an atmospheric column of air are estimated. Results show that the time trend of specific humidity exhibits some deficiencies, while the potential temperature trend is matched accurately. Furthermore, the simulated turbulent surface fluxes of sensible and latent heat are comparable to the measured fluxes, leading to similar values of the vertical divergence. The analysis of different horizontal model resolutions exhibits improved surface fluxes with increased resolution, a fact attributed to a reduced aggregation effect. Scale-interaction effects could be identified: while time trends and advection are strongly influenced by mesoscale forcing, the turbulent surface fluxes are mainly controlled by microscale processes.

Nonlinear stability of Eady's model

A nonlinear stability theorem is established for Eady's model of baroclinic flow. In particular, the Eady basic state is shown to be nonlinearly stable (for arbitrary shear) provided (Δz)/(Δy) > 2(5)^1/2f/(πN),where Δz is the height of the domain, Δy the channel width, f the Coriolis parameter, and N the buoyancy frequency. When this criterion is satisfied, explicit bounds can be derived on the disturbance potential enstrophy, the disturbance energy, and the disturbance available potential energy on the rigid lids, which are expressed in terms of the initial disturbance fields. The disturbances are completely general (with nonzero potential vorticity) and are not assumed to be of small amplitude. The results may be regarded as an extension of Arnol'd's second nonlinear stability theorem to continuously stratified quasigeostrophic baroclinic flow.

Spectral nonlocality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades

We study the degree to which Kraichnan–Leith–Batchelor (KLB) phenomenology describes two-dimensional energy cascades in α turbulence, governed by ∂θ/∂t+J(ψ,θ)=ν∇2θ+f, where θ=(−Δ)α/2ψ is generalized vorticity, and ψ^(k)=k−αθ^(k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (α=1), regular two-dimensional flow (α=2) and rotating shallow flow (α=3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5<α<10. At α=2.5 and α=10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α<4. However, downscale energy flux in the EDQNM self-similar inertial range for α>2.5 leads us to predict that any inverse cascade for α≥2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α≥2.5 is significantly steeper than the KLB prediction, while for α<2.5 we obtain the KLB spectrum.

Response of tropical cyclones to idealized climate change experiments in a global high resolution coupled general circulation model

We present an assessment of how tropical cyclone activity might change due to the influence of increased atmospheric carbon dioxide concentrations, using the UK’s High Resolution Global Environment Model (HiGEM) with N144 resolution (~90 km in the atmosphere and ~40 km in the ocean). Tropical cyclones are identified using a feature tracking algorithm applied to model output. Tropical cyclones from idealized 30-year 2×CO2 (2CO2) and 4×CO2 (4CO2) simulations are compared to those identified in a 150-year present-day simulation, which is separated into a 5-member ensemble of 30-year integrations. Tropical cyclones are shown to decrease in frequency globally by 9% in the 2CO2 and 26% in the 4CO2. Tropical cyclones only become more intese in the 4CO2, however uncoupled time slice experiments reveal an increase in intensity in the 2CO2. An investigation into the large-scale environmental conditions, known to influence tropical cyclone activity in the main development regions, is used to determine the response of tropical cyclone activity to increased atmospheric CO2. A weaker Walker circulation and a reduction in zonally averaged regions of updrafts lead to a shift in the location of tropical cyclones in the northern hemisphere. A decrease in mean ascent at 500 hPa contributes to the reduction of tropical cyclones in the 2CO2 in most basins. The larger reduction of tropical cyclones in the 4CO2 arises from further reduction of mean ascent at 500 hPa and a large enhancement of vertical wind shear, especially in the southern hemisphere, North Atlantic and North East Pacific.

Multi-site evaluation of an urban land-surface model: intra-urban heterogeneity, seasonality and parameter complexity requirements

An extensive off-line evaluation of the Noah/Single Layer Urban Canopy Model (Noah/SLUCM) urban land-surface model is presented using data from 15 sites to assess (1) the ability of the scheme to reproduce the surface energy balance observed in a range of urban environments, including seasonal changes, and (2) the impact of increasing complexity of input parameter information. Model performance is found to be most dependent on representation of vegetated surface area cover; refinement of other parameter values leads to smaller improvements. Model biases in net all-wave radiation and trade-offs between turbulent heat fluxes are highlighted using an optimization algorithm. Here we use the Urban Zones to characterize Energy partitioning (UZE) as the basis to assign default SLUCM parameter values. A methodology (FRAISE) to assign sites (or areas) to one of these categories based on surface characteristics is evaluated. Using three urban sites from the Basel Urban Boundary Layer Experiment (BUBBLE) dataset, an independent evaluation of the model performance with the parameter values representative of each class is performed. The scheme copes well with both seasonal changes in the surface characteristics and intra-urban heterogeneities in energy flux partitioning, with RMSE performance comparable to similar state-of-the-art models for all fluxes, sites and seasons. The potential of the methodology for high-resolution atmospheric modelling application using the Weather Research and Forecasting (WRF) model is highlighted. This analysis supports the recommendations that (1) three classes are appropriate to characterize the urban environment, and (2) that the parameter values identified should be adopted as default values in WRF.

Anisotropic model for granulated sea ice dynamics

A continuum model describing sea ice as a layer of granulated thick ice, consisting of many rigid, brittle floes, intersected by long and narrow regions of thinner ice, known as leads, is developed. We consider the evolution of mesoscale leads, formed under extension, whose lengths span many floes, so that the surrounding ice is treated as a granular plastic. The leads are sufficiently small with respect to basin scales of sea ice deformation that they may be modelled using a continuum approach. The model includes evolution equations for the orientational distribution of leads, their thickness and width expressed through second-rank tensors and terms requiring closures. The closing assumptions are constructed for the case of negligibly small lead ice thickness and the canonical deformation types of pure and simple shear, pure divergence and pure convergence. We present a new continuum-scale sea ice rheology that depends upon the isotropic, material rheology of sea ice, the orientational distribution of lead properties and the thick ice thickness. A new model of lead and thick ice interaction is presented that successfully describes a number of effects: (i) because of its brittle nature, thick ice does not thin under extension and (ii) the consideration of the thick sea ice as a granular material determines finite lead opening under pure shear, when granular dilation is unimportant.

Aircraft observations and model simulations of concentration and particle size distribution in the Eyjafjallajökull volcanic ash cloud

The Eyjafjallajökull volcano in Iceland emitted a cloud of ash into the atmosphere during April and May 2010. Over the UK the ash cloud was observed by the FAAM BAe-146 Atmospheric Research Aircraft which was equipped with in-situ probes measuring the concentration of volcanic ash carried by particles of varying sizes. The UK Met Office Numerical Atmospheric-dispersion Modelling Environment (NAME) has been used to simulate the evolution of the ash cloud emitted by the Eyjafjallajökull volcano during the period 4–18 May 2010. In the NAME simulations the processes controlling the evolution of the concentration and particle size distribution include sedimentation and deposition of particles, horizontal dispersion and vertical wind shear. For travel times between 24 and 72 h, a 1/t relationship describes the evolution of the concentration at the centre of the ash cloud and the particle size distribution remains fairly constant. Although NAME does not represent the effects of microphysical processes, it can capture the observed decrease in concentration with travel time in this period. This suggests that, for this eruption, microphysical processes play a small role in determining the evolution of the distal ash cloud. Quantitative comparison with observations shows that NAME can simulate the observed column-integrated mass if around 4% of the total emitted mass is assumed to be transported as far as the UK by small particles (< 30 μm diameter). NAME can also simulate the observed particle size distribution if a distal particle size distribution that contains a large fraction of < 10 μm diameter particles is used, consistent with the idea that phraetomagmatic volcanoes, such as Eyjafjallajökull, emit very fine particles.

A continuum anisotropic model of sea-ice dynamics

We develop the essential ingredients of a new, continuum and anisotropic model of sea-ice dynamics designed for eventual use in climate simulation. These ingredients are a constitutive law for sea-ice stress, relating stress to the material properties of sea ice and to internal variables describing the sea-ice state, and equations describing the evolution of these variables. The sea-ice cover is treated as a densely flawed two-dimensional continuum consisting of a uniform field of thick ice that is uniformly permeated with narrow linear regions of thinner ice called leads. Lead orientation, thickness and width distributions are described by second-rank tensor internal variables: the structure, thickness and width tensors, whose dynamics are governed by corresponding evolution equations accounting for processes such as new lead generation and rotation as the ice cover deforms. These evolution equations contain contractions of higher-order tensor expressions that require closures. We develop a sea-ice stress constitutive law that relates sea-ice stress to the structure tensor, thickness tensor and strain rate. For the special case of empty leads (containing no ice), linear closures are adopted and we present calculations for simple shear, convergence and divergence.

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Simulation of the global ENSO–Tropical cyclone teleconnection by a high-resolution coupled general circulation model

This study assesses the influence of the El Niño–Southern Oscillation (ENSO) on global tropical cyclone activity using a 150-yr-long integration with a high-resolution coupled atmosphere–ocean general circulation model [High-Resolution Global Environmental Model (HiGEM); with N144 resolution: ~90 km in the atmosphere and ~40 km in the ocean]. Tropical cyclone activity is compared to an atmosphere-only simulation using the atmospheric component of HiGEM (HiGAM). Observations of tropical cyclones in the International Best Track Archive for Climate Stewardship (IBTrACS) and tropical cyclones identified in the Interim ECMWF Re-Analysis (ERA-Interim) are used to validate the models. Composite anomalies of tropical cyclone activity in El Niño and La Niña years are used. HiGEM is able to capture the shift in tropical cyclone locations to ENSO in the Pacific and Indian Oceans. However, HiGEM does not capture the expected ENSO–tropical cyclone teleconnection in the North Atlantic. HiGAM shows more skill in simulating the global ENSO–tropical cyclone teleconnection; however, variability in the Pacific is overpronounced. HiGAM is able to capture the ENSO–tropical cyclone teleconnection in the North Atlantic more accurately than HiGEM. An investigation into the large-scale environmental conditions, known to influence tropical cyclone activity, is used to further understand the response of tropical cyclone activity to ENSO in the North Atlantic and western North Pacific. The vertical wind shear response over the Caribbean is not captured in HiGEM compared to HiGAM and ERA-Interim. Biases in the mean ascent at 500 hPa in HiGEM remain in HiGAM over the western North Pacific; however, a more realistic low-level vorticity in HiGAM results in a more accurate ENSO–tropical cyclone teleconnection.