Cylindrically symmetric flows in a Lagrangian frame

An approximate Riemann solver, in a Lagrangian frame of reference, is presented for the compressible flow equations with cylindrical and spherical symmetry, including flow in a duct of variable cross section. The scheme is applied to a cylindrically symmetric problem involving the interaction of shocks.

Evaluation of a Lagrangian box model using field measurements from EASE (Eastern Atlantic Summer Experiment) 1996

The Cambridge Tropospheric Trajectory model of Chemistry and Transport (CiTTyCAT), a Lagrangian chemistry model, has been evaluated using atmospheric chemical measurements collected during the East Atlantic Summer Experiment 1996 (EASE '96). This field campaign was part of the UK Natural Environment Research Council's (NERC) Atmospheric Chemistry Studies in the Oceanic Environment (ACSOE) programme, conducted at Mace Head, Republic of Ireland, during July and August 1996. The model includes a description of gas-phase tropospheric chemistry, and simple parameterisations for surface deposition, mixing from the free troposphere and emissions. The model generally compares well with the measurements and is used to study the production and loss of O3 under a variety of conditions. The mean difference between the hourly O3 concentrations calculated by the model and those measured is 0.6 ppbv with a standard deviation of 8.7 ppbv. Three specific air-flow regimes were identified during the campaign – westerly, anticyclonic (easterly) and south westerly. The westerly flow is typical of background conditions for Mace Head. However, on some occasions there was evidence of long-range transport of pollutants from North America. In periods of anticyclonic flow, air parcels had collected emissions of NOx and VOCs immediately before arriving at Mace Head, leading to O3 production. The level of calculated O3 depends critically on the precise details of the trajectory, and hence on the emissions into the air parcel. In several periods of south westerly flow, low concentrations of O3 were measured which were consistent with deposition and photochemical destruction inside the tropical marine boundary layer.

Evaluating a new LISFLOOD-FP formulation with data from the summer 2007 floods in Tewkesbury, UK

Two-dimensional flood inundation modelling is a widely used tool to aid flood risk management. In urban areas, the model spatial resolution required to represent flows through a typical street network often results in an impractical computational cost at the city scale. This paper presents the calibration and evaluation of a recently developed formulation of the LISFLOOD-FP model, which is more computationally efficient at these resolutions. Aerial photography was available for model evaluation on 3 days from the 24 to the 31 of July. The new formulation was benchmarked against the original version of the model at 20 and 40 m resolutions, demonstrating equally accurate simulation, given the evaluation data but at a 67 times faster computation time. The July event was then simulated at the 2 m resolution of the available airborne LiDAR DEM. This resulted in more accurate simulation of the floodplain drying dynamics compared with the coarse resolution models, although maximum inundation levels were simulated equally well at all resolutions tested.

Prediction of visibility and aerosol within the operational Met Office unified model. I: Model formulation and variational assimilation

The formulation and performance of the Met Office visibility analysis and prediction system are described. The visibility diagnostic within the limited-area Unified Model is a function of humidity and a prognostic aerosol content. The aerosol model includes advection, industrial and general urban sources, plus boundary-layer mixing and removal by rain. The assimilation is a 3-dimensional variational scheme in which the visibility observation operator is a very nonlinear function of humidity, aerosol and temperature. A quality control scheme for visibility data is included. Visibility observations can give rise to humidity increments of significant magnitude compared with the direct impact of humidity observations. We present the results of sensitivity studies which show the contribution of different components of the system to improved skill in visibility forecasts. Visibility assimilation is most important within the first 6-12 hours of the forecast and for visibilities below 1 km, while modelling of aerosol sources and advection is important for slightly higher visibilities (1-5 km) and is still significant at longer forecast times

Review of the formulation of present‐generation stratospheric chemistry‐climate models and associated external forcings

The goal of the Chemistry‐Climate Model Validation (CCMVal) activity is to improve understanding of chemistry‐climate models (CCMs) through process‐oriented evaluation and to provide reliable projections of stratospheric ozone and its impact on climate. An appreciation of the details of model formulations is essential for understanding how models respond to the changing external forcings of greenhouse gases and ozonedepleting substances, and hence for understanding the ozone and climate forecasts produced by the models participating in this activity. Here we introduce and review the models used for the second round (CCMVal‐2) of this intercomparison, regarding the implementation of chemical, transport, radiative, and dynamical processes in these models. In particular, we review the advantages and problems associated with approaches used to model processes of relevance to stratospheric dynamics and chemistry. Furthermore, we state the definitions of the reference simulations performed, and describe the forcing data used in these simulations. We identify some developments in chemistry‐climate modeling that make models more physically based or more comprehensive, including the introduction of an interactive ocean, online photolysis, troposphere‐stratosphere chemistry, and non‐orographic gravity‐wave deposition as linked to tropospheric convection. The relatively new developments indicate that stratospheric CCM modeling is becoming more consistent with our physically based understanding of the atmosphere.

Origin of regional climate differences: role of boundary conditions and model formulation in two GCMs

Model differences in projections of extratropical regional climate change due to increasing greenhouse gases are investigated using two atmospheric general circulation models (AGCMs): ECHAM4 (Max Planck Institute, version 4) and CCM3 (National Center for Atmospheric Research Community Climate Model version 3). Sea-surface temperature (SST) fields calculated from observations and coupled versions of the two models are used to force each AGCM in experiments based on time-slice methodology. Results from the forced AGCMs are then compared to coupled model results from the Coupled Model Intercomparison Project 2 (CMIP2) database. The time-slice methodology is verified by showing that the response of each model to doubled CO2 and SST forcing from the CMIP2 experiments is consistent with the results of the coupled GCMs. The differences in the responses of the models are attributed to (1) the different tropical SST warmings in the coupled simulations and (2) the different atmospheric model responses to the same tropical SST warmings. Both are found to have important contributions to differences in implied Northern Hemisphere (NH) winter extratropical regional 500 mb height and tropical precipitation climate changes. Forced teleconnection patterns from tropical SST differences are primarily responsible for sensitivity differences in the extratropical North Pacific, but have relatively little impact on the North Atlantic. There are also significant differences in the extratropical response of the models to the same tropical SST anomalies due to differences in numerical and physical parameterizations. Differences due to parameterizations dominate in the North Atlantic. Differences in the control climates of the two coupled models from the current climate, in particular for the coupled model containing CCM3, are also demonstrated to be important in leading to differences in extratropical regional sensitivity.

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.

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

Mean motions induced by baroclinic instability in a jet

A study is made of the zonal-mean motions induced by a growing baroclinic wave in several contexts, under the framework of three different analysis schemes: the conventional Eulerian mean (EM), the transformed Eulerian mean (TEM), and the generalized Lagrangian mean (GLM). The effect of meridional shear in the initial jet on these induced mean motions is considered by treating the instability problem in the context of the two-layer model. The conceptual simplicity of the TEM formulation is shown to be useful in diagnosing the dynamics of instability, much as it has been found helpful in many problems of wave, mean-flow interaction. In addition, it is found that the TEM vertical velocity is a very good indicator of the GLM vertical velocity. However, the GLM meridional velocity is always convergent towards the centre of instability activity, and is not at all well represented by the nondivergent TEM meridional velocity. In comparing the results with Uryu's (1979) calculation of the GLM circulation induced by a growing Eady wave, it is found that the inclusion of meridional jet shear in the present work leads to some strikingly different effects in the GLM zonal wind acceleration. In the case of pure baroclinic instability treated by Uryu, the Eulerian and Stokes accelerations nearly cancel each other in the centre of the channel, leaving a weak Lagrangian acceleration opposed to the Eulerian one. In the more general case of mixed baroclinic-barotropic instability, however, the Eulerian and Stokes accelerations can reinforce one another, leading to a very strong Lagrangian zonal wind

An urban parameterization for a global climate model. Part I: Formulation and evaluation for two cities

Urbanization, the expansion of built-up areas, is an important yet less-studied aspect of land use/land cover change in climate science. To date, most global climate models used to evaluate effects of land use/land cover change on climate do not include an urban parameterization. Here, the authors describe the formulation and evaluation of a parameterization of urban areas that is incorporated into the Community Land Model, the land surface component of the Community Climate System Model. The model is designed to be simple enough to be compatible with structural and computational constraints of a land surface model coupled to a global climate model yet complex enough to explore physically based processes known to be important in determining urban climatology. The city representation is based upon the “urban canyon” concept, which consists of roofs, sunlit and shaded walls, and canyon floor. The canyon floor is divided into pervious (e.g., residential lawns, parks) and impervious (e.g., roads, parking lots, sidewalks) fractions. Trapping of longwave radiation by canyon surfaces and solar radiation absorption and reflection is determined by accounting for multiple reflections. Separate energy balances and surface temperatures are determined for each canyon facet. A one-dimensional heat conduction equation is solved numerically for a 10-layer column to determine conduction fluxes into and out of canyon surfaces. Model performance is evaluated against measured fluxes and temperatures from two urban sites. Results indicate the model does a reasonable job of simulating the energy balance of cities.

Solutions of the fully compressible semi-geostrophic system

The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordinates. In addition, we provide an alternative proof of the earlier result on the existence of weak solutions of this system expressed in the so-called geostrophic, or dual, coordinates. The proofs are based on the optimal transport formulation of the problem and on recent general results concerning transport problems posed in the Wasserstein space of probability measures.