The knowledge of the lightning-induced nitrogen oxides (LNO_x) source is important for understanding and predicting the nitrogen oxides and ozone distributions in the troposphere and their trends, the oxidising capacity of the atmosphere, and the lifetime of trace gases destroyed by reactions with OH. This knowledge is further required for the assessment of other important NO_x sources, in particular from aviation emissions, the stratosphere, and from surface sources, and for understanding the possible feedback between climate changes and lightning. This paper reviews more than 3 decades of research. The review includes laboratory studies as well as surface, airborne and satellite-based observations of lightning and of NO_x and related species in the atmosphere. Relevant data available from measurements in regions with strong LNO_x influence are identified, including recent observations at midlatitudes and over tropical continents where most lightning occurs. Various methods to model LNO_x at cloud scales or globally are described. Previous estimates are re-evaluated using the global annual mean flash frequency of 44±5 s⁻¹ reported from OTD satellite data. From the review, mainly of airborne measurements near thunderstorms and cloud-resolving models, we conclude that a "typical" thunderstorm flash produces 15 (2–40)×10²⁵ NO molecules per flash, equivalent to 250 mol NO_x or 3.5 kg of N mass per flash with uncertainty factor from 0.13 to 2.7. Mainly as a result of global model studies for various LNO_x parameterisations tested with related observations, the best estimate of the annual global LNO_x nitrogen mass source and its uncertainty range is (5±3) Tg a⁻¹ in this study. In spite of a smaller global flash rate, the best estimate is essentially the same as in some earlier reviews, implying larger flash-specific NO_x emissions. The paper estimates the LNO_x accuracy required for various applications and lays out strategies for improving estimates in the future. An accuracy of about 1 Tg a⁻¹ or 20%, as necessary in particular for understanding tropical tropospheric chemistry, is still a challenging goal.

Aviation alters the composition of the atmosphere globally and can thus drive climate change and ozone depletion. The last major international assessment of these impacts was made by the Intergovernmental Panel on Climate Change (IPCC) in 1999. Here, a comprehensive updated assessment of aviation is provided. Scientific advances since the 1999 assessment have reduced key uncertainties, sharpening the quantitative evaluation, yet the basic conclusions remain the same. The climate impact of aviation is driven by long-term impacts from CO2 emissions and shorter-term impacts from non-CO2 emissions and effects, which include the emissions of water vapour, particles and nitrogen oxides (NOx). The present-day radiative forcing from aviation (2005) is estimated to be 55 mW m−2 (excluding cirrus cloud enhancement), which represents some 3.5% (range 1.3–10%, 90% likelihood range) of current anthropogenic forcing, or 78 mW m−2 including cirrus cloud enhancement, representing 4.9% of current forcing (range 2–14%, 90% likelihood range). According to two SRES-compatible scenarios, future forcings may increase by factors of 3–4 over 2000 levels, in 2050. The effects of aviation emissions of CO2 on global mean surface temperature last for many hundreds of years (in common with other sources), whilst its non-CO2 effects on temperature last for decades. Much progress has been made in the last ten years on characterizing emissions, although major uncertainties remain over the nature of particles. Emissions of NOx result in production of ozone, a climate warming gas, and the reduction of ambient methane (a cooling effect) although the overall balance is warming, based upon current understanding. These NOx emissions from current subsonic aviation do not appear to deplete stratospheric ozone. Despite the progress made on modelling aviation's impacts on tropospheric chemistry, there remains a significant spread in model results. The knowledge of aviation's impacts on cloudiness has also improved: a limited number of studies have demonstrated an increase in cirrus cloud attributable to aviation although the magnitude varies: however, these trend analyses may be impacted by satellite artefacts. The effect of aviation particles on clouds (with and without contrails) may give rise to either a positive forcing or a negative forcing: the modelling and the underlying processes are highly uncertain, although the overall effect of contrails and enhanced cloudiness is considered to be a positive forcing and could be substantial, compared with other effects. The debate over quantification of aviation impacts has also progressed towards studying potential mitigation and the technological and atmospheric tradeoffs. Current studies are still relatively immature and more work is required to determine optimal technological development paths, which is an aspect that atmospheric science has much to contribute. In terms of alternative fuels, liquid hydrogen represents a possibility and may reduce some of aviation's impacts on climate if the fuel is produced in a carbon-neutral way: such fuel is unlikely to be utilized until a ‘hydrogen economy’ develops. The introduction of biofuels as a means of reducing CO2 impacts represents a future possibility. However, even over and above land-use concerns and greenhouse gas budget issues, aviation fuels require strict adherence to safety standards and thus require extra processing compared with biofuels destined for other sectors, where the uptake of such fuel may be more beneficial in the first instance.

Turbulence in the convective boundary layer (CBL) uniformly heated from below and topped by a layer of uniformly stratified fluid is investigated for zero mean horizontal flow using large-eddy simulations (LES). The Rayleigh number is effectively infinite, the Froude number of the stable layer is 0.09 and the surface roughness height relative to the height of the convective layer is varied between 10⁻⁶ and 10⁻². The LES uses a finite-difference method to integrate the three-dimensional grid-volume-averaged Navier–Stokes equations for a Boussinesq fluid. Subgrid-scale (SGS) fluxes are determined from algebraically approximated second-order closure (SOC) transport equations for which all essential coefficients are determined from the inertial-range theory. The surface boundary condition uses the Monin–Obukhov relationships. A radiation boundary condition at the top of the computational domain prevents spurious reflections of gravity waves. The simulation uses 160 × 160 × 48 grid cells. In the asymptotic state, the results in terms of vertical mean profiles of turbulence statistics generally agree very well with results available from laboratory and atmospheric field experiments. We found less agreement with respect to horizontal velocity fluctuations, pressure fluctuations and dissipation rates, which previous investigations tend to overestimate. Horizontal spectra exhibit an inertial subrange. The entrainment heat flux at the top of the CBL is carried by cold updraughts and warm downdraughts in the form of wisps at scales comparable with the height of the boundary layer. Plots of instantaneous flow fields show a spoke pattern in the lower quarter of the CBL which feeds large-scale updraughts penetrating into the stable layer aloft. The spoke pattern has also been found in a few previous investigations. Small-scale plumes near the surface and remote from strong updraughts do not merge together but decay while rising through large-scale downdraughts. The structure of updraughts and downdraughts is identified by three-dimensional correlation functions and conditionally averaged fields. The mean circulation extends vertically over the whole boundary layer. We find that updraughts are composed of quasi-steady large-scale plumes together with transient rising thermals which grow in size by lateral entrainment. The skewness of the vertical velocity fluctuations is generally positive but becomes negative in the lowest mesh cells when the dissipation rate exceeds the production rate due to buoyancy near the surface, as is the case for very rough surfaces. The LES results are used to determine the root-mean-square value of the surface friction velocity and the mean temperature difference between the surface and the mixed layer as a function of the roughness height. The results corroborate a simple model of the heat transfer in the surface layer.

It is shown that certain existing phenomenological models of turbulence in terms of differential equations for the Reynolds stresses Rαβ=〈u′α u′β〉 do not guarantee realizable solutions. The known realizability conditions are Rαβ⩾0 for α=β and Rαβ2⩾Rαα Rββ for α≠β. A stronger requirement is that the matrix Rαβ be positive semi-definite. This implies three conditions like non-negative eigenvalues or non-negative principal invariants. Conditions are given which must be satisfied by the model itself in order to guarantee realizable solutions for any realizable initial and boundary conditions. Some means are proposed which can be used to change the existing models into realizable ones.