High Reynolds number turbulent flows of incompressible fluids in plane channels and annuli are simulated using a finite difference procedure which integrates the Navier-Stokes equations in time and in three-dimensional space. This paper describes the finite difference procedure and the subgrid scale (SGS) motion model. The model differs from earlier ones in the following points. The finite difference equations are based on integral conservation equations for each grid volume. As a consequence the SGS stresses are defined as surface mean rather than grid volume mean values of the fluctuating velocity products. This allows us to identify and model the effects of anisotropic grids (especially unequally sided grid volumes) and anisotropic finite difference operators. In this model SGS stresses are split into two parts, one accounting for locally isotropic turbulence, the other for inhomogeneous effects. This results in a model which is meaningful even if the size of the grid volumes is very large. The SGS kinetic energy is calculated using a separate transport equation. The boundary conditions are formulated in a manner consistent with the SGS theory. The method may be used for plane channels and annuli as well, and has been used to simulate flows with up to 65,536 grid volumes. The results agree rather well with experimental values, even for a smaller number of grid volumes.

Abstract. 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)×10 25 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 Correspondence to: U. Schumann (ulrich.schumann@dlr.de) about 1 Tg a −1 or 20%, as necessary in particular for understanding tropical tropospheric chemistry, is still a challenging goal.

Abstract. The April-May, 2010 volcanic eruptions of Eyjafjallajökull, Iceland caused significant economic and social disruption in Europe whilst state of the art measurements and ash dispersion forecasts were heavily criticized by the aviation industry. Here we demonstrate for the first time that large improvements can be made in quantitative predictions of the fate of volcanic ash emissions, by using an inversion scheme that couples a priori source information and the output of a Lagrangian dispersion model with satellite data to estimate the volcanic ash source strength as a function of altitude and time. From the inversion, we obtain a total fine ash emission of the eruption of 8.3±4.2 Tg for particles in the size range of 2.8-28 µm diameter. We evaluate the results of our model results with a posteriori ash emissions using independent ground-based, airborne and space-borne measurements both in case studies and statistically. Subsequently, we estimate the area over Europe affected by volcanic ash above certain concentration thresholds relevant for the aviation industry. We find that during three episodes in April and May, volcanic ash concentrations at some altitude in the atmosphere exceeded the limits for the "Normal" flying zone in up to 14 % (6-16 %), 2 % (1-3 %) and 7 % (4-11 %), respecCorrespondence to: A. Stohl (ast@nilu.no) tively, of the European area. For a limit of 2 mg m −3 only two episodes with fractions of 1.5 % (0.2-2.8 %) and 0.9 % (0.1-1.6 %) occurred, while the current "No-Fly" zone criterion of 4 mg m −3 was rarely exceeded. Our results have important ramifications for determining air space closures and for real-time quantitative estimations of ash concentrations. Furthermore, the general nature of our method yields better constraints on the distribution and fate of volcanic ash in the Earth system.

a b s t r a c tAviation 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 CO 2 emissions and shorter-term impacts from non-CO 2 emissions and effects, which include the emissions of water vapour, particles and nitrogen oxides (NO x ). The presentday radiative forcing from aviation (2005) is estimated to be 55 mW m À2 (excluding cirrus cloud enhancement), which represents some 3.5% (range 1.3-10%, 90% likelihood range) of current anthropogenic forcing, or 78 mW m À2 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 CO 2 on global mean surface temperature last for many hundreds of years (in common with other sources), whilst its non-CO 2 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 NO x 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 NO x 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 clim...

Abstract. Airborne lidar and in-situ measurements of aerosols and trace gases were performed in volcanic ash plumes over Europe between Southern Germany and Iceland with the Falcon aircraft during the eruption period of the Eyjafjalla 1 volcano between 19 April and 18 May 2010. Flight planning and measurement analyses were supported by a refined Meteosat ash product and trajectory model analysis. The volcanic ash plume was observed with lidar directly over the volcano and up to a distance of 2700 km downwind, and up to 120 h plume ages. Aged ash layers were between a few 100 m to 3 km deep, occurred between 1 and 7 km altitude, and were typically 100 to 300 km wide. Particles collected by impactors had diameters up to 20 µm diameter, with size and age dependent composition. Ash mass concentrations were derived from optical particle spectrometers for aCorrespondence to: U. Schumann (ulrich.schumann@dlr.de) 1 Also known as Eyjafjallajökull or Eyjafjöll volcano, http://www.britannica.com/EBchecked/topic/1683937/ Eyjafjallajokull-volcano particle density of 2.6 g cm −3 and various values of the refractive index (RI, real part: 1.59; 3 values for the imaginary part: 0, 0.004 and 0.008). The mass concentrations, effective diameters and related optical properties were compared with ground-based lidar observations. Theoretical considerations of particle sedimentation constrain the particle diameters to those obtained for the lower RI values. The ash mass concentration results have an uncertainty of a factor of two. The maximum ash mass concentration encountered during the 17 flights with 34 ash plume penetrations was below 1 mg m −3 . The Falcon flew in ash clouds up to about 0.8 mg m −3 for a few minutes and in an ash cloud with approximately 0.2 mg m −3 mean-concentration for about one hour without engine damage. The ash plumes were rather dry and correlated with considerable CO and SO 2 increases and O 3 decreases. To first order, ash concentration and SO 2 mixing ratio in the plumes decreased by a factor of two within less than a day. In fresh plumes, the SO 2 and CO concentration increases were correlated with the ash mass concentration. The ash plumes were often visible slantwise as faint dark layers, even for concentrations below 0.1 mg m −3 .Published by Copernicus Publications on behalf of the European Geosciences Union. U. Schumann et al.: Airborne observations of the Eyjafjalla volcano ash cloud over EuropeThe large abundance of volatile Aitken mode particles suggests previous nucleation of sulfuric acid droplets. The effective diameters range between 0.2 and 3 µm with considerable surface and volume contributions from the Aitken and coarse mode aerosol, respectively. The distal ash mass flux on 2 May was of the order of 500 (240-1600) kg s −1 . The volcano induced about 10 (2.5-50) Tg of distal ash mass and about 3 (0.6-23) Tg of SO 2 during the whole eruption period. The results of the Falcon flights were used to support the responsible agencies in their decisions concerning air traffic in the presence of v...