Estimation of optimal gravity wave parameters for climate models using data assimilation

There is a current need to constrain the parameters of gravity wave drag (GWD) schemes in climate models using observational information instead of tuning them subjectively. In this work, an inverse technique is developed using data assimilation principles to estimate gravity wave parameters. Because mostGWDschemes assume instantaneous vertical propagation of gravity waves within a column, observations in a single column can be used to formulate a one-dimensional assimilation problem to estimate the unknown parameters. We define a cost function that measures the differences between the unresolved drag inferred from observations (referred to here as the ‘observed’ GWD) and the GWD calculated with a parametrisation scheme. The geometry of the cost function presents some difficulties, including multiple minima and ill-conditioning because of the non-independence of the gravity wave parameters. To overcome these difficulties we propose a genetic algorithm to minimize the cost function, which provides a robust parameter estimation over a broad range of prescribed ‘true’ parameters. When real experiments using an independent estimate of the ‘observed’ GWD are performed, physically unrealistic values of the parameters can result due to the non-independence of the parameters. However, by constraining one of the parameters to lie within a physically realistic range, this degeneracy is broken and the other parameters are also found to lie within physically realistic ranges. This argues for the essential physical self-consistency of the gravity wave scheme. A much better fit to the observed GWD at high latitudes is obtained when the parameters are allowed to vary with latitude. However, a close fit can be obtained either in the upper or the lower part of the profiles, but not in both at the same time. This result is a consequence of assuming an isotropic launch spectrum. The changes of sign in theGWDfound in the tropical lower stratosphere, which are associated with part of the quasi-biennial oscillation forcing, cannot be captured by the parametrisation with optimal parameters.

A low-order model investigation of the analysis of gravity waves in the ensemble Kalman filter.

The behavior of the ensemble Kalman filter (EnKF) is examined in the context of a model that exhibits a nonlinear chaotic (slow) vortical mode coupled to a linear (fast) gravity wave of a given amplitude and frequency. It is shown that accurate recovery of both modes is enhanced when covariances between fast and slow normal-mode variables (which reflect the slaving relations inherent in balanced dynamics) are modeled correctly. More ensemble members are needed to recover the fast, linear gravity wave than the slow, vortical motion. Although the EnKF tends to diverge in the analysis of the gravity wave, the filter divergence is stable and does not lead to a great loss of accuracy. Consequently, provided the ensemble is large enough and observations are made that reflect both time scales, the EnKF is able to recover both time scales more accurately than optimal interpolation (OI), which uses a static error covariance matrix. For OI it is also found to be problematic to observe the state at a frequency that is a subharmonic of the gravity wave frequency, a problem that is in part overcome by the EnKF.However, error in themodeled gravity wave parameters can be detrimental to the performance of the EnKF and remove its implied advantages, suggesting that a modified algorithm or a method for accounting for model error is needed.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part I: gravity wave forcing

Parameterization schemes for the drag due to atmospheric gravity waves are discussed and compared in the context of a simple one-dimensional model of the quasi-biennial oscillation (QBO). A number of fundamental issues are examined in detail, with the goal of providing a better understanding of the mechanism by which gravity wave drag can produce an equatorial zonal wind oscillation. The gravity wave–driven QBOs are compared with those obtained from a parameterization of equatorial planetary waves. In all gravity wave cases, it is seen that the inclusion of vertical diffusion is crucial for the descent of the shear zones and the development of the QBO. An important difference between the schemes for the two types of waves is that in the case of equatorial planetary waves, vertical diffusion is needed only at the lowest levels, while for the gravity wave drag schemes it must be included at all levels. The question of whether there is downward propagation of influence in the simulated QBOs is addressed. In the gravity wave drag schemes, the evolution of the wind at a given level depends on the wind above, as well as on the wind below. This is in contrast to the parameterization for the equatorial planetary waves in which there is downward propagation of phase only. The stability of a zero-wind initial state is examined, and it is determined that a small perturbation to such a state will amplify with time to the extent that a zonal wind oscillation is permitted.

Constraints on wave drag parameterization schemes for simulating the quasi-biennial oscillation. Part II: combined effects of gravity waves and equatorial planetary waves

This study examines the effect of combining equatorial planetary wave drag and gravity wave drag in a one-dimensional zonal mean model of the quasi-biennial oscillation (QBO). Several different combinations of planetary wave and gravity wave drag schemes are considered in the investigations, with the aim being to assess which aspects of the different schemes affect the nature of the modeled QBO. Results show that it is possible to generate a realistic-looking QBO with various combinations of drag from the two types of waves, but there are some constraints on the wave input spectra and amplitudes. For example, if the phase speeds of the gravity waves in the input spectrum are large relative to those of the equatorial planetary waves, critical level absorption of the equatorial planetary waves may occur. The resulting mean-wind oscillation, in that case, is driven almost exclusively by the gravity wave drag, with only a small contribution from the planetary waves at low levels. With an appropriate choice of wave input parameters, it is possible to obtain a QBO with a realistic period and to which both types of waves contribute. This is the regime in which the terrestrial QBO appears to reside. There may also be constraints on the initial strength of the wind shear, and these are similar to the constraints that apply when gravity wave drag is used without any planetary wave drag. In recent years, it has been observed that, in order to simulate the QBO accurately, general circulation models require parameterized gravity wave drag, in addition to the drag from resolved planetary-scale waves, and that even if the planetary wave amplitudes are incorrect, the gravity wave drag can be adjusted to compensate. This study provides a basis for knowing that such a compensation is possible.

Free gravity waves and balanced dynamics

It is shown how a renormalization technique, which is a variant of classical Krylov–Bogolyubov–Mitropol’skii averaging, can be used to obtain slow evolution equations for the vortical and inertia–gravity wave components of the dynamics in a rotating flow. The evolution equations for each component are obtained to second order in the Rossby number, and the nature of the coupling between the two is analyzed carefully. It is also shown how classical balance models such as quasigeostrophic dynamics and its second-order extension appear naturally as a special case of this renormalized system, thereby providing a rigorous basis for the slaving approach where only the fast variables are expanded. It is well known that these balance models correspond to a hypothetical slow manifold of the parent system; the method herein allows the determination of the dynamics in the neighborhood of such solutions. As a concrete illustration, a simple weak-wave model is used, although the method readily applies to more complex rotating fluid models such as the shallow-water, Boussinesq, primitive, and 3D Euler equations.

Dynamical control of the mesosphere by orographic and non-orographic gravity wave drag during the extended northern winters of 2006 and 2009

A version of the Canadian Middle Atmosphere Model (CMAM) that is nudged toward reanalysis data up to 1 hPa is used to examine the impacts of parameterized orographic and non-orographic gravity wave drag (OGWD and NGWD) on the zonal-mean circulation of the mesosphere during the extended northern winters of 2006 and 2009 when there were two large stratospheric sudden warmings. The simulations are compared to Aura Microwave Limb Sounder (MLS) observations of mesospheric temperature, carbon monoxide (CO) and derived zonal winds. The control simulation, which uses both OGWD and NGWD, is shown to be in good agreement with MLS. The impacts of OGWD and NGWD are assessed using simulations in which those sources of wave drag are removed. In the absence of OGWD the mesospheric zonal winds in the months preceding the warmings are too strong, causing increased mesospheric NGWD, which drives excessive downwelling, resulting in overly large lower mesospheric values of CO prior to the warming. NGWD is found to be most important following the warmings when the underlying westerlies are too weak to allow much vertical propagation of the orographic gravity waves to the mesosphere. NGWD is primarily responsible for driving the circulation that results in the descent of CO from the thermosphere following the warmings. Zonal mean mesospheric winds and temperatures in all simulations are shown to be strongly constrained by (i.e. slaved to) the stratosphere. Finally, it is demonstrated that the responses to OGWD and NGWD are non-additive due to their dependence and influence on the background winds and temperatures.

Phylogenetic variation in the shoot mineral concentration of angiosperms

The calcium (Ca) concentration of plant shoot tissues varies systematically between angiosperm orders. The phylogenetic variation in the shoot concentration of other mineral nutrients has not yet been described at an ordinal level. The aims of this study were (1) to quantify the shoot mineral concentration of different angiosperm orders, (2) to partition the phylogenetic variation in shoot mineral concentration between and within orders, (3) to determine if the shoot concentration of different minerals are correlated across angiosperm species, and (4) to compare experimental data with published ecological survey data on 81 species sampled from their natural habitats. Species, selected pro rata from different angiosperm orders, were grown in a hydroponic system under a constant external nutrient regime. Shoots of 117 species were sampled during vegetative growth. Significant variation in shoot carbon (C), calcium (Ca), potassium (K), and magnesium (Mg) concentration occurred between angiosperm orders. There was no evidence for systematic differences in shoot phosphorus (P) or organic-nitrogen (N) concentration between orders. At a species level, there were strong positive correlations between shoot Ca and Mg concentration, between shoot P and organic-N concentration, and between shoot K concentration and shoot fresh weight:dry weight ratio. Shoot C and cation concentration correlated negatively at a species level. Species within the Poales and the Caryophyllales had distinct shoot mineralogies in both the designed experiment and in the ecological survey.

Shoot zinc (Zn) concentration varies widely within Brassica oleracea L. and is affected by soil Zn and phosphorus (P) levels

The low availability of zinc (Zn) in soils and crops affects dietary Zn intake worldwide. This study sought to determine if the natural genetic variation in shoot Zn concentrations (Zn(shoot)) is sufficient to pursue a crop improvement breeding strategy in a leafy vegetable crop. The gene-pool of Brassica oleracea L. was sampled using a large (n = 376) diversity foundation set (DFS), representing almost all species-wide common allelic variation, and 74 commercial varieties (mostly F(1)). The DFS genotypes were grown at low and high soil phosphorus (P) levels under glasshouse and field conditions, and also in a Zn-deficient soil, with or without Zn-fertilisation, in a glasshouse. Despite the large variation in Zn(shoot) among genotypes, environment had a profound effect on Zn(shoot) The heritability of Zn(shoot) was significant, but relatively low, among 90 doubled-haploid (DH) lines from a mapping population. While several quantitative trait loci (QTL) associated with Zn(shoot) occurred on chromosomes C2, C3, C5, C7, and C9, these were generally weak and conditional upon growth conditions. Breeding for Zn(shoot) in B. oleracea is therefore likely to be challenging. Shoot P concentrations increased substantially in all genotypes under low soil Zn conditions. Conversely, only some genotypes had increased Zn(shoot) at low soil P levels. Sufficient natural genetic variation may therefore exist to study some of the interactions between Zn and P nutrition.

Contrasting arbuscular mycorrhizal communities colonizing different host plants show a similar response to a soil phosphorus concentration gradient

High soil phosphorus (P) concentration is frequently shown to reduce root colonization by arbuscular mycorrhizal (AM) fungi, but the influence of P on the diversity of colonizing AM fungi is uncertain. We used terminal restriction fragment length polymorphism (T-RFLP) of 18S rDNA and cloning to assess diversity of AM fungi colonizing maize (Zea mays), soybean (Glycene max) and field violet (Viola arvensis) at three time points in one season along a P gradient of 10280mgl1 in the field. Percentage AM colonization changed between sampling time points but was not reduced by high soil P except in maize. There was no significant difference in AM diversity between sampling time points. Diversity was reduced at concentrations of P > 25mgl1, particularly in maize and soybean. Both cloning and T-RFLP indicated differences between AM communities in the different host species. Host species was more important than soil P in determining the AM community, except at the highest P concentration. Our results show that the impact of soil P on the diversity of AM fungi colonizing plants was broadly similar, despite the fact that different plants contained different communities. However, subtle differences in the response of the AM community in each host were evident.

Modelling the effects of gravity waves on stratocumulus clouds observed during VOCALS-UK

During the VOCALS campaign spaceborne satellite observations showed that travelling gravity wave packets, generated by geostrophic adjustment, resulted in perturbations to marine boundary layer (MBL) clouds over the south-east Pacific Ocean (SEP). Often, these perturbations were reversible in that passage of the wave resulted in the clouds becoming brighter (in the wave crest), then darker (in the wave trough) and subsequently recovering their properties after the passage of the wave. However, occasionally the wave packets triggered irreversible changes to the clouds, which transformed from closed mesoscale cellular convection to open form. In this paper we use large eddy simulation (LES) to examine the physical mechanisms that cause this transition. Specifically, we examine whether the clearing of the cloud is due to (i) the wave causing additional cloud-top entrainment of warm, dry air or (ii) whether the additional condensation of liquid water onto the existing drops and the subsequent formation of drizzle are the important mechanisms. We find that, although the wave does cause additional drizzle formation, this is not the reason for the persistent clearing of the cloud; rather it is the additional entrainment of warm, dry air into the cloud followed by a reduction in longwave cooling, although this only has a significant effect when the cloud is starting to decouple from the boundary layer. The result in this case is a change from a stratocumulus to a more patchy cloud regime. For the simulations presented here, cloud condensation nuclei (CCN) scavenging did not play an important role in the clearing of the cloud. The results have implications for understanding transitions between the different cellular regimes in marine boundary layer (MBL) clouds.

EOF analysis of three records of sea-ice concentration spanning the last 30 years

Several continuous observational datasets of Artic sea-ice concentration are currently available that cover the period since the advent of routine satellite observations. We report on a comparison of three sea-ice concentration datasets. These are the National Ice Center charts, and two passive microwave radiometer datasets derived using different approaches: the NASA team and Bootstrap algorithms. Empirical orthogonal function (EOF) analyses were employed to compare modes of variability and their consistency between the datasets. The analysis was motivated by the need for a reliable, realistic sea ice climatology for use in climate model simulations, for which both the variability and absolute values of extent and concentration are important. We found that, while there are significant discrepancies in absolute concentrations, the major modes of variability derived from all records were essentially the same.

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.

Flow synthesis using gaseous ammonia in a Teflon AF-2400 tube-in-tube reactor: Paal–Knorr pyrrole formation and gas concentration measurement by inline flow titration

Using a simple and accessible Teflon AF-2400 based tube-intube reactor, a series of pyrroles were synthesised in flow using the Paal–Knorr reaction of 1,4-diketones with gaseous ammonia. An inline flow titration technique allowed measurement of the ammonia concentration and its relationship to residence time and temperature.