Using qualitative and quantitative methods to choose a habitat quality metric for air pollution policy evaluation

Atmospheric nitrogen (N) deposition has had detrimental effects on species composition in a range of sensitive habitats, although N deposition can also increase agricultural productivity and carbon storage, and favours a few species considered of importance for conservation. Conservation targets are multiple, and increasingly incorporate services derived from nature as well as concepts of intrinsic value. Priorities vary. How then should changes in a set of species caused by drivers such as N deposition be assessed? We used a novel combination of qualitative semi-structured interviews and quantitative ranking to elucidate the views of conservation professionals specialising in grasslands, heathlands and mires. Although conservation management goals are varied, terrestrial habitat quality is mainly assessed by these specialists on the basis of plant species, since these are readily observed. The presence and abundance of plant species that are scarce, or have important functional roles, emerged as important criteria for judging overall habitat quality. However, species defined as ‘positive indicator-species’ (not particularly scarce, but distinctive for the habitat) were considered particularly important. Scarce species are by definition not always found, and the presence of functionally important species is not a sufficient indicator of site quality. Habitat quality as assessed by the key informants was rank-correlated with the number of positive indicator-species present at a site for seven of the nine habitat classes assessed. Other metrics such as species-richness or a metric of scarcity were inconsistently or not correlated with the specialists’ assessments. We recommend that metrics of habitat quality used to assess N pollution impacts are based on the occurrence of, or habitat-suitability for, distinctive species. Metrics of this type are likely to be widely applicable for assessing habitat change in response to different drivers. The novel combined qualitative and quantitative approach taken to elucidate the priorities of conservation professionals could be usefully applied in other contexts

Generalized modulation theory for nonlinear gravity waves in a compressible atmosphere

This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/2–√, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition. Mathematics of Climate and Weather Forecasting, vol. 6, no. 1, 2020, pp

Waves in the gas centrifuge: Asymptotic theory and similarities with the atmosphere

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid

On strongly nonlinear gravity waves in a vertically sheared atmosphere

We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thinvertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same orderof magnitude as the background flow and hence the self-induced mean flow alters the modulation propertiesto leading order. In this theoretical study, we show that the stability of such a refracted wave depends on theclassical modulation stability criterion for each individual layer, above and below the shearing. Additionally,the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal windand the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind inthe upper layer is stronger than the wind in the lower layer.Keywords:Internal gravity waves; Modulation equations; She

An unstable mode of the stratified atmosphere under the non-traditional Coriolis acceleration

The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e., the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e. free-slip boundary at the surface and non-reflecting boundary at the top, the atmosphere at rest becomes prone to a novel unstable mode. The validity of assuming a meridionally homogeneous flow is investigated via scale analysis. Numerical experiments were conducted, and Rayleigh damping was used as a numerical approximation for the non-reflecting top boundary. Our two main results are as follows

Positive definite and mass conserving tracer transport in spectral GCMs

A new scheme that solves the advection-diffusion equation for tracers in a spectral General Circulation Model (GCM) is presented. The main ideas are (1) using a monotonic and smooth functional of the tracer as prognostic variable to ensure positive definite concentrations and continuity of all derivatives and (2) defining an adjustable tracer-mass correction as a multiplication of the tracer in grid space, giving rise to an efficient correction in spectral space. Common standard benchmark tests for two-dimensional horizontal advection using deformational wind fields show that the new scheme is accurate and essentially not diffusive. A three-dimensional test is proposed in order to validate vertical transport. Additionally to standard error norms and global tracer mass, the entropy of mixing is introduced as another conservation constraint and utilized to determine the strength of the mass correction which is a free parameter. The transport scheme is applied in a mechanistic spectral GCM from the surface to the lower thermosphere. It is extended such that the mass correction takes the diffusion and other nonconservative effects explicitly into account. By this method we estimate the mean age of air along with its dependence on the turbulent horizontal Schmidt number

Spectral stability of nonlinear gravity waves in the atmosphere

We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which represent exact solutions to the inviscid Boussinesq equations, are spectrally stable with respect to their nonlinear modulation equations under the same conditions as what is known as modulational stability from weakly nonlinear theory. In contrast to Boussinesq, the pseudo-incompressible regime does fully account for the altitudinal varying background density. Second,we show for the first time that upward-traveling non-plane wave fronts solving the inviscid nonlinear modulation equations, that compare to pseudo-incompressible theory, are unconditionally unstable. Both inviscid regimes turn out to be ill-posed as the spectra allow for arbitrarily large instability growth rates. Third, a regularization is found by including dissipative effects. The corresponding nonlinear traveling wave solutions have localized amplitude. As a consequence of the nonlinearity, envelope and linear group velocity, as given by the derivative of the frequency with respect to wavenumber, do not coincide anymore. These waves blow up unconditionally by embedded eigenvalue instabilities but the instability growth rate is bounded from above and can be computed analytically. Additionally, all three types of nonlinear modulation equations are solved numerically to further investigate and illustrate the nature of the analytic stability results

Initiation of ray tracing models: Evolution of small-amplitude gravity wave packets in non-uniform background

The present study focuses on the interaction of gravity waves in the atmosphere with the tropopause. As the vertical extent of the latter is small compared to the density scale height, wave propagation is described by the Taylor-Goldstein equation as derived from the linearised Boussinesq approximation. Of particular interest in the construction of gravity wave parameterisations for the upper atmosphere are the transmission and reflection properties of the tropopause as these determine the upward fluxes of energy and momentum carried by internal waves. A method is presented that decomposes internal waves explicitly into upward and downward propagating contributions, thus giving direct access to transmission and reflection coefficients of finite regions of non-uniform stratification in a stationary atmosphere. The scheme utilizes a piecewise constant approximation for the background stratification and matches up- and downward propagating plane wave solutions in each layer through physically meaningful coupling conditions. As a result, transmission and reflection coefficients follow immediately

Instability of the isothermal, hydrostatic equatorial atmosphere at rest under the full Coriolis acceleration

The traditional approximation neglects the cosine components of the Coriolis acceleration, and this approximation has been widely used in the study of geophysical phenomena. However, the justification of the traditional approximation is questionable under a few circumstances. In particular, dynamics with substantial vertical velocities or geophysical phenomena in the tropics have non-negligible cosine Coriolis terms. Such cases warrant investigations with the non-traditional setting, i.e., the full Coriolis acceleration. In this manuscript, we study the effect of the non-traditional setting on an isothermal, hydrostatic and compressible atmosphere assuming a meridionally homogeneous flow. Employing linear stability analysis, we show that, given appropriate boundary conditions, i.e. free-slip boundary at the surface and non-reflecting boundary at the top, the equatorial atmosphere at rest becomes unstable. Numerical experiments were conducted, and Rayleigh damping is used as a numerical approximation for the non-reflecting top boundary. Our two main results are as follows. 1) Experiments involving the full Coriolis terms exhibit exponentially growing instability while experiments subject to the same initial condition and the traditional approximation remain stable. 2) The experimental instability growth rate is close to the theoretical value. Despite the limitations of our investigations wherein only studies on the f-plane are conducted, and effects from the β-plane approximation are ignored, the presence of this instability may have physical and experimental implications for the non-traditional setting. A discussion of the limitations and implications of our study concludes our investigations. Specifically, the influence on numerical deep-atmosphere models and the validity of assuming meridionally homogeneous flow are discussed. Ray , Mark Schlutow, Rupert Klei