Wave-activity conservation laws for the three-dimensional anelastic and Boussinesq equations with a horizontally homogeneous background flow

Wave-activity conservation laws are key to understanding wave propagation in inhomogeneous environments. Their most general formulation follows from the Hamiltonian structure of geophysical fluid dynamics. For large-scale atmospheric dynamics, the Eliassen–Palm wave activity is a well-known example and is central to theoretical analysis. On the mesoscale, while such conservation laws have been worked out in two dimensions, their application to a horizontally homogeneous background flow in three dimensions fails because of a degeneracy created by the absence of a background potential vorticity gradient. Earlier three-dimensional results based on linear WKB theory considered only Doppler-shifted gravity waves, not waves in a stratified shear flow. Consideration of a background flow depending only on altitude is motivated by the parameterization of subgrid-scales in climate models where there is an imposed separation of horizontal length and time scales, but vertical coupling within each column. Here we show how this degeneracy can be overcome and wave-activity conservation laws derived for three-dimensional disturbances to a horizontally homogeneous background flow. Explicit expressions for pseudoenergy and pseudomomentum in the anelastic and Boussinesq models are derived, and it is shown how the previously derived relations for the two-dimensional problem can be treated as a limiting case of the three-dimensional problem. The results also generalize earlier three-dimensional results in that there is no slowly varying WKB-type requirement on the background flow, and the results are extendable to finite amplitude. The relationship A E =cA P between pseudoenergy A E and pseudomomentum A P, where c is the horizontal phase speed in the direction of symmetry associated with A P, has important applications to gravity-wave parameterization and provides a generalized statement of the first Eliassen–Palm theorem.

Angular momentum conservation and gravity wave drag parameterization: implications for climate models

The robustness of the parameterized gravity wave response to an imposed radiative perturbation in the middle atmosphere is examined. When momentum is conserved and for reasonable gravity wave drag parameters, the response to a polar cooling induces polar downwelling above the region of the imposed cooling, with consequent adiabatic warming. This response is robust to changes in the gravity wave source spectrum, background flow, gravity wave breaking criterion, and model lid height. When momentum is not conserved, either in the formulation or in the implementation of the gravity wave drag parameterization, the response becomes sensitive to the above-mentioned factors—in particular to the model lid height. The spurious response resulting from nonconservation is found to be nonnegligible in terms of the total gravity wave drag–induced downwelling.

Biodiversity conservation across scales: lessons from a science–policy dialogue

One of the core challenges of biodiversity conservation is to better understand the interconnectedness and interactions of scales in ecological and governance processes. These interrelationships constitute not only a complex analytical challenge but they also open up a channel for deliberative discussions and knowledge exchange between and among various societal actors which may themselves be operating at various scales, such as policy makers, land use planners, members of NGOs, and researchers. In this paper, we discuss and integrate the perspectives of various disciplines academics and stakeholders who participated in a workshop on scales of European biodiversity governance organised in Brussels in the autumn of 2010. The 23 participants represented various governmental agencies and NGOs from the European, national, and sub-national levels. The data from the focus group discussions of the workshop were analysed using qualitative content analysis. The core scale-related challenges of biodiversity policy identified by the participants were cross-level and cross-sector limitations as well as ecological, social and social-ecological complexities that potentially lead to a variety of scale-related mismatches. As ways to address these cha- llenges the participants highlighted innovations, and an aim to develop new interdisciplinary approaches to support the processes aiming to solve current scale challenges.

'Nature Conservation': a new dimension in Open Access publishing bridging science and application

This Editorial presents the focus, scope and policies of the inaugural issue of Nature Conservation, a new open access, peer-reviewed journal bridging natural sciences, social sciences and hands-on applications in conservation management. The journal covers all aspects of nature conservation and aims particularly at facilitating better interaction between scientists and practitioners. The journal will impose no restrictions on manuscript size or the use of colour. We will use an XML-based editorial workflow and several cutting-edge innovations in publishing and information dissemination. These include semantic mark-up of, and enhancements to published text, data, and extensive cross-linking within the journal and to external sources. We believe the journal will make an important contribution to better linking science and practice, offers rapid, peer-reviewed and flexible publication for authors and unrestricted access to content.

Effect of earthworm Eisenia fetida and wetland plants on nitrification and denitrification potentials in vertical flow constructed wetland.

The response of nitrification potentials, denitrification potentials, and N removal efficiency to the introduction of earthworms and wetland plants in a vertical flow constructed wetland system was investigated. Addition of earthworms increased nitrification and denitrification potentials of substrate in non-vegetated constructed wetland by 236% and 8%, respectively; it increased nitrification and denitrification potentials in rhizosphere in vegetated constructed wetland (Phragmites austrail, Typha augustifolia and Canna indica), 105% and 5%, 187% and 12%, and 268% and 15% respectively. Denitrification potentials in rhizosphere of three wetland plants were not significantly different, but nitrification potentials in rhizosphere followed the order of C. indica > T. augustifolia > P. australis when addition of earthworms into constructed wetland. Addition of earthworms to the vegetated constructed significantly increased the total number of bacteria and fungi of substrates (P < 0.05). The total number of bacteria was significantly correlated with nitrification potentials (r = 913, P < 0.01) and denitrification potentials (r = 840, P < 0.01), respectively. The N concentration of stems and leaves of C. indica were significantly higher in the constructed wetland with earthworms (P < 0.05). Earthworms had greater impact on nitrification potentials than denitrification potentials. The removal efficiency of N was improved via stimulated nitrification potentials by earthworms and higher N uptake by wetland plants.

On the group-velocity property for wave-activity conservation laws

The density and the flux of wave-activity conservation laws are generally required to satisfy the group-velocity property: under the WKB approximation (i.e., for nearly monochromatic small-amplitude waves in a slowly varying medium), the flux divided by the density equals the group velocity. It is shown that this property is automatically satisfied if, under the WKB approximation, the only source of rapid variations in the density and the flux lies in the wave phase. A particular form of the density, based on a self-adjoint operator, is proposed as a systematic choice for a density verifying this condition.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 2. pseudoenergy-based theory

This paper represents the second part of a study of semi-geostrophic (SG) geophysical fluid dynamics. SG dynamics shares certain attractive properties with the better known and more widely used quasi-geostrophic (QG) model, but is also a good prototype for balanced models that are more accurate than QG dynamics. The development of such balanced models is an area of great current interest. The goal of the present work is to extend a central body of QG theory, concerning the evolution of disturbances to prescribed basic states, to SG dynamics. Part 1 was based on the pseudomomentum; Part 2 is based on the pseudoenergy. A pseudoenergy invariant is a conserved quantity, of second order in disturbance amplitude relative to a prescribed steady basic state, which is related to the time symmetry of the system. We derive such an invariant for the semi-geostrophic equations, and use it to obtain: (i) a linear stability theorem analogous to Arnol'd's ‘first theorem’; and (ii) a small-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit. The results are analogous to their quasi-geostrophic forms, and reduce to those forms in the limit of small Rossby number. The results are derived for both the f-plane Boussinesq form of semi-geostrophic dynamics, and its extension to β-plane compressible flow by Magnusdottir & Schubert. Novel features particular to semi-geostrophic dynamics include apparently unnoticed lateral boundary stability criteria. Unlike the boundary stability criteria found in the first part of this study, however, these boundary criteria do not necessarily preclude the construction of provably stable basic states. The interior semi-geostrophic dynamics has an underlying Hamiltonian structure, which guarantees that symmetries in the system correspond naturally to the system's invariants. This is an important motivation for the theoretical approach used in this study. The connection between symmetries and conservation laws is made explicit using Noether's theorem applied to the Eulerian form of the Hamiltonian description of the interior dynamics.

Wave-activity conservation laws and stability theorems for semi-geostrophic dynamics: part 1. pseudomomentum-based theory

There exists a well-developed body of theory based on quasi-geostrophic (QG) dynamics that is central to our present understanding of large-scale atmospheric and oceanic dynamics. An important question is the extent to which this body of theory may generalize to more accurate dynamical models. As a first step in this process, we here generalize a set of theoretical results, concerning the evolution of disturbances to prescribed basic states, to semi-geostrophic (SG) dynamics. SG dynamics, like QG dynamics, is a Hamiltonian balanced model whose evolution is described by the material conservation of potential vorticity, together with an invertibility principle relating the potential vorticity to the advecting fields. SG dynamics has features that make it a good prototype for balanced models that are more accurate than QG dynamics. In the first part of this two-part study, we derive a pseudomomentum invariant for the SG equations, and use it to obtain: (i) linear and nonlinear generalized Charney–Stern theorems for disturbances to parallel flows; (ii) a finite-amplitude local conservation law for the invariant, obeying the group-velocity property in the WKB limit; and (iii) a wave-mean-flow interaction theorem consisting of generalized Eliassen–Palm flux diagnostics, an elliptic equation for the stream-function tendency, and a non-acceleration theorem. All these results are analogous to their QG forms. The pseudomomentum invariant – a conserved second-order disturbance quantity that is associated with zonal symmetry – is constructed using a variational principle in a similar manner to the QG calculations. Such an approach is possible when the equations of motion under the geostrophic momentum approximation are transformed to isentropic and geostrophic coordinates, in which the ageostrophic advection terms are no longer explicit. Symmetry-related wave-activity invariants such as the pseudomomentum then arise naturally from the Hamiltonian structure of the SG equations. We avoid use of the so-called ‘massless layer’ approach to the modelling of isentropic gradients at the lower boundary, preferring instead to incorporate explicitly those boundary contributions into the wave-activity and stability results. This makes the analogy with QG dynamics most transparent. This paper treats the f-plane Boussinesq form of SG dynamics, and its recent extension to β-plane, compressible flow by Magnusdottir & Schubert. In the limit of small Rossby number, the results reduce to their respective QG forms. Novel features particular to SG dynamics include apparently unnoticed lateral boundary stability criteria in (i), and the necessity of including additional zonal-mean eddy correlation terms besides the zonal-mean potential vorticity fluxes in the wave-mean-flow balance in (iii). In the companion paper, wave-activity conservation laws and stability theorems based on the SG form of the pseudoenergy are presented.

Nonlinear wave-activity conservation laws and Hamiltonian structure for the two-dimensional anelastic equations

Exact, finite-amplitude, local wave-activity conservation laws are derived for disturbances to steady flows in the context of the two-dimensional anelastic equations. The conservation laws are expressed entirely in terms of Eulerian quantities, and have the property that, in the limit of a small-amplitude, slowly varying, monochromatic wave train, the wave-activity density A and flux F, when averaged over phase, satisfy F = cgA where cg is the group velocity of the waves. For nonparallel steady flows, the only conserved wave activity is a form of disturbance pseudoenergy; when the steady flow is parallel, there is in addition a conservation law for the disturbance pseudomomentum. The above results are obtained not only for isentropic background states (which give the so-called “deep form” of the anelastic equations), but also for arbitrary background potential-temperature profiles θ0(z) so long as the variation in θ0(z) over the depth of the fluid is small compared with θ0 itself. The Hamiltonian structure of the equations is established in both cases, and its symmetry properties discussed. An expression for available potential energy is also derived that, for the case of a stably stratified background state (i.e., dθ0/dz > 0), is locally positive definite; the expression is valid for fully three-dimensional flow. The counterparts to results for the two-dimensional Boussinesq equations are also noted.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

Influence of earthworm Eisenia fetida on removal efficiency of N and P in vertical flow constructed wetland.

This study investigates biomass, density, photosynthetic activity, and accumulation of nitrogen (N) and phosphorus (P) in three wetland plants (Canna indica, Typha augustifolia, and Phragmites austrail) in response to the introduction of the earthworm Eisenia fetida into a constructed wetland. The removal efficiency of N and P in constructed wetlands were also investigated. Results showed that the photosynthetic rate (P n), transpiration rate (T r), and stomatal conductance (S cond) of C. indica and P. austrail were (p < 0.05) significantly higher when earthworms were present. The addition of E. fetida increased the N uptake value by above-ground of C. indica, T. augustifolia, and P. australis by 185, 216, and 108 %, respectively; and its P uptake value increased by 300, 355, and 211 %, respectively. Earthworms could enhance photosynthetic activity, density, and biomass of wetland plants in constructed wetland, resulting in the higher N and P uptake. The addition of E. fetida into constructed wetland increased the removal efficiency of TN and TP by 10 and 7 %, respectively. The addition of earthworms into vertical flow constructed wetland increased the removal efficiency of TN and TP, which was related to higher photosynthetic activity and N and P uptake. The addition of earthworms into vertical flow constructed wetland and plant harvests could be the significantly sustainable N and P removal strategy

Effect of forage conservation method on plasma lipids, mammary lipogenesis, and milk fatty acid composition in lactating cows fed diets containing a 60:40 forage-to-concentrate ratio

The effects of forage conservation method on plasma lipids, mammary lipogenesis, and milk fat were examined in 2 complementary experiments. Treatments comprised fresh grass, hay, or untreated (UTS) or formic acid treated silage (FAS) prepared from the same grass sward. Preparation of conserved forages coincided with the collection of samples from cows fed fresh grass. In the first experiment, 5 multiparous Finnish Ayrshire cows (229 d in milk) were used to compare a diet based on fresh grass followed by hay during 2 consecutive 14-d periods, separated by a 5-d transition during which extensively wilted grass was fed. In the second experiment, 5 multiparous Finnish Ayrshire cows (53 d in milk) were assigned to 1 of 2 blocks and allocated treatments according to a replicated 3 × 3 Latin square design, with 14-d periods to compare hay, UTS, and FAS. Cows received 7 or 9 kg/d of the same concentrate in experiments 1 and 2, respectively. Arterial concentrations of triacylglycerol (TAG) and phospholipid were higher in cows fed fresh grass, UTS, and FAS compared with hay. Nonesterified fatty acid (NEFA) concentrations and the relative abundance of 18:2n-6 and 18:3n-3 in TAG of arterial blood were also higher in cows fed fresh grass than conserved forages. On all diets, TAG was the principle source of fatty acids (FA) for milk fat synthesis, whereas mammary extraction of NEFA was negligible, except during zero-grazing, which was associated with a lower, albeit positive calculated energy balance. Mammary FA uptake was higher and the synthesis of 16:0 lower in cows fed fresh grass than hay. Conservation of grass by drying or ensiling had no influence on mammary extraction of TAG and NEFA, despite an increase in milk fat secretion for silages compared with hay and for FAS than UTS. Relative to hay, milk fat from fresh grass contained lower 12:0, 14:0, and 16:0 and higher S3,R7,R11,15-tetramethyl-16:0, cis-9 18:1, trans-11 18:1, cis-9,trans-11 18:2, 18:2n-6, and 18:3n-3 concentrations. Even though conserved forages altered mammary lipogenesis, differences in milk FA composition were relatively minor, other than a higher enrichment of S3,R7,R11,15-tetramethyl-16:0 in milk from silages compared with hay. In conclusion, differences in milk fat composition on fresh grass relative to conserved forages were associated with a lower energy balance, increased uptake of preformed FA, and decreased synthesis of 16:0 de novo in the mammary glands, in the absence of alterations in stearoyl-coenzyme A desaturase activity.

Present state of global wetland extent and wetland methane modelling: conclusions from a model inter-comparison project (WETCHIMP)

Global wetlands are believed to be climate sensitive, and are the largest natural emitters of methane (CH4). Increased wetland CH4 emissions could act as a positive feedback to future warming. The Wetland and Wetland CH4 Inter-comparison of Models Project (WETCHIMP) investigated our present ability to simulate large-scale wetland characteristics and corresponding CH4 emissions. To ensure inter-comparability, we used a common experimental protocol driving all models with the same climate and carbon dioxide (CO2) forcing datasets. The WETCHIMP experiments were conducted for model equilibrium states as well as transient simulations covering the last century. Sensitivity experiments investigated model response to changes in selected forcing inputs (precipitation, temperature, and atmospheric CO2 concentration). Ten models participated, covering the spectrum from simple to relatively complex, including models tailored either for regional or global simulations. The models also varied in methods to calculate wetland size and location, with some models simulating wetland area prognostically, while other models relied on remotely sensed inundation datasets, or an approach intermediate between the two. Four major conclusions emerged from the project. First, the suite of models demonstrate extensive disagreement in their simulations of wetland areal extent and CH4 emissions, in both space and time. Simple metrics of wetland area, such as the latitudinal gradient, show large variability, principally between models that use inundation dataset information and those that independently determine wetland area. Agreement between the models improves for zonally summed CH4 emissions, but large variation between the models remains. For annual global CH4 emissions, the models vary by ±40% of the all-model mean (190 Tg CH4 yr−1). Second, all models show a strong positive response to increased atmospheric CO2 concentrations (857 ppm) in both CH4 emissions and wetland area. In response to increasing global temperatures (+3.4 °C globally spatially uniform), on average, the models decreased wetland area and CH4 fluxes, primarily in the tropics, but the magnitude and sign of the response varied greatly. Models were least sensitive to increased global precipitation (+3.9 % globally spatially uniform) with a consistent small positive response in CH4 fluxes and wetland area. Results from the 20th century transient simulation show that interactions between climate forcings could have strong non-linear effects. Third, we presently do not have sufficient wetland methane observation datasets adequate to evaluate model fluxes at a spatial scale comparable to model grid cells (commonly 0.5°). This limitation severely restricts our ability to model global wetland CH4 emissions with confidence. Our simulated wetland extents are also difficult to evaluate due to extensive disagreements between wetland mapping and remotely sensed inundation datasets. Fourth, the large range in predicted CH4 emission rates leads to the conclusion that there is both substantial parameter and structural uncertainty in large-scale CH4 emission models, even after uncertainties in wetland areas are accounted for.