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

Post-normal science and the art of nature conservation

Nature conservation may be considered a post-normal science in that the loss of biodiversity and increasing environmental degradation require urgent action but are characterised by uncertainty at every level. An ‘extended peer community’ with varying skills, perceptions and values are involved in decision-making and implementation of conservation, and the uncertainty involved limits the effectiveness of practice. In this paper we briefly review the key ecological, philosophical and methodological uncertainties associated with conservation, and then highlight the uncertainties and gaps present within the structure and interactions of the conservation community, and which exist mainly between researchers and practitioners, in the context of nature conservation in the UK. We end by concluding that an openly post-normal science framework for conservation, which acknowledges this uncertainty but strives to minimise it, would be a useful progression for nature conservation, and recommend ways in which knowledge transfer between researchers and practitioners can be improved to support robust decision making and conservation enactment.

The identity of crop pollinators helps target conservation for improved ecosystem services

Insect pollinated mass flowering crops are becoming more widespread and there is a need to understand which insects are primarily responsible for the pollination of these crops so conservation measures can be appropriately targeted in the face of pollinator declines. This study used field surveys in conjunction with cage manipulations to identify the relative contributions of different pollinator taxa to the pollination of two widespread flowering crops, field beans and oilseed rape. Flower visiting pollinator communities observed in the field were distinct for each crop; while field beans were visited primarily by a few bumblebee species, multiple pollinator taxa visited oilseed, and the composition of this pollinator community was highly variable spatially and temporally. Neither pollinator community, however, appears to be meeting the demands of crops in our study regions. Cage manipulations showed that multiple taxa can effectively pollinate both oilseed and field beans, but bumblebees are particularly effective bean pollinators. Combining field observations and cage manipulations demonstrated that the pollination demands of these two mass flowering crops are highly contrasting, one would benefit from management to increase the abundance of some key taxa, whilst for the other, boosting overall pollinator abundance and diversity would be more appropriate. Our findings highlight the need for crop specific mitigation strategies that are targeted at conserving specific pollinator taxa (or group of taxa) that are both active and capable of crop pollination in order to reduce pollination deficits and meet the demands of future crop production.

Costing conservation: an expert appraisal of the pollinator habitat benefits of England’s entry level stewardship

Pollination services provided by insects play a key role in English crop production and wider ecology. Despite growing evidence of the negative effects of habitat loss on pollinator populations, limited policy support is available to reverse this pressure. One measure that may provide beneficial habitat to pollinators is England’s entry level stewardship agri-environment scheme. This study uses a novel expert survey to develop weights for a range of models which adjust the balance of Entry Level Stewardship options within the current area of spending. The annual costs of establishing and maintaining these option compositions were estimated at £59.3–£12.4 M above current expenditure. Although this produced substantial reduction in private cost:benefit ratios, the benefits of the scheme to pollinator habitat rose by 7–140 %; significantly increasing the public cost:benefit ratio. This study demonstrates that the scheme has significant untapped potential to provide good quality habitat for pollinators across England, even within existing expenditure. The findings should open debate on the costs and benefits of specific entry level stewardship management options and how these can be enhanced to benefit both participants and biodiversity more equitably.

Achieving production and conservation simultaneously in tropicalagricultural landscapes

Increasing population size and demand for food in the developing world is driving the intensification ofagriculture, often threatening the biodiversity within the farmland itself and in the surrounding land-scape. This paper quantifies bird and tree species richness, tree carbon and farmer’s gross income, andinteractions between these four variables, across an agricultural gradient in central Uganda. We showedthat higher cultivation intensities in farmed landscapes resulted in increased income but also a declinein species richness of birds and trees, and reductions in tree carbon storage. These declines were particu-larly marked with a shift from high intensity smallholder mixed cropping to plantation style agriculture.This was especially evident for birds where significant declines only occurred in plantations. Small scalefarming will likely continue to be a key source of cash income for the rural populations, and ensuring‘sustained agricultural growth’ within such systems while minimising negative impacts on biodiversityand other key ecosystem services will be a major future challenge.

The inclusion of forage mixtures in the diet of growing dairy heifers: impacts on digestion, energy utilisation, and methane emissions

Intensive farming focusing on monoculture grass species to maximise forage production has led to a reduction in the extent and diversity of species-rich grasslands. However, plant communities with higher species number (richness) are a potential strategy for more sustainable production and mitigation of greenhouse gas (GHG) emissions. Research has indicated the need to understand opportunities that forage mixtures can offer sustainable ruminant production systems. The objective of the two experiments reported here were to evaluate multiple species forage mixtures in comparison to ryegrass-dominant pasture, when conserved or grazed, on digestion, energy utilisation, N excretion, and methane emissions by growing 10–15 month old heifers. Experiment 1 was a 4 × 4 Latin square design with five week periods. Four forage treatments of: (1) ryegrass (control); permanent pasture with perennial ryegrass (Lolium perenne); (2) clover; a ryegrass:red clover (Trifolium pratense) mixture; (3) trefoil; a ryegrass:birdsfoot trefoil (Lotus corniculatus) mixture; and (4) flowers; a ryegrass:wild flower mixture of predominately sorrel (Rumex acetosa), ox-eye daisy (Leucanthemum vulgare), yarrow (Achillea millefolium), knapweed (Centaurea nigra) and ribwort plantain (Plantago lanceolata), were fed as haylages to four dairy heifers. Measurements included digestibility, N excretion, and energy utilisation (including methane emissions measured in respiration chambers). Experiment 2 used 12 different dairy heifers grazing three of the same forage treatments used to make haylage in experiment 1 (ryegrass, clover and flowers) and methane emissions were estimated using the sulphur hexafluoride (SF6) tracer technique. Distribution of ryegrass to other species (dry matter (DM) basis) was approximately 70:30 (clover), 80:20 (trefoil), and 40:60 (flowers) for experiment 1. During the first and second grazing rotations (respectively) in experiment 2, perennial ryegrass accounted for 95 and 98% of DM in ryegrass, and 84 and 52% of DM in clover, with red clover accounting for almost all of the remainder. In the flowers mixture, perennial ryegrass was 52% of the DM in the first grazing rotation and only 30% in the second, with a variety of other flower species occupying the remainder. Across both experiments, compared to the forage mixtures (clover, trefoil and flowers), ryegrass had a higher crude protein (CP) content (P < 0.001, 187 vs. 115 g kg −1 DM) and DM intake (P < 0.05, 9.0 vs. 8.1 kg day −1). Heifers in experiment 1 fed ryegrass, compared to the forage mixtures, had greater total tract digestibility (g kg −1) of DM (DMD; P < 0.008, 713 vs. 641) and CP (CPD, P < 0.001, 699 vs. 475), and used more intake energy (%) for body tissue deposition (P < 0.05, 2.6 vs. −4.9). For both experiments, heifers fed flowers differed the most compared to the ryegrass control for a number of measurements. Compared to ryegrass, flowers had 40% lower CP content (P < 0.001, 113 vs. 187 g kg −1), 18% lower DMD (P < 0.01, 585 vs. 713 g kg −1), 42% lower CPD (P < 0.001, 407 vs. 699 g kg −1), and 10% lower methane yield (P < 0.05, 22.6 vs. 25.1 g kg −1 DM intake). This study has shown inclusion of flowers in forage mixtures resulted in a lower CP concentration, digestibility and intake. These differences were due in part to sward management and maturity at harvest. Further research is needed to determine how best to exploit the potential environmental benefits of forage mixtures in sustainable ruminant production systems.

Science-based conservation and management in wetland archaeology: the example of Sutton Common, UK

This paper addresses the perception of different wetlands in and around the Humber estuary in the Bronze Age. Combining past and current research, it will be argued that the perception of intertidal wetlands was nearly diametrically opposed to the perception of riverine floodplains. This contrasting perception is reflected in the material culture of the Bronze Age, and may be explained through the particular manner in which landscapes changed following marine transgressions. This work was largely undertaken within the framework of the Humber Wetlands Survey, an integrated archaeological and palaeoenvironmental research programme funded by English Heritage since 1992

Observational and energetics constraints on the non-conservation of potential/Conservative Temperature and implications for ocean modelling

This paper seeks to elucidate the fundamental differences between the nonconservation of potential temperature and that of Conservative Temperature, in order to better understand the relative merits of each quantity for use as the heat variable in numerical ocean models. The main result is that potential temperature is found to behave similarly to entropy, in the sense that its nonconservation primarily reflects production/destruction by surface heat and freshwater fluxes; in contrast, the nonconservation of Conservative Temperature is found to reflect primarily the overall compressible work of expansion/contraction. This paper then shows how this can be exploited to constrain the nonconservation of potential temperature and entropy from observed surface heat fluxes, and the nonconservation of Conservative Temperature from published estimates of the mechanical energy budgets of ocean numerical models. Finally, the paper shows how to modify the evolution equation for potential temperature so that it is exactly equivalent to using an exactly conservative evolution equation for Conservative Temperature, as was recently recommended by IOC et al. (2010). This result should in principle allow ocean modellers to test the equivalence between the two formulations, and to indirectly investigate to what extent the budget of derived nonconservative quantities such as buoyancy and entropy can be expected to be accurately represented in ocean models.

Conservation assessments and Red Listing of the endemic Moroccan flora (monocotyledons)

Morocco constitutes an important centre of plant diversity and speciation in the Mediterranean Basin. However, numerous species are threatened by issues ranging from human activities to global climatic change. In this study, we present the conservation assessments and Red Listing of the endemic Moroccan monocotyledons according to International Union for Conservation of Nature (IUCN) criteria and categories. For each species, we include basic taxonomic information, local names and synonyms, uses, a distribution map, extent of occurrence, area of occupancy, population size and trend, a description of habitats and ecological requirements, and a discussion of the threats affecting the species and habitats. We assessed the threatened status of the endemic Moroccan monocotyledons at the species level (59 species) using the IUCN Red List criteria and categories (Version 3.1). This study shows the high extinction risk to the Moroccan monocotyledon flora, with 95% of threatened species (20% Critically Endangered, 50% Endangered, 25% Vulnerable) and only 5% not threatened (2% Near Threatened and 3% Least Concern). The flora is thus of conservation concern, which is poorly recognized, both nationally and internationally. The study presents the first part and so far the only national IUCN Red Data List for a large group of Moroccan plants, and thus provides an overview of the threatened Moroccan flora. This IUCN Red List is an important first step towards the recognition of the danger to Moroccan biodiversity hotspots, conservation of threatened species and the raising of public awareness at national and international levels.