A TVD finite difference scheme with non-uniform meshes and without upstream weighting

We present a finite difference scheme, with the TVD (total variation diminishing) property, for scalar conservation laws. The scheme applies to non-uniform meshes, allowing for variable mesh spacing, and is without upstream weighting. When applied to systems of conservation laws, no scalar decomposition is required, nor are any artificial tuning parameters, and this leads to an efficient, robust algorithm.

A review of the spatial economics of non-timber forest product extraction: implications for policy

Patterns of forest cover and forest degradation determine the size and types of ecosystem services forests provide. Particularly in low-income countries, nontimber forest product (NTFP) extraction by rural people, which provides important resources and income to the rural poor, contributes to the level and pattern of forest degradation. Although recent policy, particularly in Africa, emphasizes forest degradation, relatively little research describes the spatial aspects of NTFP collection that lead to spatial degradation patterns. This paper reviews both the spatial empirical work on NTFP extraction and related forest degradation patterns, and spatial models of behavior of rural people who extract NTFPs from forest. Despite the impact of rural people's behavior on resulting quantities and patterns of forest resources, spatial–temporal models/patterns rarely inform park siting and sizing decisions, econometric assessments of park effectiveness, development projects to support conservation, or REDD protocols. Using the literature review as a lens, we discuss the models' implications for these policies with particular emphasis on effective conservation spending and leakage.

The effectiveness of botanic garden collections in supporting plant conservation: a European case study

Europe has the greatest concentration of botanic gardens in the world, they cultivate extensive collections of plants that include samples of European threatened plant species. This study looks at the effectiveness of these collections in supporting species conservation. A three part study is presented: (1) the results of a survey and assessment of threatened plants in botanic gardens, as defined by the Bern Convention; (2) case studies illustrating current issues in the ex situ management of European threatened plant species; and (3) presentation of policy recommendations on further improving botanic garden contributions to European plant conservation. The survey indicated that of 119 European botanic gardens in 29 European countries, 105 are cultivating 308 of the 573 threatened plant species listed by the Bern Convention. The survey identified 25 botanic gardens in 14 countries undertaking 51 conservation projects focused on 27 Bern listed species. In particular this survey has established that the majority of taxa are held in a small number of collections, dominated by non-wild origin accessions, and are not adequately documented. The majority of specimens in botanic gardens are cultivated out of the range country and not contributing to a specific conservation project. We review the genetic representation and documentation of origin in collections. Existing plant collections contain representatives of populations, now lost in the wild and maintain samples of at least nine European plant taxa identified as 'Extinct in the Wild'. However, inadequate standards of record keeping has compromised the conservation value of many collections. We highlight the dangers of hybridisation and disease in ex situ collections. The results suggest that botanic garden collections are skewed towards horticulturally robust and ornamental species and do not fully reflect priorities as defined by the Bern Convention. Recognising the limitations of traditional botanic garden collections we propose that botanic gardens more effectively utilise their two core competencies, namely scientific horticulture and public display and interpretation. The unique horticultural skills resident in European botanic gardens could be more effectively utilised through the application of horticulture to the management of wild populations.

Identifying key knowledge needs for evidence-based conservation of wild insect pollinators: a collaborative cross-sectoral exercise

In response to evidence of insect pollinator declines, organisations in many sectors, including the food and farming industry, are investing in pollinator conservation. They are keen to ensure that their efforts use the best available science. We convened a group of 32 ‘conservation practitioners’ with an active interest in pollinators and 16 insect pollinator scientists. The conservation practitioners include representatives from UK industry (including retail), environmental non-government organisations and nature conservation agencies. We collaboratively developed a long list of 246 knowledge needs relating to conservation of wild insect pollinators in the UK. We refined and selected the most important knowledge needs, through a three-stage process of voting and scoring, including discussions of each need at a workshop. We present the top 35 knowledge needs as scored by conservation practitioners or scientists. We find general agreement in priorities identified by these two groups. The priority knowledge needs will structure ongoing work to make science accessible to practitioners, and help to guide future science policy and funding. Understanding the economic benefits of crop pollination, basic pollinator ecology and impacts of pesticides on wild pollinators emerge strongly as priorities, as well as a need to monitor floral resources in the landscape.

On wave action and phase in the non-canonical Hamiltonian formulation

The long time–evolution of disturbances to slowly–varying solutions of partial differential equations is subject to the adiabatic invariance of the wave action. Generally, this approximate conservation law is obtained under the assumption that the partial differential equations are derived from a variational principle or have a canonical Hamiltonian structure. Here, the wave action conservation is examined for equations that possess a non–canonical (Poisson) Hamiltonian structure. The linear evolution of disturbances in the form of slowly varying wavetrains is studied using a WKB expansion. The properties of the original Hamiltonian system strongly constrain the linear equations that are derived, and this is shown to lead to the adiabatic invariance of a wave action. The connection between this (approximate) invariance and the (exact) conservation laws of pseudo–energy and pseudomomentum that exist when the basic solution is exactly time and space independent is discussed. An evolution equation for the slowly varying phase of the wavetrain is also derived and related to Berry's phase.

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.

Non-orthogonal version of the arbitrary polygonal C-grid and a new diamond grid

Quasi-uniform grids of the sphere have become popular recently since they avoid parallel scaling bottle- necks associated with the poles of latitude–longitude grids. However quasi-uniform grids of the sphere are often non- orthogonal. A version of the C-grid for arbitrary non- orthogonal grids is presented which gives some of the mimetic properties of the orthogonal C-grid. Exact energy conservation is sacrificed for improved accuracy and the re- sulting scheme numerically conserves energy and potential enstrophy well. The non-orthogonal nature means that the scheme can be used on a cubed sphere. The advantage of the cubed sphere is that it does not admit the computa- tional modes of the hexagonal or triangular C-grids. On var- ious shallow-water test cases, the non-orthogonal scheme on a cubed sphere has accuracy less than or equal to the orthog- onal scheme on an orthogonal hexagonal icosahedron. A new diamond grid is presented consisting of quasi- uniform quadrilaterals which is more nearly orthogonal than the equal-angle cubed sphere but with otherwise similar properties. It performs better than the cubed sphere in ev- ery way and should be used instead in codes which allow a flexible grid structure.