L1-regularisation for ill-posed problems in variational data assimilation

We consider four-dimensional variational data assimilation (4DVar) and show that it can be interpreted as Tikhonov or L2-regularisation, a widely used method for solving ill-posed inverse problems. It is known from image restoration and geophysical problems that an alternative regularisation, namely L1-norm regularisation, recovers sharp edges better than L2-norm regularisation. We apply this idea to 4DVar for problems where shocks and model error are present and give two examples which show that L1-norm regularisation performs much better than the standard L2-norm regularisation in 4DVar.

On discrimination algorithms for ill-posed problems with an application to magnetic tomography

In this paper we explore classification techniques for ill-posed problems. Two classes are linearly separable in some Hilbert space X if they can be separated by a hyperplane. We investigate stable separability, i.e. the case where we have a positive distance between two separating hyperplanes. When the data in the space Y is generated by a compact operator A applied to the system states ∈ X, we will show that in general we do not obtain stable separability in Y even if the problem in X is stably separable. In particular, we show this for the case where a nonlinear classification is generated from a non-convergent family of linear classes in X. We apply our results to the problem of quality control of fuel cells where we classify fuel cells according to their efficiency. We can potentially classify a fuel cell using either some external measured magnetic field or some internal current. However we cannot measure the current directly since we cannot access the fuel cell in operation. The first possibility is to apply discrimination techniques directly to the measured magnetic fields. The second approach first reconstructs currents and then carries out the classification on the current distributions. We show that both approaches need regularization and that the regularized classifications are not equivalent in general. Finally, we investigate a widely used linear classification algorithm Fisher's linear discriminant with respect to its ill-posedness when applied to data generated via a compact integral operator. We show that the method cannot stay stable when the number of measurement points becomes large.

The impact of buffer zone size and management on illegal extraction, park protection and enforcement

Many protected areas or parks in developing countries have buffer zones at their boundaries to achieve the dual goals of protecting park resources and providing resource benefits to neighbouring people. Despite the prevalence of these zoning policies, few behavioural models of people’s buffer zone use inform the sizing and management of those zones. This paper uses a spatially explicit resource extraction model to examine the impact of buffer zone size and management on extraction by local people, both legal and illegal, and the impact of that extraction on forest quality in the park’s core and buffer zone. The results demonstrate trade-offs between the level of enforcement, the size of a buffer zone, and the amount of illegal extraction in the park; and describe implications for “enrichment” of buffer zones and evaluating patterns of forest degradation.

Spatial-temporal aspects of cost-benefit analysis for park management: an example from Khao Yai National Park, Thailand

Using a model calibrated to Khao Yai National Park in Thailand, this paper highlights the importance of generating explicitly spatial and temporal data for developing management plans for tropical protected forests. Spatial and temporal cost-benefit analysis should account for the interactions between different land uses – such as the benefits of contiguous areas of preserved land and edge effects – and the realities of villagers living near forests who rely on extracted resources. By taking a temporal perspective, this paper provides a rare empirical assessment of the importance of quasi-option values when determining optimal management plans.

The Greek pilot project: Lefka Ori National Park, Crete

This chapter presents the range of activities undertaken for the Lefka Ori National Park in Crete, Creece within the frame of INNOVA project which aimed at achieving the following outcomes: -Evaluation of protected area management effectiveness -Introduction to the concept of sustainability in protected area management -Developing of a sustainability monitoring strategy for Lefka Ori -Increase of stakeholder and public awareness, regarding the protected areas threats and values -Enable stakeholder and local community engagement in protected area management

Breeding biology of the White-headed Vulture Trigonoceps occipitalis in Kruger National Park, South Africa

Information on the breeding biology of the White-headed Vulture Trigonoceps occipitalis is limited and published data are few. Within the Kruger National Park in north-east South Africa there is a regionally important population of about 60 White-headed Vulture pairs, of which 22 pairs were monitored for five years between 2008 and 2012 to determine key aspects of their breeding biology. Across 73 pair/years the mean productivity of 55 breeding attempts was 0.69 chicks per pair. Median egg-laying date across all of the Kruger National Park was 27 June, but northern nests were approximately 30 d later than southern nests. Mean (SD) nearest-neighbour distance was 9 976  7 965 m and inter-nest distances ranged from 1 400 m to more than 20 km, but this did not differ significantly between habitat types. Breeding productivity did not differ significantly between habitat types. The results presented here are the first for this species in Kruger National Park and provide details against which future comparisons can be made.