Conditioning and preconditioning of the variational data assimilation problem

Numerical weather prediction (NWP) centres use numerical models of the atmospheric flow to forecast future weather states from an estimate of the current state. Variational data assimilation (VAR) is used commonly to determine an optimal state estimate that miminizes the errors between observations of the dynamical system and model predictions of the flow. The rate of convergence of the VAR scheme and the sensitivity of the solution to errors in the data are dependent on the condition number of the Hessian of the variational least-squares objective function. The traditional formulation of VAR is ill-conditioned and hence leads to slow convergence and an inaccurate solution. In practice, operational NWP centres precondition the system via a control variable transform to reduce the condition number of the Hessian. In this paper we investigate the conditioning of VAR for a single, periodic, spatially-distributed state variable. We present theoretical bounds on the condition number of the original and preconditioned Hessians and hence demonstrate the improvement produced by the preconditioning. We also investigate theoretically the effect of observation position and error variance on the preconditioned system and show that the problem becomes more ill-conditioned with increasingly dense and accurate observations. Finally, we confirm the theoretical results in an operational setting by giving experimental results from the Met Office variational system.

Curriculum theory, curriculum policy and the problem of ill-disciplined thinking

This paper examines the implications of policy fracture and arms length governance within the decision making processes currently shaping curriculum design within the English education system. In particular it argues that an unresolved ‘ideological fracture’ at government level has been passed down to school leaders whose response to the dilemma is distorted by the target-driven agenda of arms length agencies. Drawing upon the findings of a large scale on-line survey of history teaching in English secondary schools, this paper illustrates the problems that occur when policy making is divorced from curriculum theory, and in particular from any consideration of the nature of knowledge. Drawing on the social realist theory of knowledge elaborated by Young (2008), we argue that the rapid spread of alternative curricular arrangements, implemented in the absence of an understanding of curriculum theory, undermines the value of disciplined thinking to the detriment of many young people, particularly those in areas of social and economic deprivation.

Abundance and diversity of wild bees along gradients of heavy metal pollution

1. Wild bees are one of the most important groups of pollinators in the temperate zone. Therefore, population declines have potentially negative impacts for both crop and wildflower pollination. Although heavy metal pollution is recognized to be a problem affecting large parts of the European Union, we currently lack insights into the effects of heavy metals on wild bees. 2. We investigated whether heavy metal pollution is a potential threat to wild bee communities by comparing (i) species number, (ii) diversity and (iii) abundance as well as (iv) natural mortality of emerging bees along two independent gradients of heavy metal pollution, one at Olkusz (OLK), Poland and the other at Avonmouth (AVO), UK. We used standardized nesting traps to measure species richness and abundance of wild bees, and we recorded the heavy metal concentration in pollen collected by the red mason bee Osmia rufa as a measure of pollution. 3. The concentration of cadmium, lead and zinc in pollen collected by bees ranged from a background level in unpolluted sites [OLK: 1·3, 43·4, 99·8 (mg kg−1); AVO: 0·8, 42·0, 56·0 (mg kg−1), respectively] to a high level on sites in the vicinity of the OLK and AVO smelters [OLK: 6·7, 277·0, 440·1 (mg kg−1); AVO: 9·3, 356·2, 592·4 (mg kg−1), respectively]. 4. We found that with increasing heavy metal concentration, there was a steady decrease in the number, diversity and abundance of solitary, wild bees. In the most polluted sites, traps were empty or contained single occupants, whereas in unpolluted sites, the nesting traps collected from 4 to 5 species represented by up to ten individuals. Moreover, the proportion of dead individuals of the solitary bee Megachile ligniseca increased along the heavy metal pollution gradient at OLK from 0·2 in uncontaminated sites to 0·5 in sites with a high concentration of pollution. 5. Synthesis and applications. Our findings highlight the negative relationship between heavy metal pollution and populations of wild bees and suggest that increasing wild bee richness in highly contaminated areas will require special conservation strategies. These may include creating suitable nesting sites and sowing a mixture of flowering plants as well as installing artificial nests with wild bee cocoons in polluted areas. Applying protection plans to wild pollinating bee communities in heavy metal-contaminated areas will contribute to integrated land rehabilitation to minimize the impact of pollution on the environment.

Simple solution for a complex problem: Proanthocyanidins, galloyl glucoses and ellagitannins fit on a single calibration curve in high performance-gel permeation chromatography

This study was undertaken to explore gel permeation chromatography (GPC) for estimating molecular weights of proanthocyanidin fractions isolated from sainfoin (Onobrychis viciifolia). The results were compared with data obtained by thiolytic degradation of the same fractions. Polystyrene, polyethylene glycol and polymethyl methacrylate standards were not suitable for estimating the molecular weights of underivatized proanthocyanidins. Therefore, a novel HPLC-GPC method was developed based on two serially connected PolarGel-L columns using DMF that contained 5% water, 1% acetic acid and 0.15 M LiBr at 0.7 ml/min and 50 degrees C. This yielded a single calibration curve for galloyl glucoses (trigalloyl glucose, pentagalloyl glucose), ellagitannins (pedunculagin, vescalagin, punicalagin, oenothein B, gemin A), proanthocyanidins (procyanidin B2, cinnamtannin B1), and several other polyphenols (catechin, epicatechin gallate, epicallocatechin gallate, amentoflavone). These GPC predicted molecular weights represented a considerable advance over previously reported HPLC-GPC methods for underivatized proanthocyanidins. (C) 2011 Elsevier B.V. All rights reserved.

The key role of the western boundary in linking the AMOC strength to the north-south pressure gradient

A key idea in the study of the Atlantic meridional overturning circulation (AMOC) is that its strength is proportional to the meridional density gradient, or more precisely, to the strength of the meridional pressure gradient. A physical basis that would tell us how to estimate the relevant meridional pressure gradient locally from the density distribution in numerical ocean models to test such an idea, has been lacking however. Recently, studies of ocean energetics have suggested that the AMOC is driven by the release of available potential energy (APE) into kinetic energy (KE), and that such a conversion takes place primarily in the deep western boundary currents. In this paper, we develop an analytical description linking the western boundary current circulation below the interface separating the North Atlantic Deep Water (NADW) and Antarctic Intermediate Water (AAIW) to the shape of this interface. The simple analytical model also shows how available potential energy is converted into kinetic energy at each location, and that the strength of the transport within the western boundary current is proportional to the local meridional pressure gradient at low latitudes. The present results suggest, therefore, that the conversion rate of potential energy may provide the necessary physical basis for linking the strength of the AMOC to the meridional pressure gradient, and that this could be achieved by a detailed study of the APE to KE conversion in the western boundary current.