Approximate factorization constraint preconditioners for saddle-point matrices

We consider the application of the conjugate gradient method to the solution of large, symmetric indefinite linear systems. Special emphasis is put on the use of constraint preconditioners and a new factorization that can reduce the number of flops required by the preconditioning step. Results concerning the eigenvalues of the preconditioned matrix and its minimum polynomial are given. Numerical experiments validate these conclusions.

Fast approximate calculation of multiply scattered lidar returns

An efficient method is described for the approximate calculation of the intensity of multiply scattered lidar returns. It divides the outgoing photons into three populations, representing those that have experienced zero, one, and more than one forward-scattering event. Each population is parameterized at each range gate by its total energy, its spatial variance, the variance of photon direction, and the covariance, of photon direction and position. The result is that for an N-point profile the calculation is O(N-2) efficient and implicitly includes up to N-order scattering, making it ideal for use in iterative retrieval algorithms for which speed is crucial. In contrast, models that explicitly consider each scattering order separately are at best O(N-m/m!) efficient for m-order scattering and often cannot be performed to more than the third or fourth order in retrieval algorithms. For typical cloud profiles and a wide range of lidar fields of view, the new algorithm is as accurate as an explicit calculation truncated at the fifth or sixth order but faster by several orders of magnitude. (C) 2006 Optical Society of America.

Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic

We study global atmosphere models that are at least as accurate as the hydrostatic primitive equations (HPEs), reviewing known results and reporting some new ones. The HPEs make spherical geopotential and shallow atmosphere approximations in addition to the hydrostatic approximation. As is well known, a consistent application of the shallow atmosphere approximation requires omission of those Coriolis terms that vary as the cosine of latitude and of certain other terms in the components of the momentum equation. An approximate model is here regarded as consistent if it formally preserves conservation principles for axial angular momentum, energy and potential vorticity, and (following R. Müller) if its momentum component equations have Lagrange's form. Within these criteria, four consistent approximate global models, including the HPEs themselves, are identified in a height-coordinate framework. The four models, each of which includes the spherical geopotential approximation, correspond to whether the shallow atmosphere and hydrostatic (or quasi-hydrostatic) approximations are individually made or not made. Restrictions on representing the spatial variation of apparent gravity occur. Solution methods and the situation in a pressure-coordinate framework are discussed. © Crown copyright 2005.

Testing solutions in grass-dominated landscapes: a review of current research

In this paper we review the experimental development of agri-environment measures for use on grasslands. Sward structure has been shown to have a strong influence on birds' ability to forage in grasslands, but the effects of food abundance on foraging behaviour are poorly understood and this hinders development of grassland conservation measures. The experiments described have a dual purpose: to investigate the foraging ecology of birds on grasslands and to test candidate management measures. Most of the work featured focuses on increasing invertebrate food resources during the summer by increasing habitat heterogeneity. We also identify important gaps in the habitats provided by existing or experimental measures, where similar dual-purpose experiments are required.

Saturated salt solutions for humidity control and the survival of dry powder and oil formulations of Beauveria bassiana conidia

Oil-based formulated conidia sprayed on steel plates and conidia powder (control) of Beauveria bassiana isolate IMI 386243 were stored at temperatures from 10 to 40 degrees C in desiccators over saturated salt solutions providing relative humidities from 32 to 88%, or in hermetic storage at 40 degrees C, and moisture contents in equilibrium with 33 or 77% relative humidity. The negative semi-logarithmic relation (P < 0.005) between conidia longevity (at 40 degrees C) and equilibrium relative humidity did not differ (P > 0.25) between formulated conidia and conidia powder. Despite this, certain saturated salts provided consistently greater longevity (NaCl) and others consistently shorter longevity (KCl) for formulated conidia compared to conidia powder. These results, analysis of previous data, and comparison with hermetic storage, indicate that storage of conidia over saturated salt solutions provides inconsistent responses to environment and so may be problematic for bio-pesticide research. In hermetic storage, oil formulation was not deleterious to longevity and in the more moist environment enhanced survival periods. (c) 2005 Elsevier Inc. All rights reserved.