Conditioning of incremental variational data assimilation, with application to the Met Office system

Implementations of incremental variational data assimilation require the iterative minimization of a series of linear least-squares cost functions. The accuracy and speed with which these linear minimization problems can be solved is determined by the condition number of the Hessian of the problem. In this study, we examine how different components of the assimilation system influence this condition number. Theoretical bounds on the condition number for a single parameter system are presented and used to predict how the condition number is affected by the observation distribution and accuracy and by the specified lengthscales in the background error covariance matrix. The theoretical results are verified in the Met Office variational data assimilation system, using both pseudo-observations and real data.

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.

Meteorological phenomena in Western classical orchestral music

Depictions of the weather are common throughout the arts. Unlike in the visual arts, however, there has been little study of meteorological inspiration in music. This article catalogues and analyzes the frequencies with which weather is depicted in a sample of classical orchestral music. The depictions vary from explicit mimicry using traditional and specialized orchestral instruments, through to subtle suggestions. It is found that composers are generally influenced by their own environment in the type of weather they choose to represent. As befits the national stereotype, British composers seem disproportionately keen to depict the UK's variable weather patterns and stormy coastline

A simple analysis of thermodynamic properties for classical plasmas: I. theory

By eliminating the short range negative divergence of the Debye–Hückel pair distribution function, but retaining the exponential charge screening known to operate at large interparticle separation, the thermodynamic properties of one-component plasmas of point ions or charged hard spheres can be well represented even in the strong coupling regime. Predicted electrostatic free energies agree within 5% of simulation data for typical Coulomb interactions up to a factor of 10 times the average kinetic energy. Here, this idea is extended to the general case of a uniform ionic mixture, comprising an arbitrary number of components, embedded in a rigid neutralizing background. The new theory is implemented in two ways: (i) by an unambiguous iterative algorithm that requires numerical methods and breaks the symmetry of cross correlation functions; and (ii) by invoking generalized matrix inverses that maintain symmetry and yield completely analytic solutions, but which are not uniquely determined. The extreme computational simplicity of the theory is attractive when considering applications to complex inhomogeneous fluids of charged particles.

A comparison between classical techniques and eigenstructure assignment in the design of a longitudinal instrument landing system

Although modern control techniques such as eigenstructure assignment have been given extensive coverage in control literature there is a reluctance to use them in practice as they are often not believed to be as `visible' or as simple as classical methods. A simple aircraft example is used, and it is shown that eigenstructure assignment can be used easily to produce a more viable controller than with simple classical techniques.

Attic pottery in early Classical Thessaly. A case study from Achaia Phthiotis

This paper attributes a previously unnoticed Attic black-figured lekythos kept in the Archaeological Museum of Volos to the Pholos Group (ca. 470 BC) and discusses its findspot in the peripheral Thessalian district of Achaia Phthiotis. Beyond an art-historical appreciation of the hastily-drawn chariot scene on this lekythos and a discussion of stylistic parallels, which include a lekythos in Prague, it is argued that such lekythoi were socially important for their shape and small size that made them easily transportable. The assumed scarcity of Attic pottery in Thessaly can be questioned given that a considerable amount of Attic pottery from Thessalian locations is mentioned only in passing or remains unpublished in museum storage. Small late black-figured lekythoi predominate amongst Attic pottery shapes in Thessaly. The popularity of such lekythoi can become indicative of human mobility across the landscape and the consumption of imported (grave) goods by social groups other than elites.

Analysis of Direct Outdoor Air Cooling Efficency for Combined Variable Air Volume Air-conditioning System in Stores in Cold Climates of China

Direct outdoor air cooling contributes a lot not only to the improvement of the indoor air quality but also to the energy saving. Its full use will reduce the water chiller’s running time especially in some stores where cooling load keeps much higher and longer than that in other buildings. A novel air-conditioning system named Combined Variable Air Volume system (CVAV), combining a normal AHU with a separate outdoor air supply system, was proposed firstly by the authors. The most attractive feature of the system is its full utilization of cooling capacity and freshness of outdoor air in the transition period of the year round. On the basis of the obtain of the dynamic cooling loads of the typical shopping malls in different four cities located in cold climates in China with the aid of DOE-2, the possibility of increasing the amount of outdoor air volume of CVAV system in the transition period instead of operating the water chillers was confirmed. Moreover, a new concept, Direct Outdoor Air Cooling Efficiency (DOACE), was defined as the ratio of cooling capacity of outdoor air to the water chiller, indicating the degree of outdoor air’s utilization. And the DOACE of the CVAV was calculated and compared with that of conventional all-air constant volume air-conditioning systems, the results showed that CVAV bear much more energy saving potential with the 10%~19% higher DOACE and it is a kind of energy efficient systems and can improve the indoor air quality as well.

Conditioning model output statistics of regional climate model precipitation on circulation patterns

Dynamical downscaling of Global Climate Models (GCMs) through regional climate models (RCMs) potentially improves the usability of the output for hydrological impact studies. However, a further downscaling or interpolation of precipitation from RCMs is often needed to match the precipitation characteristics at the local scale. This study analysed three Model Output Statistics (MOS) techniques to adjust RCM precipitation; (1) a simple direct method (DM), (2) quantile-quantile mapping (QM) and (3) a distribution-based scaling (DBS) approach. The modelled precipitation was daily means from 16 RCMs driven by ERA40 reanalysis data over the 1961–2000 provided by the ENSEMBLES (ENSEMBLE-based Predictions of Climate Changes and their Impacts) project over a small catchment located in the Midlands, UK. All methods were conditioned on the entire time series, separate months and using an objective classification of Lamb's weather types. The performance of the MOS techniques were assessed regarding temporal and spatial characteristics of the precipitation fields, as well as modelled runoff using the HBV rainfall-runoff model. The results indicate that the DBS conditioned on classification patterns performed better than the other methods, however an ensemble approach in terms of both climate models and downscaling methods is recommended to account for uncertainties in the MOS methods.