A Proposed Modification to the Robert–Asselin Time Filter

The Robert–Asselin time filter is widely used in numerical models of weather and climate. It successfully suppresses the spurious computational mode associated with the leapfrog time-stepping scheme. Unfortunately, it also weakly suppresses the physical mode and severely degrades the numerical accuracy. These two concomitant problems are shown to occur because the filter does not conserve the mean state, averaged over the three time slices on which it operates. The author proposes a simple modification to the Robert–Asselin filter, which does conserve the three-time-level mean state. When used in conjunction with the leapfrog scheme, the modification vastly reduces the impacts on the physical mode and increases the numerical accuracy for amplitude errors by two orders, yielding third-order accuracy. The modified filter could easily be incorporated into existing general circulation models of the atmosphere and ocean. In principle, it should deliver more faithful simulations at almost no additional computational expense. Alternatively, it may permit the use of longer time steps with no loss of accuracy, reducing the computational expense of a given simulation.

QUAGMIRE v1.3: a quasi-geostrophic model for investigating rotating fluids experiments

QUAGMIRE is a quasi-geostrophic numerical model for performing fast, high-resolution simulations of multi-layer rotating annulus laboratory experiments on a desktop personal computer. The model uses a hybrid finite-difference/spectral approach to numerically integrate the coupled nonlinear partial differential equations of motion in cylindrical geometry in each layer. Version 1.3 implements the special case of two fluid layers of equal resting depths. The flow is forced either by a differentially rotating lid, or by relaxation to specified streamfunction or potential vorticity fields, or both. Dissipation is achieved through Ekman layer pumping and suction at the horizontal boundaries, including the internal interface. The effects of weak interfacial tension are included, as well as the linear topographic beta-effect and the quadratic centripetal beta-effect. Stochastic forcing may optionally be activated, to represent approximately the effects of random unresolved features. A leapfrog time stepping scheme is used, with a Robert filter. Flows simulated by the model agree well with those observed in the corresponding laboratory experiments.

A fast radiative transfer model for the assimilation of water vapor radiances from the Kalpana very high resolution radiometer

A fast radiative transfer model (RTM) to compute emitted infrared radiances for a very high resolution radiometer (VHRR), onboard the operational Indian geostationary satellite Kalpana has been developed and verified. This work is a step towards the assimilation of Kalpana water vapor (WV) radiances into numerical weather prediction models. The fast RTM uses a regression‐based approach to parameterize channel‐specific convolved level to space transmittances. A comparison between the fast RTM and the line‐by‐line RTM demonstrated that the fast RTM can simulate line‐by‐line radiances for the Kalpana WV channel to an accuracy better than the instrument noise, while offering more rapid radiance calculations. A comparison of clear sky radiances of the Kalpana WV channel with the ECMWF model first guess radiances is also presented, aiming to demonstrate the fast RTM performance with the real observations. In order to assimilate the radiances from Kalpana, a simple scheme for bias correction has been suggested.

The Representative Soil Sampling Scheme of England and Wales: the spatial variation of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme (RSSS) has monitored the soil of agricultural land in England and Wales since 1969. Here we describe the first spatial analysis of the data from these surveys using geostatistics. Four years of data (1971, 1981, 1991 and 2001) were chosen to examine the nutrient (available K, Mg and P) and pH status of the soil. At each farm, four fields were sampled; however, for the earlier years, coordinates were available for the farm only and not for each field. The averaged data for each farm were used for spatial analysis and the variograms showed spatial structure even with the smaller sample size. These variograms provide a reasonable summary of the larger scale of variation identified from the data of the more intensively sampled National Soil Inventory. Maps of kriged predictions of K generally show larger values in the central and southeastern areas (above 200 mg L-1) and an increase in values in the west over time, whereas Mg is fairly stable over time. The kriged predictions of P show a decline over time, particularly in the east, and those of pH show an increase in the east over time. Disjunctive kriging was used to examine temporal changes in available P using probabilities less than given thresholds of this element. The RSSS was not designed for spatial analysis, but the results show that the data from these surveys are suitable for this purpose. The results of the spatial analysis, together with those of the statistical analyses, provide a comprehensive view of the RSSS database as a basis for monitoring the soil. These data should be taken into account when future national soil monitoring schemes are designed.

The Representative Soil Sampling Scheme of England and Wales: a statistical analysis of topsoil nutrient status and pH between 1971 and 2001

The Representative Soil Sampling Scheme of England and Wales has recorded information on the soil of agricultural land in England and Wales since 1969. It is a valuable source of information about the soil in the context of monitoring for sustainable agricultural development. Changes in soil nutrient status and pH were examined over the period 1971-2001. Several methods of statistical analysis were applied to data from the surveys during this period. The main focus here is on the data for 1971, 1981, 1991 and 2001. The results of examining change over time in general show that levels of potassium in the soil have increased, those of magnesium have remained fairly constant, those of phosphorus have declined and pH has changed little. Future sampling needs have been assessed in the context of monitoring, to determine the mean at a given level of confidence and tolerable error and to detect change in the mean over time at these same levels over periods of 5 and 10 years. The results of a non-hierarchical multivariate classification suggest that England and Wales could be stratified to optimize future sampling and analysis. To monitor soil quality and health more generally than for agriculture, more of the country should be sampled and a wider range of properties recorded.

Atmosphere feedbacks during ENSO in a coupled GCM with a modified atmospheric convection scheme

The too diverse representation of ENSO in a coupled GCM limits one’s ability to describe future change of its properties. Several studies pointed to the key role of atmosphere feedbacks in contributing to this diversity. These feedbacks are analyzed here in two simulations of a coupled GCM that differ only by the parameterization of deep atmospheric convection and the associated clouds. Using the Kerry–Emanuel (KE) scheme in the L’Institut Pierre-Simon Laplace Coupled Model, version 4 (IPSL CM4; KE simulation), ENSO has about the right amplitude, whereas it is almost suppressed when using the Tiedke (TI) scheme. Quantifying both the dynamical Bjerknes feedback and the heat flux feedback in KE, TI, and the corresponding Atmospheric Model Intercomparison Project (AMIP) atmosphere-only simulations, it is shown that the suppression of ENSO in TI is due to a doubling of the damping via heat flux feedback. Because the Bjerknes positive feedback is weak in both simulations, the KE simulation exhibits the right ENSO amplitude owing to an error compensation between a too weak heat flux feedback and a too weak Bjerknes feedback. In TI, the heat flux feedback strength is closer to estimates from observations and reanalysis, leading to ENSO suppression. The shortwave heat flux and, to a lesser extent, the latent heat flux feedbacks are the dominant contributors to the change between TI and KE. The shortwave heat flux feedback differences are traced back to a modified distribution of the large-scale regimes of deep convection (negative feedback) and subsidence (positive feedback) in the east Pacific. These are further associated with the model systematic errors. It is argued that a systematic and detailed evaluation of atmosphere feedbacks during ENSO is a necessary step to fully understand its simulation in coupled GCMs.

Errors associated with the preparation of aseptic products in UK hospital pharmacies: lessons from the national aseptic error reporting scheme

Background Pharmacy aseptic units prepare and supply injectables to minimise risks. The UK National Aseptic Error Reporting Scheme has been collecting data on pharmacy compounding errors, including near-misses, since 2003. Objectives The cumulative reports from January 2004 to December 2007, inclusive, were analysed. Methods The different variables of product types, error types, staff making and detecting errors, stage errors detected, perceived contributory factors, and potential or actual outcomes were presented by cross-tabulation of data. Results A total of 4691 reports were submitted against an estimated 958 532 items made, returning 0.49% as the overall error rate. Most of the errors were detected before reaching patients, with only 24 detected during or after administration. The highest number of reports related to adult cytotoxic preparations (40%) and the most frequently recorded error was a labelling error (34.2%). Errors were mostly detected at first check in assembly area (46.6%). Individual staff error contributed most (78.1%) to overall errors, while errors with paediatric parenteral nutrition appeared to be blamed on low staff levels more than other products were. The majority of errors (68.6%) had no potential patient outcomes attached, while it appeared that paediatric cytotoxic products and paediatric parenteral nutrition were associated with greater levels of perceived patient harm. Conclusions The majority of reports were related to near-misses, and this study highlights scope for examining current arrangements for checking and releasing products, certainly for paediatric cytotoxic and paediatric parenteral nutrition preparations within aseptic units, but in the context of resource and capacity constraints.

A contour-advective semi-lagrangian numerical algorithm for simulating fine-scale conservative dynamical fields

This paper describes a novel numerical algorithm for simulating the evolution of fine-scale conservative fields in layer-wise two-dimensional flows, the most important examples of which are the earth's atmosphere and oceans. the algorithm combines two radically different algorithms, one Lagrangian and the other Eulerian, to achieve an unexpected gain in computational efficiency. The algorithm is demonstrated for multi-layer quasi-geostrophic flow, and results are presented for a simulation of a tilted stratospheric polar vortex and of nearly-inviscid quasi-geostrophic turbulence. the turbulence results contradict previous arguments and simulation results that have suggested an ultimate two-dimensional, vertically-coherent character of the flow. Ongoing extensions of the algorithm to the generally ageostrophic flows characteristic of planetary fluid dynamics are outlined.

The bond scheme

Under the bond scheme, a pre-determined series of payments would compensate farmers for lost revenues resulting from policy change. Unlike the Single Payment Scheme, payments would be fully decoupled: recipients would not have to retain farmland, or remain in agriculture. If vested in a paper asset, the guaranteed, unencumbered, income stream would be similar to that from a government bond. Recipients could exchange this for a capital sum reflecting the net present value of future payments, and reinvest in other business ventures, either on- or offfarm.With a finite, declining flow of payments, budget expenditure would reduce, releasing funds for other uses.

A numerical study of the probe method

The goal of this work is the numerical realization of the probe method suggested by Ikehata for the detection of an obstacle D in inverse scattering. The main idea of the method is to use probes in the form of point source (., z) with source point z to define an indicator function (I) over cap (z) which can be reconstructed from Cauchy data or far. eld data. The indicator function boolean AND (I) over cap (z) can be shown to blow off when the source point z tends to the boundary aD, and this behavior can be used to find D. To study the feasibility of the probe method we will use two equivalent formulations of the indicator function. We will carry out the numerical realization of the functional and show reconstructions of a sound-soft obstacle.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.