Efficient shock capturing for isentropic flows using arithmetic averaging

A shock capturing scheme is presented for the equations of isentropic flow based on upwind differencing applied to a locally linearized set of Riemann problems. This includes the two-dimensional shallow water equations using the familiar gas dynamics analogy. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver where the computational expense can be prohibitive. The scheme is applied to a two-dimensional dam-break problem and the approximate solution compares well with those given by other authors.

An efficient flux difference splitting algorithm for unsteady duct flows of a real gas

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a real gas in a single spatial coordinate. This includes flow in a duct of variable cross-section, as well as flow with slab, cylindrical or spherical symmetry, as well as the case of an ideal gas, and can be useful when testing codes for the two-dimensional equations governing compressible flow of a real gas. The resulting scheme requires an average of the flow variables across the interface between cells, and this average is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual “square root” averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and for a number of equations of state. The results compare favourably with the results from other schemes.

An efficient numerical scheme for the Euler equations

A finite difference scheme based on flux difference splitting is presented for the solution of the Euler equations for the compressible flow of an ideal gas. A linearised Riemann problem is defined, and a scheme based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency, leading to arithmetic averaging. This is in contrast to the usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. The scheme is applied to a shock tube problem and a blast wave problem. Each approximate solution compares well with those given by other schemes, and for the shock tube problem is in agreement with the exact solution.

An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

Geostatistical analysis of rainfall

Rainfall can be modeled as a spatially correlated random field superimposed on a background mean value; therefore, geostatistical methods are appropriate for the analysis of rain gauge data. Nevertheless, there are certain typical features of these data that must be taken into account to produce useful results, including the generally non-Gaussian mixed distribution, the inhomogeneity and low density of observations, and the temporal and spatial variability of spatial correlation patterns. Many studies show that rigorous geostatistical analysis performs better than other available interpolation techniques for rain gauge data. Important elements are the use of climatological variograms and the appropriate treatment of rainy and nonrainy areas. Benefits of geostatistical analysis for rainfall include ease of estimating areal averages, estimation of uncertainties, and the possibility of using secondary information (e.g., topography). Geostatistical analysis also facilitates the generation of ensembles of rainfall fields that are consistent with a given set of observations, allowing for a more realistic exploration of errors and their propagation in downstream models, such as those used for agricultural or hydrological forecasting. This article provides a review of geostatistical methods used for kriging, exemplified where appropriate by daily rain gauge data from Ethiopia.

Controls of carbon dioxide concentrations and fluxes above central London

Eddy-covariance measurements of carbon dioxide fluxes were taken semi-continuously between October 2006 and May 2008 at 190 m height in central London (UK) to quantify emissions and study their controls. Inner London, with a population of 8.2 million (~5000 inhabitants per km2) is heavily built up with 8% vegetation cover within the central boroughs. CO2 emissions were found to be mainly controlled by fossil fuel combustion (e.g. traffic, commercial and domestic heating). The measurement period allowed investigation of both diurnal patterns and seasonal trends. Diurnal averages of CO2 fluxes were found to be highly correlated to traffic. However changes in heating-related natural gas consumption and, to a lesser extent, photosynthetic activity that controlled the seasonal variability. Despite measurements being taken at ca. 22 times the mean building height, coupling with street level was adequate, especially during daytime. Night-time saw a higher occurrence of stable or neutral stratification, especially in autumn and winter, which resulted in data loss in post-processing. No significant difference was found between the annual estimate of net exchange of CO2 for the expected measurement footprint and the values derived from the National Atmospheric Emissions Inventory (NAEI), with daytime fluxes differing by only 3%. This agreement with NAEI data also supported the use of the simple flux footprint model which was applied to the London site; this also suggests that individual roughness elements did not significantly affect the measurements due to the large ratio of measurement height to mean building height.

A molluscan perspective on hydrological cycle dynamics in northwestern Europe

Shell aragonite δ18O values of unionid freshwater mussels are applied as a proxy for past river discharges in the rivers Rhine and Meuse, using a set of nine shells from selected climatic intervals during the late Holocene. A single Meuse shell derives from the Subboreal and its δ18O values are similar to modern values. The Rhine specimens represent the Subboreal, the Roman Warm Period and the Medieval Warm Period (MWP). These shells also show averages and ranges of aragonite δ18O values similar to modern specimens. This indicates that environmental conditions such as Rhine river dynamics, Alpine meltwater input and drought severity during these intervals were similar to the 20th century. These shells do not record subtle centennial to millennial climatic variation due to their relatively short lifespan and the large inter-annual and intra-seasonal variation in environmental conditions. However, they are very suitable for studying seasonal to decadal scale climate variability. The two shells with the longest lifespan appear to show decadal scale variability in reconstructed water δ18O values during the MWP, possibly forced by the North Atlantic Oscillation (NAO), which is the dominant mode of variability influencing precipitation regimes over Europe.

An urban solar flux island: measurements from London

Solar irradiance measurements from a new high density urban network in London are presented. Annual averages demonstrate that central London receives 30 ± 10 Wm-2 less solar irradiance than outer London at midday, equivalent to 9 ± 3% less than the London average. Particulate matter and AERONET measurements combined with radiative transfer modeling suggest that the direct aerosol radiative effect could explain 33 to 40% of the inner London deficit and a further 27 to 50% could be explained by increased cloud optical depth due to the aerosol indirect effect. These results have implications for solar power generation and urban energy balance models. A new technique using ‘Langley flux gradients’ to infer aerosol column concentrations over clear periods of three hours has been developed and applied to three case studies. Comparisons with particulate matter measurements across London have been performed and demonstrate that the solar irradiance measurement network is able to detect aerosol distribution across London and transport of a pollution plume out of London.

Benchmarking and setting intervention targets for key cell count parameters

Herd Companion uses routine milk‐recording records to generate twelve‐month rolling averages that indicate performance trends. This article looks at Herd Somatic Cell Count (SCC) and four other SCC‐related parameters from 252 National Milk Records (NMR) recorded herds to assess how each parameter correlates with the Herd SCC. The analysis provides evidence for the importance of targeting individual cows with high SCC recordings (>200,000 cells/ml and >500,000 cells/ml) and/or individual cows with repeatedly high SCC recordings (chronic high SCC) and/or cows that begin lactation with a high SCC recording (dry period infection) in order to achieve bulk milk Herd SCC below 200,000 cells/ml.

Evidence of cycles in European commercial real estate markets and some hypotheses

In this paper, we seek to achieve four objectives. First, we provide some contextual material concerning the performance of the UK real estate market relative to stocks and bonds over a long period. Second, we provide UK – and some non-UK European - evidence of the tendency for property demand, supply, prices and returns to fluctuate around their long term trends or averages. Third, we briefly examine some hypotheses which suggest institutional contributions to property cycles in European markets. Fourth, we suggest some reasons why the future may not be as cyclical as the past.

Standardised ileal digestibility of crude protein and amino acids of UK-grown peas and faba beans by broilers

In view of the increasing interest in home-grown legumes as components of diets for non-ruminant livestock and in an attempt to reduce the reliance on imported soya bean meal (SBM), two experiments were conducted to evaluate samples of peas and faba beans for their standardised ileal digestibility (SID) of amino acids determined with young broiler chicks. Experiment 1 evaluated six faba bean and seven pea cultivars and Experiment 2 evaluated two faba bean and three pea cultivars as well as a sample of soya bean meal provided as a reference material. Peas and beans were added at 750g/kg as the only source of protein/amino acids in a semi-synthetic diet containing the inert marker titanium dioxide; SBM was added, in a control diet, at 500g/kg. Each diet was fed to six replicates of a cage containing two Ross-type broilers for 96h at which point birds were culled allowing removal of ileal digesta. Chemical analyses allowed the calculation of the coefficient of SID of amino acids. There were no differences between samples of the same pulse species (P>0.05) but peas had higher values (P<0.05), similar to SBM, than beans. Trypsin inhibitor content (expressed as g trypsin inhibitor units/mg sample) of all pea samples was low and in the range 0.83–1.77mg/kg. There was relatively little variation in bean tannin content and composition amongst the coloured-flowered varieties; however, the white-flowered cultivar had no tannins. There was no correlation between tannin content and coefficient of SID. The content of SID of amino acids (g/kg legume) was higher in SBM when compared with peas and beans by virtue of having higher total concentrations.

A verification framework for interannual-to-decadal predictions experiments

Decadal predictions have a high profile in the climate science community and beyond, yet very little is known about their skill. Nor is there any agreed protocol for estimating their skill. This paper proposes a sound and coordinated framework for verification of decadal hindcast experiments. The framework is illustrated for decadal hindcasts tailored to meet the requirements and specifications of CMIP5 (Coupled Model Intercomparison Project phase 5). The chosen metrics address key questions about the information content in initialized decadal hindcasts. These questions are: (1) Do the initial conditions in the hindcasts lead to more accurate predictions of the climate, compared to un-initialized climate change projections? and (2) Is the prediction model’s ensemble spread an appropriate representation of forecast uncertainty on average? The first question is addressed through deterministic metrics that compare the initialized and uninitialized hindcasts. The second question is addressed through a probabilistic metric applied to the initialized hindcasts and comparing different ways to ascribe forecast uncertainty. Verification is advocated at smoothed regional scales that can illuminate broad areas of predictability, as well as at the grid scale, since many users of the decadal prediction experiments who feed the climate data into applications or decision models will use the data at grid scale, or downscale it to even higher resolution. An overall statement on skill of CMIP5 decadal hindcasts is not the aim of this paper. The results presented are only illustrative of the framework, which would enable such studies. However, broad conclusions that are beginning to emerge from the CMIP5 results include (1) Most predictability at the interannual-to-decadal scale, relative to climatological averages, comes from external forcing, particularly for temperature; (2) though moderate, additional skill is added by the initial conditions over what is imparted by external forcing alone; however, the impact of initialization may result in overall worse predictions in some regions than provided by uninitialized climate change projections; (3) limited hindcast records and the dearth of climate-quality observational data impede our ability to quantify expected skill as well as model biases; and (4) as is common to seasonal-to-interannual model predictions, the spread of the ensemble members is not necessarily a good representation of forecast uncertainty. The authors recommend that this framework be adopted to serve as a starting point to compare prediction quality across prediction systems. The framework can provide a baseline against which future improvements can be quantified. The framework also provides guidance on the use of these model predictions, which differ in fundamental ways from the climate change projections that much of the community has become familiar with, including adjustment of mean and conditional biases, and consideration of how to best approach forecast uncertainty.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Assessment of wheat cultivars for drought tolerance via osmotic stress imposed at early seedling growth stages

A study was conducted in the Department of Plant Breeding and Genetics,Sindh Agriculture University, Tandojam, Pakistan during the year 2009. Sixteen spring wheat cultivars (Triticum aestivum L.) were screened under osmotic stress with three treatments i.e. control-no PEG (polyethylene glycol), 15 percent and 25 percent PEG-6000 solution. The analysis of variance indicated significant differences among treatments for all seedling traits except seed germination percentage. Varieties also differed significantly in germination percentage, coleoptile length, shoot root length, shoot weight, root/shoot ratio and seed vigour index. However, shoot and root weights were non-significant. Significant interactions revealed that cultivars responded variably to osmotic stress treatments; hence provided better opportunity to select drought tolerant cultivars at seedling growth stages. The relative decrease over averages due to osmotic stress was 0.8 percent in seed germination, 53 percent in coleoptile length 62.9 percent in shoot length, 74.4 percent in root length, 50.6 percent in shoot weight, 45.1 percent in root weight, 30.2 percent in root/shoot ratio and 68.5 percent in seed vigour index. However, relative decrease of individual variety for various seedling traits could be more meaningful which indicated that cultivar TD-1 showed no reduction in coleoptile length, while minimum decline was noted in Anmol. For shoot length, cultivar Sarsabz expressed minimum reduction followed by Anmol. However, cultivars Anmol, Moomal, Inqalab-91, and Pavan gave almost equally lower reductions for root length suggesting their higher stress tolerance. In other words, cultivars Anmol, Moomal, Inqalab-91, Sarsabz, TD-1, ZA-77 and Pavan had relatively longer coleoptiles, shoots and roots, and were regarded as drought tolerant. Correlation coefficients among seedlings traits were significant and positive for all traits except germination percentage which had no significant correlation with any of other trait. The results indicated that increase in one trait may cause simultaneous increase in other traits; hence selection for any of these seedling attributes will lead to develop drought tolerant wheat cultivars.