Near-optimal mean value estimates for multidimensional Weyl sums

We obtain sharp estimates for multidimensional generalisations of Vinogradov’s mean value theorem for arbitrary translation-dilation invariant systems, achieving constraints on the number of variables approaching those conjectured to be the best possible. Several applications of our bounds are discussed.

Solution-free sets for sums of binary forms

In this paper, we obtain quantitative estimates for the asymptotic density of subsets of the integer lattice Z2 that contain only trivial solutions to an additive equation involving binary forms. In the process we develop an analogue of Vinogradov’s mean value theorem applicable to binary forms.

An overview of Earth's global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Seasonal trends in the stable isotopic composition of snow and meltwater runoff in a subarctic catchment at Okstindan, Norway

Seasonal variations in the stable isotopic composition of snow and meltwater were investigated in a sub-arctic, mountainous, but non-glacial, catchment at Okstindan in northern Norway based on analyses of delta(18)O and deltaD. Samples were collected during four field periods (August 1998; April 1999; June 1999 and August 1999) at three sites lying on an altitudinal transect (740-970 m a.s.l.). Snowpack data display an increase in the mean values of delta(18)O (increasing from a mean value of - 13.51 to - 11.49% between April and August), as well as a decrease in variability through the melt period. Comparison with a regional meteoric water line indicates that the slope of the delta(18)O - deltaD line for the snowpacks decreases over the same period, dropping from 7.49 to approximately 6.2. This change points to the role of evaporation in snowpack ablation and is confirmed by the vertical profile of deuterium excess. Snowpack seepage data, although limited, also suggest reduced values of deltaD, as might be associated with local evaporation during meltwater generation. In general, meltwaters were depleted in delta(18)O relative to the source snowpack at the peak of the melt (June), but later in the year (August) the difference between the two was not statistically significant. The diurnal pattern of isotopic composition indicates that the most depleted meltwaters coincide with the peak in temperature and, hence, meltwater production.

Indicators of nitrate in wetland surface and soil-waters: interactions of vegetation and environmental factors

This paper describes a new bio-indicator method for assessing wetland ecosystem health: as such, the study is particularly relevant to current legislation such as the EU Water Framework Directive, which provides a baseline of the current status Of Surface waters. Seven wetland sites were monitored across northern Britain, with model construction data for predicting, eco-hydroloplical relationships collected from five sites during 1999, Two new sites and one repeat site were monitored during 2000 to provide model test data. The main growing season for the vegetation, and hence the sampling period, was May-August during both years. Seasonal mean concentrations of nitrate (NO3-) in surface and soil water samples during 1999 ranged from 0.01 to 14.07 mg N 1(-1), with a mean value of 1.01 mg N 1(-1). During 2000, concentrations ranged from trace level (<0.01 m- N 1(-1)) to 9.43 mg N 1(-1), with a mean of 2.73 mg N 1(.)(-1) Surface and soil-water nitrate concentrations did not influence plant species composition significantly across representative tall herb fen and mire communities. Predictive relationships were found between nitrate concentrations and structural characteristics of the wetland vegetation, and a model was developed which predicted nitrate concentrations from measures of plant diversity, canopy structure and density of reproductive structures. Two further models, which predicted stem density and density of reproductive structures respectively, utilised nitrate concentration as one of the independent predictor variables. Where appropriate, the models were tested using data collected during 2000. This approach is complementary to species-based monitoring, representing a useful and simple too] to assess ecological status in target wetland systems and has potential for bio-indication purposes.

Effect of high dose selenium enriched yeast diets on the distribution of total selenium and selenium species within lamb tissues

The objective of this study was to determine the distribution of total selenium (Se) and of the proportion of total Se comprised as the selenized amino acids selenomethionine (SeMet) and selenocysteine (SeCys) within the post mortem tissues of lambs that were fed high dose selenized enriched yeast (SY), derived from a specific strain of Saccharomyces cerevisae CNCM (Collection Nationale de Culture de Micro-organism) I-3060. Thirty two Texel X Suffolk lambs (6.87 ± 0.23 kg BW) were offered both reconstituted milk replacer and a pelleted diet, both of which had been either supplemented with high SY (6.30 ± 0.18 mg Se/kg DM) or unsupplemented (0.13 ± 0.01 mg Se/kg of DM), depending on treatment designation, for a continuous period of 91 d. At enrollment and 28, 56 and 91 d following enrollment lambs were blood sampled. At the completion of the treatment period, five lambs from each treatment group were euthanased and samples of heart, liver, kidney and skeletal muscle (Longissimus Dorsi and Psoas Major) were retained for Se analysis. The inclusion of high SY increased (P < 0.001) whole blood Se concentration, reaching a maximum mean value of 815.2 ± 19.1 ng Se/mL compared with 217.8 ± 9.1 ng Se/mL in control animals. Tissue total Se concentrations were significantly (P < 0.001) higher in SY supplemented animals than in controls irrespective of tissue type; values were 26, 16, 8 and 3 times higher in skeletal muscle, liver, heart and kidney tissue of HSY lambs when compared to controls. however, the distribution of total Se and the proportions of total Se comprised as either SeMet or SeCys differed between tissue types. Selenocysteine was the predominant selenized amino acid in glandular tissues, such the liver and kidney. irrespective of treatment, although absolute values were markedly higher in HSY lambs. Conversely selenomethionine was the predominat selenized amino acid in cardiac and skeletal muscle (Longissimus Dorsi, and Psoas Major) tissues in HSY animals, although the same trend was not apparent for control lambs in which SeCys was the predominant selenized amino acid. It was concluded that there were increases in both whole blood and tissue total Se concentrations as a result of dietary supplementation with high dose of SY. Furthermore, distribution of total Se and Se species differed between both treatment designation and tissue type.

Surface determination of the air-earth electrical current density using co-located sensors of different geometry

A vertical conduction current flows in the atmosphere as a result of the global atmospheric electric circuit. The current at the surface consists of the conduction current and a locally generated displacement current, which are often approximately equal in magnitude. A method of separating the two currents using two collectors of different geometry is investigated. The picoammeters connected to the collectors have a RC time constant of approximately 3 s, permitting the investigation of higher frequency air-earth current changes than previously achieved. The displacement current component of the air-earth current derived from the instrument agrees with calculations using simultaneous data from a co-located fast response electric field mill. The mean value of the nondisplacement current measured over 9 h was 1.76 +/- 0.002 pA m(-2). (c) 2006 American Institute of Physics.

The variation of solar wind correlation lengths over three solar cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ | B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field λ_{B_{XYZ}} and of the velocity λ_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×106 km. We conclude that a linear relation between λ | B|, VB 2, and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB 2. By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ | B| correspond to the turbulent outer scale. A tail of larger λ | B| values is present at solar maximum causing the increase in mean value.

An overview of Earth’s global electric circuit and atmospheric conductivity

The Earth’s global atmospheric electric circuit depends on the upper and lower atmospheric boundaries formed by the ionosphere and the planetary surface. Thunderstorms and electrified rain clouds drive a DC current (∼1 kA) around the circuit, with the current carried by molecular cluster ions; lightning phenomena drive the AC global circuit. The Earth’s near-surface conductivity ranges from 10−7 S m−1 (for poorly conducting rocks) to 10−2 S m−1 (for clay or wet limestone), with a mean value of 3.2 S m−1 for the ocean. Air conductivity inside a thundercloud, and in fair weather regions, depends on location (especially geomagnetic latitude), aerosol pollution and height, and varies from ∼10−14 S m−1 just above the surface to 10−7 S m−1 in the ionosphere at ∼80 km altitude. Ionospheric conductivity is a tensor quantity due to the geomagnetic field, and is determined by parameters such as electron density and electron–neutral particle collision frequency. In the current source regions, point discharge (coronal) currents play an important role below electrified clouds; the solar wind-magnetosphere dynamo and the unipolar dynamo due to the terrestrial rotating dipole moment also apply atmospheric potential differences. Detailed measurements made near the Earth’s surface show that Ohm’s law relates the vertical electric field and current density to air conductivity. Stratospheric balloon measurements launched from Antarctica confirm that the downward current density is ∼1 pA m−2 under fair weather conditions. Fortuitously, a Solar Energetic Particle (SEP) event arrived at Earth during one such balloon flight, changing the observed atmospheric conductivity and electric fields markedly. Recent modelling considers lightning discharge effects on the ionosphere’s electric potential (∼+250 kV with respect to the Earth’s surface) and hence on the fair weather potential gradient (typically ∼130 V m−1 close to the Earth’s surface. We conclude that cloud-to-ground (CG) lightning discharges make only a small contribution to the ionospheric potential, and that sprites (namely, upward lightning above energetic thunderstorms) only affect the global circuit in a miniscule way. We also investigate the effects of mesoscale convective systems on the global circuit.

Effect of energy and protein supplementation on phosphorus utilization in lactating dairy cows

Two experiments were undertaken in which grass silage was used in conjunction with a series of different concentrate types designed to examine the effect of carbohydrate source, protein level and degradability on total dietary phosphorus (P) utilization with emphasis on P pollution. Twelve Holstein-Friesian dairy cows in early to mid-lactation were used in an incomplete changeover design with four periods consisting of 4 weeks each. Phosphorus intake ranged from 54 to 80 g/day and faecal P represented the principal route by which ingested P was disposed of by cows, with insignificant amounts being voided in urine. A positive linear relationship between faecal P and P intake was established. In Experiment 1, P utilization was affected by dietary carbohydrate type, with an associated output of 3.3 g faecal P/g milk P produced for all treatments except those utilizing low degradable starch and low protein supplements, where a mean value of 2.8 g faecal P/g milk P was observed. In Experiment 2, where two protein levels and three protein degradabilities were examined, the efficiency of P utilization for milk P production was not affected by either level or degradability of crude protein (CP) but a significant reduction in faecal P excretion due to lower protein and P intake was observed. In general, P utilization in Experiment 2 was substantially improved compared to the Experiment 1, with an associated output of 1.8 g faecal P/g milk P produced. The improved utilization of P in Experiment 2 could be due to lower P content of the diets offered and higher dry matter (DM) intake. For dairy cows weighing 600 kg, consuming 17-18 kg DM/day and producing about 25 kg milk, P excretion in faeces and hence P pollution to the environment might be minimized without compromising lactational performance by formulating diets to supply about 68 g P/day, which is close to recent published recommended requirements for P.

Research note: amendments to the model for predicting age at sexual maturity for growing pullets of layer strains following changes in photoperiod

A model was published by Lewis et al. (2002) to predict the mean age at first egg (AFE) for pullets of laying strains reared under non-limiting environmental conditions and exposed to a single change in photoperiod during the rearing stage. Subsequently, Lewis et al. (2003) reported the effects of two opposing changes in photoperiod, which showed that the first change appears to alter the pullet's physiological age so that it responds to the second change as though it had been given at an earlier age (if photoperiod was decreased), or later age (if photoperiod was increased) than the true chronological age. During the construction of a computer model based on these two publications, it became apparent that some of the components of the models needed adjustment. The amendments relate to (1) the standard deviation (S.D.) used for calculating the proportion of a young flock that has attained photosensitivity, (2) the equation for calculating the slope of the line relating AFE to age at transfer from one photoperiod to another, (3) the equation used for estimating the distribution of AFE as a function of the mean value, (4) the point of no return when pullets which have started spontaneous maturation in response to the current photoperiod can no longer respond to a late change in photoperiod and (5) the equations used for calculating the distribution of AFE when the trait is bimodal.

Concentrations of parabens in human breast tumours

Parabens are used as preservatives in many thousands of cosmetic, food and pharmaceutical products to which the human population is exposed. Although recent reports of the oestrogenic properties of parabens have challenged current concepts of their toxicity in these consumer products, the question remains as to whether any of the parabens can accumulate intact in the body from the long-term, low-dose levels to which humans are exposed. Initial studies reported here show that parabens can be extracted from human breast tissue and detected by thin-layer chromatography. More detailed studies enabled identification and measurement of mean concentrations of individual parabens in samples of 20 human breast tumours by high-pressure liquid chromatography followed by tandem mass spectrometry. The mean concentration of parabens in these 20 human breast tumours was found to be 20.6 +/- 4.2 ng g(-1) tissue. Comparison of individual parabens showed that methylparaben was present at the highest level (with a mean value of 12.8 +/- 2.2 ng g(-1) tissue) and represents 62% of the total paraben recovered in the extractions. These studies demonstrate that parabens can be found intact in the human breast and this should open the way technically for more detailed information to be obtained on body burdens of parabens and in particular whether body burdens are different in cancer from those in normal tissues. Copyright (C) 2004 John Wiley Sons, Ltd.

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.

Multimodel assessment of the upper troposphere and lower stratosphere: Extratropics

A multimodel assessment of the performance of chemistry-climate models (CCMs) in the extratropical upper troposphere/lower stratosphere (UTLS) is conducted for the first time. Process-oriented diagnostics are used to validate dynamical and transport characteristics of 18 CCMs using meteorological analyses and aircraft and satellite observations. The main dynamical and chemical climatological characteristics of the extratropical UTLS are generally well represented by the models, despite the limited horizontal and vertical resolution. The seasonal cycle of lowermost stratospheric mass is realistic, however with a wide spread in its mean value. A tropopause inversion layer is present in most models, although the maximum in static stability is located too high above the tropopause and is somewhat too weak, as expected from limited model resolution. Similar comments apply to the extratropical tropopause transition layer. The seasonality in lower stratospheric chemical tracers is consistent with the seasonality in the Brewer-Dobson circulation. Both vertical and meridional tracer gradients are of similar strength to those found in observations. Models that perform less well tend to use a semi-Lagrangian transport scheme and/or have a very low resolution. Two models, and the multimodel mean, score consistently well on all diagnostics, while seven other models score well on all diagnostics except the seasonal cycle of water vapor. Only four of the models are consistently below average. The lack of tropospheric chemistry in most models limits their evaluation in the upper troposphere. Finally, the UTLS is relatively sparsely sampled by observations, limiting our ability to quantitatively evaluate many aspects of model performance.

Advances in sequential data assimilation and numerical weather forecasting: an Ensemble Transform Kalman-Bucy Filter, a study on clustering in deterministic Ensemble Square Root Filters, and a test of a new time stepping scheme in an atmospheric model

This dissertation deals with aspects of sequential data assimilation (in particular ensemble Kalman filtering) and numerical weather forecasting. In the first part, the recently formulated Ensemble Kalman-Bucy (EnKBF) filter is revisited. It is shown that the previously used numerical integration scheme fails when the magnitude of the background error covariance grows beyond that of the observational error covariance in the forecast window. Therefore, we present a suitable integration scheme that handles the stiffening of the differential equations involved and doesn’t represent further computational expense. Moreover, a transform-based alternative to the EnKBF is developed: under this scheme, the operations are performed in the ensemble space instead of in the state space. Advantages of this formulation are explained. For the first time, the EnKBF is implemented in an atmospheric model. The second part of this work deals with ensemble clustering, a phenomenon that arises when performing data assimilation using of deterministic ensemble square root filters in highly nonlinear forecast models. Namely, an M-member ensemble detaches into an outlier and a cluster of M-1 members. Previous works may suggest that this issue represents a failure of EnSRFs; this work dispels that notion. It is shown that ensemble clustering can be reverted also due to nonlinear processes, in particular the alternation between nonlinear expansion and compression of the ensemble for different regions of the attractor. Some EnSRFs that use random rotations have been developed to overcome this issue; these formulations are analyzed and their advantages and disadvantages with respect to common EnSRFs are discussed. The third and last part contains the implementation of the Robert-Asselin-Williams (RAW) filter in an atmospheric model. The RAW filter is an improvement to the widely popular Robert-Asselin filter that successfully suppresses spurious computational waves while avoiding any distortion in the mean value of the function. Using statistical significance tests both at the local and field level, it is shown that the climatology of the SPEEDY model is not modified by the changed time stepping scheme; hence, no retuning of the parameterizations is required. It is found the accuracy of the medium-term forecasts is increased by using the RAW filter.