Comparing sampling needs for variograms of soil properties computed by the method of moments and residual maximum likelihood

It has been generally accepted that the method of moments (MoM) variogram, which has been widely applied in soil science, requires about 100 sites at an appropriate interval apart to describe the variation adequately. This sample size is often larger than can be afforded for soil surveys of agricultural fields or contaminated sites. Furthermore, it might be a much larger sample size than is needed where the scale of variation is large. A possible alternative in such situations is the residual maximum likelihood (REML) variogram because fewer data appear to be required. The REML method is parametric and is considered reliable where there is trend in the data because it is based on generalized increments that filter trend out and only the covariance parameters are estimated. Previous research has suggested that fewer data are needed to compute a reliable variogram using a maximum likelihood approach such as REML, however, the results can vary according to the nature of the spatial variation. There remain issues to examine: how many fewer data can be used, how should the sampling sites be distributed over the site of interest, and how do different degrees of spatial variation affect the data requirements? The soil of four field sites of different size, physiography, parent material and soil type was sampled intensively, and MoM and REML variograms were calculated for clay content. The data were then sub-sampled to give different sample sizes and distributions of sites and the variograms were computed again. The model parameters for the sets of variograms for each site were used for cross-validation. Predictions based on REML variograms were generally more accurate than those from MoM variograms with fewer than 100 sampling sites. A sample size of around 50 sites at an appropriate distance apart, possibly determined from variograms of ancillary data, appears adequate to compute REML variograms for kriging soil properties for precision agriculture and contaminated sites. (C) 2007 Elsevier B.V. All rights reserved.

Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Determining nugget: sill ratios of standardized variograms from aerial photographs to krige sparse soil data

Maps of kriged soil properties for precision agriculture are often based on a variogram estimated from too few data because the costs of sampling and analysis are often prohibitive. If the variogram has been computed by the usual method of moments, it is likely to be unstable when there are fewer than 100 data. The scale of variation in soil properties should be investigated prior to sampling by computing a variogram from ancillary data, such as an aerial photograph of the bare soil. If the sampling interval suggested by this is large in relation to the size of the field there will be too few data to estimate a reliable variogram for kriging. Standardized variograms from aerial photographs can be used with standardized soil data that are sparse, provided the data are spatially structured and the nugget:sill ratio is similar to that of a reliable variogram of the property. The problem remains of how to set this ratio in the absence of an accurate variogram. Several methods of estimating the nugget:sill ratio for selected soil properties are proposed and evaluated. Standardized variograms with nugget:sill ratios set by these methods are more similar to those computed from intensive soil data than are variograms computed from sparse soil data. The results of cross-validation and mapping show that the standardized variograms provide more accurate estimates, and preserve the main patterns of variation better than those computed from sparse data.

The method of least squares used to invert an orbit problem

Six parameters uniquely describe the orbit of a body about the Sun. Given these parameters, it is possible to make predictions of the body's position by solving its equation of motion. The parameters cannot be directly measured, so they must be inferred indirectly by an inversion method which uses measurements of other quantities in combination with the equation of motion. Inverse techniques are valuable tools in many applications where only noisy, incomplete, and indirect observations are available for estimating parameter values. The methodology of the approach is introduced and the Kepler problem is used as a real-world example. (C) 2003 American Association of Physics Teachers.

The method of predicate least squares refinement

Parameters to be determined in a least squares refinement calculation to fit a set of observed data may sometimes usefully be `predicated' to values obtained from some independent source, such as a theoretical calculation. An algorithm for achieving this in a least squares refinement calculation is described, which leaves the operator in full control of the weight that he may wish to attach to the predicate values of the parameters.

Observed and simulated precursors of stratospheric polar vortex anomalies in the Northern Hemisphere

The Northern Hemisphere stratospheric polar vortex is linked to surface weather. After Stratospheric Sudden Warmings in winter, the tropospheric circulation is often nudged towards the negative phase of the Northern Annular Mode (NAM) and the North Atlantic Oscillation (NAO). A strong stratospheric vortex is often associated with subsequent positive NAM/NAO conditions. For stratosphere–troposphere associations to be useful for forecasting purposes it is crucial that changes to the stratospheric vortex can be understood and predicted. Recent studies have proposed that there exist tropospheric precursors to anomalous vortex events in the stratosphere and that these precursors may be understood by considering the relationship between stationary wave patterns and regional variability. Another important factor is the extent to which the inherent variability of the stratosphere in an atmospheric model influences its ability to simulate stratosphere–troposphere links. Here we examine the lower stratosphere variability in 300-year pre-industrial control integrations from 13 coupled climate models. We show that robust precursors to stratospheric polar vortex anomalies are evident across the multi-model ensemble. The most significant tropospheric component of these precursors consists of a height anomaly dipole across northern Eurasia and large anomalies in upward stationary wave fluxes in the lower stratosphere over the continent. The strength of the stratospheric variability in the models was found to depend on the variability of the upward stationary wave fluxes and the amplitude of the stationary waves.

Whole crop cereals 1. Effect of method of harvest and preservation on chemical composition, apparent digestibility and energy value

A total of 133 samples (53 fermented unprocessed, 19 fermented processed. 62 urea-treated processed) of whole crop wheat (WCW) and 16 samples (five fermented unprocessed, six fermented processed, five urea-treated processed) of whole crop barley (WCB) were collected from commercial farms over two consecutive years (2003/2004 and 2004/2005). Disruption of the maize grains to increase starch availability was achieved at the point of harvest by processors fitted to the forage harvesters. All samples were subjected to laboratory analysis whilst 50 of the samples (24 front Year 1, 26 front Year 2 all WCW except four WCB in Year 2) were subjected to in vivo digestibility and energy value measurements using mature wether sheep. Urea-treated WCW had higher (P<0.05) pH, and dry matter (DM) and crude protein contents and lower concentrations of fermentation products than fermented WCW. Starch was generally lower in fermented, unprocessed WCW and no effect of crop maturity at harvest (as indicated by DM content) on starch concentrations was seen. Urea-treated WCW had higher (P<0.05) in vivo digestible organic matter contents in the DM (DOMD) in Year 1 although this was not recorded in Year 2. There was a close relationship between the digestibility values of organic matter and gross energy thus aiding the use of DOMD to predict metabolisable energy (ME) content. A wide range of ME values was observed (WCW. 8.7-11.8 MJ/kg DM; WCB 7.9-11.2 MJ/kg DM) with the overall ME/DOMD ratio (ME = 0.0156 DOMD) in line With Studies in other forages. There was no evidence that a separate ME/DOMD relationship was needed for WCB which is helpful for practical application. This ratio and other parameters were affected by year of harvest (P<0.05) highlighting the influence of environmental and Other undefined factors. The variability in the composition and nutritive value of WCW and WCB highlights the need for reliable and accurate evaluation methods to be available to assess the Value of these forages before they are included in diets for dairy cows. (C) 2008 Elsevier B.V. All rights reserved.

Effect of method of application of a fibrolytic enzyme product on digestive processes and milk production in Holstein-Friesian cows

Four multiparous cows with cannulas in the rumen and proximal duodenum were used in early lactation in a 4 x 4 Latin square experiment to investigate the effect of method of application of a fibrolytic enzyme product on digestive processes and milk production. The cows were given ad libitum a total mixed ration (TMR) composed of 57% (dry matter basis) forage (3:1 corn silage:grass silage) and 43% concentrates. The TMR contained (g/kg dry matter): 274 neutral detergent fiber, 295 starch, 180 crude protein. Treatments were TMR alone or TMR with the enzyme product added (2 kg/1000 kg TMR dry matter) either sprayed on the TMR 1 h before the morning feed (TMR-E), sprayed only on the concentrate the day before feeding (Concs-E), or infused into the rumen for 14 h/d (Rumen-E). There Was no significant effect on either feed intake or milk yield but both were highest on TMR-E. Rumen digestibility of dry matter, organic matter, and starch was unaffected by the enzyme. Digestibility of NDF was lowest on TMR-E in the rumen but highest postruminally. Total Tract digestibility was highest on TMR-E for dry matter, organic matter, and starch but treatment differences were nonsignificant for neutral detergent fiber: Corn silage stover retention time in the rumen was reduced by all enzyme treatments but postruminal transit time vas increased so the decline in total tract retention. time with enzymes was not significant. It is suggested that the tendency for enzymes to reduce particle retention time in the rumen may, by reducing the time available for fibrolysis to occur, at least partly explain the variability in the reported responses to enzyme treatment.

An evaluation of a Bayesian method of dose escalation based on bivariate binary responses

Recently, various approaches have been suggested for dose escalation studies based on observations of both undesirable events and evidence of therapeutic benefit. This article concerns a Bayesian approach to dose escalation that requires the user to make numerous design decisions relating to the number of doses to make available, the choice of the prior distribution, the imposition of safety constraints and stopping rules, and the criteria by which the design is to be optimized. Results are presented of a substantial simulation study conducted to investigate the influence of some of these factors on the safety and the accuracy of the procedure with a view toward providing general guidance for investigators conducting such studies. The Bayesian procedures evaluated use logistic regression to model the two responses, which are both assumed to be binary. The simulation study is based on features of a recently completed study of a compound with potential benefit to patients suffering from inflammatory diseases of the lung.

Stopping clinical trials because of treatment ineffectiveness: a comparison of a futility design with a method of stochastic curtailment

This paper introduces a simple futility design that allows a comparative clinical trial to be stopped due to lack of effect at any of a series of planned interim analyses. Stopping due to apparent benefit is not permitted. The design is for use when any positive claim should be based on the maximum sample size, for example to allow subgroup analyses or the evaluation of safety or secondary efficacy responses. A final frequentist analysis can be performed that is valid for the type of design employed. Here the design is described and its properties are presented. Its advantages and disadvantages relative to the use of stochastic curtailment are discussed. Copyright (C) 2003 John Wiley Sons, Ltd.

A method of synthesis of silicious inorganic ordered materials (MCM-41-SBA-1) employing polyacrylic acid-C(n)TAB-TEOS nanoassemblies

In this work we describe the synthesis of a variety of MCM-41 type hexagonal and SBA-1 type cubic mesostructures and mesoporous silicious materials employing a novel synthesis concept based on polyacrylic acid (Pac)-C(n)TAB complexes as backbones of the developing structures. The ordered porosity of the solids was established by XRD and TEM techniques. The synthesis concept makes use of Pac-C(n)TAB nanoassemblies as a preformed scaffold, formed by the gradual increase of pH. On this starting matrix the inorganic precursor species SiO2 precipitate via hydrolysis of TEOS under the influence of increasing pH. The molecular weight (MW) of Pac, as well as the length of carbon chain in C,TAB, determine the physical and structural characteristics of the obtained materials. Longer chain surfactants (C(16)TAB) lead to the formation of hexagonal phase, while shorter chain surfactants (C(14)TAB, C(12)TAB) favor the SBA-1 phase. Lower MW of Pac (approximate to2000) leads to better-organized structures compared to higher MW ( 450,000), which leads to worm-like mesostructures. Cell parameters and pore size increase with increasing polyelectrolyte and/or surfactant chain, while at the same time SEM photography reveals that the particle size decreases. Conductivity experiments provide some insight into the proposed self-assembling pathway. (C) 2003 Elsevier Inc. All rights reserved.

Simple general method of generating non-oxo, non-amavadine model octacoordinated vanadium(IV) complexes of some tetradentate ONNO chelating ligands from various oxovanadium(IV/V) compounds and structural characterization of one of them

A simple general route of obtaining very stable octacoordinated non-oxovanadium( IV) complexes of the general formula VL2 (where H2L is a tetradentate ONNO donor) is presented. Six such complexes (1-6) are adequately characterized by elemental analysis, mass spectrometry, and various spectroscopic techniques. One of these compounds (1) has been structurally characterized. The molecule has crystallographic 4 symmetry and has a dodecahedral structure existing in a tetragonal space group P4n2. The non-oxo character and VL2 stoichiometry for all of the complexes are established from analytical and mass spectrometric data. In addition, the non-oxo character is clearly indicated by the complete absence of the strong nu(v=o) band in the 925-1025 cm(-1) region, which is a signature of all oxovanadium species. The complexes are quite stable in open air in the solid state and in solution, a phenomenon rarely observed in non-oxovanadium(IV) or bare vanadium(IV) complexes.