Estimating temporal change in soil monitoring: II. Sampling from simulated fields

Design-based and model-based methods of estimating temporal change of soil properties over a finite area have been compared. Two large fields of auto- and cross-correlated data were simulated, each representing the spatial distribution of a variable at one time. The fields were then sampled repeatedly. The means of stratified and systematic random samples and geostatistical global estimates were used to infer the mean difference between the fields. All estimators were unbiased, but their variances differed. Pairing the positions on the two occasions increased the precision of the design–based estimates. Systematic sampling was slightly more precise than stratified sampling. Kriging was less precise than both because some of the sample information must be used to estimate the variograms at short lags. Neither balanced differences nor the normal formula for simple random sampling predicted the estimation variances of small (n< 50) systematic samples accurately. For larger samples the method of balanced differences performed well. If the spatial variation is unknown in advance and only small samples can be taken then stratified random sampling with two observations per stratum is the preferred design. It resulted in the best combination of precision and accuracy in predicting the sampling error.     

The elucidation of soil pattern in the Wyre Forest of the West Midlands, England. I. Multivariate distribution

The soil of the eastern 6 km² of the Wyre Forest in the West Midlands of England was surveyed by recording the soil profile at 36 points per km² chosen by stratified random sampling. Ordination by principal component analysis revealed an unclustered multi-variate distribution, which nevertheless was classified profitably into six fairly stable groups. The groups lacked spatial coherence when mapped, and a novel method of spatially weighted classification was devised to increase the spatial coherence. To be effective the spatial weight had to be very large and produced very heterogeneous groups of soil profile. Sampling was too sparse to delineate homogeneous parcels of soil, and the spatial scale of variation was not identified.     

The topology of pore structure in cracking clay soil I. The estimation of numerical density

The numerical density, N_v , of the pore structure of soil is the number of disjoint networks of pores per unit volume of soil. A method is described for estimating N_v of patterns of cracks that dominate in many clay subsoils. The cracks are photographed from numerous close-spaced parallel sections and skeletonized; by comparing the skeletonized photographs sequentially, individual networks are tracked from one section to another and counted. The average number of networks that appears or disappears per section in the sequence is a measure of the numerical density and is obtained by regressing the counts on the volume of soil spanned by the sections. The regressions for appearances and disappearances converge on one another and stabilize within 10 to 20 sections, so that N_v can be estimated for a sample of soil with moderate effort.
Estimates of N_v for cracks wider than 60 μm in subsoil of the Windsor series, sampled at two nearby sites and 5 years apart in time and determined from sections at 50 μm intervals, were approximately 32 cm⁻³ and 36cm⁻³. That of N_v in the Swanwick series subsoil nearby was about 75 cm⁻³.     

On the Akaike Information Criterion for choosing models for variograms of soil properties

A problem in the application of geostatistics to soil is to find satisfactory models for variograms of soil properties. It is usually solved by fitting plausible models to the sample variogram by weighted least squares approximation. The residual sum of squares can always be diminished, and the fit improved in that sense, by adding parameters to the model. A satisfactory compromise between goodness of fit and parsimony can be achieved by applying the Akaike Information Criterion (AIC). For a given set of data the variable part of the AIC is estimated by where n is the number of experimental points on the variogram, R is the residual sum of squares and p is the number of parameters in the model. The model to choose is the one for which  is least.
The AIC is closely related to Akaike's earlier final prediction error and the Schwarz criterion. It is also equivalent to an F test when adding parameters in nested models.     

OPTIMALLY PARTITIONING SOIL TRANSECTS

Two methods are described for locating soil boundaries on transects from multivariate data. One method (split moving-window, SMW) examines a transect through a window which is split at its mid point and the two halves compared. The window is moved along the transect and a boundary inferred wherever the difference between the two halves attains a local maximum. The other (maximum level-variance, MLV) examines all possible partitions of a transect that can be produced by a given number of boundaries or less and places boundaries in those positions that minimize the within-segment sum of squared deviations from the segment means (and hence maximize the between-segment sum of squares). The performances of the two methods are compared for two soil transects in Oxfordshire. MLV identified all major changes even where gradual, but was less reliable for small changes. SMW identified all sharp boundaries, even between soil types that are fairly similar. In its original form SMW did not identify gradual changes reliably, but its performance was improved both by omitting data near the centre of the window and by concentrating the discriminating power of the data beforehand as in MLV. SWM requires less computing than MLV.     

CERTAIN EQUILIBRIUM ION RATIOS FOR A SOLONETZIC SOIL

A method is described for determining the true equilibrium soil solution for a saline soil adjusted to various moisture contents by interpolation of ion ratios in solution before and after equilibration. Over the moisture range studied, equilibrium values were different at each moisture content. The ionic strengths of the equilibrium solutions were considered to be too high for calculation of activity coefficient and therefore concentration ratios were used instead of activity ratios. The ionic strength and ion ratios for the soil equilibrium solutions changed gradually over the moisture range 35 to 100 per cent, but abruptly over the lower moisture range (5 to 35 per cent). The expression log(Na)–½ log(Ca) is regarded as being particularly important.     

A lysimeter study of the fate of fertilizer nitrogen in spring barley crops grown on shallow soil overlying Chalk: crop uptake and leaching losses

The objective of this work was to determine the fate of fertilizer nitrogen (labelled with nitrogen-15) applied to an undisturbed shallow soil overlying Chalk contained in 10 lysimeters (80 cm diameter, 135 cm deep). Measurements are reported of the nitrogen uptake by four spring barley crops and the rate and extent of leaching of nitrate beyond the roots. The crops were fertilized with 0, 80 or 120 kg N ha^?1 in each of four years, but only the first application in 1977 was labelled with nitrogen ?15. Rainfall and irrigation approximated to the long-term average, but in two treatments dry or wet spring conditions were imposed for the 10 weeks after sowing the first crop in 1977. The dry matter and grain yields of the spring barley crops varied from year to year in the ranges 8.7–14.0 t ha^?1 and 3.5–6.1 t ha^?1 respectively. The total nitrogen harvested in the crop approximated to the amount of nitrogen applied in each year with an apparent recovery of fertilizer in the range 38–76%. The recovery of nitrogen derived from fertilizer (labelled with nitrogen-15) was 46–54% in the first crop and after 2 years rapidly declined to below 1%. The total amount of nitrogen-15 labelled fertilizer recovered in four barley crops was 49–57% of that applied. Mean annual nitrate concentrations in water draining from the base of the lysimeters were in the range 11.8–26.7 mg N 1^?1 and did not differ significantly between nitrogen fertilizer treatments (0, 80 and 120 kg N ha^?1 a^?1). In all treatments nitrate concentrations varied considerably within each growing season, with a cycle of peaks and troughs. Annual losses of nitrate were in the range 39–128 kg N ha^?1, and the mean annual losses over the 4 years varied between lysimeters from 65 to 83 kg N ha^?1. Nitrogen-15 labelled nitrate was detected in the first drainage water collected in autumn following its spring application, 5 months earlier. Recovery of fertilizer-derived nitrogen in drainage water was greatest during the winter following the second barley crop, and was 3.4–3.7% of the nitrogen-15 applied. Over the 4 years of the experiment 6.3–6.6% of labelled fertilizer was accounted for in drainage water, representing 2–3% of the total nitrogen lost by leaching.     

Comparison of immune response stimulated in sheep, rabbits and guinea pigs by the administration of multi-component clostridial vaccines

Over 3 years, the immunogenic responses of various batches of multi-component clostridial vaccines in sheep, rabbits and guinea pigs were compared. Fully susceptible healthy sheep were found to be more suitable than rabbits or guinea pigs for testing the potency of multi-component clostridial vaccines containing Clostridium novyi type B, C. perfringens type D, C. septicum and C. tetani, and recommendations are made that sheep are the preferred species for testing the potency of clostridial vaccines.