Scale‐ and location‐dependent correlation of nitrous oxide emissions with soil properties: an analysis using wavelets

This paper shows how the wavelet transform can be used to analyse the complex spatial covariation of the rate of nitrous oxide (N₂O) emissions from the soil with soil properties that are expected to control the evolution of N₂O. We use data on N₂O emission rates from soil cores collected at 4‐m intervals on a 1024‐m transect across arable land at Silsoe in England. Various soil properties, particularly those expected to influence N₂O production in the soil, were also determined on these cores. We used the adapted maximal overlap discrete wavelet transform (AMODWT) coefficients for the N₂O emissions and soil variables to compute their wavelet covariances and correlations. These showed that, over the transect as a whole, some soil properties were significantly correlated with N₂O emissions at fine spatial scales (soil carbon content), others at intermediate scales (soil water content) and others at coarse spatial scales (soil pH). Ammonium did not appear to be correlated with N₂O emissions at any scale, suggesting that nitrification was not a significant source of N₂O from these soils in the conditions that pertained at sampling. We used a procedure to detect changes in the wavelet correlations at several spatial scales. This showed that certain soil properties were correlated with N₂O emissions only under certain conditions of topography or parent material. This is not unexpected given that N₂O is generated by biological processes in the soil, so the rate of emission may be subject to one limiting factor in one environment and a different factor elsewhere. Such changes in the relationship between variables from one part of the landscape to another is not consistent with the geostatistical assumption that our data are realizations of coregionalized random variables.     

Spatial variation of ammonia volatilization from soil and its scale‐dependent correlation with soil properties

Quantitative predictions of ammonia volatilization from soil are useful to environmental managers and policy makers and empirical models have been used with some success. Spatial analysis of the soil properties and their relationship to the ammonia volatilization process is important as predictions will be required at disparate scales from the field to the catchment and beyond. These relationships are known to change across scales and this may affect the performance of an empirical model. This study is concerned with the variation of ammonia volatilization and some controlling soil properties: bulk density, volumetric water content, pH, CEC, soil pH buffer power, and urease activity, over distances of 2, 50, 500, and >2000 m. We sampled a 16 km × 16 km region in eastern England and analyzed the results by a nested analysis of (co)variance, from which variance components and correlations for each scale were obtained. The overall correlations between ammonia volatilization and the soil properties were generally weak: –0.09 for bulk density, 0.04 for volumetric water content, –0.22 for CEC, –0.08 for urease activity, –0.22 for pH and 0.18 for the soil pH buffer power. Variation in ammonia volatilization was scale‐dependent, with substantial variance components at the 2‐ and 500‐m scales. The results from the analysis of covariance show that the relationships between ammonia volatilization and soil properties are complex. At the >2000 m scale, ammonia volatilization was strongly correlated with pH (–0.82) and CEC (–0.55), which is probably the result of differences in parent material. We also observed weaker correlations at the 500‐m scale with bulk density (–0.61), volumetric water content (0.48), urease activity (–0.42), pH (–0.55) and soil pH buffer power (0.38). Nested analysis showed that overall correlations may mask relationships at scales of interest and the effect of soil variables on these soil processes is scale‐dependent.     

Non-homogeneity of variance components from spatially nested sampling of the soil

Spatially nested sampling and the associated nested analysis of variance by spatial scale is a well-established methodology for the exploratory investigation of soil variation over multiple, disparate scales. The variance components that can be estimated this way can be accumulated to approximate the variogram. This allows us to identify the important scales of variation, and the general form of the spatial dependence, in order to plan more detailed sampling by design-based or model-based methods. Implicit in the standard analyses of nested sample data is the assumption of homogeneity in the variance, i.e. that all variations from sub-station means at some scale represent a random variable of uniform variance. If this assumption fails then the comparable assumption of stationarity in the variance, which is an important assumption in geostatistics, will also be implausible. However, data from nested sampling may be analysed with a linear mixed model in which the variance components are parameters which can be estimated by residual maximum likelihood (REML). Within this framework it is possible to propose an alternative variance parameterization in which the variance depends on some auxiliary variable, and so is not generally homogeneous. In this paper we demonstrate this approach, using data from nested sampling of chemical and biogeochemical soil properties across a region in central England, and use land use as our auxiliary variable to model non-homogeneous variance components. We show how the REML analysis allows us to make inferences about the need for a non-homogeneous model. Variances of soil pH and cation exchange capacity at different scales differ between these land uses, but a homogeneous variance model is preferable to such non-homogeneous models for the variance of soil urease activity at standard concentrations of urea.     

Exploring the spatial relations between cereal yield and soil chemical properties and the implications for sampling

Abstract. In general, agricultural management has focused on differences between fields or on the gross differences within them. Recent developments in agricultural technology, yield mapping, Global Positioning Systems and variable rate applications, have made it possible to consider managing the considerable variation in soil and other properties within fields. This system is known as precision agriculture. More precise management of fields depends on a better understanding of the factors that affect crop input decisions. This paper examines the spatial variation in crop yield, soil nutrient status and soil pH within two agricultural fields using geostatistics. The observed properties vary considerably within each field. The relation between yield and the measured soil properties appears to be weak in general. However, the range of spatial correlation for yield, shown by the variogram, is similar to that of the soil chemical properties. In addition the latter changed little over two years. This suggests that information on the scale of variation of soil chemical properties can be derived from yield maps, which can also be used as a guide to a suitable sampling interval for soil properties.     

Two robust estimators of the cross‐variogram for multivariate geostatistical analysis of soil properties

If we wish to describe the coregionalization of two or more soil properties for estimation by cokriging then we must estimate and model their auto‐ and cross‐variogram(s). The conventional estimates of these variograms, obtained by the method‐of‐moments, are unduly affected by outlying data which inflate the variograms and so also the estimates of the error variance of cokriging predictions. Robust estimators are less affected. Robust estimators of the auto‐variogram and the pseudo cross‐variogram have previously been proposed and used successfully, but the multivariate problem of estimating the cross‐variogram robustly has not yet been tackled. Two robust estimators of the cross‐variogram are proposed. These use covariance estimators with good robustness properties. The robust estimators of the cross‐variogram proved more resistant to outliers than did the method‐of‐moments estimator when applied to simulated fields which were then contaminated. Organic carbon and water content of the soil was measured at 256 sites on a transect and the method‐of‐moments estimator, and the two robust estimators, were used to estimate the auto‐variograms and cross‐variogram from a prediction subset of 156 sites. The data on organic carbon included a few outliers. The method‐of‐moments estimator returned larger values of the auto‐ and cross‐variograms than did either robust estimator. The organic carbon content at the 100 validation sites on the transect was estimated by cokriging from the prediction data plus a set of variograms fitted to the method‐of‐moments estimates and two sets of variograms fitted to the robust estimates. The ratio of the actual squared prediction error to the cokriging estimate of the error variance was computed at each validation site. These results showed that cokriging using variograms obtained by the method‐of‐moments estimator overestimated the error variance of the predictions. By contrast, cokriging with the robustly estimated variograms gave reliable estimates of the error variance of the predictions.     

Estimating soil stress distribution by using depth‐dependent soil bulk‐density data

Depth‐dependent soil bulk density (BDS) is usually affected by soil‐specific factors like texture, structure, clay mineralogy, soil organic‐matter content, soil moisture content, and composition of soil solution and is also affected by external factors like overburden‐stress history or hydrological fluxes. Generally, the depth‐dependent BDS cannot be predicted or extrapolated precisely from a limited number of sampling depths. In the present paper, an easy method is proposed to estimate the state of soil mechanical stress by analyzing the packing characteristics of the profile using soil bulk‐density data. Results for homogeneous loess profiles exposed to the site‐specific climatic conditions show that the depth‐dependent relation of void ratio vs. weight of overburden soil can be described systematically so that deviations from the noncompacted reference state can be detected. We observed that precompaction increased from forest soils (reference) to agricultural soils with decreasing depth.     

不同尺度下田间土壤水分和混合电导率空间变异性与套合结构模型

应用地统计学原理和方法 ,分析了夏玉米田间 90m90m(L区 ) ,内套一个 30m 30m(M区) ,再内套一个 10m 10m(S区 ) 3个尺度下土壤含水量和电导率的空间变异性。结果表明 ,各尺度间土壤含水量的标准差和变异系数比较接近而电导率的差别较大。在L和M尺度下土壤含水量在 3个置信度下呈正态或对数正态分布 ,在S尺度下只在 0.01置信度下呈对数正态分布 ;在L尺度下土壤电导率仅在信度为 0.05和0.01时呈对数正态分布 ,在M尺度下仅在信度为 0.01时正态或对数正态分布 ,较高信度时呈对数正态分布 ,在S尺度下不呈正态或对数正态分布。各尺度下它们的空间结构可用球状模型描述 ,其变程分别约为 2.2～19.8m(土壤含水量 )和 2.5～17.2m(电导率 ) ,不同尺度间土壤含水量和电导率的空间变异结构函数差别较大 ,用套合结构模型能更好地描述不同尺度下土壤含水量和电导率的空间变异性。     

土壤属性空间预测中变异函数套合模型的表达与参数估计

针对当前地统计学方法中理论变异函数的参数估计多集中于对单一理论模型的参数估计,而缺乏对多尺度套合模型参数估计的研究现状,该文首先根据多尺度套合模型的特征,提出其在计算机中的统一叠加表达形式,从经验半方差散点图判断模型类型及参数取值范围,然后用遗传算法进行参数估计,并用Matlab R2010a开发了应用程序,最后以土壤养分（有机质和全钾）为例,与当前流行的地统计软件对比,证实了所提方法不仅在理论模型参数估计精度上优于传统估值方法（对比R2,分别提高6.32%和83.47%）,而且后期的Kriging插值结果的精度上更是大大优于传统方法的插值精度,证明该文所提方法在精度和套合结构支持方面均具有优势。     

Short‐term transformations of lead and cadmium compounds in soil after contamination

The behaviour and fate of trace metals, in particular lead and cadmium, when they contaminate the soil as atmospheric fall‐out are not well understood. To improve our understanding, we incorporated pure compounds of lead and cadmium into samples taken from surface horizons of three chemically contrasting soils and monitored the changes in their speciation by analysing the soil solution. In most instances the concentrations of trace metals in solution were maximal during the first few days after mixing the contaminants with the soil, and depended strongly on soil type. The exception was when the contaminant was added as sulphide particles. The initial speciation of metals also influenced their solubility, following a decreasing order which did not depend on the soil type:
Lead sulphide was progressively oxidized, but cadmium sulphide was hardly dissolved. When lead was added as sulphate, between 10 and 20% of lead particles dissolved, regardless of the soil type. For the other species, dissolution was enhanced at lower soil pH. Thermodynamic calculations with the WinHumic V program indicated that the solution was not saturated with respect to lead sulphate. We conclude that dissolution must be limited by the adsorption of inhibitors on reactive surfaces. The calculations also showed that precipitation of chloropyromorphite probably controls lead concentration in leachate from the acid organic soil. Finally, both soil type and initial speciation of contaminants control the behaviour of trace metals in soils for a time greater than a cropping season and must be considered for understanding their environmental impact.     

On-line soil mechanical resistance mapping and correlation with soil physical properties for precision agriculture

Measurement of local soil strength may be used for real time regulation of tillage parameters in precision agriculture. Cartography of soil physical properties will also facilitate the study of their influence on plant development and yields. The aim of this research was to develop and test in field conditions a sensor measuring on-line soil strength variations. The sensor was constituted of a thin blade pulled in the soil at constant depth and speed and a beam which transferred the soil–blade forces to a transducer fixed on the machine. This transducer measured the draft force (F_x), the vertical force (F_z) and the moment (M_y). A field experiment was performed in 2 ha field of silt soil (Hesbaye, Belgium). A soil strength map of the field was established by pulling the sensor at 5 m interline separation by a tractor equipped with a DGPS receiver. The relationship between the recorded forces and several soil physical parameters was studied by identifying 10 control plots on the sensor track. In each of them, cone index penetrometry profiles and soil water content were measured. Soil samples were taken in the centre of the plots to determine cohesion and internal friction angle, simple compression resistance, Atterberg limits, granulometry and pF curves. Triaxial tests identified over-consolidated soils in plots situated in the pounds of the field. Based on the parameters measured in the other plots, significant relationships were established between (1) a global penetrometry index and the F_x and M_y solicitations measured by the sensor (r²=81%); (2) gravimetric water content and the vertical force F_z (r²=78%). Interpolation by inverse distance with a range of 45 m gave the best result for the cartography of the three measured signals (F_x, F_z and M_y). The confrontation of those maps with pedological and topographic maps together with the statistical relationships and the farmer’s knowledge of the field showed high consistency. The results of this experiment in field conditions are encouraging and show the promising perspective of technological innovations allowing on-line characterisation of soil physical state for precision agriculture.     

Choosing functions for semi-variograms of soil properties and fitting them to sampling estimates

The semi-variogram is central to geostatistics and the single most important tool in geo-statistical applications to soil. Mathematical functions for semi-variograms must be conditional negative semi-definite, and there are only a few families of simple function that meet this demand. These include the transitive models with finite a priori variance deriving from moving average processes. The spherical and exponential schemes are the most often encountered members. The other major group is that of unbounded models in which the variance appears to increase without limit. The linear model is the most common in this group. If more complex models are needed they can be formed by combining two or more simple models. The usual estimator of the semi-variance is often considered inefficient and to be sensitive to departures from normality in the data. It is compared with a robust estimator and shown to be generally preferable in being unbiased and having confidence intervals that are no wider. For routine analysis, fitting models to sample semi-variograms by weighted least squares approximation, with weights proportional to the expected semi-variance, is preferred to the more elaborate and computationally demanding statistical procedures of generalized least squares and maximum likelihood. The Akaike information criterion is recommended for selecting the best model from several plausible ones to describe the observed variation in soil, though for kriging it may be desirable to validate the chosen model. Examples of models fitted to soil semi-variograms are shown and compared.     

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.     

Validation of topsoil texture derived from agricultural soil maps by current dense soil sampling

Agricultural soil maps were created to facilitate the management of fields. Such maps, at very large scale (1:5000), cover almost the entire agricultural land in Poland. These maps can be very useful for precision field management. However, they were prepared about 40–50 years ago using old mapping techniques with mainly field (organoleptic) examination of soil. For this reason it is necessary to verify agreement between such maps with the current soil status. In the case of detection of disagreements it is important to identify the causes and propose methods for improving soil maps. Only few studies were made in this aspect. The soil texture (ST) of the upper layer, as presented on the agricultural soil maps from the 1960s and 1970s, was compared with the actual ST of the same four fields in northern and central Poland. For laboratory ST determination, soil samples were collected in a dense sampling network. On average, the agreement of the ST presented on the agricultural soil maps and determined in this study was classified as medium for three fields and good for one field. However, the presence of field areas with poor agreement between the ST determined in this study and that shown on the agricultural maps was detected in all investigated fields. Identified causes for this comprised imprecision of ST determination using the organoleptic method, the generalization of the soil quality maps, and erosion processes during the years between soil mapping and this investigation. The improvement of ST presentation on the large scale soil maps might be achieved by quite denser soil sampling for ST analysis supported by ECa, yield and NDVI maps.     

Comparison of soil sampling devices used for sampling submerged soils

Abstract

Environmental sampling designed for soil chemical analyses requires precise procedural collection methods. Furthermore, soils which are submerged, represent an enigmatic sampling situation as the sample is withdrawn through the overlaying liquid layer. Contamination may arise from the liquid as well as solid material above the collected sample. A procedural problem is that close‐faced, lined samplers do not provide enough axial friction to maintain the sample within the sampler. Since the choice of proper sampling equipment is critical in site assessments, we compared two types of soil probes in this study. Both samples were nickel (Ni)‐chromium (Cr) plated having 2‐cm diameter bores. One was an open‐faced slotted sampler while the other was a closed‐faced sampler with a PETG copolyester liner. The open‐faced slotted sampler had no significantly different Ni or Cr content than did the PETG‐lined probe and maintained the soil within the sampling tube.     

Model‐based analysis using REML for inference from systematically sampled data on soil

The general linear model encompasses statistical methods such as regression and analysis of variance (anova ) which are commonly used by soil scientists. The standard ordinary least squares (OLS) method for estimating the parameters of the general linear model is a design‐based method that requires that the data have been collected according to an appropriate randomized sample design. Soil data are often obtained by systematic sampling on transects or grids, so OLS methods are not appropriate. Parameters of the general linear model can be estimated from systematically sampled data by model‐based methods. Parameters of a model of the covariance structure of the error are estimated, then used to estimate the remaining parameters of the model with known variance. Residual maximum likelihood (REML) is the best way to estimate the variance parameters since it is unbiased. We present the REML solution to this problem. We then demonstrate how REML can be used to estimate parameters for regression and anova ‐type models using data from two systematic surveys of soil. We compare an efficient, gradient‐based implementation of REML (ASReml) with an implementation that uses simulated annealing. In general the results were very similar; where they differed the error covariance model had a spherical variogram function which can have local optima in its likelihood function. The simulated annealing results were better than the gradient method in this case because simulated annealing is good at escaping local optima.     

Shrinkage of clay soils: A statistical correlation with other soil properties

The hypothesis that the shrinkage of soils is greater when expansible minerals are dominant was tested with 63 soils containing between 40 and 64% clay. Shrinkage between pF 2 and 4 (0.1 and 10 bar) correlated significantly with the expansible mineral content (measured by ethylene glycol retention) for remoulded but not for dried and rewetted specimens. Shrinkage between pF 4 and 6 (10 and 10³ bar) was strongly correlated with the expansible mineral content for both kinds of specimens. The physical significance of the results is discussed, and it is concluded that interlamellar shrinkage is not the principal component of bulk shrinkage.     

A world dataset of derived soil properties by FAO–UNESCO soil unit for global modelling

A standardized dataset of derived soil properties for the 106 soil units considered on FAO-UNESCO's 1:5 million scale Soil Map of the World is presented. It was derived from a statistical analysis of the 4353 soil profiles held in the WISE (World Inventory of Soil Emission) database, which was developed at the International Soil Reference and Information Centre (ISRIC) for the geographic quantification of soil factors that control processes of global change. Median values are presented by soil unit for selected soil properties including: pH(H₂O); organic carbon content; cation exchange capacity; sum of exchangeable Ca²⁺, Mg²⁺ and K⁺; exchangeable sodium percentage; bulk density; total porosity; available water capacity; soil drainage class; and gravel content class. Medians for these variables are presented both for the topsoil (0–30 cm) and subsoil (30–100 cm), where applicable. The data set can help to refine ratings for soil quality in global environmental models pending the availability of comprehensive georeferenced databases on soil and terrain resources such as SOTER, the World Soil and Terrain Database. In a Geographical Information System (GIS) it can be linked to the units shown on the digital Soil Map of the World through the legend code.     

A case study on the estimation accuracy of soil properties and fertilizer rates for different soil‐sampling grids

Soil testing is used to help make fertilizer recommendations for greater yields and profits. But the increase of soil‐sampling density raises costs of sample collection and analyses. The aim of this study was to compare grid‐cell sampling densities (1, 2, and 4 ha) in terms of the estimation accuracy of macronutrients (P, K, Mg) availability and pH and to investigate how sampling density affects the amount of fertilizers and lime recommended and correctly applied to winter wheat (Triticum aestivum L.). The distribution of liming requirements and available nutrients were quite similar for the 1‐ and 2‐ha grids but notably different for the 4‐ha grid. However, the whole‐field average values of pH and P, K, and Mg concentrations in soil obtained for different sampling densities were very similar, thus placing, respectively, the soil of the studied area in the same class of liming needs and nutrient availability. The range and estimation errors of these parameters decreased with sampling‐grid size increase. The amount of lime and fertilizers to be applied on the field and the portion of a field correctly limed or fertilized depended on the soil chemical property considered. If one treats the 1‐ha grid as the reference and the most correct soil‐sampling approach, 2‐ha grid offered the greatest part of the field to be adequately fertilized with lime, P, and K. However, fertilization with Mg was much more appropriate if the recommendation was based on 4‐ha, than on a 2‐ha soil‐sampling grid. To gain an insight into soil variation and soil process occurring at small scale, laboratory and geostatistical analyses on individual soil samples may be necessary in some cases. Possibly, such costly research can deliver relevant information which could be then applied into farmer's practice.     

用典范相关分析研究宁南宽谷丘陵区不同土地利用方式土壤酶活性与肥力因子的关系

土壤酶素有生物催化剂之称[1-2],既参与包括土壤生物化学过程在内的自然界物质循环,又是植物营养元素的活性库[3-4].土壤酶活性与土壤状况的关系历来为各国学者所关注[5-8],应用通径分析研究土壤酶活性与土壤性质的关系也有一些报道[9-10].