Optimized spatial sampling of soil for estimation of the variogram by maximum likelihood

Recent studies have attempted to optimize the configuration of sample sites for estimation of the variogram by the usual method-of-moments. This paper shows that objective functions can readily be defined for estimation by the method of maximum likelihood. In both cases an objective function can only be defined for a specified variogram so some prior knowledge about the spatial variation of the property of interest is necessary.This paper describes the principles of the method, using Spatial Simulated Annealing for optimization, and applies optimized sample designs to simulated data. For practical applications it seems that the most fruitful way of using the technique is for supplementing simple systematic designs that provide an initial estimate of the variogram.     

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。     

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.     

Optimal interpolation and isarithmic mapping of soil properties: I The semi‐variogram and punctual kriging

Kriging is a means of spatial prediction that can be used for soil properties. It is a form of weighted local averaging. It is optimal in the sense that it provides estimates of values at unrecorded places without bias and with minimum and known variance. Isarithmic maps made by kriging are alternatives to conventional soil maps where properties can be measured at close spacings. Kriging depends on first computing an accurate semi‐variogram, which measures the nature of spatial dependence for the property. Estimates of semi‐variance are then used to determine the weights applied to the data when computing the averages, and are presented in the kriging equations. The method is applied to three sets of data from detailed soil surveys in Central Wales and Norfolk. Sodium content at Plas Gogerddan was shown to vary isotropically with a linear semi‐variogram. Ordinary punctual kriging produced a map with intricate isarithms and fairly large estimation variance, attributed to a large nugget effect. Stoniness on the same land varied anisotropically with a linear semi‐variogram, and again the estimation error of punctual kriging was fairly large. At Hole Farm, Norfolk, the thickness of cover loam varied isotropically, but with a spherical semi‐variogram. Its parameters were estimated and used to krige point values and produce a map showing substantial short‐range variation.     

Free‐Form estimation of soil hydraulic properties using Wind’s method

Transient evaporation experiments offer the potential to determine simultaneously the soil hydraulic properties necessary to simulate water flow in unsaturated soils. We present a new algorithm for determining the retention and conductivity curve from evaporation experiments which uses Wind’s method with a free‐form soil water retention function. Our algorithm estimates nodal values of volumetric water content and derives a smooth and monotone retention curve by cubic Hermite interpolation. A multilevel routine increases the number of nodes and their adequate number is identified by a performance criterion which balances goodness of fit, the cross correlation between the estimated water contents and the number of degrees of freedom. We calculate point values of unsaturated hydraulic conductivity by the instantaneous profile method and discard unreliable conductivity estimates by a statistical filter criterion. Results for three synthetic data sets including an uncertainty analysis of the estimated retention curves show that the algorithm is suitable to identify, both correctly and precisely, the soil hydraulic properties. An application to a real data set confirms these results. In order to enable the free‐form functions to be used in numerical flow simulations, we extrapolate the retention function to the dry range and compute a coupled conductivity function based on the Mualem model. Major advantages of the proposed method are the enormous flexibility provided by the free‐form functions, the low level of parameter cross‐correlation in comparison with classic parametric functions, and the possibility of assessing the uncertainty of the retention curve individually in different ranges of pressure head.     

Using regression models in design‐based estimation of spatial means of soil properties

The precision of design‐based sampling strategies can be increased by using regression models at the estimation stage. A general regression estimator is given that can be used for a wide variety of models and any well‐defined sampling design. It equals the π estimator plus an adjustment term that accounts for the differences between the π estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The regression estimator and ratio estimator follow from certain assumptions on the model and the sampling design. These are compared with the π estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple regression estimator to that of the π estimator was approximately 55%. The bias of the simple regression estimator was negligibly small. The confidence interval estimators were valid for all sample sizes except for n = 10. Also the ratio estimator was approximately unbiased, and the confidence interval estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio estimator assumes that the intercept of the regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55% of the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) regression estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) regression estimator was more precise than the π estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the regression estimator was less precise than the π estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.     

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.     

A comparison of some robust estimators of the variogram for use in soil survey

The standard estimator of the variogram is sensitive to outlying data, a few of which can cause overestimation of the variogram. This will result in incorrect variances when estimating the value of a soil property by kriging or when designing a sampling grid to map the property to a required precision. Several robust estimators of the variogram, based on location and scale estimation, have been proposed as improvements. They seem to be suitable for analysis of soil data in circumstances where the standard estimator is likely to be affected by outliers. Robust estimators are based on assumptions about the distribution of the data which will not always hold and which need not be made in kriging or in estimating the variogram by the standard estimator. The estimators are reviewed. Simulation studies show that the robust estimators vary in their susceptibility to moderate skew in the underlying distribution, but that the effects of outliers are generally greater. The estimators are applied to some soil data, and the resulting variograms used for ordinary kriging at sites in a separate validation data set. In most cases the variograms derived from the standard estimator gave kriging variances which appeared to overestimate the mean squared error of prediction (MSEP). Kriging with variograms based on robust estimators sometimes gave kriging variances which underestimated the MSEP or did not differ significantly from it. Estimates of kriging variance and the MSEP derived from the validation data were generally close to estimates from cross‐validation on the prediction set used to derive the variograms. This indicates that variogram models derived from different estimators could be compared by cross‐validation.     

Biochar impact on the estimation of the colorimetric‐based enzymatic assays of soil

This study was carried out in order to assess the influence of biochar applications on the estimation of colorimetric‐based enzymatic assays and to verify the effectiveness of the most common methods. Since most methods used to determine enzymatic activities in the soil are based on colorimetry, biochar may absorb substrates and/or coloured products thereby distorting the analytical result. Biochar was added to two soils, with different textures and cation exchangeable capacities, at a rate of 2% (w/w), and seven enzyme activities were determined following standard methods. The biochar amendment lowered the spectrophotometer reading of the activity of FDAase and dehydrogenase in the sandy soil. In the three enzymatic activities based on p‐nitrophenol production (β‐glucosidase, phosphatase and arylsulphatase), the addition of biochar did not change the enzyme assays. The biochar led to an overestimation in terms of the protease and urease activities in the sandy soil. In the clay loamy soil, biochar did not change the response of any of the enzyme activities tested. A biochar dose of up to 2% only guarantees the effectiveness of the most common spectrophotometric methods for not excessively sandy soils.     

Intelligent estimation of spatially distributed soil physical properties

Spatial analysis of soil samples is often times not possible when measurements are limited in number or clustered. To obviate potential problems, we propose a new approach based on the self-organizing map (SOM) technique. This approach exploits underlying nonlinear relation of the steady-state geomorphic concave–convex nature of hillslopes (from hilltop to bottom of the valley) to spatially limited soil textural data. The topographic features are extracted from Shuttle Radar Topographic Mission elevation data; whereas soil textural (clay, silt, and sand) and hydraulic data were collected in 29 spatially random locations (50 to 75 cm depth). In contrast to traditional principal component analysis, the SOM identifies relations among relief features, such as, slope, horizontal curvature and vertical curvature. Stochastic cross-validation indicates that the SOM is unbiased and provides a way to measure the magnitude of prediction uncertainty for all variables. The SOM cross-component plots of the soil texture reveals higher clay proportions at concave areas with convergent hydrological flux and lower proportions for convex areas with divergent flux. The sand ratio has an opposite pattern with higher values near the ridge and lower values near the valley. Silt has a trend similar to sand, although less pronounced. The relation between soil texture and concave–convex hillslope features reveals that subsurface weathering and transport is an important process that changed from loss-to-gain at the rectilinear hillslope point. These results illustrate that the SOM can be used to capture and predict nonlinear hillslope relations among relief, soil texture, and hydraulic conductivity data.     

Considerations on cross‐linking by bivalent cations in soil organic matter with low exchange capacity

A soil's cation exchange capacity (CEC) is expected to be relatively inert against changes in cation loading. In this study, we treated a soil sample originating from the organic layer of a forest soil with various bivalent cations after removing the native cations. Sorption isotherms and cation exchange capacity were determined, the latter using the BaCl₂ method. Sorption showed Langmuir characteristics, with the maximum coverage (Q_max) increasing in the order Ba²⁺ < Ca²⁺ < Mg²⁺, but being clearly smaller than the initial load of native exchangeable cations. The Langmuir coefficient, k_Me, depended oppositely to the order obtained for Q_max. CEC increased upon cation treatment and it varied by a factor of almost two. The unexpected variation of CEC was explained by the low cation exchange capacity of the organic matter such that not all functional groups are close enough to be bridged and the second charge of a bivalent cation is not neutralized by the organic functional group. The Langmuir sorption type, and Q_max being smaller than the content of sorption sites and being largest for Mg, suggested that only a part of the sites can be cross‐linked and at least part of the cross‐links are formed by hydrated cations. Thermodynamic considerations allowed reconstruction of two contrasting processes during CEC determination by Ba²⁺: Case A: the disruption of cross‐links, which increases with the cationic strength and the cation load before CEC determination, but does not require structural re‐orientation in the SOM matrix, and Case B: the formation of new cross‐links during CEC determination, depending only on the content of unoccupied sites before CEC determination and requiring structural re‐organization of the matrix and thus a minimum matrix flexibility. The use of bivalent cations for CEC determination may thus result in an overestimation of CEC for organic matter with low CEC. This has, however, promising potential when comparing CEC determined with monovalent cations and bivalent cations. Using a set of bivalent cations, may allow probing distribution of distances between functional groups in the organic matter and even characterize the matrix rigidity of the cation‐cross‐linked network.     

Using soil knowledge for the evaluation of mid‐infrared diffuse reflectance spectroscopy for predicting soil physical and mechanical properties

Mid‐infrared diffuse reflectance spectroscopy can provide rapid, cheap and relatively accurate predictions for a number of soil properties. Most studies have found that it is possible to estimate chemical properties that are related to surface and solid material composition. This paper focuses on prediction of physical and mechanical properties, with emphasis on the elucidation of possible mechanisms of prediction. Soil physical properties that are based on pore‐space relationships such as bulk density, water retention and hydraulic conductivity cannot be predicted well using MIR spectroscopy. Hydraulic conductivity was measured using a tension‐disc permeameter, excluding the macropore effect, but MIR spectroscopy did not give a good prediction. Properties based on the soil solid composition and surfaces such as clay content and shrink‐swell potential can be predicted reasonably well. Macro‐aggregate stability in water can be predicted reasonably as it has a strong correlation with carbon content in the soil. We found that most of the physical and mechanical properties can be related back to the fundamental soil properties such as clay content, carbon content, cation exchange capacity and bulk density. These connections have been explored previously in pedotransfer functions studies. The concept of a spectral soil inference system is reiterated: linking the spectra to basic soil properties and connecting basic soil properties to other functional soil properties via pedotransfer functions.     

Near‐infrared spectroscopy for rapid estimation of microbial properties in reclaimed mine soils

Several chemical and microbial properties of mine soils need to be measured for comprehensive assessment of the reclamation success. The objective of this study was to evaluate the ability of NIR spectroscopy to predict organic C (C_org), total N (N_t), and several microbial properties of mine soils reclaimed for forestry. Soils samples (n = 154) were collected at two reclaimed areas in central and S Poland, and their spectra in the NIR region (including the visible range, 400–2500 nm) were recorded. A half of the samples was used to develop calibration equations, and another half was used for validation. The modified partial least squares regression was applied to build calibration equations using the whole spectrum (0 to 2nd derivative). The best predictions were obtained for C_org and N_t (ratio of standard deviation to standard error of prediction in the validation stage [RPD] = 3.4 and 4.1; the regressions coefficients [a] of linear regression [measured against predicted values] = 0.94 and 0.96; correlation coefficients [r] = 0.96 and 0.97, respectively). Very well predictive models applicable for quantitative measurements were obtained also for microbial biomass, basal respiration, and the activities of dehydrogenase and acid phosphatase (RPD = 2.3–2.5, a = 0.90–0.99, r = 0.90–0.92). Prediction of urease activity was slightly worse (RPD = 2.1, a = 0.88, r = 0.87) but sufficient for rough estimation. The obtained results indicated the ability of NIR spectroscopy to predict complex soil microbial properties. Therefore, application of this analytical method may improve the assessment of recovery of microbial functions in reclaimed post‐mining barrens.     

基于Markov链地统计模型的区域土壤性质研究进展

土壤水力学性质的空间变异对于区域土壤水分溶质循环模拟研究至关重要。基于Markov链的条件模拟是一种能融合多源信息技术的地统计学模拟方法,与传统插值法和基于变异函数的条件模拟相比有诸多优势。目前,该方法在土壤水力学性质空间变异性领域的研究并未全面展开。实现区域土壤水力学模型参数的随机模拟,对于实现区域土壤水分运动和溶质运移的随机模拟,分析土壤水力学性质空间变异性对土壤水分运动和溶质运移模拟结果的影响,特别是参数采样点变化对土壤水分运动和溶质运移结果影响的不确定性等研究都有重要意义。本文旨在综述基于Markov链的地统计学模拟在土壤学相关领域的研究进展,以期为区域模拟中面临的参数获取难题提供帮助,为区域农业生产管理,水分高效利用,农田生态环境保护提供科学依据。     

Usefulness of near‐infrared spectroscopy for the prediction of chemical and biological soil properties in different long‐term experiments

The prediction accuracy of visible and near‐infrared (Vis‐NIR) spectroscopy for soil chemical and biological parameters has been variable and the reasons for this are not completely understood. Objectives were (1) to explore the predictability of a series of chemical and biological properties for three different soil populations and—based on these heterogeneous data sets—(2) to analyze possible predictive mechanisms statistically. A number of 422 samples from three arable soils in Germany (a sandy Haplic Cambisol and two silty Haplic Luvisols) of different long‐term experiments were sampled, their chemical and biological properties determined and their reflectance spectra in the Vis‐NIR region recorded after shock‐freezing followed by freeze‐drying. Cross‐validation was carried out for the entire population as well as for each population from the respective sites. For the entire population, excellent prediction accuracies were found for the contents of soil organic C (SOC) and total P. The contents of total N and microbial biomass C and pH were predicted with good accuracy. However, prediction accuracy for the other properties was less: content of total S was predicted approximately quantitatively, whereas Vis‐NIR spectroscopy could only differentiate between high and low values for the contents of microbial N, ergosterol, and the ratio of ergosterol to microbial biomass C. Contents of microbial biomass P and S, basal respiration, and qCO₂ could not be predicted. Prediction accuracies were greatest for the entire population and the Luvisol at Garte, followed by the Luvisol at Hohes Feld, whereas the accuracy for the sandy Cambisol was poor. The poor accuracy for the sandy Cambisol may have been due to only smaller correlations between the measured properties and the SOC content compared to the Luvisols or due to a general poor prediction performance for sandy soils. Another reason for the poor accuracy may have been the smaller range of contents in the sandy soil. Overall, the data indicated that the accuracy of predictions of soil properties depends largely on the population investigated. For the entire population, the usefulness of Vis‐NIR for the number of chemical and biological soil properties was evident by markedly greater correlation coefficients (measured against Vis‐NIR predicted) compared to the Pearson correlation coefficients of the measured properties against the SOC content. However, the cross‐validation results are valid only for the closed population used in this study.     

Use of different chemometric approaches for an estimation of soil properties at field scale with near infrared spectroscopy

Visible and near infrared spectroscopy (vis‐NIRS) may be useful for an estimation of soil properties in arable fields, but the quality of results are often variable depending on the applied chemometric approach. Partial least squares regression (PLSR) may be replaced by approaches which employ supervised learning methods or variable selection procedures in order to increase the proportion of informative wavelengths used in the estimation procedure, to reduce the noise of the spectra and to find the best fitting solution. Objectives were (1) to compare the usefulness of PLSR with either PLSR combined with a genetic algorithm (GA‐PLSR) or support vector machine regression (SVMR) for an estimation of soil organic carbon (SOC), total nitrogen (N), pH, cation exchange capacity (CEC) and soil texture for surface soils (0–5 cm, n = 144) of an arable field in Bangalore (India) and (2) to test and optimize different calibration strategies for GA‐PLSR for an improved estimation of soil properties. PLSR was useful for an estimation of SOC, N, sand and clay. In the cross‐validation (n = 96), accuracies of estimated soil properties generally decreased in the order GA‐PLSR > SVMR > PLSR. However, the order of estimation accuracies for the random validation sample (n = 48) changed to SVMR > GA‐PLSR > PLSR for SOC, N, pH, and CEC, whereas for clay the order changed to SVMR > PLSR > GA‐PLSR. A sequential procedure, which used the most frequently selected wavelengths of the GA‐PLSR runs, proved to be useful for an improved estimation of SOC and N. Overall, SVMR especially improved estimations of SOC and clay, whereas GA‐PLSR was particularly useful for SOC and N and it was the only approach which successfully estimated CEC in cross‐validation and validation.     

Effects of soil conservation on soil properties of citrus orchards in the Three‐Gorges Area,China

Mountain region citrus production systems occupy large parts of the landscape prone to soil erosion in the Three‐Gorges Area of China. Several soil conservation measures, such as terracing hedgerows, are widely implemented in citrus orchards to control soil erosion. However, little is known about the effect of those measures on soil properties. The objective of this work was to analyse the changes of soil properties in citrus orchards subjected to different conservation measures. Experiments were conducted in four plots: control plot (SC, sloping orchard without conservation measures), sloping orchard with contour hedgerows (SCH), terraced orchard (TC) and terraced orchard with grass cover (TCG). Samples of soil surface from 0 to 15 cm were collected to analyse texture, bulk density (BD), aggregate stability, saturated hydraulic conductivity, soil organic matter (SOM) and soil nutrients. The spatial variability of those properties was also evaluated at slope and field scales. The results showed that the three conservation measures significantly increased saturated hydraulic conductivity, aggregate stability, SOM and available N, P, K, but decreased BD. The terracing with grass cover measures were the most effective in improving soil fertility among the three measures. The average SOM, available P, N, K in TCG were 0·27, 0·50, 1·74 and 1·72 and these rates are larger than for the in SC. Compared to SC, silt content was increased the SCH, while clay content was increased with TC and TCG. There was a downslope increase in clay content and total N but a decrease in gravels in the SC plot. However, that trend did not exist in the other plots. At the field scale, the soil aggregate stability and total nitrogen were significantly higher near the hedgerow under SCH, and the available N was significantly higher in the middle position under TC; the other soil properties had no significant trends based on the distance to hedgerow or stone bunds. Results of this study will contribute to a further understanding of the environmental influence of soil conservation measures. Copyright © 2010 John Wiley & Sons, Ltd.     

Long‐term‐fertilization effects on soil organic carbon,physical properties,and wheat yield of a loess soil

The large dryland area of the Loess Plateau (China) is subject of developing strategies for a sustainable crop production, e.g., by modifications of nutrient management affecting soil quality and crop productivity. A 19 y long‐term experiment was employed to evaluate the effects of fertilization regimes on soil organic C (SOC) dynamics, soil physical properties, and wheat yield. The SOC content in the top 20 cm soil layer remained unchanged over time under the unfertilized plot (CK), whereas it significantly increased under both inorganic N, P, and K fertilizers (NPK) and combined manure (M) with NPK (MNPK) treatments. After 18 y, the SOC in the MNPK and NPK treatments remained significantly higher than in the control in the top 20 cm and top 10 cm soil layers, respectively. The MNPK‐treated soil retained significant more water than CK at tension ranges from 0 to 0.25 kPa and from 8 to 33 kPa for the 0–5 cm layer. The MNPK‐treated soil also retained markedly more water than the NPK‐treated and CK soils at tensions from 0 to 0.75 kPa and more water than CK from 100 to 300 kPa for the 10–15 cm layer. There were no significant differences of saturated hydraulic conductivity between three treatments both at 0–5 and 10–15 cm depths. In contrast, the unsaturated hydraulic conductivity in the MNPK plot was lower than in the CK plot at depths of 0–5 cm and 10–15 cm. On average, wheat yields were similar under MNPK and NPK treatments and significantly higher than under the CK treatment. Thus, considering soil‐quality conservation and sustainable crop productivity, reasonably combined application of NPK and organic manure is a better nutrient‐management option in this rainfed wheat–fallow cropping system.