Estimating variograms of soil properties by the method-of-moments and maximum likelihood

Variograms of soil properties are usually obtained by estimating the variogram for distinct lag classes by the method‐of‐moments and fitting an appropriate model to the estimates. An alternative is to fit a model by maximum likelihood to data on the assumption that they are a realization of a multivariate Gaussian process. This paper compares the two using both simulation and real data. The method‐of‐moments and maximum likelihood were used to estimate the variograms of data simulated from stationary Gaussian processes. In one example, where the simulated field was sampled at different intensities, maximum likelihood estimation was consistently more efficient than the method‐of‐moments, but this result was not general and the relative performance of the methods depends on the form of the variogram. Where the nugget variance was relatively small and the correlation range of the data was large the method‐of‐moments was at an advantage and likewise in the presence of data from a contaminating distribution. When fields were simulated with positive skew this affected the results of both the method‐of‐moments and maximum likelihood. The two methods were used to estimate variograms from actual metal concentrations in topsoil in the Swiss Jura, and the variograms were used for kriging. Both estimators were susceptible to sampling problems which resulted in over‐ or underestimation of the variance of three of the metals by kriging. For four other metals the results for kriging using the variogram obtained by maximum likelihood were consistently closer to the theoretical expectation than the results for kriging with the variogram obtained by the method‐of‐moments, although the differences between the results using the two approaches were not significantly different from each other or from expectation. Soil scientists should use both procedures in their analysis and compare the results.     

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.     

Regression analysis in a spatial-temporal context: Least squares, generalized least squares, and the use of the bootstrap

In many ecological studies, data are collected at different locations over time, with interest in building a regression model for how one variable depends on its past values and current values of a predictor variable. Our motivation is an example in vestigating the effects of mouse populations on the level of gypsy moth populations within a model accounting for the previous year’s gypsy moth values. With such data, the error term will of ten contain autocorrelationover time as well as contemporaneouscorrelation over series at a fixed time. A common approach in practice is the use of simple least squares or the use of two-stage generalized least squares. The standard errors and tests that are typically used either ignore the correlationin the errorsor, if they do account for the errorstructure, ignore the uncertainty that comes from estimating the correlation structure. There are also con cerns regarding bias in the estimated coefficients and variance/correlation parameters. We in vestigate these issues mainly in the context of our example, which invol ves 8 location and 10 years of data, relying on simulations due to the absence of exact small-sample results. Among other results, we find the potential for gross underestimation of the standard errors of the coefficients with the use of standard generalized least squares methods. A bootstrap method is developed for this context, applied to the example, and evaluated via simulations. The bootstrap estimates of standard errors performed rather well in the settings we examined, supporting the use of the bootstrap in the analysis of our example and suggesting the potential of the bootstrap more generally.     

基于贝叶斯最大熵的黄河三角洲土壤含盐量空间分布预测

黄河三角洲土壤盐渍化问题是制约当地农业生产和生态稳定的关键因素。为了准确掌握盐渍土的空间分布,提高土壤含盐量的空间预测精度,本研究根据2022年5月黄河三角洲的193个采样点两个深度土壤含盐量分析数据,结合高程和Landsat9遥感影像等数据,采用地理加权回归（Geographically Weighted Regression, GWR）模型构造区间型软数据,进而建立贝叶斯最大熵（Bayesian Maximum Entropy, BME）模型对研究区土壤含盐量的分布进行了预测,并同传统的地统计模型普通克里金（Ordinary Kriging, OK）及GWR模型的预测结果进行了比较。结果表明：BME模型对土壤含盐量的预测精度要高于另外两种模型。与OK相比, BME的预测误差在土壤表层和底层分别降低25%和21%,R2分别提高了0.5432和0.3527,BME作为本研究最佳土壤含盐量空间预测模型,展现了多源数据整合及非线性估计的优势。黄河三角洲表层土壤盐渍化率（88%）高于底层（68%）,大体呈现由西南到东北方向上土壤含盐量递增的趋势,沿海地区大于内陆地区,黄河三角洲北部是整个区域盐渍化最为严重的地区。     

Prediction of soil organic matter using a spatially constrained local partial least squares regression and the Chinese vis–NIR spectral library

We need to determine the best use of soil vis–NIR spectral libraries that are being developed at regional, national and global scales to predict soil properties from new spectral readings. To reduce the complexity of a calibration dataset derived from the Chinese vis–NIR soil spectral library (CSSL), we tested a local regression method that combined geographical sub‐setting with a local partial least squares regression (local‐PLSR) that uses a limited number of similar vis–NIR spectra (k‐nearest neighbours). The central idea of the local regression, and of other local statistical approaches, is to derive a local prediction model by identifying samples in the calibration dataset that are similar, in spectral variable space, to the samples used for prediction. Here, to derive our local regressions we used Euclidean distance in spectral space between the calibration dataset and prediction samples, and we also used soil geographical zoning to account for similarities in soil‐forming conditions. We tested this approach with the CSSL, which comprised 2732 soil samples collected from 20 provinces in the People's Republic of China to predict soil organic matter (SOM). Results showed that the prediction accuracy of our spatially constrained local‐PLSR method (R² = 0.74, RPIQ = 2.6) was better than that from local‐PLSR (R² = 0.69, RPIQ = 2.3) and PLSR alone (R² = 0.50, RPIQ = 1.5). The coupling of a local‐PLSR regression with soil geographical zoning can improve the accuracy of local SOM predictions using large, complex soil spectral libraries. The approach might be embedded into vis–NIR sensors for laboratory analysis or field estimation.     

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.     

Use of an inverse method and geostatistics to estimate soil hydraulic conductivity for spatial variability analysis

A field method for determining the soil hydraulic properties using a parameter estimation technique is presented. Input data for the inverse problem are soil-water potentials and soil-water contents measured at different soil depths and different times during a field transient drainage experiment. For the water retention function the parametric relation suggested by Van Genuchten was adopted. For the hydraulic conductivity function the relation proposed by Van Genuchten and the exponential relation were adopted.

With the proposed method soil hydraulic properties along a transect of a volcanic Vesuvian soil were determined using as boundary condition the unit gradient of total potential at the bottom of the soil profile. Geostatistics were used to describe the spatial variability of hydraulic conductivity characteristics of the soil here considered.

Finally, results obtained using this method were compared with those of the simplified method suggested by Sisson and Van Genuchten based on a unit gradient water flow model.     

Estimating the water retention curve from soil properties: comparison of linear, nonlinear and concomitant variable methods

The unsaturated soil hydraulic functions involving the soil–water retention curve (SWRC) and the hydraulic conductivity provide useful integrated indices of soil quality. Existing and newly devised methods were used to formulate pedotransfer functions (PTFs) that predict the SWRC from readily available soil data. The PTFs were calibrated using a large soils database from Hungary. The database contains measured soil–water retention data, the dry bulk density, sand, silt and clay percentages, and the organic matter content of 305 soil layers from some 80 soil profiles. A three-parameter van Genuchten type function was fitted to the measured retention data to obtain SWRC parameters for each soil sample in the database. Using a quasi-random procedure, the database was divided into “evaluation” (EVAL) and “test” (TEST) parts containing 225 and 80 soil samples, respectively. Linear PTFs for the SWRC parameters were calculated for the EVAL database. The PTFs used for this purpose particle-size percentages, dry bulk density, organic matter content, and the sand/silt ratio, as well as simple transforms (such as logarithms and products) of these independent variables. Of the various independent variables, the eight most significant were used to calculate the different PTFs. A nonlinear (NL) predictive method was obtained by substituting the linear PTFs directly into the SWRC equation, and subsequently adjusting the PTF parameters to all retention data of the EVAL database. The estimation error (SSQ) and efficiency (EE) were used to compare the effectiveness of the linear and nonlinearly adjusted PTFs. We found that EE of the EVAL and the TEST databases increased by 4 and 7%, respectively, using the second nonlinear optimization approach. To further increase EE, one measured retention data point was used as an additional (concomitant) variable in the PTFs. Using the 20 kPa water retention data point in the linear PTFs improved the EE by about 25% for the TEST data set. Nonlinear adjustment of the concomitant variable PTF using the 20 kPa retention data point as concomitant variable produced the best PTF. This PTF produced EE values of 93 and 88% for the EVAL and TEST soil data sets, respectively.     

Estimating soil frictional resistance to metal probes and its relevance to the penetration of soil by roots

Friction accounts for a large proportion of the resistance to a penetrometer probe, often much more so than to a plant root. The contribution of frictional resistance to penetrometer resistance was investigated in five soils with texture ranging from sandy loam to silty clay. The effect on penetration resistance of rotating the conical tip of the probe was studied in both intact cores of undisturbed field soil, and in cores remoulded from sieved soil. Rotation altered the orientation of the vector of frictional resistance towards a direction perpendicular to the probe axis, and so decreased the component of frictional resistance that opposed the axial penetration of the probe. The decrease in friction was greater for probes with a semiangle of 5° than those with a 30° semiangle and was more than half of the total resistance to a nonrotating probe in 15 out of the 16 cases studied. A theoretical treatment of the effect of rotation period on probe resistance showed good agreement with the experimental results. The penetration resistance of a metal probe is related to that of a root in terms of frictional resistance and factors such as the penetration rate. When all frictional resistance was subtracted from the resistance measured to the penetration of a 5 semiangle probe, the remaining resistance was similar to that measured for roots growing in the same soil.     

Factorial kriging analysis: a useful tool for exploring the structure of multivariate spatial soil information

Most studies of relations between soil properties fail to take account of their regionalized nature because of the lack of appropriate methods. This paper describes a geostatistical technique, factorial kriging analysis, that bridges the gap between classical multivariate analysis and a univariate geostatistical approach. The basic feature of the method is the fitting of a linear model of coregionalization, i.e. all experimental simple and cross-variograms are modelled with a linear combination of basic variogram functions. A particular variance-covariance matrix, the coregionalization matrix, can then be associated with each spatial scale defined by the range of the basic variogram function. Each coregionalization matrix describes relationships between variables at a given spatial scale. A principal component analysis of these matrices produces a set of components, the regionalized factors, that reflect the main features of the multivariate information for each spatial scale and whose scores are estimated by cokriging. The technique is described and illustrated with three case studies based on a simulated data set and soil survey data. The results are compared with those of the principal component analysis of the variance-covariance matrix and the variogram matrices.     

土壤制图中土壤类型配色模型构建与应用

在全国1∶5万土壤图集制图中,土壤类型的配色既需表现土类等高级类型的分布特征,也要表现土属等较低级类型的差别。我国土壤低级类型众多,且1∶5万基本比例尺图幅达2万余幅,采用传统人工设色方法进行土壤制图,不仅效率低,而且难以保持图幅间土壤颜色的协调一致性。针对这一技术难题,本研究采用图幅间相似配色方法和人机交互的设计思想,通过建立1个多层级管理色库、人工设置土壤类型的Q配色单元及其多个近似色系(色组),建立了Q配色单元的避让选色和区域土壤特征分析等5个组件模型,构建了土壤类型配色模型(SCO-Model)。该模型在大比例尺土壤制图中不仅反映了区域土壤的总体分布特征,也表达了土壤类型间的差异,特别是实现了大比例尺土壤制图中土壤类型的快速智能配色,大大提高了制图效率。     

Soil biochemical activities and the geometric mean of enzyme activities after application of sewage sludge and sewage sludge biochar to soil

There is a need to improve the way in which wastes, such as sewage sludges, are managed and a potential way to proceed would be to transform them into biochar. On the other hand, there is a growing interest in the use of soil biochemical properties as indicators of soil quality because they are sensitive to alterations in soil management. Thus, we have studied the effect of a biochar obtained from sewage sludge on soil biochemical properties in an organic soil using two doses of biochar and comparing these results with the control soil and with soils amended with the same two doses of unpyrolyzed sewage sludge. Microbial biomass C, soil respiration, net N mineralization and several enzyme activities (dehydrogenase, β-glucosidase, phosphomoesterase and arylsulphatase) were monitored. The geometric mean of enzyme activities (GMea) was used as a soil quality index. Individual biochemical properties showed a different response to the treatments, while GMea showed an increase in the quality of soils amended with the high biochar dose and a decrease in those amended with a high sewage sludge dose. The geometric mean of enzyme activities was a suitable index to condense the whole set of soil enzyme values in a single numerical value, which was sensitive to management practices.     

Development of an express method for measuring soil nitrate,phosphate, potassium,and pH for future in-field application

Background

In practical farming, there is often a need for short-term availability of information on the soil nutrient status.

Aims

To develop a new express method for the extraction of major plant-available nutrients and measurement of soil nutrients. In future, this method shall serve for in-field measurements of soil samples with an ion-sensitive field-effect transistor (ISFET).

Methods

Various extraction conditions such as type of extractant, soil-to-solution ratio, time, and intensity were investigated on a broad selection of dried soil samples in the laboratory. Based on 83 field-moist soil samples with varying clay contents, these conditions were compared to standard laboratory methods.

Results

With increasing extraction time, the nutrient concentrations increased. When the soil-to-solution ratio was reduced, a greater share of nutrients was extracted, independent of soil type. H₂O and 0.01 M CaCl₂ and standard calcium-acetate-lactate (CAL) solution proved to be too weak in the short period to reach the ISFET sensor measurement range. Higher concentrated CAL solutions performed much better. Finally, a 5-min CaCl₂ extraction followed by the removal of an aliquot for the determination of soil pH and NO₃⁻ was found to be effective. The remaining solution was then mixed with 0.20 M CAL solution for the analysis of H₂PO₄⁻ and K⁺ at 10 min of extra extraction time. This extraction method showed very good correlations with the values based on the German laboratory reference methods for pH (R² = 0.91) and for nitrate (R² = 0.95). For phosphorus and potassium, we obtained an R² of 0.70 and 0.81, respectively, for all soils. When soils were grouped according to clay content higher correlations were found.

Conclusions

A new express method based on a wet-chemical approach with a soil preparation procedure was successfully developed and validated. This seems to be a valuable basis for future in-field measurements via ISFET.     

Adsorption of chloride and nitrate by variable charge soils in relation to the electric charge of the soil

A cell consisting of a chloride-selective electrode and a nitrate-selective electrode was directly put in the soil suspension to determine the concentration ratio NO₃^?/Cl^? for studying the adsorption of these two ions by three soil samples from variable charge soils. It was found that such factors as the iron oxide content of the soil, the pH of the suspension, the concentration of the respective anion, the kind of accompanying cations, and the dielectric constant of solvent etc. can all affect the amounts and the ratio of the two anions adsorbed. The adsorption was chiefly caused by coulombic force, but another mechanism, presumably a covalent force between the anion and the metal atom on the surface of soil particles, may also be involved, at least for chloride ions.     

Nodulation,growth and yield of soybeans as affected by paddy straw application to soil

The application of paddy straw to soil improved the yield of soybeans significantly in a light-textured red sandy loam soil with a pH of 5.6. Whereas the nodulation was unaffected in the crop grown under rainfed conditions it was improved in the irrigated summer crop of soybeans. Grain yield was significantly increased in treatment receiving straw at 3 t/ha. Addition of dung slurry as a source of inoculum for straw decomposition or a second inoculation of plants with Rhizobium failed to affect nodulation and yield of soybeans.     

A Bayesian framework for model calibration, comparison and analysis: Application to four models for the biogeochemistry of a Norway spruce forest

Four different parameter-rich process-based models of forest biogeochemistry were analysed in a Bayesian framework consisting of three operations: (1) Model calibration, (2) Model comparison, (3) Analysis of model-data mismatch.Data were available for four output variables common to the models: soil water content and emissions of N₂O, NO and CO₂. All datasets consisted of time series of daily measurements. Monthly averages and quantiles of the annual frequency distributions of daily emission rates were calculated for comparison with equivalent model outputs. This use of the data at model-appropriate temporal scale, together with the choice of heavy-tailed likelihood functions that accounted for data uncertainty through random and systematic errors, helped prevent asymptotic collapse of the parameter distributions in the calibration.Model behaviour and how it was affected by calibration was analysed by quantifying the normalised RMSE and r² for the different output variables, and by decomposition of the MSE into contributions from bias, phase shift and variance error. The simplest model, BASFOR, seemed to underestimate the temporal variance of nitrogenous emissions even after calibration. The model of intermediate complexity, DAYCENT, simulated the time series well but with large phase shift. COUP and MoBiLE-DNDC were able to remove most bias through calibration.The Bayesian framework was shown to be effective in improving the parameterisation of the models, quantifying the uncertainties in parameters and outputs, and evaluating the different models. The analysis showed that there remain patterns in the data - in particular infrequent events of very high nitrogenous emission rate - that are unexplained by any of the selected forest models and that this is unlikely to be due to incorrect model parameterisation.     

On‐farm comparison of variable rates of nitrogen with uniform application to maize on canopy reflectance,soil nitrate,and grain yield

Recent development in canopy optical‐sensing technology provides the opportunity to apply fertilizer variably at the field scale according to spatial variation in plant growth. A field experiment was conducted in Ottawa, Canada, for two consecutive years to determine the effect of fertilizer nitrogen (N) input at variable‐ vs. uniform‐application strategies at the V6–V8 growth stage, on soil mineral N, canopy reflectance, and grain yield of maize (Zea mays L.). The variable N rates were calculated using an algorithm derived from readings of average normalized difference vegetation index (NDVI) of about 0.8 m × 4.6 m, and N fertilizer was then applied to individual patches of the same size of NDVI readings (0.8 m × 4.6 m) within a plot (2184 m²). Canopy reflectance, expressed as NDVI, was monitored with a hand‐held spectrometer, twice weekly before tasseling and once a week thereafter until physiological maturity. Soil mineral N (0–30 cm depth) was analyzed at the V6 and VT growth stages. Our data show that both variable and uniform‐application strategies for N side‐dressings based on canopy‐reflectance mapping data required less amount of N fertilizer (with an average rate of 80 kg N ha^–1 as side‐dressing in addition to 30 kg N ha^–1 applied at planting), and produced grain yields similar to and higher nitrogen‐use efficiency (NUE) than the preplant fully fertilized (180 kg N ha^–1) treatment. No difference was observed in either grain yield or NUE between the variable‐ and uniform‐application strategies. Compared to unfertilized or fully fertilized treatments, the enhancements in grain yield and NUE of the variable‐rate strategy originated from the later N input as side‐dressing rather than the variation in N rates. The variable‐rate strategy resulted in less spatial variations in soil mineral N at the VT growth stage and greater spatial variations in grain yield at harvest than the uniform‐rate strategy. Both variable‐ and uniform‐application strategies reduced spatial variations in soil mineral N at the VT stage and grain yield compared to the unfertilized treatment. The variable‐rate strategy resulted in more sampling points with high soil mineral N than the uniform‐rate strategy at the VT stage.