Estimation of soil salinity in semi‐arid land using a geostatistical model

Soil salinity is one of the great problems in arid and semi‐arid environments. The estimation and prediction of spatial soil salinity may be considered as a stochastic process, observed at irregular locations in space. Environmental variables usually show spatial dependence among observations which is an important drawback to traditional statistical methods. Geostatistical techniques that analyse and describe the spatial dependence and quantify the scale and intensity of the spatial variation, provides spatial information for local estimation of soil salinity. In this paper we propose a Gaussian Spatial Linear Mixed Model (GSLMM), which involves a non‐parametric term, accounting for a deterministic trend given by exogenous variables, and a parametric component defining the purely spatial random variation, possibly due to latent spatial processes. We focus here on the analysis of the relationship between soil electrical conductivity as a parameter related directly to soil salinity as well as sodium content (sodicity) to identify spatial variations in these parameters. This kind of methodology is demonstrated as a useful tool for environmental land management. Copyright © 2007 John Wiley & Sons, Ltd.     

Maximum likelihood estimation of regression parameters with spatially dependent discrete data

Generalized estimating equations (GEEs) have been successfully used to estimate regression parameters from discrete longitudinal data. GEEs have been adapted for spatially correlated count data with less success. It is convenient to model correlated counts as lognormal-Poisson, where a latent lognormal random process carries all correlation. This model limits correlation and can lead to negative bias of standard errors. Moreover, correlation is not the best dependence measure for highly nonnormal data. This article proposes a model which yields maximum likelihood (ML) estimates of regression parameters when the response is discrete and spatially dependent. This model employs a spatial Gaussian copula, bringing the discrete distribution into the Gaussian geostatistical framework, where correlation completely describes dependence. The model yields a log-likelihood for regression parameters that can be maximized using established numerical methods. The proposed procedure is used to estimate the relationship between Japanese beetle grub counts and soil organic matter. These data exhibit residual correlation well above the lognormal-Poisson correlation limit, so that model is not appropriate. The data and MATLAB code are available online. Simulations demonstrate that negative bias in GEE standard errors leads to nominal 95% confidence coverage less than 62% for moderate or strong spatial dependence, whereas ML coverage remains above 82%.     

Multilevel Latent Gaussian Process Model for Mixed Discrete and Continuous Multivariate Response Data

We propose a Bayesian model for mixed ordinal and continuous multivariate data to evaluate a latent spatial Gaussian process. Our proposed model can be used in many contexts where mixed continuous and discrete multivariate responses are observed in an effort to quantify an unobservable continuous measurement. In our example, the latent, or unobservable measurement is wetland condition. While predicted values of the latent wetland condition variable produced by the model at each location do not hold any intrinsic value, the relative magnitudes of the wetland condition values are of interest. In addition, by including point-referenced covariates in the model, we are able to make predictions at new locations for both the latent random variable and the multivariate response. Lastly, the model produces ranks of the multivariate responses in relation to the unobserved latent random field. This is an important result as it allows us to determine which response variables are most closely correlated with the latent variable. Our approach offers an alternative to traditional indices based on best professional judgment that are frequently used in ecology. We apply our model to assess wetland condition in the North Platte and Rio Grande River Basins in Colorado. The model facilitates a comparison of wetland condition at multiple locations and ranks the importance of in-field measurements.     

Improving Crop Model Inference Through Bayesian Melding With Spatially Varying Parameters

An objective for applying a Crop Simulation Model (CSM) in precision agriculture is to explain the spatial variability of crop performance and to help guide decisions related to the site-specific management of crop inputs. CSMs require inputs related to soil, climate, management, and crop genetic information to simulate crop yield. In practice, however, measuring these inputs at the desired high spatial resolution is prohibitively expensive. We propose a Bayesian modeling framework that melds a CSM with sparse data from a yield monitoring system to deliver location specific posterior predicted distributions of yield and associated unobserved spatially varying CSM parameter inputs. These products facilitate exploration of process-based explanations for yield variability. The proposed Bayesian melding model consists of a systemic component representing output from the physical model and a residual spatial process that compensates for the bias in the physical model. The spatially varying inputs to the systemic component arise from a multivariate Gaussian process, while the residual component is modeled using a univariate Gaussian process. Due to the large number of observed locations in the motivating dataset, we seek dimension reduction using low-rank predictive processes to ease the computational burden. The proposed model is illustrated using the Crop Environment Resources Synthesis (CERES)-Wheat CSM and wheat yield data collected in Foggia, Italy.     

A Non-Gaussian Spatial Generalized Linear Latent Variable Model

We consider a spatial generalized linear latent variable model with and without normality distributional assumption on the latent variables. When the latent variables are assumed to be multivariate normal, we apply a Laplace approximation. To relax the assumption of marginal normality in favor of a mixture of normals, we construct a multivariate density with Gaussian spatial dependence and given multivariate margins. We use the pairwise likelihood to estimate the corresponding spatial generalized linear latent variable model. The properties of the resulting estimators are explored by simulations. In the analysis of an air pollution data set the proposed methodology uncovers weather conditions to be a more important source of variability than air pollution in explaining all the causes of non-accidental mortality excluding accidents.     

Estimation and Prediction in the Spatial Linear Model

Often in environmental monitoring studies interesting ecological factors will be observed at several locations repeatedly over time. Generally these space-time data are subject to a sequential spatial data analysis. In geostatistics, spatial data describing an environmental phenomenon like the pH value in precipitation at several locations are regarded as a realisation from a stochastic process. Component models are used to interpret the spatial variation of the process. Decomposing the spatial process into single components is based on the theory of linear models. Trend surface analysis is seen to be the geostatistical method for best linear unbiased estimation (BLUE) of the trend component, whereas universal kriging is equivalent to best linear unbiased prediction (BLUP) of the realisation of the spatial process. Furthermore trend surface analysis and universal kriging are shown to agree with the estimation of fixed effects and prediction of fixed and random effects in mixed linear models. Since estimation and prediction for spatial data result in different interpolations the differences are explained also graphically by example. The example uses acid-precipitation monitoring data. The extension of these spatial methods for application to space-time problems by combination with dynamic linear models is treated in the discussion.     

似然函数形式对水稻物候期模型品种参数校正的影响

针对传统高斯正态似然函数(Gaussian likelihood function,GLF)在观测数据存在测量误差和模型算法结构复杂时无法描述模型残差异方差特点,造成马尔科夫链蒙特卡洛(Markov chain Monte Carlo,MCMC)算法进行模型参数校正时结果存在偏差的问题,通过引入变异系数(coefficient of variation,CV)变换的高斯似然函数(GLF with CV transformation,GLF-CV)和BC(Box-Cox)变换的高斯似然函数(GLF with BC transformation,GLF-BC)对观测数据和模型结构造成的异方差进行特征描述,并比较了参数校正效果及模型不确定度(uncertainty ratio,UR)。以2004—2009年高要雪花粘(早熟)、2001—2004年兴化武育粳3号(中熟)、1991—2004年六安汕优63号(晚熟)3个生态点的田间栽培试验数据为基础,RiceGrow和Oryza2000物候期模型为对象,利用仿射不变马尔科夫链蒙特卡洛集成采样(ensemble sampling for affin...     

Using sequential Gaussian simulation to assess the field-scale spatial uncertainty of soil water content

Soil water content (SWC) has a vital role in a variety of hydrological processes such as infiltration, runoff and erosion. Mapping the spatial pattern of SWC is then essential for appropriate addressing of these processes. Geostatistics is often used to characterize the spatial variability of SWC. This information may be used for estimating SWC e.g., by ordinary kriging (OK) or modeling location-specific uncertainty (local uncertainty) of the estimates by indicator kriging (IK). Kriging-based algorithms however smooth out the details and are incapable of detecting multi-location uncertainty (spatial uncertainty) of SWC estimates. Sequential Gaussian simulation (sGs) can model the spatial uncertainty through generation of several equally probable stochastic realizations. In this study sGs is used to map SWC spatial distribution and to provide a quantitative measure of its spatial uncertainty in particular. The SWC measurements were performed on 157 soil samples taken from an 18 ha erosion experiment field in Lower Austria. The results show that the spatial pattern of SWC is well recognized using the sGs as the simulated models reproduce the sample statistics including histogram and semivariogram model reasonably well. The difference among realizations is used to provide a quantitative measure of spatial uncertainty of SWC estimates. Knowledge of spatial uncertainty is helpful to evaluate the delineation of vulnerable areas to erosion.     

Examining Extreme Weather Effects on Birth Weight From the Individual Effect to Spatiotemporal Aggregation Effects

Extreme weather events are related to low birth weight. Monitoring this relationship in the context of climate change has a wide range of public health implications, as birth weight is a key indicator of many life course health outcomes, and climate change increases both frequency and intensity of extreme weather events. However, most birth weight data are not available with sufficient spatial and temporal resolution. The current study examined the relationship between birth weight and weather variables in a series of aggregations, from individual birth outcomes to month-county, season-county, and county-only mean birth weights. Data were based on a 20?% sample of White mothers aged 19 to 38 from the United States Natality Data Files, and the baseline model was for the 1974?C1978 and 1984?C1988 periods with 2,269,009 and 2,652,552 individual birth records, respectively. The evaluation was based on multiple regression for aggregation effects, and conditional autoregressive and spatial association models for spatial clustering effects. The results show that the number of extreme cold and hot days during the birth month is inversely associated with birth weight, and that temporal aggregation by month-county or season-county was likely to preserve the relationship between birth weight and extreme weather from the individual model. While both conditional autoregressive and spatial association models can remove some spatial autocorrelation, the spatial association approach may not work effectively without further modifying the existing method.     

黄土沟壑区小流域土壤pH值的空间分布及条件模拟

土壤pH值是影响土壤养分有效性和化学物质在土壤中行为的主要因素,研究土壤pH值的空间分布特征对于土壤养分管理和土壤污染预测具有重要意义。该文用地统计学方法研究了环境因素复杂的黄土高原小流域土壤pH值空间分布特征。结果表明,黄土沟壑区小流域土壤pH值具有球形—指数套合模型的空间结构特征,其空间异质性主要来源于流域内土地利用和土壤侵蚀等随机因素。与有机质协同的Kriging法能较好地对土壤pH值进行估值,其估值范围小于实测数据,估值误差来源于复杂的环境因素。序贯高斯条件模拟的土壤pH值范围与实测数据接近,模拟的平均值低于实测数据,模拟误差来源于模拟过程中独特的Kriging算法及高斯特性。     

Assessing Molybdenum Adsorption onto an Industrial Soil and Iron Minerals

Spatial accuracy of hydrologic modeling inputs influences the output from hydrologic models. A pertinent question is to know the optimal level of soil sampling or how many soil samples are needed for model input, in order to improve model predictions. In this study, measured soil properties were clustered into five different configurations as inputs to the Soil and Water Assessment Tool (SWAT) simulation of the Castor River watershed (11-km² area) in southern Quebec, Canada. SWAT is a process-based model that predicts the impacts of climate and land use management on water yield, sediment, and nutrient fluxes. SWAT requires geographical information system inputs such as the digital elevation model as well as soil and land use maps. Mean values of soil properties are used in soil polygons (soil series); thus, the spatial variability of these properties is neglected. The primary objective of this study was to quantify the impacts of spatial variability of soil properties on the prediction of runoff, sediment, and total phosphorus using SWAT. The spatial clustering of the measured soil properties was undertaken using the regionalized with dynamically constrained agglomerative clustering and partitioning method. Measured soil data were clustered into 5, 10, 15, 20, and 24 heterogeneous regions. Soil data from the Castor watershed which have been used in previous studies was also set up and termed “Reference”. Overall, there was no significant difference in runoff simulation across the five configurations including the reference. This may be attributable to SWAT's use of the soil conservation service curve number method in flow simulation. Therefore having high spatial resolution inputs for soil data may not necessarily improve predictions when they are used in hydrologic modeling.     

华北平原典型区土壤肥力低下区识别及限制因子分析

采用序贯高斯模拟方法对山东禹城市土壤质量指数的空间表征进行了评价,并深入分析了土壤肥力低下区的范围及其主要限制因子。结果表明,禹城市西南和中部土壤肥力质量指数较高,肥力质量较低的区域主要分布在该市北部、西北和东南三个区域。利用土壤肥力质量与产量的关系,确定禹城市土壤肥力低下的判定阈值为0.55,该市大部分区域土壤质量指数处于该阈值以上,仅在北部、西北和东南三个相对独立的区域共有2 494 hm2的耕地土壤肥力低下的风险较高。该市北部肥力低下区的主要限制因子是土壤质地和全磷含量,西北部主要受土壤盐化限制,而东南部的土壤肥力低下区则受土壤速效养分低、土壤盐化、质地较差以及土壤全氮含量不足等多个限制因子影响。     

土壤水分动态的随机模拟研究

本文把随机模拟方法应用于土壤水分的定量研究之中,并假定土壤水分的变化序列满足时间序列的通用加法模型。经检验证明:土壤水分变化序列由一确定的周期分量与一非确定的随机分量迭加而成。周期分量反映了气候的周期性波动和作物需水对土壤水分变化的影响,随机分量则反映了随机性的气候波动对土壤水分的影响,经对陕西武功、山西永济和陕西扶风三站土壤水分变化过程的模拟,其结果表明,该方法能以较高精度预测或模拟土壤水分在长时期內的动态变化过程,为采取灌溉排水和蓄水保墒等调节农田土壤水分的技术措施提供科学依据。     

基于农机空间运行轨迹的作业状态自动识别试验

以物联网为代表的现代信息技术在农机作业管理领域的发展应用,实现了农机作业过程的定位监控,但现有农机远程监管系统对海量农机空间位置数据仅实现了远程存储、显示和简单分析,难以满足农机精准管理和数据智能处理的要求。该文采用数据挖掘中的聚类和空间数据分析方法,结合农机空间运行轨迹的特点,研究了基于空间运行轨迹点的农机作业状态自动识别算法;设计实现了典型农机运行状态自动识别方法,定量分析了农机作业班次内田间作业时间、空行转移时间、停歇时间的量化构成。农机试验表明:发展的基于空间索引和网格密度的聚类算法精度达89%以上。农机作业状态自动识别为农机作业生产率、农机利用率和作业成本核算提供了定量依据。     

Multivariate conditional stochastic simulation of soil heterotrophic respiration at plot scale

Soil heterotrophic respiration fluxes at plot scale exhibit substantial spatial and temporal variability. Within this study secondary information was used to spatially predict heterotrophic respiration. Chamber-based measurements of heterotrophic respiration fluxes were repeated for 15 measurement campaigns within a bare 13 × 14 m² soil plot. Soil water contents and temperatures were measured simultaneously with the same spatial and temporal resolution. Further, we used measurements of soil organic carbon content and apparent electrical conductivity as well as the prior measurement of the target variable. The previous variables were used as co-variates in a stepwise multiple linear regression analysis to spatially predict bare soil respiration. In particular the prior measurement of the target variable, the soil water content and the apparent electrical conductivity, showed a certain, even though limited, predictive power. In the first step we applied external drift kriging and regression kriging to determine the improvement of using co-variates in an estimation procedure in comparison to ordinary kriging. The improvement using co-variates ranged between 40 and 1% for a single measurement campaign. The difference in improving the prediction of respiration fluxes between external drift kriging and regression kriging was marginal. In a second step we applied sequential Gaussian simulations conditioned with external drift kriging to generate more realistic spatial patterns of heterotrophic respiration at plot scale. Compared to the estimation approaches the conditional stochastic simulations revealed a significantly improved reproduction of the probability density function and the semivariogram of the original point data.     

A Bayesian Approach to Fitting Gibbs Processes with Temporal Random Effects

We consider spatial point pattern data that have been observed repeatedly over a period of time in an inhomogeneous environment. Each spatial point pattern can be regarded as a ??snapshot?? of the underlying point process at a series of times. Thus, the number of points and corresponding locations of points differ for each snapshot. Each snapshot can be analyzed independently, but in many cases there may be little information in the data relating to model parameters, particularly parameters relating to the interaction between points. Thus, we develop an integrated approach, simultaneously analyzing all snapshots within a single robust and consistent analysis. We assume that sufficient time has passed between observation dates so that the spatial point patterns can be regarded as independent replicates, given spatial covariates. We develop a joint mixed effects Gibbs point process model for the replicates of spatial point patterns by considering environmental covariates in the analysis as fixed effects, to model the heterogeneous environment, with a random effects (or hierarchical) component to account for the different observation days for the intensity function. We demonstrate how the model can be fitted within a Bayesian framework using an auxiliary variable approach to deal with the issue of the random effects component. We apply the methods to a data set of musk oxen herds and demonstrate the increased precision of the parameter estimates when considering all available data within a single integrated analysis.     

滨海盐土盐分空间分布的条件模拟和不确定性研究

以海涂围垦区为例,利用普通克立格插值法和序贯高斯条件模拟方法对土壤盐分的空间分布进行估值和模拟,并利用序贯指示条件模拟进行不确定性评价。结果表明,样区东南区域土壤盐分含量较高而北部区域盐分含量低。由普通克立格法得到的土壤盐分的空间分布整体比较连续,具有明显的平滑效应,估值结果数据的分布频率趋于平缓。序贯高斯条件模拟结果整体分布相对离散,突出了原始数据分布的波动性,其模拟结果数据的分布频率相对集中。预测精度上,序贯高斯条件模拟的预测结果精度相对较高。以评价标准204mSm-1作为土壤盐分含量的阈值进行的序贯指示条件模拟结果显示,在土壤盐分含量较高的东南部地区,超过阈值的概率超过75%,而北部很多盐分相对含量低的地区,超过阈值的概率值都低于25%。以超阈值概率为0.9、0.85和0.8三个值来选取盐分的高值风险区进行空间不确定评价,结果表明,联合概率比单点统计的概率更为严格,在划分较大范围高盐风险区域时,最好同时采用联合概率来进行信度评价。     

Cokriging particle size fractions of the soil

It is often necessary to predict the distribution of mineral particles in soil between size fractions, given observations at sample sites. Because the contents in each fraction necessarily sum to 100%, these values constitute a composition, which we may assume is drawn from a random compositional variate. Elements of a D‐component composition are subject to non‐stochastic constraints; they are constrained to lie on a D– 1 dimensional simplex. This means we cannot treat them as realizations of unbounded random variables such as the multivariate Gaussian. For this reason, there are theoretical reasons not to use ordinary cokriging (or ordinary kriging) to map particle size distributions. Despite this, the compositional constraints on data on particle size fractions are not always accounted for by soil scientists. The additive log‐ratio (alr) transform can be used to transform data from a compositional variate into a form that can be treated as a realization of an unbounded random variable. Until now, while soil scientists have made use of the alr transform for the spatial prediction of particle size, there has been concern that the simple back‐transform of the optimal estimate of the alr‐transformed variables does not yield the optimal estimate of the composition. A numerical approximation to the conditional expectation of the composition has been proposed, but we are not aware of examples of its application and it has not been used in soil science. In this paper, we report two case studies in which we predicted clay, silt and sand contents of the soil at test sites by ordinary cokriging of the alr‐transformed data followed by both the direct (biased) back‐transform of the estimates and the unbiased back‐transform. We also computed estimates by ordinary cokriging of the untransformed data (which ignores the compositional constraints on the variables) for comparison. In one of our case studies, the benefit of using the alr transform was apparent, although there was no consistent advantage in using the unbiased back‐transform. In the other case study, there was no consistent advantage in using the alr transform, although the bias of the simple back‐transform was apparent. The differences between these case studies could be explained with respect to the distribution on the simplex of the particle size fractions at the two sites.     

用电子鼻区分霉变燕麦及其传感器阵列优化

应用电子鼻对燕麦（Avena sativa L）霉变程度进行区分,为了提高区分准确度,对电子鼻传感器阵列进行了优化的研究。每天随机选择10个燕麦样品进行电子鼻检测,试验连续进行5 d,将检测数据耦合入非线性双稳态随机共振系统,以外部Gaussian白噪声激励系统产生共振,选择输出信噪比特征值进行主成分分析,初期试验主成分1和主成分2贡献率之和为96.43%,且相同霉变程度样品离散度较大,不同霉变程度样品之间距离较近。为了提高电子鼻对霉变燕麦样品区分效果,进行了电子鼻传感器负荷加载分析,优化选择了传感器阵列,优化后主成分1和主成分2贡献率之和为99.31%,相同霉变程度燕麦样品的聚合度更高,使不同霉变程度燕麦样品之间的区分更加明显,为进一步的定量化检测奠定了基础。     

海涂围垦区土壤盐分空间变异性随机模拟与不确定性评价

以苏北海涂围垦区典型地块为例, 把随机模拟技术引入土壤盐分空间变异性研究中, 利用普通克里格法和序贯高斯模拟方法对土壤盐分的空间分布进行估值和模拟, 将随机模拟值与克里格插值及实测值进行对比分析, 并采用序贯指示模拟对土壤盐分空间分布的不确定性进行评价。结果表明: 由普通克里格法得到的土壤盐分空间分布整体比较连续, 具有明显的平滑效应, 减小了数据间的空间差异性, 改变了数据的空间结构; 序贯高斯模拟结果整体分布相对离散, 突出了原始数据分布的波动性。对非盐化土、轻度盐化土、中度盐化土和重度盐化土的空间不确定性进行的序贯指示模拟结果显示, 围垦后研究区耕层土壤盐渍化的发生概率已显著降低。轻度盐化土的高概率区是改良利用的主要区域, 宜采用农业生物改良措施, 对中度盐化土高概率区应通过完善田间灌排设施以加强改良治理, 客土法是重度盐化土高概率区较为高效的改良治理途径。