贝叶斯最大熵地统计学方法及其在土壤和环境科学上的应用

贝叶斯最大熵(Bayesian Maximum Entropy,BME)地统计学方法是近年来出现的一种时空地统计学新方法。相对于传统的克里金方法,该法具有坚实的认识论框架和方法学基础。它不需要作线性估值、空间匀质和正态分布的假设,能够融入先验知识和软数据,并且不会损失其中蕴含的有用信息,提高了分析精度。本文首先介绍了BME的基本理论及其估值方法,随后简单描述了该方法的理论发展过程及其在土壤和环境科学上的应用情况,最后对该方法的应用做了总结与展望。经过国外研究者多年的开发和实践,BME方法已经被证明是一个理论上较为成熟,能够应用到实际研究中的优秀地统计学方法,在资源环境评估上有着广泛的应用前景。     

Pedometric mapping of soil organic matter using a soil map with quantified uncertainty

This paper compares three models that use soil type information from point observations and a soil map to map the topsoil organic matter content for the province of Drenthe in the Netherlands. The models differ in how the information on soil type is obtained: model 1 uses soil type as depicted on the soil map for calibration and prediction; model 2 uses soil type as observed in the field for calibration and soil type as depicted on the map for prediction; and model 3 uses observed soil type for calibration and a pedometric soil map with quantified uncertainty for prediction. Calibration of the trend on observed soil type resulted in a much stronger predictive relationship between soil organic matter content and soil type than calibration on mapped soil type. Validation with an independent probability sample showed that model 3 out‐performed models 1 and 2 in terms of the mean squared error. However, model 3 over‐estimated the prediction error variance and so was too pessimistic about prediction accuracy. Model 2 performed the worst: it had the largest mean squared error and the prediction error variance was strongly under‐estimated. Thus validation confirmed that calibration on observed soil type is only valid when the uncertainty about soil type at prediction sites is explicitly accounted for by the model. We conclude that whenever information about the uncertainty of the soil map is available and both soil property and soil type are observed at sampling sites, model 3 can be an improvement over the conventional model 1.     

The indicator approach to categorical soil data

In this paper, the first of two, we present the indicator approach to describe the spatial variability of categorical soil data. Indicator kriging is used to obtain conditional probabilities of soil data classes at unsampled locations. A new concept of map purity is defined. Using Sequential Indicator Simulation (SIS), equiprobable realizations of classified maps can be drawn which reflect the probability of occurrence of each class and honour the observed spatial connectivity patterns of the classes and the classes found at the observation sites. When categorical data are used for land resources assessment, the uncertainties accruing from map impurities can be assessed by performing the analysis on each of the maps generated by SIS. In Part I1 of this series, the methods are demonstrated using a case study on the mapping of water table classes and a land use suitability analysis for pasture.     

基于贝叶斯最大熵和多源数据的作物需水量空间预测

作物需水量是灌溉工程规划、设计和管理的重要基础数据,充分利用多源数据和先验知识,快速经济地获取精度较高的区域作物需水量对于区域水资源的优化配置具有重要意义。为精确预测作物需水量,该文以长系列实际监测和校核作物系数后计算得到的作物需水量为硬数据,利用硬数据确定获得最大熵的约束条件,根据软数据获取渠道的不同(部分年份缺失的站点数据、文献中获得的数据、利用灌溉试验数据库中的作物需水量资料,采用协同克立格方法获得的数据、考虑主要地形因子和主要气象要素的影响,采用主成分分析和地理加权回归(geographically weighted regression,GWR)方法获得作物需水量数据以及遥感数据),提出不同来源软数据的概率密度函数表达方法,采用贝叶斯最大熵(Bayesian maximum entropy,BME)方法对不同来源的作物需水量信息进行有机整合。结果表明:除硬数据+文献软数据外,其他数据整合呈现一致结果。华北地区冬小麦作物需水量在豫南地区较小,中部地区黄河北岸有连片的相对高值区,山东需水量相对较高,冀东北的乐亭、唐山附近有相对低值区。除硬数据+文献软数据比不整合的精度低9.41%外,其他软数据源均可不同程度地提高整合效果,硬数据+克立格软数据、硬数据+GWR软数据和硬数据+除文献数据外的其他软数据分别比不整合的精度提高85.33%、85.75%和91.69%。对考虑地形、气象等要素的多源数据进行整合可更好地反映冬小麦作物需水量空间分布的细节,显著提高估算精度,为稀疏监测站点地区水土资源的精准管理和优化配置提供数据支撑。     

Estimating the local mean for Bayesian maximum entropy by generalized least squares and maximum likelihood, and an application to the spatial analysis of a censored soil variable

The Bayesian maximum entropy (BME) method is a valuable tool, with rigorous theoretical underpinnings, with which to predict with soft (imprecise) data. The methodology uses a general knowledge base to derive a joint prior distribution of the data and the prediction by the criterion of maximum entropy; the hard (precise) and soft data are then processed using this prior distribution to yield a posterior distribution that provides the BME prediction. The general knowledge base commonly consists of the mean and covariance functions, which may be extracted from the data. The common method for extracting the mean function from the data is a generalized least squares (GLS) approach. However, when the soft data take the form of intervals of plausible values, this method can result in errors in the BME predictions. This paper suggests a maximum likelihood (ML) method for fitting the local mean. The two methods are compared in terms of their predictions, firstly on simulated random fields and then on a case study to predict the depth of soil using some censored data. The results show that the ML method can result in more accurate BME predictions; the degree of improvement over the GLS method depends on the parameters of the spatial covariance model.     

Integrating soil map information in modelling the spatial variation of continuous soil properties

This paper presents two indicator algorithms that integrate soil map information into modelling the spatial variation of continuous soil properties: these are simple indicator kriging with varying means and the Markov–Bayes algorithm. Both methods are used to evaluate probabilities for copper and cobalt deficiencies in the Borders Region of Scotland. Results are compared with maps obtained by the polygonal method (Thiessen polygons) and an indicator kriging algorithm that does not use soil map information. Accounting for soil map information is shown to improve delineation of the deficient areas, especially where the sampling is sparse. Test locations are classified as deficient or not so as to minimize an expected cost of mis-classification that is derived from local probability distributions of copper or cobalt and functions measuring the cost of overestimating or underestimating metal concentrations. The comparison of classification results with actual copper and cobalt concentrations at test locations shows that the two proposed algorithms can decrease substantially the economic loss attached to misclassification.     

Quantification of soil properties based on external information by means of fuzzy‐set theory

The increasing demand for improved large‐scale thematic maps of soil properties for use in such areas as hydrological modeling and landscape planning requires the inclusion of external information in the computerized construction of soil maps. As this data is often purely qualitative, regionalization methods are called for, that permit consideration of uncertain empirical information. A method based on fuzzy‐set theory is presented, which enables a GIS‐based quantification of soil properties with no loss of content input when transforming ”︁soft” data. This approach, which is also applicable to other tasks, is demonstrated by the construction of maps of soil properties based on uncertain qualitative information from the Hessian Forestry Survey and the small‐scale soil map of Hesse (1:50.000). Quality and uncertainty can be judged from a separate map of uncertainty indices. The thematic output map of the available water capacity of the rooting zone in the Dietzhölztal (Hesse) research site prepared using the fuzzy approach provided an increase of 101 % in spatial resolution compared with the 1:50.000 soil map.     

Probabilistic soil mapping by Bayesian inference to assess suitability for derocking in northwest Syria

Land reclamation by rock removal has wide potential in areas with shallow or rocky soils. In northwest Syria, this practice is hindered in its implementation by a lack of physical soil suitability data, principally soil rockiness and soil depth to hard rock. These soil properties were surveyed in a limited study area, resulting in a hard‐boundary thematic soil map (64–94% accuracy per property). Bayesian inference is proposed as a low‐cost upscaling method that yields a set of pixel‐based probability maps, providing improved input for spatial decision support models. Whereas the achieved spatial upscaling (from 2510 to 19 100 ha) outweighed the decrease in overall accuracy (down to 26–57%), probability maps require dedicated validation and manipulation procedures. This research contributes to methods for the creation, validation and interpretation of probabilistic soil property maps for quantitative land evaluation. First, we evaluated three postprocessing and validation methods for probabilistic soil property maps, identifying the use of ‘prediction rates’ as the best approach in a spatial planning context. Next, we demonstrated how the maps can support decision‐making for land management activities by simulating the expected losses and gains from interventions, in a decision‐theoretic approach. Based on the simulations, the investments in large‐scale derocking projects in northwest Syria will pay off in terms of increased agricultural productivity in less than 10 years.     

Usability of soil survey soil texture data for soil health indicator scoring

Soil textural information is an important component underlying other soil health indicators. Soil texture analysis is a common procedure, but it can be labor intensive and expensive. Soil texture data typically are available from the Soil Survey Geographic (SSURGO) database, which may be an option for determining soil health texture groups (SHTG). The SSURGO database provides soil texture information in the soil map unit (SMU) name, taxonomic class category (family), and detailed values (≤ 2 mm soil fraction) of percent sand, silt and clay by soil horizon. The objective of this study was to examine the possibility of using SSURGO data for SHTG at the 147-ha Cornell University Willsboro Research Farm in New York state as an alternative for soil texture data determined manually on collected soil core samples. Comparative results revealed that representative values for soil texture from the SSURGO database generally matched measured mean values for all SMUs.     

GIS‐based regionalization of soil profiles with Classification and Regression Trees (CART)

A map of soil texture profiles was derived from readily available spatial data in combination with information from soil profiles using CART (classification and regression trees). The primary purpose was to provide a regionalized predictor for the vertical hydraulic conductivity profiles to be used as an input variable to an evapo‐transpiration model. In contrast to former studies, the texture of 110 soil profiles taken in the 10 km² area was not averaged vertically but the profiles were grouped according to their hydraulic properties. Therefore, it was possible to include site specific profiles, e.g. with histic or argillic horizons. Despite of small sampling quantities (110 soil profiles grouped into 8 classes) a prediction probability of 60 to 70 % was achieved in most classes. The resulting map provides valuable information for the granulometric and hydrologic characterization of the study area.<?show $6#>     

Accounting for variability within map units when linking a pesticide fate model to soil survey

The aim of this study was to estimate the probability of exceedance (POE) of the USEPA health advisory level for particular pesticides in groundwater beneath citrus groves in southwestern Florida. The approach included bootstrapping to assess the uncertainty of the model output due to the variability of soil input data; a weather generator to provide daily rainfall amounts; daily evapotranspiration by the Blaney-Criddle (FAO) method; and a program written to compute POE values. Bootstrapping enabled us to assess the uncertainty of soils inputs by generating pseudo-profiles of soils from pedon characterization data. These pseudo-profiles were used in Monte Carlo simulations that captured the variance of selected soil parameters within soil taxonomic units. Single-name map units (i.e., consociations) were represented by no fewer than three actual pedon characterization data sets for the named soil and/or closely similar soil(s). In the case of a multiple-name map unit (i.e., soil association or soil complex), no fewer than three actual pedons of named and/or similar soils were used to generate pseudo-profiles for each of the named soils in the map unit. Inputs were linked to the pesticide fate model Chemical Movement in Layered Soil, CMLS (Nofziger and Hornsby) to produce cumulative probability curves showing the fraction of applied pesticide leaching below the 1-m depth. This curve was then used to determine the POE for various soil delineations in the groves within the watershed. Multiple POEs were generated for multiple-named map units; the rule was to select the higher(est) POE value as an estimator of environmental risk for each such map unit. Thematic maps are then created using soil and land use coverages and POE's for various pesticides evaluated.

Our approach suggests that the use of cumulative probability functions and probabilities of exceedance of health standards (USEPA HAL) provides needed integration of the uncertainties associated with input parameters, the significance of which can be easily grasped by decision officials. The use of environmental fate models to predict pesticide behavior in soils throughout a landscape has brought about intense scrutiny of soil attribute data and map unit delineations far beyond that envisioned for the present progressive soil survey. The authors also recognize that uncertainties in model formulation, pesticide fate parameters and toxicity further complicate assessments of this nature.     

综合BME和BNN法的农田土壤水分与养分分布空间插值

掌握农田土壤水分和养分的空间分布特征是实现农田土壤精确管理及实施精确农业的重要依据。以有限的采样信息为基础,通过多种空间分析理论的融合,形成优势互补的综合方法,对提高土壤变量空间分布模拟和绘图精度具有重要意义。该文将贝叶斯最大熵法(Bayesian maximum entropy,BME)和贝叶斯人工神经网络方法(Bayesian neural networks,BNN)结合形成一种空间插值新方法,即用BNN法表达估值的不确定性,并将其结果融入现代地质统计学BME法中,用融入BNN法结果的BME法(Bayesian maximum entropy method combined with Bayesian neural networks,BMENN)模拟土壤变量的空间分布。以江苏省扬州市区北部某田块的土壤水分、有机质、全氮、碱解氮、速效钾和速效磷6种土壤特性的采样数据为例,运用交叉验证法,将BMENN法对土壤变量的估值精度与BNN法、普通克立格法(ordinary Kriging,OK)进行了比较。结果表明:与OK法和BNN法相比,BMENN法将估计方差(mean squared error,MSE)缩小2.26%~23.54%,具有最小的估计方差和接近于0的平均绝对误差(mean error,ME);BMENN法的估计值与实测值相关系数更大(r=0.62~0.89),具有更高的相关程度;MSE的组成分析表明,BMENN法再现变量波动程度和波动大小的能力更强;从模拟的空间分布图来看,BMENN法绘制的空间分布图更连续,"牛眼"较少,更符合土壤变量的地学规律。BMENN法对于利用有限数据信息提高土壤变量空间分布模拟精度具有重要意义,并可为土壤管理、精准农业的实施以及区域环境规划等提供科学依据。     

Employing elevation data for efficient mapping of soil pollution on floodplains

Abstract The co-regionalization between relative elevation and zinc concentration was used to map zinc concentration in the soil of the Geul floodplain in the southern Netherlands by co-kriging from 154 observations. Point co-kriging and point kriging for estimating zinc content in the soil were compared in terms of kriging variances. Another 45 samples were used to compare the precision of the estimated values in terms of squared and absolute estimation errors. Point co-kriging produced better estimates of zinc concentration than either simple point kriging or linear regression from the relative elevation data alone. Moreover, the estimation variances for co-kriging are substantially smaller than those for kriging. The results suggest that knowledge of geomorphological processes can often improve the quality of interpolation maps of properties that are expensive to measure.     

Spatial prediction of USDA‐ great soil groups in the arid Zarand region,Iran: comparing logistic regression approaches to predict diagnostic horizons and soil types

The main objectives of this study were to compare binary logistic regression as an indirect approach and multinomial logistic regression as a direct approach to produce soil class maps in the Zarand region of southeast Iran. With indirect prediction, the occurrence of relevant diagnostic horizons was first mapped, and subsequently, various maps were combined for a pixel‐wise classification by combining the presence or absence of diagnostic horizons. In direct prediction, the dependent variable was the great group itself, so the probability distribution of the great soil groups was directly predicted. Among the predictors, the geomorphology map was identified as an important tool for digital soil mapping approaches as it helped to increase the accuracy. The results of prediction showed larger mean probability values for each great soil group in the areas actually covered by the great soil groups compared with other areas, indicating the reliability of the prediction. In most predictions, the global purity was slightly better than the actual purity for the models; however, both models provided poor predictions for Haplocambids and Calcigypsids. The results showed that soils with better prediction were those much influenced by topographical and geomorphological characteristics and soils with very poor accuracy of prediction were only slightly influenced by topographical and geomorphological characteristics. An advantage of the indirect method is that it gives insight into the causes of errors in prediction at the scale of diagnostic horizons, which helps in the selection of better covariates.     

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。     

土壤侵蚀模型研究进展

国内外土壤侵蚀模型的发展过程,可以大致划分为经验统计模型、物理过程模型与分布式模型三个阶段.就这三个阶段,介绍了国内外土壤侵蚀模型的研究成果.并将地理信息系统(GIS)在土壤侵蚀模型中的应用分为三类,一是以GIS为工具,利用GIS提取模型所需因子,然后按照模型要求利用GIS的图形运算和地图代数运算,最后得到计算结果.二是将GIS与土壤侵蚀模型作为两个不同的系统,考虑结合方法的问题.三是利用GIS开发新的模型或改善已有模型.     

Assessment of soil erosion hazard and prioritization for treatment at the watershed level: Case study in the Chemoga watershed,Blue Nile basin,Ethiopia

Soil erosion by water is the most pressing environmental problem in Ethiopia, particularly in the Highlands where the topography is highly rugged, population pressure is high, steeplands are cultivated and rainfall is erosive. Soil conservation is critically required in these areas. The objective of this study was to assess soil erosion hazard in a typical highland watershed (the Chemoga watershed) and demonstrate that a simple erosion assessment model, the universal soil loss equation (USLE), integrated with satellite remote sensing and geographical information systems can provide useful tools for conservation decision‐making. Monthly precipitation, soil map, a 30‐m digital elevation model derived from topographic map, land‐cover map produced from supervised classification of a Land Sat image, and land use types and slope steepness were used to determine the USLE factor values. The results show that a larger part of the watershed (>58 per cent of total) suffers from a severe or very severe erosion risk (>80 t ha⁻¹ y⁻¹), mainly in the midstream and upstream parts where steeplands are cultivated or overgrazed. In about 25 per cent of the watershed, soil erosion was estimated to exceed 125 t ha⁻¹ y⁻¹. Based on the predicted soil erosion rates, the watershed was divided into six priority categories for conservation intervention and 18 micro‐watersheds were identified that may be used as planning units. Finally, the method used has yielded a fairly reliable estimation of soil loss rates and delineation of erosion‐prone areas. Hence, a similar method can be used in other watersheds to prepare conservation master plans and enable efficient use of limited resources. Copyright © 2009 John Wiley & Sons, Ltd.     

A comprehensive approach to soil‐atmosphere trace‐gas flux estimation with static chambers

A new procedure (HMR) for soil‐atmosphere trace‐gas flux estimation with static chambers is presented. It classifies data series into three categories according to criteria based on the application of a particular non‐linear model and provides statistical data analyses for all categories. The two main categories are non‐linear and linear concentration data, for which data are analysed by, respectively, the non‐linear model and linear regression. The third category is represented by concentration data within the range of experimental error, or noise, from sites with no significant flux. Data in this category may be analysed by linear regression or simply classified as no flux. The particular non‐linear model has been selected among alternatives because its exponential curvature generally fits non‐linear static chamber concentration data well, and because it can be proven, mathematically, to be robust against horizontal gas transport through the soil or leaks in the chamber. The application of the HMR procedure is demonstrated on 244 data series of nitrous oxide accumulation over time. On average, 47% of these data were non‐linear, with an average flux increase over linear regression of 52%. The classification and analysis of data with a small signal‐to‐noise ratio requires special attention, and it is demonstrated how diagnostic graphical plots may be used to select the appropriate data analysis. The HMR procedure has been implemented as a free add‐on package for the free software R and is available for download through CRAN ( http://www.r‐project.org ).