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1.
Geostatistical estimates of a soil property by kriging are equivalent to the best linear unbiased predictions (BLUPs). Universal kriging is BLUP with a fixed‐effect model that is some linear function of spatial co‐ordinates, or more generally a linear function of some other secondary predictor variable when it is called kriging with external drift. A problem in universal kriging is to find a spatial variance model for the random variation, since empirical variograms estimated from the data by method‐of‐moments will be affected by both the random variation and that variation represented by the fixed effects. The geostatistical model of spatial variation is a special case of the linear mixed model where our data are modelled as the additive combination of fixed effects (e.g. the unknown mean, coefficients of a trend model), random effects (the spatially dependent random variation in the geostatistical context) and independent random error (nugget variation in geostatistics). Statisticians use residual maximum likelihood (REML) to estimate variance parameters, i.e. to obtain the variogram in a geostatistical context. REML estimates are consistent (they converge in probability to the parameters that are estimated) with less bias than both maximum likelihood estimates and method‐of‐moment estimates obtained from residuals of a fitted trend. If the estimate of the random effects variance model is inserted into the BLUP we have the empirical BLUP or E‐BLUP. Despite representing the state of the art for prediction from a linear mixed model in statistics, the REML–E‐BLUP has not been widely used in soil science, and in most studies reported in the soils literature the variogram is estimated with methods that are seriously biased if the fixed‐effect structure is more complex than just an unknown constant mean (ordinary kriging). In this paper we describe the REML–E‐BLUP and illustrate the method with some data on soil water content that exhibit a pronounced spatial trend.  相似文献   

2.
Nematodes are indicators of soil quality and soil health. Knowledge of the relationships between nematode-based soil quality indices and environmental properties is beneficial for assessing environmental threats on soil biota. This study evaluated the spatial distribution of nematode-based soil quality indices in a 23-ha heavy metal-polluted nature reserve using geostatistical methods. We expected that a selection of abiotic soil properties (pH and moisture, clay, organic matter, cadmium (Cd), and zinc (Zn) contents) could explain a significant portion of the spatial variation of the indices and that regression kriging could more accurately model their spatial distribution than ordinary kriging. A stratified simple random sampling scheme was used to select 80 locations where soil samples were taken to extract nematodes and derive the indices. The area had a distinct gradient in soil properties with Cd and Zn content ranging from 0.07 to 68.9 and 5.3 to 1329 mg kg-1, respectively. Linear regression models were fitted to describe the relationships between the indices and soil properties. By also modelling the spatial correlation structure of regression residuals using spherical semivariograms, regression kriging was used to produce maps of the indices. The regression models explained between 21% and 44% of the total original variance in the indices. Soil pH was a significant explanatory variable in almost all cases, while heavy metal conent had a remarkably low effect. In some cases, the regression residuals had spatial structure. Independent validation indicated that in all cases, regression kriging performed slightly better because of having lower values of the root mean square prediction error and a mean prediction error closer to zero than ordinary kriging. This study showed the importance of soil properties in explaining the spatial distribution of biological soil quality indices in ecological risk assessment.  相似文献   

3.
土地混合使用制度下土壤硝态氮分布的地理空间制图研究   总被引:5,自引:0,他引:5  
Mapping the spatial distribution of soil nitrate-nitrogen (NO3-N) is important to guide nitrogen application as well as to assess environmental risk of NO3-N leaching into the groundwater. We employed univariate and hybrid geostatistical methods to map the spatial distribution of soil NO3-N across a landscape in northeast Florida. Soil samples were collected from four depth increments (0-30, 30-60, 60-120 and 120-180 cm) from 147 sampling locations identified using a stratified random and nested sampling design based on soil, land use and elevation strata. Soil NO3-N distributions in the top two layers were spatially autocorrelated and mapped using lognormal kriging. Environmental correlation models for NO3-N prediction were derived using linear and non-linear regression methods, and employed to develop NO3-N trend maps. Land use and its related variables derived from satellite imagery were identified as important variables to predict NO3-N using environmental correlation models. While lognormal kriging produced smoothly varying maps, trend maps derived from environmental correlation models generated spatially heterogeneous maps. Trend maps were combined with ordinary kriging predictions of trend model residuals to develop regression kriging prediction maps, which gave the best NO3-N predictions. As land use and remotely sensed data are readily available and have much finer spatial resolution compared to field sampled soils, our findings suggested the effcacy of environmental correlation models based on land use and remotely sensed data for landscape scale mapping of soil NO3-N. The methodologies implemented are transferable for mapping of soil NO3-N in other landscapes.  相似文献   

4.
High quality, agricultural nutrient distribution maps are necessary for precision management, but depend on initial soil sample analyses and interpolation techniques. To examine the methodologies for and explore the capability of interpolating soil properties based on neural network ensemble residual kriging, a silage field at Hayes, Northern Ireland, UK, was selected for this study with all samples being split into independent training and validation data sets. The training data set, comprised of five soil properties: soil pH, soil available P, soil available K, soil available Mg and soil available S,was modeled for spatial variability using 1) neural network ensemble residual kriging, 2) neural network ensemble and 3) kriging with their accuracies being estimated by means of the validation data sets. Ordinary kriging of the residuals provided accurate local estimates, while final estimates were produced as a sum of the artificial neural network (ANN) ensemble estimates and the ordinary kriging estimates of the residuals. Compared to kriging and neural network ensemble,the neural network ensemble residual kriging achieved better or similar accuracy for predicting and estimating contour maps. Thus, the results demonstrated that ANN ensemble residual kriging was an efficient alternative to the conventional geo-statistical models that were usually used for interpolation of a data set in the soil science area.  相似文献   

5.
Several methods,including stepwise regression,ordinary kriging,cokriging,kriging with external drift,kriging with varying local means,regression-kriging,ordinary artificial neural networks,and kriging combined with artificial neural networks,were compared to predict spatial variation of saturated hydraulic conductivity from environmental covariates.All methods except ordinary kriging allow for inclusion of secondary variables.The secondary spatial information used was terrain attributes including elevation,slope gradient,slope aspect,profile curvature and contour curvature.A multiple jackknifing procedure was used as a validation method.Root mean square error (RMSE) and mean absolute error (MAE) were used as the validation indices,with the mean RMSE and mean MAE used to judge the prediction quality.Prediction performance by ordinary kriging was poor,indicating that prediction of saturated hydraulic conductivity can be improved by incorporating ancillary data such as terrain variables.Kriging combined with artificial neural networks performed best.These prediction models made better use of ancillary information in predicting saturated hydraulic conductivity compared with the competing models.The combination of geostatistical predictors with neural computing techniques offers more capability for incorporating ancillary information in predictive soil mapping.There is great potential for further research and development of hybrid methods for digital soil mapping.  相似文献   

6.
应用土壤质地预测干旱区葡萄园土壤饱和导水率空间分布   总被引:7,自引:4,他引:3  
田间表层土壤饱和导水率的空间变异性是影响灌溉水分入渗和土壤水分再分布的主要因素之一,研究土壤饱和导水率的空间变化规律,有助于定量估计土壤水分的空间分布和设计农田的精准灌溉管理制度。为了探究应用其他土壤性质如质地、容重、有机质预测土壤饱和导水率空间分布的可行性,试验在7.6 hm2的葡萄园内,采用均匀网格25 m×25 m与随机取样相结合的方式,测定了表层(0~10 cm)土壤饱和导水率、粘粒、粉粒、砂粒、容重和有机质含量,借助经典统计学和地统计学,分析了表层土壤饱和导水率的空间分布规律、与土壤属性的空间相关性,并对普通克里格法、回归法和回归克里格法预测土壤饱和导水率空间分布的结果进行了对比。结果表明:1)土壤饱和导水率具有较强的变异性,平均值为1.64 cm/d,变异系数为1.17;2)表层土壤饱和导水率60%的空间变化是由随机性或小于取样尺度的空间变异造成;3)土壤饱和导水率与粘粒、粉粒、砂粒和有机质含量具有一定空间相关性,而与土壤容重几乎没有空间相关性;4)在中值区以土壤属性辅助的回归克里格法对土壤饱和导水率的预测精度较好,在低值和高值区其与普通克里格法表现类似。研究结果将为更好地描述土壤饱和导水率空间变异结构及更准确地预测其空间分布提供参考。  相似文献   

7.
县域土壤质量数字制图方法比较   总被引:3,自引:1,他引:2  
土壤质量研究几乎涵盖土壤研究的所有领域,土壤质量制图理论与方法是土壤质量研究的一项重要研究内容。该研究以北京市密云县为研究区,基于土壤质量评价最小数据集和指数和法计算的土壤质量指数,探究了在地学模型支持下区域土壤质量数字制图方法。研究设计了5种区域土壤质量数字制图方法,并比较了不同方法的空间数字制图精度。结果显示,目前广泛使用的基于参评指标空间插值结果的土壤质量数字制图方法精度最低、工序较繁琐,且无法反映研究区景观高度异质的特点;而基于计算后的土壤质量指数(soil quality index,SQI),借助于地统计学方法的土壤质量数字制图方法相对比较科学合理,其中又以基于计算后的SQI和回归克里格法预测效果最好,均方根误差最小,仅为0.01897,相对于基于参评指标空间插值结果的土壤质量数字制图方法,精度相对提高率最大,达到50%以上。综合考虑空间制图精度、工序的繁简程度,在该研究设计的5种方法中基于计算的SQI和回归克里格法最佳,该法避免了地统计插值在景观高度异质区的应用局限性,预测结果与实际最为相符。  相似文献   

8.
It is widely recognized that using correlated environmental factors as auxiliary variables can improve the prediction accuracy of soil properties. In this study, a radial basis function neural network (RBFNN) model combined with ordinary kriging (OK) was proposed to predict spatial distribution of four soil nutrients based on the same framework used by regression kriging (RK). In RBFNN_OK, RBFNN model was used to explain the spatial variability caused by the selected auxiliary factors, while OK was used to express the spatial autocorrelation in RBFNN prediction residuals. The results showed that both RBFNN_OK and RK presented prediction maps with more details. However, RK does not always obtain mean errors (MEs) which were closer to 0 and lower root mean square errors (RMSEs) and mean relative errors (MREs) than OK. Conversely, MREs of RBFNN_OK were much closer to 0 and its RMSEs and MREs were relatively lower than OK and RK. The results suggest that RBFNN_OK is a more unbiased method with more stable prediction performance as well as improvement of prediction accuracy, which also indicates that artificial neural network model is more appropriate than regression model to capture relationships between soil variables and environmental factors. Therefore, RBFNN_OK may provide a useful framework for predicting soil properties.  相似文献   

9.
Apparent electrical conductivity of soil (ECa) is a property frequently used as a diagnostic tool in precision agriculture, and is measured using vehicle‐mounted proximal sensors. Crop‐yield data, which is measured by harvester‐mounted sensors, is usually collected at a higher spatial density compared to ECa. ECa and crop‐yield maps frequently exhibit similar spatial patterns because ECa is primarily controlled by the soil clay content and the interrelated soil moisture content, which are often significant contributors to crop‐yield potential. By quantifying the spatial relationship between soil ECa and crop yield, it is possible to estimate the value of ECa at the spatial resolution of the crop‐yield data. This is achieved through the use of a local regression kriging approach which uses the higher‐resolution crop‐yield data as a covariate to predict ECa at a higher spatial resolution than would be prudent with the original ECa data alone. The accuracy of the local regression kriging (LRK) method is evaluated against local kriging (LK) and local regression (LR) to predict ECa. The results indicate that the performance of LRK is dependent on the performance of the inherent local regression. Over a range of ECa transect survey densities, LRK provides greater accuracy than LK and LR, except at very low density. Maps of the regression coefficients demonstrated that the relationship between ECa and crop yield varies from year to year, and across a field. The application of LRK to commercial scale ECa survey data, using crop yield as a covariate, should improve the accuracy of the resultant maps. This has implications for employing the maps in crop‐management decisions and building more robust calibrations between field‐gathered soil ECa and primary soil properties such as clay content.  相似文献   

10.
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.  相似文献   

11.
地统计软件包的开发及在土壤空间变异中的应用   总被引:8,自引:0,他引:8  
Geo-STATer是一个用来进行半方差分析、地统计估值和模拟的工具软件。它除了具备传统统计学的基本统计分析功能外,还集成了地统计学的几项主要功能:单变量半方差分析、交互变量半方差分析、半方差函数模型拟合、空间插值方法(包括普通克立格法、协同克立格法和逆距离加权法)。本文介绍了该软件的总体设计思路、主要功能模块和开发实现,并用实例土壤数据演示了软件的操作计算过程并将计算结果与其它的地统计软件进行了比较。结果表明.Geo-STATer软件具有较好的运算效率和精度.可以运用于土壤特性的空间变异性研究和插值制图,并能与其他专业模型进行集成开发.服务于田间精确施肥管理系统的开发。  相似文献   

12.
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.  相似文献   

13.
The German soil protection regulation (BBodSchV) requires the investigation and evaluation of sites with known, or suspected contamination. The purpose of this study is the application of geostatistical methods to locate hazardous zones within such a site and to estimate the amount and uncertainty of the contaminant load in these zones. The study site is an area around a metal smelter in the city of Nordenham, Germany, where among other heavy metals, Cd was released to the environment by dust emissions for many decades. In an earlier study soil cores were taken in the area and analyzed for Cd using various extraction methods. After translation of data to results corresponding to a single extraction method using linear regression analysis, Cd concentrations were mapped by ordinary and lognormal kriging. Crossvalidation showed that both methods perform similarly. However, neither ordinary nor lognormal kriging were able to account for the uncertainty of the kriged estimates. We repeated ordinary kriging with a relative variogram having a unit sill. The estimated relative kriging variance was scaled locally. This method considerably improved the estimation of uncertainty. Subsequently, we estimated Cd contents for the land use dependent size of support as specified in the BBodSchV. The kriged Cd estimates as well as their uncertainty were evaluated with regard to limits set by the BBodSchV. Parts of the area which may be declared safe based on merely the kriged estimates, can actually exceed a sanction or test limit by a chance of up to 50 % when uncertainty is also considered. Within the BBodSchV a recommended limit should therefore always be accompanied by a tolerable uncertainty that it may be exceeded on a given support (e.g. 5 %).  相似文献   

14.
研究不同模型对土壤有机质空间预测的性能差异对制定更加科学合理的采样策略、提升采样效率和提高土壤空间预测精度有着重要的指导意义。本研究将6496个土壤样点按8∶2的比例分层随机分成训练集与验证集,应用普通克里格、随机森林以及随机森林-回归克里格三种有代表性的数字化土壤制图(Digital Soil Mapping,DSM)模型,对河南省许昌市耕地表层土壤有机质含量及空间分布进行预测,对三种模型性能表现进行综合评价。三种模型输出的预测结果显示:研究区耕地表层土壤有机质含量水平一般,均值为18.70 ~ 18.81 g kg?1,变异系数0.15 ~ 0.17,属中等强度变异;空间分布总体格局为西北与西南部分山地褐土区、东南部砂姜黑土区表层有机质含量高,中北部脱潮土、石灰性潮土区表层有机质含量低。验证结果表明:三种模型性能表现无明显差距,预测精度基本一致,输出结果对研究区耕地表层土壤有机质变异解释百分比在33% ~ 34%之间,在相同和相近尺度土壤有机质空间预测案例研究里属中等水平。在协变量有限且样点分布较为均匀的情况下,普通克里格模型便于快速获得研究区目标变量的空间分布;如果协变量比较丰富且易于收集利用,或是进行空间预测的同时还需要甄别不同因素对目标变量的影响大小,则建议采用随机森林模型;协变量有限,但样点密度较大时,随机森林-回归克里格模型可能是对目标变量进行空间预测的不错选择。  相似文献   

15.
从数据的统计特征分析、异常值筛选及处理、实验半变异函数计算及拟合等方面对普通克里格计算过程中的精度控制问题进行了初步研究,并以天津市东南郊区土壤砷(As)空间分布评估为例,分析了在多步骤精度控制下普通克里格法估计土壤污染物空间分布的可靠性。结果表明,研究区土壤As表现出了明显的累积特征,且监测值为正态分布,异常值较少且为局部异常值,实验半变异函数表现出明显的各向异性。在较严格的精度控制下,普通克里格估值的最优无偏特性可以得到较好的体现,其对土壤As的空间分布的估计精度可以达到较高的水平。  相似文献   

16.
利用数字高程模型改进高山灰岩坑土壤pH值预测   总被引:1,自引:0,他引:1  
Among spatial interpolation techniques,geostatistics is generally preferred because it takes into account the spatial correlation between neighbouring observations in order to predict attribute values at unsampled locations.A doline of approximately 15 000 m 2 at 1 900 m above sea level (North Italy) was selected as the study area to estimate a digital elevation model (DEM) using geostatistics,to provide a realistic distribution of the errors and to demonstrate whether using widely available secondary data provided more accurate estimates of soil pH than those obtained by univariate kriging.Elevation was measured at 467 randomly distributed points that were converted into a regular DEM using ordinary kriging.Further,110 pits were located using spatial simulated annealing (SSA) method.The interpolation techniques were multi-linear regression analysis (MLR),ordinary kriging (OK),regression kriging (RK),kriging with external drift (KED) and multi-collocated ordinary cokriging (CKmc).A cross-validation test was used to assess the prediction performances of the different algorithms and then evaluate which methods performed best.RK and KED yielded better results than the more complex CKmc and OK.The choice of the most appropriate interpolation method accounting for redundant auxiliary information was strongly conditioned by site specific situations.  相似文献   

17.
This paper addresses the issue of incorporating a digital elevation model into the mapping of annual and monthly erosivity values in the Algarve region (Portugal). Besides linear regression of erosivity against elevation, three geostatistical algorithms are introduced: simple kriging with varying local means (SKlm), kriging with an external drift (KED) and colocated cokriging. Cross validation indicates that the straightforward linear regression, which ignores the information provided by neighboring climatic stations, yields the largest prediction errors in most situations. Smaller prediction errors are produced by SKlm and KED that both use elevation to inform on the local mean of erosivity; kriging with an external drift allows one to assess the relation between the two variables within each kriging search neighborhood instead of globally as for simple kriging with varying local means. The best results are generally obtained using cokriging that incorporates the secondary information directly into the computation of the erosivity estimate. The trade-off cost is the inference and modeling of three direct and cross semivariograms.  相似文献   

18.
The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.  相似文献   

19.
Agricultural activities in the Netherlands cause high nitrogen and phosphorous fluxes from soil to ground- and surface water. A model chain (STONE) has been developed to study and predict the magnitude of the resulting ground- and surface water pollution under different environmental conditions. STONE has three main components, namely: 1) the fertiliser distribution model CLEAN; 2) the atmospheric transport and deposition model OPS; and 3) the soil and soil-water quality model ANIMO. The goal of this study was to assess the accuracy of the STONE model output by comparing model predictions with independent observations, while accounting for spatial variation and differences in spatial support. The specific STONE output considered was mineral phosphorous concentration in the top soil. Predictions from STONE are made at the block support and, specifically, for 500 × 500 m grid cells, whereas the observations are on a point support. Therefore, aggregation of the point observations or disaggregation of the STONE model predictions is needed in order to test the accuracy of the STONE model. This study used the aggregation route. Specifically, ordinary and regression block kriging were used to aggregate the point observations to the block support. Overall, there was a good correspondence between the kriged observations and the STONE predictions, with no evidence of bias in the model predictions. However, there were meaningful differences locally, which was partly attributed to the smoothing of the kriging interpolator. Closer inspection revealed that not all of the differences could be attributed to measurement errors in the phosphorous observations and interpolation errors in the kriged phosphorous maps. Thus, it was demonstrated that the STONE output suffers from input and/or model errors. However, quantification of these errors was restricted by the fairly large interpolation uncertainty of the kriged phosphorous observations. Nevertheless, the spatial pattern of error in the STONE predictions could be partly attributed to combinations of landuse and soil type.  相似文献   

20.
【目的】在陆地生态系统中, 土壤全氮和有机碳是重要的生态因子。本研究基于土壤调查获得大量土壤剖面的空间和属性信息,研究河北的土壤有机碳和全氮的空间分布特征,为河北的土壤养分监测和管理提供科学依据,同时也为其他类似地区土壤采样提供参考,减少采样成本。【方法】运用传统统计学和地统计学分析方法,以变异函数为工具,初步分析了河北土壤全氮和有机碳的空间变异特征,并应用普通克立格法和回归克里格法进行插值, 得出全氮和有机碳含量的分布格局。【结果】研究区土壤有机碳和全氮的平均值分别为15.25 g/kg和1.23 g/kg,变异系数分别为0.73和0.63,属于中等强度变异。经对数转换后,土壤有机碳和全氮均符合正态分布。选择球状模型作为土壤有机碳和全氮的半方差函数理论模型,土壤有机碳和全氮的块金值/基台值的比值分别为1.8%和1.2%,有机碳和全氮的块金系数均小于25%,表明有机碳和全氮具有强烈的空间相关性。有机碳和全氮空间变异的尺度范围不同,分别为50.400 km和59.200 km。研究区的有机碳总体空间分布规律是有机碳在北部较高、南部较低,呈自北向南递减趋势,土壤全氮与有机碳的空间分布趋势相似,但有机碳的空间变异特征较全氮明显,这种空间分布格局主要受环境因子、 土壤质地、 土壤类型以及土地利用类型等的影响,其中环境因子中的气温和海拔对有机碳和全氮的影响较大。通过比较普通克里格和回归克里格的预测结果,回归克里格能较好地反映东南部有机碳和全氮较低地区的局部变异外,对于西北部的山区也能更好地反映碳、 氮与地形及气候等因素的关系。【结论】河北土壤有机碳和全氮的空间变异和分布特征较为类似,受地形地貌、 气候等因素的影响。通过比较普通克里格法和回归克里格法的空间预测结果,回归克里格法可以消除环境因子的影响,从而得到更准确的空间预测结果,因此建议使用回归克里格法进行预测,以期获得一个更为准确的土壤有机碳和全氮的空间预测结果。  相似文献   

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