Interpolation Of Soil Properties Research Articles

GIS Interpolation and Mapping of Soil Physicochemical Properties in Deep Medium Black Soils of Established Citrus Orchards

Soil properties are an important factor for orchard establishment, precise nutrient management and sustainable production of fruit crops. Therefore, it is important to assess the spatial distribution of fundamental soil properties in well-established orchards. Hence an attempt has been made to assess the extent of soil properties and its spatial distribution in citrus orchards in medium black soils of Madhya Pradesh. The present study was conducted for the assessment of the spatial distribution of physicochemical properties viz. pH, electrical conductivity (EC) and soil organic carbon (SOC) of citrus orchards in medium-deep black soils of India. Results revealed that soil pH ranged from 6.83-8.84 (mean 7.80), soil EC varied from 0.07-0.34dS m-1 (mean 0.18 dS m-1) and soil organic carbon ranged from 0.13-0.89% (mean 0.47%) in 0-20 cm of surface soil layer. Geostatistical analysis showed that the slope of the prediction function of best-fit model (exponential) for soil pH, EC and SOC was 0.31, 0.22 and 0.77, respectively. The corresponding values of root mean square error (RMSE) were 0.35, 0.03, and 0.14. Interpolation of soil properties indicated that 89.2 % area had soil pH between 7.20 to 8.00, 83.4 % area had soil EC between 0.10 to 0.20 dS m-1, while>90 % area had SOC content ranged from 0.25 to 0.75%. Geo-statistical analysis revealed that spatial dependency was moderate for pH and strong spatial dependency was estimated for EC and SOC content. Based on RMSE and slope of prediction function, an exponential model was best-fit model in ordinary kriging for interpolation of measured soil properties.

An l1-regularized total variation minimization model for soil interpolation based on geostatistical priors

Geostatistical interpolation of soil properties is highly demanded to assess the status of soil conditions. Recently, methods based on compressed sensing (CS) have been developed to improve the interpolation results to handle cases of limited observations. Here, we used the total variation, an equivalent concept of spatial autocorrelation, to modify the conventional CS interpolation model (CS-V) for soil science and form a new model, l1-TV. The spatial structure information in the variogram models was taken as geostatistical priors to produce ideal results. Examples of interpolation of soil electrical conductivity and heavy metals content were employed to validate and illustrate this new model. A comparison of the interpolation results of ordinary kriging (OK), CS-V and l1-TV showed that the CS method had an advantage over OK when the spatial correlation of soil properties was strong. A significant improvement in l1-TV was also exhibited; that is, the new model can provide more stable performance and show good adaptability to changes in soil spatial correlation. Furthermore, the generation of soil maps from a large number of environmental variables within the l1-TV framework is a promising application for further research.

Interpolation of soil properties from geostatistical priors and DCT-based compressed sensing

The distribution of and variation in soil properties are spatially correlated and commonly obtained through interpolation techniques and point source surveys. The contradiction between sample limitation and data demand has become an obstacle to generating accurate distribution maps with conventional methods, such as geostatistical or machine learning methods. To weaken the negative impact of limited data and obtain a more accurate distribution map, we introduce a new interpolation method called CS-V into soil science. The method combines compressed sensing (CS), which is a novel signal recovery technique, with the traditional geostatistical prior and generates a distribution map by solving a sparse recovery problem. Two datasets, a complete measurement set of soil electrical conductivity (EC) and a discrete point set of soil organic matter (SOM), were used to validate the feasibility and investigate the characteristics of the method. The compressibility of the soil distribution map was first validated through the EC dataset to provide the fundamentals of CS-V. The comparison between the results of CS-V and ordinary kriging (OK) shows that CS-V can provide a higher prediction accuracy and a wider estimation range. In addition, considering the two parameters of the sparse recovery problem, the regularized parameter λ is the decisive factor that controls the interpolation results, and the influence of searching space k is diluted when λ is large enough. The CS-V method is suitable as an alternative interpolation method in soil science in the case of limited measurement data.

Kriging and Simulation in Gaussian Random Fields Applied to Soil Property Interpolation

Spatial modeling is increasingly prominent in many fields of science as statisticians attempt to characterize variability of the processes that are spatially indexed. This paper shows that the Gaussian random field framework is useful for characterizing spatial statistics for soil properties. A sample of soil properties in 94 spatial locations are taken from a field (186.35m×211.44m) wide in northern Ethiopia, Karsa-Malima. We use observations of organic carbon (OC) from the site in our study. Box-Cox transformation is used because of OC follows non-Gaussian distributions. We develop ordinary kriging which is universal kriging with unknown trend models which enables us to predict any point within the field even outside the field up to the “Range” of the model. In this thesis work we predict 100×100 grids (10000 points) using kriging interpolation models. More over in each of these 10000 locations 1000 conditional simulations are made. Interestingly prediction using universal kriging and mean of conditional simulations agree in expectation and kriging variance. For covariance and/or variogram modeling and for parameter estimation we used least square principle and maximum likelihood estimation method. The classical geostatistical approach known as kriging is used as a spatial model for spatial prediction with associated spatial variances. Moreover, conditional simulation is performed. From ordinary kriging model results, predictions are accurate when predictions are close to observation locations. Prediction variance in the observed locations is close to the nugget effect.

English

The knowledge of spatial distribution of soil attributes, particularly chemical ones, which is very relevant for agricultural planning. Several studies have focused on spatial interpolation of soil properties, but only a few of them have been undertaken in sub-Saharan Africa. This study aims to analyse the spatial variability of hydrogen potential (pH) and electric conductivity (EC) within an agricultural region in Cuamba district of Mozambique. Efficiency of a deterministic and a stochastic interpolator were compared, namely Inverse Distance Weighting (IDW) and Ordinary kriging, respectively. Soil samples were collected at random locations scattered through the study region, and were later analyzed in water and soil laboratory. These point data were then used to produce interpolated surfaces of soil chemical properties. Efficiency of spatial interpolation methods was assessed based on prediction errors’ statistics derived from cross-validation. Results show that ordinary kriging was less biased and more accurate than IDW at samples’ locations. Hence, maps produced using the former method are a valuable contribution for the spatial characterization of soil quality, according to its chemical properties. Considering the spatial patterns of pH, southeast area is characterized by clayey soils, which has a high fertility potential for food crops. Key words: Geostatistics, inverse distance weighting , kriging, electric conductivity, pH.

Adaptive Surface Modeling of Soil Properties in Complex Landforms

Abstract: Spatial discontinuity often causes poor accuracy when a single model is used for the surface modeling of soil properties in complex geomorphic areas. Here we present a method for adaptive surface modeling of combined secondary variables to improve prediction accuracy during the interpolation of soil properties (ASM-SP). Using various secondary variables and multiple base interpolation models, ASM-SP was used to interpolate soil K+ in a typical complex geomorphic area (Qinghai Lake Basin, China). Five methods, including inverse distance weighting (IDW), ordinary kriging (OK), and OK combined with different secondary variables (e.g., OK-Landuse, OK-Geology, and OK-Soil), were used to validate the proposed method. The mean error (ME), mean absolute error (MAE), root mean square error (RMSE), mean relative error (MRE), and accuracy (AC) were used as evaluation indicators. Results showed that: (1) The OK interpolation result is spatially smooth and has a weak bull's-eye effect, and the IDW has a stronger ‘bull’s-eye’ effect, relatively. They both have obvious deficiencies in depicting spatial variability of soil K+. (2) The methods incorporating combinations of different secondary variables (e.g., ASM-SP, OK-Landuse, OK-Geology, and OK-Soil) were associated with lower estimation bias. Compared with IDW, OK, OK-Landuse, OK-Geology, and OK-Soil, the accuracy of ASM-SP increased by 13.63%, 10.85%, 9.98%, 8.32%, and 7.66%, respectively. Furthermore, ASM-SP was more stable, with lower MEs, MAEs, RMSEs, and MREs. (3) ASM-SP presents more details than others in the abrupt boundary, which can render the result consistent with the true secondary variables. In conclusion, ASM-SP can not only consider the nonlinear relationship between secondary variables and soil properties, but can also adaptively combine the advantages of multiple models, which contributes to making the spatial interpolation of soil K+ more reasonable.

Spatial variability of Soil fertility using soil chemical data, Atrush area, Duhok, Kurdistan region, Iraq

One of the basic factors in sustainable crop production is enhancing soil quality based on the soil fertility and returning absorbed nutrition by plants to the soil. In this spatial research variability of soil properties in Atrush area in Duhok province, Iraq was conducted based on the 15 soil samples with randomized method were taken from different locations. Statistical analysis by SPSS and spatial distribution and interpolation of soil properties by GS+software was done. Results showed all studied soil parameters such as pH, EC, %OM, percent of sand, silt and clay, %total N, available P and K hadanormal distribution. Strong spatial dependence related tothepercent of organic matter, sand and clay percent, percent of total nitrogen, available phosphorus and potassium while pH, EC, and percent of silt showed moderate spatial dependence. The variogram model were spherical for pH, EC, %OM, %clay and % total nitrogen while for sand percent and available P were linear and for available K and percent of silt were exponential. Spatial interpolation accuracy and precision by MAE, MBE and RMSE showed Kriging prediction maps for pH, EC, %OM, %N, and available K had most accurate predictions with the lowest error, therefore, it can provide useful information about urban planning and environmental management.

Spatial variability of soil erodibility factor using geo-statistics method in Duhok dam watershed, Kurdistan region, Iraq

Soil erosion is one of the crucial problems in watershed and environmental management. It is obvious soil and water management can reduce soil losses and land degradation. One of the important factors in universal soil loss equation (USLE) to determine rate of erosion is soil erodibility factor. It is related to intrinsic properties of the soil properties. By determining and evaluating this factor, soil erosion can be decreased to minimum amount. Traditional methods such as regression models cannot estimate precision of variables and don’t take spatial variability of soil properties. By using geo-statistical methods all changes in soil properties in distribution can be estimated with less error and high accuracy. In this research, by using 30 point of soil samples of Duhok dam watershed, the spatial variability of soil erodibility factor and some of soil properties such as percent of organic matter, particle size distribution and soil structure were obtained. Then graphical interpolation of soil properties was performed by using Kriging method. The statistical results showed that most variables had a normal distribution. Variability analysis on soil attributes according to soil erodibility, showed that exponential, spherical and linear to sill models was the most models to predict spatial variability of studied soil parameters. The Soil spatial variability pattern, is similar to silt and very fine sand pattern due to high effect of this factor on soil erodibility. According to the kriging map, soil erodibility in the east, south and north parts of the studied area is more than other parts. Soil erodibility in this location of research area based on estimation map showed need to more attention for conservation the soil and control erosion.

Ensemble Learning for Spatial Interpolation of Soil Potassium Content Based on Environmental Information

One important method to obtain the continuous surfaces of soil properties from point samples is spatial interpolation. In this paper, we propose a method that combines ensemble learning with ancillary environmental information for improved interpolation of soil properties (hereafter, EL-SP). First, we calculated the trend value for soil potassium contents at the Qinghai Lake region in China based on measured values. Then, based on soil types, geology types, land use types, and slope data, the remaining residual was simulated with the ensemble learning model. Next, the EL-SP method was applied to interpolate soil potassium contents at the study site. To evaluate the utility of the EL-SP method, we compared its performance with other interpolation methods including universal kriging, inverse distance weighting, ordinary kriging, and ordinary kriging combined geographic information. Results show that EL-SP had a lower mean absolute error and root mean square error than the data produced by the other models tested in this paper. Notably, the EL-SP maps can describe more locally detailed information and more accurate spatial patterns for soil potassium content than the other methods because of the combined use of different types of environmental information; these maps are capable of showing abrupt boundary information for soil potassium content. Furthermore, the EL-SP method not only reduces prediction errors, but it also compliments other environmental information, which makes the spatial interpolation of soil potassium content more reasonable and useful.

Development of a surface modeling method for mapping soil properties

High accuracy surface modeling (HASM) is a method which can be applied to soil property interpolation. In this paper, we present a method of HASM combined geographic information for soil property interpolation (HASM-SP) to improve the accuracy. Based on soil types, land use types and parent rocks, HASM-SP was applied to interpolate soil available P, Li, pH, alkali-hydrolyzable N, total K and Cr in a typical red soil hilly region. To evaluate the performance of HASM-SP, we compared its performance with that of ordinary kriging (OK), ordinary kriging combined geographic information (OK-Geo) and stratified kriging (SK). The results showed that the methods combined with geographic information including HASM-SP and OK-Geo obtained a lower estimation bias. HASM-SP also showed less MAEs and RMSEs when it was compared with the other three methods (OK-Geo, OK and SK). Much more details were presented in the HASM-SP maps for soil properties due to the combination of different types of geographic information which gave abrupt boundary for the spatial variation of soil properties. Therefore, HASM-SP can not only reduce prediction errors but also can be accordant with the distribution of geographic information, which make the spatial simulation of soil property more reasonable. HASM-SP has not only enriched the theory of high accuracy surface modeling of soil property, but also provided a scientific method for the application in resource management and environment planning.

An Overview of High Accuracy Surface Modeling of Soil Properties

Abstract High accuracy surface modeling (HASM) of soil properties is regarded as an important topic for the fields of pedometrics and “digital soil”. The HASM method, constructed by Yue et al., is a spatial interpolation technique based on the fundamental theorem of surfaces. In this paper, we will give an overview of high accuracy surface modeling of soil properties. Soil properties for the interpolation were measured on 150 samples of topsoil (0–20 cm) in a red soil region of Jiangxi Province, China. Predicted and measured values were compared using the mean error (ME), mean absolute error (MAE) and root mean square error (RMSE). First, HASM has more accuracy than the classical interpolator including kriging, inverse distance weighting (IDW) and splines. Second, in order to improve the calculation speed for HASM applied in soil interpolation, multigrid has been combined in HASM (HASM-MG). HASM-MG can be considered as an accurate method for interpolating soil properties on the premise of improving the calculation speed, and it advances the practicability of HASM applied in soil property interpolation. Third, modified HASM method based on the incorporation of ancillary variables was developed for improving interpolation of soil properties (HASM-SP). To evaluate the performance of HASM-SP, it was compared with ordinary kriging (OK), ordinary kriging combined geographical information (OK-Geo) and stratified kriging (SK). HASM-SP not only showed less MAEs and RMSEs, but also presented much more details due to the abrupt boundary from spatial variation of geographical information. Therefore, HASM can be considered not only as an alternative, accurate and high speed method for interpolating soil properties, but also can make the map more consistent with the true geographical information.

A coherent geostatistical approach for combining choropleth map and field data in the spatial interpolation of soil properties

Information available for mapping continuous soil attributes often includes point field data and choropleth maps (e.g. soil or geological maps) that model the spatial distribution of soil attributes as the juxtaposition of polygons (areas) with constant values. This paper presents two approaches to incorporate both point and areal data in the spatial interpolation of continuous soil attributes. In the first instance, area-to-point kriging is used to map the variability within soil units while ensuring the coherence of the prediction so that the average of disaggregated estimates is equal to the original areal datum. The resulting estimates are then used as local means in residual kriging. The second approach proceeds in one step and capitalizes on: 1) a general formulation of kriging that allows the combination of both point and areal data through the use of area-to-area, area-to-point, and point-to-point covariances in the kriging system, 2) the availability of GIS to discretize polygons of irregular shape and size, and 3) knowledge of the point-support variogram model that can be inferred directly from point measurements, thereby eliminating the need for deconvolution procedures. The two approaches are illustrated using the geological map and heavy metal concentrations recorded in the topsoil of the Swiss Jura. Sensitivity analysis indicates that the new procedures improve prediction over ordinary kriging and traditional residual kriging based on the assumption that the local mean is constant within each mapping unit.

Surface modelling of soil properties based on land use information

High accuracy surface modelling (HASM) is a spatial interpolation technique based on the fundamental theorem of surfaces. This study proposed a modified HASM method based on the incorporation of ancillary land use information (HASM_LU) for improved interpolation of soil properties. To assess its feasibility, a total of 150 samples were collected in different land use types (woodlands, croplands and grasslands) of a typical red soil region in the middle part of Jiangxi Province, China. Observations on soil pH, alkali-hydrolyzable N (AN), total C, N, K, Al, Ca, Mg and Zn were interpolated. To evaluate the performance of HASM_LU, it was compared with four other interpolators: HASM, ordinary kriging with land use information (OK_LU), stratified kriging (SK) and regression-kriging using a generalized linear model (RK_GLM). To do so, predicted and measured values were compared using the mean error (ME), mean absolute error (MAE), root mean square error (RMSE) and prediction efficiency (PE). The results have shown that HASM_LU generally performs better than HASM, OK_LU, SK and RK_GLM with a lower estimation bias, MAE and RMSE as well as greater PE. In particular, the RMSE of HASM_LU for AN was smaller than that of HASM by 33.4%; that of OK_LU, 1.6%; that of SK, 41.5%; and that of RK_GLM, 67.6%. The largest difference in PE occurred when comparing HASM_LU with HASM for N (57.95%), with OK_LU (7.18%) for K, with SK (125.16%) for Zn and with RK_GLM (100.21%) for AN. The HASM_LU maps of soil properties present more details and more accurate spatial patterns. The good performance of HASM_LU can be attributed to the adequate surface modelling ability of HASM, combined with incorporation of information on abrupt spatial boundaries introduced by land use.

Spatial Variability and Correlation of Selected Soil Properties in the Ap Horizon of a CRP Grassland

Knowledge of the spatial variability of soil properties in agricultural fields is important for implementing various precision agricultural management practices. This article examines spatial variation of selected soil physical and chemical properties and explores their spatial correlation in the Ap horizon of a Lihen sandy loam soil (sandy, mixed, frigid Entic Haplustoll) within a field of grass-alfalfa Conservation Reserve Program (CRP) land. Soil measurements were made on a 16 x 36-m grid sampling pattern. Soil properties including penetration resistance (PR), bulk density (rho b), and gravimetric water content (theta m) were measured by collecting undisturbed soil cores from 5- to 10-cm and 20- to 25-cm depths. Additional disturbed soil samples were collected for particle size distribution, electrical conductivity (EC(e)), and pH analysis. The two depths were averaged for the assessment of spatial distribution, relationships and interpolation of soil properties. Soil saturated hydraulic conductivity (K(s)) and total porosity (epsilon(T)) for the 0- to 25-cm depth were estimated from rho b , theta m , and volumetric water content at field capacity (FC) level. Soil properties were analyzed using both classical and geostatistical methods that included descriptive statistics, semivariograms, cross-semivariograms, spatial kriged and co-kriged prediction maps and interpolation. Results indicated that small to moderate spatial variability existed across the field for soil properties studied . Furthermore, cross-semivariograms exhibited a strong negative spatial interdependence between soil PR and theta m, epsilon(T), and lnK(s). Spatial variability of soil theta(m), rho b, PR, ECe, pH, and clay content and their spatial correlation in the Ap horizon of the CRP grassland were attributed to a combination of previous farming practices, topographic characteristics, vegetation history, soil erosion, and weather conditions at this site.

Surface modelling of soil pH

In addition to classical methods, namely kriging, Inverse Distance Weighting (IDW) and splines, which have been frequently used for interpolating the spatial patterns of soil properties, a relatively more accurate surface modelling technique is being developed in recent years, namely high accuracy surface modelling (HASM). It has been used in the numerical tests, DEM construction and the interpolation of climate and ecosystem changes. In this paper, HASM was applied to interpolate soil pH for assessing its feasibility of soil property interpolation in a red soil region of Jiangxi Province, China. Soil pH was measured on 150 samples of topsoil (0–20 cm) for the interpolation and comparing the performance of HASM, kriging, IDW and splines. The mean errors (MEs) of interpolations indicate little bias of interpolation for soil pH by the four techniques. HASM has less mean absolute error (MAE) and root mean square error (RMSE) than kriging, IDW and splines. HASM is still the most accurate one when we use the mean rank and the standard deviation of the ranks to avoid the outlier effects in assessing the prediction performance of the four methods. Therefore, HASM can be considered as an alternative and accurate method for interpolating soil properties. Further researches of HASM are needed to combine HASM with ancillary variables to improve the interpolation performance and develop a user-friendly algorithm that can be implemented in a GIS package.

Spatial interpolation of soil nutrients using algebra hyper-curve neural network

Spatial distribution of and interpolation methods for soil nutrients are the basis of soil nutrient management in precision agriculture. For study of application potential and characteristics of algebra hyper-curve neural network(AHCNN) in delineating spatial variability and interpolation of soil properties , 956 soil samples were taken from a 50 hectare field with 20 m interval for alkaline hydrolytic nitrogen measurement . The test data set consisted of 100 random samples extracted from the 956 samples, and the training data set extracted from the remaining samples using 20, 40, 60, 80, 100 and 120 m grid intervals. Using the AHCNN model, three training plans were designed, including plan AHC1, using spatial coordinates as the only network input, plan AHC2, adding information of four neighboring points as network input, and plan AHC3, adding information of six neighboring points as network input. The interpolation precision of AHCNN method was compared with that of Kriging method. When the number of training samples was big, interpolation precisions of Kriging and AHCNN were similar. When the number of training samples was small, the precisions of both methods deteriorated. Since AHCNN method has no request on data distribution and it is non-linearization of neutron input variables, it is suitable for delineation of spatial distribution of nonlinear soil properties. In addition, AHCNN has an advantage of adaptive self-adjustment of model parameters, which makes it proper for soil nutrient spatial interpolation. After comparison of mean absolute error d , root mean squared error RMSE, and mean relative error d %, and the spatial distribution maps generated from different methods, it can be concluded that using spatial coordinates as the only network input cannot simulate the characteristics of soil nutrient spatial variability well, and the simulation results can be improved greatly after adding neighboring sample points’ information and the distance effect as network input. When the number of samples was small, interpolation precision can be improved after properly increasing the number of neighboring sample points. It was also showed that evaluation of interpolation precision using conventional error statistic indexes was defective, and the spatial distribution map should be used as an important evaluation factor. Keywords: algebra hyper-curve neural network (AHCNN), spatial interpolation, soil nutrients, spatial variability, Kriging interpolation DOI: 10.3965/j.issn.1934-6344.2008.01.051-056 Citation: Chen Liping, Zhao Chunjiang, Huang Wenqian, Chen Tian’en, Wang Jihua, Liu Zhenyan, et al. Spatial interpolation of soil nutrients using algebra hyper-curve neural network. Int J Agric & Biol Eng. 2008; 1(1): 51

Interpolating Soil Properties Using Kriging Combined with Categorical Information of Soil Maps

Kriging interpolation is frequently used for mapping soil properties in the analysis and interpretation of spatial variation of soil. Mapping quality could affect the performance of site‐specific management. Soil map–delineation in existing soil maps showing abrupt changes at the boundaries between different soil types can provide valuable categorical information for interpreting variation in soil properties. In this study, map units were used to group sampled observations, and the variation in soil properties was separated into two parts: (i) between soil types (i.e., soil type effect) and (ii) within each soil type (i.e., residual). A kriging model combined with soil map–delineation, taking into account the variation components of soil type effect and residual, was proposed. A comparison of performance of kriging combined with soil map–delineation (KSMD) and ordinary kriging (OK) was performed to assess the feasibility of KSMD for improving the interpolation of soil properties. Real data of soil properties (sand, silt, and clay contents; pH; and Mehlich‐3 Ca and P) in a field of midwestern Taiwan were used for illustration. The analysis of variance table revealed that the contribution of soil types is a significant source of the spatial variation of soil. The spatial variation components of soil type effect and residual were thus determined for KSMD. When comparing KSMD and OK, the mean errors of KSMD and OK estimations were similar. However, decreases in estimation of imprecision for KSMD relative to OK (DIP %) for the 127 validation locations for sand, silt, and clay contents; pH; and Mehlich‐3 Ca and P were 34, 40, 48, 20, 42, and 3%, respectively. These results suggested that the proposed KSMD method could use the information of soil map–delineation to increase precision of the interpolation of soil properties.

Effects of interpolation and data resolution on methane emission estimates from rice paddies

Rice paddies are an important source of the greenhouse gas methane (CH4). Global methane emission estimates are highly uncertain and do not account for effects of interpolation or data resolution errors. This paper determines such scaling effects for the influence of soil properties on calculated CH4 emissions for the island of Java, Indonesia. The effects of different interpolation techniques, variograms and neighbor optimization were tested for soil properties by cross-validation. Interpolated organic carbon values were not significantly different from the original soil samples, in contrast to interpolated soil iron contents. Interpolation of soil properties coupled to a process-based model on CH4emissions led to a significant change in distribution of calculated CH4 emissions, i.e., the variance decreased. Effects of data resolution were examined by interpolating soil properties to derive data at different data resolutions and then calculating CH4 emissions by applying the process-based model at these resolutions. The soil properties did not differ significantly for different data resolutions, in contrast to calculated CH4 emissions. These scaling effects were caused by the combination of interpolation and a non-linear model. Real scaling effects may even be larger because small-scale variability was not accounted for. Scaling effects, including those caused by small-scale variability, have to be considered to achieve unbiased and less uncertain global CH4emissions estimates from rice paddies.

Spatial Dependence and Interpolation of Soil Properties in West Sumatra, Indonesia: II. Co‐regionalization and Co‐kriging

AbstractCo‐kriging was used to interpolate values of topsoil 0.5 M NaHCO3‐extractable P at 234 locations in West Sumatra, Indonesia, by exploiting its spatial covariance with a more densely sampled property, 25% HCl‐extractable P. NaHCO3‐P and HCl‐P had been sampled at 52 and 107 locations, respectively, in a nongeometric pattern across the 106 650 has region. Isotropic semivariograms of NaHCO3‐P and HCl‐P and their cross semivariogram showed spatial dependence over 6.3, 4.2, and 10.4 km, respectively, at the sampling scale used. The map of co‐kriged values for NaHCO3‐P showed a similar regional pattern but more local detail than that achieved by kriging from NaHCO3‐P samples alone. Co‐kriging reduced estimation variances (relative to kriging) by up to 40% in areas where sampling density of NaHCO3‐P was lowest. Co‐kriging variances exceeded those of kriging by up to 10% in areas where sampling density of NaHCO3‐P was high. In such areas, the covariate HCl‐P had little effect on the interpolated value but still added a component to the estimation variance. Co‐kriging could not be used to interpolate values for extreme locations where there were no NaHCO3‐P samples within the radius of the kriging neighborhood. Despite local improvement in estimation precision the full benefits of co‐kriging interpolation are not universally obtained from nongeometric variate‐covariate sampling patterns.