Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter
|
|
- Marsha Fay Spencer
- 6 years ago
- Views:
Transcription
1 Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter Ku Wang Department of Geographical Science, Minjiang University, , Fuzhou, China Chuanrong Zhang 1 and Weidong Li Department of Geography and Center of Environmental Sciences and Engineering, University of Connecticut, Storrs, Connecticut Abstract: Soil organic matter (SOM) is an important component of soils, and knowing the spatial distribution and variation of SOM is the premise for sustainably utilizing soils. The objective of this study was to compare geographically weighted regression (GWR) with regression kriging (RK) for estimating the spatial distribution of SOM using field-sample data in SOM and auxiliary data in correlated environmental variables (e.g., elevation, slope, ferrous minerals index, and Normalized Difference Vegetation Index). Results showed that GWR was a relatively better method and could provide promising results for SOM prediction in comparison with RK. The map interpolated by GWR showed similar spatial patterns influenced by environmental variables and the nonapparent effect of data outliers, but with higher accuracies, compared to that interpolated by RK. INTRODUCTION Soil organic matter (SOM) is one of the important components of soils. Although it accounts for only a small percentage of soil materials, its influence on many soil properties is significant. For instance, SOM has great impacts on soil structure, arability, water holding capacity, and capability of nutrient supply and conservation (Reeves, 1997; Aref and Wander, 1998). Soil organic matter is also considered a gigantic store of organic carbon (C). It is estimated that soil holds approximately three times more C than terrestrial vegetation and twice as much as the atmosphere (Eswaran et al., 1993; Davidson et al., 2000). Therefore, it is important to understand the spatial distribution and variation of SOM for purposes such as environmental protection and sustainable development of agriculture. At regional scales, the spatial distribution of SOM is not only affected by natural ecological processes but also by intensive human activities. However, due to its complex variability, it is difficult to obtain detailed SOM information for large areas. The traditional method of acquiring detailed SOM data is intensive field soil surveys 1 Corresponding author; chuanrong.zhang@uconn.edu 915 GIScience & Remote Sensing, 2012, 49, No. 6, p Copyright 2012 by Bellwether Publishing, Ltd. All rights reserved.
2 916 wang et al. followed by laboratory sample analysis, which is very time consuming and expensive. In addition, sometimes detailed survey and sampling can be difficult to carry out in some regions where access is constrained by topography and other factors. The high cost of collecting SOM data at many locations has created a strong need for effective methods of inferring continuous spatial information about SOM, such as quantitative interpolation methods. A number of prediction methods have been suggested to interpolate SOM from sparse sampling points into continuous surfaces, varying from regression methods (such as simple linear regressions, nonlinear regressions, inverse distance weighting, generalized linear models, and regression trees) to geostatistical methods (such as ordinary kriging [OK], ordinary cokriging [OCK], regression kriging [RK]) and other hybrid techniques (e.g., McKenzie, 1999; Robinson and Metternicht, 2006; Grimm et al., 2008). Among the aforementioned approaches, OK is a commonly used method to estimate the unsampled locations by calculating weighted averages of observed samples of the target variable. While OK intends to minimize the prediction error variance, this approach conducts interpolation relying solely on point samples of the target variable and does not consider auxiliary information. Thus it requires dense sample data to conduct a reasonable interpolation, and is limited by the quantity and density of samples (Pang et al., 2009). Influenced by the same spatial processes or regional conditions, the spatial distribution of SOM has great correlations with other environmental factors. To consider the coregionalization feature, OCK has been employed to improve the prediction accuracy by utilizing an auxiliary variable (Goovaerts, 1998; Li et al., 2006). By incorporating easily acquired auxiliary data, which have close relations to the target variable, OCK has been used for purposes of reducing sampling density and improving prediction accuracy. Another alternative kriging approach to incorporate auxiliary environmental variables is a hybrid interpolation approach, called RK (Odeh et al., 1995). Regression kriging first uses ordinary regression on auxiliary environmental variables to obtain the trend component and then uses simple or ordinary kriging to interpolate the residuals from the regression model. Therefore, it can incorporate a number of environmental variables in prediction. Results from previous studies proved that RK could greatly improve prediction accuracy. Regression kriging has been applied to modeling or mapping the spatial variability of soil properties in some studies in the literature (e.g., Baxter and Oliver, 2005). Comparison studies of RK and OCK (Knotters et al., 1995; Eldeiry and Garcia, 2009) showed that RK had obvious advantages over OCK: the former generated much less of a smoothing effect and also has fewer parameters to compute. The strong smoothing effect of OCK may represent a major drawback on predictions based on the data of multiple environmental variables. In addition, the difficulty in fitting a suitable linear model to the co-regionalization matrix is also a serious concern, especially when auxiliary variables are not strongly correlated with the primary variable and have different correlation ranges (Myers, 1982). Although RK is able to take auxiliary data into account, it adopts the stationary assumption. This means that parameters of RK do not change over different locations. However, many environmental variables are spatially heterogeneous, which implies that every location has an intrinsic degree of uniqueness due to its situation with respect to the rest of the study area. Thus applying a single set of global parameters may not be adequate to describe the relations between the target variable and
3 spatial distribution of soil organic matter 917 auxiliary environmental variables. Geographically weighted regression (GWR) was specifically designed to deal with issues of non-stationarity by measuring local relationships between the target variable and explanatory variables, which differ from location to location (Fotheringham et al., 2002). Unlike RK, which depends on a single set of variogram and/or regression parameters to summarize global relationships, GWR estimates local regression parameters, and its model performance varies across a study region; thus it is a local regression procedure developed to deal with the non- stationarity issue (Yu et al., 2009). Similar to RK, GWR is also able to incorporate a number of auxiliary environmental variables. Recently, GWR was extensively used to model spatial distributions and relationships in a variety of different fields, particularly to investigate spatial non-stationarity between the target variable and the explanatory variables (e.g., Tu and Xia, 2008; Kamarianakis et al., 2008; Mitchell and Yuan, 2010). However, based on our knowledge, studies using this approach to model the spatial distribution and variation of soil properties have been rare and specific comparison studies between GWR and RK have not been found. We found that Mishra et al. (2010) was the only application case study that used GWR in predicting soil properties. The objective of this study is to compare the performance of GWR with RK in estimating the spatial distribution and variation of SOM. It should be noted that this study does not intend to find a superior spatial prediction or interpolation method, but rather mainly to verify whether GWR is a suitable method for estimating the spatial distribution and variation of SOM at a regional scale. Study Area STUDY AREA AND DATA The study area is located in Longyan, Fujian Province, China ( E., N) (Fig.1), covering a total area of km 2. Elevations in this area decrease from the north, east, and west toward the south and center, with altitudes ranging from 140 m to 1120 m. It has a subtropical monsoon humid climate with abundant but seasonally uneven rainfall. The annual mean precipitation is 1600 mm but over half falls during the rainy season (April June) when storms are frequent. Drought conditions occur in autumn, as both frequency and amount of precipitation decrease significantly. The annual mean temperature is 19.1 C, the coldest temperature is 3.4 C in January, and the hottest is 35.4 C in July. The main geomorphic types are river valley alluvial plains, red-earth hills, red sandstone hills, and granite and metamorphic rock mountains. The soils in the area are dominated by Haplic Acrisols and Stagnic Anthrosols, dotted with Ferralic Cambisols. Data Sets and Data Processing Field Sample Data. Surface soil samples from the 0 to 20 cm horizon were collected at randomly selected sites in the study region during November The total number of selected sample sites was 353 (Fig. 1). Coordinates and elevations of the sample sites were recorded using a GPS (GARMIN) instrument with accuracies ranging from 3 to 15 meters. One thousand grams of mixed soil at each site was collected
4 918 wang et al. Fig. 1. The study area and sampling sites. and further prepared in the laboratory for chemical analysis. Soil organic matter was measured using the potassium dichromate volumetric method (SOM = SOC 1.724) after air drying, grinding, and sieving. To assess the prediction accuracies of RK and GWR approaches, we randomly divided the field sample data set of SOM into a validation data set with 115 samples (one-third of the total) and the calibration data set with the other 238 samples (two-thirds of the total) (Fig. 1). Environmental Data. We collected several environmental data sets, which included: a digital elevation model (DEM) (grid format, m resolution) from the Fujian Provincial Geomatics Center, China; an ETM+ remote sensing image (January 2000) downloaded from International Scientific Data Service Platform ( and a land use map (shapefile format of ESRI) from the Land and Resources Department of Fujian Province, China. The environmental indicators included elevation, slope, slope aspect, Normalized Difference Vegetation Index (NDVI), the distance from sample point to river (DIST), land use type, and ferrous mineral index (FMI). Elevation data were acquired directly from the DEM. Slope and aspect data were also calculated from the DEM using the spatial analyst module of ArcGIS. The unit of slope adopted here is degrees, and it ranges from 0 to 70. Aspect data are qualitative data representing directions, and range from 0 to 360 from the north direction. Here, a cosine function was used to transfer slope aspect into quantitative data, with values
5 spatial distribution of soil organic matter 919 ranging from 1 to 1. 2 Normalized Difference Vegetation Index data were derived from the ETM+ image using the following equation (e.g., Pavel and Kappas, 2008) NDVI = (Band4 Band3)/(Band4 + Band3). (1) Because underground water greatly influences the accumulation and decomposition of SOM (Jiang et al., 1987), it was used as a factor to analyze the variation of SOM. However, underground water data is difficult to obtain for large areas, so the distances of sample locations to a river and elevation were jointly used to describe the underground water level. In general, if a sample site is close to a river and located at a lower elevation, it can be assumed that its underground water level is shallow, and vice versa. FMI data were obtained from the ETM+ image using the ratio Band5/Band4 using ERDAS IMAGINE software. This index reflects the mineralization intensity of soil ingredients; the higher the intensity of soil mineralization, the lower SOM content (Zech et al., 1997). There are several land use types in the study area, such as forest, meadow, paddy land, dry land, garden, bare land, and village, which should have impacts on SOM. Because land use belongs to the category of qualitative data, quantitative transformation is needed for land use data to be used with other quantitative data in regression models. In this study, FRAGSTATS, a landscape analysis package, was used to calculate land use patch index. Here, the area-weighted mean shape index (AWMSI) of patches was used for quantitative transformation of land use data. It was thought that this index represented the impact of human activity on the land; the larger the value, the more complex the patches as a result of human activity (Gao and Li, 2011; Wang et al., 2009). Ordinary Kriging METHODS Ordinary kriging is based on the theory of regionalized variables, which assumes that the variables involved are random but spatially correlated at some scales (Matheron, 1971). Assume Z(x i ) is a regionalized variable, which has a variogram (autovariogram) γ(h), a function describing the spatial dependence of a spatially random field or stochastic process z(u). The variogram can be estimated by h = Nh zu 2N h i zu i + h 2 i = 1 (2) where h is the spatial lag between two locations; N(h) is the number of observed data pairs with the lag h; and z(u i ) and z(u i + h) are two measured values at locations u i and u i + h, respectively. To describe the experimental variogram for use in kriging, a mathematical model has to be fitted to the experimental variogram. Ordinary kriging is an optimal technique that provides unbiased estimates with minimum and known errors. In this study, the traditional OK was used in RK and it is expressed as 2 The value of cosine aspect of slope (COSA) indicates the degree of northerliness (Lian et al., 2006).
6 920 wang et al. n z x 0 = i x 0 zx i i = 1 n with a constraint i x 0 = 1. Here, z*(x 0 ) is the estimated value of the variable z i = 1 at location x 0 ; z(x i ) is the measured data; λ i (x 0 ) refers to the weights associated with the measured values, which are estimated by the stationary OK system; and n is the number of measured values within a neighborhood. Regression Kriging In the case of RK, the soil property at an unsampled location x 0 is estimated by summing the predicted drift and residual z x 0 = mˆ x 0 + ê x 0, (4) (3) where mˆ is the drift, which is usually fitted with a linear regression, and ê is the residual, which is estimated using OK. RK can be expressed as p n zx, (5) 0 = ˆ k q k x 0 + i x 0 ex i q 0 x 0 = 1 k = 0 i = 1 where ˆ k represents the k-th estimated coefficient of the drift model, q k (x 0 ) is the k-th external explanatory variable or predictor at location x 0, p is the number of predictors, λ i (x 0 ) are weights determined by the covariance function of the residuals, and e(x i ) is the regression residual at location x i. The first part of the right hand side of Equation (5) represents the linear regression and the second part represents kriging of the residuals. Apparently, RK combines both the regression of the target variable (SOM) based on the environmental factors (such as NDVI, elevation, etc.), which are used as explanatory co-variables, and the kriging of the regression residuals (Odeh et al., 1995). Regression kriging is based on the idea that the deterministic component of the dependent variable can be explained by regression and the residuals are assumed to describe the spatially varying but self-dependent components (Sun et al., 2012). We interpolated the spatial distribution of SOM by RK using five steps: (1) determine the LnSOM (i.e., Ln-transformed SOM) drift model using multiple linear regression (MLR); (2) derive the LnSOM drift model residuals at the sample locations; (3) model the covariance structure of the LnSOM drift model residuals using a variogram model; (4) interpolate the LnSOM drift model residuals using ordinary kriging; (5) add the LnSOM drift model surface to the interpolated residuals at each prediction point. Geographically Weighted Regression Geographically weighted regression is an extension of the traditional regression in which variations in rates of change are allowed in order that regression coefficients
7 spatial distribution of soil organic matter 921 are specific to a location rather than being global estimates (Brunsdon et al., 1998; Fotheringham et al., 1998). Suppose there are series of explanatory variables {x ij } and dependent variables {y i }, i = 1, 2,, m, j = 1, 2,, n, a conventional linear regression fitted by the ordinary least squares (OLS) method is expressed as n y i = 0 + j x ij + i, (6) j = 1 where y i is the value of the dependent variable y at location i, β 0 is the intercept, β j is the coefficient for independent predictor variable x j. ε i represents the error term, which is generally assumed to be independent and normally distributed with zero means and constant variance σ 2. In this model, each of the parameters can be thought of as the parameter between one of the independent variables and the dependent variable. This type of regression is known as global because of the assumption of spatial stationarity of its parameter estimates, which means that a single model is fitted to all of the sample data and is applied equally to the entire study area of interest. The regression model and its coefficients are constant across the study area, assuming the relationships between the dependent and independent variables to be spatially constant. However, variations or spatial non-stationarity in relationships between the dependent and independent variables over space commonly exist in spatial data sets and the assumption of stationarity or structural stability over space may be unrealistic (Fotheringham et al., 1998). So, when analyzing spatial data, we should take into account spatial non-stationarity. The local regression approach, known as GWR, recognizes explicitly that the parameter estimates in a regression model can vary across the space in which the regression model is calibrated. Geographically weighted regression allows the parameter estimates to be a function of location. The local estimation of the parameters with GWR is expressed by the following equation y i = n 0 u i, v i + j u i, v i x ij + i, (7) j = 1 where (u i, v i ) is the spatial location of the i-th observation and β j (u i, v i ) is the value of the j-th parameter at location i. The regression parameters of this equation are estimated at each location i(u i, v i ). Therefore, this GWR model can measure spatial variations in relationships. The parameters in the GWR model can be calibrated using the weighted least squares approach. In matrix form, the parameters of the GWR model at each location i are estimated by ˆ u i, v i = X T W u i, v i X 1 X T W u i, v i Y, (8) where W(u i, v i ) is an (m m) spatial weighting diagonal matrix with m being the number of observed data for regression point i, X is an [m (n +1)] independent data matrix with n being the number of explanatory variables, and Y is an (m 1) dependent data vector.
8 922 wang et al. To estimate parameters in the GWR model, it is important to decide the spatial weighting matrix, which can be calculated by different methods. One method is to specify W(u i, v i ) as a continuous and monotonic decreasing function of distance d ij between point i and point j. For adaptive kernel size, the weight of each point can be calculated by applying the Gaussian function d ij w ij =, h w ij = 0, if d ij h if d ij h, (9) where w ij is the weight of location j in the space at which data are observed for estimating the dependent variable at location i, and h is referred as a bandwidth. This function is a distance decay function, in which the weights of farther distant points from an unsampled location i decrease and the weights will practically fall to zero for those observations that are sufficiently distant from location i to be estimated (beyond the bandwidth). In this study, the adaptive method was employed to calculate kernels of GWR. The selection of the weighting function and optimal bandwidth h was accomplished by minimizing the corrected Akaike Information Criterion (AIC) as described in Fotheringham et al. (2002). The Akaike Information Criterion and varied bandwidths were calibrated to process the regression models. In the processing of the GWR regression models, weights and bandwidths decreased in the densely sampled places and increased in the sparsely sampled places (Jaimes et al., 2010). Evaluation The prediction accuracy of different approaches was evaluated by comparing the validation data (i.e., remaining observed data), which were not used for interpolation, with the predicted data. Mean error (ME) and root mean square error (RMSE) were used to verify prediction accuracy. Mean error is expressed as n 1 ME = -- zx, (10) n i, y i + z x i, y i i = 1 where n is the number of SOM observations in the validation dataset, z(x i,y i ) and z*(x i,y i ) are values of the observed and the predicted SOM, respectively; and x i and y i are the location coordinates. Root mean square error is expressed as RMSE = n 1 -- zx. (11) n i, y i z x i, y i 2 i = 1 Exploratory Data Analysis RESULTS Regression and geostatistical analysis perform best on normally distributed data. When non-normality is apparent, transformations of the data to make them
9 spatial distribution of soil organic matter 923 Table 1. Summary Statistics of SOM Sample Data and Ln-Transformed Data N Min. Max. Mean Median STD Skew STDE of skew Kurt. STDE of kurt. SOM (g/kg) LnSOM a N = number of samples; Min. = minimum; Max. = maximum; STD = standard deviation; skew = skewness; kurt. = kurtosis; STDE = standard error; LnSOM = Ln-transformed soil organic matter. approximately normal should be helpful. Table 1 provides a statistical summary of the entire SOM data set of 353 observations. The observed SOM varies from 7.25 to 52.3 g/kg, which means there are great variations of SOM in the study area. The value of skewness is and that of kurtosis is 0.674, indicating that the SOM data are approximately normally distributed. However, the Kolmogorov-Smirnov (K-S) test produced a significant coefficient (p-value = 0.04 < 0.05), which indicates that the data set may need a normal transformation. Here, the p-value is the probability of obtaining a result at least as extreme as the one that was actually observed, given that the null hypothesis (here, the null hypothesis is that the data accord with a normal distribution) is true. If the p-value is less than the required significance level, the null hypothesis is rejected. On the contrary, if the p-value is not less than the required significance level, the evidence is insufficient to reject the normality of data. In K-S test, 0.05 and 0.01 are the two frequently used significance levels, representing, respectively, the significant and very significant levels. In this study, we used a logarithmic function to perform the data transformation. We confirmed a final normal data distribution through the result of the K-S test (p-value = > 0.05). The Ln-transformed data values vary from 1.98 to A Pearson correlation analysis (Barnes et al., 2005) was performed to check the relationships between the Ln-transformed SOM and the environmental factors, including ELEVATION, SLOPE, COSA, NDVI, DIST, AWMSI, and FMI. Correlation coefficients among these variables are listed in Table 2. The results of the correlation analysis indicate that SOM has significant correlations with almost all of the environmental variables except for COSA. Positive correlations exist with ELEVATION, NDVI, SLOPE, DIST, and AWMSI, and a negative correlation occurs with FMI. However, there are also significant correlations among the environmental variables themselves, such as ELEVATION with NDVI, slope, FMI, and AWMSI; and DIST with ELEVATION, NDVI, and FMI. To reduce the multicollinearity problem, a stepwise linear regression was performed for dropping closely related predictor variables. Table 3 shows the results of the stepwise linear regressions using all variables. Based on the results, we chose the linear regression model e, which considers five environmental variables of ELEVATION, FMI, DIST, SLOPE, and NDVI, to be our final multiple linear regression (MLR) model. This model explains 60 percent of the variance in SOM (adjusted R 2 = 0.600) and has a significant F-test result (p-value = < 0.05). The MLR model is expressed as
10 924 wang et al. Table 2. Pearson Correlation Matrix Between SOM and Environmental Variables a LnSOM NDVI DIST ELEVA- TION SLOPE COSA FMI AWMSI LnSOM 1.517**.180**.728**.333** **.226** NDVI 1.198**.512**.343** **.208** DIST 1.363**.187** ** ELEVA- TION 1.538** **.333** SLOPE **.137* COSA FMI 1.219** AWMSI 1 a LnSOM = Ln-transformed soil organic matter; NDVI = Normalized Difference Vegetation Index; DIST = the nearest distance from sample locations to river; COSA = cosine value of aspect of slope; FMI = ferrous minerals index; AWMSI = area-weighted mean shape index calculated from the land use patches. * = correlation is significant at the 0.05 level (2-tailed); ** = correlation is significant at the 0.01 level (2-tailed). The 2-tailed test is a statistical test used in inference, in which a given statistical hypothesis, H 0 (the null hypothesis: there is no relationship between variables here), will be rejected when the value of the test statistic is either sufficiently small or sufficiently large. The test is named after the tail of data under the far left and far right of a bell-shaped normal data distribution, or bell curve. The numbers 0.05 and 0.01 represent significant and very significant levels, respectively. LnSOM = elevation 0.453FMI 0.008slope NDVI (13) Note that based on the results of the stepwise regressions, the regression coefficient of DIST is zero. SOM Interpolated by RK and GWR Table 4 lists the fitted parameters of the variogram models for the Ln-transformed SOM and its residuals. Parameters of the variogram models include the following information: (1) nugget (C 0 ), standing for the level of random variation within the data; (2) sill (C 0 + C), representing the total magnitude of spatial variability; (3) range, describing the spatial dependence of the variability; (4) ratio C/(C 0 + C), reflecting the proportion of spatially structured variance (C) in the total spatial variability (C 0 + C); the larger the value, the higher the spatial structure dependence in SOM data (Cambardella et al., 1994); (5) R 2, indicating how well the model fits the experimental variogram data although it is not as sensitive or robust as the Residual Sums of Squares (RSS) value for best-fit calculations; (6) RSS, showing an exact measure of how well the model fits the experimental variogram data; the lower the RSS value, the better the model fits. LnSOM and its residuals show a clear spatial dependence (Table 4). Both variogram models have approximately the same form and nugget but the residual variogram
11 spatial distribution of soil organic matter 925 Table 3. Results of the Stepwise Linear Regression Analysis Using Seven Independent Variables Models a R 2 Adjusted R 2 Std. error of the estimate Change statistics R 2 change F change Sig. F change a b c d e a. Predictors: (Constant), ELEVATION. b. Predictors: (Constant), ELEVATION, FMI. c. Predictors: (Constant), ELEVATION, FMI, SLOPE. d. Predictors: (Constant), ELEVATION, FMI, SLOPE, DIST. e. Predictors: (Constant), ELEVATION, FMI, SLOPE, DIST, NDVI. Dependent Variable: LnSOM (i.e., Ln-transformed SOM). Table 4. Parameters of the Omni-directional Exponential Semivariogram Models for the Ln-transformed SOM and its Residuals Variogram model C 0 (nugget) C 0 +C (sill) C/C 0 +C Range (m) R 2 RSS LnSOM Exponential , e-04 Residuals Exponential , e-05 model has a somewhat smaller sill and range (Fig. 2), which is often found in practice (Hengl et al., 2004). We interpolated the spatial distribution of SOM using GWR with a variable bandwidth (spatially adaptive kernel) that adapts for the density of sample data at each regression location. The optimal kernel size for our study was determined through an interactive statistical optimization process to minimize the AIC. In addition to providing estimates of regression coefficients, t-statistics, and goodness-of-fit for each location, the ArcGIS software also provides several statistical tests to determine whether the GWR model is more useful than the MLR model. The results of the statistical tests show that the AIC value for the GWR (1103.8) is far lower than that for MLR (2233.9). This indicates that the local model provides a better fit to the sample data even after accounting for differences in degrees of freedom. The adjusted R 2 generated by the GWR (0.9262) is much higher than that by MLR (0.5688). This means that GWR has a large improvement in explained variance. Figure 3 shows the spatial distributions of SOM interpolated using RK and GWR. It can be seen that the prediction maps generated by both methods show a similar spatial pattern or trend: high values of SOM usually are concentrated in high mountains where little human disturbance occurs while lower values of SOM mostly occur in dry land, paddy land, or other land at low elevation where soil is frequently disturbed by human activities. In addition, the minimum and maximum values predicted by both
12 926 wang et al. Fig. 2. Variograms of LnSOM (left graph) and its residuals (right graph) fitted using exponential models. Fig. 3. Maps of SOM predicted by RK (left) and GWR (right). RK and GWR are beyond the minimum and maximum values of the observed sample data (Fig. 3). This indicates that both predicted maps reflect changes in elevation, slope, and other environmental factors, and generate much detailed spatial information about the distribution of SOM. An apparent difference is that the SOM map generated by RK shows more variations in the flat area of the floodplain than that generated by GWR. This should be related to the fact that RK incorporates the autocorrelation of sample data residuals whereas the GWR method used here did not consider autocorrelation, because the environmental variables (i.e., ELEVATION, FMI, SLOPE, and NDVI) should not change much in such a flat area. This further means RK is more sensitive to the spatial variation of SOM sample data (particularly outliers) than GWR is. Another difference is that the predicted SOM values on the low hills in the southern region are apparently higher, with clearer detail in the GWR map than in the RK map.
13 spatial distribution of soil organic matter 927 Table 5. Comparison of the Performances of RK and GWR using ME, RMSE, maximum ( and +) Errors of Predictions and Their Coefficients of Regression (adjusted R 2 ) with Validation Data Maximum ( ) error (g/kg) Maximum (+) error (g/kg) ME (g/kg) RMSE (g/kg) Adjusted R 2 RK GWR This means GWR is more sensitive to the spatial variation of environmental variables than RK is. Comparison of the General Prediction Accuracies of RK and GWR To further assess the performances of RK and GWR, the 115 validation points were used for the purpose of testing the prediction accuracies of the two methods. Table 5 shows the comparison results. If the prediction is unbiased, the ME and RMSE will be expected to be zero. Thus, for an accurate prediction model, their absolute values should be as small as possible. It can be seen from Table 5 that the maximum errors generated by RK are much larger in terms of their absolute values than those generated by GWR. Both ME and RMSE produced by GWR have smaller absolute values than those generated by RK. These statistical values indicate that the prediction accuracy of GWR is higher than that of RK. Note that the negative ME value for RK illustrates that the method underestimated SOM in space. A similar conclusion can also be drawn from the error distribution at validation sampling sites (Fig. 4), which clearly shows that at some locations large errors were produced by the RK method. In addition, the adjusted R 2 values between the observed SOM data and the predicted data at the validation sites also indicate that the GWR performed better (adjusted R 2 = 0.909) than did RK (adjusted R 2 = 0.699). DISCUSSION It was noticed in this study that RK and GWR produced some estimated values beyond the value range of the observed data. For example, the predicted maximum value is g/kg for RK and g/kg for GWR; both values are far larger than the observed maximum value of 52.3 g/kg. This issue may come from the process of back transformation of the estimated Ln-transformed data (Cho et al., 2009). When the observed data were transformed by a logarithmic function for fitting to a normal distribution, the back transformation may generate extreme values. To verify this fact, we also tested the prediction results using non-transformed original data for both RK and GWR. The results indicate that the maximum estimated values, 63.4 g/kg by RK and 63.8 g/kg by GWR, are close to the maximum observed value. As a best linear predictor, OK has its own characteristics: it considers the autocorrelation of sample data, the predicted value is identical to the observed value if the predicted point occurs at a sampling site, and the interpolation accuracy is higher near
14 928 wang et al. Fig. 4. Errors of predictions by RK and GWR at the 115 validation sample sites. the sampling point than farther away from the sampling point. While RK uses ordinary linear regressions to estimate the trend component, it partially inherits the characteristics of OK, which is used for estimating the residuals at unsampled locations. On this point, GWR is different because it is based on local regression and usually does not consider the autocorrelation of sample data; thus the values predicted by GWR are not always the same as the observed values on the sampling sites. GWR prediction mainly depends on the regression coefficients established by its neighboring SOM data and environmental factors. Because of this the map interpolated by GWR is more continuous in transition and less affected by sample values, particularly extreme values (i.e., outliers), than that created by RK, and it also inherits more closely the spatial variation characteristics of the incorporated environmental factors. The spatial kernel function and the bandwidth used in the model fitting process have an impact on the estimation of the GWR coefficients. The bandwidth is the radius of the search circle around each point being estimated and controls the distance decay in the weighting function (Guo et al., 2008). Changing the spatial kernel function or the bandwidth may change the coefficient estimates. Therefore, in this study we used an adaptive kernel function to reduce the limited data problem in some areas and we selected the optimal bandwidth by minimizing the AIC (Koutsias et al., 2010). From this aspect, the number of samples is not an absolutely crucial factor in this study. As long as there are enough observation points, which can represent most of the explanatory variables in space, they may meet the needs of the regressions. It is expected that land use may have a good relationship with SOM (e.g., Lettens et al., 2004), but the factor was removed in this study in the process of the stepwise regression. We used AWMSI as an indicator for land use. However, this case study did not show AWMSI to be a good index reflecting the impacts of land use on the spatial distribution of SOM. Other indices may be tested in future research to determine whether they more properly represent the impact of land use. In addition, most of the sampling points in this study are located in cultivated lands (especially in paddy soils), and the samples located in forest lands account for only a small percentage. The asymmetrical distribution of the sampling points may lead to a decrease in the correlation coefficients between SOM and environmental variables, and has a further impact on
15 spatial distribution of soil organic matter 929 prediction accuracy. Hence, more samples in complex environments or better sampling designs are needed in order to improve the estimation accuracy of GWR. CONCLUSIONS The spatial distribution maps of SOM interpolated by RK and GWR and the validation analysis show that there are some differences among the predicted results by the different methods. The interpolation maps using GWR and RK both capture many details. However, the map interpolated by GWR shows higher global accuracy, and also appears to be more realistic in depicting the details of the SOM patterns impacted by environmental factors in nature. In general, GWR is more sensitive to the spatial variation of environmental variables, whereas RK is more sensitive to the spatial variation of SOM sample data, particularly outliers. Although RK, by integrating the merits of OK and MLR, takes both spatial autocorrelation and auxiliary environmental variables into consideration, its model is still constructed on the basis of the spatial stationary assumption. Thus it does not deal with non-stationary spatial relationships of variables within the study area. The GWR approach, however, overcomes the limitation to some extent by using non-stationary regression models, which have different parameters at different locations. This may be one important reason why GWR produced the more realistic results of SOM with higher global accuracy in this study. In summary, the following conclusions may be made from this study: (1) Similar to the often-used RK in soil science, GWR is able to incorporate a variety of multiple auxiliary environmental factors into its modeling process. (2) The performance of GWR for estimating the spatial distribution and variation of SOM in the study area is good, and even better than that of RK in terms of prediction accuracy and realistic patterns. This result agrees with Mishra et al. (2010). Based on these considerations, we think RK and GWR each may have their respective applicable fields. Regression kriging may be more suitable for spatial predictions in relatively uniform environments, especially those suitable for gathering strongly autocorrelated data via regular grid sampling. Conversely, GWR is more effective in spatial predictions involving complex environments and spatially varied correlation relationships between a dependent variable and multiple explanatory variables. In addition, compared to RK, GWR may have higher requirements for the density of sample data for effectively estimating local parameters. ACKNOWLEDGMENTS We thank the reviewers very much for constructive comments that proved useful in revision of the manuscript. We gratefully acknowledge support for this research from the National Natural Science Foundation of China (No ), Natural Science Foundation of Fujian Province, China (Grant No. 2012J01179), and Science and Technological Project of the Educational Commission of Fujian Province, China (Grant No. JA11202). REFERENCES Aref, S., and M. M. Wander, 1998, Long-Term Trends of Corn Yield and Soil Organic Matter in Different Crop Sequences and Soil Fertility Treatments on the Morrow Plot, Advances in Agronomy, 62:
16 930 wang et al. Barnes, C. W., Kinkel, L. L., and J. V. Groth, 2005, Spatial and Temporal Dynamics of Puccinia andropogonis on Comandra umbellata and Andropogon gerardii in a Native Prairie, Canadian Journal of Botany, 83: Baxter, S. and M. Oliver, 2005, The Spatial Prediction of Soil Mineral N and Potentially Available N Using Elevation, Geoderma, 128: Brunsdon, C., Fotheringham, S., and M. Charlton, 1998, Spatial Nonstationarity and Autoregressive Models, Environment and Planning A, 30: Cambardella, C. A., Moorman, T. B., Novak, J. M., Parkin, T. B., Karlen, D. L., Turco, R. F., and A. E. Konopka, 1994, Fieldscale Variability of Soil Properties in Central Iowa Soils, Soil Science Society of America Journal, 58: Cho, S., Lambert, D. M., Kim, S. G., and S. Jung, 2009, Extreme Coefficients in Geographically Weighted Regression and Their Effects on Mapping, GIScience & Remote Sensing, 46(3): Davidson, E. A., Trumbore, S., and R. Amundson, 2000, Biogeochemistry: Soil Warming and Organic Carbon Content, Nature, 408: Eldeiry, A. and L. A. Garcia, 2009, Comparison of Regression Kriging and Cokriging Techniques to Estimate Soil Salinity Using Landsat Images, paper presented at The 29th Annual Hydrology Days, Fort Collins, CO, March 25 27, Eswaran, H., Berg, E. V. D., and P. Reich, 1993, Organic Carbon in Soil of the World, Soil Science Society of America Journal, 57: Fotheringham, A. S., Brunsdon, C. A., and M. E. Charlton, 2002, Geographically Weighted Regression: The Analysis of Spatially Varying Relationships, New York, NY: John Wiley & Sons. Fotheringham, A. S., Charlton, M. E., and C. Brundson, 1998, Geographically Weighted Regression: A Natural Evolution of the Expansion Method for Spatial Data, Environment and Planning A, 30: Gao, J. B. and S. C. Li, 2011, Detecting Spatially Non-stationary and Scale-Dependent Relationships between Urban Landscape Fragmentation and Related Factors Using Geographically Weighted Regression, Applied Geography, 31: Goovaerts, P., 1998, Ordinary Cokriging Revisited, Mathematical Geology, 30: Grimm, R., Behrens, T., Märker, M., and H. Elsenbeer, 2008, Soil Organic Carbon Concentrations and Stocks on Barro Colorado Island Digital Soil Mapping Using Random Forests Analysis, Geoderma, 146: Guo, L., Ma, Z., and L. Zhang, 2008, Comparison of Bandwidth Selection in Application of Geographically Weighted Regression: a Case Study, Canadian Journal of Forest Research, 38: Hengl, T., Heuvelink, G., and A. Stein, 2004, A Generic Framework for Spatial Prediction of Soil Variables Based on Regression Kriging, Geoderma, 122(1 2): Jaimes, N. B. P., Sendra, J. B., Delgado, M. G., and R. F. Plata, 2010, Exploring the Driving Forces Behind Deforestation in the State of Mexico (Mexico) Using Geographically Weighted Regression, Applied Geography, 30: Jiang, J. R., Zhong, S. L., Yuan, Z. P., Xiao, R. L., and Y. Z. Zhang, 1987, Effect of Different Cropping System and Underwater Level on Content of Soil Organic Matter and Ferric Oxide in Paddy Soil, Journal of Hunan Agricultural University (Natural Sciences), 3:25 30.
17 spatial distribution of soil organic matter 931 Kamarianakis, Y., Feidas, H., Kokolatos, G., Chrysoulakis, N., and V. Karatzias, 2008, Evaluating Remotely Sensed Rainfall Estimates Using Nonlinear Mixed Models and Geographically Weighted Regression, Environmental Modelling & Software, 23: Knotters, M., Brus, D. J., and J. H. Oude Voshaar, 1995, A Comparison of Kriging, Cokriging and Kriging Combined with Regression for Spatial Interpolation of Horizon Depth with Censored Observations, Geoderma, 67: Koutsias, N., Martínez-Fernández, J., and B. Allgöwer, 2010, Do Factors Causing Wildfires Vary in Space? Evidence from Geographically Weighted Regression, GIScience & Remote Sensing, 47(2): Lettens, S., van Orshoven, J., van Wesemael, B., and B. Muys, 2004, Soil Organic and Inorganic Carbon Contents of Landscape Units in Belgium Derived Using Data from 1950 to 1970, Soil Use and Management, 20: Li, Z., Zhang, Y. K., Schilling, K., and M. Skopec, 2006, Cokriging Estimation of Daily Suspended Sediment Loads, Journal of Hydrology, 327: Lian, G., Guo, X. D., Fu, B. J., and C. X. Hu, 2006, Spatial Variability and Prediction of Soil Organic Matter at County Scale on the Loess Plateau, Progress in Geography, 25: (in Chinese). Matheron, G., 1971, The Theory of Regionalized Variables and its Applications, Fontainebleu, France: CMMF, Les Cahiers du center de Morphologie Mathematique de Fontainebleau 5. McKenzie, N. J., 1999, Spatial Prediction of Soil Properties Using Environmental Correlation, Geoderma, 89: Mishra, U., Lal, R., Liu, D., and M. van Meirvenne, Predicting the Spatial Variation of the Soil Organic Carbon Pool at a Regional Scale, Soil Science Society of America Journal, 74: Mitchell, M. and F. Yuan, 2010, Assessing Forest Fire and Vegetation Recovery in the Black Hills, South Dakota, GIScience & Remote Sensing, 47(2): Myers, D. E., 1982, Matrix Formulation of Co-Kriging, Mathematical Geology, 14: Odeh, I. O. A., McBratney, A. B., and D. J. Chittleborough, 1995, Further Results on Prediction of Soil Properties from Terrain Attributes: Heterotopic Cokriging and Regression-Kriging, Geoderma, 67: Pang, S., Li, T. X., Wang, Y. D., and H. Y. Yu, 2009, Spatial Interpolation and Sample Size Optimization for Soil Copper (Cu) Investigation in Cropland Soil at County Scale Using Cokriging, Agricultural Sciences in China, 8: Pavel, A. P. and M. Kappas, 2008, Reducing Uncertainty in Modeling the NDVI- Precipitation Relationship: A Comparative Study Using Global and Local Regression Techniques, GIScience & Remote Sensing, 45(1): Reeves, D. W., 1997, The Role of Soil Organic Matter in Maintaining Soil Quality in Continuous Cropping Systems, Soil Tillage Research, 43: Robinson, T. P. and G. Metternicht, 2006, Testing the Performance of Spatial Interpolation Techniquesfor Mapping Soil Properties, Computers and Electronics in Agriculture, 50: Sun, W., Minasny, B., and A. McBratney, 2012, Analysis and Prediction of Soil Properties Using Local Regression-Kriging, Geoderma, :16 23.
18 932 wang et al. Tu, J., and Z. G. Xia, 2008, Examining Spatially Varying Relationships Between Land Use and Water Quality Using Geographically Weighted Regression I: Model Design and Evaluation, The Science of the Total Environment, 407: Wang, K., Wang, H. J., Shi, X. Z., Weindorf, D. C., Yu, D. S., Liang, Y., and D. M. Shi, 2009, Landscape Analysis of Dynamic Soil Erosion in Subtropical China: A Case Study in Xingguo County, Jiangxi Province, Soil and Tillage Research, 105: Yu, D., Peterson, N. A., and R. J. Reid, 2009, Exploring the Impact of Non-normality on Spatial Non-stationarity in Geographically Weighted Regression Analyses: Tobacco Outlet Density in New Jersey, GIScience & Remote Sensing, 46(3): Zech, W., Senesi, N., Guggenberger, G., Kaiser, K., Lehmann, J., Miano, T. M., Miltner, A., and G. Schroth, 1997, Factors Controlling Humification and Mineralization of Soil Organic Matter in the Tropics, Geoderma, 79:
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
More informationASPECTS REGARDING THE USEFULNESS OF GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) FOR DIGITAL MAPPING OF SOIL PARAMETERS
Lucrări Ştiinţifice vol. 52, seria Agronomie ASPECTS REGARDING THE USEFULNESS OF GEOGRAPHICALLY WEIGHTED REGRESSION (GWR) FOR DIGITAL MAPPING OF SOIL PARAMETERS C. PATRICHE 1, I. VASILINIUC 2 1 Romanian
More informationPRODUCING PROBABILITY MAPS TO ASSESS RISK OF EXCEEDING CRITICAL THRESHOLD VALUE OF SOIL EC USING GEOSTATISTICAL APPROACH
PRODUCING PROBABILITY MAPS TO ASSESS RISK OF EXCEEDING CRITICAL THRESHOLD VALUE OF SOIL EC USING GEOSTATISTICAL APPROACH SURESH TRIPATHI Geostatistical Society of India Assumptions and Geostatistical Variogram
More informationFuzhou, Fujian , China b Department of Geography and Center for Environmental
This article was downloaded by: [University of Connecticut] On: 09 June 2014, At: 08:40 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office:
More informationEffect of Land Use Types on the Spatial Prediction of Soil Nitrogen
Effect of Land Use Types on the Spatial Prediction of Soil Nitrogen Mingkai Qu Department of Resource and Environmental Information, College of Resources and Environment, Huazhong Agricultural University,
More informationA GEOSTATISTICAL APPROACH TO PREDICTING A PHYSICAL VARIABLE THROUGH A CONTINUOUS SURFACE
Katherine E. Williams University of Denver GEOG3010 Geogrpahic Information Analysis April 28, 2011 A GEOSTATISTICAL APPROACH TO PREDICTING A PHYSICAL VARIABLE THROUGH A CONTINUOUS SURFACE Overview Data
More informationModeling Spatial Variation in Stand Volume of Acacia mangium Plantations Using Geographically Weighted Regression
FORMATH Vol. 9 (2010): 103 122 103 Modeling Spatial Variation in Stand Volume of Acacia mangium Plantations Using Geographically Weighted Regression Tiryana, T., Tatsuhara, S. & Shiraishi, N. Keywords:
More informationCombining Regressive and Auto-Regressive Models for Spatial-Temporal Prediction
Combining Regressive and Auto-Regressive Models for Spatial-Temporal Prediction Dragoljub Pokrajac DPOKRAJA@EECS.WSU.EDU Zoran Obradovic ZORAN@EECS.WSU.EDU School of Electrical Engineering and Computer
More informationSatellite and gauge rainfall merging using geographically weighted regression
132 Remote Sensing and GIS for Hydrology and Water Resources (IAHS Publ. 368, 2015) (Proceedings RSHS14 and ICGRHWE14, Guangzhou, China, August 2014). Satellite and gauge rainfall merging using geographically
More informationInterpolation and 3D Visualization of Geodata
Marek KULCZYCKI and Marcin LIGAS, Poland Key words: interpolation, kriging, real estate market analysis, property price index ABSRAC Data derived from property markets have spatial character, no doubt
More informationModeling Spatial Pattern of Precipitation with GIS and Multivariate Geostatistical Methods in Chongqing Tobacco Planting Region, China
Modeling Spatial Pattern of Precipitation with GIS and Multivariate Geostatistical Methods in Chongqing Tobacco Planting Region, China Xuan Wang,2, Jiake Lv,2,*, Chaofu Wei 2, and Deti Xie 2 College of
More informationInvestigation of Monthly Pan Evaporation in Turkey with Geostatistical Technique
Investigation of Monthly Pan Evaporation in Turkey with Geostatistical Technique Hatice Çitakoğlu 1, Murat Çobaner 1, Tefaruk Haktanir 1, 1 Department of Civil Engineering, Erciyes University, Kayseri,
More informationPedometric Techniques in Spatialisation of Soil Properties for Agricultural Land Evaluation
Bulletin UASVM Agriculture, 67(1)/2010 Print ISSN 1843-5246; Electronic ISSN 1843-5386 Pedometric Techniques in Spatialisation of Soil Properties for Agricultural Land Evaluation Iuliana Cornelia TANASĂ
More informationGeostatistics: Kriging
Geostatistics: Kriging 8.10.2015 Konetekniikka 1, Otakaari 4, 150 10-12 Rangsima Sunila, D.Sc. Background What is Geostatitics Concepts Variogram: experimental, theoretical Anisotropy, Isotropy Lag, Sill,
More informationExploratory Spatial Data Analysis (ESDA)
Exploratory Spatial Data Analysis (ESDA) VANGHR s method of ESDA follows a typical geospatial framework of selecting variables, exploring spatial patterns, and regression analysis. The primary software
More informationIndex. Geostatistics for Environmental Scientists, 2nd Edition R. Webster and M. A. Oliver 2007 John Wiley & Sons, Ltd. ISBN:
Index Akaike information criterion (AIC) 105, 290 analysis of variance 35, 44, 127 132 angular transformation 22 anisotropy 59, 99 affine or geometric 59, 100 101 anisotropy ratio 101 exploring and displaying
More informationGLOBAL SYMPOSIUM ON SOIL ORGANIC CARBON, Rome, Italy, March 2017
GLOBAL SYMPOSIUM ON SOIL ORGANIC CARBON, Rome, Italy, 2-23 March 207 Spatial Distribution of Organic Matter Content in Plough Layer of Balikh Flood Plain Soils Northeastern of Syria Hussam H. M. Husein
More informationSpatial Data Mining. Regression and Classification Techniques
Spatial Data Mining Regression and Classification Techniques 1 Spatial Regression and Classisfication Discrete class labels (left) vs. continues quantities (right) measured at locations (2D for geographic
More informationTransiogram: A spatial relationship measure for categorical data
International Journal of Geographical Information Science Vol. 20, No. 6, July 2006, 693 699 Technical Note Transiogram: A spatial relationship measure for categorical data WEIDONG LI* Department of Geography,
More informationGeog 210C Spring 2011 Lab 6. Geostatistics in ArcMap
Geog 210C Spring 2011 Lab 6. Geostatistics in ArcMap Overview In this lab you will think critically about the functionality of spatial interpolation, improve your kriging skills, and learn how to use several
More informationKriging method for estimation of groundwater resources in a basin with scarce monitoring data
36 New Approaches to Hydrological Prediction in Data-sparse Regions (Proc. of Symposium HS. at the Joint IAHS & IAH Convention, Hyderabad, India, September 9). IAHS Publ. 333, 9. Kriging method for estimation
More informationSoil Moisture Modeling using Geostatistical Techniques at the O Neal Ecological Reserve, Idaho
Final Report: Forecasting Rangeland Condition with GIS in Southeastern Idaho Soil Moisture Modeling using Geostatistical Techniques at the O Neal Ecological Reserve, Idaho Jacob T. Tibbitts, Idaho State
More informationSPATIAL-TEMPORAL TECHNIQUES FOR PREDICTION AND COMPRESSION OF SOIL FERTILITY DATA
SPATIAL-TEMPORAL TECHNIQUES FOR PREDICTION AND COMPRESSION OF SOIL FERTILITY DATA D. Pokrajac Center for Information Science and Technology Temple University Philadelphia, Pennsylvania A. Lazarevic Computer
More informationABSTRACT INTRODUCTION. J. Soil Sci. Soc. Sri Lanka, Vol. 23, 2011
J. Soil Sci. Soc. Sri Lanka, Vol. 23, 2011 ORIGINAL PAPER ACCEPTED FOR PUBLICATION IN JOURNAL OF SOIL SCIENCE SOCIETY OF SRI LANKA SPATIAL VARIABILITY OF SOIL TEXTURE, ORGANIC CARBON AND CATION EXCHANGE
More informationGridding of precipitation and air temperature observations in Belgium. Michel Journée Royal Meteorological Institute of Belgium (RMI)
Gridding of precipitation and air temperature observations in Belgium Michel Journée Royal Meteorological Institute of Belgium (RMI) Gridding of meteorological data A variety of hydrologic, ecological,
More informationGeographically weighted regression approach for origin-destination flows
Geographically weighted regression approach for origin-destination flows Kazuki Tamesue 1 and Morito Tsutsumi 2 1 Graduate School of Information and Engineering, University of Tsukuba 1-1-1 Tennodai, Tsukuba,
More informationSection 2.2 RAINFALL DATABASE S.D. Lynch and R.E. Schulze
Section 2.2 RAINFALL DATABASE S.D. Lynch and R.E. Schulze Background to the Rainfall Database The rainfall database described in this Section derives from a WRC project the final report of which was titled
More informationSpatial Downscaling of TRMM Precipitation Using DEM. and NDVI in the Yarlung Zangbo River Basin
Spatial Downscaling of TRMM Precipitation Using DEM and NDVI in the Yarlung Zangbo River Basin Yang Lu 1,2, Mingyong Cai 1,2, Qiuwen Zhou 1,2, Shengtian Yang 1,2 1 State Key Laboratory of Remote Sensing
More informationImplementation of CLIMAP and GIS for Mapping the Climatic Dataset of Northern Iraq
Implementation of CLIMAP and GIS for Mapping the Climatic Dataset of Northern Iraq Sabah Hussein Ali University of Mosul/Remote sensing Center KEYWORDS: CLIMAP, GIS, DEM, Climatic, IRAQ ABSTRACT The main
More informationVALIDATION OF SPATIAL INTERPOLATION TECHNIQUES IN GIS
VALIDATION OF SPATIAL INTERPOLATION TECHNIQUES IN GIS V.P.I.S. Wijeratne and L.Manawadu University of Colombo (UOC), Kumarathunga Munidasa Mawatha, Colombo 03, wijeratnesandamali@yahoo.com and lasan@geo.cmb.ac.lk
More informationChanges in Texas Ecoregions
Comment On Lesson Changes in Texas Ecoregions The state of Texas can be divided into 10 distinct areas based on unique combinations of vegetation, topography, landforms, wildlife, soil, rock, climate,
More informationTime: the late arrival at the Geocomputation party and the need for considered approaches to spatio- temporal analyses
Time: the late arrival at the Geocomputation party and the need for considered approaches to spatio- temporal analyses Alexis Comber 1, Paul Harris* 2, Narumasa Tsutsumida 3 1 School of Geography, University
More information11/8/2018. Spatial Interpolation & Geostatistics. Kriging Step 1
(Z i Z j ) 2 / 2 (Z i Zj) 2 / 2 Semivariance y 11/8/2018 Spatial Interpolation & Geostatistics Kriging Step 1 Describe spatial variation with Semivariogram Lag Distance between pairs of points Lag Mean
More informationTypes of Spatial Data
Spatial Data Types of Spatial Data Point pattern Point referenced geostatistical Block referenced Raster / lattice / grid Vector / polygon Point Pattern Data Interested in the location of points, not their
More informationAdvances in Locally Varying Anisotropy With MDS
Paper 102, CCG Annual Report 11, 2009 ( 2009) Advances in Locally Varying Anisotropy With MDS J.B. Boisvert and C. V. Deutsch Often, geology displays non-linear features such as veins, channels or folds/faults
More informationCREATION OF DEM BY KRIGING METHOD AND EVALUATION OF THE RESULTS
CREATION OF DEM BY KRIGING METHOD AND EVALUATION OF THE RESULTS JANA SVOBODOVÁ, PAVEL TUČEK* Jana Svobodová, Pavel Tuček: Creation of DEM by kriging method and evaluation of the results. Geomorphologia
More informationA Geostatistical Approach to Predict the Average Annual Rainfall of Bangladesh
Journal of Data Science 14(2016), 149-166 A Geostatistical Approach to Predict the Average Annual Rainfall of Bangladesh Mohammad Samsul Alam 1 and Syed Shahadat Hossain 1 1 Institute of Statistical Research
More informationSimulating the spatial distribution of clay layer occurrence depth in alluvial soils with a Markov chain geostatistical approach
ENVIRONMETRICS Environmetrics 2010; 21: 21 32 Published online 27 March 2009 in Wiley InterScience (www.interscience.wiley.com).981 Simulating the spatial distribution of clay layer occurrence depth in
More informationThe Study of Soil Fertility Spatial Variation Feature Based on GIS and Data Mining *
The Study of Soil Fertility Spatial Variation Feature Based on GIS and Data Mining * Chunan Li, Guifen Chen **, Guangwei Zeng, and Jiao Ye College of Information and Technology, Jilin Agricultural University,
More informationA Preliminary Analysis of the Relationship between Precipitation Variation Trends and Altitude in China
ATMOSPHERIC AND OCEANIC SCIENCE LETTERS, 2011, VOL. 4, NO. 1, 41 46 A Preliminary Analysis of the Relationship between Precipitation Variation Trends and Altitude in China YANG Qing 1, 2, MA Zhu-Guo 1,
More informationAssessment of Three Spatial Interpolation Models to Obtain the Best One for Cumulative Rainfall Estimation (Case study: Ramsar District)
Assessment of Three Spatial Interpolation Models to Obtain the Best One for Cumulative Rainfall Estimation (Case study: Ramsar District) Hasan Zabihi, Anuar Ahmad, Mohamad Nor Said Department of Geoinformation,
More informationMapping the Spatial Variability of Soil Acidity in Zambia
Agronomy 2014, 4, 452-461; doi:10.3390/agronomy4040452 Article OPEN ACCESS agronomy ISSN 2073-4395 www.mdpi.com/journal/agronomy Mapping the Spatial Variability of Soil Acidity in Zambia Lydia M. Chabala
More informationENGRG Introduction to GIS
ENGRG 59910 Introduction to GIS Michael Piasecki October 13, 2017 Lecture 06: Spatial Analysis Outline Today Concepts What is spatial interpolation Why is necessary Sample of interpolation (size and pattern)
More informationSpatial Interpolation & Geostatistics
(Z i Z j ) 2 / 2 Spatial Interpolation & Geostatistics Lag Lag Mean Distance between pairs of points 1 y Kriging Step 1 Describe spatial variation with Semivariogram (Z i Z j ) 2 / 2 Point cloud Map 3
More informationGEOSPATIAL ANALYSIS OF ATMOSPHERIC HAZE EFFECT BY SOURCE AND SINK LANDSCAPE
GEOSPATIAL ANALYSIS OF ATMOSPHERIC HAZE EFFECT BY SOURCE AND SINK LANDSCAPE Tiantian YU a, Kai XU a, Zhaoxiang YUAN b a. Faculty of Information Engineering, China University of Geosciences (Wuhan), Wuhan
More information4th HR-HU and 15th HU geomathematical congress Geomathematics as Geoscience Reliability enhancement of groundwater estimations
Reliability enhancement of groundwater estimations Zoltán Zsolt Fehér 1,2, János Rakonczai 1, 1 Institute of Geoscience, University of Szeged, H-6722 Szeged, Hungary, 2 e-mail: zzfeher@geo.u-szeged.hu
More informationSpatial Backfitting of Roller Measurement Values from a Florida Test Bed
Spatial Backfitting of Roller Measurement Values from a Florida Test Bed Daniel K. Heersink 1, Reinhard Furrer 1, and Mike A. Mooney 2 1 Institute of Mathematics, University of Zurich, CH-8057 Zurich 2
More informationPrecipitation processes in the Middle East
Precipitation processes in the Middle East J. Evans a, R. Smith a and R.Oglesby b a Dept. Geology & Geophysics, Yale University, Connecticut, USA. b Global Hydrology and Climate Center, NASA, Alabama,
More informationIt s a Model. Quantifying uncertainty in elevation models using kriging
It s a Model Quantifying uncertainty in elevation models using kriging By Konstantin Krivoruchko and Kevin Butler, Esri Raster based digital elevation models (DEM) are the basis of some of the most important
More informationUsing Spatial Statistics Social Service Applications Public Safety and Public Health
Using Spatial Statistics Social Service Applications Public Safety and Public Health Lauren Rosenshein 1 Regression analysis Regression analysis allows you to model, examine, and explore spatial relationships,
More informationROeS Seminar, November
IASC Introduction: Spatial Interpolation Estimation at a certain location Geostatistische Modelle für Fließgewässer e.g. Air pollutant concentrations were measured at different locations. What is the concentration
More informationSPATIO-TEMPORAL ANALYSIS OF PRECIPITATION AND TEMPERATURE DISTRIBUTION OVER TURKEY
SPATIO-TEMPORAL ANALYSIS OF PRECIPITATION AND TEMPERATURE DISTRIBUTION OVER TURKEY P. A. Bostan a, Z. Akyürek b a METU, Geodetic and Geographic Inf. Tech. Natural and App. Sciences, 06531 Ankara, Turkey
More informationRelationships between Soil salinity and geopedological units in Saveh plain, Iran
Available online at www.scholarsresearchlibrary.com Annals of Biological Research, 2012, 3 (5):2292-2296 (http://scholarsresearchlibrary.com/archive.html) ISSN 0976-1233 CODEN (USA): ABRNBW Relationships
More informationSpatial Analysis 1. Introduction
Spatial Analysis 1 Introduction Geo-referenced Data (not any data) x, y coordinates (e.g., lat., long.) ------------------------------------------------------ - Table of Data: Obs. # x y Variables -------------------------------------
More informationGeostatistical analysis of surface soil texture from Zala county in western Hungary
Geostatistical analysis of surface soil texture from Zala county in western Hungary K. Adhikari *,**, A. Guadagnini **, G. Toth * and T. Hermann *** * Land Management and Natural Hazards Unit, Institute
More informationSpatiotemporal Analysis of Environmental Radiation in Korea
WM 0 Conference, February 25 - March, 200, Tucson, AZ Spatiotemporal Analysis of Environmental Radiation in Korea J.Y. Kim, B.C. Lee FNC Technology Co., Ltd. Main Bldg. 56, Seoul National University Research
More informationStochastic Hydrology. a) Data Mining for Evolution of Association Rules for Droughts and Floods in India using Climate Inputs
Stochastic Hydrology a) Data Mining for Evolution of Association Rules for Droughts and Floods in India using Climate Inputs An accurate prediction of extreme rainfall events can significantly aid in policy
More informationSupporting Information for: Effects of payments for ecosystem services on wildlife habitat recovery
Supporting Information for: Effects of payments for ecosystem services on wildlife habitat recovery Appendix S1. Spatiotemporal dynamics of panda habitat To estimate panda habitat suitability across the
More informationRef.: Spring SOS3003 Applied data analysis for social science Lecture note
SOS3003 Applied data analysis for social science Lecture note 05-2010 Erling Berge Department of sociology and political science NTNU Spring 2010 Erling Berge 2010 1 Literature Regression criticism I Hamilton
More informationUSING GIS CARTOGRAPHIC MODELING TO ANALYSIS SPATIAL DISTRIBUTION OF LANDSLIDE SENSITIVE AREAS IN YANGMINGSHAN NATIONAL PARK, TAIWAN
CO-145 USING GIS CARTOGRAPHIC MODELING TO ANALYSIS SPATIAL DISTRIBUTION OF LANDSLIDE SENSITIVE AREAS IN YANGMINGSHAN NATIONAL PARK, TAIWAN DING Y.C. Chinese Culture University., TAIPEI, TAIWAN, PROVINCE
More informationSpatial analysis of annual rainfall using ordinary kriging techniques and lognormal kriging in the Cheliff watershed. Algeria.
15 th International Conference on Environmental Science and Technology Rhodes, Greece, 31 August to 2 September 2017 Spatial analysis of annual rainfall using ordinary kriging techniques and lognormal
More informationGlossary. The ISI glossary of statistical terms provides definitions in a number of different languages:
Glossary The ISI glossary of statistical terms provides definitions in a number of different languages: http://isi.cbs.nl/glossary/index.htm Adjusted r 2 Adjusted R squared measures the proportion of the
More informationGIS
sanaein@gmail.com Astaraei @ferdowsi.um.ac.ir mghaemi @gmail.com negarsiabi @gmail.com. GIS ok ( D-K) RK CO-k RS GIS lesch Corwin Isaaks Srivastava Hengl Laslettet Webster Burgess Goovaerts kriging cokriging.
More informationAdvanced analysis and modelling tools for spatial environmental data. Case study: indoor radon data in Switzerland
EnviroInfo 2004 (Geneva) Sh@ring EnviroInfo 2004 Advanced analysis and modelling tools for spatial environmental data. Case study: indoor radon data in Switzerland Mikhail Kanevski 1, Michel Maignan 1
More informationPropagation of Errors in Spatial Analysis
Stephen F. Austin State University SFA ScholarWorks Faculty Presentations Spatial Science 2001 Propagation of Errors in Spatial Analysis Peter P. Siska I-Kuai Hung Arthur Temple College of Forestry and
More informationOn dealing with spatially correlated residuals in remote sensing and GIS
On dealing with spatially correlated residuals in remote sensing and GIS Nicholas A. S. Hamm 1, Peter M. Atkinson and Edward J. Milton 3 School of Geography University of Southampton Southampton SO17 3AT
More informationGEOSTATISTICS. Dr. Spyros Fountas
GEOSTATISTICS Dr. Spyros Fountas Northing (m) 140550 140450 140350 Trent field Disturbed area Andover 140250 Panholes 436950 437050 437150 437250 437350 Easting (m) Trent Field Westover Farm (Blackmore,
More informationHamid Mohebzadeh. Department of Water Engineering, Faculty of Agriculture, Bu-Ali Sina University, Hamedan, Iran
American-Eurasian J. Agric. & Environ. Sci., 8 (): 64-76, 08 ISSN 88-6769 IDOSI Publications, 08 DOI: 0.589/idosi.aejaes.08.64.76 Comparison of Methods for Fitting the Theoretical Variogram to the Experimental
More information1Department of Demography and Organization Studies, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX
Well, it depends on where you're born: A practical application of geographically weighted regression to the study of infant mortality in the U.S. P. Johnelle Sparks and Corey S. Sparks 1 Introduction Infant
More informationInfluence of parameter estimation uncertainty in Kriging: Part 2 Test and case study applications
Hydrology and Earth System Influence Sciences, of 5(), parameter 5 3 estimation (1) uncertainty EGS in Kriging: Part Test and case study applications Influence of parameter estimation uncertainty in Kriging:
More informationChapter-1 Introduction
Modeling of rainfall variability and drought assessment in Sabarmati basin, Gujarat, India Chapter-1 Introduction 1.1 General Many researchers had studied variability of rainfall at spatial as well as
More informationInterpolating Raster Surfaces
Interpolating Raster Surfaces You can use interpolation to model the surface of a feature or a phenomenon all you need are sample points, an interpolation method, and an understanding of the feature or
More informationUsing object oriented technique to extract jujube based on landsat8 OLI image in Jialuhe Basin
Journal of Image Processing Theory and Applications (2016) 1: 16-20 Clausius Scientific Press, Canada Using object oriented technique to extract jujube based on landsat8 OLI image in Jialuhe Basin Guotao
More informationPrediction of Soil Properties Using Fuzzy Membership
Prediction of Soil Properties Using Fuzzy Membership Zhu, A.X. 1,2 ; Moore, A. 3 ; Burt, J. E. 2 1 State Key Lab of Resources and Environmental Information System, Institute of Geographical Sciences and
More informationGeoDa-GWR Results: GeoDa-GWR Output (portion only): Program began at 4/8/2016 4:40:38 PM
New Mexico Health Insurance Coverage, 2009-2013 Exploratory, Ordinary Least Squares, and Geographically Weighted Regression Using GeoDa-GWR, R, and QGIS Larry Spear 4/13/2016 (Draft) A dataset consisting
More informationPreliminary Research on Grassland Fineclassification
IOP Conference Series: Earth and Environmental Science OPEN ACCESS Preliminary Research on Grassland Fineclassification Based on MODIS To cite this article: Z W Hu et al 2014 IOP Conf. Ser.: Earth Environ.
More informationSpatial Variation in Infant Mortality with Geographically Weighted Poisson Regression (GWPR) Approach
Spatial Variation in Infant Mortality with Geographically Weighted Poisson Regression (GWPR) Approach Kristina Pestaria Sinaga, Manuntun Hutahaean 2, Petrus Gea 3 1, 2, 3 University of Sumatera Utara,
More informationSPATIAL VARIABILITY MAPPING OF N-VALUE OF SOILS OF MUMBAI CITY USING ARCGIS
SPATIAL VARIABILITY MAPPING OF N-VALUE OF SOILS OF MUMBAI CITY USING ARCGIS RESHMA RASKAR - PHULE 1, KSHITIJA NADGOUDA 2 1 Assistant Professor, Department of Civil Engineering, Sardar Patel College of
More informationESTIMATION OF LANDFORM CLASSIFICATION BASED ON LAND USE AND ITS CHANGE - Use of Object-based Classification and Altitude Data -
ESTIMATION OF LANDFORM CLASSIFICATION BASED ON LAND USE AND ITS CHANGE - Use of Object-based Classification and Altitude Data - Shoichi NAKAI 1 and Jaegyu BAE 2 1 Professor, Chiba University, Chiba, Japan.
More informationCopyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Chapter 15. SPATIAL INTERPOLATION 15.1 Elements of Spatial Interpolation 15.1.1 Control Points 15.1.2 Type of Spatial Interpolation 15.2 Global Methods 15.2.1 Trend Surface Models Box 15.1 A Worked Example
More informationGeographically Weighted Regression as a Statistical Model
Geographically Weighted Regression as a Statistical Model Chris Brunsdon Stewart Fotheringham Martin Charlton October 6, 2000 Spatial Analysis Research Group Department of Geography University of Newcastle-upon-Tyne
More informationANALYSIS OF VEGETATION DISTRIBUTION IN URBAN AREAS: SPATIAL ANALYSIS APPROACH ON A REGIONAL SCALE
ANALYSIS OF VEGETATION DISTRIBUTION IN URBAN AREAS: SPATIAL ANALYSIS APPROACH ON A REGIONAL SCALE Kiichiro Kumagai Department of Civil and Environmental System Engineering, Setsunan University 17-8 Ikedanakamachi,
More information7 Geostatistics. Figure 7.1 Focus of geostatistics
7 Geostatistics 7.1 Introduction Geostatistics is the part of statistics that is concerned with geo-referenced data, i.e. data that are linked to spatial coordinates. To describe the spatial variation
More informationSpati-temporal Changes of NDVI and Their Relations with Precipitation and Temperature in Yangtze River Catchment from 1992 to 2001
Spati-temporal Changes of NDVI and Their Relations with Precipitation and Temperature in Yangtze River Catchment from 1992 to 2001 ZHANG Li 1, CHEN Xiao-Ling 1, 2 1State Key Laboratory of Information Engineering
More informationBasics in Geostatistics 2 Geostatistical interpolation/estimation: Kriging methods. Hans Wackernagel. MINES ParisTech.
Basics in Geostatistics 2 Geostatistical interpolation/estimation: Kriging methods Hans Wackernagel MINES ParisTech NERSC April 2013 http://hans.wackernagel.free.fr Basic concepts Geostatistics Hans Wackernagel
More informationSPATIAL VARIABILITY OF AVAILABLE NUTRIENTS AND SOIL CARBON UNDER ARABLE CROPPING IN CANTERBURY
SPATIAL VARIABILITY OF AVAILABLE NUTRIENTS AND SOIL CARBON UNDER ARABLE CROPPING IN CANTERBURY Weiwen Qiu, Denis Curtin and Mike Beare The New Zealand Institute for Plant & Food Research Limited, Private
More informationEvaluating sustainable transportation offers through housing price: a comparative analysis of Nantes urban and periurban/rural areas (France)
Evaluating sustainable transportation offers through housing price: a comparative analysis of Nantes urban and periurban/rural areas (France) Julie Bulteau, UVSQ-CEARC-OVSQ Thierry Feuillet, Université
More informationSpatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China
Environ Geol (28) 53:1139 1147 DOI 1.17/s254-7-91-8 ORIGINAL ARTICLE Spatial variability of soil organic matter and nutrients in paddy fields at various scales in southeast China Xingmei Liu Æ Keli Zhao
More informationIntroduction. Semivariogram Cloud
Introduction Data: set of n attribute measurements {z(s i ), i = 1,, n}, available at n sample locations {s i, i = 1,, n} Objectives: Slide 1 quantify spatial auto-correlation, or attribute dissimilarity
More informationSupplementary material: Methodological annex
1 Supplementary material: Methodological annex Correcting the spatial representation bias: the grid sample approach Our land-use time series used non-ideal data sources, which differed in spatial and thematic
More informationGeography Class XI Fundamentals of Physical Geography Section A Total Periods : 140 Total Marks : 70. Periods Topic Subject Matter Geographical Skills
Geography Class XI Fundamentals of Physical Geography Section A Total Periods : 140 Total Marks : 70 Sr. No. 01 Periods Topic Subject Matter Geographical Skills Nature and Scope Definition, nature, i)
More informationA STUDY OF MEAN AREAL PRECIPITATION AND SPATIAL STRUCTURE OF RAINFALL DISTRIBUTION IN THE TSEN-WEN RIVER BASIN
Journal of the Chinese Institute of Engineers, Vol. 24, No. 5, pp. 649-658 (2001) 649 A STUDY OF MEAN AREAL PRECIPITATION AND SPATIAL STRUCTURE OF RAINFALL DISTRIBUTION IN THE TSEN-WEN RIVER BASIN Jet-Chau
More informationModeling of Atmospheric Effects on InSAR Measurements With the Method of Stochastic Simulation
Modeling of Atmospheric Effects on InSAR Measurements With the Method of Stochastic Simulation Z. W. LI, X. L. DING Department of Land Surveying and Geo-Informatics, Hong Kong Polytechnic University, Hung
More informationAnother Look at Non-Euclidean Variography
Another Look at Non-Euclidean Variography G. Dubois European Commission DG Joint Research Centre Institute for Environment and Sustainability, Ispra, Italy. Email: gregoire.dubois@jrc.it ABSTRACT: Tobler
More informationMAPPING LAND USE/ LAND COVER OF WEST GODAVARI DISTRICT USING NDVI TECHNIQUES AND GIS Anusha. B 1, Sridhar. P 2
MAPPING LAND USE/ LAND COVER OF WEST GODAVARI DISTRICT USING NDVI TECHNIQUES AND GIS Anusha. B 1, Sridhar. P 2 1 M. Tech. Student, Department of Geoinformatics, SVECW, Bhimavaram, A.P, India 2 Assistant
More informationARIMA modeling to forecast area and production of rice in West Bengal
Journal of Crop and Weed, 9(2):26-31(2013) ARIMA modeling to forecast area and production of rice in West Bengal R. BISWAS AND B. BHATTACHARYYA Department of Agricultural Statistics Bidhan Chandra Krishi
More informationLecture 5 Geostatistics
Lecture 5 Geostatistics Lecture Outline Spatial Estimation Spatial Interpolation Spatial Prediction Sampling Spatial Interpolation Methods Spatial Prediction Methods Interpolating Raster Surfaces with
More informationEarth s Major Terrerstrial Biomes. *Wetlands (found all over Earth)
Biomes Biome: the major types of terrestrial ecosystems determined primarily by climate 2 main factors: Depends on ; proximity to ocean; and air and ocean circulation patterns Similar traits of plants
More informationModeling Spatial Pattern of Precipitation with GIS and Multivariate Geostatistical Methods in Chongqing Tobacco Planting Region, China
Modeling Spatial Pattern of Precipitation with GIS and Multivariate Geostatistical Methods in Chongqing Tobacco Planting Region, China Xuan Wang, Jiake Lv, Chaofu Wei, Deti Xie To cite this version: Xuan
More informationEffect of land cover / use change on soil erosion assessment in Dubračina catchment (Croatia)
European Water 57: 171-177, 2017. 2017 E.W. Publications Effect of land cover / use change on soil erosion assessment in Dubračina catchment (Croatia) N. Dragičević *, B. Karleuša and N. Ožanić Faculty
More information