2.
Hengl, Tomislav; Heuvelink, Gerard B. M.; Rossiter, David G.
About regression-kriging: From equations to case studies Journal Article
In: Computers & Geosciences, vol. 33, no. 10, pp. 1301-1315, 2007, ISSN: 0098-3004, (Spatial Analysis).
Abstract | Links | BibTeX | Tags: Environmental predictors, GSTAT, MODIS, Multiple regression, Spatial prediction, SRTM
@article{HENGL20071301,
title = {About regression-kriging: From equations to case studies},
author = {Tomislav Hengl and Gerard B. M. Heuvelink and David G. Rossiter},
url = {https://www.sciencedirect.com/science/article/pii/S0098300407001008},
doi = {https://doi.org/10.1016/j.cageo.2007.05.001},
issn = {0098-3004},
year = {2007},
date = {2007-01-01},
journal = {Computers & Geosciences},
volume = {33},
number = {10},
pages = {1301-1315},
abstract = {This paper discusses the characteristics of regression-kriging (RK), its strengths and limitations, and illustrates these with a simple example and three case studies. RK is a spatial interpolation technique that combines a regression of the dependent variable on auxiliary variables (such as land surface parameters, remote sensing imagery and thematic maps) with simple kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called “Universal Kriging†(UK) and “Kriging with External Drift†(KED), where auxiliary predictors are used directly to solve the kriging weights. The advantage of RK is the ability to extend the method to a broader range of regression techniques and to allow separate interpretation of the two interpolated components. Data processing and interpretation of results are illustrated with three case studies covering the national territory of Croatia. The case studies use land surface parameters derived from combined Shuttle Radar Topography Mission and contour-based digital elevation models and multitemporal-enhanced vegetation indices derived from the MODIS imagery as auxiliary predictors. These are used to improve mapping of two continuous variables (soil organic matter content and mean annual land surface temperature) and one binary variable (presence of yew). In the case of mapping temperature, a physical model is used to estimate values of temperature at unvisited locations and RK is then used to calibrate the model with ground observations. The discussion addresses pragmatic issues: implementation of RK in existing software packages, comparison of RK with alternative interpolation techniques, and practical limitations to using RK. The most serious constraint to wider use of RK is that the analyst must carry out various steps in different software environments, both statistical and GIS.},
note = {Spatial Analysis},
keywords = {Environmental predictors, GSTAT, MODIS, Multiple regression, Spatial prediction, SRTM},
pubstate = {published},
tppubtype = {article}
}
This paper discusses the characteristics of regression-kriging (RK), its strengths and limitations, and illustrates these with a simple example and three case studies. RK is a spatial interpolation technique that combines a regression of the dependent variable on auxiliary variables (such as land surface parameters, remote sensing imagery and thematic maps) with simple kriging of the regression residuals. It is mathematically equivalent to the interpolation method variously called “Universal Kriging†(UK) and “Kriging with External Drift†(KED), where auxiliary predictors are used directly to solve the kriging weights. The advantage of RK is the ability to extend the method to a broader range of regression techniques and to allow separate interpretation of the two interpolated components. Data processing and interpretation of results are illustrated with three case studies covering the national territory of Croatia. The case studies use land surface parameters derived from combined Shuttle Radar Topography Mission and contour-based digital elevation models and multitemporal-enhanced vegetation indices derived from the MODIS imagery as auxiliary predictors. These are used to improve mapping of two continuous variables (soil organic matter content and mean annual land surface temperature) and one binary variable (presence of yew). In the case of mapping temperature, a physical model is used to estimate values of temperature at unvisited locations and RK is then used to calibrate the model with ground observations. The discussion addresses pragmatic issues: implementation of RK in existing software packages, comparison of RK with alternative interpolation techniques, and practical limitations to using RK. The most serious constraint to wider use of RK is that the analyst must carry out various steps in different software environments, both statistical and GIS.
1.
Hengl, Tomislav; Heuvelink, Gerard B. M.; Stein, Alfred
A generic framework for spatial prediction of soil variables based on regression-kriging Journal Article
In: Geoderma, vol. 120, no. 1, pp. 75-93, 2004, ISSN: 0016-7061.
Abstract | Links | BibTeX | Tags: Environmental correlation, Factor analysis, Logit transformation, Spatial prediction, Visualisation
@article{HENGL200475,
title = {A generic framework for spatial prediction of soil variables based on regression-kriging},
author = {Tomislav Hengl and Gerard B. M. Heuvelink and Alfred Stein},
url = {https://www.sciencedirect.com/science/article/pii/S0016706103002787},
doi = {https://doi.org/10.1016/j.geoderma.2003.08.018},
issn = {0016-7061},
year = {2004},
date = {2004-01-01},
journal = {Geoderma},
volume = {120},
number = {1},
pages = {75-93},
abstract = {A methodological framework for spatial prediction based on regression-kriging is described and compared with ordinary kriging and plain regression. The data are first transformed using logit transformation for target variables and factor analysis for continuous predictors (auxiliary maps). The target variables are then fitted using step-wise regression and residuals interpolated using kriging. A generic visualisation method is used to simultaneously display predictions and associated uncertainty. The framework was tested using 135 profile observations from the national survey in Croatia, divided into interpolation (100) and validation sets (35). Three target variables: organic matter, pH in topsoil and topsoil thickness were predicted from six relief parameters and nine soil mapping units. Prediction efficiency was evaluated using the mean error and root mean square error (RMSE) of prediction at validation points. The results show that the proposed framework improves efficiency of predictions. Moreover, it ensured normality of residuals and enforced prediction values to be within the physical range of a variable. For organic matter, it achieved lower relative RMSE than ordinary kriging (53.3% versus 66.5%). For topsoil thickness, it achieved a lower relative RMSE (66.5% versus 83.3%) and a lower bias than ordinary kriging (0.15 versus 0.69 cm). The prediction of pH in topsoil was difficult with all three methods. This framework can adopt both continuous and categorical soil variables in a semi-automated or automated manner. It opens a possibility to develop a bundle algorithm that can be implemented in a GIS to interpolate soil profile data from existing datasets.},
keywords = {Environmental correlation, Factor analysis, Logit transformation, Spatial prediction, Visualisation},
pubstate = {published},
tppubtype = {article}
}
A methodological framework for spatial prediction based on regression-kriging is described and compared with ordinary kriging and plain regression. The data are first transformed using logit transformation for target variables and factor analysis for continuous predictors (auxiliary maps). The target variables are then fitted using step-wise regression and residuals interpolated using kriging. A generic visualisation method is used to simultaneously display predictions and associated uncertainty. The framework was tested using 135 profile observations from the national survey in Croatia, divided into interpolation (100) and validation sets (35). Three target variables: organic matter, pH in topsoil and topsoil thickness were predicted from six relief parameters and nine soil mapping units. Prediction efficiency was evaluated using the mean error and root mean square error (RMSE) of prediction at validation points. The results show that the proposed framework improves efficiency of predictions. Moreover, it ensured normality of residuals and enforced prediction values to be within the physical range of a variable. For organic matter, it achieved lower relative RMSE than ordinary kriging (53.3% versus 66.5%). For topsoil thickness, it achieved a lower relative RMSE (66.5% versus 83.3%) and a lower bias than ordinary kriging (0.15 versus 0.69 cm). The prediction of pH in topsoil was difficult with all three methods. This framework can adopt both continuous and categorical soil variables in a semi-automated or automated manner. It opens a possibility to develop a bundle algorithm that can be implemented in a GIS to interpolate soil profile data from existing datasets.
