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; Toomanian, Norair; Reuter, Hannes I.; Malakouti, Mohammad J.
Methods to interpolate soil categorical variables from profile observations: Lessons from Iran Journal Article
In: Geoderma, vol. 140, no. 4, pp. 417-427, 2007, ISSN: 0016-7061, (Pedometrics 2005).
Abstract | Links | BibTeX | Tags: Categorical variables, Fuzzy -means, MODIS, Multinominal logistic regression, Regression-kriging, Terrain parameters
@article{HENGL2007417,
title = {Methods to interpolate soil categorical variables from profile observations: Lessons from Iran},
author = {Tomislav Hengl and Norair Toomanian and Hannes I. Reuter and Mohammad J. Malakouti},
url = {https://www.sciencedirect.com/science/article/pii/S0016706107001218},
doi = {https://doi.org/10.1016/j.geoderma.2007.04.022},
issn = {0016-7061},
year = {2007},
date = {2007-01-01},
journal = {Geoderma},
volume = {140},
number = {4},
pages = {417-427},
abstract = {The paper compares semi-automated interpolation methods to produce soil-class maps from profile observations and by using multiple auxiliary predictors such as terrain parameters, remote sensing indices and similar. The Soil Profile Database of Iran, consisting of 4250 profiles, was used to test different soil-class interpolators. The target variables were soil texture classes and World Reference Base soil groups. The predictors were 6 terrain parameters, 11 MODIS EVI images and 17 physiographic regions (polygon map) of Iran. Four techniques were considered: (a) supervised classification using maximum likelihoods; (b) multinominal logistic regression; (c) regression-kriging on memberships; and (d) classification of taxonomic distances. The predictive capabilities were assessed using a control subset of 30% profiles and the kappa statistics as criterion. Supervised classification and multinominal logistic regression can lead to poor results if soil-classes overlap in the feature space, or if the correlation between the soil-classes and predictors is low. The two other methods have better predictive capabilities, although both are computationally more demanding. For both mapping of texture classes and soil types, the best prediction was achieved using regression-kriging of indicators/memberships (κ=45%, κ=54%). In all cases kappa was smaller than 60%, which can be explained by the preferential sampling plan, the poor definition of soil-classes and the high variability of soils. Steps to improve interpolation of soil-class data, by taking into account the fuzziness of classes directly on the field are further discussed.},
note = {Pedometrics 2005},
keywords = {Categorical variables, Fuzzy -means, MODIS, Multinominal logistic regression, Regression-kriging, Terrain parameters},
pubstate = {published},
tppubtype = {article}
}
The paper compares semi-automated interpolation methods to produce soil-class maps from profile observations and by using multiple auxiliary predictors such as terrain parameters, remote sensing indices and similar. The Soil Profile Database of Iran, consisting of 4250 profiles, was used to test different soil-class interpolators. The target variables were soil texture classes and World Reference Base soil groups. The predictors were 6 terrain parameters, 11 MODIS EVI images and 17 physiographic regions (polygon map) of Iran. Four techniques were considered: (a) supervised classification using maximum likelihoods; (b) multinominal logistic regression; (c) regression-kriging on memberships; and (d) classification of taxonomic distances. The predictive capabilities were assessed using a control subset of 30% profiles and the kappa statistics as criterion. Supervised classification and multinominal logistic regression can lead to poor results if soil-classes overlap in the feature space, or if the correlation between the soil-classes and predictors is low. The two other methods have better predictive capabilities, although both are computationally more demanding. For both mapping of texture classes and soil types, the best prediction was achieved using regression-kriging of indicators/memberships (κ=45%, κ=54%). In all cases kappa was smaller than 60%, which can be explained by the preferential sampling plan, the poor definition of soil-classes and the high variability of soils. Steps to improve interpolation of soil-class data, by taking into account the fuzziness of classes directly on the field are further discussed.
