Testing the performance of spatial interpolation techniques for mapping soil properties

doi:10.1016/j.compag.2005.07.003

Computers and Electronics in Agriculture

Volume 50, Issue 2, February 2006, Pages 97-108

https://doi.org/10.1016/j.compag.2005.07.003 Get rights and content

Abstract

In this paper, we implement and compare the accuracy of ordinary kriging, lognormal ordinary kriging, inverse distance weighting (IDW) and splines for interpolating seasonally stable soil properties (pH, electric conductivity and organic matter) that have been demonstrated to affect yield production.

The choice of the exponent value for IDW and splines as well as the number of the closest neighbours to include was decided from the root mean squared error (RMSE) statistic, obtained from a cross-validation procedure. Experimental variograms were fitted with the exponential, spherical, Gaussian and linear models using weighted least squares. The model with the smallest residual sum of squares (RSS) was further interrogated to find the number of neighbours that returned the best cross-validation result.

Overall, all of the methods gave similar RMSE values. On this experimental field, ordinary kriging performed best for pH in the topsoil and lognormal ordinary kriging gave the best results when applied to electrical conductivity in the topsoil. IDW interpolated subsoil pH with the greatest accuracy and splines surpassed kriging and IDW for interpolating organic matter.

In all uses of IDW, the power of one was the best choice, which may due to the low skewness of the soil properties interpolated. In all cases, a value of three was found to be the best power for splines. Lognormal kriging performed well when the dataset had a coefficient of skewness larger than one. No other summary statistics offered insight into the choice of the interpolation procedure or its parameters. We conclude that many parameters would be better identified from the RMSE statistic obtained from cross-validation after an exhaustive testing.

Introduction

Implementation of variable-rate technology can provide considerable financial gains to the farming industry. However, its effectiveness relies on the accuracy of the spatial interpolation used to define the spatial variability of soil properties.

The accuracy of interpolation methods for spatially predicting soil properties has been analysed in several studies. Kravchenko and Bullock (1999) compared inverse distance weighting (IDW), ordinary kriging and lognormal ordinary kriging for soil properties (phosphorous (P) and potassium (K)) from 30 experimental fields. They found that if the underlying dataset is lognormally distributed and contains less than 200 points, lognormal ordinary kriging generally outperforms both ordinary kriging and IDW; otherwise, ordinary kriging is more successful. Further, Laslett et al. (1987) also found ordinary (isotropic) kriging to be a better method than IDW for interpolating pH. In fact, Laslett et al. (1987) judged splines to be a better than both IDW and kriging. In contrast, Gotway et al. (1996) observed better results than kriging for soil organic matter and nitrogen when using IDW. Weber and Englund (1992) also found that IDW produced better results than kriging (with lognormal kriging outperforming ordinary kriging).

There have been many conflicting reports concerning the use of basic statistics to predetermine both interpolation methods and their parameters. For example, Kravchenko and Bullock (1999) report a significant improvement in accuracy of soil properties interpolated using IDW by manipulating the exponent value. They found that data with high skewness (>2.5) were often best estimated with a power of four (five out of eight datasets) and for most of the soil properties with low skewness (<1), a power of one yielded the most accurate estimates (9 out of 15 datasets). Alternatively, Weber and Englund (1994) report that IDW with a power of one resulted in a better estimation for data with skewness coefficients in the range of four to six when interpolating blocks of contaminant waste sites. Likewise, a larger exponent produced better estimations when the data had low skewness.

For organic matter, in particular, Gotway et al. (1996) found that the accuracy of the inverse distance method increased as the exponent value increased. Their findings show that properties with a low coefficient of variation (<25%) were better explained by a higher power, in most cases a power of four. In addition, datasets with a high coefficient of variation gave best results when a power of one was used. On the contrary, Kravchenko and Bullock (1999) found no significant correlation between the exponent value used for IDW and the coefficient of variation.

Given the variability of results obtained by these previous studies the research reported hereafter aims to:

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Assess the accuracy of various well-known interpolation techniques for mapping soil pH, electrical conductivity and organic matter through manipulation of the various parameters attributable to each technique;
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Determine if non-spatial statistics could assist in determining the best interpolation method to implement without using exhaustive test parameters;
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Identify the spatial prediction method that best illustrates the spatial variability of the soil properties studied. This would enable the identification of areas where remediation is required to improve crop growth.

Section snippets

Kriging

The presence of a spatial structure where observations close to each other are more alike than those that are far apart (spatial autocorrelation) is a prerequisite to the application of geostatistics (Goovaerts, 1999). The experimental variogram measures the average degree of dissimilarity between unsampled values and a nearby data value (Deutsch and Journel, 1998), and thus can depict autocorrelation at various distances. The value of the experimental variogram for a separation distance of h

Study area and sampling design

The study area is a 60 ha paddock, called ‘Ardgowan’ on a dry land sheep and cropping farm, located in the Shire of Wickepin, in the South West of Western Australia. As a result of ongoing research activities in the application of remote sensing to agriculture, 100 soil samples were collected at 10 and 30 cm depth (Fig. 1), geo-referenced using a GPS receiver (accuracy of ±5 m) and analysed for organic matter, electrical conductivity and soil pH. Organic matter was assayed using the ‘loss on

Visualization and exploratory data analysis

Fig. 2 summarises the methods and techniques applied in this research for spatial prediction and comparative evaluation of the soil properties. This begins with a visual analysis by screening the data values to identify incorrect coordinate information and illogical data points. Visualization is also used to quickly identify the presence or absence of spatial autocorrelation. Description of the data values is achieved via basic summary statistics, including means, medians, variances and

Data visualization

Fig. 3a shows the spatial distribution of the topsoil pH, classified into quartiles, depicting that the bulk of the data have a critical pH range of 4.40–4.75. The classified map of subsoil pH (Fig. 3b) exhibits a good degree of autocorrelation with similarly classified values clustering together in space. Fig. 3c shows the spatial distribution of topsoil electrical conductivity, which illustrates that generally, the paddock does not seem to have a salinity problem in the topsoil (all values

Conclusions

This study has shown that, out of the four spatial prediction methods used, there is not one single interpolator that can produce chief results for the generation of continuous soil property maps all of the time, particularly with a dataset that has not been designed with one particular interpolator in mind. Overall, all of the methods gave similar RMSE values, using the cross-validation technique for evaluation. Ordinary kriging performed best for pH in the topsoil and lognormal kriging

Acknowledgements

This research has been supported by the Australian Research Council (ARC), under the Strategic Partnership with the Industry Scheme (SPIRT). The authors also thank Georgina Warren and Jacob Delfos for the collection of the soil samples. Additionally, we acknowledge industry partners SpecTerra Systems Pty Ltd. and the Department of Agriculture of Western Australia. Finally, the authors value the constructive comments of two anonymous reviewers as they significantly improved the quality of the

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Testing the performance of spatial interpolation techniques for mapping soil properties

Abstract

Introduction

Section snippets

Kriging

Study area and sampling design

Visualization and exploratory data analysis

Data visualization

Conclusions

Acknowledgements

Geoderma

Creating continuous surfaces from point data

Other forms of soil degradation

Uses and abuses of cross-validation in geostatistics

Math. Geol.

GSLIB: Geostatistical Software Library and User's Guide.

Low cost remote sensing approach for designing effective sampling strategies of soil properties for site-specific crop management

Soil acidification

Comparison of kriging and inverse-distance methods for mapping soil parameters

Am. J. Soil Sci.