Optimal Spatial Interpolation of Soil Properties to Assist Precision Agriculture Todd P. Robinson1 and Graciela Metternicht2 1,2,
Deparment of Spatial Spatial Sciences Curtin University of Technology GPO Box U 1987, Perth WA 6845 1 Email:
[email protected] 2 Email:
[email protected]
ABSTRACT Site-specific crop management requires matching resource application and agronomic practices with soil and crop requirements, as they vary in space and time within a field. As such, information on the composition of soils at either farm or paddock scale is essential. Soil composition over an entire paddock might not be uniform, so, for instance, it may not be efficient to fertilise an entire paddock if only the northeast corner show deficiencies. Furthermore, it is not possible to sample every centimetre of the paddock, as this would be a very time consuming and costly procedure. Ideally, we should be able to collect enough sample points so that continuos maps of soil properties can be produced using accurate spatial interpolation techniques, and good judgements can be made about the soil composition of an entire paddock. In this paper we implement and compare four types of interpolation techniques, namely ordinary kriging, lognormal ordinary kriging, inverse distance weighting (IDW) and splines to derive an optimal interpolation for seasonally stable soil properties that have demonstrated to affect yield production (e.g. pH, electric conductivity and organic matter). Careful and judicious choice of the exponent value for IDW and splines and 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 was further interrogated to find the optimum number of neighbours using a cross-validation procedure. Overall, all of the methods gave similar RMSE values. 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 cases of IDW the power of one was the best choice, which is possibly due to the low skewness inherent in all of the soil properties. Splines performed best where the data had a low coefficient of kurtosis (possibly suggesting it has difficulties fitting polynomials to several different populations) and a relatively high variance. Lognormal kriging performed well when the dataset had a coefficient of skewness larger than one.
KEYWORDS: Interpolation, spatial prediction, kriging, IDW, inverse distance weighting, splines, soil properties, precision agriculture, geostatistics, soil mapping, jackknife, cross-validation, soil prediction.
INTRODUCTION Certain soil properties influence the productivity of agricultural land. Consequently, farmers need to know what the composition of their existing soil is so that it can be improved or alternative crops grown. The composition of a soil property over an entire paddock is unlikely to be homogeneous; therefore, soil remediation may not be required for
the entire paddock. For example, consider an application to acidity - if only the northeast corner of a paddock is acidic, it would not be appropriate (and certainly not economic) to apply lime to the entire paddock. Correct determination of the amount and the location to apply lime can provide considerable financial gains to the farmer. The effectiveness of applying, for instance, a differential liming technique depends on the reliability of a spatial interpolation of the soil property values at unsampled locations. All interpolation methods are subject to error. For example, in some areas the value interpolated may be an overestimate or an underestimate, so there is still some inability to determine exactly where and how much remediation is required. Nonetheless, the greater the accuracy of the interpolation, the better the application to precision farming and, thus, an effective implementation of variable rate technology. The interpolation techniques commonly used in agriculture to produce continuous maps of soil properties, in approximate order of use are: kriging (in a broad sense), inverse distance weighting (IDW) and splines (eg. Kravchenko and Bullock, 1999; Gotway et al., 1996; Laslett et al., 1987). All three methods are exact, which means the interpolation of the values at sampled points is unchanged, or in other words the prediction honours the data (Laslett et al., 1987). Both inverse distance weighting and kriging estimate values at unsampled locations based on the measurements from the surrounding locations with certain weights attached to each of the measurements (Kravchenko and Bullock, 1999), whilst splines join together a series of polynomials of degree p, which attempt to describe the surface (Webster and Oliver, 2001). The accuracy of these 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 then lognormal ordinary kriging generally outperforms both ordinary kriging and IDW; otherwise, ordinary kriging is more successful, based on the results obtained from the mean error, mean absolute error and correlation coefficient. Further, Laslett et al. (1987) also found ordinary (isotropic) kriging to be a better method than IDW when they interpolated pH in CaCl 2, using samples from 121 sites. In fact, Laplacian smoothing splines was better than both IDW and kriging for pH in CaCl2, for Laslett et al. (1987), where the sum of squared errors is used as the criteria for comparison. To determine whether ordinary kriging or lognormal kriging would return a better estimation of phosphorous or potassium, Kravchenko and Bullock (1999) use the Kolmogorov-Smirnov goodness-of-fit parameter (D). For their study, if the value for D, obtained by fitting the data with lognormal distribution, is less than the value of D from using normal distribution, lognormal ordinary kriging produces better results. In cases where D from normal distribution is smaller or “roughly equivalent” to D with a lognormal distribution, ordinary kriging should be preferred, which introduces some subjectivity into the decision. Other deciding parameters, from an exploratory data analysis, are the coefficient of variation, the number of data points, skewness and kurtosis. Specifically, they found that the coefficient of variation needs to be greater than 40 percent to apply lognormal ordinary kriging with values less than 40 percent producing large negative mean errors between measured and estimated values. Furthermore, ordinary kriging seemed to produce similar or better results than lognormal kriging when the datasets contain more than 200 points, regardless of whether the data are normally or lognormally distributed. Moreover, Kravchenko and Bullock (1999) found that IDW is significantly improved by selecting an optimal number of neighbours and manipulation of the exponent value. Unfortunately, these values cannot be found a priori, but through trial and error. Tomczak (1998) mitigates this trial and error, by applying cross-validation to optimize the IDW interpolation parameters. Kravchenko and Bullock (1999) found that data with high skewness (>2.5) were often best estimated with a power of four (five out of eight datasets). Furthermore, for most of the data with low skewness (
