Abstract
Given the high costs of soil sampling, low and extra-low sampling densities are still being used. Low-density soil sampling usually does not allow the computation of experimental variograms reliable enough to fit models and perform interpolation. In the absence of geostatistical tools, deterministic methods such as inverse distance weighting (IDW) are recommended but they are susceptible to the “bull’s eye” effect, which creates non-smooth surfaces. This study aims to develop and assess interpolation methods or approaches to produce soil test maps that are robust and maximize the information value contained in sparse soil sampling data. Eleven interpolation procedures, including traditional methods, a newly proposed methodology, and a kriging-based approach, were evaluated using grid soil samples from four fields located in Central Alberta, Canada. In addition to the original 0.4 ha⋅sample−1 sampling scheme, two sampling design densities of 0.8 and 3.5 ha⋅sample−1 were considered. Among the many outcomes of this study, it was found that the field average never emerged as the basis for the best approach. Also, none of the evaluated interpolation procedures appeared to be the best across all fields, soil properties, and sampling densities. In terms of robustness, the proposed kriging-based approach, in which the nugget effect estimate is set to the value of the semi-variance at the smallest sampling distance, and the sill estimate to the sample variance, and the IDW with the power parameter value of 1.0 provided the best approaches as they rarely yielded errors worse than those obtained with the field average.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
The data supporting this study's findings are available from the authors, but restrictions apply to the availability of these data. Olds College of Agriculture & Technology and project partners own the rights to the dataset. Data are available from the authors upon reasonable request and with permission from Olds College of Agriculture & Technology and project partners.
References
Agterberg, F. P. (1984). Trend surface analysis. Spatial statistics and models (pp. 147–171). Springer.
Akiba, T., Sano, S., Yanase, T., Ohta, T., & Koyama, M. (2019). Optuna. Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery & data mining (pp. 2623–2631). ACM.
Alberta Ministry of Agriculture and Irrigation. (n.d.). Phosphorus management in crops. https://www.alberta.ca/phosphorus-management-in-crops. Accessed 23 February 2024
Barnes, R. J. (1991). The variogram sill and the sample variance. Mathematical Geology, 23(4), 673–678. https://doi.org/10.1007/BF02065813
Cambardella, C. A., Moorman, T. B., Novak, J. M., Parkin, T. B., Karlen, D. L., Turco, R. F., & Konopka, A. E. (1994). Field-Scale variability of soil properties in central Iowa soils. Soil Science Society of America Journal, 58(5), 1501–1511. https://doi.org/10.2136/sssaj1994.03615995005800050033x
Chilès, J.-P., & Delfiner, P. (2012). Geostatistics. Wiley.
Deb, K., Pratap, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 6(2), 182–197. https://doi.org/10.1109/4235.996017
Erickson, B., & Lowenberg-Deboer, J. (2021). 2021 Precision agriculture dealership survey. https://ag.purdue.edu/digitalag/_media/croplife-report-2021.pdf
Franke, R., & Nielson, G. (1980). Smooth interpolation of large sets of scattered data. International Journal for Numerical Methods in Engineering, 15(11), 1691–1704. https://doi.org/10.1002/nme.1620151110
Fulton, J. P., Shearer, S. A., Higgins, S. F., Darr, M. J., & Stombaugh, T. S. (2005). Rate response assessment from various granualar VRT applicators. Transactions of the ASAE, 48(6), 2095–2103. https://doi.org/10.13031/2013.20086
Goovaerts, P. (1999). Geostatistics in soil science: State-of-the-art and perspectives. Geoderma, 89(1–2), 1–45. https://doi.org/10.1016/S0016-7061(98)00078-0
Hengl, T., Nussbaum, M., Wright, M. N., Heuvelink, G. B. M., & Gräler, B. (2018). Random forest as a generic framework for predictive modeling of spatial and spatio-temporal variables. PeerJ. https://doi.org/10.7717/peerj.5518
Isaaks, E. H., & Srivastava, R. M. (1989). Applied geostatistics. Oxford Univeristy Press, Inc.
Kravchenko, A. N. (2003). Influence of spatial structure on accuracy of interpolation methods. Soil Science Society of America Journal, 67(5), 1564–1571. https://doi.org/10.2136/sssaj2003.1564
Kravchenko, A., & Bullock, D. G. (1999). A comparative study of interpolation methods for mapping soil properties. Agronomy Journal, 91(3), 393–400. https://doi.org/10.2134/agronj1999.00021962009100030007x
Larocque, G., Dutilleul, P., Pelletier, B., & Fyles, J. W. (2007). Characterization and quantification of uncertainty in coregionalization analysis. Mathematical Geology, 39(3), 263–288. https://doi.org/10.1007/s11004-007-9086-8
Laslett, G. M., & McBratney, A. B. (1990). Estimation and implications of instrumental drift, random measurement error and nugget variance of soil attributes—A case study for soil pH. Journal of Soil Science, 41(3), 451–471. https://doi.org/10.1111/j.1365-2389.1990.tb00079.x
Liu, L., Zheng, X., Wei, X., Kai, Z., & Xu, Y. (2021). Excessive application of chemical fertilizer and organophosphorus pesticides induced total phosphorus loss from planting causing surface water eutrophication. Scientific Reports, 11(1), 1–8. https://doi.org/10.1038/s41598-021-02521-7
Michelon, G. K., Bazzi, C. L., Upadhyaya, S., de Souza, E. G., Magalhães, P. S. G., Borges, L. F., et al. (2019). Software AgDataBox-Map to precision agriculture management. SoftwareX, 10, 100320. https://doi.org/10.1016/j.softx.2019.100320
Pebesma, E. J. (2004). Multivariable geostatistics in S: The gstat package. Computers and Geosciences, 30(7), 683–691. https://doi.org/10.1016/j.cageo.2004.03.012
Pereira, G. W., Valente, D. S. M., de Queiroz, D. M., de Coelho, A. L. F., Costa, M. M., & Grift, T. (2022). Smart-map: an open-source QGIS plugin for digital mapping using machine learning techniques and ordinary kriging. Agronomy, 12(6), 1350. https://doi.org/10.3390/agronomy12061350
Pereira, G. W., Valente, D. S. M., de Queiroz, D. M., Santos, N. T., & Fernandes-Filho, E. I. (2022b). Soil mapping for precision agriculture using support vector machines combined with inverse distance weighting. Precision Agriculture, 23(4), 1189–1204. https://doi.org/10.1007/s11119-022-09880-9
R Core Team. (2022). R: A language and environment for statistical computing. R Core Team.
Robinson, T. P., & Metternicht, G. (2006). Testing the performance of spatial interpolation techniques for mapping soil properties. Computers and Electronics in Agriculture, 50(2), 97–108. https://doi.org/10.1016/j.compag.2005.07.003
Shepard, D. (1968). A two-dimensional interpolation function for irregularly-spaced data. In R. B. S. Blue & A. M. Rosenberg (Eds.), Proceedings of the 1968 23rd ACM national conference (pp. 517–524). ACM Press.
Sobjak, R., de Souza, E. G., Bazzi, C. L., Opazo, M. A. U., Mercante, E., & Aikes Junior, J. (2023). Process improvement of selecting the best interpolator and its parameters to create thematic maps. Precision Agriculture, 24(4), 1461–1496. https://doi.org/10.1007/s11119-023-09998-4
Wadoux, A. M. J. C., Heuvelink, G. B. M., de Bruin, S., & Brus, D. J. (2021). Spatial cross-validation is not the right way to evaluate map accuracy. Ecological Modelling, 457, 109692. https://doi.org/10.1016/j.ecolmodel.2021.109692
Wadoux, A. M. J. C., Marchant, B. P., & Lark, R. M. (2019). Efficient sampling for geostatistical surveys. European Journal of Soil Science, 70(5), 975–989. https://doi.org/10.1111/ejss.12797
Webster, R., & Oliver, M. A. (1992). Sample adequately to estimate variograms of soil properties. Journal of Soil Science, 43(1), 177–192. https://doi.org/10.1111/j.1365-2389.1992.tb00128.x
Webster, R., & Oliver, M. A. (2007). Geostatistics for environmental scientists. Wiley. https://doi.org/10.1002/9780470517277
Acknowledgements
We thank Olds College of Agriculture & Technology and Olds College Center for Innovation for providing the infrastructure, support, and data for the development of this project. We also thank the Canadian Agri-Food Automation and Intelligence Network (CAAIN), Mitacs, and Telus for the funds provided for the project and data collection. This research is part of the “Agricultural Multi-Layer Data Fusion to Support Cloud-Based Agricultural Advisory Services” project funded through the Mitacs Accelerate program.
Author information
Authors and Affiliations
Contributions
Conceptualization: FHSK, VA; Methodology: FHSK, VA, PD, and AM; Formal analysis and investigation: FHSK; Writing—original draft preparation: FHSK; Writing—review and editing: PD, VA, and AM; Funding acquisition: AM, VA, and FHSK; Supervision: VA, AM, and PD.
Corresponding author
Ethics declarations
Conflict of interest
The research leading to these results received funding from the Canadian Agri-Food Automation and Intelligence Network (CAAIN), Mitacs, and Telus. The authors declare they have no financial interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Karp, F.H.S., Adamchuk, V., Dutilleul, P. et al. Comparative study of interpolation methods for low-density sampling. Precision Agric (2024). https://doi.org/10.1007/s11119-024-10141-0
Accepted:
Published:
DOI: https://doi.org/10.1007/s11119-024-10141-0