Tuning spatial parameters of Geographical Random Forest: the case of agricultural drought

Machine learning algorithms are widely used methods in geographical research. However, these algorithms are not properly exploiting the underlying spatial relationships present in the geographical data. One of the approaches, which addresses this problem, is based on an ensemble of local models, which are constructed from samples in close proximity to the location of prediction. This concept was applied to the Random Forest (RF) algorithm, creating a Geographical Random Forest (GRF). This study aims to further develop GRF by tuning the spatial parameters for each location in case of agricultural drought. In addition to tuning, the explanatory property of RF within the framework GRF is explored. Four machine learning models were constructed; regular RF, regular RF with spatial covariates, GRF, and GRF with the tuning of spatial parameters. Models were evaluated using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Although the decrease in RMSE in this very case is relatively small, the method may provide higher improvement with different datasets.

1. Bauer-Marschallinger, B., Paulik, C., Hochstöger, S., Mistelbauer, T., Modanesi, S., Ciabatta, L., Massari, C., Brocca, L., Wagner, W. (2018): Soil moisture from fusion of scatterometer and SAR: Closing the scale gap with temporal filtering. Remote Sensing 10(7), 1030. CrossRef

2. Berk, R. A. (2008): Statistical Learning as a Regression Problem. In: Statistical Learning from a Regression Perspective. Springer Series in Statistics. Springer, New York, NY. CrossRef

3. Beven, K. J., Kirkby, M. J. (1979): A physically based, variable contributing area model of basin hydrology/Un modèle à base physique de zone d'appel variable de l'hydrologie du bassin versant. Hydrological Sciences Journal 24(1), 43-69. CrossRef

4. Bot, A., Benites, J. (2005): The importance of soil organic matter: Key to drought-resistant soil and sustained food production. In: Food & Agriculture Org. Breiman, L. (2001). Random forests. Machine Learning 45, 5-32. CrossRef

5. Brunsdon, C., Fotheringham, A. S., Charlton, M. (1998): Geographically weighted regression. Journal of the Royal Statistical Society: Series D (The Statistician) 47(3), 431-443. CrossRef

6. Copernicus Global Land service (2023): Soil Water Index. https://land.copernicus.eu/global/products/swi.

7. Cornes, R. C., van der Schrier, G., van den Besselaar, E. J., Jones, P. D. (2018): An ensemble version of the E‐OBS temperature and precipitation data sets. Journal of Geophysical Research: Atmospheres 123(17), 9391-9409. CrossRef

8. Cotrufo, M. F., Ranalli, M. G., Haddix, M. L., Six, J., Lugato, E. (2019): Soil carbon storage informed by particulate and mineral-associated organic matter. Nature Geoscience 12, 989-994. CrossRef

9. 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 6: e5518. CrossRef

10. Hokstad, V., Tiganj, D. (2020): Spatial modelling of unconventional wells in the Niobrara Shale play: a descriptive, and a predictive approach. Master's thesis. Norwegian School of Economics.

11. Hoque, M. A., Pradhan, B., Ahmed, N., Sohel, Md. S. I. (2021): Agricultural drought risk assessment of Northern New South Wales, Australia using geospatial techniques. In: Science of the Total Environment 756: 143600. CrossRef

12. European Union, Copernicus Land Monitoring Service (2019): Corine Land Cover. European Environment Agency (EEA), https://land.copernicus.eu/en.

13. European Union, Copernicus Land Monitoring Service (2016): EU - Digital Elevation Model 1.1. European Environment Agency (EEA), https://land.copernicus.eu/en.

14. Fernández-Delgado, M., Cernadas, E., Barro, S., Amorim, D. (2014): Do we need hundreds of classifiers to solve real world classification problems? Journal of Machine Learning Research 15, 3133-3181, https://jmlr.org/papers/volume15/delgado14a/delgado14a.pdf.

15. Fotheringham, A. S., Charlton, M., Brunsdon, C. (1996): The geography of parameter space: an investigation of spatial non-stationarity. International Journal of Geographical Information Systems 10(5), 605-627. CrossRef

16. Fotheringham, A. S., Brunsdon, C., Charlton, M. (2003): Geographically weighted regression: the analysis of spatially varying relationships. John Wiley & Sons. Chichester.

17. Georganos, S., Grippa, T., Gadiaga, A. N., Linard, C., Lennert, M., Vanhuysse, S., Mboga, N., Wolff, E., Kalogirou, S. (2019): Geographical random forests: a spatial extension of the random forest algorithm to address spatial heterogeneity in remote sensing and population modelling. Geocarto International 36(2), 121-136. CrossRef

18. Jain, K. V., Pandey, R. P., Jain, M. K. (2015): Spatio-temporal assessment of vulnerability to drought. Natural Hazards 76, 443-469. CrossRef

19. Kuhn, M., Johnson, K. (2013): Applied predictive modeling. Springer. New York. CrossRef

20. Liaw, A., Wiener, M. (2002): Classification and regression by randomForest. Race News 2, 18-22, https://cogns.northwestern.edu/cbmg/LiawAndWiener2002.pdf.

21. Lugato, E., Lavallee, J. M., Haddix, M. L., Panagos, P., Cotrufo, M. F. (2021): Different climate sensitivity of particulate and mineral-associated soil organic matter. Nature Geoscience 14, 295-300. CrossRef

22. Magesh, N. S., Chandrasekar, N., Soundranayagam, J. P. (2011): Morphometric evaluation of Papanasam and Manimuthar watersheds, parts of Western Ghats, Tirunelveli district, Tamil Nadu, India: a GIS approach. Environmental Earth Sciences 64, 373-381. CrossRef

23. Sourav, M., Mishra, A., Trenberth, K. E. (2018): Climate Change and Drought: A Perspective on Drought Indices. Current Climate Change Reports 4, 145-163. CrossRef

24. Paulik, C., Dorigo, W., Wagner, W., Kidd, R. (2014): Validation of the ASCAT Soil Water Index using in situ data from the International Soil Moisture Network. International journal of Applied Earth Observation and Geoinformation 30, 1-8. CrossRef

25. Orgiazzi, A., Ballabio, C., Panagos, P., Jones, J., Fernández‐Ugalde, O. (2018): LUCAS Soil, the largest expandable soil dataset for Europe: a review. European Journal of Soil Science 69(1), 140-153. CrossRef

26. Panagos, P., Liedekerke, M. V., Jones, A., Montanarella, L. (2012): European Soil Data Centre: Response to European policy support and public data requirements. Land Use Policy 29(2), 329-338. CrossRef

27. Panagos, P., Liedekerke, M. V., Borrelli, P., Köninger, J., Ballabio, C., Orgiazzi, A., Lugato, E. (2022): European Soil Data Centre 2.0: Soil data and knowledge in support of the EU policies. European Journal of Soil Science 73(6), e13315. CrossRef

28. Probst, P., Boulesteix, A. L. (2017): To tune or not to tune the number of trees in random forest. Journal of Machine Learning Research 18, 1-18. CrossRef

29. Probst, P., Wright, M. N., Boulesteix, A. L. (2018): Hyperparameters and tuning strategies for random forest. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 9(3), e1301. CrossRef

30. Mishra, A. K, Singh, V. P. (2010): A review of drought concepts. Journal of Hydrology 391(1-2), 202-216. CrossRef

31. Rahmati, O., Falah, F., Dayal, K. S., Deo, R. C., Mohammadi, F., Biggs, T., Moghaddam, D. D., Naghibi S. A., Bui, D. T. (2019): Machine learning approaches for spatial modeling of agricultural droughts in the south-east region of Queensland Australia. Science of the Total Environment 699, 134230. CrossRef

32. Rahmati, O., Panahi, M., Kalantari, Z., Soltani, E., Falah, F., Dayal, K. S., Mohammadi, F., Deo, R. C., Tiefenbacher, J., Bui, D. T. (2020): Capability and robustness of novel hybridized models used for drought hazard modeling in southeast Queensland, Australia. Science of the Total Environment 718, 134656. CrossRef

33. Shashank, S., Pandey, A. C. (2015): Delineation of groundwater potential zone in hard rock terrain of India using remote sensing, geographical information system (GIS) and analytic hierarchy process (AHP) techniques. Geocarto International 30(4), 402-421. CrossRef

34. Simpson, E. H. (1951): The interpretation of interaction in contingency tables. Journal of the Royal Statistical Society: Series B (Methodological) 13(2), 238-241. CrossRef

35. Thomas, T., Jaiswal, R. K., Galkate, R., Nayak, P. C., Ghosh, N. C. (2016): Drought indicators-based integrated assessment of drought vulnerability: a case study of Bundelkhand droughts in central India. Natural Hazards 81, 1627-1652. CrossRef

36. Wilhelmi, O. V., Wilhite, D. A. (2002): Assessing vulnerability to agricultural drought: a Nebraska case study. Natural Hazards 25, 37-58. CrossRef

37. Yang, M., Mou, Y., Meng, Y., Liu, S., Peng, C., Zhou, X. (2020): Modeling the effects of precipitation and temperature patterns on agricultural drought in China from 1949 to 2015. Science of the Total Environment 711, 135139. CrossRef