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The Influence Of The Interpolation Method In The Management Zones Generation
1K. Schenatto, 2C. L. Bazzi, 1V. Bier, 1E. Souza
1. Western Paraná State University
2. Technological Federal University of Paraná
The definition of management zones (MZ) allows the concepts of precision agriculture (PA) to be used even in small producers. Methods for defining these MZ were created and are being used, obtaining satisfactory results with different crops and parameters (FLEMING & WESTFALL, 2000; ORTEGA & SANTIBÁÑEZ, 2007; MILANI et al., 2006). Through methodologies, the attributes that are influencing the productivity are selected and thematic maps are generated with the selected layers interpolating the data and performing clustering methods for a desired data (K-Means, Fuzzy C-Means, empirical methods), generating the MZ. After this step, the MZ may be evaluated using the average comparison (ANOVA) and variance reduction (VR) aiming to identify if the divisions were executed correctly. Several interpolation methods, with different levels of complexity, are available in literature (CARVALHO et al., 2002). The inverse of the distance raised to a power (IDW) and the kriging are the interpolation methods mosted used for PA. The difference between them is how the weights are assigned to different samples (MIRANDA et al., 2009). For IDW, the weight factor is predetermined by the value of the chosen power, as it becomes larger, provides less influence from distant points (MAZZINI & SCHETTINI, 2009). IDW requires a more simple analysis, which can make the process less costly and according to Souza et al.(2010), can provide similar results to kriging. The kriging uses geostatistics to perform interpolation, a fact that according to Alves and Vecchia (2011) makes it advantageous over other methods. Kriging relies on mathematical and statistical models, as well as auto-correlation  notions (JAKOB and YOUNG, 2006), but needs a plus in-depth knowledge in geostatistics (NEGREIROS et al., 2010; ANDRIOTTI, 2002), furthermore the number of samples should not be too small (MOLIN, 2003; ANDRIOTTI, 2002). In studies comparing the interpolation methods to generate thematic maps, several authors obtained better results in kriging compared to the IDW (MELLO et al., 2003; CARVALHO; ASSAD, 2005; SILVA et al., 2008; GARDIMAN JUNIOR, et al., 2012; SOUZA et al., 2010 ). However, there are studies demonstrating the IDW being more or as efficient as the kriging (ALVES & VECCHIA, 2011; BAZZI et al., 2008; COELHO et al., 2009). The objective of this study was to evaluate whether the type of interpolation used in the generation of thematic maps influences the quality of MZ. Yield, chemical, physical, and altimetric data were used  in an area of 15.5 ha, collected through a grid of 40 sampling points, concerning two harvests (2011 and 2012), collected with harvesting monitors. The harvest data was previously filtered and the outliers were removed. The interpolation inverse distance, inverse distance squared and kriging were used. MZ were generated using the K-Means and Fuzzy C-Means clustering methods. To select the layers for the Mz generation, the method used by Bazzi et al., (2013) was used. For 2011 the layer altitude was selected as for 2012, mechanical penetration resistance  in depth of 0‑10 cm to generate the Mz. It was concluded that the interpolator has not influenced the generation of Mz, and that a less robust interpolator (IDW) can be used to generate thematic maps that are used to define MZ.
 
Keyword: K-Means, Fuzzy C-Means, Interpolate data, kriging