**3. Results and discussion**

nodesize value was set to 5 for each terminal node, as usually selected in regression studies. The mtry value chosen in this study was according to Liaw and Wiener [49], which proposes an amount corresponding to one third of the total number of

*Multifunctionality and Impacts of Organic and Conventional Agriculture*

Although Na showed a significant correlation at the two depths, according to the Pearson correlation analysis, the preliminary results using the random forest (RF) model were very unsatisfactory. Thus, exceptionally for this property, the RF model has been replaced by ordinary kriging (OK). Semivariograms were used to analyze the spatial structure of the Na, and to generate predictive maps, in both depths. The OK was performed in R software, through krige function [46]. OK model is the most familiar type of kriging and provides an accurate estimate for an area around a

The model's performance was evaluated based on independent validation set, which was not used in the training procedure. Thereby, the 290 soil samples were randomly divided into 2 independent datasets in the R software; one of these was used in the training process (200 soil samples) and another for the validation process (90 soil samples). The analysis of the model's performance was based on the correlation between the measured values (validation samples) and estimated

r

where "d" is the difference between the observed and estimated values and "n"

The RMSE is a measure of the overall error of the estimation and commonly is used to estimate the error or uncertainty in places where the error was not measured directly; thereby, the higher the values of RMSE, the greater the differences

overestimation (positive values) or underestimation (negative values); values close

Management zones were defined in this study according to potential for agriculture, considering variability of soil key properties along profile depth, importance of soil properties for the land management, and the performance of the models to predict the spatial variation of the properties. Based on the maps for the selected soil key properties, an unsupervised classification was performed by using a series of input raster bands (Na, CEC, clay, and sand) using the Iso Cluster and

The Iso Cluster tool uses a modified iterative optimization clustering procedure, also known as the migrating means technique. The algorithm separates all cells into the user-specified number of distinct unimodal groups in the multidimensional space of the input bands; the iso prefix of the isodata clustering algorithm is an abbreviation for the iterative self-organizing way of performing clustering. In the clustering process, during each iteration, all samples are assigned to existing cluster centers, and new means are recalculated for every class. The optimal number of

*ME* <sup>¼</sup> <sup>1</sup> *n* X*n i*¼1

between the datasets [52]. The ME gives the bias and allows evaluation of

Maximum Likelihood Classification tools from ArcGIS Desktop 10.3.

classes to specify is usually unknown. Therefore, it is advised to enter a

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 *n* X*<sup>n</sup> <sup>i</sup>*¼<sup>1</sup> *<sup>d</sup>*<sup>2</sup> *i*

), the root mean square

*di* (2)

(1)

predictor variables for regression problems.

values, calculated by the coefficient of determination (R2

is the number of samples used in the validation process.

error (RMSE), and mean error (ME), presented as Eqs. (1) and (2):

*RMSE* ¼

measure sample [51].

to zero are preferable.

**44**

**2.4 Definition of management zones**
