Tutorial 2 is based on tutorial 1 with a few alterations. 1) the variogram is standardized by dividing the semivariance by the standard deviation of that field, 2) only the wheat fields are used for the analysis so that the results are more easily compared, and 3) a time component is added; for 5 time steps the correlation between range and sill is determined and the development over time is analyzed (there was no biomass data for these dates).

**Part 1 and 2**

*Standardizing of variogram*

var@variogram$gamma=var@variogram$gamma/cellStats(ras,’sd’,na.rm=TRUE,asSample=TRUE)

where var is the Formal Class RasterVariogram. The variance column in this class can be accessed by @variogram$gamma. This column is replaced by the standardized variance, by dividing the existing column by the standard deviation. The standard deviation is calculated with the cellStats function. The input raster is ras, and ‘sd’ is the statistical option for standard deviation. na.rm=TRUE is a logical to remove NA values, and lastly, the asSample=TRUE means that the denominator for the standard deviation is n-1.

Doing the same analysis but now just focusing on one crop does not improve the results. Pearson’s correlation coefficients are low and insignificant with a correlation coefficient for Range vs Biomass of -0.31 (p-value is 0.3461) and a correlation coefficient for Sill vs Biomass of 0.35 (p-value is 0.2922). For the color coded scatter plot there is no pattern visible for the relationship between the sill, range, and biomass.

**Part 3**

For part 3 the range and sill values for all wheat fields at 5 different dates is determined. The correlation between range and sill for every date is determined. This Pearson correlation coefficient is then analyzed over time. It seems that there is an increase in correlation over time. There seems to be a high correlation with a 5%-significant p-value of 0.047.