## 2 Materials and Methods
We analysed all indicators with each other and examined whether there was a linear relationship between them, defined by the correlation coefficient \(r\):  
\[r=\ \frac{\sum_{i=1}^{n}\left(X_{i}-\ \overline{X}\right)\left(Y_{i}-\ \overline{Y}\right)}{\sqrt{\sum_{i=1}^{n}\left(X_{i}-\ \overline{X}\right)^{2}}\sqrt{\sum_{i=1}^{n}\left(Y_{i}-\ \overline{Y}\right)^{2}}} \tag{1}\]  
where:  
\(X_{i}\)--variable \(X\) observed at time \(i\),  
\(\overline{X}\)--arithmetic mean of the \(X\) variables in time series,  
\(Y_{i}\)--variable \(Y\) observed at time \(i\),  
\(\overline{Y}\)--arithmetic mean of variables \(Y\) in time series  
\(n\)--range of time series examined  
The correlation coefficient measures the two-sided linear dependence of the two variables and acquires values from the range \(<\)\(-\)1.1\(>\), where \(r\) = 1 exists between variables positive linear dependence. In the case of \(r\) = \(-\)1, negative dependence is demonstrated. If the correlation \(n\) = 0, there is no dependency between \(X\) and \(Y\). The correlation coefficient may also have other values which can be classified as follows:  
\(0<|\,r|<0.3\) low level of dependency between variables,  
\(0.3\leq|\,r|<0.5\) moderate level of dependency between variables,  
\(0.5\leq|\,r|<0.7\) medium level of dependency between variables,  
\(0.7\leq|\,r|<1\) a strong level of dependency between variables. For pairs of indicators with a correlation coefficient higher than 10.5\(|\), we then performed a regression analysis, expressing the relationship between variables numerically. By empirical determination of the type of analytical function and its numeric constants, we express the progress of the measured values of the dependent variable (\(y\)) at the changing values of the argument (\(x\)) of the independent variable. The regression model defines what change to variable (\(y\)) is caused by the change in variable \(x\). However, in addition to variable \(x\), variable (\(y\)) is influenced by other factors that we may identify as random effects. We refer to these random effects in a function as a random component of the model. Then the regression function will be expressed as follows:  
\[y_{i}=f(x_{i})+\varepsilon_{i} \tag{2}\]  
where  
\(i\) = 1-\(n\), \(n\) is the number of observations,  
\(x_{i}\)--the values of the explanatory variable that the experimentalist has chosen,  
\(y_{i}\)--the value of the explained variable found at given values (\(x_{i}\)),  
\[R^{2}=1-\frac{\sum_{i=1}^{n}\left(y_{i}-\hat{y}_{i}\right)^{2}}{\sum_{i=1}^{n }\left(y_{i}-\overline{y}\right)^{2}} \tag{3}\]  
\(\varepsilon_{i}\)--accidental observation error  
\(n\)--number of observations. We have verified the quality of the regression model through coefficient of determination (\(R^{2}\)), which takes values from interval \(<\)0.1\(>\). \(R^{2}\)--expresses by how much percentage (0-100%) we can calculate the regression line to explain the variability of the empirical values. The closer the coefficient of determination is to (1), the more precise the regression function is. With the usage of non-parametric analysis of variance (ANOVA) through the Wilcox test, we analysed the dispersion of values with the influence of time and depth measurement. By means of the Wilcox test, we verified a zero hypothesis (H0) at the significance level alpha = 0.05. The zero hypotheses define the equality of the achieved values of the indicator regardless of the time or measurement depth. H0 (time effect) = There are no statistically significant differences in the values of indicator with the influence of time. H0 (effect of the depth measurement) = There are no statistically significant differences in the values of the indicator due to the depth of measurement. At a \(p\)-value of <0.05 H0 is rejected in favor of the alternative HA hypothesis. HA is defined as follows:  
HA (time effect) = There are statistically significant differences in the values of the indicator with the influence of the time.