# Geohydroology of a Reference Mediterranean Catchment (Cilento UNESCO Geopark, Southern Italy)
## 2 Materials and Methods
### Hysteretic Analysis  
In the scientific literature, numerous studies have been carried out on the chemical parameters of waters to enhance our knowledge of catchment transport pathways and source areas during storm events. The non-linear correlation between the discharge and the chemical parameters, described by the hysteretic loops, led the researchers to develop a synthetic index for the characterization of the hysteresis in terms of size and shape. The researchers in [25] proposed a new hysteretic index (h) that can be used for a wide range of variables and can be applied to datasets where the dependent variable decreases during an event. The method is based on the computation of definite integrals on the increasing and decreasing rating curve of the independent variable [25]. The authors defined the rising curve as the part of the curve of the independent variable related to the beginning of the dilution phase on the chemograph up to the minimum EC value. The falling limb is on the part of the curve of the independent variable, which corresponds with the recovery phase of the chemograph. The procedure proposed by [25] for h index calculation involves the following steps:  
1. Normalization of the two variables for each single event, ranging between 0 and 1:  
\[\text{u(t)}=\frac{\text{x(t)-x}_{\text{min}}}{\text{x}_{\text{max}}-\text{x}_ {\text{min}}}, \tag{2}\]  
\[\text{v(t)}=\frac{\text{y(t)-y}_{\text{min}}}{\text{y}_{\text{max}}-\text{y}_ {\text{min}}}, \tag{3}\]  
where x(t) and y(t) are the two variables at time t; x\({}_{\text{min}}\), x\({}_{\text{max}}\), y\({}_{\text{min}}\) and y\2. Computation of the definite integrals \(\text{Ar}[i,j]\) and \(\text{Af}[i,j]\) of the functions \(vr(u)\) and \(\textit{vf}(u)\) on intervals \([i,j]\) for the rising (\(r\)) and the falling (\(f\)) curve:  
\[A_{r[i,j]}=\int_{i}^{j}v_{r}(u)du, \tag{4}\]  
\[A_{f[i,j]}=\int_{i}^{j}v_{f}(u)du, \tag{5}\]  
where \(i\) and \(j\) represent the lower and upper limits of integration, respectively, and can assume any value from \(u=0\) to \(u=1\). The integrals can be computed on intervals of different widths delimited by selected points, \(i\) and \(j\), of the independent variable \(u\). The choice of the intervals of integrations should depend on the quality and resolution of the data and the rate at which the dependent variable changes with respect to the independent variable. 3. Determination of the differences between the definite integrals on the rising and falling curves computed for the same intervals, \([i,j]\):  
\[\Delta A_{[i,j]}=A_{r[i,j]}-A_{f[i,j]} \tag{6}\]  
Clockwise loops have all \(\Delta\text{A}[i,j]>0\), anticlockwise loops have all \(\Delta\text{A}[i,j]<0\), linear relations (no hysteresis) have all \(\Delta\text{A}[i,j]=0\), while eight-shaped hysteretic patterns are characterized by \(\Delta\text{Amin}<0\) and \(\Delta\text{A}\text{A}\text{A}\text{A}\  
The degree of slope exhibited by Ciciriello river basin headwater varied from 0 to 64, as shown in Figure 7. The slope map distribution of the whole catchment (Figure 7b) and of the left side (Figure 7b1) were positive skewed. A normal distribution, instead, is shown in Figure 7b2 for the right side. The slope map is quite different between the right and left side, where the detected maximum values were, respectively, 57 and 63 degrees, and the average ones were 21 and 28, respectively. The classified map (Figure 7c) shows a major presence of lands with a slope between 15 and 25 degrees. The left side (Figure 7c1) shows a high presence of hillslope with a slope between 14 and 20 degrees, while the major slope on the right hand (Figure 7c2) ranged between 25 and 35 degrees. Figure 6: Elevation map classification derived by the Regional Technical Map (CTR) (**a**), frequency distribution on the un-classified elevation map on the catchment (**b**) and on the left (**b1**) and right side of the catchment (**b2**). Frequency distribution on the classified elevation map (**c**) and on the left (**c1**) and right side of the catchment (**c2**).