## 2 Materials and Methods
### Development of ANN Model for Predicting HM Concentrations
#### 2.6.2 Selection of Variables for the Model  
To predict HM concentrations in stormwater, the general formula was used:  
\[\text{HMC(t)}=\text{f}\left(\text{t}_{\text{s}}\text{,}\text{G}\text{,}\text{ A}\text{,}\text{Z}_{\text{i}}\text{,}\text{Q}\text{,}\text{P}_{\text{i}}\text{,} \text{t}_{\text{r}}\text{,}\text{t}_{\text{bd}}\text{,}\text{V}_{\text{i}} \text{,}\text{T}\text{,}\text{w}\text{,}\text{T}_{\text{sn}}\text{,}\text{T} _{\text{f}}\right)\text{,} \tag{1}\]  
where HMC (t)--heavy metal concentrations in time t, G--event type (rainfall, snowmelt), A--catchment area; Z;--land use; Q--stormwater flow rate in the SWTP gauging section of the analysed  
Figure 2: Methodology of the development of multi-layer perceptron (MLP) model for predicting the selected pollutant concentrations in stormwater.  
catchment; P\({}_{\rm i}\), t\({}_{\rm r}\), b\({}_{\rm bd}\)--variables describing rainfall characteristics, including P\({}_{\rm i}\) (total depth--P\({}_{\rm tot}\), maximum ten minutes rainfall depth--P\({}_{\rm(10)}\)); t\({}_{\rm r}\)--rainfall duration, t\({}_{\rm bd}\)--inter-event time; Vi, T, w, T\({}_{\rm sn}\), T\({}_{\rm f}\)--variables characterising meteorological conditions and air quality based on Vi--visibility, T--air temperature, w--wind speed, T\({}_{\rm sn,f}\)--number of days with snowfall (or fog) preceding the event and t\({}_{\rm s}\) --time measured from rainfall onset to the instant, for which stormwater quality is to be determined (precipitation events).  
In order to thoroughly identify the physics of the analysed phenomena, the following parameters were studied for the inter-event (rainless) period (t\({}_{\rm bd}\)): average values, variance in the values (x\({}_{\rm i}\)--independent variables found in Equation (1)) of visibility, wind speed and air temperature. The values of variance (range: from minimum to maximum) for individual variables in the period t\({}_{\rm bd}\) are as follows: visibility (0.65-72 km, mean 34 km), wind speed (0.3-30 m/s, mean 10 m/s) and air temperature (0.4-19.2 \({}^{\circ}\)C, mean 6.1 \({}^{\circ}\)C).  
Based on the measurements of the variables above x\({}_{\rm i}\) (t\({}_{\rm 0}\)) (where t\({}_{\rm 0}\) = 0 - t\({}_{\rm bd}\)), trends in variable changes were shown in the period of concern by determining the values of coefficients in the linear model (estimated with the least squares method) x\({}_{\rm i}\) = a\({}_{\rm i}\)t + b\({}_{\rm i}\) (Figure 3).  
The analyses demonstrated that the values of coefficient a = t\({}_{\rm g}\)\(\alpha\) range from \(-\)3.48 to 5.55, from \(-\)8.5 to 1.6, and from \(-\)2.85 to 1.4. These values indicate considerable variability of trends in changes in weather conditions during the analysed inter-event periods, which may have significant impact on pollutant deposition on the catchment surface.  
For snowmelt events, t is measured from the minimum flow value Q\({}_{\rm min}\) (t = 0), which is the basis for identifying a specific event of given character. HMC(t) values are calculated for successive values of Q(t+i) \(>\) Q\({}_{\rm min}\) obtained from the measurements in snowmelt events.  
Two hypotheses are formulated in the Fisher-Snedecor test: (i) the null hypothesis (H\({}_{\rm 0}\)), in which structural parameters are not significantly different from zero (\(\alpha_{\rm 1}\) = \(\alpha_{\rm 2}\) =... \(\alpha_{\rm k}\) = 0) and (ii) the alternative hypothesis (H\({}_{\rm A}\)), according to which at least one parameter is found that is significantly different from zero (\(\alpha_{\rm 1}\) \(\
eq\) 0, \(\alpha_{\rm 2}\) \(\
eq\) 0,..., \(\alpha_{\rm k}\) \(\
eq\) 0).