# The Calculated Circadian Effects of Light Exposure from Commuting
## 2 Materials and Methods
### Calculations of the Circadian Effects of Lights
#### 2.2.2 Circadian Stimulus  
Another method for quantifying the circadian impact of light is through the circadian stimulus (_CS_) [17; 18]. _CS_ represents the percentage of melatonin suppression evoked by light [24]. The non-linear model was initially developed based on spectral sensitivity data published by several researchers [25; 26], and the model has been modified multiple times since it was initially proposed [18]. Instead of modeling the five different spectral sensitivity functions--one for each photoreceptor type--_CS_ quantifies the total circadian effect from light. Given the SID, _CS_ can be calculated with Equations (2) and (3):  
\[CS=0.7-\frac{0.7}{1+\left(\frac{CL_{A}}{355.7}\right)^{1.1026}} \tag{2}\]  
\[CL_{A}=\left\{\begin{array}{c}1  
cloudy group, and the total for each commuting mode. In total, 732 SID measurements were collected during these 21 trips. Table 3 shows the number of SID measurements that were taken for each commuting mode in the different weather conditions, reflecting the uneven sample size of each group. Figure 3 shows the representative relative spectral power distributions measured for each of the three commuting modes for the two weather conditions. It is clear that the interior lighting in the trains dominates daylight, as the spectral power distributions for the train trips predominately correspond to those of white light-emitting diodes (LEDs). The average values and standard deviations for the illuminance, the five \(\alpha\)-optic irradiances (S-cone, M-cone, L-cone, rhodopic, and melanopic), CS, and EML for each of the three commuting modes are shown in Table 4. The table also distinguishes the results for the sunny and cloudy weather conditions. Box plots of the measured corneal illuminances and the five calculated \(\alpha\)-opic irradiance values are shown in Figure 4. One-way analysis of variance (ANOVA) tests (\(p<0.05\)) of the illuminance and the five \(\alpha\)-optic irradiances were performed in MATLAB to determine whether there are statistically significant differences between the different modes of commuting in different weather conditions. Any significant differences (\(p<0.05\)) are denoted with asterisks in Figure 4. The average illuminances and the average \(\alpha\)-optic irradiances are higher for the sunny weather conditions than the cloudy conditions for each mode of commuting. The average illuminances and average \(\alpha\)-optic irradiances are highest for the walking mode of commuting, while driving resulted in the lowest light exposure. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Driving** & **Train** & **Walking** \\ \hline Sunny & 5 & 4 & 5 \\ Cloudy & 2 & 3 & 2 \\ Total & 7 & 7 & 7 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The number of trips for each commuting mode in different weather conditions. Figure 3: _Cont._ \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Driving** & **Train** & **Walking** \\ \hline Sunny & 222 & 69 & 116 \\ Cloudy & 97 & 195 & 33 \\ Total & 319 & 264 & 149 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of SID measurements for each commuting mode in different weather conditions.