## 3 Statistical Analysis
### Hourly Values
#### 3.1.5 Estimated Net Shortwave Radiation (\(R_{ns}\))  
The short-wave input to a horizontal surface (\(G\)) consists of both direct-beam (\(B\)) and diffuse (\(D\)) radiation, so that \(G=B+D\). On a cloudless day, \(D\) is about 15-25% of \(G\) and the rest represent direct-beam radiation. The pattern of \(G\) is of course controlled by the azimuth and altitude of the Sun relative to the horizon, with a single peak at local solar noon. The azimuth and altitude are controlled by Earth-Sun geometrical relationships and vary with latitude, time of day, and date. The peak of \(G\) for a clear summer day is approximately 1000 W/m\({}^{2}\) and the peak of \(G\) for a winter clear day is about 550 W/m\({}^{2}\). On a cloudy day \(G\) is equal to \(D\). Then, the net short-wave radiation (\(R_{ns}\)) is given by:  
\[R_{ns}=G-R \tag{29}\]  
The reflected short-wave radiation (\(R\)) depends on the value of \(G\) and the surface albedo (\(\rho\)), so that:  
\[R=\rho*G \tag{30}\]  
Although \(\rho\) for most surfaces is not perfectly constant through the day, as a first approximation is a reduced mirror-image of \(G\). At this site the annual average of \(\rho\) is 0.17, so that approximately one sixth of \(G\) is lost through the ground reflection.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multicolumn{13}{c}{\(B_{n}\)[W/m\({}^{2}\)]} \\ \hline
**Month** & **N** & **Mean** & **StDev** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **N** & **Mean** & **StDev** & **Min** & **Q1** & **Median** & **Q3** & **Max** \\ \hline
1 & 1841 & 298 & 312 & 0 & 2 & 175 & 584 & 940 & 1841 & 130 & 156 & 0 & 1 & 53 & 235 & 546 \\
2 & 1796 & 467 & 331 & 0 & 87 & 547 & 771 & 960 & 1796 & 236 & 208 & 0 & 22 & 201 & 421 & 671 \\
3 & 2187 & 382 & 315 & 0 & 26 & 399 & 655 & 946 & 2187 & 225 & 220 & 0 & 6 & 167 & 399 & 744 \\
4 & 2318 & 424 & 315 & 0 & 76 & 461 & 716 & 945 & 2318 & 287 & 265 & 0 & 22 & 234 & 507 & 866 \\
5 & 2576 & 552 & 262 & 0 & 396 & 638 & 765 & 869 & 2576 & 389 & 267 & 0 & 133 & 399 & 632 & 832 \\
6 & 2548 & 571 & 280 & 0 & 399 & 671 & 790 & 930 & 2548 & 407 & 289 & 0 & 122 & 412 & 678 & 905 \\
7 & 2627 & 611 & 250 & 0 & 487 & 708 & 799 & 9917 & 2627 & 434 & 280 & 0 & 168 & 461 & 704 & 890 \\
8 & 2473 & 615 & 247 & 0 & 509 & 701 & 798 & 907 & 2473 & 418 & 266 & 0 & 166 & 447 & 665 & 845 \\
9 & 2197 & 526 & 232 & 0 & 395 & 614 & 707 & 834 & 2197 & 332 & 218 & 0 & 122 & 353 & 535 & 679 \\
10 & 2052 & 503 & 283 & 0 & 281 & 599 & 730 & 899 & 2052 & 274 & 204 & 0 & 75 & 268 & 457 & 697 \\
11 & 1821 & 293 & 300 & 0 & 0 & 175 & 603 & 874 & 1821 & 134 & 156 & 0 & 0 & 53 & 263 & 519 \\
12 & 1800 & 343 & 323 & 0 & 2 & 276 & 667 & 896 & 1800 & 143 & 153 & 0 & 0 & 76 & 289 & 473 \\ Year & 26,236 & 478 & 307 & 0 & 169 & 574 & 743 & 960 & 26,236 & 298 & 258 & 0 & 40 & 261 & 507 & 905 \\ \hline \multicolumn{13}{c}{_G[W/m\({}^{2}\)]_} \\ \hline
**Month** & **N** & **Mean** & **StDev** & **Min** & **Q1** & **Median** & **Q3** & **Max** & **N** & **Mean** & **StDev** & **Min** & **Q1** & **Median** & **Q3** & **Max** \\ \hline
1 & 1600 & 138 & 80 & 0 & 75 & 114 & 193 & 403 & 1600 & 311 & 177 & 7 & 156 & 287 & 461 & 737 \\
2 & 1594 & 125 & 77 & 0 & 68 & 104 & 160 & 444 & 1594 & 428 & 223 & 14 & 228 & 439 & 630 & 907 \\
3 Therefore, \(R_{ns}\) on a clear day is approximately of about 0.83 \(\times\)\(G\) in magnitude. The diurnal variation of \(R_{ns}\) for each month of the year is shown in Figure 19a. The maximum peak of \(R_{ns}\) in the summer months is about 750 W/m\({}^{2}\). The monthly variability of \(R_{ns}\) irradiances is shown in Figure 19b. High variability is observed in the summer months.