#### Analysis of UVB irradiance values

The study of the most representative statistical indices of UVB irradiance has been carried out for all the measurement stations. Monthly statistics for the whole measurement period (2000–2009) were calculated using daily values. The most representative statistical indices are analyzed. The skewness (a measure of the asymmetry of the probability distribution of a real-valued random variable) and the kurtosis (a descriptor of the shape of the probability distribution) of the distribution have also been studied.

For all the 14 measurement stations, the monthly statistics have been analyzed. As an example, Tables 2 and 3 show the results obtained during July and December at solar noon. Those months usually present the highest and lowest records of UVB irradiance for all the stations (Table 4). Only in Barcelona the UVB irradiance is slightly higher in June than in July. The values of the arithmetic mean and the median (described as the numerical value separating the higher half of the probability distribution from the lower half) are very similar, with the difference between them following no pattern for any month. On July, these differences represent always <3% of the mean value (*e.g.* Madrid, Ciudad Real, Valencia and Murcia). In some stations, these relative differences reach values between 3% and 5% at the beginning and the end of the day, (*e.g.* A Coruña, Santander, Valladolid, Zaragoza, Badajoz, Palma de Mallorca, El Arenosillo and Málaga). There are some stations where these relative differences reach 3% and 4% only in specific cases at solar noon (Barcelona [twice], Roquetes and Badajoz [once]). On December, these differences are in all cases <3% at A Coruña, Santander, Palma de Mallorca, Ciudad Real, Badajoz and Murcia. Relative differences between 3% and 5% are observed close to sunrise and sunset in Barcelona, Madrid, Roquetes, Valencia and El Arenosillo. Differences greater than 3% and up to 7% were observed occasionally at noon at Zaragoza (once), Valladolid, Barcelona, Roquetes and Valencia (twice) and El Arenosillo (three times).

Table 2. Statistical indices of the hourly UVB irradiance, in July, at solar noon for each location. | Mean | SD | Median | Mx | Mn | *Q* _{1} | *Q* _{3} | *Q* _{3} − *Q*_{1} | *V* | P5 | P95 | Kurtosis | Skewness |
---|

A Coruña | 1255 | 128 | 1242 | 1544 | 1026 | 1169 | 1349 | 179 | 7.1 | 1099 | 1482 | −0.4 | −0.4 |

Santander | 1224 | 124 | 1217 | 1514 | 952 | 1126 | 1318 | 191 | 7.8 | 1054 | 1401 | −0.2 | −0.1 |

Valladolid | 1623 | 94 | 1646 | 1788 | 1375 | 1558 | 1692 | 133 | 4.1 | 1463 | 1737 | 0.3 | −0.7 |

Zaragoza | 1498 | 75 | 1525 | 1601 | 1341 | 1447 | 1563 | 115 | 3.8 | 1363 | 1591 | −0.7 | −0.6 |

Barcelona | 1317 | 110 | 1362 | 1460 | 1039 | 1274 | 1388 | 113 | 4.3 | 1089 | 1430 | 0.8 | −1.2 |

Madrid | 1665 | 64 | 1683 | 1769 | 1482 | 1625 | 1708 | 83 | 2.5 | 1567 | 1748 | 0.7 | −0.8 |

Roquetes | 1419 | 155 | 1466 | 1617 | 1007 | 1331 | 1521 | 189 | 6.6 | 1140 | 1612 | 0.5 | −1.0 |

Palma | 1451 | 102 | 1460 | 1608 | 1208 | 1382 | 1519 | 136 | 4.7 | 1287 | 1604 | −0.4 | −0.3 |

Valencia | 1389 | 80 | 1410 | 1515 | 1206 | 1339 | 1449 | 110 | 4.0 | 1258 | 1507 | −0.6 | −0.4 |

Ciudad real | 1726 | 87 | 1753 | 1855 | 1486 | 1671 | 1793 | 121 | 3.5 | 1574 | 1824 | 1.0 | −1.0 |

Badajoz | 1680 | 69 | 1697 | 1793 | 1479 | 1657 | 1727 | 69 | 2.1 | 1549 | 1751 | 1.7 | −1.2 |

Murcia | 1584 | 75 | 1589 | 1687 | 1350 | 1561 | 1629 | 68 | 2.1 | 1459 | 1685 | 2.5 | −1.2 |

Arenosillo | 1644 | 113 | 1675 | 1825 | 1346 | 1593 | 1727 | 133 | 4.0 | 1410 | 1781 | 1.3 | −1.1 |

Malaga | 1564 | 77 | 1585 | 1679 | 1358 | 1524 | 1604 | 79 | 2.6 | 1404 | 1665 | 1.5 | −1.1 |

Table 3. Statistical indices of the hourly UVB irradiance, in December, at solar noon for each location. | Mean | SD | Median | Mx | Mn | *Q* _{1} | *Q* _{3} | *Q* _{3} − *Q*_{1} | *V* | P5 | P95 | Kurtosis | Skewness |
---|

A Coruña | 160 | 23 | 166 | 374 | 112 | 211 | 315 | 103 | 19.7 | 167 | 359 | −0.8 | 0.1 |

Santander | 168 | 21 | 169 | 400 | 138 | 194 | 283 | 88 | 18.6 | 154 | 329 | −0.1 | 0.5 |

Valladolid | 209 | 23 | 208 | 514 | 161 | 257 | 394 | 136 | 20.9 | 182 | 466 | −0.9 | 0.1 |

Zaragoza | 217 | 29 | 217 | 543 | 198 | 285 | 410 | 124 | 17.8 | 222 | 492 | −0.2 | 0.4 |

Barcelona | 218 | 23 | 213 | 527 | 242 | 289 | 399 | 109 | 15.9 | 254 | 496 | 0.0 | 0.9 |

Madrid | 238 | 20 | 236 | 517 | 213 | 315 | 459 | 144 | 18.7 | 235 | 508 | −1.0 | 0.1 |

Roquetes | 218 | 47 | 220 | 525 | 253 | 337 | 436 | 98 | 12.7 | 288 | 506 | −0.6 | 0.0 |

Palma | 268 | 33 | 272 | 491 | 262 | 336 | 402 | 65 | 8.8 | 301 | 476 | −0.2 | 0.4 |

Valencia | 238 | 31 | 245 | 538 | 254 | 329 | 418 | 88 | 11.8 | 268 | 488 | −0.2 | 0.3 |

Ciudad real | 286 | 23 | 280 | 649 | 260 | 371 | 519 | 148 | 16.7 | 293 | 588 | −0.5 | 0.2 |

Badajoz | 275 | 36 | 276 | 595 | 271 | 371 | 492 | 121 | 14.0 | 298 | 571 | −0.7 | 0.2 |

Murcia | 307 | 31 | 312 | 636 | 335 | 401 | 503 | 101 | 11.2 | 338 | 582 | −0.2 | 0.5 |

Arenosillo | 348 | 53 | 359 | 695 | 300 | 432 | 590 | 157 | 15.4 | 321 | 680 | −0.8 | 0.1 |

Malaga | 343 | 34 | 340 | 655 | 364 | 425 | 542 | 117 | 12.1 | 373 | 605 | −0.9 | 0.2 |

Table 4. Monthly mean values of UVB irradiance (in mW m^{−2}) at solar noon for each location. | A Coruña | Santander | Valladolid | Zaragoza | Barcelona | Madrid | Roquetes | Palma | Valencia | Ciudad real | Badajoz | Murcia | Arenosillo | Malaga |
---|

January | 188 | 186 | 237 | 237 | 272 | 286 | 279 | 320 | 293 | 332 | 325 | 370 | 416 | 431 |

February | 350 | 321 | 464 | 460 | 418 | 479 | 411 | 464 | 459 | 561 | 510 | 564 | 570 | 612 |

March | 584 | 593 | 777 | 740 | 693 | 803 | 749 | 768 | 738 | 896 | 862 | 862 | 893 | 909 |

April | 853 | 864 | 1001 | 1018 | 943 | 1065 | 978 | 1024 | 981 | 1157 | 1100 | 1102 | 1137 | 1136 |

May | 1062 | 1041 | 1251 | 1234 | 1145 | 1286 | 1148 | 1228 | 1130 | 1345 | 1328 | 1292 | 1324 | 1301 |

June | 1215 | 1174 | 1569 | 1463 | 1348 | 1538 | 1408 | 1418 | 1346 | 1630 | 1557 | 1548 | 1549 | 1529 |

July | 1255 | 1224 | 1623 | 1498 | 1317 | 1665 | 1419 | 1451 | 1389 | 1726 | 1680 | 1584 | 1644 | 1564 |

August | 1177 | 1107 | 1472 | 1347 | 1207 | 1521 | 1347 | 1297 | 1237 | 1589 | 1510 | 1439 | 1564 | 1387 |

September | 887 | 900 | 1119 | 1074 | 892 | 1138 | 986 | 996 | 942 | 1226 | 1187 | 1095 | 1085 | 1166 |

October | 433 | 509 | 635 | 660 | 598 | 688 | 678 | 711 | 649 | 785 | 745 | 760 | 771 | 822 |

November | 259 | 238 | 329 | 351 | 342 | 370 | 393 | 374 | 374 | 440 | 444 | 450 | 510 | 486 |

December | 160 | 168 | 209 | 217 | 218 | 238 | 218 | 268 | 238 | 286 | 275 | 307 | 348 | 343 |

In July, the absolute maxima oscillate between 1460 mW m^{−2} in Barcelona and 1855 mW m^{−2} in Ciudad Real, whereas the absolute minima vary from 953 mW m^{−2} in Santander to 1486 mW m^{−2} in Ciudad Real. The difference (in percentage) between the values of the absolute minimum and the P_{5} percentile vary between 1.9% (Valencia) and 12.5% (Murcia). These are systematically larger than those observed between the absolute maxima and P_{95} percentiles, which vary between 0.3% (Badajoz) and 7.0% (Santander). The absolute extreme values (maximum and minimum) have been compared against their corresponding quartile values (*Q*_{3} and *Q*_{1}, respectively) to understand if they are representative of the UVB records for all the stations. The differences between the *Q*_{1} quartiles and the absolute minima vary from 7% (Madrid) to 21% (Roquetes), with a mean value of 12%. The mean value of the difference between the *Q*_{3} quartiles and the absolute maxima is 5%, and oscillates between 2% (Valladolid) and 12% (Santander). Therefore, these maximum and minimum values can be considered representative of the UVB irradiance at solar noon as they are not uncommon extreme values for July.

In December, the absolute maxima of the UVB irradiance observed at noon vary from 374 mW m^{−2} in A Coruña to 696 mW m^{−2} in El Arenosillo, whereas the absolute minima are between 112 mW m^{−2} in A Coruña and 365 mW m^{−2} in Malaga. As it happened for July, the difference between the values of the absolute minimum and the P_{5} percentile is systematically larger than that observed between the absolute maxima and P_{95} percentiles. These differences vary from 1.5% (Madrid) to 17% (Santander), with a mean value of 6.6% (for the absolute minima and P_{5}), and from 1% (Murcia) to 49% (A Coruña), with a mean value of 11.7% (for the absolute maxima and P_{95}). The comparison of the extreme values with their corresponding quartiles shows a mean value of 39% for the difference between the *Q*_{1} quartiles and the absolute minima, and a variation between 10% (Barcelona) and 88% (A Coruña). The differences between the *Q*_{3} quartiles and the absolute maxima oscillate from 11% (Madrid) to 29% (Santander), and show a mean value of 19%. These values are greater than those observed in July, indicating that the extreme values of the UBV irradiance at solar noon are less representative in December than in July.

The coefficient of interquartilar variation (*V* index, defined as *V* = 100 (*Q*_{3} − *Q*_{1})/(*Q*_{3} + *Q*_{1})), which is a nonparametric measurement that does not depend on the shape of the population distribution, has been used to study the variability of the UVB irradiance at solar noon. It can be observed that July presents low values of the *V* index, meaning high stability, that fluctuate between 2.1 in Badajoz and Murcia and 7.8 in Santader, with a mean value of 4.2. Less stability is observed in December, with the *V* index varying from 8.8 in Palma de Mallorca to 20.9 in Valladolid, with a mean value of 15.3. This higher value of the *V* index in December is due to the major presence of clouds during winter, leading to less stability in the UVB levels.

The skewness in July is low, and always displays negative values, indicating that the UVB irradiance values at noon are slightly shifted to the left of the arithmetic mean. It exceeds the unity only in Roquetes and Ciudad Real (−1.0), El Arenosillo and Málaga (−1.1) and Barcelona, Badajoz and Murcia (−1.2). In December, the skewness is lower than that obtained in July, and always displays positive values, which indicates that the UVB irradiance values at solar noon are slightly shifted to the right of the arithmetic mean. It only displays a value greater than 0.5 in Barcelona (with a value of 0.9).

The kurtosis in July displays values generally <1 for all the stations. It only takes values >1 in the southern part of the Iberian Peninsula: Ciudad Real (1.0), Badajoz (1.7), Murcia (1.5), El Arenosillo (1.3) and Málaga (1.5). In those cases, the distribution function of the UVB irradiance is leptokurtic, with most data close to the mean value and a larger peak than the normal distribution. In December, the kurtosis reaches unity only in Madrid (−1.0). In this month, the UVB irradiance distribution function is always platykurtic, with the data showing a weaker peak than the normal distribution function.

For each station, we have calculated the monthly averages of the hourly mean values of the UVB irradiance. The daily evolution of these values for the period 2000–2009 for all the stations shows great symmetry respect to the maximum value is observed. In all cases, the peak irradiance is placed at solar noon in July, except in Barcelona, where it is observed in June. The minimum values are obtained in all cases in December. As an example, Fig. 1 shows the daily evolution of monthly mean hourly values of UVB irradiance (mW m^{−2}) during the period 2000–2009, in Barcelona and Málaga.

#### Analysis of UVB radiant exposure values

The most representative statistical indices of daily integrated values of the UVB radiant exposure in kJ m^{−2} have also been analyzed for all the 14 stations, similarly to the hourly irradiance analysis. The median and the arithmetic mean values are very much alike. The differences between them do not seem to follow any pattern, except that the average is always greater than the median. The relative differences range from 2% in Málaga to 10% in El Arenosillo (Huelva), with an average of 6%.

The absolute maximum values oscillate between 33966 J m^{−2} in Santander and 44122 J m^{−2} in Valencia, both in July. The Zaragoza, Madrid, Palma de Mallorca and El Arenosillo (Huelva) stations have values above 40000 J m^{−2} in June and July, as well as Valencia in June, July and August. On the other hand, the absolute minimum values oscillate between 1795 J m^{−2} in A Coruña and 6362 J m^{−2} in Málaga, both in December. The differences between the absolute minima and the P_{5} percentiles (in percentage) are significantly higher than those between the absolute maxima and the P_{95} percentiles. In the first case, the differences range from 15% (Valencia) to 54% (El Arenosillo), whereas in the second case the differences are comprised between 4% (Badajoz) and 13% (Santander).

To check whether the absolute extreme values (maximum and minimum) are representative of the stations we have compared them with their respective quartiles (*Q*_{3} and *Q*_{1}, respectively). The differences between the *Q*_{1} quartiles and the minima range from 80% (Malaga) to 192% (A Coruña and Zaragoza), with an average of 138%, which means that the minima are atypical values of the UVB radiant exposure for all the stations. The differences between the *Q*_{3} quartiles and the maxima oscillate between 21% (Murcia and Málaga) and 30% (Santander and Barcelona), with an average of 25%, indicating that the maxima cannot be considered representative of the UVB radiant exposure at solar noon for all the stations.

The variability of the UVB radiant exposure has been assessed by means of the *V* index, which fluctuates between 2.0 (Valladolid and Palma de Mallorca) and 7.0 (Roquetes, Tarragona), with an average of 3.6. The *V* index reaches its lowest value during summer, implying higher stability of the UVB radiant exposure, which could be due to a lesser presence of clouds during summer for all the stations.

The skewness is very low. The average values range between 0.1 and 0.3, with monthly peaks between 1.2 and −2.1. The whole set of values is slightly above the average for all the stations. Although the distribution is random, it exhibits a positive asymmetry. On the other hand, the kurtosis is also random for some stations at particular months. The average for each station is around −1.4, therefore the distribution is platykurtic. This means that the distribution has a flatter peak around its mean, which causes thin tails within the distribution.

We have calculated the radiant exposure values at each station for an average year. For this, we have used daily averages for the whole 10-year database. The daily values of the UVB radiant exposure for this average year show large shifts, suggesting that the prediction of radiant exposure is not possible on a daily scale. The monthly mean values of the UVB radiant exposure present a quite regular, but asymmetrical variation, with the maximum values occurring in June and July, whereas the minimum values occur in December. The drop in the summer–autumn period (August–November) is considerably steeper than the rise in the winter–spring period (February–June). This unevenness suggests the use of median values instead of arithmetic mean values in the statistical analysis of the data. As an example, Fig. 2 shows the annual evolution of daily mean values and monthly mean daily values of UVB radiant exposure (J m^{−2}) during the period 2000–2009, in Málaga.

In the study of the biological effects of UVB radiation, it can be interesting to know the accumulated UVB solar radiant exposure (J m^{−2}) on a time period. In our case, the accumulated UVB hourly values exceed 40000 J m^{−2} in July for the Madrid, Valencia and Palma de Mallorca stations, whereas in December only the Malaga station is above 5000 J m^{−2}. We can conclude that the maximum monthly radiant exposure occurs in July, except for Barcelona station where it happens in June. On the other hand, the minimum radiant exposure occurs in December for all stations. We have also studied the mean daily values of the accumulated UVB radiant exposure for an average year. The values oscillate between 5400 kJ m^{−2} in Santander and 7800 kJ m^{−2} in Ciudad Real (Fig. 3).

To study the differences between the measurement stations we have created a standard year for each of them using cumulated daily values of UVB radiant exposure obtained adding up the hourly mean values calculated from the 10 year data, and then we have calculated the linear regressions for the comparison of each station with Malaga, which is considered as the reference because it is the one with the lowest latitude. Figure 4 shows the slopes of the linear least squares fittings obtained (with *R*^{2} > 0.93 for all cases). The slopes for the stations close to the coast present values below 1, which indicates lower values of UVB radiant exposure than those obtained in Malaga, with values between 1% lower for Palma and 14% lower for Santander. On the contrary, the slopes for the stations located inland show values above 1, indicating greater values of UVB radiant exposure than those obtained in Malaga, with values between 3% higher for Murcia and 15% higher for Ciudad Real. These results agree with the distribution of the mean values obtained previously, and with the continentality effect, which causes that the values inland are lower than in the coast.