Long time series of volcanic radiative forcing

To study the volcanic influence on climate on a historical time scale, it is necessary to provide long time series of volcanic forcing. This problem is matched with the question of missing observations. Therefore Simkin et al. (1981) define a reporting index which is the number of volcanoes active per decade as a percentage of the number of volcanoes known at the start of each decade. Their reporting index, covering the last 600 years, shows 3 quasi-constant levels with two jumps in between. The first level is before 1500. Then knowledge of volcanoes increased dramatically so that a second level is reached lasting until the mid of the 18th century where the second jump leads to the third level. Thus, to avoid the influence of incomplete observation, we study forcing time series only since 1500. In principle, it would be no problem to estimate volcanic $AOD$ and forcing time series from the beginning of the $VEI$ series (about 10.000 years ago) where only coarse information about few eruptions is available: For the first 5 centuries A.D. only 6 eruptions with $VEI$=6 are reported by Simkin et al. (1981). During the second and third 5 centuries A.D. only 2 eruptions with $VEI \ge 6$ are reported. Furthermore it is important to know not only the year of eruption but also the month to make reasonable use of the aerosol-transport and radiation-transfer parameterization. Even for strong eruptions occurring before the last century this information is often not available. In order to investigate the lack of information about the month of eruption we compare the volcanic forcing of the Billy Mitchell eruption (Bougainville, 6.1$^{\circ}$ S, 155$^{\circ}$ E) in 1580 for the case that the eruption with $VEI=6$ occurred in January with the case that the eruption occurred in July. The results are given in Figure 7. It can clearly be seen, that the knowledge of the date of eruption (at least the month) is important to quantify the spatio-temporal patterns of the forcing. Therefore, evaluating long time series of volcanic forcing in the desired spatio-temporal resolution, needs further knowledge of the date of eruption. Although the spatio-temporal patterns of the forcing depend strongly on the month of eruption, a three-year average forcing (year of eruption and following 2 years) depends not significantly on the eruption date as can be seen in Table 7. The $t$-value for a significant difference on the 80% level is 1.294 which is not exceeded by any of the different average values given in Table 7. Thus, if we are only interested in volcanic forcing time series of a three year average and 4 latitude belts, we can estimate the forcing even if we know only the year of eruption but not the month. Annually averaged values of estimated volcanic forcing since 1500 are given in Figure 8.