Abstract. The eruption of Eyjafjallajökull volcano in 2010 lasted for 39 days, 14 April–23 May. The eruption had two explosive phases separated by a phase with lava formation and reduced explosive activity. The height of the plume was monitored every 5 min with a C-band weather radar located in Keflavík International Airport, 155 km distance from the volcano. Furthermore, several web cameras were mounted with a view of the volcano, and their images saved every five seconds. Time series of the plume-top altitude were constructed from the radar observations and images from a web camera located in the village Hvolsvöllur at 34 km distance from the volcano. This paper presents the independent radar and web camera time series and performs cross validation. The results show good agreement between the time series for the range when both series are available. However, while the radar altitudes are semi-discrete the data availability was much higher than for the web camera, indicating how essential weather radars are as eruption plume monitoring devices. The echo top radar series of the altitude of the volcanic plume are publicly available from the Pangaea Data Publisher (http://dx.doi.org/10.1594/PANGAEA.760690).

Magma flow during volcanic eruptions causes surface deformation that can be used to constrain the location, geometry and internal pressure evolution of the underlying magmatic source 1 . The height of the volcanic plumes during explosive eruptions also varies with magma flow rate, in a nonlinear way 2,3 . In May 2011, an explosive eruption at Grímsvötn Volcano, Iceland, erupted about 0.27 km 3 denserock equivalent of basaltic magma in an eruption plume that was about 20 km high. Here we use Global Positioning System (GPS) and tilt data, measured before and during the eruption at Grímsvötn Volcano, to show that the rate of pressure change in an underlying magma chamber correlates with the height of the volcanic plume over the course of the eruption. We interpret ground deformation of the volcano, measured by geodesy, to result from a pressure drop within a magma chamber at about 1.7 km depth. We estimate the rate of magma discharge and the associated evolution of the plume height by differentiating the co-eruptive pressure drop with time. The time from the initiation of the pressure drop to the onset of the eruption was about 60 min, with about 25% of the total pressure change preceding the eruption. Near-real-time geodetic observations can thus be useful for both timely eruption warnings and for constraining the evolution of volcanic plumes.

Abstract. The eruption of Eyjafjallajökull volcano in 2010 lasted for 39 days, 14 April–23 May. The eruption had two explosive phases separated by a phase with lava formation and reduced explosive activity. The height of the plume was monitored every 5 min with a C-band weather radar located in Keflavík International Airport, 155 km distance from the volcano. Furthermore, several web cameras were mounted with a view of the volcano, and their images saved every five seconds. Time series of the plume-top altitude were constructed from the radar observations and images from a web camera located in the village Hvolsvöllur at 34 km distance from the volcano. This paper presents the independent radar and web camera time series and performs cross validation. The echo top radar series of the altitude of the volcanic plume are publicly available from the Pangaea Publishing Network (http://doi.pangaea.de/10.1594/PANGAEA.760690).

S U M M A R YWe have developed a new robust maximum likelihood method for estimating the unbiased mean inclination from inclination-only data. In paleomagnetic analysis, the arithmetic mean of inclination-only data is known to introduce a shallowing bias. Several methods have been introduced to estimate the unbiased mean inclination of inclination-only data together with measures of the dispersion. Some inclination-only methods were designed to maximize the likelihood function of the marginal Fisher distribution. However, the exact analytical form of the maximum likelihood function is fairly complicated, and all the methods require various assumptions and approximations that are often inappropriate. For some steep and dispersed data sets, these methods provide estimates that are significantly displaced from the peak of the likelihood function to systematically shallower inclination. The problem locating the maximum of the likelihood function is partly due to difficulties in accurately evaluating the function for all values of interest, because some elements of the likelihood function increase exponentially as precision parameters increase, leading to numerical instabilities. In this study, we succeeded in analytically cancelling exponential elements from the log-likelihood function, and we are now able to calculate its value anywhere in the parameter space and for any inclination-only data set. Furthermore, we can now calculate the partial derivatives of the log-likelihood function with desired accuracy, and locate the maximum likelihood without the assumptions required by previous methods. To assess the reliability and accuracy of our method, we generated large numbers of random Fisher-distributed data sets, for which we calculated mean inclinations and precision parameters. The comparisons show that our new robust Arason-Levi maximum likelihood method is the most reliable, and the mean inclination estimates are the least biased towards shallow values.

Volcanic lightning has intrigued observers through the centuries. Several likely processes have been proposed to explain the electrification of volcanic plumes, including quenching magma‐water interactions, the fracturing or internal friction of fine grained ash, and the freezing of plume water at height. Scarce measurements of volcanic lightning have not been able to distinguish between proposed ideas. The Eyjafjallajökull volcanic eruption in Iceland in April–May 2010 may have revealed its charge mechanism. During its 39 days, the eruption went through a few phases while the conditions of the ambient atmosphere also changed, but at different times. The most surprising change in the lightning activity occurred on 11 May, with no obvious change in the physical eruption character or strength. During 3–10 May there was no lightning recorded by long‐range networks, followed by intense activity 11–20 May. The change in lightning activity coincided with a change in the conditions of the ambient atmosphere. At this time the altitude of the isotherms for droplet freezing (about −20°C) dropped drastically below the plume top. Therefore, it appears that the atmospheric conditions around the plume were influencing or even controlling some of the lightning activity. The critical plume top temperature, which appears to have turned on and off the observed lightning activity during the Eyjafjallajökull eruption is estimated to be between −20° and −24°C. We conclude that a significant charge generation process of the observed volcanic lightning is probably analogous to processes in meteorological thunderclouds.