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This paper demonstrates the usefulness of approaching the dynamic study of the precise positioning of a network of permanent global positioning system (GPS) stations through functional data analysis. The displacement data for each GPS station, obtained from observations of the global navigation satellite system, are a discrete sample of the positioning curve. The aim of this paper is to reconstruct the original functions in order to use them as functional data. In the method presented in this paper, the geodetic series are obtained first by processing the GPS data with respect to a reference station. Second, for each station, a cleaning process is applied to eliminate the values considered as outliers, and the missing values are imputed by using a Kalman filter. Finally, the original functions are reconstructed by using smoothing techniques and by evaluating several bases of functions. Moreover, these functions are treated with statistical techniques for functional data. This procedure is applied to the permanent stations of the south of the Iberian peninsula and the north of Africa (SPINA) network. The topocentric series: east, north and up are analysed. In the analysis of the positioning curves, there is observed a synchronized behaviour of the functions in those periods of time with important seismic activity. This behaviour also appears in the analysis of the second principal component of the East and up dimensions. Furthermore, the first two principal components of the East coordinate enable us to make a classification of the stations in the SPINA network. The classification made is consistent with the previous knowledge of the tectonic plates in the studied area.

Traditionally volcanic-hazard assessments have been applied to stratovolcanoes, where volcanic hazard maps represent important tools for volcanic crisis management and land-use planning. In recent years, several improvements have been made for monogenetic volcanic fields focused on, among other things, the development of spatial models to deal with one of the main problems in these areas, namely the unknown vent location. However, volcanic hazard maps of monogenetic volcanic fields present some significant differences with respect to those developed for stratovolcanoes, including the fact that they commonly represent multiple eruptive processes spread over the possible vent opening area. Likewise, the scientific communication of the volcanic-hazard assessment and how this information is comprehended are critical issues in the development of mitigation strategies for monogenetic volcanic fields. In this research, we focused on developing volcanic hazard maps using simple numerical hazard models in combination with a random approach for vent location to cover the whole vent opening area. We added some spatial methods to better manage potentially affected areas. The maps were designed for use in a digital environment (Geographic Information System) by Civil Protection professionals in high-risk monogenetic volcanic fields on small oceanic islands. The methodology presented does not use susceptibility base maps for hazard assessment to avoid possible underestimation of low probability areas by Civil Protection. The methodology represents an attempt to respond to the most important questions of where, when and how a new eruption might take place in a monogenetic volcanic field. The example presented here was developed for La Palma (Canary Islands).

The 2011 volcanic unrest at El Hierro Island illustrated the need for a Volcanic Alert System (VAS) specifically designed for the management of volcanic crises developing after long repose periods. The VAS comprises the monitoring network, the software tools for analysis of the monitoring parameters, the Volcanic Activity Level (VAL) management, and the assessment of hazard. The VAS presented here focuses on phenomena related to moderate eruptions, and on potentially destructive volcano-tectonic earthquakes and landslides. We introduce a set of new data analysis tools, aimed to detect data trend changes, as well as spurious signals related to instrumental failure. When data-trend changes and/or malfunctions are detected, a watchdog is triggered, issuing a watch-out warning (WOW) to the Monitoring Scientific Team (MST). The changes in data patterns are then translated by the MST into a VAL that is easy to use and understand by scientists, technicians, and decision-makers. Although the VAS was designed specifically for the unrest episodes at El Hierro, the methodologies may prove useful at other volcanic systems.

El Hierro Island in the Canary Archipelago recently experienced a submerged eruption a few kilometers off its southern shore, detected 2011 October 10 on the island’s south-rift alignment. The seismic activity suddenly increased around mid 2011 July, and ground deformation was then detected on the only geodetic benchmark that is continuously observed by global navigation satellite systems techniques and provides public data access. Based on that information, several other global navigation satellite system signal receivers were deployed on the island to provide continuous observation. For data collected by these receivers, a processing strategy was applied to achieve millimeter-level half-hourly positioning solutions. Position updates every 24 h are satisfactory to determine tectonic-plates’ velocities. Updates near 1 s or less are required to characterize seismic waves. In between, minute-level updates are well suited for monitoring active volcano's inflation or deflation, providing an optimal time resolution of the local ground deformation. In half-hourly positioning solutions, the heterogeneous satellites’ distribution in their orbital planes gives different constraints during satellite-constellation revolution, which can bias the solutions. Also, several geophysical influences can bias the solutions, including those related to gravitational movements. These influences have mostly semi-diurnal periodicities and may be considered Gaussian colored noise on the position’s time series. Daily solutions that average out these influences can be applied in active volcanoes, but they can impose some limitations because they average the daily deformation, and the update waiting time is not suitable when near real-time surveillance is mandatory. These semi-diurnal biases do need to be removed or minimized to achieve millimeter-level sub-daily positioning solutions, however, and to do so, a discrete Kalman filter was applied to enhance the half-hourly positioning solutions required during El Hierro’s 2011–2012 unrest and eruption. Throughout El Hierro’s volcanic activity, there were correlations between ground deformation and seismic activity. Many times the deformation preceded the earthquakes, though at other times the seismic activity was followed by the ground deformation response. This correlation is the outcome of ground deformation taking place as the result of energy accommodation, whereas seismic events correspond to energy release. Hence, those observed correlations indicate that the Kalman filter-enhanced half-hourly positioning solutions measured local ground deformation accurately; they were not a mathematical "trick" producing a spurious precision.

Deception Island is one of the most visited places in Antarctica. There are biological, geological, and archeological features that are major attractions within Port Foster, its horse shoe-shaped natural inner bay, and two scientific bases that are occupied during austral summers. Deception Island is an active volcano, however, and needs to be monitored in order to reduce risk to people on the island. Surface deformation in response to fluid pressure is one of the main volcanic activities to observe. Automated data acquisition and processing using the global navigation satellite systems allow measurements of surface deformation in near real time. Nevertheless, the positioning repeatability in sub-daily solutions is affected by geophysical influences such as ocean tidal loading, among others. Such periodic influences must be accurately modeled to achieve similar repeatability as daily solutions that average them. However, a single solution each 24 h will average out the deformation suffered during that period, and the position update waiting time can be a limitation for near real-time purposes. Throughout the last five austral summer campaigns in Deception, using simultaneous wireless communications between benchmarks, a processing strategy was developed to achieve millimeter-level half-hourly positioning solutions that have similar repeatability as those given by 24-h solutions. For these half-hourly solutions, a tidal analysis was performed to assess any mismodeling of ocean tide loading, and a discrete Kalman filter was designed and implemented to enhance the sub-daily positioning repeatability. With these solutions, the volcano-dynamic activity resulting in localized surface deformation for the last five austral summer campaigns is addressed. Although based on only three carefully located benchmarks, it is shown that Deception has been shortening and subsiding during these last 4 years. The method’s accuracy in baselines up to a few hundred kilometers assures its applicability to other volcanoes worldwide.