Ash In Atmosphere Research Articles

The effect of wind and plume height reconstruction methods on the accuracy of simple plume models — a second look at the 2010 Eyjafjallajökull eruption

Real-time monitoring of volcanic ash plumes with the aim to estimate the mass eruption rate is crucial for predicting atmospheric ash concentration. Mass eruption rates are usually assessed by 0D and 1D plume models, which are fast and require only a few observational input parameters, often only the plume height. A model’s output, however, depends also on the plume height data handling strategy (sampling rate, gap reconstruction methods and statistical treatment), especially in long-term eruptions with incomplete plume height records. To represent such an eruption, we used Eyjafjallajökull 2010 to test the sensitivity of six simple and two explicitly wind-affected plume models against 22 data handling strategies. Based on photogrammetric measurements, the wind deflection of the plume was determined and used to recalibrate radar-derived height data. The resulting data was then subjected to different data handling strategies, before being used as input for the plume models. The model results were compared to the erupted mass measured on the ground, allowing us to assess the prediction accuracy of each combination of data handling strategy and model. Combinations that provide highest prediction accuracies vary, depending on data coverage, eruption intensity and fragmentation mechanism. However, for this type of moderate-to-weak eruption (VEI 3 in terms of maximum intensity), the most important factor was found to be the prevailing wind speed. When wind speeds exceed 20 m/s, most combinations of strategies and models provide predictions that underestimate the erupted mass by more than 40%. Under such conditions, the optimal choice of data handling strategy and plume model is of particular importance.

Workflows for Construction of Spatio-Temporal Probabilistic Maps for Volcanic Hazard Assessment

Probabilistic hazard assessments for studying overland pyroclastic flows or atmospheric ash clouds under short timelines of an evolving crisis, require using the best science available unhampered by complicated and slow manual workflows. Although deterministic mathematical models are available, in most cases, parameters and initial conditions for the equations are usually only known within a prescribed range of uncertainty. For the construction of probabilistic hazard assessments, accurate outputs and propagation of the inherent input uncertainty to quantities of interest are needed to estimate necessary probabilities based on numerous runs of the underlying deterministic model. Characterizing the uncertainty in system states due to parametric and input uncertainty, simultaneously, requires using ensemble based methods to explore the full parameter and input spaces. Complex tasks, such as running thousands of instances of a deterministic model with parameter and input uncertainty require a High Performance Computing infrastructure and skilled personnel that may not be readily available to the policy makers responsible for making informed risk mitigation decisions. For efficiency, programming tasks required for executing ensemble simulations need to run in parallel, leading to twin computational challenges of managing large amounts of data and performing CPU intensive processing. The resulting flow of work requires complex sequences of tasks, interactions, and exchanges of data, hence the automatic management of these workflows are essential. Here we discuss a computer infrastructure, methodology and tools which enable scientists and other members of the volcanology research community to develop workflows for construction of probabilistic hazard maps using remotely accessed computing through a web portal.

Estimates of plume height from infrasound for regional volcano monitoring

Present efforts in volcano monitoring, particularly in Southeast Asia, rely on the combination of local data (generally gathered at less than 100 km from the volcano), and satellite remote sensing. While this combination has its strengths, there are still weaknesses that the use of ground-based remote sensing data - such as distant infrasound measurements - could help alleviate. Infrasound offers tools for detecting and characterizing volcanic plumes independent of cloud cover and time of day. Larger volcanic eruptions generate infrasound that is related to the plume and offers a unique view into eruption dynamics within the context of monitoring. Past research has demonstrated that infrasound can be used to estimate source parameters, such as the rate at which material is ejected from volcanic vents during eruptions; these are key input parameters into empirical and numerical models to estimate the height of volcanic plumes, atmospheric ash transport and dispersion. Here, we demonstrate the use of remote infrasound in estimating the height of volcanic plumes, including a case study on the May 30, 2014 plume from the volcano Sangeang Api in Indonesia. We were able to determine the plume height using infrasound gathered from 2000 to over 5000 km distance from the volcano. During the January 2020 eruption of Taal volcano in the Philippines, this method was applied to remote infrasound recorded 1650 km to the east. We show that our workflow can be implemented in near real-time, offering an effective tool for rapid plume height measurement, including associated uncertainties, when volcanic clouds are not visible from the ground or space.

Ensemble-Based Data Assimilation of Volcanic Ash Clouds from Satellite Observations: Application to the 24 December 2018 Mt. Etna Explosive Eruption

Accurate tracking and forecasting of ash dispersal in the atmosphere and quantification of its uncertainty are of fundamental importance for volcanic risk mitigation. Numerical models and satellite sensors offer two complementary ways to monitor ash clouds in real time, but limits and uncertainties affect both techniques. Numerical forecasts of volcanic clouds can be improved by assimilating satellite observations of atmospheric ash mass load. In this paper, we present a data assimilation procedure aimed at improving the monitoring and forecasting of volcanic ash clouds produced by explosive eruptions. In particular, we applied the Local Ensemble Transform Kalman Filter (LETKF) to the results of the Volcanic Ash Transport and Dispersion model HYSPLIT. To properly simulate the release and atmospheric transport of volcanic ash particles, HYSPLIT has been initialized with the results of the eruptive column model PLUME-MoM. The assimilation procedure has been tested against SEVIRI measurements of the volcanic cloud produced during the explosive eruption occurred at Mt. Etna on 24 December 2018. The results show how the assimilation procedure significantly improves the representation of the current ash dispersal and its forecast. In addition, the numerical tests show that the use of the sequential Ensemble Kalman Filter does not require a precise initialization of the numerical model, being able to improve the forecasts as the assimilation cycles are performed.

Modeling Ash Dispersal From Future Eruptions of Taupo Supervolcano

AbstractHazard analysis at caldera volcanoes is challenging due to the wide range of eruptive and environmental conditions that can plausibly occur during renewed activity. Taupo volcano, New Zealand, is a frequently active and productive rhyolitic caldera volcano that has hosted the world's youngest known supereruption and numerous smaller explosive events. To assess ashfall hazard from future eruptions, we have simulated atmospheric ash dispersal using the Ash3d model. We consider five eruption scenarios spanning magma volumes of 0.1–500 km3 and investigate the main factors governing ash dispersal in modern atmospheric conditions. Our results are examined in the context of regional synoptic weather patterns (Kidson types) that provide a framework for assessing the variability of ashfall distribution in different wind fields. For the smallest eruptions (~0.1‐km3 magma), ashfall thicknesses >1 cm are largely confined to the central North Island, with dispersal controlled by day‐to‐day weather and the dominance of westerly winds. With increasing eruptive volume (1–5‐km3 magma), ashfall thicknesses >1 cm would likely reach major population centers throughout the North Island. Dispersal is less dependent on weather patterns as the formation of a radially expanding umbrella cloud forces ash upwind or crosswind, although strong stratospheric winds significantly restrict umbrella spreading. For large eruptions (50–500‐km3 magma), powerful expansion of the umbrella cloud results in widespread ashfall at damaging thicknesses (>10 cm) across most of the North Island and top of the South Island. Synoptic climatology may prove a useful additional technique for long‐term hazard planning at caldera volcanoes.

Recent Developments and Applications of Acoustic Infrasound to Monitor Volcanic Emissions

Volcanic ash is a well-known hazard to population, infrastructure, and commercial and civil aviation. Early assessment of the parameters that control the development and evolution of volcanic plumes is crucial to effective risk mitigation. Acoustic infrasound is a ground-based remote sensing technique—increasingly popular in the past two decades—that allows rapid estimates of eruption source parameters, including fluid flow velocities and volume flow rates of erupted material. The rate at which material is ejected from volcanic vents during eruptions, is one of the main inputs into models of atmospheric ash transport used to dispatch aviation warnings during eruptive crises. During explosive activity at volcanoes, the injection of hot gas-laden pyroclasts into the atmosphere generates acoustic waves that are recorded at local, regional and global scale. Within the framework of linear acoustic theory, infrasound sources can be modelled as multipole series, and acoustic pressure waveforms can be inverted to obtain the time history of volume flow at the vent. Here, we review near-field (<10 km from the vent) linear acoustic wave theory and its applications to the assessment of eruption source parameters. We evaluate recent advances in volcano infrasound modelling and inversion, and comment on the advantages and current limitations of these methods. We review published case studies from different volcanoes and show applications to new data that provide a benchmark for future acoustic infrasound studies.

Low efficiency of large volcanic eruptions in transporting very fine ash into the atmosphere

Volcanic ash clouds are common, often unpredictable, phenomena generated during explosive eruptions. Mainly composed of very fine ash particles, they can be transported in the atmosphere at great distances from the source, having detrimental socio-economic impacts. However, proximal settling processes controlling the proportion (ε) of the very fine ash fraction distally transported in the atmosphere are still poorly understood. Yet, for the past two decades, some operational meteorological agencies have used a default value of ε = 5% as input for forecast models of atmospheric ash cloud concentration. Here we show from combined satellite and field data of sustained eruptions that ε actually varies by two orders of magnitude with respect to the mass eruption rate. Unexpectedly, we demonstrate that the most intense eruptions are in fact the least efficient (with ε = 0.1%) in transporting very fine ash through the atmosphere. This implies that the amount of very fine ash distally transported in the atmosphere is up to 50 times lower than previously anticipated. We explain this finding by the efficiency of collective particle settling in ash-rich clouds which enhance early and en masse fallout of very fine ash. This suggests that proximal sedimentation during powerful eruptions is more controlled by the concentration of ash than by the grain size. This has major consequences for decision-makers in charge of air traffic safety regulation, as well as for the understanding of proximal settling processes. Finally, we propose a new statistical model for predicting the source mass eruption rate with an unprecedentedly low level of uncertainty.

Volcanic Ash Contributes to Climate Cooling

A new study shows that atmospheric ash reflects solar radiation months after volcanic eruptions.

Influence of the composition and viscosity of volcanic ashes on their adhesion within gas turbine aeroengines

This paper presents experimental investigations into adhesion characteristics of four types of (Icelandic) volcanic ash (VA). Firstly, powder (∼5–50 μm) was injected into a modified vacuum plasma spray set-up and the fractional mass of particles that adhered to a substrate was measured. Secondly, large (∼6 mm), dense pellets of each ash were heated and projected at a substrate, with their impact response monitored via high speed photography. The four ashes fall into two groups of two, one with high Si content (>20%) and the other containing less Si, but higher levels of lower valence cations (such as Ca, Mg & Fe). The glass transition temperatures were all relatively low (∼650–750 °C), favouring particle adhesion on surfaces in gas turbines. All of the ashes tended to adhere, especially with higher gas temperatures and impingement velocities. However, this tendency was much greater for the two ashes with high levels of the lower valence cations. The high speed photography confirmed that this was due to these two ashes having much lower viscosities (at high strain rates). This behaviour could not have been predicted solely on the basis of Tg or glass content values. However, these cations act as “network-modifiers” in silica-based glasses, effecting sharp reductions in melt viscosity, so inferences about the danger of specific VA may be possible from simple compositional analysis. In any event, it's clearly important for VA being generated during any particular eruption to be sampled (presumably by drones) and analysed, rather than relying solely on remote measurement of atmospheric ash levels.

Aerosol radiative forcing from the 2010 Eyjafjallajökull volcanic eruptions

AbstractAlthough the 2010 volcanic eruptions of Eyjafjallajökull did not exert a large climate forcing, several features of their emissions favored weaker aerosol cooling or stronger warming than commonly attributed to volcanic events. These features include a high ratio of fine ash to SO2, occurrence near reflective surfaces exposed to strong insolation, and the production of very little stratospheric sulfate. We derive plausible ranges of optical properties and top‐of‐atmosphere direct radiative forcing for aerosol emissions from these events and find that shortwave cooling from sulfate was largely offset by warming from ash deposition to cryospheric surfaces and longwave warming from atmospheric ash and sulfate. Shortwave forcing from atmospheric ash was slightly negative in the global mean under central estimates of optical properties, though this forcing term was uniquely sensitive to the simulated distribution of clouds. The forcing components sum to near climate‐neutral global mean 2010 instantaneous (−1.9 mWm−2) and effective (−0.5 mWm−2) radiative forcing, where the latter is elevated by high efficacy of snow‐deposited ash. Ranges in net instantaneous (−7.3 to +2.8 mWm−2) and effective (−7.2 to +4.9 mWm−2) forcing derived from sensitivity studies are dominated by uncertainty in ash shortwave absorptivity. Forcing from airborne ash decayed quickly, while sulfate forcing persisted for several weeks and ash deposits continued to darken snow and sea ice surfaces for months following the eruption. Despite small global forcing, monthly averaged net forcing exceeded 1 Wm−2 in some regions. These findings indicate that ash can be an important component of climate forcing from high‐latitude volcanic eruptions and in some circumstances may exceed sulfate forcing.

The effect of Etna volcanic ash clouds on the Maltese Islands

In this paper, we have studied in depth the effect of Etna volcanic ash clouds on the Maltese Islands. Research was carried out to gather information about Etna's eruptions that impacted the Maltese Islands, starting with historical eruptions dating back to the 14th century continuing to present day. A statistical approach was utilized to provide tephra deposit load and ash concentration using PUFF — a model which simulates the transport, dispersion and sedimentation of volcanic ash. Three different eruptive scenarios that characterize Etna's recent activity were considered; the first scenario representing the 2001 eruption (Sc1), the second scenario representing the July 1998 eruption (Sc2) whilst the third scenario represents the recent activity in 2011–2012 (Sc3). We found that the time taken for the volcanic ash cloud to reach the Maltese Islands, when the wind direction is toward the south-west ranges from 4 to 6h. The probability that an Etna volcanic cloud reaches Malta during an eruption is about 15% per annum. The now calibrated model may be now used to produce deposit load and cumulative columnar load (i.e. summation from maximum height of volcanic cloud to ground) of volcanic ash in atmosphere for the Maltese area and help the aviation authorities and Malta airport to make decisions during Etna eruptions. This will be of direct use to local communities and aviation.

Simulation of SEVIRI infrared channels: a case study from the Eyjafjallajökull April/May 2010 eruption

Abstract. Infrared satellite images are widely and successfully used to detect and follow atmospheric ash from erupting volcanoes. We describe a new radiative transfer model framework for the simulation of infrared radiances, which can be compared directly with satellite images. This can be helpful to get insight into the processes that affect the satellite retrievals. As input to the radiative transfer model, the distribution of ash is provided by simulations with the FLEXPART Lagrangian particle dispersion model, meteorological cloud information is adopted from the ECMWF analysis and the radiative transfer modelling is performed with the MYSTIC 3-D radiative transfer model. The model framework is used to study an episode during the Eyjafjallajökull eruption in 2010. It is found that to detect ash by the reverse absorption retrieval technique, accurate representation of the ash particle size distribution is required. Detailed investigation of individual pixels displays the radiative effects of various combinations of ash, liquid water and ice clouds. In order to be clearly detectable, the ash clouds need to be located at some distance above other clouds. If ash clouds are mixed with water clouds or are located only slightly above water clouds, detection of the ash becomes difficult. Simulations were also made using the so-called independent pixel approximation (IPA) instead of the fully 3-D radiative transfer modelling. In the two simulations, different clouds (or different parts of the clouds) or the ground are effectively emitting radiation towards the instrument, thus causing differences in the brightness temperature of up to ± 25 K. The presented model framework is useful for further studies of the processes that affect satellite imagery and may be used to test both new and existing ash retrieval algorithms.

The ash dispersion over Europe during the Eyjafjallajökull eruption – Comparison of CMAQ simulations to remote sensing and air-borne in-situ observations

The dispersion of volcanic ash over Europe after the outbreak of the Eyjafjallajökull on Iceland on 14 April 2010 has been simulated with a conventional three-dimensional Eulerian chemistry transport model system, the Community Multiscale Air Quality (CMAQ) model. Four different emission scenarios representing the lower and upper bounds of the emission height and intensity were considered. The atmospheric ash concentrations turned out to be highly variable in time and space. The model results were compared to three different kinds of observations: Aeronet aerosol optical depth (AOD) measurements, Earlinet aerosol extinction profiles and in-situ observations of the ash concentration by means of optical particle counters aboard the DLR Falcon aircraft. The model was able to reproduce observed AOD values and atmospheric ash concentrations. Best agreement was achieved for lower emission heights and a fraction of 2% transportable ash in the total volcanic emissions. The complex vertical structure of the volcanic ash layers in the free troposphere could not be simulated. Compared to the observations, the model tends to show vertically more extended, homogeneous aerosol layers. This is caused by a poor vertical resolution of the model at higher altitudes and a lack of information about the vertical distribution of the volcanic emissions. Only a combination of quickly available observations of the volcanic ash cloud and atmospheric transport models can give a comprehensive picture of ash concentrations in the atmosphere.

Simulations of the 2010 Eyjafjallajökull volcanic ash dispersal over Europe using COSMO–MUSCAT

The ash plume of the Icelandic volcano Eyjafjallajökull covering Europe in April and May 2010 has notably attracted the interest of atmospheric researchers. Emission, transport, and deposition of the volcanic ash are simulated with the regional chemistry-transport model COSMO–MUSCAT. Key input parameters for transport models are the ash injection height, which controls the ash layer height during long-range transport, and the initial particle size distribution, which influences the sedimentation velocity. For each model layer, relative release rates are parameterised using stereo-derived plume heights from NASA’s space-borne Multi-angle Imaging SpectroRadiometer (MISR) observations near the source. With this model setup the ash is emitted at several levels beneath the maximum plume heights reported by the Volcanic Ash Advisory Centre (VAAC) London. The initial particle size distribution used in COSMO–MUSCAT is derived from airborne in-situ measurements. In addition, the impact of different injection heights on the vertical distribution of the volcanic ash plume over Europe is shown. Ash emissions at specific control levels allow to assess the relative contribution of each layer to the spatial distribution after transport. The model results are compared to aerosol optical depths from European Sun photometer sites, lidar profiles measured over Leipzig/Germany, and ground-based microphysical measurements from several German air quality stations. In particular the good agreement between modelled vertical profiles of volcanic ash and lidar observations indicates that using the MISR stereo-height retrievals to characterize atmospheric ash input provide an alternative to injection height models in case of lacking information on eruption dynamics. ► The transport of the Icelandic volcano ash plume is simulated with a regional model. ► For parameterising injection heights MISR satellite retrievals are used. ► The model is evaluated with ground-based in-situ and remote sensing measurements. ► The impact of the injection height on the ash plume distribution is studied. ► MISR stereo-height retrievals can be an alternative to injection height models.

Infrasound from Tungurahua Volcano 2006–2008: Strombolian to Plinian eruptive activity

Strombolian to Plinian activity from Tungurahua Volcano, Ecuador has been recorded by the autonomous infrasound arrays of the Acoustic Surveillance for Hazardous Eruptions (ASHE) project since early 2006. Our studies suggest that acoustic energy release during large eruptions does appear to broadly scale with eruption intensity. This manuscript provides a detailed chronology and characterization of Tungurahua's eruptive activity between 2006 and 2008 and demonstrates the ability to constrain source parameters of significant eruptions, such as onset, duration, and escalation, at regional distances by combining infrasound and remote sensing techniques. The ASHE system in Ecuador automatically detected over 20,000 volcanic explosions at an array 37 km from Tungurahua and was successful at notifying the onset, escalation, and cessation of a hazardous February 2008 eruption with a latency of 5 min. Elevated infrasonic energy from sustained and intense Tungurahua eruptions correlates well with ash column heights and their lateral extent during the study period. The spectra of these sustained explosive eruptions appear to be recurrent, readily recognizable, and indicative of volcanic jetting and significant atmospheric ash injection. The paroxysmal Plinian phase of the August 2006 eruption produced an ash cloud that extended well into the stratosphere (> 24 km), coinciding with a shift of the dominant jetting frequency from 0.25 Hz to below 0.1 Hz, and radiation of over 5 × 10 7 W of acoustic power. Transient explosions were often marked by minor or no ash release and are presumed to be more gas-rich. A change in the acoustic spectrum of volcanic jetting was also detected in the transition from a sustained to collapsed eruption column at the end of the July 14, 2006 eruption. The jetting spectrum at Tungurahua during a period of sustained pyroclastic density current production changes from a typical double-peaked to a single-peaked spectrum, suggesting remote acoustic monitoring can help ascertain the stability and dynamics of an eruptive column.

Simulation of the 1980 eruption of Mount St. Helens using the ash-tracking model PUFF

The dispersal of volcanic ash from the May 18, 1980 eruption of Mount St. Helens (MSH) has been simulated using the Lagrangian ash-tracking model PUFF. Previous applications of the model were limited to smaller, short-lived eruptions with ash dispersal occurring mainly within the troposphere. Two high-resolution atmospheric reanalysis datasets (ERA-40 and NCEP/NCAR-40) allowed MSH ash cloud dispersal to be simulated up to 30 km elevation. The 1980 eruption was divided into two distinct eruptive phases, (1) an initial, relatively short-lived blast/surge phase that injected ash up to 30 km and (2) a subsequent nine-hour plinian phase that maintained an average eruption column height of 16 km. Using PUFF, the two phases of the MSH eruption were modeled separately based on a range of individual input parameters and then combined to produce an integrated simulation of the entire eruption. The trajectory and areal extent of the modeled atmospheric ash cloud best match the actual distribution of MSH ash when input parameters are set to values inferred from satellite and radar data collected on May 18, 1980. The prevailing wind field exerts the strongest control on the advection and ultimate position of the modeled ash cloud, making the maximum column height and the vertical distribution of ash the most sensitive of the PUFF input parameters for this event. The results indicate that the PUFF model works well at simulating the dispersal of ash injected well into the lower stratosphere from a moderate, relatively long-lived eruption, such as MSH. However, attempts to use PUFF to recreate some granulometric aspects of the MSH fallout deposit, such as the maximum particle size as a function of distance from source, were not successful. PUFF consistently predicts much greater fallout distances for small ash particles (< 500 µm) than actually observed in the MSH deposit. The effective settling velocities used by the PUFF model appear to be too slow to accurately predict fallout distances of small ash particles. As a consequence the PUFF model may overestimate the duration of ash loading in the atmosphere associated with the distal fine ash component of explosive eruptions.

The VOL‐CALPUFF model for atmospheric ash dispersal: 2. Application to the weak Mount Etna plume of July 2001

Here the application of the VOL‐CALPUFF model by Barsotti et al. to a weak plume erupted from Mount Etna in July 2001 is presented and discussed. The reconstruction of the explosive event was obtained by using high‐resolution weather forecasts, produced by a mesoscale nonhydrostatic model, and volcanic source data coming from observations and analytical studies. The plume rise and atmospheric dispersal models were investigated over 5 d of eruption mostly in terms of column height, aerial ash concentration, and ground deposition. Modeling results are shown as a function of various source conditions and compared to independent observations derived from satellite images and deposit mapping. The application of VOL‐CALPUFF clearly highlights the crucial role played by meteorological conditions in determining dispersal dynamics. Some of the most important effects described by the model are (1) the large wind field influence on the plume height determination and tilting, (2) the contrasting dispersal patterns of ash particles of different sizes, (3) the complex and somehow nonintuitive distribution of ash on the ground resulting in preferential directions of dispersal and quite irregular deposit patterns, and (4) the impossibility to reproduce both the column height and the deposit accumulation pattern by adopting a steady state vent mass flow rate over the investigated 4‐d period due to observed temporal changes in eruption dynamics. Modeling results also suggest the need for further integration of simulation outcomes with remote sensing and field reconstructions on ash dispersal processes in future.

The VOL‐CALPUFF model for atmospheric ash dispersal: 1. Approach and physical formulation

We present a new modeling tool, named VOL‐CALPUFF, that is able to simulate the transient and three‐dimensional transport and deposition of volcanic ash under the action of realistic meteorological and volcanological conditions throughout eruption duration. The new model derives from the CALPUFF System, a software program widely used in environmental applications of pollutant dispersion, that describes the dispersal process in both the proximal and distal regions and also in the presence of complex orography. The main novel feature of the model is its capability of coupling a Eulerian description of plume rise with a Lagrangian representation of ash dispersal described as a series of diffusing packets of particles or puffs. The model is also able to describe the multiparticle nature of the mixture as well as the tilting effects of the plume due to wind action. The dispersal dynamics and ash deposition are described by using refined orography‐corrected meteorological data with a spatial resolution up to 1 km or less and a temporal step of 1 h. The modeling approach also keeps the execution time to a few minutes on common PCs, thus making VOL‐CALPUFF a possible tool for the production of ash dispersal forecasts for hazard assessment. Besides the model formulation, this paper presents the type of outcomes produced by VOL‐CALPUFF, shows the effect of main model parameters on results, and also anticipates the fundamental control of atmospheric conditions on the ash dispersal processes. In the companion paper, Barsotti and Neri present a first thorough application of VOL‐CALPUFF to the simulation of a weak plume at Mount Etna (Italy) with the specific aim of comparing model predictions with independent observations.