Seasonal ground deformation at subglacial Katla Volcano, Iceland: observations and models

Abstract

Changes at the surface of a volcanic edifice, such as snow or hydrological loading, ice cap melting, and flank destabilization, can cause significant surface deformation. Understanding the contribution of surface processes to ground deformation is therefore important for monitoring the state of the underlying volcanic system. The Katla Volcano in Iceland lies under Mýrdalsjökull, the fourth largest glacier in Iceland, and undergoes the largest seasonal deformation of all Icelandic volcanoes: up to 4 cm horizontally and 3 cm vertically at the Austmannsbunga (AUST) Global Navigation Satellite System (GNSS) station. The last confirmed eruption of Katla occurred in 1918. Since then, episodes of elevated seismicity and jökulhlaups (sudden glacial outburst floods) have been recorded at the volcano, the most noticeable in 1955, 1999, 2011, and 2024. During the 2024 jökulhlaup, horizontal displacement of up to 7 cm was recorded at AUST. In this work, elastic three-dimensional finite element method models were implemented to quantify surface deformation from seasonal load changes. The models include realistic bedrock topography and ice unloading based on recent data collected at Mýrdalsjökull. A deformation model considering only seasonal snow unloading can reproduce within uncertainty the observed GNSS vertical surface displacements. It can also explain the horizontal signals at GNSS stations located outside the glacier, although not at GNSS stations located on nunataks inside Mýrdalsjökull. An additional deformation source must be considered to explain the residual cm-scale horizontal displacement at these stations. We model the residual signal using a thermo-poro-elastic cylindrical source. The best-fit source is a cylinder located at the surface that produces cm-scale horizontal deformation with limited vertical deformation. The shallow source depth derived from the inversion and the surface deformation recorded at AUST during the jökulhlaup series in 2024 and 2025 suggests that seasonal deformation is not strictly related to magmatic activity. We infer that changes within the hydrologic system of the glacier are responsible for most of the horizontal deformation at Katla.

1 Introduction

Surface ground deformation at active volcanoes is commonly attributed to fluid processes at depth, such as magma storage, propagation, or geothermal processes (Biggs et al., 2014; Battaglia et al., 2006; Sparks et al., 2012; Parks et al., 2024; Lanzi et al., 2023). Geodetic modeling of ground deformation in relation to such processes is important for understanding and assessing the potential hazards posed by the volcanic unrest (Cannavò et al., 2015). However, surface loading, such as snow loading, also causes ground deformation (Grapenthin et al., 2006; Heki, 2001).

The subglacial Katla Volcano in South Iceland experiences the largest known seasonal deformation of all volcanoes in Iceland, which has largely been attributed to snow loading during winters and melting of snow and glacial ice during summers (Albino et al., 2010; Pinel et al., 2007). It is important to understand what processes are contributing to this signal because short-term loading has been demonstrated to affect subsurface stress conditions and potentially trigger eruptions across a wide variety of volcanoes (Gaete et al., 2020; Yates et al., 2024; Pinel and Albino, 2013; Albino et al., 2010). Understanding the individual contributions of surface loading processes and volcanic unrest to a recorded surface deformation signal can be challenging, particularly when many short-term processes have cyclical components (Albino et al., 2010; Petrosino et al., 2021; Yates et al., 2024). Solid Earth tides (SETs) and ocean tidal loading (OTL) cause crustal stress changes, affecting observable gas formation, emission rates, gravity changes, seismicity, and/or ground deformation (Francis and Mazzega, 1990; Yamamoto et al., 2001; Bredemeyer and Hansteen, 2014; Dinger et al., 2019; Dumont et al., 2023). SET reflects an elastic solid Earth response to external forcing accompanied by stress changes of up to 1 kPa for semidiurnal to fortnightly tides (Johnston and Mauk, 1972). Subaqueous and coastal volcanoes are additionally affected by OTL, modulating magmatic activity and seismicity (McNutt and Beavan, 1987; Tolstoy, 2015; Miguelsanz et al., 2021). As much as 250 cm of seasonal snow loading at Ruapehu Volcano, New Zealand, similarly causes up to 3–10 kPa pressure change (Yates et al., 2024). Seasonal and daily deformation has furthermore been recorded at volcanoes in conjunction with meteoric rain events (Petrosino et al., 2021; Rebscher et al., 2000), as well as eruption triggering (Violette et al., 2001; Rebscher et al., 2000; Gaete et al., 2020). At Merapi Volcano, ground deformation was recorded during volcanic unrest and meteoric rain events, highlighting the importance of understanding different processes recorded in surface deformation, especially when rainfall impacts eruptive behavior (Rebscher et al., 2000).

Many types of models have been developed to simulate volcanogenic ground deformation sources, such as those related to magma accumulation, withdrawal, and dike intrusions. At volcanoes, analytical solutions are commonly used due to their simplicity and computational efficiency. Such models use simplified geometries for the source (e.g., point, sphere, or rectangular dislocation) and consider the host-rock medium as an elastic half space (Mogi, 1958; McTigue, 1987; Okada, 1985; Segall, 2019; Dzurisin, 2006; Arnadottir et al., 1991). The numerical finite element method (FEM) was developed in the late 20th century and has since been used to model surface deformation at volcanoes (Logan, 2017; Masterlark et al., 2012; Trasatti et al., 2008; Manconi et al., 2009a; Dieterich and Decker, 1975). Although analytical models remain a better choice for near real-time monitoring of volcanic unrest due to their lowered computational expense, the FEM has allowed for models to better reflect our current understanding of natural conditions: incorporating considerations for edifice topography, crustal heterogeneities, inelastic rheology, subsurface structures such as faults, and spatially varying surface loading conditions. (Greiner and Geirsson, 2024; Hickey et al., 2015; Currenti et al., 2007; Karaoğlu et al., 2016; Schmidt et al., 2013; Grapenthin et al., 2006; Masterlark, 2007).

A variety of processes can cause short-term surface loading at volcanoes. Seasonal ground deformation due to snow accumulation and subsequent melting is known to produce up to centimeter-scale displacements (Pinel et al., 2007; Heki, 2001). Most of the deformation due to snow loading is in the vertical component with minimal horizontal deformation (Drouin et al., 2016; Heki, 2001; Grapenthin et al., 2006). Centimeter-scale horizontal displacements have also been observed that are not directly related to snow accumulation (Silverii et al., 2020). The observed seasonal deformation signal is inferred to be smoothed due to the percolation of water following spring snow melt into the ground (Heki, 2001; Grapenthin et al., 2006; Silverii et al., 2020). Additionally, glaciers have their own processes, such as long-term advance and retreat, and their own hydrologic systems (Cuffey and Paterson, 2010). Changes in glacier hydrology can produce pressure changes at its base of up 80% of the ice overburden pressure (Harper et al., 2005). Changes in surface loading may modulate magmatic behavior by impacting the production of melt in the base of the lithosphere and magma propagation in the upper crust (Aubry et al., 2022; Sigmundsson et al., 2010; Schmidt et al., 2013). Additionally, jökulhlaups occur when a large amount of water is suddenly released from the glacier. This water can melt suddenly from contact with lava during subglacial eruptions or flash boiling of geothermal systems, or accumulate more slowly related to geothermal activity (Björnsson, 1992).

Katla is a subglacial volcano in the southern part of the Eastern Volcanic Zone (EVZ) of Iceland (Figure 1) (Thordarson and Larsen, 2007). It is overlain by the Mýrdalsjökull glacier, which is the fourth largest glacier in Iceland, covering approximately 600 km² (Björnsson et al., 2000). Mýrdalsjökull receives the most precipitation measured in Iceland, up to 10 m of water equivalent (Ágústsson et al., 2013). The Katla Caldera is elliptical with a 14 km SE–NW major axis and a 9 km SW–NE minor axis. It is filled with ice that is up to 750 m thick (Björnsson et al., 2000). While the Mid-Atlantic Rift transects Iceland roughly southwest to northeast, Katla lies within a volcanic flank zone where little to no crustal spreading occurs (Sigmundsson et al., 2020). Katla has had 21 confirmed eruptions (breaking through the ice cover) since the 9th century, and the most recent was in 1918. Larsen (2000) calculated an average repose time of 47 years with a maximum deviation of 34 years.

FIGURE 1

Jóhannesson and Sæmundsson (2009).

Katla has been experiencing uplift and outward horizontal movement since at least 1993, when episodic Global Navigation Satellite System (GNSS) measurements began on nunataks in Mýrdalsjökull (Geirsson et al., 2010; Sturkell et al., 2008). This has led some to conclude that magma is accumulating under Katla (Sturkell et al., 2003; 2008; Pinel et al., 2007; Sturkell et al., 2010), while another study suggested that deformation was the result of Glacial Isostatic Adjustment (GIA) (Spaans et al., 2015). From 1967–1995, optical leveling tilt measurements were carried out around Mýrdalsjökull (Tryggvason, 2000). The results were interpreted in terms of deformation associated with seasonal surface loading, although somewhat inconclusive due to the sparse temporal resolution of the measurements (Tryggvason, 2000). In 1999, the first two continuous GNSS (cGNSS) stations were installed at the edges of Mýrdalsjökull: SOHO and HVOL, with additional stations being installed in the following years (Geirsson et al., 2006) (Figure 1). The largest seasonal deformation signal in Iceland has been measured at the Austmannsbunga (AUST) station, which has been running continuously since 2010 (Drouin et al., 2016).

Seismicity is prevalent at Katla. Multiple studies have been conducted over the years, revealing two distinct earthquake clusters: one within the caldera, and one located 2–3 km west of the western caldera rim, called Goabunga (Einarsson and Brandsdóttir, 2000; Jónsdóttir et al., 2007). Both clusters experienced seasonality in the rates of seismicity, having higher rates from July to October (Einarsson and Brandsdóttir, 2000; Tryggvason, 1973; Jónsdóttir et al., 2007). Another seasonal seismic cluster appeared on the southern flank of Katla in 2011, attributed to either glacial or volcanogenic origin (Sgattoni et al., 2016). The caldera seismic cluster is shallow, less than 5 km deep, with annual modulation of activity inferred to originate from both changes in surface snow loading and shallow subsurface changes in pore pressure (Jónsdóttir et al., 2007), suggested to be approximately 0.03 MPa (Einarsson and Brandsdóttir, 2000).

Mýrdalsjökull hosts many ice cauldrons caused by increased and localized heat flux at the base of the glacier (Björnsson, 1975; Guðmundsson et al., 2007; Magnússon et al., 2021; Jóhannesson et al., 2020) (Figure 1). Ice cauldrons can be temporary, only active during a few months or years when there is new/increased geothermal upwelling or during subglacial eruptions, or they can be long-lived from stable geothermal activity (Björnsson, 1975). Jökulhlaups, or leakage of geothermal meltwater from the ice cauldrons on Mýrdalsjökull, occur several times each year. Jökulhlaups in the rivers emanating from Mýrdaljökull, not attributed to confirmed volcanic eruptions, span from peak discharges of a few tens to thousands m³/s to smaller leakage events solely identified as increased conductivity in the river drainage (Einarsson, 2019). Jökulhlaups draining from the ice cauldrons with both a peak discharge exceeding 1000 m³/s and a net discharge of 10 million m³ occurred in 1955, 1999, 2011, and 2024 (Rist, 1967; Sigurðsson et al., 2000; Guðmundsson and Sólnes, 2013; Magnússon et al., 2024). All of these jökulhlaups were accompanied by elevated seismicity and/or seismic tremor, but the cause of these jökulhlaups has been debated and attributed either to minor subglacial eruptions (Larsen, 2000; Sgattoni et al., 2017) or geothermal activity (Galeczka et al., 2014). Both jökulhlaups of significant drainage and smaller leakage events are most common during the peak of the summer. Drainage of meltwater from beneath the ice cauldrons often induces surface elevation changes within the glacial ice. Regular monitoring of elevation changes at the ice cauldrons of Mýrdalsjökull has been carried out since 1999 (Guðmundsson et al., 2007).

Understanding the effect of seasonal snow loading is important at ice-covered volcanoes because these systems can be sensitive to shallow surface changes. Observations recorded during a series of jökulhlaups during the summers of 2024 and 2025 suggest that the drainage of the hydrologic system could contribute to the observed seasonal deformation at Katla. Here, we develop FEM models to explain recorded deformation by incorporating new models of seasonal snow loading and additional subsurface processes at Katla.

2 Materials and methods

2.1 Seasonal ground deformation from GNSS observations

cGNSS is the most commonly used method to observe seasonal ground deformation signals, due to its high temporal resolution (Heki, 2001; Grapenthin et al., 2006; Drouin et al., 2016). To estimate the seasonal signal at Katla, we used eight cGNSS stations operated by the Icelandic Meteorological Office, including two stations on nunataks high on the glacier (Figure 1). The data were analyzed at the University of Iceland using the GIPSY/OASIS II (Zumberge et al., 1997) software, in the ITRF2014 reference frame (Altamimi et al., 2016; Geirsson et al., 2010). We consider observations from 2015 until late 2025. Prior to 2015, the nearby Eyjafjallajökull Volcano (25 km west of Katla) was deforming and affecting the observed data at Katla (Spaans et al., 2015; Sturkell et al., 2008).

The steady displacement of a GNSS station (in the absence of a sudden offset or change in deformation rates) as a function of time can be approximated as the superposition of an initial value, a linear trend, and an annual signal (Drouin et al., 2016). We use the following equation to estimate the linear and, more importantly, the annual/seasonal signal in all components of the cGNSS stations:where refers to an intercept at = 0, is the linear component of the signal, and represents the annual components, and is time in units of years. For the time series we study, we compute the linear and annual components of the observed deformation signal and do not include semi-annual components in the time-series fit. This is because using annual components only allows us to easily identify the onset of the summer and winter deformation periods.

The GGMatlab toolbox was used to estimate a linear detrending rate and an annual signal for each component of the GNSS data (Herring, 2003). We find that Equation 1 fits the observed cGNSS time series relatively well; therefore, the combined influence of plate motion, GIA, and long-term volcanic unrest produces a first-order, linear trend during the study period. The uncertainties were estimated using the RealSigma algorithm (Herring, 2003). The inferred and parameters can be used to alternatively express the annual signal in terms of amplitude and phase, which were then used to calculate the peak-to-peak values of the annual components of displacements (Figure 2a). The inferred peak-to-peak displacement refers to the average observed annual signal from the onset of summer deformation to the onset of winter deformation at each cGNSS station from 2015 until late 2025. We identify the onset of the summer deformation as beginning when the first peak in the amplitude of the annual signal is reached, regardless of whether it is a maximum or minimum, and the onset of winter deformation occurs when the second peak is reached half a year later. The onset of summer deformation was determined at each station and each component individually. Therefore, the dates of the onset of summer deformation vary between stations to capture the maximum amount of annual deformation at each station. For all stations, the vertical component of displacement during summer always starts from a minimum and uplifts. The estimated maximum amount of peak-to-peak annual deformation, with separate values estimated for each displacement component (north, east, up), is used as our observed data when comparing to the predicted deformation from our FEM modeling, including considerations for seasonal snow loading.

FIGURE 2

2.2 Snow load

We model the average seasonal snow unloading from late May through October, corresponding to the onset and termination of the glacial summer on the Mýrdalsjökull ice cap (Belart et al., 2020; Bernat et al., 2023). To obtain a robust estimate of the spatial variability in surface loading, we simulate the surface mass balance using the COSIPY snowpack model (Sauter et al., 2020), forced with the CARRA climate reanalysis (Schyberg et al., 2020). The resulting mass-balance fields are corrected for local melt and snowfall biases using more than 120 high-resolution DEMs covering the ice cap between 2012 and 2023 (Liebsch et al., 2025). We then compute the mean difference in seasonal loading between May and October across the 2012–2023 period, which provides a spatially variable estimate of the net snow unloading. The inferred surface snow elevation changes from observations and an estimate of density changes from snow to glacial ice are converted to an estimated elevation change equivalent to meters of water.

We incorporate this spatially varying unloading field into a three-dimensional (3D) FEM model to evaluate its effect on ground deformation at Katla. Compared to the previous two-dimensional (2D) axis-symmetrical models that used disk surface unloading (Albino et al., 2010), our 3D model captures the spatial variability of snow melting patterns. Surface pressure change is applied perpendicular to the local topographic surface and is calculated aswhere density of water is (1000 kg/m³) and is the gravitational acceleration. is the mass change during glacial summer in meters of water equivalent. Hence, it describes the load as the equivalent volume of liquid water per square meter.

2.3 Jökulhlaups in 2024 and 2025

The Icelandic Meteorological Office operates a flood monitoring network around the Mýrdalsjökull icecap. The network consists of nine hydrological stations located in the main jökulhlaup pathways. After a large jökulhlaup in 1999, the network was expanded, and the hydrological station in Skálm was among the stations installed that year. After the sudden jökulhlaup in Skálm in July 2024, a new flood warning station was installed in Leirá-Syðri, upstream of Skálm (Figure 1). The hydrological station in Leirá-Syðri is 3 km from the edge of the glacier where the jökulhlaups emerged in 2024 and 2025. The purpose of the new hydrological station in Leirá-Syðri is to provide a timely warning before a jökulhlaup reaches the hydrological station in Skálm, which is located on Road 1 in South Iceland.

We use data from the hydrological stations in Skálm and Leirá-Syðri. The hydrological stations measure water level, conductivity, and water temperature in near-real time. The first signs of a jökulhlaup on the hydrological stations are a significant increase in conductivity and a rising water level. During the July 2024 jökulhlaup, seismic tremor was also detected on seismic stations on and around the Mýrdalsjökull ice cap, which we used to roughly estimate the travel time of the jökulhlaup from the subglacial cauldrons to the hydrological station in Skálm.

The AUST cGNSS station is located on a nunatak on the northeastern part of the Katla Caldera rim, 1.5–2 km northeast of ice cauldrons 13 and 14 (Magnússon et al., 2021), the source of the 2024 and 2025 jökulhlaups (Figure 1). The total volume of water released from cauldrons 13 and 14 during these jökulhlaups could not be estimated from the river level measurements of the hydrological stations in Skálm and Leirá-Syðri. However, the volume of released water could be estimated from differencing digital elevation models (DEM) of cauldrons 13 and 14 generated before and after the jökulhlaups. From the onset of the jökulhlaup in July 2024 until 20 August, a maximum lowering of 40 m was observed. The volume of the integrated lowering of these cauldrons was 21 million m³ (Magnússon et al., 2024). Assuming that this volume corresponds to the ice melted beneath the cauldrons results in a mass loss of 19 million tons. Some of this mass loss occurred in the weeks after the main jökulhlaup on 27 July, but river level measurements suggest that the main part of the mass loss was associated with the first jökulhlaup. The jökulhlaup in July 2024, therefore, falls into the size category of the 1955, 1999, and 2011 jökulhlaups (Rist, 1967; Sigurðsson et al., 2000; Guðmundsson and Sólnes, 2013). The volume of the most prominent jökulhlaup in 2025, occurring in early July, could also be estimated from DEM differencing (Magnússon et al., 2025). This jökulhlaup was much smaller than the main jökulhlaup in 2024. From 6 July to 13 August 2025, the maximum lowering at the center of cauldron 13 was 21 m, and the volume of the integrated lowering of cauldrons 13 and 14 was estimated at 7 million m³. River level measurements show that most of this volume/mass loss occurred during the first jökulhlaup in early July.

2.4 Model description

2.4.1 Finite element model

To investigate the different effects of snow loading conditions at Katla on ground deformation, we created an FEM model using the COMSOL Multiphysics software, version 6.2 (COMSOL, 2025). The model is 3D, elastic, homogeneous, and incorporates topography from a surface digital elevation model (DEM) for the unglaciated sections (Náttúrufræðistofnun, 2025) and a DEM of the subglacial bedrock (Magnússon et al., 2021). An elastic model was chosen due to the short time span of the observed peak-to-peak annual displacements. We placed virtual GNSS stations, as forced nodes, in the FEM model to extract displacements for direct comparison to observed values. A simple model of ground deformation from surface loading is Boussinesq’s problem, where radial and vertical displacements are calculated from a point load,and

where is the applied load, is Poisson’s ratio, is the shear modulus, and is the radial distance from the point (Davis and Selvadurai, 1996). An FEM model with point-like surface unloading was benchmarked to Boussinesq’s problem (Equations 3, 4) to ensure there were no edge or boundary effects, and the mesh was sufficiently refined. The model domain is 200 × 200 km wide and 50 km thick. The mesh is composed of approximately 200,000 tetrahedral elements with a maximum element size of 500 m located around areas of interest.

The seasonal snow unloading at Katla was modeled using the snow model described in Section 2.2. It was implemented into COMSOL as an interpolation and used to create a surface boundary condition with the spatially varying surface pressure , as calculated by Equation 2. There is no material within the model representing glacial ice as over a seasonal timescale, the glacier will flow viscously and not deform elastically. The spatially varying surface pressure boundary condition is applied on top of the surface topography. We include no pressure condition in the model due to the overall thickness of Mýrdalsjökull. This was done because we focus only on seasonal snowmelt during the summer and, therefore, do not consider long-term changes in the ice mass of the glacier.

Predicted displacements at each cGNSS station are extracted from the FEM model and compared to the cGNSS displacements derived in Section 2.1.

2.4.2 Analytical thermo-poro-elastic model

The residual GNSS horizontal seasonal deformation signal observed at Katla (see Section 3.1) after modeling surface snow unloading indicated the need to employ an additional deformation source. The open-source, Python-based volcanic and seismic source modeling (VSM) tool (Trasatti, 2022) was used to invert for this secondary source. Preliminary tests evidenced a very shallow depth for an isotropic pressurized source. Based on the shallow depth and non-magmatic nature of this additional deformation source, we employ a non-time-dependent thermo-poro-elastic (TPE) cylindrical source (Nespoli et al., 2021). This model provides deformation and stress change in volcanic and hydrothermal areas induced by pore pressure and temperature changes across the cylindrical geometry. Its parameters are the cylinder center (latitude, longitude, and depth), radius, thickness, and potency . The potency in the TPE source is given bywhere is the change in source pressure, (see Equation 6) is the poroelastic parameter as introduced by Biot (Biot, 1941; Nespoli et al., 2023; 2026), is the coefficient of thermal expansion, and is the temperature change, which was assumed to be zero for this study (Nespoli et al., 2021). The parameter can also be written in the terms of isothermal, drained bulk modulus and the bulk modulus of the solid constituent of the poroelastic medium using the following relation (Rinaldi et al., 2010):The TPE source has been included as a new deformation source in the VSM portfolio (Silverii et al., 2025). The Neighborhood algorithm global optimization within VSM was used for the inversion. For all VSM inversions, the shear modulus was set as 23 GPa and Poisson’s ratio as 0.25.

3 Results

3.1 Observed seasonal deformation signal

All cGNSS stations used in this study show both a vertical and a horizontal seasonal ground deformation signal, which were fit with Equation 1 (Figure 2). Figure 2a shows the best-fit curve, as estimated by Equation 1, for the linear and annual displacement components of the AUST station. The vertical annual signal is more prominent at all stations than the horizontal, although some stations, such as AUST and ENTC, also have prominent annual horizontal signals (Figure 3). The peak-to-peak displacement of the vertical annual signal ranges from a maximum of 31 mm at AUST to a minimum of 9.5 mm at HVOL (Supplementary Table S1). At AUST, the horizontal peak-to-peak signal is the largest, with an average of 48 mm. The smallest horizontal signal occurs at station SOHO with 0.5 mm of peak-to-peak deformation in the east component. The seasonal summer peak-to-peak deformation signal for each station is found in Supplementary Table S1.

FIGURE 3

The observed cGNSS seasonal signals during summers 2015–2025 show a broad pattern of uplift, recorded at all stations (Figure 4). The horizontal seasonal displacements for stations located outside of the glacier show movement away from the glacier. For the stations located on nunataks within Mýrdalsjökull (AUST and ENTC), the horizontal signal is larger than that of the far-field stations but is generally in the direction of the accumulation zone of the glacier and Katla Caldera.

FIGURE 4

In this study, the seasonal deformation signal has been modeled as a sinusoidal signal (Equation 1) in both the vertical and horizontal directions. This is a good estimate for the observed vertical deformation pattern. For the horizontal deformation pattern at nunatak stations AUST and ENTC, this is a simplification of the observations. The horizontal seasonal summer displacement at these stations is focused on a short time interval, which is much more rapid than that of winter (Figure 2b). The overall signal at these sites is more reminiscent of a sawtooth pattern than a sinusoidal one. This sawtooth pattern in the cGNSS data at AUST and ENTC occurs over many summer seasons, leading us to infer that this is a typical behavior at these stations.

We did not calculate the seasonal deformation based on a set time period but instead calculated it based on the day of year (DOY) when uplift starts for the vertical and when the horizontal displacement reaches its first peak in the amplitude of the annual signal, regardless of whether it is a maximum or minimum (Table 1). The timing of the onset of summer deformation (average of the 2015–2025 period) for the vertical component is first recorded at both FIM2 and GOLA on DOY 126 (6 May), and the last cGNSS station to begin uplifting is GRFS on DOY 167 (16 June). This change can be compared to the estimated average DOY of maximum annual load and the onset of summer mass reduction (snow melting) at Mýrdalsjökull, across the whole glacier, which is DOY 122 (2 May) based on the glaciological modeling (see Section 2.2). There is a slight phase lag of 4–45 days between the onset of summer snow melt at Mýrdalsjökull and the onset of summer deformation. Note, however, that the DOY for the onset of summer mass reduction is an average of the whole glacier and does not account for earlier melting at lower elevations. The timing of the onset of horizontal deformation is more variable with DOYs between 57 and 154, both occurring at the SOHO station in the east and north components, respectively. There is less confidence in the summer deformation onset for stations with estimated peak-to-peak annual displacements smaller than 1 mm (Table 1).

3.2 Deformation from snow loading

Using the FEM model described in Section 2.4.1, we calculated the predicted glacial summer ground deformation at each cGNSS station. We assume a constant Young’s modulus and Poisson’s ratio for the elastic medium of the FEM model. Poisson’s ratio is fixed to 0.25, and Young’s modulus was optimized to obtain the minimum residuals between the modeled and the observed vertical displacements. The best-fitting Young’s modulus is 28 GPa. A model using this Young’s modulus produces the predicted cGNSS deformation field in Figure 5. The modeled vertical displacements are comparable to the observed vertical displacements, and thus, we conclude that snow unloading can explain most of the observed vertical motion. Maximum uplift, as predicted by our model, occurs at AUST, close to the center of the glacier, which agrees with observations. The residuals calculated from the difference between the model predictions and observed values also show that, overall, the vertical signals are well fit by a model of solely ice unloading (Figure 6). The mean residual for the vertical signal is −2.6 mm.

FIGURE 5

FIGURE 6

The modeled horizontal displacements due to snow load variations are largest at the edge of the glacier, compared to the center, and all vectors are directed outward from the glacier (Figure 5). This can explain the horizontal deformation observed at cGNSS stations outside of the glacier, as evidenced by the minimal residual signal at these stations in Figure 6. Several stations, such as OFEL and FIM2, are not perfectly fit by our model. These stations may be influenced by snow loading outside of the glacier as this is not modeled in our FEM model. For the stations on nunataks within the glacier, the predicted deformation from snow loading cannot explain either the magnitude or the direction of these signals, as shown in Figure 6. To model the horizontal deformation at AUST and ENTC, we must consider an additional deformation source (see Section 3.4).

3.3 Solid Earth deformation and the 2024 and 2025 jökulhlaups

The jökulhlaups in 2024 and 2025 coincide with solid Earth deformation at AUST. In this study, we use the floods as an example of shallow surface drainage events and compare them to the timing of recorded solid Earth deformation.

We consider periods when conductivity in Skálm and Leirá-Syðri is above 200 , along with rising water levels, to be jökulhlaups or smaller geothermal leakage events. The largest jökulhlaup in 2024–2025 is the July 2024 event and coincides with approximately 5 cm of deformation in both the north and east components at AUST in the week preceding the release of the floodwater (Figure 7). This is larger than the predicted seasonal deformation in the horizontal components at AUST during an average year (Supplementary Table S1). During the July 2024 jökulhlaup, the vertical component at AUST is largely unaffected during the same time period. Additional jökulhlaups occur throughout August and September in 2024, and there is deformation at AUST that coincides with the release of floodwater, although at a smaller level than during the July 2024 event (Figure 7A).

FIGURE 7

In July 2025, a second series of jökulhlaups began from the same cauldrons as in 2024. Again, the increase in conductivity in Skálm (See Figure 7B) and Leirá-Syðri (see Supplementary Figure S2) coincides with cm-scale solid Earth deformation at AUST. During the first jökulhlaup on 8 July 2025, there is approximately 5 cm of deformation in the north component and 2 cm of deformation in the east (Figure 7B). There is also noticeable deformation at AUST during the jökulhlaups on 19 July, 1 August, 24 August, and 1 September 2025, although it is smaller than the 8 July event. During the 2025 jökulhlaup series, the north component of AUST records more displacement than the east component. This contrasts with the 2024 jökulhlaup, where both horizontal components experienced equivalent displacement. Additionally, there is no significant displacement recorded in the up component of displacement at AUST during the 2024 jökulhlaups, but there is approximately 1 cm, or more, of vertical displacement during each jökulhlaup in 2025 (Figure 7B). This could indicate that the 2025 jökulhlaups had a different source or mechanism than the 2024 jökulhlaups. Regardless, both jökulhlaup series in 2024 and 2025 are sudden drainage events in the hydrological system of the glacier.

3.4 Poroelastic model of the hydrologic system

Using the residuals from the FEM model predictions of deformation due to snow loading and the observed seasonal signal data, we used the VSM tool to find the best-fit of a TPE cylindrical source. The inversion results presented in this study are meant to be an investigatory model to see if reasonable deformation source parameters can recreate the residual observed horizontal deformation signal after removing predicted deformation from snow loading. A TPE source was chosen over simple elastic models, such as a point source (Mogi, 1958), spherical source (McTigue, 1987), or ellipsoid (Fialko et al., 2001), due to the large residual horizontal and minimal vertical signals, and the likelihood of a very shallow source near to or inside the glacier causing the deformation. A single cylindrical TPE source is considered to be a simplified hypothetical model for the hydrologic system at Katla.

When inversions were run with all parameters free, the best-fit result was a very shallow source with a small radius, with an unrealistically high pressure change (on the order of tens of MPa). For every inversion we ran, the best-fit TPE source was at the minimum depth boundary. Due to how shallow the best-fit source is, it is highly unlikely to represent a shallow magma body, but it could coincide with the shallow surface processes occurring at the base of the glacier. These models provided a good fit with the observed displacement at the AUST station, but not at ENTC, with minimal predicted displacements at other sites. Given the uncertainty associated with the residual data, and to avoid unrealistic solutions (e.g., source thickness greater than the depth to the center of the source), we limit the unknowns by fixing the thickness parameter. The source thickness was fixed to 250 m, which is half of the thickness of a source found in a geothermal area in a caldera setting in Campi Flegrei, Italy (Nespoli et al., 2021).

Very little is known about the geothermal system or shallow surface conditions at Katla due to the presence of thick ice, so further simplifications were made. We assumed that there was no temperature change in the TPE source. There is limited knowledge on the appropriate values to use for (Equation 5) in volcanic geothermal areas, in particular for the subglacial geothermal system of Katla. We set equal to 10 GPa, according to Nespoli et al. (2021), Nespoli et al. (2023), and Nespoli et al. (2026), for studies on the geothermal system of the Campi Flegrei Caldera in Italy, which is comparable with the Katla geothermal system. When temperature change does not occur, Equation 5 shows that the potency of the TPE scales with the ratio of the pressure change and the parameter.

The pressure change in the TPE source was considered to lie within a range of permissible values from glaciological observations. The maximum permissible value was chosen based on observations of pressure change at the base of a glacier during winter to early-spring transition. For Bench Glacier in Alaska (United States), the pressure at the base of the glacier was inferred to change from 90% of the overburden pressure in the winter to 50% overburden pressure in approximately a week (Harper et al., 2005). We use a 40% change of the overburden pressure to be an upper estimate of the seasonal pressure drop at the base of a glacier. The average thickness of Mýrdalsjökull within the caldera is 450 m (Magnússon et al., 2021). In our case, the average overburden pressure, with an estimated average density of 900 kg/m³, is 3.9 MPa. Because 40% of the overburden pressure would be approximately 1.6 MPa, we use a representative 1.5 MPa pressure drop as a realistic upper boundary estimate for maximum change at Mýrdalsjökull. Equation 5 was used to calculate the potency value set as the maximum permissible value in the VSM inversion, which is −⁻⁵.

The best-fit result of the VSM inversion is a TPE source centered at 63.664682°N 0.3 km, −19.106118°W 0.25 km, with a radius of 1.6 0.2 km (Figure 8). The best-fit depth is 125 + 50 m, which is the shallowest we could allow, given the fixed source thickness of 250 m. The best-fit potency is −5 +⁻⁵, at the maximum boundary of permissible potency we allowed. The uncertainties were determined by computing the half-width of the frequency density (Trasatti et al., 2015; Trasatti, 2022; Sambridge, 1999). The misfit of the predicted displacements from the VSM inversion and the input residual displacements from the FEM model predictions is 0.0968.

FIGURE 8

The result is a deformation source located within the Katla Caldera and close to AUST, encapsulating ice cauldrons 13 and 14. The predicted deformation from the VSM inversion is largest at AUST, with significant horizontal deformation, predicted 2.8 cm (Figure 8), although it does not fully capture the extent of the observed horizontal displacement, 4.8 cm is observed. There is also predicted vertical deformation at AUST of −1.3 cm, which is not reflected in the input data. The deformation field is very localized to AUST, with very little predicted deformation at ENTC, despite there being a significant horizontal signal in the input data. Our use of only one deformation source may not be the best for modeling the residual signal between the FEM model considering only snow loading, and the observed seasonal signal. Multiple deformation sources may be able to better recreate the signal at both AUST and ENTC. Our parameter marginal distributions for latitude, longitude, and radius estimates are well constrained (Figure 9), while the parameter marginal distributions of depth and potency are on the minimum and maximum boundary, respectively. We find a limited correlation between the radius and potency in our inversion (Figure 9) and observe no significant correlation between the other free parameters. We also acknowledge that using a fixed thickness of the TPE source, rather than having it as a free parameter, amplifies the correlation between radius and potency.

FIGURE 9

4 Discussion

4.1 Ground deformation from snow loading at Katla

Seasonal ground deformation from snow loading is recorded across Iceland. The largest recorded annual deformation in Iceland is at AUST (Grapenthin et al., 2006; Drouin et al., 2016), possibly because the winter precipitation at Mýrdalsjökull is the highest reported in Iceland (Ágústsson et al., 2013). Seasonal snow-loading-induced ground deformation is recorded across the world in high snow accumulation areas such as Japan (Heki, 2001), Svalbard (Kierulf et al., 2022), and Alaska (Freymueller et al., 2008; Fu et al., 2012). Deformation from snow loading is recorded most prominently in the vertical component, oftentimes on the order of several centimeters (Heki, 2001; Drouin et al., 2016; Kierulf et al., 2022; Fu et al., 2012). Horizontal deformation from snow loading is rarely considered, but it has been reported on the order of millimeters (Grapenthin et al., 2006).

The FEM model, including spatially varying snow unloading, can explain, within uncertainties, the vertical seasonal deformation observed, up to 3 cm peak-to-peak, at all cGNSS stations used in this study (Figures 5a, 10). It can also explain the horizontal deformation at cGNSS stations outside of Mýrdalsjökull. However, it cannot explain the horizontal deformation, in both magnitude and direction, at cGNSS stations located on nunataks (AUST and ENTC) (Figures 5b, 10). Based on our modeling approach and the 3D seasonal unloading model, the best-fitting Young’s modulus is 28 GPa. From surface unloading models, we infer Young’s modulus of near-surface layers and for depths from 0 to up to the radius of the load (in this study 10 km), which is in agreement with the minimum value of 29 5 GPa found in previous seasonal loading models performed at Mýrdalsjökull (Pinel et al., 2007). Previous studies investigating surface loading from a glacial surge in Iceland suggest Young’s modulus values, in their one-layer elastic half-space model, of 46 GPa, although it is noted that their Poisson’s ratio is lower than ours, 0.17 (Auriac et al., 2014). Another study in Iceland at the Krafla Volcano suggested a local weak layer within the Krafla Caldera up to 4 km depth with a Young’s modulus of 7 GPa and a regional Young’s modulus of 30 GPa (Lanzi et al., 2023). Our estimate of 28 GPa for the Young’s modulus is within the range of values from previous studies in Iceland.

FIGURE 10

If the Young’s modulus value is decreased in the FEM model, then the vertical deformation would over-predict the observed seasonal displacement. This over-prediction from snow loading could account for the predicted vertical subsidence from the VSM inversion (Figure 8) and produce a net displacement that is equivalent to the observed displacement. Additionally, there may be influence from regional snow loading in the cGNSS data that is unmodeled in our snow loading model because it only encompasses the glacier. Regardless, adjusting the Young’s modulus will affect the predicted magnitude of deformation from the FEM model, but it will not change the direction of the prediction. A model of only snow unloading will never be able to recreate the direction of observed displacements at the nunatak stations, independent of the value of the Young’s modulus.

4.2 Hydrologic deformation signals

During the jökulhlaup series in 2024 and 2025, up to 5 cm of horizontal displacement was recorded at AUST in the week prior to the floods (Figure 7). There is high temporal correlation between deformation at AUST and increased conductivity in the Skálm and Leirá-Syðri rivers, demonstrating that there is significant horizontal solid Earth deformation from changes in the hydrology at Katla. While there was some vertical deformation recorded at AUST in association with the 2025 jökulhlaup series, most displacements are in the horizontal components during both the 2024 and 2025 series. Active motion of silicic cryptodomes has been suggested for west of the Katla Caldera (Soosalu et al., 2006; Lacasse et al., 2007). AUST is located on a silicic dome; hence, it is not impossible that the dome responds to glacier-induced pressure changes in the magma reservoir. However, due to the lack of other indications of cryptodome movement, we do not consider this.

The horizontal seasonal signal was modeled as a sinusoidal pattern, although the deformation time series has more of a sawtooth pattern at the AUST and ENTC nunatak stations (Figure 2b). The rapid displacements recorded in the sawtooth pattern in the horizontal components at AUST are consistent in shape, magnitude, and direction with the displacements associated with the 2024 and 2025 jökulhlaup series (Figure 7). Additionally, the rapid sawtooth deformation at AUST typically occurs during the beginning of July, during a similar time of year as the first jökulhlaups of the 2024 and 2025 series. This sawtooth pattern occurs only in the horizontal components of the nunatak stations. The far-field cGNSS stations appear to have sinusoidal horizontal deformation, although the low signal-to-noise ratio makes this difficult to discern. On average, the horizontal component of the seasonal signal is smaller than the vertical, except at the nunatak stations where the magnitude of deformation is similar across all components (Supplementary Table S1). The onset time of horizontal summer deformation is distributed over a 14-week period from DOY 57 to DOY 154 (Table 1). In contrast, the vertical signal at all cGNSS stations is well modeled as a sinusoidal signal. The average onset of vertical summer deformation occurs within a 5-week period (6 May and 16 June), in agreement with summer melting of Mýrdalsjökull, onset 2 May through August (Ágústsson et al., 2013). A study of seasonal signals from snow loading across Iceland by Drouin et al. (2016) also estimates the beginning of summer uplift at GNSS stations around Mýrdalsjökull to initiate between DOY 125 and 150 (5 May and 30 May). We estimate a phase lag of 4–45 days between the average onset of summer snow melt at Mýrdalsjökull and the onset of vertical cGNSS deformation. This is similar to the inferred phase lag between the infiltration of groundwater, and thus changes in pore pressure, and the onset of GNSS displacement at Long Valley Caldera (United States) of 30–55 days (Silverii et al., 2020). An alternative explanation for the phase lag is the eventual influence of viscoelastic properties of the Katla magmatic system, which is not modeled here, but can cause a phase lag between an annual loading and ground deformation (Liao et al., 2023). The difference in timing, magnitude, and shape of the horizontal deformation time series between the far-field cGNSS stations and the nunatak stations, and the different DOY onset of summer deformation in horizontal and vertical displacement components, supports our conclusion that a different process is dominating the horizontal displacements at the nunatak stations from the process dominating the overall vertical displacement field.

We model the residual cm-scale horizontal signal after comparing the observed seasonal displacement to our predicted FEM model displacements at the nunatak stations, using a TPE source within the VSM software (Trasatti et al., 2008; Silverii et al., 2025). Our deformation source is a singular cylinder in a homogeneous medium (bedrock), with flat topography and no ice, meaning that it cannot extend into the ice. Thus, a shallow best-fit depth suggests hydrological changes are responsible for the observed horizontal seasonal deformation. However, in this study, we cannot discern whether these changes are from the evolution of summer drainage conditions at Mýrdalsjökull, changes in the geothermal systems at Katla, and/or changes in shallow subsurface pore pressure (Figure 10). Processes occurring englacially and at the base of the glacier are only partially represented by this model. Additionally, because only one TPE source was used, it is strongly influenced by the observations at station AUST due to the large deformation signal observed there (Figure 8). Our results from VSM may be more representative of a localized deformation source to AUST, such as ice cauldrons 13 and 14, rather than representative of the full drainage system of Mýrdalsjökull. Our inversions suggest that a shallow source is responsible for the deformation, and thus it is unlikely that the residual horizontal seasonal signal is caused by magmatic processes. Our approach to fit the vertical signal prior to the horizontal signal will necessarily result in a shallow source depth estimate because the depth is determined by the ratio of vertical to horizontal motion. Thus, it is possible that a part of the vertical motion at AUST due to loading is overestimated. However, the quality of fit to other stations in the area indicates that our approach is reasonable. Thickness was fixed to prevent the shallow best-fit TPE source from being above the surface. In our inversion, the potency and radius show a limited correlation; with increased radius, we estimate lower potency values. Our limiting upper bound on potency, based on observations made by Harper et al. (2005), forces the radius to have the minimum possible value related to this potency value.

During summer snow melt, the geothermal systems at Katla may have higher thermal output due to a reduction in surface confining pressure (Wynn et al., 2015). The geothermal heat output of the geothermal areas at Katla has been estimated to be around 1000 MW (Jóhannesson et al., 2020). Katla is a large emitter of CO₂, potentially contributing up to 4% of global emissions from non-erupting volcanoes (Ilyinskaya et al., 2018). This indicates that the geothermal systems at Katla may be very powerful and capable of producing significant seasonal hydrologic change in addition to the seasonal changes in the glacial drainage system, particularly around the late spring and early summer when geothermal activity is stimulated.

Seasonal seismicity has been observed within the Katla Caldera and is interpreted to relate to changes in surface snow loading and seasonal changes in shallow subsurface pore pressure (Jónsdóttir et al., 2007). The suggested magnitude of pore pressure change at Katla is about 0.03 MPa, based on an estimate that all summer meltwater percolates into a crust with a porosity of 10% (Einarsson and Brandsdóttir, 2000). However, the pressure change could be larger, as inferred by Harper et al. (2005) about changes associated with subglacial water drainage. The process responsible for solid Earth deformation at Long Valley Caldera is assumed to be pore pressure change, and non-volcanic seasonal seismicity has also been linked to snow melt and changes in pore pressure (Montgomery-Brown et al., 2019; Silverii et al., 2020). Montgomery-Brown et al. (2019) observe a rapid lag time of 24 days between increased water at the surface and seismicity. A study of seasonal seismicity and groundwater recharge at Mt. Hood Volcano estimates a lag time of 155 days (Saar and Manga, 2003). Fluid re-injection near the Hellisheiði geothermal system in Iceland increased pore pressure in surrounding boreholes and is the main source of 2 cm of observed ground deformation, and induced seismicity (Juncu et al., 2020). While the observed pore pressure change in Hellisheiði, 2.8–0.08 MPa (Juncu et al., 2020), is larger than the estimated change at Katla, this demonstrates that changes in pore pressure at Katla may contribute to seasonal ground deformation.

Hydrologic systems of glaciers experience seasonal changes to accommodate the changing volumes of discharge between summer and winter periods. Models of subglacial drainage evolution suggest that water pressure increases from increased melting in the spring, leading to a “spring event” in which the subglacial drainage system is reorganized into channelized flow (Harper et al., 2005; Hart et al., 2022). As this more efficient drainage system develops throughout the summer, the pressure decreases, and in the autumn/winter, the water level also decreases, which changes the subglacial hydrology back to a less efficient system due to higher relative ice overburden pressure (Harper et al., 2005; Hart et al., 2022). Using the water chemistry of an outlet river of Mýrdalsjökull, Wynn et al. (2015) suggest that little water drainage occurs from geothermal areas in winter and that the river is mostly composed of meltwater from the lower portions of the glacier. Due to the topography and high ice overburden pressures, it is unlikely that there is continual drainage from geothermal areas inside the caldera (Wynn et al., 2015). Instead, drainage of geothermal areas occurs when the headward development of channelized flow connects to the caldera region. The water pressure in this region is quickly released and equalized with the lower parts of the hydrologic system (Wynn et al., 2015). This sawtooth-like pattern of seasonal water buildup and release in the Katla Caldera could be causing the observed deformation patterns at the nunatak cGNSS stations (Figure 10). The results from the VSM inversion reveal a source near the surface of the modeled Earth. While some changes in glacier hydrology will extend to the shallow subsurface, such as sediment saturation at soft bedded glaciers (Hart et al., 2022) and subsurface pore pressure change from meltwater percolation (Einarsson and Brandsdóttir, 2000), most of the processes described above occur above the bedrock and within the glacier system. The seasonal pressure changes observed by Harper et al. (2005) are measured at the glacier-bed interface, and how far these changes propagate into the solid Earth is unknown. Processes occurring englacially or at the base of the glacier are not explicitly modeled in our TPE source inversion because the model domain is restricted to the Earth’s subsurface, but deformation from them would be captured in the observed deformation signal, which was used as input data for the VSM inversion. Additionally, Hart et al. (2022) suggest that the spring event at Skálafellsjökull, another glacier in Iceland, occurs over 4–5 days, which is a similar duration of time to the pre-jökulhlaup movement observed at AUST in 2024 and 2025. Wynn et al. (2015) also suggest that a reduction in pressure from snow loading in spring may stimulate geothermal activity at Katla, which may also contribute to the observed pre-jökulhlaup deformation at AUST. We suggest that a combination of above-surface changes occurring within and at the base of the glacier, such as drainage system reorganization, and subsurface changes, such as meltwater percolation or geothermal stimulation, cause the observed horizontal signal at the nunatak stations (Figure 10).

Horizontal seasonal ground deformation has been recorded across the world, often attributed to hydrologic changes rather than directly due to snow loading. In northern California, annual snow loading in the Sierra Nevada Mountains has caused significant horizontal ground deformation, such as cm-scale displacements recorded in Long Valley Caldera (Silverii et al., 2020), and contributed to seasonal seismicity (Kreemer and Zaliapin, 2018). Other regions have observed significant horizontal deformation attributed to water loading during monsoon seasons, such as the Amazon (Fu et al., 2013) and the Himalaya region (Chanard et al., 2014). Our study demonstrates that glaciated regions, such as Katla, also experience horizontal deformation as a result of seasonal changes in glacier hydrology. However, our study suggests more localized deformation, due to our observations of significant hydrologic signals only at nunatak stations at Katla.

4.3 Conclusion

Seasonal snow loading at Katla can explain observed vertical and far-field horizontal deformation but not the horizontal deformation at cGNSS stations located on nunataks within the glacier. An inversion of the residuals between the snow loading FEM model and observed data using a thermo-poro-elastic (TPE) source required a best-fit deformation source to be very shallow. This indicates that the horizontal deformation is unlikely to be caused by modulation within a magma body but rather shallow surface processes such as changes in pore pressure, seasonal drainage of the glacier, and changes in a geothermal system. The observed displacements at the AUST cGNSS station during the 2024 and 2025 jökulhlaup series are comparable in magnitude to the observed seasonal deformation. The high temporal correlation between the floods and solid Earth deformation recorded at AUST indicates that changes in the hydrologic system of the glacier can cause significant ground deformation. Horizontal deformation at both nunatak cGNSS stations (AUST and ENTC) cannot be explained by a single cylindrical source, indicating that the hydrologic processes occurring at Mýrdalsjökull are complex. Future research is needed to better model the hydrologic system of the glacier and seasonal changes in the shallow subsurface. Regardless, this study contributes to the understanding of the seasonal ground deformation signal and participatory processes at Katla by suggesting that two distinct, but related, processes explain different aspects of the observed annual cycle of ground deformation.

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