Ocean tides trigger ice shelf rift growth and calving

Domain: earth_science
Published: 2025-07-24
Editorial outcome: major_revision

Abstract
Tabular iceberg calving reduces ice-shelf extent, affecting ocean circulation and ice-sheet stability. Here we present detailed observations of a rift on the Brunt Ice Shelf, East Antarctica, from 2017-2023 and its behaviour in the lead up to calving in January 2023. The timing of rift propagation was controlled by the rate of change of ocean tide height, wind speed, and an iceberg collision in August 2021, as well as the long-term ice dynamics. A viscoelastic rheological model is used to estimate the relative magnitude of stresses acting on the rift and to determine a critical threshold for fracture, which was exceeded during a sequence of propagation events in early 2019. The eventual calving on 22nd January 2023 occurred at the peak of a spring tide, supporting the conclusion that tides directly influenced the timing.

Introduction
Ice shelves are vital for the stability of marine-terminating ice sheets1. Sections calve from their seaward margins on multi-decadal timescales, producing discrete tabular icebergs that impact local ocean circulation and freshwater flux2,3 and form a key component of the overall mass balance of the Antarctic continent4. Irregular or accelerated rates of calving can destabilise ice shelves and reduce their ability to buttress outlet glaciers upstream5. Predicting large calving events is important in both ice sheet and coupled earth system models due to the resulting changes in model geometry, ocean properties and melt rate6,7. Nevertheless, the processes that drive fracture growth in ice remain poorly observed by field measurements and abstractly represented in models.

On ice shelves, rifts form when there is a change from compressive to extensional stress, usually occurring at the mouth of embayments or on the downstream side of islands or pinning points. Fracture growth is generally considered to be dominated by glaciological stresses8, but external influences from waves9,10, tsunamis11, ocean swell12, atmospheric extremes13, sea ice extent14,15 and iceberg collision16 have all been shown to cause or provide resistance to calving. In Greenland, tides have been implicated in tidewater glacier calving through vertical growth of crevasses associated with fluctuating water pressure17,18.

The Brunt Ice Shelf in East Antarctica has seen the growth of several rifts in the last decade and has been studied in detail by the British Antarctic Survey for over 60 years19. Local ice dynamics are dominated by the compression of ice into a small bathymetric high point known as the McDonald Ice Rumples (MIR) that is located 60 km downstream of the grounding line (Fig. 1c). The strength of the connection here is fundamental to the velocity of the ice shelf20,21, with weakening leading to substantial acceleration since calving in early 202322.

In the short term, tides cause semi-diurnal elevation changes of ±2 m and impact ice velocity by up to 100% within one day23. Tidally varying flow is observed on ice shelves around Antarctica, particularly strongly in the Weddell Sea24, and has been explained by the interaction of the ice shelves with grounded regions25 or varying sea surface slopes26. Here, we investigate the effect that tides have on fracture processes by looking at the behaviour of a rift known as Chasm-1. Long-term evolution of Chasm-1 from 2012 to 2019 is attributed to evolving stress near the MIR and spatial variation in ice properties27–29. This rift originally formed close to the grounding line in the southern part of the ice shelf and completed its intersection with the coast in January 2023, forming the 1500 km2 A-81 iceberg (Fig. 1h).

We monitored the width of Chasm-1 between 2017 and 2023 using four permanent GNSS receivers, which advect with ice flow, and a specially configured ApRES phase-sensitive radar system (Figs. 1, S1). There is no adjustment due to strain rate in intact ice, which is around 0.001 a−1. Within this six-year dataset we focus on behaviour over several shorter periods, including (1) the transition from sustained rift propagation to stagnation between February and September 2019; (2) the response immediately following a collision of iceberg A-74 in August 2021; and (3) the behaviour in the months preceding calving in 2023.

Results
a–Transition from propagation to stagnation in 2019
Between 25th November 2018 and 20th May 2019, Chasm-1 propagated 4 km in a sequence of discrete events (Fig. 1j). As the rift tip approached the MIR in June 2019, the opening rate decreased sharply, followed by a period of stagnation lasting ~two years (Fig. 1i), although the rift continued to widen. During both propagation and stagnation phases, sub-daily and fortnightly variations in rift opening angle indicate a mixture of recoverable and irrecoverable strain at the crack tip (Fig. 2a, b). We use a 1D viscoelastic model to interpret the observations, where a single time-dependent stress is responsible for both elastic and viscous deformations, which together give the total deformation30. In this model, the remote stress field satisfies the shallow shelf approximation for an ice shelf extending uniaxially in the x-direction, perpendicular to the crack31. There is no vertical variation in strain rate so observations at the surface are representative of the depth-averaged values32. We relate deviatoric stress perpendicular to the rift, \tau_{xx} to strain \epsilon using Glen’s Flow Law, where A is a viscous rate factor dependent on temperature, and n is the stress exponent33. In the viscous part, the stress-strain rate relationship is non-linear. In the elastic part, the stress-strain relationship is linear following Hooke’s Law where E0 is a material constant and a function of Young’s Modulus and Poisson’s Ratio:

\epsilon(t) = \frac{1}{E0} \tau_{xx}(t) + A \int_{0}^{t} \tau_{xx}^n dt (1)

This rheological model is the basis for a relationship between a non-dimensional stress scalar perpendicular to the rift at its tip, \zeta, and the local deformation that allow the crack to widen, represented by the rift opening angle, \psi (see Methods):

\psi(t) \propto \frac{1}{E0} \zeta(t) + A \int_{0}^{t} \zeta^n dt (2)

We determine from our observations of variability in \psi that \zeta can be split into three terms—a constant term \zeta_g, a periodic term \zeta_t that is a function of the tidal amplitude, and an irregular term \zeta_w which is a function of the wind speed:

\zeta = \zeta_g + \zeta_t + \zeta_w (3)

The opening angle variability is now attributable to combinations of each of the glacial dynamics \zeta_g, tides \zeta_t and wind \zeta_w, where the tide and wind components are scaled to match independent observations of tides and wind on the ice shelf. In the case of n=3, \zeta splits into three short-term, elastic (\psi_E) components and ten long-term, viscous (\psi_V) components:

\psi = \psi_E + \psi_V
\psi_E = \psi_{Eg} + \psi_{Et} + \psi_{Ew}
\psi_V = \psi_{Vg3} + \psi_{Vt3} + \psi_{Vw3} + \psi_{Vg2t} + \psi_{Vg2w} + \psi_{Vt2g} + \psi_{Vt2w} + \psi_{Vw2g} + \psi_{Vw2t} + \psi_{Vgtw} (4)

Furthermore, because the temporal variability in \zeta drives both the short- and long-term variability in \psi, and because there is non-linearity in the long-term behaviour caused by the rate exponent (n) but not in the short-term behaviour due to linear elasticity, the unknown scaling between \zeta and \tau_{xx} can be calculated from the relative magnitudes of the short- and long-term variability in opening angle using published values of A, E, and Poisson’s ratio. This allows absolute values of deviatoric stress to be estimated (Fig. 2).

In 2019, the overall opening rate is dominated by a single term—the viscous response due to glacial stress combined with the square of the tidal contributions. The non-linear tidal part creates the strong fortnightly variability (Fig. 2c, d), which is also seen in ice shelf velocity data24. The tidal elastic term (\psi_{Et}) accounts for most of the sub-daily variability, where narrowing of the rift occurs during falling tides. Four other components in Fig. 2 contribute slightly, while the other seven terms are negligible and not shown. For this rift over this period, the tide-induced component of stress during spring tides exceeds the glacial component due to ice shelf spreading by a factor of more than two (Fig. 2e, f). The wind-induced component is more irregular, although here it exceeds the glacial part when the wind exceeds 20 m.s-1.

Five separate rift propagation events of between 50 and 500 m occur in early 2019, observed with TerraSAR-X imagery34 (Fig. 3). These happen when peaks in wind occur simultaneously with spring tides. The model highlights that the combined tidal and wind effects push the stress above a specific threshold at least once in each of the 5- or 6-day windows when we observe propagation. Our estimate of the deviatoric stress threshold at the time of rift propagation is ~240 kPa, which is within the range of surface tensile stresses of 90–320 kPa found to correlate with the appearance of surface crevasses35.

After June 2019, the opening rate in both ApRES and GPS datasets decreased by ~40% (Figs. 1i, 2b). Our model fit indicates that tidal and wind driven components remain the same while there was a reduction of 25% in the glacial component (Fig. 2f), implying a change in wider ice flow is responsible for rift stagnation. Equivalent ApRES data from 2017 and 2018 show that when the crack tip was further from the MIR, the maximum deviatoric stresses experienced before failure were still around 240 kPa, although with weaker tidal and wind components and a stronger glacial component (Fig S2). The glacial part is also consistent with previously modelled glacial stresses of up to 140 kPa occurring during earlier propagation events in 201629. Here, the influence of tides increased as the rift extended, becoming dominant around late 2018. Propagation of the rift towards the MIR has the combined effect of reducing the length of the ligament connecting the ice shelf to the proto-iceberg and increasing the moment through which tides and winds drive open the crack (Fig. S4).

Iceberg collision
On 10th August, an iceberg known as A-74, which had calved from the northern part of the Brunt Ice Shelf in February 202113, collided with the remaining ice shelf to the west of Chasm-1. This led to rapid propagation of Chasm-1, growth of a secondary rift from the north (Fig. S5) and additional widening of 7 and 3 m at GNSS baselines TT01-KK00 and NN00-OO00 (Fig. 4g). Evidence of collision is visible in Sentinel-1 satellite imagery (Fig. 4a, b). The energy transferred into the ice shelf was sufficient to create ~7 km of new rift length. This single propagation event was greater than the total rift growth throughout the whole of 2019 due to the interaction of ordinary glacial, tidal and wind stresses, although the collision was still insufficient to cause calving.

Calving
After the collision and by the end of 2022, the opening rate of Chasm-1 had increased to 1.5 m/day at the NN00-OO00 baseline and 2 m/day at TT01-KK00 (Fig. 1g). Both GNSS baselines continued to show strong spring-neap and daily tidal variability. Calving of A-81 and a smaller unnamed section south of the MIR occurred at around 18:00 UTC on the 22nd January (Fig. 1h). An initial 20 m of movement within an hour confirmed disconnection, which coincided with the fastest rising tide during spring tide (Fig. 5d). Movement away from the ice shelf slowed on the falling tide, resuming during the following rising tide around 07:00 on the 23rd January. The detached iceberg drifted 10 km over the next week, maintaining a strong tidal dependence in drift once free from the ice shelf, with fastest movement during rising tide (Supplementary Movie 1).

Methods
Field observations
The Chasm-1 rift was monitored by GNSS, satellite and a modified ApRES system40. The GNSS receivers at sites named NN00, OO00, TT01, KK00 were Leica GS10s, which recorded their position at 30s rate for two hours each day. This data was converted into a baseline distance using RTKLIB software41. The rift tip location from September 2018 was determined from TerraSAR-X imagery where a strong backscatter contrast between the rift (high backscatter) and undamaged ice (low backscatter) indicates the tip position even when the rift is bridged by drifting snow34. Landsat-8 imagery constrains the tip location during austral summer before 2018.

The ApRES was configured with the transmitter and receiver on the eastern side of the rift, pointing horizontally across the rift, and a large metal reflector (2×4m aluminium mesh) on the western side, initially separated by around 30m (Fig. S1). This produced a strong reflection, which is converted into range assuming a velocity in air of 0.3 m/ns. The system recorded data every 10min. The uncertainty on the ApRES data (~±2mm) is substantially lower than the daily tidal changes in width (±50–100mm). We use a Savitsky-Golay filter to remove noise. The width is converted into opening angle using rift tip positions from the TerraSAR-X backscatter images, labelled manually.

Rheological model
The model is based on a Maxwell rheology where elastic strain, \epsilon_E, and viscous strain, \epsilon_V, sum to give total strain, and elastic stress \sigma_E is equal to viscous stress \sigma_V. Elastic stress is related to elastic strain through Hooke’s Law:

\sigma_E = \lambda tr[\epsilon_E] I + 2\mu\epsilon_E (5)

Also written as:

\epsilon_E = \frac{1}{2\mu} \sigma - \frac{\lambda}{2\mu(3\lambda+2\mu)} tr[\sigma] I (6)

Where \lambda = \frac{E\nu}{(1+\nu)(1-2\nu)} and \mu = \frac{E}{2(1+\nu)} are the Lamé parameters, and E and \nu are Young’s Modulus and Poisson’s ratio. We separate the depth-dependent component of \sigma as follows32:

\sigma = R - \rho g(s-z)I (7)

Here R is a resistive stress, which can be defined from principal strain rates in x and y directions, \dot{\epsilon}_{xx} and \dot{\epsilon}_{yy}, and viscosity, \eta using the shallow-shelf approximation42:

R = 4 \begin{pmatrix} 2\dot{\epsilon}_{xx} + \dot{\epsilon}_{yy} & 0 & 0 \\ 0 & 2\dot{\epsilon}_{yy} + \dot{\epsilon}_{xx} & 0 \\ 0 & 0 & 0 \end{pmatrix} (8)

R, like \sigma, can also be split into deviatoric and volumetric parts:

\tau = \sigma - \frac{1}{3} tr[\sigma] I = R - \frac{1}{3} tr[R] I (9)

So that the deviatoric stress tensor, \tau is:

\tau = 2\eta \begin{pmatrix} 2\dot{\epsilon}_{xx} + \dot{\epsilon}_{yy} & 0 & 0 \\ 0 & 2\dot{\epsilon}_{yy} + \dot{\epsilon}_{xx} & 0 \\ 0 & 0 & -(\dot{\epsilon}_{xx} + \dot{\epsilon}_{yy}) \end{pmatrix} (10)

We then simplify by restricting the ice to uniaxial strain perpendicular to the crack so that strain in the crack-parallel direction (y) is zero. This allows us to write the elastic part of the strain in terms of deviatoric stress as:

\epsilon_{E,xx} = \left( \frac{1}{2\mu} + \frac{\lambda}{2\mu(3\lambda+2\mu)} \right) \tau_{xx} (11)

For the viscous part, uniaxial strain rate means viscosity, \eta is controlled only by \tau_{xx} and the rate factor A:

\eta = \frac{1}{2} A \tau_{xx}^{n-1} (12)

So that for the viscous part, the uniaxial strain rate is:

\dot{\epsilon}_{V,xx} = A \tau_{xx}^n (13)

We now have a single stress component that influences both the elastic and viscous behaviour:

\epsilon_{xx}(t) = \epsilon_{E,xx} + \epsilon_{V,xx} = \left( \frac{1}{E0} \right) \tau_{xx}(t) + A \int_{0}^{t} \tau_{xx}^n dt (14)

As we do not directly measure a strain field ahead of the rift, or an applied stress, we must now introduce two scaling constants. This requires two further assumptions—firstly, the width of the rift is linearly proportional to strain at the crack tip. This is only reasonable when the tip is stationary and so to account for propagation events, we convert width, w, taken from ApRES measurements into the opening angle, \psi, using distance between the ApRES and the current crack tip, d, (Fig. S4):

\psi = \frac{w}{d} (15)

\epsilon = C_1 \psi (16)

This minimises any direct feedbacks between propagation and rift width. Secondly we assume that the remote stress on the ice shelf is linearly proportional to the stress that controls the fracture events:

\tau = C_2 \zeta (17)

We split this remote stress into three parts. The glacial term \zeta_g represents the combined effect of imbalance of hydrostatic forces within the shelf, which cause horizontal spreading and tensile stresses induced by flow of the ice shelf. In the model, this is held constant over short time periods of up to a month while we focus on the short-term behaviour.

The tidal term \zeta_t represents the effect of periodic ocean tides on the ice shelf. Tidal amplitude measured with GNSS at the nearby Halley Station 10–15 km is used from 2019 onwards22, while a tide model is used for 2017 and 2018 data36. The GNSS data accounts for the inverse barometer effect on sea level that is not captured in the tide model. The mechanism through which the tides influence the crack width is not directly modelled here, but there is a strong correlation between opening angle and rate of tidal amplitude change (Fig. S6), with rising tides leading to stronger widening. We find a time-lag of around 1.5 h between the tidal signal and the opening angle and use the rate of change of amplitude offset by 1.5 h as a proxy for tidally induced variability in stress. The relative contributions of the tide, wind and glacial components are unknown a priori, and so two further scaling constants are introduced C_3 and C_4:

\zeta_g = 1 (18)

\zeta_t = C_3 \frac{d(z-t_\omega)}{dt} (19)

\zeta_w = C_4 u_w^2 (20)

Where z is the detrended height above sea level of the ice shelf surface at Halley (a proxy for tidal height), u_w is the wind speed and \omega indicates the time lag between the tide and the response at the rift.

The wind term \zeta_w represents the strength of easterly winds caused by low-pressure systems to the north. These are common on the Brunt Ice Shelf with wind stresses increasing proportionally to the square of the wind speed43. Wind data are taken from a 2m weather station at Halley Station.

Assuming n=3, this model can be expanded to give a relationship between opening angle and remote longitudinal stress, with thirteen forcing terms that sum to produce the opening angle:

\psi = \frac{C_1}{E_0} \int (\zeta_g + \zeta_t + \zeta_w) dt + A C_2^3 \int (\zeta_g^3 + 3\zeta_g^2 \zeta_t + 3\zeta_g^2 \zeta_w + 3\zeta_g \zeta_t^2 + 3\zeta_g \zeta_w^2 + 6\zeta_g \zeta_t \zeta_w + \zeta_t^3 + 3\zeta_t^2 \zeta_w + 3\zeta_t \zeta_w^2 + \zeta_w^3) dt (21)

Each of the parameters C_1-4 controls an aspect of the final shape of the opening angle curve. We vary all parameters together in a four-dimensional space, then calculate the least-squares fit of each combination relative to the observations, such that the overall minimum indicates the optimal parameter values.

C_3 controls the relative magnitudes of the tidal and glacial parts and can be constrained from the viscous behaviour (the relationship between linear rate of opening and spring-neap variation). C_4 determines the relative magnitudes of the wind and tidal parts and can be constrained from the elastic behaviour during strong winds, relative to the elastic tidal behaviour. C_1 and C_2 depend on the relative amplitudes of the viscous and elastic behaviour (Fig S3) and are highly sensitive to the choice of E and A (Fig. S7). The range of values stated in the literature for E and A is large and leads to large variations in the apparent fracture threshold. Here, we use E=9 GPa44, \nu=0.3 and A=5.3×10−25 s−1 Pa−3 45, which are reasonable estimates for ice at ~−10 °C on the Brunt Ice Shelf19. The derived value of C_2 then allows us to approximate the depth-averaged deviatoric stress threshold for fracture.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscripts describes results from a field campaign on the Brunt Ice Shelf showing that rift propagation appears to be, at least partially, triggered by ocean tides and winds. This study falls into a larger cannon of studies that seek short-term environmental triggers of rifting propagation and iceberg calving. This study is the first that I am aware of that demonstrates a link between rift processes and tidal forcing. One of the challenges, however, of this type of study is that it is difficult to generalize: we do not know if the correlation with tides holds more generally for rifts in the Brunt ice shelf, much less other rifts on other ice shelves. This issue is an issue that has been difficult to overcome in many studies, but doesn’t detract from the study presented here.\nOverall, I think the study is well written, adds to the literature and will be interesting to a wider audience. However, the methodology and assumptions were difficult for me to fully follow: I struggled to understand and convince myself that some of the assumptions described in the methods are appropriate and link the empirical models to physical models. I recognize that there is a balance that needs to be met with not being overly technical so that the manuscript is accessible to a wide audience and adding more specialized jargon. But I think that some more precision in terminology and clarity in the methods might be useful for readers. This is especially true when asking readers to make the link between analogies and derivations which seem based a little bit more on insight and intuition than formal manipulations. I outline some of these issues below, recognizing that it is possible that some of these are just wording issues while others might point to issues with the methodology that need to be addressed.\n1. Cauchy stress, deviatoric stress and all that. To start, the authors use the term \"stress\" multiple times throughout the study (e.g., line 69, line 74, but also many other places). Stress is, of course, a tensor, but it is treated in the text as if it is a scalar. This is fine so long as the authors are clear that they are referring to a particular component of the stress tensor (or better yet, the traction). I also assume that the “stress” referred to is depth averaged in some sense, but this is also not stated. The more confusing problem is that the authors do not distinguish between Cauchy stress, deviatoric stress and effective stress. In fracture mechanics, the stress driving crack propagation is the Cauchy stress, but flow of ice is controlled by the deviatoric stress. This is an important distinction because the Cauchy stress can be compressive because of the hydrostatic pressure whilst the deviatoric stress remains positive. More specifically, the effective viscosity in the creep flow-law is controlled by the effective deviatoric stress, which is independent of pressure and depends on the sum of the squares of the components of the stress. This is an important distinction because the effective stress cannot be negative and depends on more than a single component of the deviatoric stress tensor. I would typically write the Equation that appears in lines 69 and 74 in terms of the effective stress (which is always positive). All of this is very confusing to readers, especially since the tidal stress shown in Figure 2 has negative values. One has to be careful (and clear) about absolute values and what is positive and negative! Here the authors would better serve readers by clearly stating what they mean by “stress” in a more precise way (it is a component of the full stress tensor? is it depth-averaged? is it deviatoric stress or a component of the Cauchy stress).\n2. Local fracture stress, remote stress and rift opening angle. Putting aside the terminology issues, the Equation in Line 69 is valid for a 1-dimensional visco-elastic material. I don’t follow the subsequent assumptions and approximations made to then transform the rheological equation in Line 69 to rift opening angle in Line 78. This seems like an analogy then a derivation, which is fine but should be stated. If we consider uni-axial loading transverse to the rift and ignore all other components of the stress tensor, then it seems like we should be able to write an equation in the form of the Equation on Line 69 with epsilon(t) denoting the component of strain transverse to the rift. The integral of the strain would be the rift opening/displacement. The rift opening angle used here appears to be defined as the ratio of the width to the length of the rift and this is, at least dimensionally, equivalent to a shear strain. This adds confusion about which component of the stress is considered. It would be helpful to clarify this, but either way, I don’t see why the factors of A and E in the Equation in 74 has been dropped. Maybe the ratio is used to scale the rift opening to rift length, but rift width in an elastic material should scale with rift length. Moreover, the rheology s a statement about material properties and has nothing to do with the various stress balances in the far-field or fracture regions. The magnitude of stresses might vary spatially and in the near vs far field, but the rheology is not a statement about the stress balance. Hence, it is not clear to me why we need both equations or why they are written in different forms.\n3. Fracture mechanics and other stuff. The methodology sketched out in Lines 218-226 argues for a relationship between the local stress near the crack tip and the far-field stress that is based on fracture mechanics. As I understand it, I think the authors are trying to infer the stress near the crack tip based on the far field stress, which is perfectly reasonable for an elastic material. I can follow the scaling presented, but given the relationships in Equations near lines 218-223 and the fact that the rift length is known, why not use the rift length in the analysis? The proportionality is given by a factor that is related to the rift length and another factor this typically of order unity (often Pi or some such). At least for an order of magnitude estimate, we could directly estimate the stress associated with different forcing without introducing arbitrary constants. In fact, an alternative interpretation of the analysis is that if we divide both sides of the Equation in line 218 by the square root of the rift half-length, then we find that the remote stress required to drive rift propagation is approximately zero given the critical stress intensity factor from lab measurements. Hence, whenever the Cauchy stress (not deviatoric stress!) is positive, the rift will propagate. This relationship only holds for linear elastic materials, which gets me into my next point.\n4. Viscoelasticty and Hoff’s analogy. As I understand it, the analogy pointed out by the authors holds for linear viscosity and linear elasticity (or power-law elasticity and power-law creep), but not between linear elasticity and power-law creep. In fact the stress singularity associated with power-law creep has been deduced and it depends on the flow-law exponent. (The singularity is exactly the same as for an elastic material if the flow law exponent is unity.). As a consequence, I don’t think that the scaling argument that the authors apply follows. Or, at least, more clarification is needed to explain why it works. The way that the authors present the methods make it seem like this is a critical flaw in the methodology or something that needs additional justification. (I apologize if I misunderstood!) However, reading through a few more times I’m not quite sure that the authors analysis really depends on this scaling argument and I wonder if the authors can simply use the rheology presented in lines 69 with some appropriate measure of transverse strain and simplify much of this exposition.\n5. My penultimate concern about the methodology is, perhaps, more of a philosophical issue. The main conclusion is that tides and, to a lesser extent winds, drive rift propagation. The concerns that I raised are all based on the physical model presented, but the authors conclusions are fundamentally based on an empirical correlation with 4 tuned coefficients (5 if the phase of the tide is included) that are fit to the data. However, we can, at the very least, provide ball park estimates of all of the stress terms based on the data collected. The drag associated with tides and winds depends quadratically on the current/wind speed, density of water/air and a drag coefficient. The wind speed is measured. The current speed can be extracted from the same tidal model used to estimate ocean height. The only unknown is the drag coefficient, which can vary over several orders of magnitude. Nonetheless, the authors can ballpark estimate the stress associated with different forcing using a range of published drag coefficients to determine if the relative contributions inferred empirically are broadly consistent with what we expect from a more physical model. If the forcing is broadly consistent, then it is a strong check on the more empirical methodology and might negate my confusion about the methods. Moreover this might even allow us to estimate the role that winds and tides have on other rifts. This would be a significant advance in the field. If the relative magnitudes are not consistent then it implies drag coefficients need to be much larger/smaller than typically inferred or something else is going on that needs additional study. Perhaps the Brunt is unusual or there is missing physics we still need to understand. This is also important to know.\n6. My final point is that it seems as though the authors are using rift widening as a proxy for rift opening. Rift widening in an elastic material is either due to a change in the stress opening the rift and/or rift propagation. In a viscoelastic material the situation is more complicated because the rift will widen due to ductile flow even with no rift propagation. In an elastic material, rift widening results in stored elastic energy that can be released by rift propagation. In a disco-elastic material, rift widening may dissipate stored elastic energy or respond passively to rift propagation. This confusion may be addressed in the manuscript, but it seems possible that the rapid rift widening stages observed are caused by rift propagation, which stand in contrast with rapid rift widening causing stress accumulation that then results in rift propagation. In other words, the direction of causality isn’t clear to me. Can the possibility that rapid rift widening is simply a response to the fact that the rift is or has recently propagated?\nMinor comments:\nA key finding is that the square of the tidal forcing results in fortnightly forcing. Recent studies, however, have increasingly shown that on ice shelves the flow-law exponent is probably closer to 4. Would this significantly affect the results? Would the fortnightly tidal affect still appear? Does a flow law exponent of 4 help with the tidal phase offset needed in the fit? If the fortnightly forcing is robust, then this seems like a useful prediction of the model based on fundamental principles that is worth further emphasizing.\nIs it possible that the connection with wind speed is related to small movements of the stations of the ice associated with torque from the wind?\nLine 84: This is the results of expanding the cubic, right? Why are the factors of 3 and 6 in the terms dropped? Line 265: This equation includes all of the factors of 3 and 6s that was missing in the main text equation. It might be easier for readers if these equations are presented in a consistent form.\nLine 100: kts—use metric units.\nWhy do tides result in a phase shifted stress? This isn't intuitive to me. Is it somehow related to the phase difference between tidal currents that drive propagation and tidal heights?", "reviewer_2": "This is an excellent, interesting and important paper that reports highly detailed observations of rift propagation and iceberg release from Brunt Ice Shelf in Antarctica, and an insightful analysis of the key forces at work. The methods are rigorous and clearly explained and the conclusions justified. Illustrations are excellent.\nI see no need for any revision of the text, except for one minor correction. On line 41, there is mention of \"velocity fluctuations of plus/minis 2 metres\", which should of course be elevation fluctuations, which correspond with velocity fluctuations. It might also be useful to add the units for 'rift opening angle' which I presume are radians (line 72 and Fig 2).\nThe main change that I think might be useful is to the title of the paper. The title only mentions tidal forcing as the trigger for both rift propagation and calving, but it is clear from the text that this is not the whole story. While rising tidal stresses clearly coincided with individual rift propagation events, iceberg collision \"affected rift growth more substantially\" (line 187), and background glaciological stresses are obviously important. So I suggest you change the headline to include reference to at least the iceberg collision event.", "reviewer_3": "Review of\n“Ocean tides trigger ice shelf rift growth and calving“\nby Marsh et al., submitted to Nature Communications, July 2024\nOverview\nThanks to its hosting of Halley Station, Brunt Ice Shelf is probably one of the best studied in Antarctica. Recent events related to fracture propagation and major iceberg calvings afforded the authors an excellent opportunity to conduct valuable in situ measurements of those changes, augmented with satellite observations, and analyzed with the use of a simplified viscoelastic rheological model. The authors use that analysis to quantify the relative importance of a set of external forcings on rift opening rates. They reach the conclusion that tides played a dominant role in rift evolution from 2019 onwards, culminating in the major calving of 2023, of which the timing was also influenced by the tides.\nI believe the in situ observations presented here to be highly valuable in the endeavour to improve understanding of ice-shelf fracture evolution. This value is accentuated by the rarity of such observations. I also think that the authors present a plausible case for the influence of tidal forcing on fracture evolution. I raise questions below about the manner by which this influence is exerted, and possible implications to the modeling approach. I should note that, while I do make comments on the modeling, I do not have sufficient experience in fracture mechanics to assess the nuances of the assumptions and simplifications that the authors make.\nFinally, I found that the manuscript in general is very well written and organized, and the figures are mostly helpful.\nMain Issues\nPossible effect of MIR: A major dynamic feature of the Brunt Ice shelf is the McDonald Ice Rumples (MIR), of which the location is indicated in Fig. 1c. My understanding is that the contact between the ice shelf and the bathymetric feature at MIR is intermittent (that is why it is not classified as an “ice rise”, where contact would be permanent). The extent of the contact would vary with the vertical movement of the shelf under the influence of tidal forcing. If this understanding is correct, then that raises the following questions with regards to the modeling approach: Are tide-induced stress and glacial stress truly independent, as seems to be the assumption made in the analysis? Relatedly, is it safe to assume glacial stress to be constant?\nTidal effect (L. 244–251): Correlations are mentioned between rift opening rates and tidal amplitudes and their changes. Is it possible to explicitly give the values of those correlations?\nWind effect (e.g., L. 252–254): Is there observational evidence to suggest that wind stress is related to rift opening changes, as in the case of the tidal effect?\nFinding C3 and C4: My understanding is that the parameters C3 and C4 are found through the optimization process described under “Model Fitting” (L. 262). In L. 271–274, there seems to be a suggestion that their values can be constrained using observation. Are the values thus derived then used as initial estimates in the least-squares fitting iterations and/or as bounds on the variations of the two parameters during those iterations?\nGNSS stations: Figure 1i suggests that GNSS measurements were made near-continuously from 2017 to 2023. Is Figure 1j showing that the locations of the GNSS stations relative to MIR did not change during that period? If yes, how were the locations of the stations maintained fixed as the ice shelf flows? Relatedly, in measuring the GPS rift widths shown in Figure 1i, was the spreading of the ice shelf taken into account?\nGeneral: Could an estimate of uncertainty be provided on the reported measurements, such as rift width and its changes at ApRES?\nOther Issues, Typos, etc.\nL. 30: Plural: “influence[s]”.\nL. 41: “experiences semi-diurnal velocity fluctuations of ±2 metres”; is this supposed to be “vertical” instead of “velocity”?\nL. 63–64: “This was followed by a period of stagnation lasting approximately two years (Fig. 1i).” Perhaps it would be worth noting in the text that even during this period, the rift continued to enlarge as measured at the GPS stations closer to the grounding line.\nFigure 1: Consider making the colors of the two GNSS measurements more distinct.\nFigure Ext. 7: I am not certain what this figure is showing, especially the circular inset."}, "author_response": "We thank the reviewers for their detailed and useful comments, in particular Reviewer 1 whose comments have greatly helped us to improve the manuscript by highlighting ways to better present our explanation of stress and improve the terminology. We respond to each reviewer in turn below (reviewer comments in red; response in black):\nReviewer #1 (Remarks to the Author):\nThis manuscript describes results from a field campaign on the Brunt Ice Shelf showing that rift propagation appears to be, at least partially, triggered by ocean tides and winds. This study falls into a larger cannon of studies that seek short-term environmental triggers of rifting propagation and iceberg calving. This study is the first that I am aware of that demonstrates a link between rift processes and tidal forcing. One of the challenges, however, of this type of study is that it is difficult to generalize: we do not know if the correlation with tides holds more generally for rifts in the Brunt ice shelf, much less other rifts on other ice shelves. This issue is an issue that has been difficult to overcome in many studies, but doesn’t detract from the study presented here.\nWe agree that tides may not be the dominant trigger of calving elsewhere, or across cracks at different orientation to tidal currents (for instance we state “The sensitivity of rifts on other ice shelves to short-term stresses will depend on their specific geometry, including the relative area of unconstrained ice on which tides and wind can act, and the ligament length attaching nascent icebergs to their ice shelves. There is a large variation in tidal range and rate of change of tide across Antarctica, and we would expect large spatial differences in susceptibility to tidally-triggered fracturing.”) Nevertheless, here there is an overwhelming tidally synchronous response of the ice shelf, increasing as calving approaches, and it is clear that tidal information may be useful in assessing calving likelihood over the short-term in some situations.\nOverall, I think the study is well written, adds to the literature and will be interesting to a wider audience. However, the methodology and assumptions were difficult for me to fully follow: I struggled to understand and convince myself that some of the assumptions described in the methods are appropriate and link the empirical models to physical models. I recognize that there is a balance that needs to be met with not being overly technical so that the manuscript is accessible to a wide audience and adding more specialized jargon. But I think that some more precision in terminology and clarity in the methods might be useful for readers. This is especially true when asking readers to make the link between analogies and derivations which seem based a little bit more on insight and intuition than formal manipulations. I outline some of these issues below, recognizing that it is possible that some of these are just wording issues while others might point to issues with the methodology that need to be addressed.\nThank you. The main aim of this paper is to present these new observational datasets, and put them into the public domain. A complex physical model (3D, viscoelastic, including fracture) is outside of the scope of this paper, and so we have relied on empirical modelling. We do not suggest that our empirical model captures everything, but it acts as a heuristic / qualitative description of what may be occurring. We have tightened up the wording to better explain the technical aspects of the methodology.\n1. Cauchy stress, deviatoric stress and all that. To start, the authors use the term \"stress\" multiple times throughout the study (e.g., line 69, line 74, but also many other places). Stress is, of course, a tensor, but it is treated in the text as if it is a scalar. This is fine so long as the authors are clear that they are referring to a particular component of the stress tensor (or better yet, the traction). I also assume that the “stress” referred to is depth averaged in some sense, but this is also not stated. The more confusing problem is that the authors do not distinguish between Cauchy stress, deviatoric stress and effective stress. In fracture mechanics, the stress driving crack propagation is the Cauchy stress, but flow of ice is controlled by the deviatoric stress. This is an important distinction because the Cauchy stress can be compressive because of the hydrostatic pressure whilst the deviatoric stress remains positive. More specifically, the effective viscosity in the creep flow-law is controlled by the effective deviatoric stress, which is independent of pressure and depends on the sum of the squares of the components of the stress. This is an important distinction because the effective stress cannot be negative and depends on more than a single component of the deviatoric stress tensor. I would typically write the Equation that appears in lines 69 and 74 in terms of the effective stress (which is always positive). All of this is very confusing to readers, especially since the tidal stress shown in Figure 2 has negative values. One has to be careful (and clear) about absolute values and what is positive and negative! Here the authors would better serve readers by clearly stating what they mean by “stress” in a more precise way (it is a component of the full stress tensor? is it depth-averaged? is it deviatoric stress or a component of the Cauchy stress).\nMany thanks. Here we are using ‘stress’ to mean a scalar depth-averaged longitudinal resistive stress, which is the rift normal stress responsible for ice shelf spreading. We assume ice thickness and density to be spatially uniform and this allows us to consider the ice shelf as a 2D plate without vertical shear. We also only consider one stress direction, the one that is perpendicular to the crack such that the crack is loaded uniaxially, (making an assumption of mode I opening). The resistive stress (R ) is the Cauchy stress minus the hydrostatic stress (e.g. Van der Veen (1998)). It is unlikely that crack propagation occurs along a perfectly vertical plane as the vertical profile is complicated by temperature and density dependencies plus water pressure, but here we assume uniform resistive stress with depth for simplicity (e.g. Rist et al., 1996). If the other components of the deviatoric stress tensor are small then variation in effective stress is only affected by variation in resistive stress and so it is reasonable to link this stress to the deformation. The ‘negative’ tidal (resistive) stress then leads to a positive effective stress which is important for the non-linearity in deformation. We do not consider 3D effects or bending, although we admit these may be important, and we assume the ice is constant density, temperature and thickness.\nThe approach we use here is based on the proposition that when the ice breaks at a particular critical depth, it has broken everywhere and will be visible at the surface. We appreciate that a simple mode 1 crack in one spatial dimension may be an oversimplification, particularly where water pressure acts at depth, but a full 3D simulation of the stress field is outside the scope of this work.\n2. Local fracture stress, remote stress and rift opening angle. Putting aside the terminology issues, the Equation in Line 69 is valid for a 1-dimensional visco-elastic material. I don’t follow the subsequent assumptions and approximations made to then transform the rheological equation in Line 69 to rift opening angle in Line 78. This seems like an analogy then a derivation, which is fine but should be stated. If we consider uni-axial loading transverse to the rift and ignore all other components of the stress tensor, then it seems like we should be able to write an equation in the form of the Equation on Line 69 with epsilon(t) denoting the component of strain transverse to the rift. The integral of the strain would be the rift opening/displacement. The rift opening angle used here appears to be defined as the ratio of the width to the length of the rift and this is, at least dimensionally, equivalent to a shear strain. This adds confusion about which component of the stress is considered. It would be helpful to clarify this, but either way, I don’t see why the factors of A and E in the Equation in 74 has been dropped. Maybe the ratio is used to scale the rift opening to rift length, but rift width in an elastic material should scale with rift length. Moreover, the rheology s a statement about material properties and has nothing to do with the various stress balances in the far-field or fracture regions. The magnitude of stresses might vary spatially and in the near vs far field, but the rheology is not a statement about the stress balance. Hence, it is not clear to me why we need both equations or why they are written in different forms.\nIt is correct that we are working in 1 dimension. The reason we use angle instead of strain across the rift is that we wish to compare the different time periods like-for-like, when the crack tip is moving. The crack width is converted to angle to normalise the distance between our instrument (ApRES) and the crack tip. The ‘raw’ width data in Figure 1 does not do this, but by converting width to opening angle, we adjust for the fact that the measurement point moves further away from the crack tip when propagation occurs. In practice it makes little difference as the angles are so small. Either way, it is not a shear strain but an adjustment to allow a direct comparison between measurements of transverse strain from different time periods with a slightly altered crack geometry.\nWe have replaced A and E into the second equation for clarity. These had been rolled into the proportionality constants as they are treated as constant over time and space.\n3. Fracture mechanics and other stuff. The methodology sketched out in Lines 218-226 argues for a relationship between the local stress near the crack tip and the far-field stress that is based on fracture mechanics. As I understand it, I think the authors are trying to infer the stress near the crack tip based on the far field stress, which is perfectly reasonable for an elastic material. I can follow the scaling presented, but given the relationships in Equations near lines 218-223 and the fact that the rift length is known, why not use the rift length in the analysis? The proportionality is given by a factor that is related to the rift length and another factor this typically of order unity (often Pi or some such). At least for an order of magnitude estimate, we could directly estimate the stress associated with different forcing without introducing arbitrary constants. In fact, an alternative interpretation of the analysis is that if we divide both sides of the Equation in line 218 by the square root of the rift half-length, then we find that the remote stress required to drive rift propagation is approximately zero given the critical stress intensity factor from lab measurements. Hence, whenever the Cauchy stress (not deviatoric stress!) is positive, the rift will propagate. This relationship only holds for linear elastic materials, which gets me into my next point.\nHere we run in difficulties in trying to accurately model fracture in a non-linear viscoelastic material, which is not fully covered by existing literature. We have not used the rift length as the rift in question is not a simple geometry (and the ice is not a elastic material). The rift also contains melange / sea ice material such that it is difficult to define it’s extent, and contrary to our model, the thickness does vary spatially.\nWe have removed some of the text on stress intensities as we are not using LEFM here.\n4. Viscoelasticty and Hoff’s analogy. As I understand it, the analogy pointed out by the authors holds for linear viscosity and linear elasticity (or power-law elasticity and power-law creep), but not between linear elasticity and power-law creep. In fact the stress singularity associated with power-law creep has been deduced and it depends on the flow-law exponent. (The singularity is exactly the same as for an elastic material if the flow law exponent is unity.). As a consequence, I don’t think that the scaling argument that the authors apply follows. Or, at least, more clarification is needed to explain why it works. The way that the authors present the methods make it seem like this is a critical flaw in the methodology or something that needs additional justification. (I apologize if I misunderstood!) However, reading through a few more times I’m not quite sure that the authors analysis really depends on this scaling argument and I wonder if the authors can simply use the rheology presented in lines 69 with some appropriate measure of transverse strain and simplify much of this exposition.\nYes we have decided to remove this as it adds complexity that is better left out in this simple empirical approach.\n5. My penultimate concern about the methodology is, perhaps, more of a philosophical issue. The main conclusion is that tides and, to a lesser extent winds, drive rift propagation. The concerns that I raised are all based on the physical model presented, but the authors conclusions are fundamentally based on an empirical correlation with 4 tuned coefficients (5 if the phase of the tide is included) that are fit to the data. However, we can, at the very least, provide ball park estimates of all of the stress terms based on the data collected. The drag associated with tides and winds depends quadratically on the current/wind speed, density of water/air and a drag coefficient. The wind speed is measured. The current speed can be extracted from the same tidal model used to estimate ocean height. The only unknown is the drag coefficient, which can vary over several orders of magnitude. Nonetheless, the authors can ballpark estimate the stress associated with different forcing using a range of published drag coefficients to determine if the relative contributions inferred empirically are broadly consistent with what we expect from a more physical model. If the forcing is broadly consistent, then it is a strong check on the more empirical methodology and might negate my confusion about the methods. Moreover this might even allow us to estimate the role that winds and tides have on other rifts. This would be a significant advance in the field. If the relative magnitudes are not consistent then it implies drag coefficients need to be much larger/smaller than typically inferred or something else is going on that needs additional study. Perhaps the Brunt is unusual or there is missing physics we still need to understand. This is also important to know.\nOur empirical measurements are broadly in line with estimates from tidal currents although drag coefficients need to be higher than usually assumed (e.g. a basal drag coefficient of between 0.001 and 0.01 (Gwyther et al., 2015) and current peaking at 0.04 m/s would produce a drag of 0.0008 to 0.008 N/m2).\nThe reason we have not included these calculations here is due to the additional 2D effects (e.g. moment) which complicate our simple model, and for which we do not have enough data. We don’t wish to repeat the work of e.g. Bassis et al., 2008, but instead seek to provide relative contributions from different sources. This is possible because of the precision with which we know the crack behaviour over multiple time scales. We now show correlations with the westerly tidal current from CATS2008 (Padman et al., 2002) in Figure Ext. 6e. The phase agrees well, but the shape of the oscillations still matches more closely with the gradient of the tidal amplitude (Ext. 6d).\n6. My final point is that it seems as though the authors are using rift widening as a proxy for rift opening. Rift widening in an elastic material is either due to a change in the stress opening the rift and/or rift propagation. In a viscoelastic material the situation is more complicated because the rift will widen due to ductile flow even with no rift propagation. In an elastic material, rift widening results in stored elastic energy that can be released by rift propagation. In a disco-elastic material, rift widening may dissipate stored elastic energy or respond passively to rift propagation. This confusion may be addressed in the manuscript, but it seems possible that the rapid rift widening stages observed are caused by rift propagation, which stand in contrast with rapid rift widening causing stress accumulation that then results in rift propagation. In other words, the direction of causality isn’t clear to me. Can the possibility that rapid rift widening is simply a response to the fact that the rift is or has recently propagated?\nNo, we are happy that the causality is in this direction. We have 10-minute resolution data and the widening is not as rapid as might be expected from a propagation event. We observe that in the short-term the propagation events have a negligible effect on this opening angle.\nMinor comments:\nA key finding is that the square of the tidal forcing results in fortnightly forcing. Recent studies, however, have increasingly shown that on ice shelves the flow-law exponent is probably closer to 4. Would this significantly affect the results? Would the fortnightly tidal affect still appear? Does a flow law exponent of 4 help with the tidal phase offset needed in the fit? If the fortnightly forcing is robust, then this seems like a useful prediction of the model based on fundamental principles that is worth further emphasizing.\nA flow law exponent of 4 would affect the results in that there would be two tidal terms that introduce a non-linearity (g^2 * t^2; and t^4). The fortnightly signal would still exist. It is possible that this dataset could be used to inform the exponent in the flow law, but we are already doing this for A.\nIs it possible that the connection with wind speed is related to small movements of the stations of the ice associated with torque from the wind?\nNo the stations are guyed very tightly and the reflector is a mesh (to avoid catching the wind).\nLine 84: This is the results of expanding the cubic, right? Why are the factors of 3 and 6 in the terms dropped? Line 265: This equation includes all of the factors of 3 and 6s that was missing in the main text equation. It might be easier for readers if these equations are presented in a consistent form.\nThis is just the components of the opening angle (and which stress components they are derived from in the subscript). The factors are not important here as it is not an equation, but a labelling of the different terms.\nLine 100: kts—use metric units.\nOK.\nWhy do tides result in a phase shifted stress? This isn't intuitive to me. Is it somehow related to the phase difference between tidal currents that drive propagation and tidal heights?\nYes it is a phase difference between the tide heights and the currents. While there is some uncertainty on the mean current, the tidally induced currents show a direct correlation without a phase shift with the widening rate. We have added a panel to Figure Ext. 6 showing this.\nReviewer #2 (Remarks to the Author):\nThis is an excellent, interesting and important paper that reports highly detailed observations of rift propagation and iceberg release from Brunt Ice Shelf in Antarctica, and an insightful analysis of the key forces at work. The methods are rigorous and clearly explained and the conclusions justified. Illustrations are excellent.\nThank you.\nI see no need for any revision of the text, except for one minor correction. On line 41, there is mention of \"velocity fluctuations of plus/minis 2 metres\", which should of course be elevation fluctuations, which correspond with velocity fluctuations. It might also be useful to add the units for 'rift opening angle' which I presume are radians (line 72 and Fig 2).\nYes this is a mistake and has been corrected. Angles in radians do not normally require units and I believe this is the case in Nature journals.\nThe main change that I think might be useful is to the title of the paper. The title only mentions tidal forcing as the trigger for both rift propagation and calving, but it is clear from the text that this is not the whole story. While rising tidal stresses clearly coincided with individual rift propagation events, iceberg collision \"affected rift growth more substantially\" (line 187), and background glaciological stresses are obviously important. So I suggest you change the headline to include reference to at least the iceberg collision event.\nWe have chosen not to change the title as while collision is important it did not cause the calving and is a less important finding. There are several other studies showing the importance of iceberg collision (i.e. it is not a new discovery) and here we wish to emphasise the critical importance of ocean tides, which have previously been overlooked.\nReviewer #3 (Remarks to the Author):\nOverview\nThanks to its hosting of Halley Station, Brunt Ice Shelf is probably one of the best studied in Antarctica. Recent events related to fracture propagation and major iceberg calvings afforded the authors an excellent opportunity to conduct valuable in situ measurements of those changes, augmented with satellite observations, and analyzed with the use of a simplified viscoelastic rheological model. The authors use that analysis to quantify the relative importance of a set of external forcings on rift opening rates. They reach the conclusion that tides played a dominant role in rift evolution from 2019 onwards, culminating in the major calving of 2023, of which the timing was also influenced by the tides.\nI believe the in situ observations presented here to be highly valuable in the endeavour to improve understanding of ice-shelf fracture evolution. This value is accentuated by the rarity of such observations. I also think that the authors present a plausible case for the influence of tidal forcing on fracture evolution. I raise questions below about the manner by which this influence is exerted, and possible implications to the modeling approach. I should note that, while I do make comments on the modeling, I do not have sufficient experience in fracture mechanics to assess the nuances of the assumptions and simplifications that the authors make.\nFinally, I found that the manuscript in general is very well written and organized, and the figures are mostly helpful.\nThank you.\nMain Issues\nPossible effect of MIR: A major dynamic feature of the Brunt Ice shelf is the McDonald Ice Rumples (MIR), of which the location is indicated in Fig. 1c. My understanding is that the contact between the ice shelf and the bathymetric feature at MIR is intermittent (that is why it is not classified as an “ice rise”, where contact would be permanent). The extent of the contact would vary with the vertical movement of the shelf under the influence of tidal forcing. If this understanding is correct, then that raises the following questions with regards to the modeling approach: Are tide-induced stress and glacial stress truly independent, as seems to be the assumption made in the analysis? Relatedly, is it safe to assume glacial stress to be constant?\nWe agree that the terminology around stresses was confusing. All the stresses we are discussing are ‘glacial stresses’ in the sense that they are acting within the ice, but we have attempted to separate them in order to determine the importance of tides (and wind). These should perhaps be better labelled as a constant background stress (which we have here called glacial), a stress that varies in correlation with the tides (which we have called tidal) and one that varies in correlation with the wind (which we have called wind). Due to the non-linearity of the flow law, oscillating crack behaviour can be related to oscillating driving stresses, but all behaviour is fundamentally controlled by the background average stress (the glacial part).\nOver long time periods the glacial stress is not constant (for instance it changes between early 2019 and late 2019), but here we focus on short-periods (~ 1 month) where we believe this assumption to be reasonable.\nWe have modified the stress terminology in response to Reviewer 1.\nTidal effect (L. 244–251): Correlations are mentioned between rift opening rates and tidal amplitudes and their changes. Is it possible to explicitly give the values of those correlations?\nCorrelations are given in Figure Ext. 6.\nWind effect (e.g., L. 252–254): Is there observational evidence to suggest that wind stress is related to rift opening changes, as in the case of the tidal effect?\nYes, the widening rate is increased during strong easterly wind events and appears to correlate with the square of the wind speed. The effect is less than for tides under normal wind speeds seen on the Brunt Ice Shelf.\nFinding C3 and C4: My understanding is that the parameters C3 and C4 are found through the optimization process described under “Model Fitting” (L. 262). In L. 271–274, there seems to be a suggestion that their values can be constrained using observation. Are the values thus derived then used as initial estimates in the least-squares fitting iterations and/or as bounds on the variations of the two parameters during those iterations?\nThe values of all parameters C1-C4 are obtained from the observations via the fitting procedure which is not iterative but provides a minimum least-squares. The ranges to search through are predefined.\nBecause of the non-linearity in ice flow, once C1-C4 are calculated the absolute value for stress can be estimated.\nGNSS stations: Figure 1i suggests that GNSS measurements were made near-continuously from 2017 to 2023. Is Figure 1j showing that the locations of the GNSS stations relative to MIR did not change during that period? If yes, how were the locations of the stations maintained fixed as the ice shelf flows? Relatedly, in measuring the GPS rift widths shown in Figure 1i, was the spreading of the ice shelf taken into account?\nThe GNSS stations advect with ice flow. They are generally moving perpendicular to the ice rumples so their distance does not change substantially. In Figure 1i the spreading of the ice shelf was not taken into account but it is known across other nearby baselines to be around 0.001 /yr. This would account for ~20 m over 6 years at NN00-OO00 and ~60 m over 6 years at TT01-KK00 which is a small percentage of the total signal. We have added some text to explain this.\nGeneral: Could an estimate of uncertainty be provided on the reported measurements, such as rift width and its changes at ApRES?\nThe uncertainty on the ApRES data (~ +/- 2mm) is substantially lower than the daily tidal changes (+/- 50-100 mm) within a day. The GPS data has a higher uncertainty but here is only used for context to the longer-term behaviour. We have added this in the Appendix.\nOther Issues, Typos, etc.\nL. 30: Plural: “influence[s]”.\nChange.\nL. 41: “experiences semi-diurnal velocity fluctuations of ±2 metres”; is this supposed to be “vertical” instead of “velocity”?\nYes.\nL. 63–64: “This was followed by a period of stagnation lasting approximately two years (Fig. 1i).” Perhaps it would be worth noting in the text that even during this period, the rift continued to enlarge as measured at the GPS stations closer to the grounding line.\nOK.\nFigure 1: Consider making the colors of the two GNSS measurements more distinct.\nWe have kept the colour scheme the same because the right-hand y-axis in panel (i) needs to match both colours (so they need to be similar). They are hopefully distinct enough that it is clear which is which.\nFigure Ext. 7: I am not certain what this figure is showing, especially the circular inset.\nWe have removed this figure."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I reviewed a previous version of this manuscript and I think the authors have largely addressed my comments.\nThere are a couple of minor points that I would encourage the authors to consider to make sure the presentation as consistent as possible. I list these below, but they are all relatively minor points related to word choices.\n1. Near line 73 (track changes version), the stress is described as a shear stress, but near line 116 the stress is described as tensile. I think the authors mean tensile in this case since near lines 241 the authors refer to Mode I opening stresses.\n2. I'm still confused by the Cauchy stress vs depth-averaged deviatoric stress vs depth-averaged resistive stress distinction here. The hydrostatic component of the pressure is unlikely to change over the time scales considered so I'm happy to drop that and for a one-dimensional model, the resistive stress and deviatoric stress are proportional to within a factor of 2. This makes the comparison with tensile deviatoric stresses (e.g., near line 116 track changes version) confusing. To compare tensile with resistive stress, don’t we need to double the tensile stresses (to account for the factor of 2)? Re-reading, I’m starting to think that the authors are actually estimating depth-averaged deviatoric stresses (?) and not resistive stresses, unless the conversion to resistive stress is done with the effective viscosity? Recognizing that the empirical model is probably only accurate to within a factor of 2, it still might be useful to sign post to readers how the conversion between deviatoric stress and resistive stress was done. The glaciological literature is plagued by missing factors of 2 associated with resistive vs deviatoric stresses.\n3. I think that the model by Brunt and MacAyeal (2014) may be relevant to the authors discussion as this study discusses the effect of tides on horizontal motion of the Ross Ice Shelf using a linearized approach. Brunt and MacAyeal (2014) use a shallow shelf numerical model, but the linearization approach is similar and I think the conclusions are analogous (although for intact ice!) and might help support the authors results\nBrunt KM, MacAyeal DR. Tidal modulation of ice-shelf flow: a viscous model of the Ross Ice Shelf. Journal of Glaciology. 2014;60(221):500-508. doi:10.3189/2014JoG13J203\n4. More tangential, the recent paper by Rendfrey et al., (2025), uses a statistical approach to infer statistically significant correlation with atmospheric extremes. This is a bigger stretch, but a conclusion from that paper is that temporally sparse data is not able to reliably distinguish between causal correlations and spurious correlations. The fact that higher resolution field results is able to avoid the spurious correlation entanglement points towards how coarse satellite imagery can be successfully combined with field observations to improve predictions.\nRendfrey TS, Bassis J, Pettersen C. Do atmospheric rivers trigger tabular iceberg calving? Journal of Glaciology. 2025;71:e8. doi:10.1017/jog.2024.94\n5. The final paragraph suggests that iceberg timing can be better predicted from environmental forcing records. However, Brunt is not a typical ice shelf. As a challenge to the authors, would we expect similar results for other ice shelves? Can results from Brunt be generalized with similar empirical coefficients?", "reviewer_3": "2nd Review of\n“Ocean tides trigger ice shelf rift growth and calving“\nby Marsh et al., submitted to Nature Communications, July 2024\nOverview\nI thank the authors for their responses to my earlier comments. Below, the authors’ responses to my previous comment are in quote marks.\nMain Issues\nPrevious reviewer comment: Possible effect of MIR: A major dynamic feature of the Brunt Ice shelf is the McDonald Ice Rumples (MIR), of which the location is indicated in Fig. 1c. My understanding is that the contact between the ice shelf and the bathymetric feature at MIR is intermittent (that is why it is not classified as an “ice rise”, where contact would be permanent). The extent of the contact would vary with the vertical movement of the shelf under the influence of tidal forcing. If this understanding is correct, then that raises the following questions with regards to the modeling approach: Are tide-induced stress and glacial stress truly independent, as seems to be the assumption made in the analysis? Relatedly, is it safe to assume glacial stress to be constant?\n\"We agree that the terminology around stresses was confusing. All the stresses we are discussing are ‘glacial stresses’ in the sense that they are acting within the ice, but we have attempted to separate them in order to determine the importance of tides (and wind). These should perhaps be better labelled as a constant background stress (which we have here called glacial), a stress that varies in correlation with the tides (which we have called tidal) and one that varies in correlation with the wind (which we have called wind). Due to the non-linearity of the flow law, oscillating crack behaviour can be related to oscillating driving stresses, but all behaviour is fundamentally controlled by the background average stress (the glacial part). Over long time periods the glacial stress is not constant (for instance it changes between early 2019 and late 2019), but here we focus on short-periods (~ 1 month) where we believe this assumption to be reasonable. We have modified the stress terminology in response to Reviewer 1.\"\nNew reviewer comment: Could you please clarify whether stress variability due to different degrees of ice-shelf grounding at MIR, due to tidally-induced vertical motion, is taken into account in the modeling.\nPrevious reviewer comment: GNSS stations: Figure 1i suggests that GNSS measurements were made near-continuously from 2017 to 2023. Is Figure 1j showing that the locations of the GNSS stations relative to MIR did not change during that period? If yes, how were the locations of the stations maintained fixed as the ice shelf flows? Relatedly, in measuring the GPS rift widths shown in Figure 1i, was the spreading of the ice shelf taken into account?\n\"The GNSS stations advect with ice flow. They are generally moving perpendicular to the ice rumples so their distance does not change substantially. In Figure 1i the spreading of the ice shelf was not taken into account but it is known across other nearby baselines to be around 0.001 /yr. This would account for ~20 m over 6 years at NN00-OO00 and ~60 m over 6 years at TT01-KK00 which is a small percentage of the total signal. We have added some text to explain this.\"\nNew reviewer comment: These statements need support. My understanding from observationally-inferred velocity fields is that flow in that part of Brunt Ice Shelf has a strong westerly component, so the stations would not be moving perpendicular to the ice rumples. Also, flow speeds according to observations are in the high 100s m/yr, so the advection of the stations over the 6-year observation period would be non-negligible (contrary to what Fig. 1j is showing). Please clarify how these factors might have affected estimates of the width of Chasm-1 between 2017 and 2023."}, "author_response": "We have made the discussion of stress in the appendix substantially clearer. We hope it is now clear how we’ve reached a model where the elastic and viscous behaviours are functions of the same stress.\n2. Yes we do think it is now clearer to refer to deviatoric stresses throughout (although we think the use of resistive stress is useful for understanding what we are doing, so we have left it in the appendix derivation). We have further elaborated on our definitions, derivations and assumptions in the appendix. We also now use E’ in the main paper, which differs from E by a factor of between 1.5 and 2 (depending on Poisson’s ratio) and which slightly modifies our overall calculated stress threshold. This means we have replotted Figures 2 and 3 (and the extended figures 2 and 7).\n3. Thank you, we have added some additional references here, including this one.\n4. This is also a valuable reference that I was previously unaware of. In the dataset we present here atmospheric events did contribute to crack growth on several occasions (in particular when they aligned with spring tides), but tides alone (plus the evolving glaciological situation) appear to have been responsible for the final calving of A-81, with no atmospheric contribution.\n5. A similarly high-resolution field dataset should be acquired on a more ‘standard’ ice shelf if possible, but I think it is feasible to generalise if crack geometry is well known.\nReviewer #3 (Remarks to the Author):\n2nd Review of\n“Ocean tides trigger ice shelf rift growth and calving“\nby Marsh et al., submitted to Nature Communications, July 2024\nOverview\nI thank the authors for their responses to my earlier comments. Below, the authors’ responses to my previous comment are in quote marks.\nMain Issues\nPrevious reviewer comment: Possible effect of MIR: A major dynamic feature of the Brunt Ice shelf is the McDonald Ice Rumples (MIR), of which the location is indicated in Fig. 1c. My understanding is that the contact between the ice shelf and the bathymetric feature at MIR is intermittent (that is why it is not classified as an “ice rise”, where contact would be permanent). The extent of the contact would vary with the vertical movement of the shelf under the influence of tidal forcing. If this understanding is correct, then that raises the following questions with regards to the modeling approach: Are tide-induced stress and glacial stress truly independent, as seems to be the assumption made in the analysis? Relatedly, is it safe to assume glacial stress to be constant?\n\"We agree that the terminology around stresses was confusing. All the stresses we are discussing are ‘glacial stresses’ in the sense that they are acting within the ice, but we have attempted to separate them in order to determine the importance of tides (and wind). These should perhaps be better labelled as a constant background stress (which we have here called glacial), a stress that varies in correlation with the tides (which we have called tidal) and one that varies in correlation with the wind (which we have called wind). Due to the non-linearity of the flow law, oscillating crack behaviour can be related to oscillating driving stresses, but all behaviour is fundamentally controlled by the background average stress (the glacial part). Over long time periods the glacial stress is not constant (for instance it changes between early 2019 and late 2019), but here we focus on short-periods (~ 1 month) where we believe this assumption to be reasonable. We have modified the stress terminology in response to Reviewer 1.\"\nNew reviewer comment: Could you please clarify whether stress variability due to different degrees of ice-shelf grounding at MIR, due to tidally-induced vertical motion, is taken into account in the modeling.\nThe terminology ‘ice rumples’ is incorrect here. The McDonald Ice Rumples is an ice rise (see for example Humbert et al., 2009). We are not able to assign the cause of the tidally-induced variability using this simple 1d model. It is possible though that it is due to variability in grounding at the MIR. However, the reason we think this is less likely is due to the phase of tide height relative to the phase of the crack widening. Under a grounding / ungrounding mechanism it would seem sensible that the greatest width would be expected to correlate with highest tide (i.e. when grounding is at a minimum). Here we see that width correlates more strongly with easterly ocean current amplitude which is around 6 hours out of phase with the tide height. We are not saying this is definitive, and certainly a more comprehensive model would provide better insight here.\nWe do show that the ‘tide-induced’ stresses and ‘glacial’ stresses are NOT independent though and that the tides enhance the overall stress in a non-linear way. We feel this is a terminology issue that we tried to rectify in the previous review but have tried again to make this clearer.\nPrevious reviewer comment: GNSS stations: Figure 1i suggests that GNSS measurements were made near-continuously from 2017 to 2023. Is Figure 1j showing that the locations of the GNSS stations relative to MIR did not change during that period? If yes, how were the locations of the stations maintained fixed as the ice shelf flows? Relatedly, in measuring the GPS rift widths shown in Figure 1i, was the spreading of the ice shelf taken into account?\n\"The GNSS stations advect with ice flow. They are generally moving perpendicular to the ice rumples so their distance does not change substantially. In Figure 1i the spreading of the ice shelf was not taken into account but it is known across other nearby baselines to be around 0.001 /yr. This would account for ~20 m over 6 years at NN00-OO00 and ~60 m over 6 years at TT01-KK00 which is a small percentage of the total signal. We have added some text to explain this.\"\nNew reviewer comment: These statements need support. My understanding from observationally-inferred velocity fields is that flow in that part of Brunt Ice Shelf has a strong westerly component, so the stations would not be moving perpendicular to the ice rumples. Also, flow speeds according to observations are in the high 100s m/yr, so the advection of the stations over the 6-year observation period would be non-negligible (contrary to what Fig. 1j is showing). Please clarify how these factors might have affected estimates of the width of Chasm-1 between 2017 and 2023.\nThe ice flow is almost exactly in a westerly direction ~ 265° (and is hundreds of metres per year). However, the crack is in a north-south direction and the MIR is almost exactly north of our instruments (TT01 and NN00 on the eastern side of the crack are slightly south-east, KK00 and O000 on the western side are slightly south-west) – there is a north arrow in panel 1b. This geometry means that ice advection moves our instruments (and Chasm-1) orthogonally with respect to the MIR.\nAll the instruments advect by ~4-5 km over this period in terms of absolute position, but their distance to the MIR changes with opposite sign (TT01 and NN00 get closer while KK00 and OO00 get further away) such that the centre of the baselines (which is what is represented here) do not move substantially. The centre of the TT01-KK00 baseline is 5.2 km from the MIR in 2017 and 5.6 km from the MIR in 2022 (+400m). The centre of the NN00-OO00 baseline is 21.2 km from the MIR in 2017 and 20.5 km from the MIR in 2022 (-700m). These changes ARE negligible relative to the crack growth of 20+ km and in no way do they influence the calculated widths which are produced from differencing the positions of the GNSS sites.\nThe primary aim of panel j is to show where the GPS baselines cross the crack relative to the advancing tip position. We have now modified this panel to account for these small changes in distance caused by the advection (although it is barely noticeable). The full GNSS data is available as a DOI with the paper if it is of interest to readers."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed all of my comments and I look forward to seeing the published version of this paper.", "reviewer_3": "3rd Review of\n“Ocean tides trigger ice shelf rift growth and calving“\nby Marsh et al., submitted to Nature Communications, July 2024\nPrevious reviewer comment: Possible effect of MIR: A major dynamic feature of the Brunt Ice shelf is the McDonald Ice Rumples (MIR), of which the location is indicated in Fig. 1c. My understanding is that the contact between the ice shelf and the bathymetric feature at MIR is intermittent (that is why it is not classified as an “ice rise”, where contact would be permanent). The extent of the contact would vary with the vertical movement of the shelf under the influence of tidal forcing. If this understanding is correct, then that raises the following questions with regards to the modeling approach: Are tide-induced stress and glacial stress truly independent, as seems to be the assumption made in the analysis? Relatedly, is it safe to assume glacial stress to be constant?\n\"We agree that the terminology around stresses was confusing. All the stresses we are discussing are ‘glacial stresses’ in the sense that they are acting within the ice, but we have attempted to separate them in order to determine the importance of tides (and wind). These should perhaps be better labelled as a constant background stress (which we have here called glacial), a stress that varies in correlation with the tides (which we have called tidal) and one that varies in correlation with the wind (which we have called wind). Due to the non-linearity of the flow law, oscillating crack behaviour can be related to oscillating driving stresses, but all behaviour is fundamentally controlled by the background average stress (the glacial part). Over long time periods the glacial stress is not constant (for instance it changes between early 2019 and late 2019), but here we focus on short-periods (~ 1 month) where we believe this assumption to be reasonable. We have modified the stress terminology in response to Reviewer 1.\"\nNew reviewer comment: Could you please clarify whether stress variability due to different degrees of ice-shelf grounding at MIR, due to tidally-induced vertical motion, is taken into account in the modeling.\nThe terminology ‘ice rumples’ is incorrect here. The McDonald Ice Rumples is an ice rise (see for example Humbert et al., 2009). We are not able to assign the cause of the tidally-induced variability using this simple 1d model. It is possible though that it is due to variability in grounding at the MIR. However, the reason we think this is less likely is due to the phase of tide height relative to the phase of the crack widening. Under a grounding / ungrounding mechanism it would seem sensible that the greatest width would be expected to correlate with highest tide (i.e. when grounding is at a minimum). Here we see that width correlates more strongly with easterly ocean current amplitude which is around 6 hours out of phase with the tide height. We are not saying this is definitive, and certainly a more comprehensive model would provide better insight here.\nWe do show that the ‘tide-induced’ stresses and ‘glacial’ stresses are NOT independent though and that the tides enhance the overall stress in a non-linear way. We feel this is a terminology issue that we tried to rectify in the previous review but have tried again to make this clearer.\nFinal reviewer comment: That MIR is an ice rise, rather than rumples, is new information to me. It seems to be new information to the authors as well, as in my initial comments I specifically mentioned that, to my knowledge, MIR is not an ice rise (see above), and the authors at the time did not contradict that statement. I have no further comment.\nPrevious reviewer comment: GNSS stations: Figure 1i suggests that GNSS measurements were made near-continuously from 2017 to 2023. Is Figure 1j showing that the locations of the GNSS stations relative to MIR did not change during that period? If yes, how were the locations of the stationsmaintained fixed as the ice shelf flows? Relatedly, in measuring the GPS rift widths shown in Figure 1i, was the spreading of the ice shelf taken into account?\n\"The GNSS stations advect with ice flow. They are generally moving perpendicular to the ice rumples so their distance does not change substantially. In Figure 1i the spreading of the ice shelf was not taken into account but it is known across other nearby baselines to be around 0.001 /yr. This would account for ~20 m over 6 years at NN00-OO00 and ~60 m over 6 years at TT01-KK00 which is a small percentage of the total signal. We have added some text to explain this.\"\nNew reviewer comment: These statements need support. My understanding from observationally-inferred velocity fields is that flow in that part of Brunt Ice Shelf has a strong westerly component, so the stations would not be moving perpendicular to the ice rumples. Also, flow speeds according to observations are in the high 100s m/yr, so the advection of the stations over the 6-year observation period would be non-negligible (contrary to what Fig. 1j is showing). Please clarify how these factors might have affected estimates of the width of Chasm-1 between 2017 and 2023.\nThe ice flow is almost exactly in a westerly direction ~ 265° (and is hundreds of metres per year). However, the crack is in a north-south direction and the MIR is almost exactly north of our instruments (TT01 and NN00 on the eastern side of the crack are slightly south-east, KK00 and O000 on the western side are slightly south-west) – there is a north arrow in panel 1b. This geometry means that ice advection moves our instruments (and Chasm-1) orthogonally with respect to the MIR.\nAll the instruments advect by ~4-5 km over this period in terms of absolute position, but their distance to the MIR changes with opposite sign (TT01 and NN00 get closer while KK00 and OO00 get further away) such that the centre of the baselines (which is what is represented here) do not move substantially. The centre of the TT01-KK00 baseline is 5.2 km from the MIR in 2017 and 5.6 km from the MIR in 2022 (+400m). The centre of the NN00-OO00 baseline is 21.2 km from the MIR in 2017 and 20.5 km from the MIR in 2022 (-700m). These changes ARE negligible relative to the crack growth of 20+ km and in no way do they influence the calculated widths which are produced from differencing the positions of the GNSS sites.\nThe primary aim of panel j is to show where the GPS baselines cross the crack relative to the advancing tip position. We have now modified this panel to account for these small changes in distance caused by the advection (although it is barely noticeable). The full GNSS data is available as a DOI with the paper if it is of interest to readers.\nFinal reviewer comment: Thank you for clarifying what is being shown in panel j. I have no further comment."}, "author_response": ""}]

Decision letter