An improved understanding of ice sheet dynamics is essential for producing accurate global and regional sea level projections. To achieve this, sophisticated ice sheet models that capture higher-order processes and feedback mechanisms are necessary. The ice sheet modeling community has increasingly recognized the importance of dynamic interactions between ice sheets and solid Earth processes over decadal and longer timescales. As ice mass changes, it exerts spatiotemporal variations in pressure on the solid Earth surface, changing bedrock topography and the geoid field, and thus sea level. These alterations in topography and sea level significantly influence marine ice sheet dynamics. They do so by affecting the retrograde bed slope, reinforcing pinning points and bedrock ridges, altering ocean heat transport patterns due to the modified shape of sub-shelf cavities, and influencing gravitational driving stress and surface mass balance through surface elevation and slope changes e.g.,.

Several established methods of varying complexity exist for capturing solid Earth feedback in ice sheet models. The most straightforward approach relies on the two-layer framework of , consisting of an elastic lithosphere overlying a viscously relaxing mantle half-space e.g.,. Building on this, introduced a formulation in which the lithosphere overlies a finite-thickness asthenosphere layer, commonly referred to as the Elastic Lithosphere Relaxing Asthenosphere (ELRA) model. A more complex method involves modeling a self-gravitating, density-stratified, viscoelastic Earth with a radially symmetric structure that typically includes an elastic lithosphere, a multi-layered Maxwellian mantle, and an inviscid core e.g.,. Generally used in glacial isostatic adjustment (GIA) studies, this class of models enables capturing the full gravitational, rotational, and deformational (GRD) feedback to ice sheet dynamics e.g.,. More comprehensive approaches, such as those involving three-dimensional Earth structure e.g., and sophisticated non-Maxwellian mantle rheology , are currently being explored to enhance our understanding of feedback mechanisms.

All these models come with caveats, especially regarding their suitability for high-resolution coupled simulations. Downsides may range from being too simplistic (e.g., half-space models) to involving complex numerical implementations that demand significant computational cost (e.g., global GIA models). As a result, many ice sheet models, including those involved in the Ice Sheet Model Intercomparison Project (ISMIP), often omit GRD feedback. Among the 16 models that contributed to the ISMIP Antarctic Ice Sheet projections extending to 2300 , only four include any representation of solid Earth feedback, and even these primarily rely on the most simplified ELRA approach. The omission of GRD feedback, or its representation through the ELRA approximation, may bias projections of grounding line retreat and sea level change e.g.,. GIA emulators and more realistic regional models are emerging as promising options that offer reduced computational cost. Further investigation is needed into both traditional geophysical modeling approaches and emerging machine learning techniques to improve model efficiency and accuracy and simplify the coupling strategy.

Here we present a simple method that enables ice sheet models to capture solid Earth feedback requiring neither additional model development nor computational cost. A primary motivation for this research is to enhance ISMIP’s current and future undertakings by enabling greater participation in coupled ice/Earth simulations, with direct implications for future Intergovernmental Panel on Climate Change (IPCC) reports that cater to planners and policymakers. We therefore focus on capturing the leading-order feedback signals over centennial timescales for radially symmetric Earth structures. We show that the direct effects of ice mass change account for over 90 % of the self-consistent GRD feedback signals in a radially symmetric Earth. In order to capture this leading process, it suffices to convolve the evolving mass change with time-variable Green’s functions that characterize the solid Earth response to unit surface loads. By leveraging an extensive library of precomputed Green’s functions available for a suite of Maxwellian Earth structures , our proposed method facilitates the swift retrieval of the evolving geoid and bedrock topography fields as ice sheet models march forward in time, thus enabling straightforward coupling between the ice sheet and the solid Earth. An efficient coupling enhances our understanding of feedback mechanisms, facilitates sensitivity analysis, and strengthens uncertainty quantification through large ensemble simulation. Ultimately, these improvements will enable more reliable projections of ice sheet contribution to sea level change.

The proposed method differs fundamentally from the commonly used ELRA framework. Rather than approximating Earth response through lithospheric flexural rigidity and asthenospheric relaxation timescales, the Green's functions employed here are derived from solutions of the governing equations of mass conservation, linear momentum conservation, and self-gravitation for a full-depth multilayered viscoelastic Earth . This provides a more realistic representation of load-induced deformation and gravitational signals, consistent with the framework adopted in modern GIA modeling. Moreover, standard ELRA implementations typically neglect geoid change and associated gravitational feedbacks, focusing solely on bedrock adjustment. As will be demonstrated below, geoid variations can be significant and are largely governed by ice mass changes. Accounting for these effects is therefore essential in coupled ice/Earth simulations.

Like any simplified/regional method, ours comes with limitations. It does not satisfy self-consistency in GRD processes , nor does it conserve mass in the global domain of ice and ocean. The effects of rotational feedback , farfield ice melting , and coastline migration are ignored. Although we show that these processes play a secondary role on the timescale of interest, they are critical in longer-timescale simulations (e.g., glacial cycles) and they can only be accounted for by recursively solving the self-consistent sea level equation e.g.,. Our method does not capture the effects of three-dimensional Earth structures , although the appropriate choice of a regionally averaged one-dimensional structure may partially mitigate this deficiency . We caution readers of these caveats for the appropriate use of our method, whose main purpose is to capture solid Earth feedback in centennial-scale simulations of modern or paleo ice sheets.

Assuming that atmospheric pressure variability does not induce meaningful solid Earth deformation on decadal and longer timescales, the surface loading problem in the present context only requires resolving the lateral mass transport between the ice sheet and the ocean. A conditional function describing the ice and ocean load on the solid Earth surface, termed the “loading function” L [kg m⁻²], at a given point in time t may be expressed as follows: 1L(x,t)=ρiH(x,t)ifH(x,t)>F(x,t)ρwR(x,t)otherwise. Here x is the 2-D position vector on the solid Earth surface, ρi is the ice density [kg m⁻³], ρw is the ocean density [kg m⁻³], H is the ice thickness [m], R is the relative sea level [m], and F is the flotation height for ice [m] (see Fig. 1).

Following , we define R as the mean sea level S [m] relative to the sea floor, both referenced to the same ellipsoid (typically WGS84). We assume the sea floor is same as the bedrock B [m]. Mathematically, 2R(x,t)=S(x,t)-B(x,t). In mean sea level S, “mean” refers to a time-mean over tides and high-frequency waves. This distinction is irrelevant in GRD modeling. However, we maintain the terminology to align with the literature.

The flotation height for ice F [m] follows the principle of hydrostatic equilibrium and is given by 3F(x,t)=ρwρimax⁡R(x,t),0. The condition in Eq. () implies that the solid Earth is loaded by the ice sheet in the grounded portion of the marine (and terrestrial) ice sheet and by the ocean otherwise (Fig. 1a).

Numerical modeling requires discretizing the continuous loading function into p computational grids (having q nodes) and m time intervals: [t0,t1],[t1,t2],…,[tm-1,tm]. Spatial grids and time intervals do not have to be uniformly discretized. We may now express Eq. (), in the units of mass [kg] and with the new notation L, in its discrete form as follows: 4L(x′,t)=L‾(x′,t0)+∑i=1mL‾(x′,ti)-L‾(x′,ti-1)H(t-ti)A(x′),=L(x′,t0)+∑i=1mΔL(x′,ti)H(t-ti), Here x′ is the position of the center of the grid-cell or element, A is the elemental area [m²], and L‾ [kg m⁻²] is the spatial mean of L over that area. As shown in Fig. 1b, we recommend placing the surface load at the grid centers, x′, instead of at the nodes or vertices, x, where we assess the solid Earth response. This is important because the Green's functions we intend to use contain inherent singularities at the loading point . In the equation, H is the Heaviside step function that takes the value of unity for t≥ti and zero otherwise. It ensures that we impose the stepwise load change on the solid Earth surface at the end of each time interval (Fig. 1c). For the period -∞<t<t1, the surface load is held constant to its initial or reference value L(x′,t0), and we assume that the solid Earth is in hydrostatic equilibrium. As such, only the change in load induces solid Earth response, which can be evaluated at any time t≥t1.

For m=1 and in the limit of p→∞ for a structured mesh (or, equivalently, A→0) , setting in Eq. () the otherwise zero loading function to unity strictly at a single computational grid and at time t=tm corresponds to a mathematical description of a point load. Harmonic solid Earth response to a point load sustained on the surface of a radially symmetric layered solid Earth is traditionally computed as the time-dependent Love numbers . We may assemble the Love numbers analytically to determine Green's functions (Appendix A). Given these functions, we can retrieve the solid Earth response signals induced by the loading function with any complexity through direct spatiotemporal convolution: 5X(x,t)=KX(α,τ)⊗ΔL(x′,t′), where X is the GRD field of interest [m], KX is the corresponding Green's function [m kg⁻¹], α is the (great circle) distance between the loading position x′ and where the response signal is determined x, and τ is the time elapsed between the loading time t′ and when the response signal is evaluated t (Fig. 1). Let ϕ and λ be the geographic latitude and longitude of the evaluation and loading points: x≡(ϕ,λ) and x′≡(ϕ′,λ′), respectively. Then, the distance between the two points can be written as α=r2arcsinsin⁡2|ϕ-ϕ′|2+cos⁡ϕcos⁡ϕ′sin⁡2|λ-λ′|2, where r is the Earth's surface radius. Note that ΔL in the equation represents the change in load over the preceding interval to the loading time (Fig. 1c).

In the present context, X denotes either the geoid change G [m] or vertical land motion (VLM). In GIA/GRD theory, where sea level change is due to lateral mass exchange between and within land (including Cryosphere) and the ocean, these quantities are directly related to relative sea level (Eq. ). The geoid is an equipotential surface of Earth’s gravity field that coincides with the mean sea level S over the ocean, while VLM represents change in bedrock elevation B .

The convolution operator ⊗ appearing in Eq. () can be straightforwardly evaluated with scientific computational tools. For example, the desired GRD signal X at a given point in space xk and time t and can be evaluated as follows: 6X(xk,t)=∑j=1p∑i=1mKX(αk,j,τi)ΔL(xj′,ti′),fortm′≤t, with p and m being the total number of loading points in space and time, respectively, and τi=t-ti′. The GRD field can be obtained by iterating over discrete points k∈[1,q], where q is the total number of computational nodes (Fig. 1b). For simulations of ice/Earth coupling at centennial timescales, we expect q to be several orders of magnitude larger than m (a direct function of coupling interval, typically 10 years). A more efficient convolution approach could involve retrieving the GRD field induced by a Heaviside load and iterating along the time dimension. Appendix B presents an algorithm for such a scheme.

A key novelty of the proposed method is the use of a precomputed library of Green’s functions that characterize the solid Earth response to applied surface point loads. We calculate time-dependent Love numbers for 644 radially stratified Maxwellian Earth models . We also derive corresponding Green's functions, relevant for estimating vertical and horizontal land motion and geoid change. These solutions are based on seismologically constrained density and elastic Earth structure, informed by high-pressure and high-temperature mineral physics , and incorporate a sufficiently broad range of lithosphere thickness and upper mantle viscosity to investigate solid Earth responses to ice sheet evolution on decadal to centennial timescales, at both individual and multiple drainage basin scales.

Solutions are available for 23×28 combinations of lithosphere thickness and upper mantle viscosity. We linearly sample 23 lithosphere thicknesses between 30 and 250 km at 10 km intervals. Upper mantle viscosity samples include 1:9×1018 Pa s (9 samples), 1:9×1019 Pa s (9 samples), and 1:10×1020 Pa s (10 samples), while the lower mantle viscosity is fixed at 2×1022 Pa s for all models. Time-dependent Love numbers and Green’s functions are sampled in log-space at 100 snapshots between 0 year (purely elastic signal) and 1000 years. Logarithmic sampling better captures early-time deformation following loading or unloading when the response evolves more rapidly (Figs. 2 and A1). Because the main purpose of this study is to enable centennial-scale simulations, we restrict sampling to the first 1000 years after loading. We further evaluate Green’s functions at 500 points along the great-circle distance. We use log-space sampling to capture the signal gradient (a higher gradient in the near field) between 100 m and 20 000 km from the point load (Fig. 2). A 100 m sampling point avoids the inherent singularity in the elastic Green’s function at the loading point, while remaining sufficient to capture high-resolution ice load variations associated with grounding line migration and the unpinning of bedrock ridges.

Seismic imaging has provided a three-dimensional view of the crust and upper mantle beneath Antarctica e.g.,, enabling characterization of spatial variations in lithosphere thickness e.g., and mantle viscosity e.g.,. These studies reveal pronounced lateral heterogeneity, indicating that using a single set of solid Earth parameters for the entire ice sheet is not appropriate for coupled simulations e.g.,. Furthermore, tomography-based mantle viscosity estimates exhibit substantial differences among themselves. While GIA-modeled regional uplift rates observed at Global Navigation Satellite Systems (GNSS) bedrock sites are generally consistent with three-dimensional seismic velocity maps, some regions may exhibit significant mismatches between GIA-inferred viscosity and that scaled from tomography . GNSS-based and GIA models that rely on relative sea level records are inherently biased toward coastal regions, where observational constraints are comparatively robust.

Regional estimates of lithosphere thickness (in the sense of mechanical strength used in GRD models) and mantle viscosity have considerable reliance on GNSS trends determined since the mid-to-late 2000s. However, these estimates remain ambiguous, primarily due to uncertainty in the load history . When loading chronologies are well-constrained, bounds on upper mantle viscosity η can be established. Despite this, uncertainties typically remain on the order of log⁡η±0.5 e.g.,. This ambiguity is particularly pronounced in regions characterized by low upper mantle viscosity (log⁡η≤19.5), which are generally associated with slow seismic velocities or relatively young (Neogene) tectonic settings. In these regions, model solutions become highly sensitive to decadal to centennial-scale changes in ice mass load. Under such conditions, the framework proposed here offers particular value by capturing significant solid Earth feedback and enabling efficient exploration of parameter space and uncertainty quantification.

Observational constraints on lithosphere thickness and mantle viscosity from geodetic data are strongest in the Antarctic Peninsula and West Antarctica, whereas substantial uncertainties remain along the sparsely sampled coasts of East Antarctica. Existing constraints are geographically clustered, with studies concentrated in regions such as Graham Land and the South Shetland Islands in the northern Peninsula, Palmer Land , and key sectors of West Antarctica, including the Amundsen Sea Embayment , Siple Coast , and the Weddell Sea Embayment . In contrast, along the extensive East Antarctic coastline, observations are limited to a few regions, such as Dronning Maud Land and the Wilkes Subglacial Embayment , leaving the underlying solid Earth structure comparatively poorly constrained. The extensive coastline from the Amery Basin to George V Coast (spanning 90° in latitude) has an especially acute data shortage e.g.,. Across these regions, studies often yield differing estimates of lithosphere thickness and upper mantle viscosity. For example, on the northern Peninsula, some studies suggest weak sensitivity to lithosphere thickness, whereas others infer a thicker lithosphere, yielding comparable viscosity values . Given these discrepancies, prescribing a single, definitive set of regional parameters that accounts for all observations remains challenging. Here, we propose representative parameter sets informed by these studies, as our goal is not to reconcile or discount prior estimates but to provide first-order guidance to ice sheet modelers to enable coupled simulations. Accordingly, we define six sets of solid Earth parameters for Antarctica (Table 1), comprising two regional configurations each for West Antarctica, East Antarctica, and the Peninsula (Fig. C1).

As listed in the table, upper mantle viscosity spans about three orders of magnitude. Figure 2 shows Green’s functions for two contrasting Earth structures relevant for marine ice sheet modeling. The Amundsen Sea Embayment, in the West Antarctic Ice Sheet (WAIS), has a thin lithosphere (60 km) and low mantle viscosity (5×1018 Pa s). In contrast, the East Antarctic Ice Sheet (EAIS) coasts have a much thicker lithosphere (120 km) and higher viscosity (5×1020 Pa s). These differences produce distinctly different responses. In the first model (WAIS-earth), the solid Earth approaches isostatic equilibrium within 250–300 years, with viscous deformation evident in less than a decade. In the East Antarctic model (EAIS-earth), noticeable relaxation develops only after about 100 years of loading.

At the other pole, the Greenland Ice Sheet (GrIS) has received comparatively less attention regarding solid Earth coupling in centennial-scale projections. Here, we provide a brief synthesis of the current state of knowledge of solid Earth structure and parameters, along with a set of recommendations (see Table 1). The data set constraining GIA in Greenland is far more extensive than those for Antarctica e.g.,. Seismic imaging reveals three-dimensional variability of lithosphere thickness and mantle viscosity , although such structure is generally localized along the Iceland plume track . Based on these observations, we recommend adopting two sets of parameters: one for the region impacted by the plume track and the other for the rest of the subcontinent. This distinction is particularly important for accurately modeling major glaciers in central east Greenland, such as Helheim and Kangerdlugssuaq.

Recent efforts to reconcile paleo constraints with modern GNSS observations in regions minimally affected by the Icelandic plume (i.e., most of the subcontinent) support a centennial-scale mantle viscosity on the order of 5×1019 Pa s . However, constraints on lithosphere thickness remain less well resolved. The inferred viscosity is typically an order of magnitude lower than values commonly adopted in GIA studies targeting millennial timescales . A broadband rheological framework with time-variable viscosity has been proposed to reconcile these differences in viscosity , although further investigation is needed to determine its necessity . For spatial guidance, maps delineating the extent of the plume track region are provided in and . Within this area (Fig. C1), we recommend adopting reduced lithosphere thickness and mantle viscosity values, similar to those in the northern Antarctic Peninsula (Table 1).

We validate the proposed method by comparing example GRD results against self-consistent solutions acquired from simulating the Ice-sheet and Sea-level System Model ISSM; . In the latter, self-consistency is sought in the ocean loading and GRD solutions for a given ice loading. We accomplish this by solving the sea level equation on an unstructured Earth's surface mesh that conserves the total mass of ice and ocean. No regional model, including ours, can resolve self-consistency in global surface loading and the solid Earth response. The critical question is how well the regional model reproduces the self-consistent solutions. For identical representation of ice loading and solid Earth in the regional and global self-consistent models, the difference in predicted GRD solutions stems from the treatment of ocean loading and the rotational feedback. Here, we aim to quantify this difference for the predicted change in VLM and geoid. All regional model solutions include only the ice loading effect. In regions with grounding line migration, we consider only ice above flotation when calculating the load. Rotational feedback is also not accounted for, as shown to be negligible by .

First, we examine the elastic Earth response to the observed trend in Antarctic ice mass change derived from the Gravity Recovery and Climate Experiment (GRACE) and its Follow On (FO) mission data. A key aspect of the load model is the significant mass loss occurring in the Amundsen Sea Sector and Wilkes Land, contrasted by a moderate mass gain in Dronning Maud Land (Fig. 3a). This pattern is also evident in the near field of self-consistent ocean loading (Fig. 3b), where there is a reduction in ocean load (equivalently, relative sea level) near the areas of ice loss and an increase in ocean load near the areas of ice gain. The predicted VLM and geoid fields show minor differences between the regional and global models, suggesting sufficient accuracy of the proposed method. Self-consistent VLM solution is systematically larger (Fig. 3d) due to the reinforcing effect of the ocean load, but this is insignificant in this case of a small sea level change (Fig. 3e). A similarly minor difference is observed in the geoid field (Fig. 3h). This discrepancy appears to be primarily driven by Earth’s rotational response, as evidenced by the pronounced degree-2, order-1 pattern in Fig. 3g.

Next, we evaluate the proposed method for two viscoelastic Earth models using a sample of the future evolution of the Antarctic Ice Sheet until 2300. We use precomputed ice sheet model solutions – “experiment 05” of ISMIP6 Antarctica 2300 projections under the Shared Socioeconomic Pathway SSP5-8.5 based on the UKESM climate model – and load the solid Earth every 10 years between 2010 and 2300 CE. In this load model, the ice sheet mass change does not contribute much to barystatic sea level during the first half of the analysis period (Fig. 4a). The sea level contribution increases rapidly after around 2150, reaching a total change of about 1.5 m. The cumulative ice thickness change suggests substantial mass loss from West Antarctica and along the coastal regions of East Antarctica (Fig.  4b). In contrast, the inland areas of the ice sheet achieve a modest mass gain.

As introduced in the previous section, we consider two Earth models representing plausible structures beneath the Amundsen Sea Embayment (WAIS-earth) and the East Antarctic coasts (EAIS-earth). In the WAIS-earth case, the predicted VLM field exhibits significantly larger amplitudes and more pronounced high wave number features (Fig. 4c) than those in the EAIS-earth case (Fig. 4e). In contrast, the EAIS-earth model yields slightly larger geoid amplitudes (Fig. C2). This difference arises because the geoid signal is primarily governed by the direct effect of surface loads, while the induced solid Earth signal is orders of magnitude smaller (see Fig. 2). Accordingly, the larger amplitudes in the EAIS-earth case reflect reduced solid Earth compensation of the gravitational potential directly associated with the imposed loading (the same for both models). Discrepancies between regional and global model solutions are small (a few percent) for both VLM and geoid fields across all considered solid Earth models. These relative differences remain consistently small over the evaluation period, as illustrated for years 2150 (Fig. C3) and 2300 (Figs. 4 and C2). These differences tend to be larger in regions of strong mass loss and associated bedrock uplift and geoid change. Overall, they primarily reflect the generally reinforcing effect – particularly at long wavelengths – of processes omitted in the regional models, especially ocean loading.

Last, we examine coupled ice/Earth simulations for Thwaites Glacier, building on a recent study by , to assess the utility of our proposed method in simulating ice sheet dynamics. Their approach uses an anisotropic mesh to capture kilometer-scale grounding line migration and allows for a coupling interval as short as one year. The ice sheet model is initialized by optimizing basal friction and ice rheology to match observed surface velocity . It handles basal melt via the PICOP parameterization . This approach relies on simulating buoyant plume-driven sub-shelf meltwater circulation within the Potsdam Ice-shelf Cavity Model (PICO) framework . Model inputs for ocean temperature, salinity, and surface mass balance are based on the Community Earth System Model (CESM) SSP5-8.5 scenario . The Earth model complies with the Maxwellian structure constrained by GNSS data and further considers a transient relaxation of the asthenosphere and upper mantle based on the laboratory experiments, the results of which are couched in the formalism of the extended Burgers material (EBM) model . See Fig. C4 for the characteristic signals of the solid Earth model.

Figure 5 shows predicted grounding line positions and barystatic contributions from a standalone ice sheet simulation and two coupled simulations: one captures the ocean loading effect and rotational feedback (i.e., self-consistent solution), and the other does not (equivalently, the proposed method). The latter coupled model excellently reproduces the self-consistent solutions, capturing the GRD effect on barystatic sea level within 1 % for most of the time. This discrepancy increases up to 2 % by the end of the simulation as a viscous response to ocean loading accumulates over time. It is insignificant compared to the large disparity in the centennial-timescale projections of the Antarctic Ice Sheet . Despite its overall strong performance, we caution that our regional model may exhibit small but potentially important local deviations from those reported here. Even kilometer-scale offsets in grounding line position near bedrock ridges can influence the timing of unpinning and subsequent ice sheet retreat by several years e.g.,.

These examples demonstrate our method's excellent ability to capturing self-consistent solutions within the ice sheet domain. We show that the predicted VLM and geoid fields and their impact on ice dynamics on decadal to centennial timescales are primarily influenced by the direct ice load, which the proposed method can easily handle. The impacts of ocean load and rotational feedback are minimal, although our method can still capture some of these signals. For instance, the ocean load near the ice sheet may be derived and refined iteratively from the VLM and geoid fields, as in the classical sea level solver. However, refined ocean loads may not perfectly align with the self-consistent solutions. Additionally, the centrifugal potential perturbed by ice (and near-field ocean) and its effect on VLM and geoid fields can be computed semi-analytically. Since the ice load alone captures most of the near-field signals with sufficient accuracy – and given that our primary focus in this paper is on the straightforward retrieval of the leading-order solid Earth signals within the ice sheet model domains – we do not recommend pursuing these higher-order signals, as it may require a more complex workflow for a minimal gain in solution accuracy.

We propose a straightforward method that enables ice sheet models to capture realistic solid Earth feedback on decadal to centennial timescales. This method only involves interpolating precomputed Green's functions and performing matrix multiplication with the evolving ice loading. Consequently, it introduces no numerical complexity and does not significantly increase computational costs for ice sheet models. We demonstrate that this method reproduces self-consistent solutions for time-dependent geoid and bedrock topography fields within the ice sheet domain. When the objective is to simplify the ice/Earth coupling strategy while retaining the leading feedback on centennial timescales, we show that ocean loading effects (driven by local or far-field ice mass loss or migrating coastlines) and rotational feedback can be neglected. However, in applications where these processes are essential – such as global glacial isostatic adjustment modeling or interhemispheric ice-sheet interactions – a fully self-consistent solution of the sea level equation remains indispensable . Our method should therefore not be interpreted as a substitute for a sea level solver.

Recent studies highlight the high sensitivity of solid Earth feedback to ice sheet model resolution and coupling time intervals e.g.,. In coupled simulations involving a global sea level solver, frequently capturing kilometer-scale features, such as subtle migrations of grounding lines and evolving bedrock ridges, can be challenging. In contrast, our approach – despite the noted limitations – allows ice sheet models to determine the spatiotemporal resolution of solid Earth response signals without added complexity or computational costs. This simplified framework provides a more accessible pathway for ice sheet modelers, including those using standalone systems with limited resources or expertise in solid Earth processes, to incorporate a reasonably accurate ice/Earth feedback without significant overhead. Moreover, this reduced-complexity approach enables shorter coupling intervals, yielding more realistic (in certain respects) ice-sheet evolution and projections, or alternatively supports larger ensemble simulations, thereby improving uncertainty quantification and offering a practical advantage for probabilistic sea level projections.

The core idea of our method is to leverage precomputed Green’s functions for a radially stratified solid Earth. Open-access tools are available to compute Love numbers and Green’s functions for a range of linear viscoelastic models such as Maxwell, Burgers, or extended Burgers materials e.g.,. An extensive collection of Green’s functions for Maxwellian Earth models is already available . This library spans a wide range of plausible solid Earth structures, from models with a thin lithosphere and relatively weak upper mantle – such as those inferred geodetically beneath the Amundsen Sea Embayment or the northern Antarctic Peninsula e.g.,, as well as from seismic constraints in the Wilkes and Aurora Subglacial Basins – to models with cratonic lithosphere and a comparatively stiff mantle, as commonly adopted in glacial isostatic adjustment studies . We aim to further extend this library by performing additional computations for more refined Earth structures, including explicit asthenosphere layering, and more general linear viscoelastic formulations that incorporate transient rheology. Such extensions may be important for accurately modeling ice/Earth feedback at drainage basin scales.