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Ice sheet models, calibrated using observational data, provide a means of projecting our current best state of the knowledge of the system state into the future, so as to obtain information about possible future behaviour. However it is important to be able to estimate the uncertainty associated with these projections. The problem of quantifying ice sheet parametric uncertainty is considered, focusing specifically on the problem of quantifying the posterior uncertainty in inferred basal sliding and rheology coefficients. These measures of uncertainty are projected forwards in time to obtain measures of uncertainty in future quantities of interest. Automated code generation and automated differentiation tools are utilised, leading to an extensible approach. The role of the observational error model in defining parametric uncertainty is considered.

The components Antarctica's subglacial hydrology -for instance water sources, sinks, flow paths and catchments- are still poorly constrained. In this work we assess the subglacial hydrology of the continent at high resolution (500m) using (1) water inputs from frictional melting derived with a higher order ice flow model combined with existing geothermal heat flux products, (2) BedMachine topography, and (3) a water flow routing model taking uncertainties into account.We present the following modelling results: probabilistic maps of water flow paths and catchments, potential subglacial lake locations, fluxes across the grounding line, and melt or freeze-on rates due to water flow. We also present locations where the drainage system configuration, such as the catchment size, is sensitive to model inputs and thus where future field investigations would be particularly valuable.

The impacts of upper-ocean mixing on primary productivity are complex and range from an entrainment of nutrients to modulating light limitations. Sea ice in turn plays an important role in determining mixing conditions through its cycles of formation and melt, and by moderating wind forcing. With sea ice conditions in the Southern Ocean projected to undergo large changes over the course of the century, understanding the relationship between sea ice and upper-ocean mixing is crucial for understanding the impacts of climate change on biological production in this region. Due to the inaccessibility of sea ice-covered waters however, mixed layer depth observations are often not available at a high temporal and spatial resolution. Here we present an analysis of sea ice-mixed layer depth relationships during a 40-year regional ocean-sea ice simulation of the West Antarctic Peninsula (WAP) and Bellingshausen Sea, a highly biologically productive region of global importance. The relationship between winter sea ice and spring mixed layer depth shows clear differences on and off the WAP continental shelf, with decadal variations in the location of the boundary between negative and positive correlations. Potential mechanisms causing this effect are considered in detail, including the nonlinear relationship between sea ice cover and turbulent mixing, the transport of sea ice within the region, and a difference in the timing of the sea ice seasonal cycle between the two regions. The transport of warm Circumpolar Deep Water onto the shelf is also discussed. The presented findings have implications for the spatial distribution of primary producers in a more ice-free future WAP.

The Amundsen Sea Sector has some of the highest thinning rates of ice shelves in Antarctica, thought to be driven by high, but interannually variable, ocean driven melt rates. This thinning can lead to increased ice flow speeds, eventually leading to sea level rise. To fully represent these processes and other feedbacks, a fully coupled ice/ocean model must be used. Therefore, a fully synchronous mass conservative coupled ice-sheet/ocean model of the Amundsen Sea Sector has been developed. This new coupled model builds upon previous coupling developments and involves coupling of the WAVI ice-sheet model to the 3D ocean model MITgcm, via the Streamice ice-sheet model. Coupled model projections are presented, examining ice grounding line retreat rates and ice mass loss, along with ocean driven melt rate evolution. The sensitivity of these results to ocean forcings is shown, specifically the thickness of the relatively warm Circumpolar Deep Water layer and its variability. In addition, we discuss the impact of the present-day initialisation and tuning of the coupled model.

We use numerical modelling to address several questions related to the future evolution of Thwaites Glacier over the next 50 years. The importance of Thwaites Ice Shelf for upstream grounded flow is investigated by quantifying the buttressing stresses along the grounding line. Removing the ice shelf changes the stress regime along the grounding line by less than 20%. This change is small compared to many, if not most, grounding lines of the Antarctic Ice Sheet, and much smaller than corresponding changes for the neighboring Pine Island and Pope, Smith and Kohler glaciers. Transient ice-flow modelling experiments show that mass loss from Thwaites Glacier over the next 50 years is insignificantly affected by removal of the ice shelf. We then explore the consequences of the proposed marine ice-cliff instability for Thwaites Glacier. For recently proposed calving laws, where the calving rate increases sharply with cliff height, we do not observe an onset of an unstable calving front retreat. Further numerical modelling experiments for future climatic forcing scenarios will be presented, including uncertainty quantification. Interactions between the ice and the ocean are studied using a coupled ice+ocean modelling framework. As shown before in several studies, we find when simulating its future evolution, that Thwaites Glacier can enter unstable periods of self-enhancing retreat. This appears to be a very robust result, and this behavior is found in all model runs, including coupled ice+ocean simulations.

The COVID-19 pandemic created an extreme natural experiment in which sudden changes in human behavior and economic activity resulted in significant declines in nitrogen oxide (NOx) emissions, immediately after strict lockdowns were imposed. Here we examined the impact of multiple waves and response phases of the pandemic on nitrogen dioxide (NO2) dynamics and the role of meteorology in shaping relative contributions from different emission sectors to NO2 pollution in post-pandemic New York City. Long term (> 3.5 years), high frequency measurements from a network of ground-based Pandora spectrometers were combined with TROPOMI satellite retrievals, meteorological data, mobility trends, and atmospheric transport model simulations to quantify changes in NO2 across the New York metropolitan area. The stringent lockdown measures after the first pandemic wave resulted in a decline in top-down NOx emissions by approx. 30 % on top of long-term trends, in agreement with sector-specific changes in NOx emissions. Ground-based measurements showed a sudden drop in total column NO2 in spring 2020, by up to 36 % in Manhattan and 19 %–29 % in Queens, New Jersey (NJ), and Connecticut (CT), and a clear weakening (by 16 %) of the typical weekly NO2 cycle. Extending our analysis to more than a year after the initial lockdown captured a gradual recovery in NO2 across the NY/NJ/CT tri-state area in summer and fall 2020, as social restrictions eased, followed by a second decline in NO2 coincident with the second wave of the pandemic and resurgence of lockdown measures in winter 2021. Meteorology was not found to have a strong NO2 biassing effect in New York City after the first pandemic wave. Winds, however, were favorable for low NO2 conditions in Manhattan during the second wave of the pandemic, resulting in larger column NO2 declines than expected based on changes in transportation emissions alone. Meteorology played a key role in shaping the relative contributions from different emission sectors to NO2 pollution in the city, with low-speed (

Ice shelf shape directly controls ocean heat intrusions, melting near the grounding line, and buttressing. Little is known about what determines ice-shelf shape because ice-ocean coupled simulations typically aim at projecting Antarctica's contribution to sea-level rise and they do not resolve small-scale ice-ocean interactive processes. We conduct ice-ocean coupled simulations for an idealized high-resolution, Pine-Island-like model configuration. We show that ocean melting and ice stretching caused by acceleration thin the ice shelf from the grounding line toward the ice shelf front, consistent with previous studies. In the across-flow direction, ocean melting and ice advection cancel each other out and flatten the ice shelf. More than one-third of the ice thinning from grounding line to ice front can be attributed to ocean melting at depths shallower than 500 m. Our results emphasize the importance of interactive processes between the entire ice shelf and the ocean for determining the ice shelf shape. Plain Language Summary Antarctic ice flows into the ocean and forms a floating extension of land ice called an ice shelf. The ice shelf shape directly controls the amount of ocean heat intrusions, melting near the grounding line, and buttressing. However, little is understood about ice-ocean interactive processes determining ice shelf shape because (a) ocean modelers apply a constant cavity geometry, (b) ice modelers mostly assume simplified melting parameterization, and (c) ice-ocean coupled simulations typically aim at projections of Antarctica's sea-level contributions and they require long model integration. We conduct ice-ocean coupled simulations for an idealized high-resolution Pine-Island-like model configuration. Basal melting and ice stretching create a typical ice shelf shape with steep thinning near the grounding line followed by gradual thinning toward the ice shelf front. In the across-flow direction, ice divergence from the center advects ice toward edges, compensating for melt-driven thinning and flattening ice shelf shape. We also show that ice melting at shallow depths contributes to about one-third of ice-shelf thinning. Although it is thought that ice shelf melting at the grounding line dominantly controls ice shelf behavior, our results suggest the importance of ice-ocean interactive processes for the entire ice shelf cavity for determining the ice shelf shape.

Mass loss due to dynamic changes in ice sheets is a significant contributor to sea level rise, and this contribution is expectedto increase in the future. Numerical codes simulating the evolution of ice sheets can potentially quantify this future contribution.However, the uncertainty inherent in these models propagates into projections of sea level rise, and hence is crucialto understand. Key variables of ice sheet models, such as basal drag or ice stiffness, are typically initialized using inversionmethodologies to ensure that models match present observations. Such inversions often involve tens or hundreds of thousandsof parameters, with unknown uncertainties and dependencies. The computationally intensive nature of inversions along withtheir high number of parameters mean traditional methods such as Monte Carlo are expensive for uncertainty quantification.Here we develop a framework to estimate the posterior uncertainty of inversions, and project them onto sea level change projections over the decadal timescale. The framework treats parametric uncertainty as multivariate Gaussian, and exploits theequivalence between the Hessian of the model and the inverse covariance of the parameter set. The former is computed efficientlyvia algorithmic differentiation, and the posterior covariance is propagated in time using a time-dependent model adjointto produce projection error bars. This work represents an important step in quantifying the internal uncertainty of projectionsof ice-sheet models.

The West Antarctic Ice Sheet has the potential to contribute up to 3m of sea level rise over the next few centuries. There is considerable uncertainty over the rate at which ice loss will occur, caused in part by a lack of knowledge about the bed topography beneath the ice sheet, which influences ice flow and retreat. Since direct bed topography observations are often further apart than ice sheet models require, we explore instead what we can learn about bed topography from high resolution observations of the ice surface, which are openly available. We apply an inversion methodology based on linear perturbation theory and developed by Gudmundsson (2003, 2008) to ice surface data from Pine Island Glacier, and present the bed topography results. Comparison to high-resolution radar sounding of the bed topography of Pine Island Glacier from the iSTAR 2013-14 ground surveys allows us to assess the success of the inversion methodology. We identify regions of the glacier where the landforms we see are likely to be artefacts, and regions where unknown and interesting landforms are likely to exist. This methodology has the potential to be extremely useful in regions where direct observations of bed topography are sparse, and for identifying areas where more observations would be of particularly high benefit.

Subglacial water at the base of the ice sheet has been shown to impact ice flow and its discharge into the ocean – which modifies ocean properties and melt rates of fringing ice shelves. Subglacial water, generated from frictional heating and geothermal heat flux, collects in hydrological sinks which store and release water in episodic events. These events, interpreted as water moving in and out of active lakes, have a signature at the surface of the ice sheet which can be detected and quantified by satellite altimetry. By quantifying the volume of water involved in these active events, it is possible to obtain insight into processes otherwise hidden from view. In particular, observing the gain in volume following a drainage event provides constraints on hydrological recharge rates, subglacial water fluxes, and processes leading to basal melt water production. Such a method was applied to the inventory of Antarctic active subglacial lakes using CryoSat’s radar altimeter observations over the 2010-2020 period. Out of 136 known lakes, 13 lakes show clear signs of recharge during the observation period. From these we can extract recharge rates, which act as a lower bound on subglacial melt production. These rates are compared against rates of recharge derived by routing modelled subglacial melt production across the Antarctic Ice Sheet. We demonstrate that, for connected subglacial lake networks, satellite observations can provide a robust validation dataset for sub-glacial melt models. Our results show that, at a local level, estimates of melt water flux is highly dependent on the routing method chosen. We also highlight subglacial lakes where observed rates of recharge are too high to be explained by our current knowledge of the bed and of processes responsible for subglacial melting rates.

Meltwater forms at the base of the Antarctic Ice Sheet due to geothermal heat flux (GHF) and basal frictional dissipation. Despite the relatively small volume, this meltwater has a profound effect on ice-sheet stability, controlling the dynamics of the ice sheet and the interaction of the ice sheet with the ocean. However, observations of subglacial melting and hydrology in Antarctica are limited. Here we use numerical modelling to assess subglacial melt rates and hydrology beneath the Antarctic Ice Sheet. Our case study, focused on the Amery Ice Shelf catchment, shows that total subglacial melting in the catchment is 6.5 Gt yr-1, over 50% larger than previous estimates. Uncertainty in estimates of GHF leads to a variation in total melt of ±7%. The meltwater provides an extra 8% flux of freshwater to the ocean in addition to contributions from iceberg calving and melting of the ice shelf. GHF and basal dissipation contribute equally to the total melt rate, but basal dissipation is an order of magnitude larger beneath ice streams. Remote-sensing observations, from CryoSat-2, indicating active subglacial lakes and ice-shelf basal melting constrain subglacial hydrology modelling. We observe a network of subglacial channels that link subglacial lakes and trigger isolated areas of sub-ice-shelf melting close to the grounding line. Building upon this Amery case study, we expand our analysis to quantify subglacial melt rates and hydrology beneath the entire Antarctic Ice Sheet.

Fenics_ice is a finite element model framework written in Python that quantifies the initialization uncertainty for time-dependent ice sheet models. Here, we apply for the first time this framework to real ice streams in the Amundsen basin: Smith, Pope and Kohler Glaciers. We quantify the degree to which observational uncertainty translates to parametric uncertainty (posterior uncertainty of inversions for basal drag and ice stiffness fields) and to uncertainty in projected quantities of interest (QoIs) such as sea level contribution. The framework implements the Shallow Shelf Approximation (SSA), and implements a control methods approach to invert for the basal drag and ice stiffness fields. Beginning with a cost function optimization which can allow for either gridded or point-cloud velocities, we generate a low-rank approximation to the posterior covariance of the parameters through the use of the cost function Hessian. In our work, the Hessian is calculated through algorithmic differentiation (AD) using the “complete” Hessian rather than the Gauss–Newton approximation. We then project the covariance on a linearization of the time-dependent ice sheet model (again using AD to generate the linearization) to estimate the growth of QoI uncertainty over time. We then show the model framework and capabilities when applied to these ice streams and our future plans to scale our framework into a larger domain.

Cordillera Blanca glaciers represent the greatest glacial freshwater reserve in tropical South America and have been shrinking substantially over recent decades, posing a threat to future water resources in the Peruvian Ancash region. A crucial step to better understand the evolution of these glaciers under changing conditions is to establish robust reconstructions of their past response to climate fluctuations. Such reconstructions are limited in the tropical Andes, which inhibits our understanding of the climatic drivers of tropical glacier length and surface mass balance changes. The relative importance of temperature versus precipitation rate changes on glacier length changes is therefore still debated in the region. Here, we present 42 cosmogenic 10Be exposure ages from moraine boulder samples, establishing for the first time a comprehensive chronology for Late-glacial, Holocene and Neoglacial advances of four distinct Cordillera Blanca mountain glaciers. We use this chronology to constrain a series of moraine-matching numerical model-run simulations conducted for each dated glacier advance using a spatially-distributed ice-flow model coupled with a positive degree-day surface mass balance parameterisation. These simulations aim at modelling and estimating former three-dimensional glacier geometries, equilibrium line altitudes, surface mass balance properties and their evolution through time. This analysis also enables us to use glacier surface mass balance as a proxy for past atmospheric temperature and precipitation variations at the time of the reconstructed glacier advances. This new, multi-method glacier reconstruction enables, for the Cordillera Blanca: 1) novel glacio-geomorphological interpretations, 2) an improved understanding of glacier extent, surface mass balance and volume change during the Late-glacial, Holocene and Neoglacial phases of advance, and 3) new estimations of paleoclimate conditions required for the reconstructed glacier events to occur.

Ice shelf melt rates near grounding lines are a few orders of magnitude higher than other locations. This intense melting close tothe grounding zone is crucial as it induces ice shelf thinning, further acceleration of ice flow, and grounded ice loss. However,little is revealed about ice and ocean processes determining peak ice shelf melt rates close to the grounding line because (1) oceanmodelers apply a constant cavity geometry, (2) ice modelers typically assume some parameterizations for determining ice shelf melt rates,and (3) ice-ocean coupled simulations typically require long model integration, necessitating coarse resolution, and they are not able toresolve small-scale processes near grounding zones. Here, we develop an idealized high-resolution Pine-Island-like model configuration (250m, 500m, and 1km horizontal and 10 m vertical grid spacings) and conduct ice-ocean coupled simulation for 20 years after 60 years ofinitialization. We show that ice slope and ice shelf melt rate close to the grounding zone increases with higher grid resolution but iceshelf geometry converges towards the highest resolution solution. We are also able to simulate the formation of sub-ice shelf channels byapplying seasonally varying oceanic conditions. We also present our preliminary results of ice-ocean coupled realistic Pine Islandsimulation using unprecedentedly high horizontal and vertical resolution (200m horizontal and 10 m vertical grid spacings). This isa step towards understanding the ice-ocean interacting mechanisms determining ice shelf shape and melt rate, which is crucial forimproved projections of future Antarctic ice loss.

In the last decade, the number of ice-sheet models has increased substantially, in line with the growth of the glaciological community. These models use solvers based on different approximations of ice dynamics. In particular, several depth-integrated dynamics approximations have emerged as fast solvers capable of resolving the relevant physics of ice sheets at the continen- tal scale. However, the numerical stability of these schemes has not been studied systematically to evaluate their effectiveness in practice. Here we focus on three such solvers, the so-called Hybrid, L1L2-SIA and DIVA solvers, as well as the well-known SIA and SSA solvers as boundary cases. We investigate the numerical stability of these solvers as a function of grid resolution and the state of the ice sheet. Under simplified conditions with constant viscosity, the maximum stable timestep of the Hybrid solver, like the SIA solver, has a quadratic dependence on grid resolution. In contrast, the DIVA solver has a maximum timestep that is independent of resolution, like the SSA solver. Analysis indicates that the L1L2-SIA solver should behave similarly, but in practice, the complexity of its implementation can make it difficult to maintain stability. In realistic simulations of the Greenland ice sheet with a non-linear rheology, the DIVA and SSA solvers maintain superior numerical stability, while the SIA, Hybrid and L1L2-SIA solvers show markedly poorer performance. At a grid resolution of ∆x = 4 km, the DIVA solver runs approximately 15 times faster than the Hybrid and L1L2-SIA solvers. Our analysis shows that as resolution increases, the ice-dynamics solver can act as a bottleneck to model performance. The DIVA solver emerges as a clear outlier in terms of both model performance and its representation of the ice-flow physics itself.

The Marine Ice Sheet-Ocean Model Intercomparison Project (MISOMIP) is a community effort sponsored by the Climate and Cryosphere (CliC) project. MISOMIP aims to design and coordinate a series of MIPs—some idealized and realistic—for model evaluation, verification with observations, and future projections for key regions of the West Antarctic Ice Sheet (WAIS). The first phase of the project, MISOMIP1, was an idealized, coupled set of experiments that combined elements from the MISMIP+ and ISOMIP+ standalone experiments for ice-sheet and ocean models, respectively. These MIPs had 3 main goals: 1) to provide simplified experiments that allow model developers to compare their results with those from other models; 2) to suggest a path for testing components in the process of developing a coupled ice sheet-ocean model; and 3) to enable a large variety of parameter and process studies that branch off from these basic experiments.Here, we describe preliminary analysis of the MISOMIP1 results. Eight models in 14 configurations participated in the MIP. In keeping with analysis of the MISMIP+ experiment, we find that the choice of basal friction parameterizations in the ice-sheet component (Weertman vs. Coulomb limited) has a particularly significant impact on the rate of ice-sheet retreat but the choice of stress approximation (SSA, SSA* or L1Lx) seems to have little impact. Models with Coulomb-limited basal friction also tend to be those with the highest melt rates, confirming a positive feedback between melt and retreat in the MISOMIP1 configuration seen in previous work. The ocean component’s treatment of the boundary layer below the ice shelf also has a significant impact on melt rates and resulting retreat, consistent with findings based on ISOMIP+. Feedbacks between the components lead to localized features in the melt rates and the ice geometry not seen in standalone simulations, though the ~2-km horizontal and ~20-m vertical resolution of these simulations appears to be too coarse to produce long-lived, sub-ice-shelf channels seen at higher resolution.

Active subglacial lakes have been identified throughout Antarctica, offering a window into subglacial environments and their impact on ice sheet mass balance. We use high-resolution altimetry measurements over the Thwaites Glacier to show that a lake system underwent a second episode of drainage activity in 2017, only four years after another substantial drainage event. Our observations suggest significant modifications of the drainage system between the two events, with 2017 experiencing greater upstream discharge, faster lake-to-lake connectivity, and the transfer of water within a closed system. Measured rates of lake recharge during the inter-drainage period are significantly larger than modelled estimates, suggesting processes which drive subglacial melt production are currently underestimated. Our study highlights new methods of exploring subglacial environments through the application of altimetry, with potential applications for studying subglacial lakes across Antarctica

Thwaites Glacier in West Antarctica is one of the regions of the fastest accelerating ice thinning and highest observed ice loss. The topography of the bed beneath the glacier is a key control of future ice loss, but is not currently well enough known to satisfy the requirements of ice sheet models predicting glacier behaviour. It has previously been suggested that in fast flowing ice streams the shapes of landforms at the bed should be reflected in the ice surface morphology, which is known to a much higher resolution. Indeed, recently published radar grids from Pine Island Glacier reveal bed landforms with a definite resemblance to the ice surface above them. Here, we present a new high resolution bed topography map of Thwaites Glacier, inverted from REMA and ITSLIVE data using linear perturbation theory, a mathematical formulation of this resemblance between bed and surface. As it is based on linear physics, this method is faster than mass conservation and streamline diffusion interpolation, the two main techniques utilised by existing bed topography products in this region. Furthermore, as the theory is based on both mass and momentum balance, it provides a physically consistent estimate of elevation and basal slipperiness, in contrast to these more widely used methods. The resulting bed matches well with existing airborne and swath radar surveys, with significant detail between these radar lines. Variation in the results obtained using different reference models provides a measure of validity of the linear perturbation theory. Due to the importance of form drag in patterns of ice retreat, the inverted topographic features are potentially important for the future behaviour of Thwaites Glacier.

Hundreds of millions of people depend strongly on hydrological inputs in the mountainous regions of China and central Asia. Glacier runoff is a major contributor to this hydrological forcing, yet many glaciers in the region have undergone mass loss in recent years and this mass loss is expected to continue or increase in response to climatological change. As such it is important to assess the large-scale response of High Mountain Asia glaciers to climate change , and its effects on hydrology. We present here preliminary modelling investigations of glacier change and hydrological impacts in response to high-resolution climate model projections over the 21st century as a component of the project SWARM (Impacts Assessment to Support WAter Resources Management and Climate Change Adaptation for China). Our model chain consists of i) Open Global Glacier Model (OGGM), which allows for high-resolution glacier flowline modelling of multiple glaciers, and ii) the Framework for Understanding Structural Errors (FUSE) a modular framework for snow and hydrology modelling, which we used to assemble and run three hydrological models over the whole of China. Both FUSE and OGGM are forced by an ensemble of bias-corrected CORDEX-East Asia regional climate models (in turn forced by CMIP5 general circulation models), and outputs of OGGM are provided to FUSE. We discuss our application of OGGM to 80,000 glaciers in Chinese river catchments; our efforts to calibrate the mass balance model using an expanded set of geodetic mass balance constraints; and finally the projections of glacier, snow and streamflow changes in the 21st century. In particular, we discuss the robustness and uncertainties in the projections as sampled by our multi-model ensemble.

Active subglacial lakes have been identified throughout Antarctica, offering a window into subglacial environments and into controls on ice dynamics. Between June 2013 and January 2014 a system of connected subglacial lakes drained in unison under the Thwaites glacier in the West Antarctic ice sheet, the first time that such a system has been observed in the Amundsen Sea Sector. Estimates based on catchment scale melt production suggested that lake drainages of this type should occur every 20 to 80 years. We collected elevations from January 2011 to December 2019 over the Thwaites lake region using the CryoSat-2 swath interferometric mode and ICEsat-2 land ice elevations, as well as ice velocity from the Sentinel-1 SAR mission since 2014. Using various elevation time series approaches, we obtain time dependent elevations over each lake. Results indicate that the upstream lakes undertake a second episode of drainage during mid-2017, only 3 years after the previous event, and that a new lake drained. Unlike the 2013-2014 episode, this new drainage episode contributed to filling one of the downstream lake with no evidence of further downstream activity. This new sub-glacial lake activity under Thwaites offer the possibility to explore lake connectivity, subglacial melt production and the interaction with ice dynamics.

In recent years, there have been great advances in coupled ice sheet-ocean modelling, to the point where ice-ocean interactions can be represented in global climate models — with potential to greatly improve forecasting of marine ice-sheet loss and sea level rise in the coming century and beyond. However, initialisation of coupled ice sheet-ocean models has not yet been properly examined; and initialisation approaches applied to ocean and coupled atmosphere-ocean models may not be appropriate due to the long time scales inherent in dynamic ice sheets. Moreover, as ocean melt rates and ice-shelf geometry strongly influence each other, nonphysical transients in incorrectly initialised coupled ice-ocean models may persist for longer than in ice-sheet models alone.In this work, two approaches to coupled initialisation are considered using a synchronously coupled ice-ocean model. The two approaches are based on two commonly used approaches to ice sheet model initialisation: “snapshot” calibration, where ice-sheet basal and internal parameters are configured to optimise fit with observed surface velocity; and “transient” calibration, where these parameters are configured to jointly optimise fit with velocity and geometry change; however, the transient calibration makes use of the ocean component to ensure the ice model is not subject to “initialisation shock” from ocean melting. The approaches are applied to Smith Glacier, a small but fast-thinning glacier in West Antarctica, and the model is forced under ocean warming scenarios in multidecadal runs. Initially there is much faster retreat seen in the Snapshot-calibrated simulation, but this difference decays over several decades, and ultimately the Transiently-calibrated model sees more retreat.The experiments further suggest that Smith Glacier is not likely to exhibit Marine Ice Sheet instability in the next century. But the methods discrepancy has strong implications for glaciers which are susceptible to this instability.

A glacial flow model of Smith, Pope and Kohler Glaciers is calibrated by means of control methods against time varying, annually resolved observations of ice height and velocities, covering the period 2002 to 2011. The inversion – termed "transient calibration" – produces an optimal set of time-mean, spatially varying parameters together with a time-evolving state that accounts for the transient nature of observations and the model dynamics. Serving as an optimal initial condition, the estimated state for 2011 is used, with no additional forcing, for predicting grounded ice volume loss and grounding line retreat over the ensuing 30 years. The transiently calibrated model predicts a near-steady loss of grounded ice volume of approximately 21 km3 a−1 over this period, as well as loss of 33 km2 a−1 grounded area. We contrast this prediction with one obtained following a commonly used "snapshot" or steady-state inversion, which does not consider time dependence and assumes all observations to be contemporaneous. Transient calibration is shown to achieve a better fit with observations of thinning and grounding line retreat histories, and yields a quantitatively different projection with respect to ice volume loss and ungrounding. Sensitivity studies suggest large near-future levels of unforced, i.e., committed sea level contribution from these ice streams under reasonable assumptions regarding uncertainties of the unknown parameters.

We apply an optimized method to the adjoint generation of a time-evolving land ice model through algorithmic differentiation (AD). The optimization involves a special treatment of the fixedpoint iteration required to solve the nonlinear stress balance, which differs from a straightforward application of AD software, and leads to smaller memory requirements and in some cases shorter computation times of the adjoint. The optimization is done via implementation of the algorithm of Christianson [1994] for reverse accumulation of fixed-point problems, with the AD tool OpenAD. For test problems, the optimized adjoint is shown to have far lower memory requirements, potentially enabling larger problem sizes on memory-limited machines. In the case of the land ice model, implementation of the algorithm allows further optimization by having the adjoint model solve a sequence of linear systems with identical (as opposed to varying) matrices, greatly improving performance. The methods introduced here will be of value to other efforts applying AD tools to ice models, particularly ones which solve a "hybrid" shallow ice / shallow shelf approximation to the Stokes equations.