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Abstract. We introduce a new software package called “icepack” for modeling the flow of glaciers and ice sheets.The icepack package is built on the finite element modeling library Firedrake, which uses the Unified Form Language (UFL), a domain-specific language embedded into Python for describing weak forms of partial differential equations.The diagnostic models in icepack are formulated through action principles that are specified in UFL.The components of each action functional can be substituted for different forms of the user's choosing, which makes it easy to experiment with the model physics.The action functional itself can be used to define a solver convergence criterion that is independent of the mesh and requires little tuning on the part of the user. Theicepack package includes the 2D shallow ice and shallow stream models.We have also defined a 3D hybrid model based on spectral semi-discretization of the Blatter–Pattyn equations.Finally, icepack includes a Gauss–Newton solver for inverse problems that runs substantially faster than the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method often used in the glaciological literature.The overall design philosophy of icepack is to be as usable as possible for a wide a swath of the glaciological community, including both experts and novices in computational science. 

Abstract. Reconstructions of past temperature and precipitation are fundamental to modeling the Greenland Ice Sheet and assessing its sensitivity to climate. Paleoclimate information is sourced from proxy records and climate-model simulations; however, the former are spatially incomplete while the latter are sensitive to model dynamics and boundary conditions. Efforts to combine these sources of information to reconstruct spatial patterns of Greenland climate over glacial–interglacial cycles have been limited by assumptions of fixed spatial patterns and a restricted use of proxy data. We avoid these limitations by using paleoclimate data assimilation to create independent reconstructions of mean-annual temperature and precipitation for the last 20 000 years. Our method uses oxygen isotope ratios of ice and accumulation rates from long ice-core records and extends this information to all locations across Greenland using spatial relationships derived from a transient climate-model simulation. Standard evaluation metrics for this method show that our results capture climate at locations without ice-core records. Our results differ from previous work in the reconstructed spatial pattern of temperature change during abrupt climate transitions; this indicates a need for additional proxy data and additional transient climate-model simulations. We investigate the relationship between precipitation and temperature, finding that it is frequency dependent and spatially variable, suggesting that thermodynamic scaling methods commonly used in ice-sheet modeling are overly simplistic. Our results demonstrate that paleoclimate data assimilation is a useful tool for reconstructing the spatial and temporal patterns of past climate on timescales relevant to ice sheets. 

Abstract. Sometime during the middle to late Holocene (8.2 ka to ∼ 1850–1900 CE), the Greenland Ice Sheet (GrIS) was smaller than its currentconfiguration. Determining the exact dimensions of the Holocene ice-sheetminimum and the duration that the ice margin rested inboard of its currentposition remains challenging. Contemporary retreat of the GrIS from itshistorical maximum extent in southwestern Greenland is exposing a landscapethat holds clues regarding the configuration and timing of past ice-sheetminima. To quantify the duration of the time the GrIS margin was near itsmodern extent we develop a new technique for Greenland that utilizes in situcosmogenic 10Be–14C–26Al in bedrock samples that have becomeice-free only in the last few decades due to the retreating ice-sheet margin atKangiata Nunaata Sermia (n=12 sites, 36 measurements; KNS), southwest Greenland. To maximizethe utility of this approach, we refine the deglaciation history of the regionwith stand-alone 10Be measurements (n=49) and traditional 14C agesfrom sedimentary deposits contained in proglacial–threshold lakes. We combineour reconstructed ice-margin history in the KNS region with additionalgeologic records from southwestern Greenland and recent model simulations ofGrIS change to constrain the timing of the GrIS minimum in southwestGreenland and the magnitude of Holocene inland GrIS retreat, as well as to explore theregional climate history influencing Holocene ice-sheet behavior. Our10Be–14C–26Al measurements reveal that (1) KNS retreated behindits modern margin just before 10 ka, but it likely stabilized near thepresent GrIS margin for several thousand years before retreating fartherinland, and (2) pre-Holocene 10Be detected in several of our sample sitesis most easily explained by several thousand years of surface exposure duringthe last interglaciation. Moreover, our new results indicate that the minimumextent of the GrIS likely occurred after ∼5 ka, and the GrISmargin may have approached its eventual historical maximum extent as early as∼2 ka. Recent simulations of GrIS change are able to match thegeologic record of ice-sheet change in regions dominated by surface massbalance, but they produce a poorer model–data fit in areas influenced by oceanicand dynamic processes. Simulations that achieve the best model–data fitsuggest that inland retreat of the ice margin driven by early to middleHolocene warmth may have been mitigated by increased precipitation. Triple10Be–14C–26Al measurements in recently deglaciated bedrockprovide a new tool to help decipher the duration of smaller-than-present iceover multiple timescales. Modern retreat of the GrIS margin in southwestGreenland is revealing a bedrock landscape that was also exposed during themigration of the GrIS margin towards its Holocene minimum extent, but it has yetto tap into a landscape that remained ice-covered throughout the entireHolocene.