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ERROR: type should be string, got "https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. Evaluating different geothermal heat flow maps as basal boundary conditions during\n1\nspin up of the Greenland ice sheet\n2\n3\nTong ZHANG1, William COLGAN2, Agnes WANSING3, Anja LØKKEGAARD2, Gunter LEGUY4\n4\nWilliam LIPSCOMB4, and Cunde XIAO1\n5\n6\n1State Key Laboratory of Earth Surface Processes and Resource Ecology, Beijing Normal\n7\nUniversity, Beijing, CHINA\n8\n2Geological Survey of Denmark and Greenland, DENMARK\n9\n3Kiel University, Kiel, GERMANY\n10\n4National Center for Atmospheric Research, UNITED STATES\n11\n12\nCorresponding author: Tong Zhang, tzhang@bnu.edu.cn\n13\n14\nABSTRACT\n15\nThere is currently poor scientific agreement whether the ice-bed interface is frozen or\n16\nthawed beneath approximately one-third of the Greenland ice sheet. This disagreement in basal\n17\nthermal state results, at least partly, from a diversity of opinion in the subglacial geothermal heat\n18\nflow basal boundary condition employed in different ice-flow models. Here, we employ seven\n19\nGreenland geothermal heat flow maps in widespread use to 10,000-year spin ups of the\n20\nCommunity Ice Sheet Model (CISM). We perform both a fully unconstrained transient spin up,\n21\nas well as a nudged spin up that conforms to Ice Sheet Model Intercomparison Project for\n22\nCMIP6 (ISMIP6) protocol. Across the seven heat flow maps, and regardless of unconstrained or\n23\nnudged spin up, the spread in basal ice temperatures exceeds 10°C over large areas of the ice-\n24\nbed interface. For a given heat flow map, thawed-bedded ice-sheet area is consistently larger\n25\nunder unconstrained spin ups than nudged spin ups. Under the unconstrained spin up, thawed-\n26\nbedded area ranges from 33.5 to 60.0% across the seven heat flow maps. Perhaps\n27\ncounterintuitively, the highest iceberg calving fluxes are associated with the lowest heat flows\n28\n(and vice versa) for both unconstrained and nudged spin ups. This highlights the direct, and\n29\nnon-trivial, influence of choice of heat flow boundary condition on the simulated equilibrium\n30\nthermal state of the ice sheet. We suggest that future ice-flow model intercomparisons should\n31\nemploy a range of basal heat flow maps, and limit direct intercomparisons to simulations\n32\nemploying a common heat flow map. 33\n34 The Cryosphere INTRODUCTION\n35\nThere is presently a tremendous diversity of opinion regarding the geothermal heat flow\n36\nbeneath the Greenland ice sheet due to a paucity of direct measurements of geothermal heat\n37\nflow beneath the ice-sheet interior. While many subaerial, submarine and shallow subglacial\n38\nmeasurements have been made around the ice-sheet periphery, deep subglacial\n39\nmeasurements have only been made at six deep ice coring sites within the ice-sheet interior\n40\n(Camp Century, DYE-3, GRIP, GISP2, NGRIP and NEEM). Consequently, the magnitude and\n41\nspatial distribution of Greenland’s subglacial geothermal heat flow remains poorly constrained\n42\nacross the seven unique Greenland heat flow models presently in widespread use (Figure 1)\n43\n[Shapiro and Ritzwoller, 2004; Rezvanbehbahani et al., 2017; Martos et al., 2018; Greve, 2019;\n44\nLucazeau, 2019; Artemieva, 2019; Colgan et al., 2022]. These individual geothermal heat flow\n45\nmodels are derived from a variety of techniques that interpret a variety of geophysical variables\n46\n(Table 1). We briefly discuss broad differences in the methodology and geophysical input\n47\nvariables of these existing heat flow maps. 48 The Rezvanbehbahani et al. [2017], Lucazeau [2019] and Colgan et al. [2022] heat flow\n49\nmaps are perhaps methodologically most similar. These three maps use machine learning or\n50\ngeostatistics to predict heat flow as a function of diverse geophysical variables such as\n51\ntopography, tectonic age, observed gravity and magnetic field etc. They differ not only in the\n52\napplied method but also in the utilized set of geophysical variables and their domains. Whereas\n53\nRezvanbehbahani et al. [2017] and Lucazeau [2019] only used global data, Colgan et al. [2022]\n54\nsubstituted global datasets with Greenland specific local data. In contrast, the Shapiro and\n55\nRitzwoller [2004], Martos et al. [2018] and Artemieva [2019] heat flow maps all employ\n56\nlithospheric models of varying complexity and more specific geophysical variables to infer heat\n57\nflow. Shapiro and Ritzwoller [2004] correlate the seismic shear wave velocities of the upper 300\n58\nkm with heat flow observations and use this connection to predict heat flow from tomography\n59\ndata in areas without heat flow observations. Martos et al. [2018] use magnetic data to infer the\n60\nCurie temperature depth. Artemieva [2019] assumes an isostatic equilibrium and translates the\n61\ncorresponding topographic residuals to temperature anomalies which are then converted to a\n62\nlithosphere-asthenosphere boundary undulation. ABSTRACT There is currently poor scientific agreement whether the ice-bed interface is frozen or\n16\nthawed beneath approximately one-third of the Greenland ice sheet. This disagreement in basal\n17\nthermal state results, at least partly, from a diversity of opinion in the subglacial geothermal heat\n18\nflow basal boundary condition employed in different ice-flow models. Here, we employ seven\n19\nGreenland geothermal heat flow maps in widespread use to 10,000-year spin ups of the\n20\nCommunity Ice Sheet Model (CISM). We perform both a fully unconstrained transient spin up,\n21\nas well as a nudged spin up that conforms to Ice Sheet Model Intercomparison Project for\n22\nCMIP6 (ISMIP6) protocol. Across the seven heat flow maps, and regardless of unconstrained or\n23\nnudged spin up, the spread in basal ice temperatures exceeds 10°C over large areas of the ice-\n24\nbed interface. For a given heat flow map, thawed-bedded ice-sheet area is consistently larger\n25\nunder unconstrained spin ups than nudged spin ups. Under the unconstrained spin up, thawed-\n26\nbedded area ranges from 33.5 to 60.0% across the seven heat flow maps. Perhaps\n27\ncounterintuitively, the highest iceberg calving fluxes are associated with the lowest heat flows\n28\n(and vice versa) for both unconstrained and nudged spin ups. This highlights the direct, and\n29\nnon-trivial, influence of choice of heat flow boundary condition on the simulated equilibrium\n30\nthermal state of the ice sheet. We suggest that future ice-flow model intercomparisons should\n31\nemploy a range of basal heat flow maps, and limit direct intercomparisons to simulations\n32\nemploying a common heat flow map. 33 34 1 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere Of the 21\n87\nparticipating models submissions within ISMIP6, twelve prescribed geothermal heat flow\n88\naccording to Shapiro and Ritzwoller [2004], five prescribed it according to Greve [2019], two\n89\nprescribed it as a hybrid assimilation of four older geothermal heat flow models [Pollack et al.,\n90\n1993; Tarasov and Peltier, 2003; Fox Maule et al., 2009; Rogozhina et al., 2016], and one\n91\nprescribed a spatially uniform geothermal heat flow. 92\nFor Greenland, the ISMIP6 ensemble suggests that ~40% of the ice-sheet bed is frozen,\n93\nmeaning basal ice temperatures below the pressure-melting-point temperature, and ~33% of\n94\nthe ice-sheet bed is thawed, meaning basal ice temperatures at the pressure-melting-point\n95\n[MacGregor et al., 2022]. The ISMIP6 ensemble disagrees on whether the basal thermal state is\n96\nfrozen or thawed beneath the remaining ~28% of the ice sheet. It is unclear what portion of this\n97\ndisagreement is associated with the use of differing geothermal heat flow boundary conditions\n98\nacross ISMIP6 ensemble members. The potential influence of geothermal heat flow boundary\n99\ncondition on basal ice temperature also remains unclear. For example, basal ice that is 1°C\n100\nbelow pressure-melting-point temperature deforms approximately ten times more than ice 10°C\n101\nbelow the pressure-melting-point temperature at the same driving stress [Hooke, 2019]. 102 Despite the clear links between geothermal heat flow and ice dynamics, a standardized\n85\ngeothermal heat flow as the basal thermal boundary condition was not prescribed in the Ice\n86\nSheet Model Intercomparison Project for CMIP6 (ISMIP6) [Goelzer et al., 2020]. Of the 21\n87\nparticipating models submissions within ISMIP6, twelve prescribed geothermal heat flow\n88\naccording to Shapiro and Ritzwoller [2004], five prescribed it according to Greve [2019], two\n89\nprescribed it as a hybrid assimilation of four older geothermal heat flow models [Pollack et al.,\n90\n1993; Tarasov and Peltier, 2003; Fox Maule et al., 2009; Rogozhina et al., 2016], and one\n91\nprescribed a spatially uniform geothermal heat flow. 92 For Greenland, the ISMIP6 ensemble suggests that ~40% of the ice-sheet bed is frozen,\n93\nmeaning basal ice temperatures below the pressure-melting-point temperature, and ~33% of\n94\nthe ice-sheet bed is thawed, meaning basal ice temperatures at the pressure-melting-point\n95\n[MacGregor et al., 2022]. The ISMIP6 ensemble disagrees on whether the basal thermal state is\n96\nfrozen or thawed beneath the remaining ~28% of the ice sheet. The Cryosphere Both latter methods then infer heat flow from\n63\nthe respective isotherms by applying a thermal model. The Greve [2019] heat flow map is rather\n64\nunique in using paleoclimatic forcing of an ice-flow model to infer heat flow with a minimum of\n65\ngeophysical variables. 66\nIn North Greenland, there is especially poor agreement among the present generation of\n67\ngeothermal heat flow models. Some models infer a widespread North Greenland high heat-flow\n68 In North Greenland, there is especially poor agreement among the present generation of\n67\ngeothermal heat flow models. Some models infer a widespread North Greenland high heat-flow\n68 2 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere anomaly (e.g. [Greve, 2019]), some do not (e.g. [Lucazeau, 2019]). Other models offer products\n69\nwith and without this high heat-flow anomaly (e.g. [Rezvanbehbahani et al., 2017]). There are\n70\nnumerous secondary disagreements as well, including if a model infers traces of the Iceland\n71\nHotspot Track transiting from West to East Greenland [Martos et al., 2018], or if a model infers\n72\nelevated heat flow in East Greenland in closer proximity to the Mid-Atlantic Ridge [Artemieva,\n73\n2019], or if a model infers a low heat-flow anomaly associated with the North Atlantic Craton in\n74\nSouth Greenland [Colgan et al., 2022]. 75\nGeothermal heat flow comprises a critical basal thermal boundary condition in\n76\nGreenland ice sheet models. It can significantly influence basal ice temperature and rheology,\n77\nwhich in turn influences basal meltwater production and friction [Karlsson et al., 2021]. Given\n78\nthe nonlinear relation between ice temperature and rheology, and that most ice deformation\n79\noccurs in the deepest ice layers, relatively small changes in basal ice temperature can result in\n80\nrelatively large changes in ice velocity [Hooke, 2019]. In extreme cases, diminished geothermal\n81\nheat flow along subglacial ridges may contribute to the formation of massive refrozen basal ice\n82\nmasses [Colgan et al., 2021], or sharply enhanced geothermal heat flow may contribute to the\n83\nonset of major ice-flow features [Smith-Johnsen et al., 2020]. 84\nDespite the clear links between geothermal heat flow and ice dynamics, a standardized\n85\ngeothermal heat flow as the basal thermal boundary condition was not prescribed in the Ice\n86\nSheet Model Intercomparison Project for CMIP6 (ISMIP6) [Goelzer et al., 2020]. The Cryosphere It is unclear what portion of this\n97\ndisagreement is associated with the use of differing geothermal heat flow boundary conditions\n98\nacross ISMIP6 ensemble members. The potential influence of geothermal heat flow boundary\n99\ncondition on basal ice temperature also remains unclear. For example, basal ice that is 1°C\n100\nbelow pressure-melting-point temperature deforms approximately ten times more than ice 10°C\n101\nbelow the pressure-melting-point temperature at the same driving stress [Hooke, 2019]. 102 3 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere 4\nIn preparation for ISMIP7, there is a clear motivation to more fully explore the choice of\n103\ngeothermal heat flow boundary condition on modeled basal ice temperatures. Here, we spin up\n104\nan ice-flow model with seven different geothermal heat flow boundary conditions. This allows us\n105\nto isolate the influence of choice of geothermal heat flow boundary condition on simulated\n106\nthermal state and ice flow. We also discuss the pros and cons of these seven Greenland\n107\ngeothermal heat flow products in the specific context of potential utility for ISMIP7 Greenland ice\n108\nflow simulations. 109\n110\nMETHODS\n111\nWe use the Community Ice Sheet Model (CISM) [Lipscomb et al., 2019; Goelzer et al.,\n112\n2020]. These simulations were run on a regular 4 km grid with ten vertical layers, using a\n113\nhigher-order velocity solver with a depth-integrated viscosity approximation based on Goldberg\n114\n[2011]. There is no dependence of basal sliding on basal temperature or water pressure. All\n115\nfloating ice is assumed to calve immediately. For partly grounded cells at the marine margin,\n116\nbasal shear stress is weighted using a grounding-line parameterization. 117\nWe perform two types of ice-sheet spin ups that we denote Case 1 and Case 2. The\n118\nCase 1 spin up iteratively nudges the friction coefficients in the basal-sliding power law to\n119\nminimize misfit against observed present-day ice thickness. In this spin up, we use a classic\n120\nWeertman-type nonlinear basal friction law [Weertman, 1979]:\n121\nـdž = ƭ Ǚdž\n1/m−1Ǚdž\n(1)\n122\nWhere ـdž is the basal traction, Ǚdž is the basal velocity, and m is a dimensionless constant that\n123\nwe adopt as 3. C is the friction coefficient, in units of Pa yr m-1, that is nudged during spin-up. The Cryosphere 124\nThe Case 1 spin up directly conforms to ISMIP6 protocol [Goelzer et al., 2020; Nowicki et al.,\n125\n2020]. 126\nIn contrast, the Case 2 spin up is fully transient, meaning that it does not constrain or\n127\nnudge the basal sliding parameters towards observed present-day ice thickness. In this spin up,\n128\nwe use a pseudo-plastic sliding law [Aschwanden et al., 2016]:\n129\nـdž =−ـLJ\nǙdž\n|Ǚdž|1−qǙ0\nǕ\n(2)\n130\nwhere ـLJ is the transient yield stress in Pa, q is a dimensionless pseudo-plastic exponent\n131\nthat we adopt as 0.5, and Ǚ0 is a threshold speed that we adopt as 100 m/a. We assume a\n132\nspatially and temporally constant friction coefficient, which allows ice thickness to evolve away\n133\nfrom present-day observations. While the Case 1 spin up ice geometry matches present-day,\n134 In preparation for ISMIP7, there is a clear motivation to more fully explore the choice of\n103\ngeothermal heat flow boundary condition on modeled basal ice temperatures. Here, we spin up\n104\nan ice-flow model with seven different geothermal heat flow boundary conditions. This allows us\n105\nto isolate the influence of choice of geothermal heat flow boundary condition on simulated\n106\nthermal state and ice flow. We also discuss the pros and cons of these seven Greenland\n107\ngeothermal heat flow products in the specific context of potential utility for ISMIP7 Greenland ice\n108\nflow simulations. 109 We use the Community Ice Sheet Model (CISM) [Lipscomb et al., 2019; Goelzer et al.,\n2\n2020]. These simulations were run on a regular 4 km grid with ten vertical layers, using a\n3\nhigher-order velocity solver with a depth-integrated viscosity approximation based on Goldberg\n4\n[2011]. There is no dependence of basal sliding on basal temperature or water pressure. All\n5\nfloating ice is assumed to calve immediately. For partly grounded cells at the marine margin,\n6\nbasal shear stress is weighted using a grounding-line parameterization. 7 We perform two types of ice-sheet spin ups that we denote Case 1 and Case 2. The\n118\nCase 1 spin up iteratively nudges the friction coefficients in the basal-sliding power law to\n119\nminimize misfit against observed present-day ice thickness. In this spin up, we use a classic\n120\nWeertman-type nonlinear basal friction law [Weertman, 1979]:\n121 ـdž = ƭ Ǚdž\n1/m−1Ǚdž\n(1) dž\n,\ndž\ny,\nwe adopt as 3. The Cryosphere 139 Under both Case 1 and 2 spin-ups, the ice sheet was initialized with present-day\n140\nthickness and bed topography [Morlighem et al., 2017] and an idealized vertical englacial\n141\ntemperature profile. The ice sheet was then spun up for 10,000 years under surface mass\n142\nbalance and surface temperature forcing from a 1980–1999 climatology provided by the MAR\n143\nregional climate model [Fettweis et al., 2017]. By the end of spin-up, the ice sheet is assumed to\n144\nhave achieved a transient equilibrium, with transient englacial ice temperatures no longer\n145\ninfluenced by the initial englacial temperature assumption. Here, we use the CISM bed interface\n146\ntemperature field (‘btemp’) to represent the ice-bed temperature. We assume this field is at\n147\ntransient equilibrium following both Case 1 and 2 spin ups (Figure 2). 148 We repeat the Case 1 and Case 2 spin ups seven times each without modification in\n149\ntheir configuration and execution, only substituting the prescribed geothermal heat flow serving\n150\nas the basal boundary condition each time (Table 1) . Each of the seven heat flow maps is re-\n151\ngridded from their native grid to the CISM grid using bilinear interpolation. For heat flow maps\n152\nthat are only available onshore, meaning they omit offshore, or submarine, areas of the CISM\n153\ndomain, we similarly infill fjord heat flow values using bilinear interpolation. 154 These seven maps provide a diverse representation of the magnitude and spatial\n155\ndistribution of Greenland heat flow, with the mean heat flow within the CISM ice-sheet domain\n156\nranging from ~42 mW m-2 in the Colgan et al. [2022] map to ~64 mW m-2 in the Lucazeau [2019]\n157\nmap. For Rezvanbehbahani et al. [2017] we use the middle range scenario of NGRIP = 135 mW\n158\nm-2. For Artemieva [2019], we use the “model 1” scenario, which adopts a deeper continental\n159\nMoho depth than the “model 2”. For Colgan et al. [2022] we use their recommended “without\n160\nNGRIP” scenario. 161 Of the seven heat flow maps that we consider, only two are global maps [Shapiro and\n162\nRitzwoller, 2004; Lucazeau, 2019], the remaining five are Greenland-specific maps. Of these\n163\nfive Greenland-specific maps, all but Colgan et al. [2022] are limited to the onshore domain,\n164\nexcluding the offshore domain (Figure 1; Table 1). The Cryosphere C is the friction coefficient, in units of Pa yr m-1, that is nudged during spin-up. 124\nThe Case 1 spin up directly conforms to ISMIP6 protocol [Goelzer et al., 2020; Nowicki et al.,\n125\n2020]. 126 In contrast, the Case 2 spin up is fully transient, meaning that it does not constrain or\n127\nnudge the basal sliding parameters towards observed present-day ice thickness. In this spin up,\n128\nwe use a pseudo-plastic sliding law [Aschwanden et al., 2016]:\n129 ـdž =−ـLJ\nǙdž\n|Ǚdž|1−qǙ0\nǕ\n(2) ـdž =−ـLJ\nǙdž\n|Ǚdž|1−qǙ0\nǕ\n(2) ـdž =−ـLJ\nǙdž\n|Ǚdž|1−qǙ0\nǕ\n(2) where ـLJ is the transient yield stress in Pa, q is a dimensionless pseudo-plastic exponent\n131 where ـLJ is the transient yield stress in Pa, q is a dimensionless pseudo-plastic exponent\n131 where ـLJ is the transient yield stress in Pa, q is a dimensionless pseudo-plastic exponent\n131\nthat we adopt as 0 5 and Ǚ0 is a threshold speed that we adopt as 100 m/a We assume a\n132 where ـLJ is the transient yield stress in Pa, q is a dimensionless pseudo-plastic exponent\n131\nthat we adopt as 0.5, and Ǚ0 is a threshold speed that we adopt as 100 m/a. We assume a\n132\nspatially and temporally constant friction coefficient, which allows ice thickness to evolve away\n133\nfrom present-day observations. While the Case 1 spin up ice geometry matches present-day,\n134 that we adopt as 0.5, and Ǚ0 is a threshold speed that we adopt as 100 m/a. We assume a\n132\nspatially and temporally constant friction coefficient, which allows ice thickness to evolve away\n133\nfrom present-day observations. While the Case 1 spin up ice geometry matches present-day,\n134 4 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere there can be appreciable biases in ice thickness under the non-nudged Case 2 spin up. The\n135\nCase 2 spin up does not conform to ISMIP6 protocol. It is foreseeable, however, that the\n136\nforthcoming ISMIP7 protocol will encourage fully transient spin ups. Transient spin ups are\n137\narguably more physically-based than nudged spin ups, but it is more challenging to reproduce a\n138\nspecific (present-day) ice-sheet configuration with them. The Cryosphere The seven heat flow maps are evaluated\n165\nagainst differing numbers of in-situ heat flow observations within a Greenland domain defined\n166\nas <500 km from Greenlandic shores. The Rezvanbehbahani et al. [2017], Martos et al. [2018]\n167\nand Greve[2019] heat flow maps employed ≤9 primarily subglacial in-situ observations from\n168 5 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere deep boreholes in the ice-sheet interior. The remaining four maps employed significantly more\n169\nin-situ heat flow observations (≥278), including more subaerial, submarine and shallow\n170\nsubglacial measurements, associated with progressively improving versions of the International\n171\nHeat Flow Database [Jessop et al., 1976; Fuchs et al., 2021]. 172\n173\nRESULTS\n174\nCase 1 spin up\n175\nThe Colgan et al. [2022] heat flow map, which has the lowest mean geothermal heat\n176\nflow of all seven products, yields the smallest area of thawed basal temperatures (21.8%) and\n177\nthe coldest basal temperature anomaly relative to ensemble mean (Figure 3; Table 2). 178\nConversely, the relatively high Martos et al. [2018] heat flow map, which has the third highest\n179\nmean heat flow of all seven products, yields twice the area of thawed basal temperatures\n180\n(54.4%) and one of the warmest basal temperature anomalies relative to ensemble mean. 181\nAcross the seven-member ensemble, however, there is considerable variation in magnitude and\n182\nspatial distribution of ensemble spread in basal ice temperatures (Figure 4). The seven heat\n183\nflow maps yield broadly similar modeled basal ice temperatures RMSEs of between 1.0 and\n184\n2.8 °C in comparison to observed basal ice temperatures at 27 Greenland ice sheet boreholes\n185\n(Figure 5) [Løkkegaard et al., 2022]. 186\nGenerally, ensemble spread in modeled ice-bed temperature approaches zero in the\n187\nablation area, especially in Central West Greenland, where basal thermal state is thawed\n188\nregardless of choice of heat flow map. Ensemble spread is generally largest along the main flow\n189\ndivide of the ice sheet. At South Dome, the ensemble spread exceeds 10°C over an ~105 km2\n190\narea. This highlights that choice of heat flow map has a substantial influence on simulated basal\n191\nthermal state over the North Atlantic Craton. Case 2 spin up\n208 Similar to the Case 1 spin up, the Case 2 spin up also yields the smallest area of thawed\n209\nbasal temperatures (33.5%) with the Colgan et al. [2022] lowest mean geothermal heat flow\n210\nmap and the largest area of thawed basal temperatures (60.0%) with the Martos et al. [2018]\n211\nrelatively high mean geothermal heat flow map (Figure 9). Critically, the thawed-bedded area for\n212\na given heat flow map is consistently larger under the Case 2 (transient) spin up than Case 1\n213\n(nudged) spin up (Table 2). Basal ice temperatures are accordingly warmer under Case 2 spin\n214\nup than Case 1 spin up (Figure 10). As ice-sheet sensitivity generally increases with the\n215\nthawed-bedded area over which basal movement and subglacial hydrology can occur, this\n216\nsuggests that transient ice-sheet spin ups may be regarded as more sensitive than nudged\n217\nones. The apparent ice-temperature warming effect of a transient spin up appears to increase\n218\nwith decreasing heat flow. The shift towards warmer basal temperatures under Case 2 spin up\n219\nis most apparent in the Colgan et al. [2022] lowest mean geothermal heat flow map, where the\n220\ntemperature difference is >5 °C beneath a large portion of Central Greenland. All heat flow\n221\nmaps present large differences in basal ice temperature between Case 1 and Case 2 spin ups\n222\nin regions of fast ice flow around the ice sheet periphery. 223 The spatial pattern of Case 2 ensemble agreement broadly follows that of Case 1,\n224\nalthough the Case 2 agreement is generally poorer. This is attributable to the unconstrained\n225\nnature of the Case 2 spin up. The magnitude and spatial distribution of ensemble spread in\n226\nbasal ice temperatures under Case 2 spin up largely reflects that of Case 1 spin up, the Case 2\n227\nensemble spread is smaller in Central East Greenland, and larger for peripheral ice caps,\n228\nespecially Flade Isblink in Northeast Greenland (Figure 4). The Case 2 spin up reproduces the\n229\nobserved basal ice temperatures at 27 Greenland ice sheet boreholes with an RMSE of\n230\nbetween 1.5 and 2.8 °C (Figure 5) [Løkkegaard et al., 2022]. This is not significantly different\n231\nfrom the RMSE range of the Case 1 spin up. The Cryosphere Accordingly, iceberg calving\n203\nis highest in the lowest heat flow simulations (Figure 8). The relatively narrow ensemble spread\n204\nin iceberg calving (~1%; 2 Gt yr-1 ensemble range against 322 Gt yr-1 ensemble mean) is\n205\nultimately constrained to surface mass balance forcing at transient equilibrium. 206\n207 Lucazeau [2019] and Colgan et al. [2022] maps yield, respectively, low and high ice-velocity end\n201\nmembers. Similarly, within the Rezvanbehbahani et al. [2017] simulation, the low heat-flow\n202\nanomaly in southeast Greenland yields a high ice-velocity anomaly. Accordingly, iceberg calving\n203\nis highest in the lowest heat flow simulations (Figure 8). The relatively narrow ensemble spread\n204\nin iceberg calving (~1%; 2 Gt yr-1 ensemble range against 322 Gt yr-1 ensemble mean) is\n205\nultimately constrained to surface mass balance forcing at transient equilibrium. 206\n207 The Cryosphere While the Northeast Greenland Ice Stream is\n192\nthawed regardless of choice of heat flow map, there is also an ~105 km2 area in Central East\n193\nGreenland where ensemble spread exceeds 10°C. Finally, choice of heat flow map appears to\n194\ninfluence whether the North Greenland ablation area is thawed or frozen. 195\nThe Case 1 spin up nudges the ice-flow model towards present-day ice thickness by\n196\niteratively adjusting basal friction coefficients. The ensemble differences in adjusted basal\n197\nfriction coefficient generally reaches a maximum where ice velocities reach a minimum (Figure\n198\n6). Perhaps counterintuitively, the highest surface ice velocities are associated with the lowest\n199\ngeothermal heat flows (Figure 7) For example the high and low heat flow end members of the\n200 Generally, ensemble spread in modeled ice-bed temperature approaches zero in the\n187\nablation area, especially in Central West Greenland, where basal thermal state is thawed\n188\nregardless of choice of heat flow map. Ensemble spread is generally largest along the main flow\n189\ndivide of the ice sheet. At South Dome, the ensemble spread exceeds 10°C over an ~105 km2\n190\narea. This highlights that choice of heat flow map has a substantial influence on simulated basal\n191\nthermal state over the North Atlantic Craton. While the Northeast Greenland Ice Stream is\n192\nthawed regardless of choice of heat flow map, there is also an ~105 km2 area in Central East\n193\nGreenland where ensemble spread exceeds 10°C. Finally, choice of heat flow map appears to\n194\ninfluence whether the North Greenland ablation area is thawed or frozen. 195 The Case 1 spin up nudges the ice-flow model towards present-day ice thickness by\n196\niteratively adjusting basal friction coefficients. The ensemble differences in adjusted basal\n197\nfriction coefficient generally reaches a maximum where ice velocities reach a minimum (Figure\n198\n6). Perhaps counterintuitively, the highest surface ice velocities are associated with the lowest\n199\ngeothermal heat flows (Figure 7). For example, the high and low heat flow end members of the\n200 6 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere Lucazeau [2019] and Colgan et al. [2022] maps yield, respectively, low and high ice-velocity end\n201\nmembers. Similarly, within the Rezvanbehbahani et al. [2017] simulation, the low heat-flow\n202\nanomaly in southeast Greenland yields a high ice-velocity anomaly. Case 2 spin up\n208 [2022] heat flow maps that\n250\nyield substantially thicker ice in North Greenland also yield lower ice temperatures there. 251\nSimilarly, the Greve [2019] and Lucazeau [2019] heat flow maps that yield substantially thinner\n252\nice in North Greenland also yield faster velocities there. While relative velocity differences in the\n253\nice-sheet interior can appear striking in both magnitude and extent, there are also velocity\n254\ndifferences around the ice-sheet periphery, which strongly influences the iceberg calving from\n255\ntidewater glaciers. Iceberg calving under Case 2 (transient) spin up has a greater ensemble\n256\nspread (~5%; 18 Gt yr-1 ensemble range against 365 Gt yr-1 ensemble mean) than under Case 1\n257\n(nudged) spin up (Figure 8). Similar to the Case 1 spin up, however, the Colgan et al. [2022]\n258\nlowest heat flow map again has the highest iceberg calving flux, while the relatively high Martos\n259\net al. [2018] and Greve [2019] heat flow maps have substantially lower iceberg calving fluxes at\n260\nequilibrium. 261\n262\nDISCUSSION\n263\nThe apparent association of higher ice velocities with lower geothermal heat flows under\n264\nCase 1 spin up outwardly appears to be a clear artifact of nudging the basal friction coefficient\n265\nduring spin up. This effect has previously been described as the surface velocity paradox,\n266\nwhereby constraining an ice flow model to match observed ice thickness results in\n267\nunderestimating deformational velocities where basal sliding is present, and overestimating\n268 Empirical temperature observations therefore justify neither the Case 1 nor Case 2 spin up\n235\napproach. 236\nIn comparison to the Case 1 spin ups, the Case 2 spin ups generally result in thicker ice\n237\nin East Greenland and thinner ice in West Greenland (Figure 11). These substantial differences\n238\nin ice thickness (i.e. ±100 m) are clearly attributable to the fully transient nature of Case 2 spin\n239\nups in comparison to the nudging of Case 1 spin ups towards observed present-day ice\n240\ngeometry. Specific Case 2 spin ups can yield very different ice thicknesses. For example, the\n241\nShapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps yield substantially thicker\n242\nthan observed ice in North Greenland, while the Greve [2019] and Lucazeau [2019] heat flow\n243\nmaps yield substantially thinner than observed ice in North Greenland. Case 2 spin up\n208 Basal ice temperatures are better resolved by\n232\nCase 1 spin up for three heat flow maps, and better resolved by Case 2 spin up for two heat\n233\nflow maps, with the remaining two heat flow maps yielding the same RMSE under both spin ups. 234 7 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere Empirical temperature observations therefore justify neither the Case 1 nor Case 2 spin up\n235\napproach. 236\nIn comparison to the Case 1 spin ups, the Case 2 spin ups generally result in thicker ice\n237\nin East Greenland and thinner ice in West Greenland (Figure 11). These substantial differences\n238\nin ice thickness (i.e. ±100 m) are clearly attributable to the fully transient nature of Case 2 spin\n239\nups in comparison to the nudging of Case 1 spin ups towards observed present-day ice\n240\ngeometry. Specific Case 2 spin ups can yield very different ice thicknesses. For example, the\n241\nShapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps yield substantially thicker\n242\nthan observed ice in North Greenland, while the Greve [2019] and Lucazeau [2019] heat flow\n243\nmaps yield substantially thinner than observed ice in North Greenland. Similarly, the ice\n244\nthickness at South Dome varies considerably across the seven heat flow map simulations. The\n245\nmagnitude of ice thickness differences associated with heat flow maps is non-trivial, and the\n246\nspatial distribution is complex. 247\nThere are considerable velocity differences across the seven Case 2 spin up simulations. 248\nGenerally, these velocity differences are negatively correlated with the ice thickness differences. 249\nFor example, the Shapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps that\n250\nyield substantially thicker ice in North Greenland also yield lower ice temperatures there. 251\nSimilarly, the Greve [2019] and Lucazeau [2019] heat flow maps that yield substantially thinner\n252\nice in North Greenland also yield faster velocities there. While relative velocity differences in the\n253\nice-sheet interior can appear striking in both magnitude and extent, there are also velocity\n254\ndifferences around the ice-sheet periphery, which strongly influences the iceberg calving from\n255\ntidewater glaciers. Case 2 spin up\n208 Similarly, the ice\n244\nthickness at South Dome varies considerably across the seven heat flow map simulations. The\n245\nmagnitude of ice thickness differences associated with heat flow maps is non-trivial, and the\n246\nspatial distribution is complex. 247 Empirical temperature observations therefore justify neither the Case 1 nor Case 2 spin up\n235\napproach\n236 There are considerable velocity differences across the seven Case 2 spin up simulations. 248\nGenerally, these velocity differences are negatively correlated with the ice thickness differences. 249\nFor example, the Shapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps that\n250\nyield substantially thicker ice in North Greenland also yield lower ice temperatures there. 251\nSimilarly, the Greve [2019] and Lucazeau [2019] heat flow maps that yield substantially thinner\n252\nice in North Greenland also yield faster velocities there. While relative velocity differences in the\n253\nice-sheet interior can appear striking in both magnitude and extent, there are also velocity\n254 There are considerable velocity differences across the seven Case 2 spin up simulations. 248\nGenerally, these velocity differences are negatively correlated with the ice thickness differences. 249\nFor example, the Shapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps that\n250\nyield substantially thicker ice in North Greenland also yield lower ice temperatures there. 251 Case 2 spin up\n208 Iceberg calving under Case 2 (transient) spin up has a greater ensemble\n256\nspread (~5%; 18 Gt yr-1 ensemble range against 365 Gt yr-1 ensemble mean) than under Case 1\n257\n(nudged) spin up (Figure 8). Similar to the Case 1 spin up, however, the Colgan et al. [2022]\n258\nlowest heat flow map again has the highest iceberg calving flux, while the relatively high Martos\n259\net al. [2018] and Greve [2019] heat flow maps have substantially lower iceberg calving fluxes at\n260\nequilibrium. 261\n262\nDISCUSSION\n263\nThe apparent association of higher ice velocities with lower geothermal heat flows under\n264\nCase 1 spin up outwardly appears to be a clear artifact of nudging the basal friction coefficient\n265\nduring spin up. This effect has previously been described as the surface velocity paradox,\n266\nwhereby constraining an ice flow model to match observed ice thickness results in\n267\nunderestimating deformational velocities where basal sliding is present, and overestimating\n268 Empirical temperature observations therefore justify neither the Case 1 nor Case 2 spin up\n235\napproach. 236\nIn comparison to the Case 1 spin ups, the Case 2 spin ups generally result in thicker ice\n237\nin East Greenland and thinner ice in West Greenland (Figure 11). These substantial differences\n238\nin ice thickness (i.e. ±100 m) are clearly attributable to the fully transient nature of Case 2 spin\n239\nups in comparison to the nudging of Case 1 spin ups towards observed present-day ice\n240\ngeometry. Specific Case 2 spin ups can yield very different ice thicknesses. For example, the\n241\nShapiro and Ritzwoller [2004] and Colgan et al. [2022] heat flow maps yield substantially thicker\n242\nthan observed ice in North Greenland, while the Greve [2019] and Lucazeau [2019] heat flow\n243\nmaps yield substantially thinner than observed ice in North Greenland. Similarly, the ice\n244\nthickness at South Dome varies considerably across the seven heat flow map simulations. The\n245\nmagnitude of ice thickness differences associated with heat flow maps is non-trivial, and the\n246\nspatial distribution is complex. 247\nThere are considerable velocity differences across the seven Case 2 spin up simulations. 248\nGenerally, these velocity differences are negatively correlated with the ice thickness differences. 249\nFor example, the Shapiro and Ritzwoller [2004] and Colgan et al. DISCUSSION\n263 8 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere deformational velocities where basal sliding is absent [Ryser et al., 2014]. Avoiding this surface\n269\nvelocity paradox is the main motivation for undertaking the Case 2 spin up, in which basal\n270\nfriction coefficients are not nudged. Under Case 2 spin up, during which ice thicknesses are not\n271\nconstrained, there is clearly more variation in the geometry, velocity and thermal state of the ice\n272\nsheet at the end of the 10,000-year fully transient spin up. Perhaps counterintuitively, however,\n273\nthe highest iceberg calving fluxes remain associated with the lowest heat flow maps (and vice\n274\nversa for lowest iceberg calving fluxes). In fully transient Case 2 simulations, this behavior\n275\ncannot be attributed to a model artifact from the surface velocity paradox associated with\n276\nnudging in Case 1 spin up. We instead speculate that a substantial portion of this variability\n277\nsimply reflects increased ice thicknesses under decreased heat flow. 278 The potential influence of anomalously high geothermal heat flow on contemporary local\n279\nice-sheet form and flow has been previously highlighted, with suggestions including: the onset\n280\nof the Northeast Greenland ice stream may be associated with elevated geothermal heat flow\n281\n[Fahnestock et al., 2001]; there may be a feedback between deeply-incised glaciers and\n282\ntopographic enhancement of local geothermal heat flow [van der Veen et al., 2007]; and that the\n283\ntransit of the Iceland hotspot may have deposited anomalous heat into the subglacial\n284\nlithosphere that influences ice flow today [Alley et al., 2019]. Our evaluation suggests\n285\nknowledge of where anomalously low geothermal heat flow may be influencing contemporary\n286\nregional ice-sheet form and flow can help constrain choice of heat flow map. For example, the\n287\nwidespread presence of Last Glacial Period ice in the ablation area across North Greenland\n288\nsuggests that heat flow must be sufficiently low to prevent basal melt across the region\n289\n[MacGregor et al., 2020]. This broad condition is only characteristic of a minority of the heat flow\n290\nmaps we evaluate, specifically the Shapiro and Ritzwoller [2004], Rezvanbehbahani et al. [2017]\n291\nand Colgan et al. [2022] maps. 292 South Dome appears to be the most sensitive portion of the ice sheet to choice of\n293\ngeothermal heat flow basal boundary condition. DISCUSSION\n263 Here, we evaluate simulated basal temperature against observed\n322\nbasal temperature at 27 selected Greenland boreholes. This evaluation appears to provide\n323\nsome insight on which heat flow map or spin up approach is most locally suitable. Rather than\n324\nquantitative comparisons against point temperature observations, however, there seems to be\n325\nvalue in qualitative comparisons between heat flow map and large-scale ice sheet features,\n326\nsuch as evaluating which heat flow map can yield widespread frozen-bedded in North\n327\nGreenland under contemporary conditions. Naturally, evaluation of these seven heat flow maps\n328\nwould be strengthened by using more than a single community ice flow model, as we do here. 329\nWithin our simulation ensemble, the unconstrained spin ups may generally be regarded\n330\nas simulating more sensitive ice sheets than the nudged spin ups, as the unconstrained spin\n331\nups yield greater thawed-bedded area and higher iceberg calving flux. While most recent ice-\n332\nsheet simulations projecting Greenland's future sea-level contribution have largely focused on\n333\nnudged spin ups, our simulation ensemble unsurprisingly suggests that unconstrained transient\n334\nspin up is required to fully resolve the choice of geothermal heat flow boundary condition on ice-\n335\nsheet geometry and velocity. Given the strong influence of choice of geothermal heat flow on ice\n336 beneath South Dome characteristic of the Rezvanbehbahani et al. [2017] map are more likely to\n303\nyield an Eemian-persistent South Dome than paleo-ice-sheet simulations that adopt the high\n304\nheat flow beneath South Dome characteristic of the Lucazeau [2019] map. Simply put, choice of\n305\nheat flow map influences not only contemporary simulations of ice-sheet form and flow, but also\n306\npaleo-ice-sheet simulations as well. 307 Given the non-linear dependence of deformational velocity on ice temperature, properly\n310\nresolving the thermal state of the Greenland ice sheet is critical for generating reliable ice-flow\n311\nsimulations. We have performed both nudged and unconstrained, transient ice-sheet spin ups of\n312\n10,000 years in duration employing seven geothermal heat flow models. Under a nudged spin\n313\nup, we find that the thawed-bedded ice-sheet area ranges from 21.8 to 54.4% across these heat\n314\nflow models. Under a fully unconstrained, transient spin up, the thawed-bedded ice-sheet area\n315\nis consistently larger, ranging from 33.5 to 60.0%. The transient spin up also yields inter-\n316\nsimulation differences in both ice thickness and velocity that are large in magnitude and extent. DISCUSSION\n263 There, choice of heat flow map results in an\n294\nensemble spread in ice-bed temperature of >10°C over an area the size of Iceland. There is\n295\ncurrently a poor level of scientific understanding whether South Dome persisted through the\n296\nEemian interglacial, with some ice-sheet reconstructions suggesting persistence of the ice\n297\nsheet’s southern lobe [Quiquet et al., 2013; Stone et al., 2013] and others suggesting local\n298\ndeglaciation [Otto-Bliesner et al., 2006; Helsen et al., 2013]. Our evaluation specifically\n299\nhighlights substantial disagreement over geothermal heat flow within the North Atlantic Craton\n300\nthat underlies South Dome. Similar to the contemporary persistence of Last Glacial Period ice in\n301\nNorth Greenland, we speculate that paleo-ice-sheet simulations that adopt the low heat flow\n302 9 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere beneath South Dome characteristic of the Rezvanbehbahani et al. [2017] map are more likely to\n303\nyield an Eemian-persistent South Dome than paleo-ice-sheet simulations that adopt the high\n304\nheat flow beneath South Dome characteristic of the Lucazeau [2019] map. Simply put, choice of\n305\nheat flow map influences not only contemporary simulations of ice-sheet form and flow, but also\n306\npaleo-ice-sheet simulations as well. 307\n308\nSUMMARY REMARKS\n309\nGiven the non-linear dependence of deformational velocity on ice temperature, properly\n310\nresolving the thermal state of the Greenland ice sheet is critical for generating reliable ice-flow\n311\nsimulations. We have performed both nudged and unconstrained, transient ice-sheet spin ups of\n312\n10,000 years in duration employing seven geothermal heat flow models. Under a nudged spin\n313\nup, we find that the thawed-bedded ice-sheet area ranges from 21.8 to 54.4% across these heat\n314\nflow models. Under a fully unconstrained, transient spin up, the thawed-bedded ice-sheet area\n315\nis consistently larger, ranging from 33.5 to 60.0%. The transient spin up also yields inter-\n316\nsimulation differences in both ice thickness and velocity that are large in magnitude and extent. 317\nThis ensemble of simulations highlights that sector-scale ice flow, both peripheral and interior,\n318\ncan be described as at least moderately sensitive to choice of heat flow. 319\nThe recent effort to compile all Greenland englacial temperature observations into a\n320\nstandardized database now permits the thermal state of ice-sheet simulations to be evaluated\n321\nagainst all empirical data. DISCUSSION\n263 317\nThis ensemble of simulations highlights that sector-scale ice flow, both peripheral and interior,\n318\ncan be described as at least moderately sensitive to choice of heat flow. 319 10 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere dynamics that we document, it seems prudent to limit the direct intercomparison of ice-sheet\n337\nsimulations to those using a common heat flow map. Similar to employing a range of commonly\n338\nprescribed climate forcing scenarios, it would be ideal for future ISMIP ensembles to employ a\n339\nrange of commonly prescribed basal forcing conditions. 340\n341\nACKNOWLEDGEMENTS\n342\nT.Z. and C.X. thank the Natural Science Foundation of China grant (42271133), Faculty of\n343\nGeographical Sciences, Beijing Normal University (2022-GJTD-01) and the State Key\n344\nLaboratory of Earth Surface Processes and Resource Ecology (2022-ZD-05) for financial\n345\nsupport. A.L. and W.C. thank the Independent Research Fund Denmark (Sapere Aude 8049-\n346\n00003) and the Novo Nordisk Foundation (Center for Sea-Level and Ice-Sheet Prediction) for\n347\nfinancial support. A.W. thanks the European Space Agency and the German Research Council\n348\n(DFG) for their financial support through the projects 4D-Greenland and GreenCrust. G.L. and\n349\nW.L. were supported by the National Center for Atmospheric Research, which is a major facility\n350\nsponsored by the National Science Foundation under Cooperative Agreement no. 1852977. 351\nComputing and data storage resources for CISM simulations, including the Cheyenne\n352\nsupercomputer (https://doi.org/10.5065/D6RX99HX), were provided by the Computational and\n353\nInformation Systems Laboratory (CISL) at NCAR. 354\n355\nDATA AVAILABILITY\n356\nTo help accelerate community efforts towards exploring the influence of geothermal heat flow on\n357\nice-sheet simulations, we have deposited a copy of the seven geothermal heat flow maps that\n358\nwe evaluate here at Zenodo (https://doi.org/10.5281/zenodo.7891577). Interpolated versions of\n359\nthese seven geothermal heat flow datasets are provided on a common coarse-resolution .nc\n360\ngrid that conforms with CISM standards. 361\n362\nAUTHOR CONTRIBUTIONS\n363\nT.Z. and W.C. conceptualized this study and were responsible for formal analysis. A.L. and A.W. 364\nprovided data curation. T.Z., C.X., W.L. and G.L. provided funding, resources, and software. All\n365\nauthors participated in interpretation of the data and writing of the manuscript. 366\n367\nCOMPETING INTERESTS\n368\nThe contact author has declared that none of the authors has any competing interests. REFERENCES\n371 Artemieva, I. Lithosphere structure in Europe from thermal isostasy. Earth-Science Reviews,\n372\n188, 454–468, https://doi.org/10.1016/j.earscirev.2018.11.004, 2019. 373 Alley, R., D. Pollard, B. Parizek, S. Anandakrishnan, M. Pourpoint, N. Stevens, J. MacGregor,\n374\nK. Christianson, A. Muto and N. Holschuh. 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Similar to employing a range of commonly\n338\nprescribed climate forcing scenarios, it would be ideal for future ISMIP ensembles to employ a\n339\nrange of commonly prescribed basal forcing conditions. 340 dynamics that we document, it seems prudent to limit the direct intercomparison of ice-sheet\n337\nsimulations to those using a common heat flow map. Similar to employing a range of commonly\n338\nprescribed climate forcing scenarios, it would be ideal for future ISMIP ensembles to employ a\n339\nrange of commonly prescribed basal forcing conditions. 340 T.Z. and C.X. thank the Natural Science Foundation of China grant (42271133), Faculty of\n343\nGeographical Sciences, Beijing Normal University (2022-GJTD-01) and the State Key\n344\nLaboratory of Earth Surface Processes and Resource Ecology (2022-ZD-05) for financial\n345\nsupport. 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D., Lüthi, M. P., Doyle, S., Thomsen, H.,\n444\nFisher, D., Harper, J., Aschwanden, A., Vinther, B. M., Dahl-Jensen, D., Zekollari, H.,\n445\nMeierbachtol, T., McDowell, I., Humphrey, N., Solgaard, A., Karlsson, N. B., Khan, S. A.,\n446\nHills, B., Law, R., Hubbard, B., Christoffersen, P., Jacquemart, M., Fausto, R. S., and\n447\nColgan, W. T.: Greenland and Canadian Arctic ice temperature profiles, The Cryosphere\n448\nDiscussions [preprint], https://doi.org/10.5194/tc-2022-138, 2022. 449 13 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere 487\nRogozhina, I., Petrunin, A., Vaughan, A., Steinberger, B., Johnson, J., Kaban, M., Calov, R.,\n488\nRickers, F., Thomas, M., and Koulakov, I.: Melting at the base of the Greenland ice\n489 Rogozhina, I., Petrunin, A., Vaughan, A., Steinberger, B., Johnson, J., Kaban, M., Calov, R.,\n488\nRickers, F., Thomas, M., and Koulakov, I.: Melting at the base of the Greenland ice\n489 14 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere Weertman, J. The Unsolved General Glacier Sliding Problem. 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Past, 9, 621–639,\n505\nhttps://doi.org/10.5194/cp-9-621-2013, 2013. 506 Tarasov, L. and Peltier, W. R.: Greenland glacial history, borehole constraints, and Eemian\n507\nextent, Journal of Geophysical Research: Solid Earth, 108, 2143,\n508\nhttps://doi.org/10.1029/2001JB001731, 2003. 509 van der Veen, C., Leftwich, T., Von Frese, R., Csatho, B., and Li, J. Subglacial topography and\n510\ngeothermal heat flux: Potential interactions with drainage of the Greenland ice sheet. 511\nGeophysical Research Letters, 34, L12501, https://doi.org/10.1029/2007GL030046,\n512\n2007. 513 Weertman, J. The Unsolved General Glacier Sliding Problem. Journal of Glaciology, 23: 97-115. 514\nhttp://doi.org/10.3189/S0022143000029762, 1979. 515 15 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere TABLES\n518\n519\nTable 1 - Characteristics of the seven geothermal heat flow models we explore as basal thermal\n520\nboundary conditions: methodology used to derive each model, number of geophysical datasets\n521\nemployed by each model, number of in-situ heat flow observations considered by each model,\n522\naverage heat flow (± standard deviation) within a common CISM Greenland ice sheet area, and\n523\nthe domain coverage of each model. Adopted from Colgan et al. [2022] and arranged from\n524\nlowest to highest average geothermal heat flow beneath the ice sheet. The Cryosphere 525\n526\nModel\nMethodology\nGeophysical\ndatasets\n[unitless]\nGreenland\nobservations\n[unitless]\nGeothermal\nheat flow\n[mW m-2]\nDomain\ncoverage\nColgan et al. [2022]\nMachine\nlearning model\n12\n419\n41.8 ± 5.3\nGreenland;\noceanic and\ncontinental\nRezvanbehba\nhani et al. [2017]\nMachine\nlearning model\n20\n9\n54.1 ± 20.4\nGreenland;\ncontinental\nonly\nShapiro and\nRitzwoller\n[2004]\nSeismic\nsimilarity\nmodel\n4\n278\n55.7 ± 9.4\nGlobal;\noceanic and\ncontinental\nArtemieva\n[2019]\nThermal\nisostasy\nmodel\n8\n290\n56.4 ± 12.6\nGreenland;\ncontinental\nonly\nMartos et al. [2018]\nForward\nlithospheric\nmodel\n5\n8\n60.1 ± 6.6\nGreenland;\ncontinental\nonly\nGreve [2019]\nPaleoclimate\nand ice flow\nmodel\n3\n8\n63.3 ± 19.1\nGreenland;\ncontinental\nonly\nLucazeau\n[2019]\nGeostatistical\nmodel\n14\n314\n63.8 ± 7.1\nGlobal;\noceanic and\ncontinental\n527\n528 526\nModel\nMethodology\nGeophysical\ndatasets\n[unitless]\nGreenland\nobservations\n[unitless]\nGeothermal\nheat flow\n[mW m-2]\nDomain\ncoverage\nColgan et al. [2022]\nMachine\nlearning model\n12\n419\n41.8 ± 5.3\nGreenland;\noceanic and\ncontinental\nRezvanbehba\nhani et al. [2017]\nMachine\nlearning model\n20\n9\n54.1 ± 20.4\nGreenland;\ncontinental\nonly\nShapiro and\nRitzwoller\n[2004]\nSeismic\nsimilarity\nmodel\n4\n278\n55.7 ± 9.4\nGlobal;\noceanic and\ncontinental\nArtemieva\n[2019]\nThermal\nisostasy\nmodel\n8\n290\n56.4 ± 12.6\nGreenland;\ncontinental\nonly\nMartos et al. [2018]\nForward\nlithospheric\nmodel\n5\n8\n60.1 ± 6.6\nGreenland;\ncontinental\nonly\nGreve [2019]\nPaleoclimate\nand ice flow\nmodel\n3\n8\n63.3 ± 19.1\nGreenland;\ncontinental\nonly\nLucazeau\n[2019]\nGeostatistical\nmodel\n14\n314\n63.8 ± 7.1\nGlobal;\noceanic and\ncontinental\n527 527\n528 16 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. 529\nTable 2 - Thawed-bedded ice-sheet area associated with Case 1 (nudged) and\n530\n(unconstrained) spin-ups of 10,000-years duration for the seven geothermal hea\n531\n532\nModel\nCase 1\nCase 2\nColgan et al. [2022]\n21.8%\n33.5%\nRezvanbehbahani et al. [2017]\n43.0%\n48.0%\nShapiro and Ritzwoller [2004]\n35.5%\n44.3%\nArtemieva [2019]\n50.2%\n52.8%\nMartos et al. [2018]\n54.4%\n60.0%\nGreve [2019]\n53.6%\n57.4%\nLucazeau [2019]\n52.5%\n59.7%\n533 529\nTable 2 - Thawed-bedded ice-sheet area associated with Case 1 (nudged) and Case 2\n530\n(unconstrained) spin-ups of 10,000-years duration for the seven geothermal heat flow da\n531 533 17 17 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere 534\n535 FIGURES FIGURES\n534\n535\n536\nFigure 1 - (a-g): The seven geothermal heat flow maps considered as basal thermal boundary\n537\nconditions, expressed as anomalies from their ensemble mean. Colorbars saturate about 10\n538\nand 100 mW m-2. (i): Ensemble mean. Units for all plots mW m-2. 539 Figure 1 - (a-g): The seven geothermal heat flow maps considered as basal thermal boundary\n537\nconditions, expressed as anomalies from their ensemble mean. Colorbars saturate about 10\n538\nand 100 mW m-2. (i): Ensemble mean. Units for all plots mW m-2. 539 18 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere\n540\nFigure 2 - Case 1: (a-g) Ice-bed temperature relative to pressure melting point at transient\n541\nequilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n542\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n543\nCase 2 in Figure 9.)\n544\n545 The Cryosphere 540\nFigure 2 - Case 1: (a-g) Ice-bed temperature relative to pressure melting point at transient\n541\nequilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n542\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare agains\n543\nCase 2 in Figure 9.)\n544 Figure 2 - Case 1: (a-g) Ice-bed temperature relative to pressure melting point at transient\n541\nequilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n542\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n543\nCase 2 in Figure 9.)\n544 19 19 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere 546\nFigure 3 - Case 1: (a-g) Relative anomaly from ensemble mean in ice-bed temperature at\n547\ntransient equilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n548\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n549\nCase 2 in Figure 10.)\n550\n551 5 6\nFigure 3 - Case 1: (a-g) Relative anomaly from ensemble mean in ice-bed temperature at\n547\ntransient equilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n548\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n549\nCase 2 in Figure 10.)\n550 20 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. The Cryosphere CC BY 4.0 License. The Cryosphere 552\n553\nFigure 4 - (a) and (b): Ensemble agreement in basal thermal state (frozen or thawed) across\n554\nthe seven heat flow maps (a: Case 1, b: Case 2). Units are the fraction of simulations that\n555\nsuggest thawed bed. (c) and (d): Ensemble spread (the difference between maximum and\n556\nminimum values for different experiments) in basal ice temperature across the seven heat flow\n557\nmaps (c: Case 1, d: Case 2). Units are °C. 558\n559 552 52 553\nFigure 4 - (a) and (b): Ensemble agreement in basal thermal state (frozen or thawed) across\n554\nthe seven heat flow maps (a: Case 1, b: Case 2). Units are the fraction of simulations that\n555\nsuggest thawed bed. (c) and (d): Ensemble spread (the difference between maximum and\n556\nminimum values for different experiments) in basal ice temperature across the seven heat flow\n557\nmaps (c: Case 1, d: Case 2). Units are °C. 558\n559 21 The Cryosphere\n560\nFigure 5 - Modeled ice-bed temperature across the seven heat flow maps versus observed ice-\n561\nbed temperature at 27 Greenland ice sheet boreholes where ice temperatures have been\n562\nobserved. (a-g) Modeled versus observed comparison across the seven geothermal heat flow\n563\nmaps. Case 1 spin ups shown in blue. Case 2 spin ups shown in red. 564\n565 The Cryosphere 560\nFigure 5 - Modeled ice-bed temperature across the seven heat flow maps versus observed ice-\n561\nbed temperature at 27 Greenland ice sheet boreholes where ice temperatures have been\n562\nobserved. (a-g) Modeled versus observed comparison across the seven geothermal heat flow\n563\nmaps. Case 1 spin ups shown in blue. Case 2 spin ups shown in red. 564\n565 22 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere The Cryosphere\n566\nFigure 6 - Case 1: (a-g) The basal friction coefficient at transient equilibrium using the seven\n567\ngeothermal heat flow maps, expressed as anomalies from the ensemble mean. Units are % and\n568\ncolorbars saturate at ±100%. (i) Ensemble mean basal friction coefficient at transient equilibrium. 569\nUnits are Pa yr m-1, with the colorbar saturating at 106 Pa yr m-1. The Cryosphere 570\n571 566\nFigure 6 - Case 1: (a-g) The basal friction coefficient at transient equilibrium using the seven\n567\ngeothermal heat flow maps, expressed as anomalies from the ensemble mean. Units are % and\n568\ncolorbars saturate at ±100%. (i) Ensemble mean basal friction coefficient at transient equilibrium. 569\nUnits are Pa yr m-1, with the colorbar saturating at 106 Pa yr m-1. 570\n571 23 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere\n572\nFigure 7 - Case 2: (a-g) Surface ice velocity at transient equilibrium using the seven geothermal\n573\nheat flow maps, expressed as anomalies from their ensemble mean. Units are % and colorbars\n574\nsaturate at ±100%. (i) Ensemble mean surface ice velocity at transient equilibrium. Units are m\n575\nyr-1. 576\n577 The Cryosphere 572\nFigure 7 - Case 2: (a-g) Surface ice velocity at transient equilibrium using the seven geothermal\n573\nheat flow maps, expressed as anomalies from their ensemble mean. Units are % and colorbars\n574\nsaturate at ±100%. (i) Ensemble mean surface ice velocity at transient equilibrium. Units are m\n575\nyr-1. 576\n577 Figure 7 - Case 2: (a-g) Surface ice velocity at transient equilibrium using the seven geothermal\n573\nheat flow maps, expressed as anomalies from their ensemble mean. Units are % and colorbars\n574\nsaturate at ±100%. (i) Ensemble mean surface ice velocity at transient equilibrium. Units are m\n575\nyr-1. 576\n577 24 24 The Cryosphere\n578\n579\nFigure 8 - Total Greenland ice sheet calving flux over the 10,000-year spin up using the seven\n580\ngeothermal heat flow maps for Case 1 (a) and Case 2 (b). Units are Gt yr-1. The first 500 years\n581\nof the simulations are not shown due to artifacts associated with model initialization. 582\n583\nhttps://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere 578\n579\nFigure 8 - Total Greenland ice sheet calving flux over the 10,000-year spin up using the seven\n580\ngeothermal heat flow maps for Case 1 (a) and Case 2 (b). Units are Gt yr-1. The first 500 years\n581\nof the simulations are not shown due to artifacts associated with model initialization. The Cryosphere 582\n583 9 579\nFigure 8 - Total Greenland ice sheet calving flux over the 10,000-year spin up using the seven\n580\ngeothermal heat flow maps for Case 1 (a) and Case 2 (b). Units are Gt yr-1. The first 500 years\n581\nof the simulations are not shown due to artifacts associated with model initialization. 582\n583 25 25 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere\n584\n585\nFigure 9 - Case 2: (a-g) Ice-bed temperature relative to pressure melting point at transient\n586\nequilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n587\ntemperature. Units in all plots °C below pressure-melting-point temperature. (compare against\n588\nCase 2 in Figure 2). 589\n590 The Cryosphere 584\n585 585\nFigure 9 - Case 2: (a-g) Ice-bed temperature relative to pressure melting point at transient\n586\nequilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n587\ntemperature. Units in all plots °C below pressure-melting-point temperature. (compare against\n588\nCase 2 in Figure 2). 589\n590 26 26 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere\n591\nFigure 10 - Case 2: (a-g) Relative anomaly from ensemble mean in ice-bed temperature at\n592\ntransient equilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n593\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n594\nCase 1 in Figure 3.)\n595\n596 The Cryosphere Figure 10 - Case 2: (a-g) Relative anomaly from ensemble mean in ice-bed temperature at\n592\ntransient equilibrium using the seven geothermal heat flow maps. (i) Ensemble mean ice-bed\n593\ntemperature. Units in all plots °C below pressure-melting-point temperature. (Compare against\n594\nCase 1 in Figure 3.)\n595 27 27 https://doi.org/10.5194/tc-2023-102\nPreprint. Discussion started: 30 June 2023\nc⃝Author(s) 2023. CC BY 4.0 License. The Cryosphere\n599\n600\nFigure 11 - Case 2: (a-g) Anomaly in ice thickness at Case 2 transient spin up, in comparison to\n601\nCase 1 nudged spin up, using the seven geothermal heat flow maps. Units in all plots m and\n602\nexpressed as Case 2 minus Case 1. 603\n604 The Cryosphere 599\n600 600\nFigure 11 - Case 2: (a-g) Anomaly in ice thickness at Case 2 transient spin up, in comparison to\n601\nCase 1 nudged spin up, using the seven geothermal heat flow maps. The Cryosphere Units in all plots m and\n602\nexpressed as Case 2 minus Case 1. 603\n604 28 28"