Estimating the basal melt rate at NorthGRIP using a Monte Carlo technique

ArticleinAnnals of Glaciology 45(1):137-142 · October 2007with 91 Reads
Abstract
From radio-echo sounding (RES) surveys and ice core data it can be seen that the ice sheet is melting at the base in a large area in Northern Greenland. The RES images reveal internal layers in the ice. The layers are former deposition surfaces and are thus isochrones. Undulations of the isochrones in regions where the base is smooth suggest that the basal melt rate changes over short distances. This indicates that the geothermal heat flux is very high and has large spatial variability in Northern Greenland. In this study, the basal melt rate at the NorthGRIP drill site in North-Central Greenland is calculated by inverse modelling. We use simple one- and two-dimensional flow models to simulate the ice flow along the NNW-trending ice ridge leading to NorthGRIP. The accumulation is calculated from a dynamical model. Several ice flow parameters are unknown and must be estimated along with the basal melt rate using a Monte Carlo method. The Monte Carlo inversion is constrained by the observed isochrones, dated from the timescale established for the NorthGRIP ice core. The estimates of the basal melt rates around NorthGRIP are obtained from both the one- and two-dimensional models. Combining the estimated basal melt rates with the observed borehole temperatures allows us to convert the basal melt rates to geothermal heat flow values. From the two-dimensional model we find the basal melt rate and geothermal heat flux at NorthGRIP to be 6.1 mm a−1 and 129 mW m−2, respectively.
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    This study analyzes the uncertainties in the models of the Greenland Ice Sheet (GIS) that arise from ill-constrained geothermal heat flux (GHF) distribution. Within the context of dynamic GIS modeling, we consider the following questions: (i) What is the significance of the differences between the existing GHF models for the GIS modeling studies? (ii) How well does the modeled GIS controlled by the GHF models agree with the observational data? (iii) What are the relative contributions of uncertainties in GHF and climate forcing to the misfit between the observed and modeled present-day GIS? The results of paleoclimatic simulations suggest that differences in the GHF models have a major effect on the history and resulting present-day state of the GIS. The ice sheet model controlled by any of these GHF forcings reproduces the observed GIS state to only a limited degree and fails to reproduce either the topography or the low basal temperatures measured in southern Greenland. By contrast, the simulation controlled by a simple spatially uniform GHF forcing results in a considerably better fit with the observations, raising questions about the use of the three GHF models within the framework of GIS modeling. Sensitivity tests reveal that the misfit between the modeled and measured temperatures in central Greenland is mostly due to inaccurate GHF and Wisconsin precipitation forcings. The failure of the ice sheet model in southern Greenland, however, is mainly caused by inaccuracies in the surface temperature forcing and the generally overestimated GHF values suggested by all GHF models.
  • Article
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    The influence of subglacial water on the dynamics of ice flow has been the object of increasing interest in the past decade. In this study we focus on large-scale, long-term changes in surface elevation over North East Greenland, and the corresponding changes in subglacial water routes. Our results show that over time-scales ranging from decades to millennia the area may experience redistribution of and fluctuation in subglacial water outflux under the main glacier outlets. The fluctuations in subglacial water routing occur even in the absence of external forcing. Based on these results we conclude that changes in the subglacial water routes are an intrinsic part of the drainage basin dynamics, where the subglacial system is likely always in a transient state. The results also imply that fluctuations at the margins observed at present might originate from changes several hundred kilometres upstream. Since surface elevation changes may propagate upstream over time-scales much longer than the observational period, the cause of the fluctuations may not be present in current observational records.
  • Article
    On Earth and on Mars, ice masses experience changes in precipitation, temperature, and radiation. In a new climate state, flowing ice masses will adjust in length and in thickness, and this response toward a new steady state has a characteristic timescale. However, a flowing ice mass has a predictable shape, which is a function of ice temperature, ice rheology, and surface mass-exchange rate. In addition, the time for surface-shape adjustment is shorter than the characteristic time for significant deformation or displacement of internal layers within a flowing ice mass; as a result, surface topography is more diagnostic of flow than are internal-layer shapes. Because the shape of Gemina Lingula, North Polar Layered Deposits indicates that it flowed at some time in the past, we use its current topography to infer characteristics of those past ice conditions, or past climate conditions, in which ice-flow rates were more significant than today. A plausible range of near-basal ice temperatures and ice-flow enhancement factors can generate the characteristic geometry of an ice mass that has been shaped by flow over reasonable volume-response timescales. All plausible ice-flow scenarios require conditions that are different from present-day Mars, if the basal layers are pure ice.
  • Article
    The surface and basal boundary conditions exert an important control on the thermo-dynamic state of the Greenland Ice Sheet but their representation in numerical ice sheet models is poorly constrained due to the lack of observations. Here, we investigate a land-terminating sector of western Greenland and (1) quantify differences between new observations and commonly used boundary condition datasets, and (2) demonstrate the impact of improved boundary conditions on simulated thermo-dynamics in a higher-order numerical flow model. We constrain near-surface temperature with measurements from two 20 m boreholes in the ablation zone and 10 m firn temperature from the percolation zone. We constrain basal heat flux using in-situ measurement in a deep bedrock hole at the study area margin and other existing assessments. To assess boundary condition influences on simulated thermal-mechanical processes, we compare model output to multiple full-thickness temperature profiles collected in the ablation zone. Our observation-constrained basal heat flux is <50% of commonly used representations. In contrast, measured near-surface temperatures are up to 90% warmer than common surface temperature datasets. Application of lower basal heat flux increases a model cold bias compared to the measured temperature profiles, and causes frozen basal conditions across the ablation zone. Temperate basal conditions are re-established by our warmer surface boundary. Warmer surface ice and firn can introduce three times more energy to the modeled ice mass than what is lost at the bed from reduced basal heat flux, indicating that the thermo-mechanical state of the ice sheet is highly sensitive to near-surface effects.
  • Article
    Ground and airborne radar depth-sounding of the Greenland and Antarctic ice sheets have been used for many years to remotely determine characteristics such as ice thickness, subglacial topography, and mass balance of large bodies of ice. Ice coring efforts have supported these radar data to provide ground truth for validation of the state (wet or frozen) of the interface between the bottom of the ice sheet and the underlying bedrock. Subglacial state governs the friction, flow speed, transport of material, and overall change of the ice sheet. In this paper, we utilize machine learning and classifier combination to model water presence from airborne polar radar data acquired on Greenland in 1999 and 2007. The underlying method results in radar independence, allowing model transfer from 1999 to 2007 radar data to produce water presence maps of the Greenland ice sheet with differing radars. We focus on how to construct a successful set of classifiers capable of high classification accuracy. Utilizing multiple machine learning algorithms is shown to be successful for this classification problem, achieving 86% classification accuracy in the best case. Several heuristics are presented for constructing teams of multiple classifiers for predicting subglacial water presence. The presented methodology could also be applied to radar data acquired over the Antarctic ice sheet.
  • Article
    Little information exists on biogeochemical transformations in aquatic ecosystems beneath polar ice sheets (i.e., water-saturated sediments, streams, rivers, and lakes) and their role in global elemental cycles. Subglacial environments may represent important sources of atmospheric CO2 and/or CH4 during deglaciation, thus acting as amplifiers in the climate system. However, the role of subglacial environments in global climate processes has been difficult to assess given the absence of biogeochemical data from the basal zones of inland polar ice sheets. Here, we report on the concentrations of CO2, CH4, and H2 in samples of refrozen basal water recovered at a depth of ~3,042 meters below the surface during the North Greenland Ice Core Project (NGRIP). CH4 and H2 concentrations in the NGRIP samples were approximately 60- and 700-fold higher, respectively, relative to air-equilibrated water, whereas CO2 was ~fivefold lower. Metabolic pathways such as (1) methanogenesis, (2) organic matter fermentation, carboxydotrophic, and/or methylotrophic activity, and (3) CO2 fixation provide plausible biotic explanations for the observed CH4, H2, and CO2 concentrations, respectively.
  • Article
    We analyze the internal stratigraphy in radio-echo sounding data of the northeast Greenland ice stream to infer past and present ice dynamics. In the upper reaches of the ice stream, we propose that shear-margin steady-state folds in internal reflecting horizons (IRHs) form due to the influence of ice flow over spatially varying basal lubrication. IRHs are generally lower in the ice stream than outside, likely because of greater basal melting in the ice stream from enhanced geothermal flux and heat of sliding. Strain-rate modeling of IRHs deposited during the Holocene indicates no recent major changes in ice-stream vigor or extent in this region. Downstream of our survey, IRHs are disrupted as the ice flows into a prominent overdeepening. When combined with additional data from other studies, these data suggest that upstream portions of the ice stream are controlled by variations in basal lubrication whereas downstream portions are confined by basal topography.
  • Article
    Full-text available
    On entering an era of global warming, the stability of the Greenland ice sheet (GIS) is an important concern, especially in the light of new evidence of rapidly changing flow and melt conditions at the GIS margins. Studying the response of the GIS to past climatic change may help to advance our understanding of GIS dynamics. The previous interpretation of evidence from stable isotopes (delta(18)O) in water from GIS ice cores was that Holocene climate variability on the GIS differed spatially and that a consistent Holocene climate optimum-the unusually warm period from about 9,000 to 6,000 years ago found in many northern-latitude palaeoclimate records-did not exist. Here we extract both the Greenland Holocene temperature history and the evolution of GIS surface elevation at four GIS locations. We achieve this by comparing delta(18)O from GIS ice cores with delta(18)O from ice cores from small marginal icecaps. Contrary to the earlier interpretation of delta(18)O evidence from ice cores, our new temperature history reveals a pronounced Holocene climatic optimum in Greenland coinciding with maximum thinning near the GIS margins. Our delta(18)O-based results are corroborated by the air content of ice cores, a proxy for surface elevation. State-of-the-art ice sheet models are generally found to be underestimating the extent and changes in GIS elevation and area; our findings may help to improve the ability of models to reproduce the GIS response to Holocene climate.
  • Article
    From temperature measurements down through the 3001 m deep borehole at the North Greenland Icecore Project (NorthGRIP) drill site, it is now clear that the ice at the base, 3080 m below the surface, is at the pressure-melting point. This is supported by the measurements on the ice core where the annual-layer thicknesses show there is bottom melting at the site and upstream from the borehole. Surface velocity measurements, internal radio-echo layers, borehole and ice-core data are used to constrain a time-dependent flow model simulating flow along the north-northwest-trending ice-ridge flowline, leading to the NorthGRIP site. Also time-dependent melt rates along the flowline are calculated with a heat-flow model.The results show the geothermal heat flow varies from 50 to 200 mW m-2 along the 100 km section of the modeled flowline. The melt rate at the NorthGRIP site is 0.75 cm a-1, but the deep ice in the NorthGRIP core originated 50 km upstream and has experienced melt rates as high as 1.1 cm a-1.
  • Article
    The North Greenland Icecore Project (NorthGRIP) deep drilling site (75degrees05'47" N, 42degrees19'42" W) is located at the north-northwest ridge of the Greenland ice sheet, 320 km from Summit. A strain net has been established around the NorthGRIP site and surveyed with global positioning system. Our results show that ice flows with a horizontal surface velocity of 1.329 +/- 0.015 m a(-1) along the ridge. Estimated principal surface strain rates at NorthGRIP are epsilon(1) = (-0.4 +/- 0.6) x 10(-5) a(-1) and epsilon(2) = (7.1 +/- 0.6) x 10(-5) a(-1), in the directions along and transverse to the north-northwest ridge, respectively, i.e. ice is compressed along the ridge but stretched transverse to the ridge. Possible implications of the observed flow pattern for the stratigraphy are discussed. The average thickening rate in the strain-net area is found to be partial derivativeH/partial derivativet = 0.00 +/- 0.04 m a(-1), in agreement with previous estimates of mass balance in high-elevation areas of Greenland.
  • Article
    We developed two 150-MHz coherent radar depth sounders for ice thickness measurements over the Greenland ice sheet. We developed one of these using connectorized components and the other using radio frequency integrated circuits (RFICs). Both systems are designed to use pulse compression techniques and coherent integration to obtain the high sensitivity required to measure the thickness of more than 4 km of cold ice. We used these systems to collect radar data over the interior and margins of the ice sheet and several outlet glaciers. We operated both radar systems on the NASA P-3B aircraft equipped with GPS receivers. Radar data are tagged with GPS-derived location information and are collected in conjunction with laser altimeter measurements. We have reduced all data collected since 1993 and derived ice thickness along all flight lines flown in support of Program for Regional Climate Assessment (PARCA) investigations and the North Greenland Ice Core Project. Radar echograms and derived ice thickness data are placed on a server at the University of Kansas (http://tornado.rsl.ukans.edu/Greenlanddata.htm) for easy access by the scientific community. We obtained good ice thickness information with an accuracy of +/-10 m over 90% of the flight lines flown as a part of the PARCA initiative. In this paper we provide a brief description of the system along with samples of data over the interior, along the 2000-m contour line in the south and from a few selected outlet glaciers.
  • Article
    Existing accumulation maps with reported errors of about 20% are determined from sparsely distributed ice cores and pits. A more accurate accumulation rate might be obtained by generating continuous profiles of dated layers from high-resolution radar mapping of near-surface internal layers in the ice sheet (isochrones). To generate such profiles we designed and developed an ultrawideband radar for high-resolution mapping of internal layers in the top 200 m of ice and tested it at the North Greenland Ice Core Project drill site. Reflection profiles of 2- and 10-km length reveal horizons that we correlate with electrical conductivity measurement (ECM) recordings. Our results show that the radar-determined depth of internal layers is within +/-2 m of that in an ice core collected at a nearby location. Preliminary frequency analyses of layer reflections reveal that the reflections are strongest at the 500-1000 MHz frequency range. Long-term accumulation rate computed from radar data is within 5% of that obtained from snow pits.
  • Article
    Full-text available
    Probabilistic formulation of inverse problems leads to the definition of a probability distribution in the model space. This probability distribution combines a priori information with new information obtained by measuring some observable parameters (data). As, in the general case, the theory linking data with model parameters is nonlinear, the a posteriori probability in the model space may not be east to describe (it may be multimodal, some moments may not be defined, etc.). When analyzing an inverse problem, obtaining a maximum likelihood model is usually not sufficient, as we normally also wish to have information on the resolution power of the data. In the general case we may have a large number of model parameters, and an inspection of the marginal probability densities of interest may be impractical, or even useless. But it is possible to pseudorandomly generate a large collection of models according to the posterior probability distribution and to analyze and display the models in such a way that information on the relative likelihoods of model properties is conveyed to the spectator. This can be accomplished by means of an efficient Monte Carlo method, even in cases where no explicit formula for the a priori distribution is available. The most well known importance sampling method, the Metropolis algorithm, can be generalized, and this gives a method that allows analysis of (possible highly nonlinear) inverse problems with complex a priori information and data with an arbitrary noise distribution.
  • Article
    Full-text available
    Accurate modeling of ice sheets requires proper information on boundary conditions, including the geothermal heat flow (or heat-flow density (HFD)). Traditionally, one uniform HFD value is adopted for the entire modeled domain. We have calculated a distributed, high-resolution HFD dataset for an approximate core area (Sweden and Finland) of the Scandinavian ice sheet, and imbedded this within lower-resolution data published for surrounding regions. Within the Last Glacial Maximum ice margin, HFD varies with a factor of as much as 2.8 (HFD values ranging between 30 and 83 mW m−2), with an average of 49 mW m−2. This average value is 17% higher than 42 mW m−2, a common uniform value used in ice-sheet modeling studies of Fennoscandia. Using this new distributed dataset on HFD, instead of a traditional uniform value of 42 mW m−2, yields a 1.4 times larger total basal meltwater production for the last glacial cycle. Furthermore, using the new dataset in high-resolution modeling results in increased spatial thermal gradients at the bed. This enhances and introduces new local and regional effects on basal ice temperatures and melt rates. We observed significant strengthening of local 'ice streaming', which in one case correlates to an ice-flow event previously interpreted from geomorphology. Regional to local variations in geothermal heat flow need to be considered for proper identification and treatment of thermal and hydraulic bed conditions, most likely also when studying Laurentide, Greenland and Antarctic ice sheets.
  • Article
    A new deep ice-core drilling site has been identified in north Greenland at 75.12°N, 42.30°W, 316 km north-northwest (NNW) of the GRIP drill site on the summit of the ice sheet. The ice thickness here is 3085 m; the surface elevation is 2919 m. The North GRIP (NGRIP) site is identified so that ice of Eemian age (115-130 ka BP, calendar years before present) is located as far above bedrock as possible and so the thickness of the Eemian layer is as great as possible. An ice-flow model, similar to the one used to date the GRIP ice core, is used to simulate the flow along the NNW-trending ice ridge. Surface and bedrock elevations, surface accumulation-rate distribution and radio-echo sounding along the ridge have been used as model input. The surface accumulation rate drops from 0.23 m ice equivalent year-1 at GRIP to 0.19 m ice equivalent year-1 50 km from GRIP. Over the following 300 km the accumulation is relatively constant, before it starts decreasing again further north. Ice thicknesses up to 3250 m bring the temperature of the basal ice up to the pressure-melting point 100-250 km from GRIP. The NGRIP site is located 316 km from GRIP in a region where the bedrock is smooth and the accumulation rate is 0.19 m ice equivalent year-1. The modeled basal ice here has always been a few degrees below the pressure-melting point. Internal radio-echo sounding horizons can be traced between the GRIP and NGRIP sites, allowing us to date the ice down to 2300 m depth (52 ka BP). An ice-flow model predicts that the Eemian-age ice will be located in the depth range 2710-2800 m, which is 285 m above the bedrock. This is 120 m further above the bedrock, and the thickness of the Eemian layer of ice is 20 m thicker, than at the GRIP ice-core site.
  • Article
    The North Greenland Icecore Project (NorthGRIP) drill site was chosen in order to obtain a good Eemian record. At the present depth, 3001m, the Eemian interstadial has yet to be seen. Clearly the flow in this area is poorly understood and needs further investigation. After a review of specific features of the bottom topography, it is believed that the geology changes along the flowline. In order to investigate whether this explains the observed age-depth relationship at NorthGRIP, the inverse Monte Carlo method has been applied to a simple model. The inversion reveals that the main reason no Eemian is observed is a high basal melt rate (2.7mm a-1). The melting is a consequence of a higher geothermal heat flux than the expected 51mWm-2 of the Precambrian shield. From our analyses it is concluded that the geothermal heat flux at NorthGRIP is 98 mWm-2. The high basal melt rate also gives rise to sliding at the bed. In addition to these results, an accumulation model has been established specifically for NorthGRIP. These results are essential for further modelling of the NorthGRIP flow and depth-age relationship.
  • Article
    Modeling the temperature profile along the GRIP deep bore at the summit of the Greenland ice sheet leads to conversion factors that allow interpretation of the dated stable isotope profile as a climatic temperature record spanning the last 113,000 years. When corrected for surface elevation changes, the late glacial to Boreal temperature shift appears to have been 22 degrees C in central Greenland. The warming at the end of the last glaciation probably began earlier in Greenland, than in Antarctica.
  • Article
    The superb quality of the climate chronology archived in the Summit, Greenland ice cores (GRIP, GISP2) testifies that the Greenland Ice Sheet divide has been generally stable through the last glacial cycle. The ice sheet has experienced a broad range of paleoclimate conditions, ice sheet margin configurations, and internal dynamical adjustments in glacial–interglacial transitions, however. It is unlikely that the Summit region escaped shifts in ice divide position, geometry, elevation, and flow characteristics. Details of this dynamical history are important to several aspects of ice core studies. The magnitudes of pure and simple shearing, reconstruction of vertical ice velocity, the explicit location of the ice divide, and the divide ‘residence time’ at different locations are all of interest in interpretation of climatic variables and physical properties of ice in the ice cores. We apply a three-dimensional, thermomechanical ice sheet model to examine the evolution of these dynamical variables over the last 160 kyr in central Greenland. While a high-elevation ice dome is present in the Summit region throughout the simulation, ice divide migrations of up to 150 km are predicted. All points in the vicinity of the Summit ice cores, including the modern divide, have been subject to flowline shifts and variable, non-zero shear deformation during the adjustment from glacial to Holocene conditions, from ca. 10 ka to the present. Modelled divide peregrinations and strain rate history are consistent with the observed disturbance of deep ice in the GRIP and GISP2 ice cores, which has muddled paleoclimate reconstructions for the last interglacial (Eemian) period in Greenland. Dynamical excursions are also evident north of the modern summit, where the NGRIP ice core is currently being drilled [Dahl-Jensen et al., J. Glaciol. 43 (1997) 300–306]. However, the prevailing flow direction and deformation regime at the NGRIP site are much more stable than those at GRIP and GISP2 in the simulations. Combined with the greater depth of ice at this site, this lends cautious optimism to the hope that Eemian ice at NGRIP may contain an intact record of Eemian climate.
  • Article
    The evolution of the Greenland ice sheet during the last 150,000 years, in response to a climate history derived from a Greenland ice-margin oxygen-18 record, is simulated by means of a three-dimensional, time-dependent ice-sheet model. The calculations indicate that the ice sheet displayed considerable thinning and ice-margin retreat during the last interglacial (the Eemian) and during a warm interstadial c. 100,000 yr B.P., resulting in a splitting up of the ice sheet into a central-northern and a southern part. However, the ice sheet in Central Greenland survived the warm stages with almost unchanged surface elevations as compared with the present.
  • Article
    We show that robust regressions can be established between relative sea-level (RSL) data and benthic foraminifera oxygen isotopic ratios from the North Atlantic and Equatorial Pacific Ocean over the last climatic cycle. We then apply these regressions to long benthic isotopic records retrieved at one North Atlantic and one Equatorial Pacific site to build a composite RSL curve, as well as the associated confidence interval, over the last four climatic cycles. Our proposed reconstruction of RSL is in good agreement with the sparse RSL data available prior to the last climatic cycle. We compute bottom water temperature changes at the two sites and at one Southern Indian Ocean site, taking into account potential variations in North Atlantic local deep water δ18O. Our results indicate that a Last Glacial Maximum (LGM) enrichment of the ocean mean oxygen isotopic ratio of 0.95‰ is the lowest value compatible with unfrozen deep waters in the Southern Indian Ocean if local deep water δ18O did not increase during glacials with respect to present. Such a value of the LGM mean ocean isotopic enrichment would impose a maximum decrease in local bottom water δ18O at the North Atlantic site of 0.30‰ during glacials.
  • Article
    Full-text available
    Two deep ice cores from central Greenland, drilled in the 1990s, have played a key role in climate reconstructions of the Northern Hemisphere, but the oldest sections of the cores were disturbed in chronology owing to ice folding near the bedrock. Here we present an undisturbed climate record from a North Greenland ice core, which extends back to 123,000 years before the present, within the last interglacial period. The oxygen isotopes in the ice imply that climate was stable during the last interglacial period, with temperatures 5 degrees C warmer than today. We find unexpectedly large temperature differences between our new record from northern Greenland and the undisturbed sections of the cores from central Greenland, suggesting that the extent of ice in the Northern Hemisphere modulated the latitudinal temperature gradients in Greenland. This record shows a slow decline in temperatures that marked the initiation of the last glacial period. Our record reveals a hitherto unrecognized warm period initiated by an abrupt climate warming about 115,000 years ago, before glacial conditions were fully developed. This event does not appear to have an immediate Antarctic counterpart, suggesting that the climate see-saw between the hemispheres (which dominated the last glacial period) was not operating at this time.