Simple models for the simulation of submarine melt for a Greenland glacial system model

Abstract

Abstract. Two hundred marine-terminating Greenland outlet glaciers deliver more than half of the annually accumulated ice into the ocean and have played an important role in the Greenland ice sheet mass loss observed since the mid1990s. Submarine melt may play a crucial role in the mass balance and position of the grounding line of these outlet glaciers. As the ocean warms, it is expected that submarine melt will increase, potentially driving outlet glaciers retreat and contributing to sea level rise. Projections of the future contribution of outlet glaciers to sea level rise are hampered by the necessity to use models with extremely high resolution of the order of a few hundred meters. That requirement in not only demanded when modeling outlet glaciers as a stand alone model but also when coupling them with highresolution 3-D ocean models. In addition, fjord bathymetry data are mostly missing or inaccurate (errors of several hundreds of meters), which questions the benefit of using computationally expensive 3-D models for future predictions. Here we propose an alternative approach built on the use of a computationally efficient simple model of submarine melt based on turbulent plume theory. We show that such a simple model is in reasonable agreement with several available modeling studies. We performed a suite of experiments to analyze sensitivity of these simple models to model parameters and climate characteristics. We found that the computationally cheap plume model demonstrates qualitatively similar behavior as 3-D general circulation models. To match results of the 3-D models in a quantitative manner, a scaling factor of the order of 1 is needed for the plume models. We applied this approach to model submarine melt for six representative Greenland glaciers and found that the application of a line plume can produce submarine melt compatible with observational data. Our results show that the line plume model is more appropriate than the cone plume model for simulating the average submarine melting of real glaciers in Greenland.

Modeling the response of Greenland outlet glaciers to global warming using a coupled flow line–plume model

“…However, such models are computationally too expensive and therefore impractical for simulating the response of the entire GrIS to climate change on centennial timescales. At the same time, recent studies demonstrate that the simple line plume model by Jenkins (2011) is an adequate tool to simulate plume behavior (Jackson et al, 2017) and to determine submarine melt rates for marine-terminated glaciers (Beckmann et al, 2018). Since the plume model is significantly less computationally expensive than 3-D ocean models, it represents an alternative approach to introduce ice-ocean interaction into the GrIS model and still maintain the model's ability to perform a large set of centennial-scale experiments.…”

“…Simulating the glacier dynamics with 3-D ice sheet models requires very high spatial resolution ( 1 km) resulting in high computational cost (e.g., Aschwanden et al, 2016) and so far they cannot be used for centennial timescales. To reduce the computational cost we instead use a depth-and width-integrated one-dimensional ice flow model Nick et al, 2013) coupled to a line plume model (Beckmann et al, 2018). Unlike Amundson and Carroll (2018), who used the maximum melt rate as a frontal ablation factor for tidewater glaciers, we take into account the entire profile along the submerged part of the outlet glacier to calculate the submarine melt rate with the plume model ( Fig.…”

Simulation of the future sea level contribution of Greenland with a new glacial system model

“…Here, we opt for the new version of SICOPOLIS v3.3 (Bernales et al, 2017). This version includes hybrid dynamics, incorporating longitudinal and lateral stresses via the shelfy-stream approximation (SStA; MacAyeal, 1989) longitudinal and lateral stresses, which are important for nearer-margin fast flow areas, along with horizontal plane shear (Hindmarsh, 2004) via the shallow ice approximation (SIA), important for the slow-flow regions in the more central regions of the ice sheet.…”

“…It is based on the shallow ice approximation for grounded ice (Hutter, 1983;Morland, 1984) and the shallow shelf approximation for floating ice (Morland, 1987;MacAyeal, 1989). Recently, hybrid shallow-ice and shelfy-stream dynamics have been added as an option for ice streams (Bernales et al, 2017). The rheology is that of an incompressible, heat-conducting, power-law fluid (Glen's flow law; e.g.…”

“…In the hybrid mode, a threshold of r thr = 0 applies to the slip ratio (Eq. 8 in Bernales et al, 2017), i. e., the SStA equations are solved over the entire ice sheet, and the ice velocities are the weighted sum from the SIA and SStA velocities with the slip ratio as weight. The boundary conditions and initialization method to yield the Rignot and Mouginot (2012).…”