Viscous transfer of momentum across a shallow laminar flow

In a shallow channel, the flow transfers most of its momentum vertically. Based on this observation, one often neglects the momentum that is transferred across the stream – the core assumption of the shallow-water theory. In the context of viscous flows, this approximation is referred to as the ‘lubrication theory’, in which one assumes that the shear stress exerted by the fluid on the substrate over which it flows is proportional to its velocity. Here, we revise this theory to account for the momentum that viscosity transfers across a shallow laminar flow, while keeping the problem low-dimensional. We then test the revised lubrication theory against analytical and numerical solutions of the exact problem. We find that, at a low computational cost, the present theory represents the actual flow more accurately than the classical lubrication approximation. This theoretical improvement, devised with laboratory rivers in mind, should also apply to other geophysical contexts, such as ice flows or forming lava domes.

Basal Water Storage Variations beneath Antarctic Ice Sheet Inferred from Multi-source Satellite Data

Antarctic basal water storage variations (BWSV) refer to the mass variations of liquid water beneath Antarctic ice sheet. Identifying these variations is critical to understand the behaviour of ice sheet, yet it is rarely accessible to direct observation. We presented a layered gravity density forward/inversion method for estimating Antarctic BWSV from multi- source satellite observation data, and relevant models. Results reveal spatial variability of BWSV with the mean rate of 43 ± 13 Gt/yr during 2003–2009, which is 21 Gt/yr lower than basal melting rate. This indicates that the basal meltwater beneath Antarctic ice sheet is decreasing with the rate of −21 ± 13 Gt/yr, accounting for 28 % of the mass balance rate (−76 Gt/yr, Shepherd et al. (2018)), and the basal water migrations between basal drainage systems and oceans is non-ignorable in estimating basal mass balance of Antarctic ice sheet. Similar spatial distribution of basal water increases regions and locations of active subglacial lakes indicates that basal water storage in most active subglacial lakes is increasing. In most region of Antarctic ice sheet except Amundsen Sea coast region, the comparison of spatial BWSV and ice velocity displays a positive correlation between considerable basal water increases and rapid/accelerated ice flows, which indicates that BWSV appear to have an important effect on ice flows. Accordingly, we infer that further enhanced flow velocities are expected if basal water continues to increase in these regions.

Basal Water Storage Variations beneath Antarctic Ice Sheet

Antarctic basal water storage variations (BWSV) contain basal water migrations and basal melting. Identifying these variations are critical to understand the behaviour of ice sheet, yet it is rarely accessible to direct observation. We presented a layered gravity density forward/inversion method for constructing Antarctic basal mass balance (BMB) estimates from multisource satellite observation data, and evaluated BWSV based on basal melting rate. As an example, spatial annual BWSV trend during 2003–2009 are estimated. Results reveal spatial variability of BWSV, with the rate of 46.3 Gt/y. Similar spatial distribution between basal water increases regions and locations of active subglacial lakes indicates that basal water storage in most active subglacial lakes are increasing. Comparison of spatial BWSV and ice surface velocity display a positive correlation between considerable basal water decreases and rapid ice flows, however, exceptions are when the massive rapid ice flows connected to huge ice shelves that hold up by surrounding terrains, that slows down the basal water discharge outward.

Surface velocity of the Northeast Greenland Ice Stream (NEGIS): assessment of interior velocities derived from satellite data by GPS

The Northeast Greenland Ice Stream (NEGIS) extends around 600 km upstream from the coast to its onset near the ice divide in interior Greenland. Several maps of surface velocity and topography of interior Greenland exist, but their accuracy is not well constrained by in situ observations. Here we present the results from a GPS mapping of surface velocity in an area located approximately 150 km from the ice divide near the East Greenland Ice-core Project (EastGRIP) deep-drilling site. A GPS strain net consisting of 63 poles was established and observed over the years 2015–2019. The strain net covers an area of 35 km by 40 km, including both shear margins. The ice flows with a uniform surface speed of approximately 55 m a−1 within a central flow band with longitudinal and transverse strain rates on the order of 10−4 a−1 and increasing by an order of magnitude in the shear margins. We compare the GPS results to the Arctic Digital Elevation Model and a list of satellite-derived surface velocity products in order to evaluate these products. For each velocity product, we determine the bias in and precision of the velocity compared to the GPS observations, as well as the smoothing of the velocity products needed to obtain optimal precision. The best products have a bias and a precision of ∼0.5 m a−1. We combine the GPS results with satellite-derived products and show that organized patterns in flow and topography emerge in NEGIS when the surface velocity exceeds approximately 55 m a−1 and are related to bedrock topography.

Surface velocity of the Northeast Greenland Ice Stream (NEGIS): Assessment of interior velocities derived from satellite data by GPS

The Northeast Greenland Ice Stream (NEGIS) extends around 600 km upstream from the coast to its onset near the ice divide in interior Greenland. Several maps of surface velocity and topography in the interior Greenland exist, but the accuracy is not well constrained by in situ observations and limiting detailed studies of flow structures and shear margins near the onset of NEGIS. Here we present the results from a GPS mapping of surface velocity in an area located approximately 150 km from the ice divide near the East Greenland Ice-core Project (EastGRIP) deep drilling site (75°38’ N, 35°60’ W). A GPS strain net consisting of 63 poles was established and observed over the years 2015–2019. The strain net covers 35 km along NEGIS and 40 km across NEGIS, including both shear margins. The ice flows with a uniform surface speed of approximately 55 m a−1 within a > 10 km wide central flow band with strain rates in the order of 10−4 a−1. The strain rates increase in the shear margins by an order of magnitude, and 10–20 m deep shear margin troughs mark a zone with enhanced longitudinal stretching, transverse compression and shear. We compare the GPS results to the Arctic Digital Elevation Model (ArcticDEM) and a list of satellite-based surface velocity products in order to evaluate these products. For each velocity product, we determine the bias and precision of the velocity compared to the GPS observations, as well as the smoothing of the velocity products needed to obtain optimal precision. The best products have a bias and precision of ~0.5 m a−1. We combine the GPS results with satellite-based products and show that organized patterns in flow and topography emerge in the NEGIS ice stream when the surface velocity exceeds approximately 55 m a−1 and are related to bedrock topography.