Session M02: DFD/GPC Focus Session: Planetary Flows in Climate

Submarine melting of glaciers and its effect on climate

Rising global air and ocean temperatures have been identified as drivers of the observed increase in the discharge of ice from the Antarctic and Greenland ice sheets. At present the Greenland Ice Sheet mass loss accounts for one quarter of the observed global sea level rise (7.5 ± 1.8 mm from 1992 to 2011) and it is crucial to understand the mechanisms and drivers of this loss to improve our ability to predict future sea-level rise and prepare global societies for its consequences.

Greenland’s glacial fjords constitute a key link between the ocean and the ice sheet. Understanding their dynamics, particularly submarine melting at the glaciers’ edges and the export of freshwater, is important for understanding Greenland’s current transformations, their impact on the climate system and predicting future changes, both to the Greenland Ice Sheet and the climate.

Submarine melting of glaciers, and the associated flux of meltwater, are affected both by the fjord stratification and the discharge of surface runoff at the base of a glacier, i.e. subglacial discharge. The distribution of the subglacial discharge, i.e. single or multiple plumes and/or line vs. point source plumes, has been observed to influence the magnitude and distribution of submarine melting of glaciers. Furthermore, plumes’ sediment loads influence the turbulent heat transport and consequently submarine melting.   

Granular flow decoherence precedes failure of glacial ice mélange

Predicting impending failure in disordered systems is a principal goal in many fields ranging from earthquake detection to glassy, granular, and mechanical metamaterials. In most cases, particle and bond-level information plays a crucial role in predicting failure, yet this level of detail is often unavailable for complex geophysical systems. In flowing granular materials, machine learning techniques and acoustic emissions analyses demonstrate precursors to failure; yet, real-time detection remains an elusive goal. Here we show that failure of ice mélange, a large-scale granular material that is pushed through fjords by tidewater glaciers, is preceded by a loss of coherent flow. Ice mélange forms due to the rapid calving of large icebergs, especially during summer months, and is exacerbated by a warming climate. This granular collection of broken icebergs then fills the fjord and buttresses the glacier as a floating granular material. By analyzing terrestrial radar data sampled every 3-minutes, we find that the spatial pattern of strain rates within ice mélange develops large-scale fluctuations as early as 1 hour before an iceberg calving event. We also use a particle dynamics model to show how these fluctuations are likely due to buckling and rearrangements of the quasi-two-dimensional ice mélange. Additionally, our analog laboratory experiments with floating plastic icebergs allow us to correlate the loss of coherence with the decrease in buttressing force on a mock glacier terminus. Our results directly implicate ice mélange as a mechanical inhibitor of calving along tidewater glaciers, and further demonstrate the potential for real-time detection of failure in geophysical granular materials.   

Inferring flow law of ice shelves using physics-informed neural networks

Ice shelves are thin films of gravity current floating above sea water. While the nonlinear rheology (e.g. flow law) of ice is measurable with laboratory experiments. The well-known lab-measurement-based model of ice rheology, Glen's law, has been applied to ice sheet models for decades. Yet this flow law doesn't capture processes occurring at much larger time scales such as decades and over long distances such as thousands of kilometers. Here we use physics-informed neural networks to infer ice rheology from the real data of ice velocity, thickness, and surface height. Neural network has been proved as a universal function approximator. Leveraging this property with automatic differentiation and gradient descent optimization, physics-informed neural networks (PINNs) was developed to include physical equations into loss function as an additional constraint to train the neural network to approximate the solution of the equations, as well as be able to infer unknown physical quantities in the equation from given data sets. We demonstrate PINNs' ability to infer the flow law of ice with an idealized example, and explore its robustness against noisy and sparse datasets. Our finding can be extended to identify the flow law of observational data.    

A thermomechanical model for frost heave and subglacial frozen fringe

Ice-infiltrated sediment, known as a frozen fringe, leads to phenomena such as frost heave, ice lenses, and meters of debris-rich ice under glaciers. Here we study the fluid physics of interstitial freezing water in sediments and focus on the conditions relevant for subglacial environments. We describe the thermomechanics of liquid water flow through and freezing in ice-saturated frozen sediments. The force balance that governs the frozen fringe thickness depends on the weight of the overlying material, the thermomolecular force between ice and sediments across premelted films of liquid, and the water pressure within liquid films that is required by flow according to Darcy's law. We combine this mechanical model with an enthalpy method which conserves energy across phase change interfaces on a fixed computational grid. The force balance and enthalpy model together determine the evolution of the frozen fringe thickness and our simulations predict frost heave rates and ice lens spacing. We explicitly account for the formation of ice lenses, regions of pure ice that cleave the fringe at the depth where the interparticle force vanishes. Our model results allow us to predict the thickness of a frozen fringe and the spacing of ice lenses at the base of glaciers.   

Deriving scaling laws for extreme weather events using the Buckingham-PI theorem

Changes in extreme weather events such as heatwaves, droughts, and cold spells under climate change are questions of significant scientific and societal importance. Currently, quantifying changes in such extreme events relies on state-of-the-art climate models; however, model biases and infrequent occurrence of extreme events complicate obtaining conclusive answers. Having scaling laws for how the key characteristics of extreme events, such as their duration, frequency, intensity, and size depend on the mean state can help with constraining the model projections and also learning about future extreme events from paleo data. The Buckingham-PI theorem has a long and successful history in fluid mechanics; however, it is not often used in climate science. Here, we show examples of the successful application of the Buckingham-PI theorem to derive scaling laws for the size and duration of the midlatitude persistent anticyclones, i.e., the extreme-causing blocking events. The scaling laws derived for a simple prototype of the midlatitude circulation (a two-layer QG model) are shown to work in a hierarchy of climate models and explain some of the observed changes in blocking characteristics under climate change in state-of-the-art, CMIP-type, climate models.    

Nonlinear generation of long waves and the reversal of eddy momentum fluxes in a two-layer quasi-geostrophic model

The direction of eddy momentum fluxes in the Earth's midlatitude atmopshere has historically been explained by the interaction between waves and the zonal-mean flow in the quasi-geostrophic theory. While qualitativly adequate in the Earth-like regime, we show that the theory of wave-mean flow interactions becomes less accurate as β or the surface drag decreases. Using a two-layer quasi-geostrophic model of a baroclinic jet on a β-plane, statistically steady states are explored in which the vertically integrated eddy momentum flux is divergent at the center of the jet, rather than convergent as in the Earth-like regime. We show that the divergence is caused by long waves, generated by breaking of short unstable waves near their critical latitudes. Quasi-linear models with no wave-wave interaction can qualitatively capture the Earth-like regime but not the regime with momentum flux divergence at the center of the jet, because the nonlinear wave breaking and long wave generation processes are missing. The fact that the direction of eddy momentum fluxes can be altered by changing parameters in this idealized model challenges our understanding of this central aspect of the general circulation and has implications on the observed reversal of potential vorticity fluxes.    

Large-scale organization development in precipitating shallow cumulus convection

Clouds forming in the atmospheric boundary layer, typically the lowermost 4 km of the atmosphere, have a large impact on the Earth's energy balance and are one of the largest sources of uncertainty in climate projections. The development of precipitation in shallow cumulus clouds changes the spatial structure of convection and creates large-scale organization. The development of convective organization is studied using large-eddy simulations (LES) of the trade-wind boundary layer observed during the Rain In Cumulus over the Ocean campaign. The LES employ extensive horizontal domains, up to 160 x 160 km in the horizontal directions, and fine resolution (40 m). The development of large-scale organization develops rapidly and has a large impact on the turbulent-flow statistics. The structure of the flow organization and turbulence strongly depend on the LES domain size. In contrast, mean profiles do not depend on computational domain size. It is shown that large-scale organization primarily affects the horizontal fluctuations in the flow through the creation of local cloud-system circulations rather that changes to the individual cumulus-topped convective elements.   

Global Kinetic Energy Content of Oceanic Scales from Satellites and Models

How much energy resides in the oceanic mesoscales? What is their temporal variation? Traditionally, the mesoscales have been treated as deviations from a long-time mean. Here, we apply a coarse-grained decomposition of the ocean's surface geostrophic flow derived from satellite and numerical model products. In the extra-tropics we find that roughly 60% of the global surface geostrophic kinetic energy is at scales between 100 km and 500 km, peaking at 300 km. Our analysis also reveals a clear seasonality in the kinetic energy with a spring peak. We show that traditional mean-fluctuation (or Reynolds) decomposition is unable to robustly disentangle length-scales since the time-mean flow consists of a significant contribution (greater than 50%) from scales < 500 km. By coarse-graining in both space and time, we find that every length-scale evolves over a wide range of time-scales. Consequently, a running time-average of any duration reduces the energy content of all length-scales, including those larger than 1000 km, and is not effective at removing length-scales smaller than 300 km. By contrasting our spatio-temporal analysis of numerical model and satellite products, we show that the AVISO gridded satellite product suppresses temporal variations of less than 10 days for all length-scales, especially between 100 km and 500 km.   

Oceanic Eddy-killing by Wind from Global Satellite Observations

While wind is the primary driver of the oceanic general circulation, we find that it kills the ocean's most energetic motions --its mesoscale eddies-- at an average rate of 50 GW. We use satellite observations and a recent method to disentangle multi-scale processes on the sphere. A length-scale analysis of air-sea energy transfer on the entire globe had not been undertaken before, to our knowledge. In fact, we show that the temporal mean-eddy decomposition (i.e. Reynolds averaging) commonly used in oceanography fails to unravel eddy-killing. Our results present the first evidence that eddy-killing is a major seasonal sink for the oceanic eddies, peaking in winter. We find that eddy-killing removes a substantial fraction (up to 90%) of the wind power input in western boundary currents such as the Gulf Stream and Kuroshio. This process, often overlooked in analyses and models, is a major dissipation pathway for mesoscales, the ocean's most energetic scales.   

Quantification of the ocean-continent cistern problem

The ocean basins have almost exactly the correct surface area and average depth to hold Earth’s water. We model the dynamics that is hypothesized to be responsible for this using three materials corresponding to the continent material, earth’s mantle material, and oceanic water.  These are exposed to three processes: continent thickening from forces from mantle convection cells, subaerial continent erosion, and conservation of all materials. A numerical model that includes quantified values of all these features produces ocean, continent, and ocean-mantle surfaces that are relatively flat within certain parameter ranges.  There, they duplicate the well-known double maximum in Earth’s surface area versus elevation (the hypsometric curve). Large values of erosion rates compared to thickening rates produce the result that almost all water resides within the ocean basins. The resulting dimensionless numbers are discussed along with comments about the energy flux ratio between internal heat generation and solar heating.