Modelling the transfer of supraglacial meltwater to the bed of Leverett Glacier, Southwest Greenland

This is the final version of the article. Available from EGU via the DOI in this record.Meltwater delivered to the bed of the Greenland Ice Sheet is a driver of variable ice-motion through changes in effective pressure and enhanced basal lubrication. Ice surface velocities have been shown to respond rapidly both to meltwater production at the surface and to drainage of supraglacial lakes, suggesting efficient transfer of meltwater from the supraglacial to subglacial hydrological systems. Although considerable effort is currently being directed towards improved modelling of the controlling surface and basal processes, modelling the temporal and spatial evolution of the transfer of melt to the bed has received less attention. Here we present the results of spatially distributed modelling for prediction of moulins and lake drainages on the Leverett Glacier in Southwest Greenland. The model is run for the 2009 and 2010 ablation seasons, and for future increased melt scenarios. The temporal pattern of modelled lake drainages are qualitatively comparable with those documented from analyses of repeat satellite imagery. The modelled timings and locations of delivery of meltwater to the bed also match well with observed temporal and spatial patterns of ice surface speed-ups. This is particularly true for the lower catchment ( < 1000 m a.s.l.) where both the model and observations indicate that the development of moulins is the main mechanism for the transfer of surface meltwater to the bed. At higher elevations (e.g. 1250-1500 m a.s.l.) the development and drainage of supraglacial lakes becomes increasingly important. At these higher elevations, the delay between modelled melt generation and subsequent delivery of melt to the bed matches the observ ed delay between the peak air temperatures and subsequent velocity speed-ups, while the instantaneous transfer of melt to the bed in a control simulation does not. Although both moulins and lake drainages are predicted to increase in number for future warmer climate scenarios, the lake drainages play an increasingly important role in both expanding the area over which melt accesses the bed and in enabling a greater proportion of surface melt to reach the bed.We acknowledge the College of Physical Sciences, University of Aberdeen, the Leverhulme Trust through a Study Abroad Studentship and the Swedish Radiation Safety Authority, for funding awarded to C. Clason. Data collection was supported by the UK Natural Environment Research Council (through a studentship to I. Bartholomew and grants to P. Nienow and D. Mair) and the Edinburgh University Moss Centenary Scholarship (I. Bartholomew)

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation

A review on sparse solutions in optimal control of partial differential equations

In this paper a review of the results on sparse controls for partial differential equations is presented. There are two different approaches to the sparsity study of control problems. One approach consists of taking functions to control the system, putting in the cost functional a convenient term that promotes the sparsity of the optimal control. A second approach deals with controls that are Borel measures and the norm of the measure is involved in the cost functional. The use of measures as controls allows to obtain optimal controls supported on a zero Lebesgue measure set, which is very interesting for practical implementation. If the state equation is linear, then we can carry out a complete analysis of the control problem with measures. However, if the equation is nonlinear the use of measures to control the system is still an open problem, in general, and the use of functions to control the system seems to be more appropriate.This work was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2014-57531-P

Contribution of glaciers to water, energy and food security in mountain regions: current perspectives and future priorities

Mountain glaciers are crucial sources of fresh water, contributing directly and indirectly to water, energy and food supplies for hundreds of millions of people. Assessing the impact of diminishing glacial meltwater contributions to the security of this resource is critical as we seek to manage and adapt to changing freshwater dynamics in a warming world. Both water quantity and quality influence water (in)security, so understanding the fluxes of water, sediment and contaminants through glacial and proglacial systems is required for holistic assessment of meltwater contribution to downstream resource security. In this paper we consider the socio-environmental role of and pressures on glacier-fed waters, discuss key research priorities for the assessment of both the quantity and quality of meltwater and reflect on the importance of situating our understanding within a transdisciplinary and inclusive research landscape

Functional Dissection of the Proton Pumping Modules of Mitochondrial Complex I

A catalytically active subcomplex of respiratory chain complex I lacks 14 of its 42 subunits yet retains half of its proton-pumping capacity, indicating that its membrane arm has two pump modules

Unravelling and understanding local perceptions of water quality in the Santa basin, Peru

Water quality is an integral part of water security. Measuring the physico-chemical indicators for water quality can provide an objective picture of water health, but it does not provide information on lived experiences related to water quality, expectations of water resources, nor how the quality of water affects its usage. Perceptual information and traditional ecological knowledge on water quality can help to understand interactions between water and people, and thereby support locally appropriate sustainable water resource strategies. Accordingly, our project sought to collect and synthesise insights from local perspectives on water quality in the upper Santa River basin, Peru, a region where water quality directly relates to people’s livelihoods. Perceptual data was collected via the Nuestro Rio mobile app (N = 149) as well as walking interviews (n = 84) (July-August 2021) in two main study areas, Olleros and Catac. We find that water quality perspectives differ within, and between, study areas and communities, however four overarching themes were identified, and are explored here: i) environmental indicators for water quality; ii) water uses; and iii) perceived causes of water quality; iv) water quality perceptions behind emotions. Most rural participants felt the main cause of poor water quality was mineral pollution, likely linked to local geology, however we also found that local perceptions of water quality depend on water usage, directly linked to domestic water use and agricultural livelihoods. Qualitative data highlighted the complex relationships between water quality, perceptions and emotions. More inclusive citizen-based science that considers what people observe, think and feel about the quality of their rivers can help provide a much deeper contextual understanding of dynamic human-water systems, with further benefits for improving water management and policy implementation

Sparse initial data indentification for parabolic pde and its finite element approximations

We address the problem of inverse source identification for parabolic equations from the optimal control viewpoint employing measures of minimal norm as initial data. We adopt the point of view of approximate controllability so that the target is not required to be achieved exactly but only in an approximate sense. We prove an approximate inversion result and derive a characterization of the optimal initial measures by means of duality and the minimization of a suitable quadratic functional on the solutions of the adjoint system. We prove the sparsity of the optimal initial measures showing that they are supported in sets of null Lebesgue measure. As a consequence, approximate controllability can be achieved efficiently by means of controls that are activated in a finite number of pointwise locations. Moreover, we discuss the finite element numerical approximation of the control problem providing a convergence result of the corresponding optimal measures and states as the discretization parameters tend to zero.The first author was supported by Spanish Ministerio de Economía y Competitividad under project MTM2011-22711. The third author was supported by the Advanced Grant NUMERIWAVES/FP7-246775 of the European Research Council Executive Agency, FA9550-14-1-0214 of the EOARD-AFOSR, FA9550-15-1-0027 of AFOSR, the BERC 2014-2017 program of the Basque Government, the MTM2011-29306 and SEV-2013-0323 Grants of the MINECO, the CIMI-Toulouse Excellence Chair in PDEs, Control and Numerics and a Humboldt Award at the University of Erlangen-Nürnberg