On exact solutions and numerics for cold, shallow, and thermocoupled ice sheets

This three section report can be regarded as an extended appendix to (Bueler, Brown, and Lingle 2006). First we give the detailed construction of an exact solution to a standard continuum model of a cold, shallow, and thermocoupled ice sheet. The construction is by calculation of compensatory accumulation and heat source functions which make a chosen pair of functions for thickness and temperature into exact solutions of the coupled system. The solution we construct here is ``TestG'' in (Bueler and others, 2006) and the steady state solution ``Test F'' is a special case. In the second section we give a reference C implementation of these exact solutions. In the last section we give an error analysis of a finite difference scheme for the temperature equation in the thermocoupled model. The error analysis gives three results, first the correct form of the Courant-Friedrichs-Lewy (CFL) condition for stability of the advection scheme, second an equation for error growth which contributes to understanding the famous ``spokes'' of (Payne and others, 2000), and third a convergence theorem under stringent fixed geometry and smoothness assumptions.Comment: 16 pages, two C codes; extended appendix to Bueler, Brown, and Lingle, "Exact solutions to the thermocoupled shallow ice approximation: effective tools for verification," submitted to J. Glacio

Efficient Nonlinear Solvers for Nodal High-Order Finite Elements in 3D

Conventional high-order finite element methods are rarely used for industrial problems because the Jacobian rapidly loses sparsity as the order is increased, leading to unaffordable solve times and memory requirements. This effect typically limits order to at most quadratic, despite the favorable accuracy and stability properties offered by quadratic and higher order discretizations. We present a method in which the action of the Jacobian is applied matrix-free exploiting a tensor product basis on hexahedral elements, while much sparser matrices based on Q 1 sub-elements on the nodes of the high-order basis are assembled for preconditioning. With this "dual-order” scheme, storage is independent of spectral order and a natural taping scheme is available to update a full-accuracy matrix-free Jacobian during residual evaluation. Matrix-free Jacobian application circumvents the memory bandwidth bottleneck typical of sparse matrix operations, providing several times greater floating point performance and better use of multiple cores with shared memory bus. Computational results for the p-Laplacian and Stokes problem, using block preconditioners and AMG, demonstrate mesh-independent convergence rates and weak (bounded) dependence on order, even for highly deformed meshes and nonlinear systems with several orders of magnitude dynamic range in coefficients. For spectral orders around 5, the dual-order scheme requires half the memory and similar time to assembled quadratic (Q 2) elements, making it very affordable for general us

Computation of a combined spherical-elastic and viscous-half-space earth model for ice sheet simulation

This report starts by describing the continuum model used by Lingle & Clark (1985) to approximate the deformation of the earth under changing ice sheet and ocean loads. That source considers a single ice stream, but we apply their underlying model to continent-scale ice sheet simulation. Their model combines Farrell's (1972) elastic spherical earth with a viscous half-space overlain by an elastic plate lithosphere. The latter half-space model is derivable from calculations by Cathles (1975). For the elastic spherical earth we use Farrell's tabulated Green's function, as do Lingle & Clark. For the half-space model, however, we propose and implement a significantly faster numerical strategy, a spectral collocation method (Trefethen 2000) based directly on the Fast Fourier Transform. To verify this method we compare to an integral formula for a disc load. To compare earth models we build an accumulation history from a growing similarity solution from (Bueler, et al.~2005) and and simulate the coupled (ice flow)-(earth deformation) system. In the case of simple isostasy the exact solution to this system is known. We demonstrate that the magnitudes of numerical errors made in approximating the ice-earth system are significantly smaller than pairwise differences between several earth models, namely, simple isostasy, the current standard model used in ice sheet simulation (Greve 2001, Hagdorn 2003, Zweck & Huybrechts 2005), and the Lingle & Clark model. Therefore further efforts to validate different earth models used in ice sheet simulations are, not surprisingly, worthwhile.Comment: 36 pages, 16 figures, 3 Matlab program

\u3ci\u3eEragrostis Curvula\u3c/i\u3e Effects on Above and Below-Ground Plant Species Richness and Diversity

Monitoring and managing the soil seed bank is fundamental to land management as it constitutes the future generations of invasive plant communities. Invasive plants have traits that result in high recruitment through increased seed generation, short seed dormancy and phenotypic plasticity. Furthermore, invasive plants with growth forms that inhibit the growth and recruitment of other species can lead to monocultures and associated reduction in above-ground biodiversity, potentially negatively impacting the soil seed bank diversity and ecosystem functions and services. Eragrostis curvula is one such species that has many of these invasive traits, including high propagule generation, and can exclude plant species from establishing in the above-ground population, thus negatively impacting above-ground biodiversity, as measured by species richness and Shannon diversity index. However, our findings suggest it has not significantly impacted the soil seed bank species diversity or richness across eight sites within the Snowy Monaro region when competition is removed as a limiting factor. Our findings provide valuable information on a path to invasive plant species management. If E. curvula above-ground biomass is controlled, other species dormant in the soil seed bank may recruit in the ecosystem, provided they remain viable in the soil seed bank. However, to date, our research has not investigated the species composition of these sites in detail. With such a high density of potentially germinating seeds in a soil seed bank and the adverse effects the species can have on the above-ground species diversity and richness, E. curvula needs integrated management to mitigate its spread and ecosystem and economic impact

The ecological and physiological drivers and the development of improved landscape detection of the invasive perennial, Eragrostis curvula, across the southern tablelands of NSW, Australia

This thesis addresses managing and quantifying the associated impacts of the invasive species Eragrostis curvula, a non-native grass that poses ecological and economic threats in Australia. It aims to understand its ecological impacts to improve management strategies for sustainable ecosystems. The study utilised convolutional neural networks to assess the feasibility of using drone imagery for early detection of E. curvula infestations, a relatively new endeavour in invasive species management in Australian grassland systems. Key findings from this research highlight E. curvula's significant association with species richness and diversity, revealing a reduction in biodiversity in areas dominated by the grass. Eragrostis curvula appears to exhibit some degree of drought tolerance in the form of biomass retention, which in part likely explains its dominance over other species. Moreover, the presence of herbicide-resistant E. curvula populations underscored the challenges of relying on chemical controls and the necessity for integrated management strategies. The investigation into E. curvula's ecological dynamics revealed that variables, such as temperature, proximity to roads and watercourses, significantly influence its distribution. This suggests that E. curvula's spread can be partly attributed to human activities and climatic suitability, underlining the importance of considering these factors in management plans. The significant findings advocate a shift towards integrated management approaches incorporating technological advancements for early detection and monitoring alongside traditional control methods. The insights generated from this research hold implications for natural resource management agencies and restoration ecologists, providing a robust foundation for informed decision-making in ongoing invasive species management

Sustainable agriculture in the Arabian/Persian Gulf region utilizing marginal water resources: Making the best of a bad situation

One way to encourage agricultural self-sufficiency in arid regions is to increase the productivity of conventional freshwater agriculture. Another way is to develop and implement novel strategies and technologies that do not deplete scarce freshwater. Here we describe several options for countries in the Gulf region to increase their agricultural production by taking advantage of a lesser used resource-marginal water. Marginal water can be treated sewage effluent, produced oilfield water, brackish groundwater or seawater. We describe how this resource can be used to grow salt-tolerant forage crops, microalgae and aquaculture crops. Policies needed to implement and/or scale-up such practices are also outlined. 2018 by the authors.Scopu