+ Statement of Need
+ Ice sheet models allow us to simulate the behaviour and evolution
+ of ice sheets, which are large masses of glacial land and marine ice.
+ There are two main uses of ice sheet models: firstly, prognostic use,
+ which involves making predictions about the future of ice sheets.
+ Prognostic predictions often relate to sea level rise contributions:
+ the world’s two largest ice sheets, located in Antarctica and
+ Greenland, hold enough ice to raise sea levels by approximately 58 and
+ 7 meters, respectively
+ (Bamber
+ et al., 2018); prognostic modelling of these ice sheets enables
+ us to make predictions on (for example) how much of this ice will be
+ lost
+ (Edwards
+ et al., 2021), to investigate the possibility of runaway ice
+ loss
+ (DeConto
+ et al., 2021), and analyze whether or not such instabilities
+ have already been initiated
+ (Favier
+ et al., 2014). Secondly, ice sheet models are also used
+ diagnostically, which involves using a model to investigate processes
+ controlling the behaviour of an ice sheet, such as how loss of ice
+ shelves – the floating extensions of ice sheets – influences ice flow
+ speed
+ (Joughin
+ et al., 2021), how different bed conditions affect ice sliding
+ (De
+ Rydt et al., 2021), and probing the conditions under which
+ so-called ‘tipping-points’ might be passed
+ (Schoof,
+ 2007).
+ On the long (100s of kilometers) length scales that are relevant to
+ ice sheets, ice behaves approximately as a highly viscous fluid with a
+ shear-thinning rheology (meaning that as the ice deforms, it becomes
+ thinner and flows more easily). WAVI.jl
+ (Wavelet-based Adaptive-grid Vertically-integrated Ice-sheet-model) is
+ a Julia package for the numerical solution of an accurate
+ approximation to the Stokes equations, which describe conservation of
+ mass and momentum in such a fluid. This approximation, which is
+ appropriate for fluid flows with a high aspect ratio (as is the case
+ for the vast majority of ice sheets), treats longitudinal and lateral
+ stresses as depth-independent, but accounts for vertical velocity
+ gradients in the nonlinear viscosity and in the treatment of basal
+ stress
+ (Goldberg,
+ 2011).
+ Physically, ice sheets do not stand alone, but are forced by other
+ parts of the climate system. For example, the rapid changes that have
+ occurred in the West Antarctic Ice Sheet in the previous decades are
+ understood to have been driven by an increase in oceanic heat content
+ reaching the floating ice shelves which fringe this region
+ (Pritchard
+ et al., 2012). For basal melting in particular,
+ WAVI.jl includes a broad range of community
+ melt rate parametrizations
+ (Asay-Davis
+ et al., 2017), as well as a developmental coupling with the
+ ocean general circulation model MITgcm
+ (Marshall
+ et al., 1997). More generally, WAVI.jl
+ leverages Julia’s multiple dispatch paradigm to create a simple,
+ user-friendly interface for embedding models of other physical
+ processes, such as accumulation, ice damage, ice shelf calving, and
+ solid earth effects, into WAVI.jl.
+ WAVI.jl is designed to be usable by anyone
+ interested in ice sheet modelling, from students with no programming
+ experience to expert researchers in the field, and everyone in
+ between. To facilitate detailed research, including simulations at
+ high spatial and temporal resolution, WAVI.jl
+ employs a number of tools to improve computational speed, including
+ multithreading capabilities, an adaptive numerical grid and a
+ wavelet-based preconditioner
+ (Arthern
+ & Williams, 2017). To facilitate accessibility,
+ WAVI.jl includes a simple, user friendly API,
+ which is aided by Julia’s convenient syntax. In addition, the GitHub
+ repository in which the code is stored includes a number of
+ well-documented examples, which demonstrate the software’s
+ capabilities in a wide variety of situations.
+
+ Schematic diagram of a marine ice sheet-shelf system,
+ whose flow may be simulated using WAVI.jl. Labels and text indicate
+ features of the
+ software.
+ ![]()
+
+ WAVI.jl is the successor to a similar code,
+ written in the proprietary programming language MATLAB, which was
+ never publicly released. This previous code has been used extensively
+ as research software [e.g.
+ (Arthern
+ & Williams, 2017),
+ (Arthern
+ et al., 2015)], as well as having participated in the most
+ recent ice sheet model intercomparison exercise
+ (Cornford
+ et al., 2020), which acts as a benchmark for ice-flow models.
+ The new version, WAVI.jl, has also been
+ verified independently against these benchmark experiments.
+ There exists a wide variety of ice sheet models with varying levels
+ of complexity. Examples include (but are certainly not limited to) the
+ Ice Sheet System Model
+ (Larour
+ et al., 2012), the Parallel Ice Sheet Model
+ (Bueler
+ & Brown, 2009), BISICLES
+ (Cornford
+ et al., 2013), Elmer/Ice
+ (Gagliardini
+ et al., 2013), and Úa
+ (Gudmundsson,
+ 2019). Every ice sheet model makes approximations in order to
+ facilitate the numerical solution of the appropriate governing
+ equations; since these equations have no analytic solutions, the
+ intercomparison between ice sheet models is of
+ paramount importance when assessing the trustworthiness of models;
+ WAVI.jl contributes to this community of ice
+ sheet models (a brief overview of the technical differences between
+ such models can be found in
+ (Cornford
+ et al., 2020)). WAVI.jl is also, to our
+ knowledge, the first ice sheet model written entirely in Julia and,
+ alongside other accessible ice sheet models such as IcePack
+ (Shapero
+ et al., 2020), helps to make ice sheet modelling more
+ accessible.
+
+