By Elizabeth Hunke
When compared to the last 1,450 years, the current transformations in Arctic sea ice cover are unprecedented [3]. Sea ice, which is a complicated material, has captured the attention of researchers, forecasters, and business stakeholders alike. This fascination is rooted in sea ice’s impact on everything from global weather patterns to transnational commerce to local wildlife. As such, it carries enormous environmental, economic, and political consequences.
Scientific and software requirements, computational expense, and human support all compete for limited resources and ultimately define the model that is selected for application. The desire to understand and predict sea ice raises the question of whether more complex models—which incorporate a larger number and greater fusion of environmental processes and physics—can address the many concerns. For example, balancing short-term versus long-term predictions and local versus global impacts are significant challenges for the one-size-fits-all approach to model development. A multi-pronged solution is thus necessary.
Questions Grow as Sea Ice Shrinks
There are no “good” or “bad” sea-ice models; instead, there are models that are built to address certain needs. Ship captains must know where ice exists — a very local and short-term need that could lead to dire consequences if not addressed properly. Conversely, a shipping company that plans its routes years in advance must discern the general weather outlook rather than specific storms, the consequences of which are squarely economic. In either case, employing a model that does not address the user’s needs can result in undesirable outcomes.
Ship operations are a classic example of sea-ice model applications, but new issues continue to arise as the ice melts at an increasing pace. The demand for access to natural resources in the Arctic, such as oil and fisheries, will escalate with the melting; search-and-rescue services and environmental hazard avoidance support will also be needed. The peoples of the Arctic, who depend on sea ice for their livelihoods and transportation over ice roads, will feel the impact of alterations in ice cover. Moreover, expanding sovereignty claims in the Arctic Ocean complicate the international response to ice and ocean changes.
Although most sea ice is far from mid-latitude locations like the continental U.S., it still directly affects the weather there. The melting ice and consequent warming Arctic alters the dynamics of the polar vortex — a low-pressure area of swirling cold air over the Arctic region. The vortex’s strength is weakening, thus allowing cold-air outbreaks and atmospheric blocking patterns to wreak havoc on the normally fast-moving mid-latitude weather systems. Global weather patterns are rapidly changing as a result, which presents new challenges for weather forecasting worldwide.
Step one in sussing out a solution for these challenges is modeling when and where changes in sea ice will occur.
The Complexity of Complex Models
Due to the many relevant questions and needs related to Arctic sea ice cover, one may think that complex sea-ice models are more effective. For some applications—especially research—this is often true. The sea-ice models used for most climate projections are based on an ice thickness distribution \(g(h)\), which is the fractional area of a grid cell covered by ice in the range \((h, h+dh)\):
\[ \frac{\partial g}{\partial t} = -\nabla \cdot (g {\bf u}) + \psi - \frac{\partial}{\partial h} (f g) + L. \tag1 \]
The distribution evolves based on the ice’s convergence (\(\bf{u}\) is velocity), mechanical redistribution \(\psi\), thermodynamic growth and melt rate \(f\), and lateral melting \(L\). This is the fundamental equation that underlies sea-ice physics because it integrates all of the relevant processes (see Figure 1) and generates the model’s ultimate product: the ice volume per unit area, \(\int h\,g(h)\,dh\).
Figure 1. Most of the physics in state-of-the-art sea-ice models can be represented within a single grid cell (i.e., a column). Thermodynamics (melting and freezing); hydrologic properties of the ice, such as the presence of liquid water on top of the ice and percolating through it; and morphological changes associated with ice deformation and ridging all contribute to sea-ice evolution within a column. Many of the other processes occur in the atmosphere and ocean components, and the sea-ice model must take them into account as part of its energy balances. The large-scale motion of ice across the ocean’s surface, which models must represent correctly to simulate the planet’s surface reflectivity, is missing in this schematic. Figure courtesy the CICE Consortium.
One of the most important concepts in sea-ice physics is that \(f\) depends critically on ice thickness \(h\). Thinner ice grows and melts much more quickly than thicker ice, and climate grid cells often contain many different sea ice thicknesses. More thin-ice categories are therefore provided in the discretized distribution—that is, more resolution of thinner ice occurs in thickness space—to accurately capture the large variation in \(f\). Climate models require an ice thickness distribution to capture important climate feedback processes, such as the ice-ocean albedo feedback. When open water appears within the ice pack, it absorbs extra solar radiation because of its dark color; as it warms, it melts more ice and exposes more ocean surface to the sun.
Figure 2. 12-hour forecast of sea-ice opening rates (percent per day) associated with divergence and shear from the U.S. Navy ocean-ice model GOFS-3.1 [4]. Sea-ice models can capture fine-scale characteristics, such as ubiquitous cracks in the ice called leads. Large leads are visible from space, and zooming in to smaller regions reveals progressively smaller cracks — a somewhat scale-invariant property. Cracks influence the strength of the sea ice, and current models can represent ice movement and deformation at large and fine scales by incorporating a description of leads’ formation and evolution. Simulated leads might not be oriented correctly, which could present problems for Arctic transportation in or on the ice. Figure courtesy of Richard Allard of the U.S. Naval Research Laboratory at NASA’s Stennis Space Center.
The next generation of sea-ice models are beginning to include a joint thickness and floe-size distribution \(g(r,h)\), where \(r\) is the floe size and \(g\) represents the fractional area of a grid cell that is covered by ice in the ranges \((r, r+dr)\) and \((h, h+dh)\) [5]. In addition to the processes in \((1)\), the joint distribution evolves subject to lateral growth, lateral melt, new ice growth, floe welding, and wave fracture — all of which potentially enhance the modeled albedo feedback. Unfortunately, these models are computationally expensive on 10 km
2 scale meshes and cannot resolve the fine detail required by mariners (typically on scales less than 0.1 km
2). Coarse model resolution can obscure areas where ice is converging and thus poses a danger to ships, and where it is thin and easier to pass through. Nevertheless, research codes produce output that is of interest to operational forecast users, such as ice motion and deformation (see Figure 2).
Atmosphere and ocean models provide data that is used to drive the future predictions of sea-ice models. These models have their own biases, and atmospheric and oceanic processes often dominate the sea-ice physics. For example, summer shortwave and longwave radiation terms are large, roughly balancing each other out; small changes in the atmosphere (such as cloudiness) can shift the balance and lead to greater freezing or melt.
Short-term forecasts are initial-value problems, and forecasters hence incorporate observational data [6] to achieve more realistic results, often using simpler sea-ice models that require fewer resources. This data assimilation process can greatly increase the complexity and cost of modeling systems, which must run multiple times to ascertain a level of uncertainty.
Balancing data assimilation with the physical modeling required for prediction presents a fundamental challenge. A problem from a sea-ice modeler’s perspective is that data assimilation can make the model physics irrelevant, or even change the model’s natural state so much that the modeled physical processes are unrealistic. The timescales between very short-term and long-term simulations are difficult to predict, as they are influenced by both the initial conditions and the physical response to forcing changes over time.
A Future Framework
Climate modelers and operational forecasters have different needs. Modelers require conservation, but data assimilation makes that impossible. And mariners require probabilistic risk analyses, which research models can provide, though not at the requisite level of detail. The evolution of current modeling systems is sufficient for standard climate scales, but the fine-scale forecasts that mariners need demand a modeling revolution.
These communities do share some common needs, including computational efficiency, column physics that are independent of horizontal scale, and uncertainty measures. Unlike a rigid universal model, a modeling framework that includes common solutions to common needs could allow the user to toggle variables and processes on or off based on their applications. In addition, this type of framework provides research code developers with the opportunity to contribute more directly to operational forecasting upgrades, and enables operational centers to provide validation guidance for further model development. The CICE Consortium is based on this concept.
The U.S. Department of Energy is funding the development of a discrete element approach for sea-ice dynamics [7] to model the ice pack at fine spatial scales, leveraging decades of sea-ice column physics advances with the ultimate promise of greater efficiency on new computing architectures. Embedding a discrete element model within selected grid cells of larger-scale sea-ice models could provide higher resolution where it is needed, therefore offering an opportunity for researchers to bridge operational needs for small-scale details and large-scale computational challenges.
This article is based on Elizabeth Hunke's invited talk at the 2020 SIAM Conference on Mathematics of Planet Earth, which took place virtually this August. Hunke's presentation is available on SIAM's YouTube Channel.
Acknowledgments: I extend special thanks to the co-authors of the publication [2] that inspired this article for their insight and perspectives across sea-ice modeling communities during the "Defining a Cutting-edge Future for Sea Ice Modelling” workshop, which took place in Laugarvatn, Iceland in September 2019 [1]. The workshop was supported through the European Union’s Horizon 2020 Research and Innovation programme under grant agreement no. 824084, and by the Energy Exascale Earth System Model project of the U.S. Department of Energy’s Office of Science Biological and Environmental Research.
References
[1] Blockley, E., Vancoppenolle, M., Hunke, E., Bitz, C., Feltham, D., Lemieux, J.F., …, Schroeder, D. (2020) The future of sea ice modelling: Where do we go from here? Bull. Am. Meteor. Soc., 101(8), E1304-E1311.
[2] Hunke, E., Allard, R., Blain, P., Blockley, E., Feltham, D., Fichefet, T., …, Zhang, J. (2020). Should sea-ice modeling tools designed for climate research be used for short-term forecasting? Curr. Clim. Change Rep. Retrieved from https://doi.org/10.1007/s40641-020-00162-y.
[3] Kinnard, C., Zdanowicz, C.M., Fisher, D.A., Isaksson, E., de Vernal, A., & Thompson, L.G. (2011). Reconstructed changes in Arctic sea ice over the past 1,450 years. Nature, 479(7374), 509-512.
[4] Metzger, E.J., Smedstad, O.M., Thoppil, P.G., Hurlburt, H.E., Cummings, J.A., Wallcraft, A.J., …, DeHaan, C.J. (2014). US Navy operational global ocean and Arctic ice prediction systems. Oceanography, 27(3), 32-43.
[5] Roach, L.A., Horvat, C., Dean, S.M., & Bitz, C.M. (2018). An emergent sea ice floe size distribution in a global coupled ocean-sea ice model. J. Geophys. Res. Oceans, 123(6), 4322-4337.
[6] Strong, C., & Golden, K.M. (2017, April 3). Filling the sea ice gap with harmonic functions. SIAM News, 50(3), p. 1.
[7] Turner, A.K. (2017). A new discrete element sea-ice model for Earth system modeling. U.S. Department of Energy Office of Science: Los Alamos National Laboratory. Retrieved from https://www.osti.gov/servlets/purl/1346837.
Elizabeth Hunke holds degrees in applied mathematics and is a scientist in the T-3 Fluid Dynamics and Solid Mechanics Group at Los Alamos National Laboratory (LANL). She has served as a U.S. delegate to the International Arctic Science Committee and was a Rothschild Fellow for the Isaac Newton Institute for Mathematical Sciences. Hunke leads the CICE Consortium and is LANL’s program manager for the U.S. Department of Energy’s Earth and Environmental Systems Sciences Division.