Theory, Modeling, and Impact of the Sea Ice Floe Size Distribution

Abstract

This dissertation explores the evolution of floes, the individual pieces that comprise Earth's sea ice cover, from the perspective of the local and regional climatic evolution of Earth's polar areas. Each individual floe is identified with its horizontal size and thickness. The distribution of floe sizes and thicknesses is an important climate variable, determining the response of sea ice to atmospheric and oceanic forcing, affecting feedbacks in the coupled ice-ocean-atmosphere system, and controlling sea ice melting rates. Modern climate models do not simulate the evolution of floes, nor the floe size distribution. I first present a predictive model for the joint statistical distribution of floe sizes and thicknesses (FSTD). This model simulates the response of floes to thermodynamic forcing (melting/freezing), collisions between floes, and fracture due to ocean surface waves. The representation of each process is based on analytic conservation laws derived for the FSTD, considering that sea ice is a collection of floes. The model is tested under different forcing scenarios to establish these conservation properties and demonstrate its usability in future climate studies. To compare this model evolution to observations, I analyze the results of simulations of the FSTD, coupled to a mixed-layer ocean model. A long-held paradigm in sea ice modeling is that the FSTD is scale-invariant (i.e., represented by a power law) in floe size. Yet this is contradicted by the observational record: when the range of resolved floe sizes is large, observations are fit to two power laws, covering different size ranges, and with different slopes. Using this coupled framework, I show the emergence of such ``double power-law'' distributions, due to the interaction of different processes that act a different floe length scales. In some cases, such as when a steady-state develops between the advection of ice into and out of the domain and collisions between floes, I show the emergence of a power-law FSTD. Generally, the FSTD does not evolve as a power law, and I indicate how errors caused by relying on a power-law fit may lead to significant biases in estimating sea ice evolution. I finally show explicitly how the floe size distribution affects sea ice melt rates, and therefore climate response. I study the relationship between ocean eddies and floe size, by considering how sub-mesoscale ocean eddies may be energized at the edge of individual sea ice floes. Using idealized coupled model studies, I demonstrate that sharp gradients in the ocean's temperature and salinity may develop at the edge of melting floes. These gradients are unstable to baroclinic instabilities that develop into ocean eddies, mixing heat and salinity laterally and vertically with eddy length scales on the order of several kilometers. The horizontal mixing by these eddies brings warm water to under the edge of individual floes and melts them at a rate that depends on the floe perimeter, and therefore on floe size. For model experiments that begin with the same ice concentration, volume, albedo, and external forcing, but with floe sizes ranging from 1km to 50 km, the time it takes to melt ice can vary by several months, showing that an initial ice cover with more floes (smaller floe size) melts faster. This demonstrates that a model of the FSTD indeed needs to be included in climate models to more accurately represent the response of sea ice to climate change.