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MEOPAR Winter School in Environmental Modeling Notes

Participant intros

Jenna Joyce: UoOttawa w/ Jackie Dawson

  • Shipping in the Arctic (Corridors)
  • Corridors & Environment/Culturally significant areas coexistence

##Sea Ice Modeling

Important sea ice processes

  • Sea ice growth (open water + basal) -- once cover is established, growth happens at the bottom
  • Sea ice melt (surface + basal)
  • Sea ice dynamics (~2% of wind speed) -- Ice Motion in the Arctic Basin -- International Arctic Buoy Program -- Observed sea ice deformations: RGPS obs -- Pressure ridges from convergence+shear -> Bad for shipping. -- sea ice deformations affects sea ice thickness through formation of ridges and leads -- Heat flux through new leads can be 1-2 orders of magnitude higher than over thick ice (Maykut, 1978) -- 25-40% of ice formation occurs in leads.

Represetation of these processes in sea ice models

  • Continuum approximation: easy for ocean, hard for sea ice because of ice floes
  • Lagrangian modeling of ice flows, complex and expensive to model
  • Eulerian model: Ice Thickness distribution -> simpler/more efficient One/many thickness category models. Multi-thickness category allow better representation of growth and failure (ice is only as strong as the thinnest ice) Discretize the concentration between thickness categories

Sea ice momentum equation

  • Inertial
  • Coriolis
  • air stress
  • water stress
  • SSH tilt: sliding ice!
  • rheology
Air and water stresses

Skin vs Form drag. Can ~ form drag by having stronger skin drag, but people are developing proper form drag approx

Sea ice rheologies
  • Mostly VP model, but there are other alternatives
  • Elastic strain + plastic deformations Justification for a plastic formulation:
  • Deformations are sporadic
  • Deformations are irreversible
  • Sea ice deforms like other granular material

Sea ice resists compression then fails, can maybe resist a little bit of tension, but not much because of lots of randomly oriented craks

For small stress, ice is "honey times a million": really viscous and moves very little For large stress, ice fails and gets deformed

In 2D:

  • Shear + convergence: Pressure ridge
  • Shear + divergence: Leads

If concentration is small enough, rheology becomes negligible and the momentum balance is typically between air and ocean.

  • Hibler P = P* \bar{h} exp(-C(1-A)) by intuition
  • Rothrock: From first princibles

but Ungermann 2017 have better results using Hibler....

The ITD equation

  • Transport
  • Redistribution
  • Vertical growth or melt
  • Lateral melt

Redistribution to prevent concentrations to go >1 by advection.

Calculation of vertical growth/melt
  • Melt on top depending on radiation + air heat flux. If calculated T_s > 0, keep it at 0 and use the heat to melt ice.
  • Growth or melt at the bottom depending on heat flux differences and ice heat capacity.

Solve the vertical heat diffusion equation to get temperatures. Need conductivity

Snow and ice are very good insulator. 30cm snow is enough to slow ice growth to thick (~2m) ice rates for thin ice.

Most of the salt is rejected during ice formation. -> Drive convective mixing Rest of it is in brine pockets, which affects heat properties so it should be represented, but it is usually prescribed instead.

Numerical implementations

Ice velocity and thickness are coupled nonlinear equations

Use discretized equations to solve it. Ex.: CICE (B-Grid), LIM and MITGCM (C-Grid)

Explicit: Solve for new velocity field using known values: \Delta t \leq \frac{m \Delta x2}{2 \zeta} --> time step of 0.01s for 10km resolution. Useless

Implicit: Solve for new velocity field using unknown, new values. Solve big matrix-vectors system. OR Use EVP to add fake elastic waves and damp them out every time step. Can be noisy if residual elastic waves persist.

Advection and the CFL condition

~1m/s velocity with 10km resolution: 167 min time step BUT there can be a plastic wave propagating through solid ice at 25m/s which needs smaller time step to resolve, otherwise it blows up.

Splitting in time by solving momentum and then advecting ice parameters. Would need to do both together. IMEX approach to do both

Recent model developments

Drag representation

Replace skin drag with increased roughness with form drag and proper current drag for the thickness of ocean cells. (F. Roy 2015)

Simulations of landfast ice

Pressure ridge grounding holds ice on the coast. (See: Mahoney et al. 2007, Lemieux et al, 2015) Landfast ice off Laptev sea from grounding of sea ice ridges Landfast ice off ?? sea from tensile strength Landfast ice off Greenland from grounding of icebergs

Wave-ice interactions

(See Dumon et al., JGR, 2011) g(h) thickness distribution says nothing about floes j(h,D) is the distribution of thickness and "diameter of floes"

Salt in ice

(See Vancopenolle et al, 2009)

Albedo of ice and melt ponds

(See Flocco et al, 2010 and Hunke et al, 2013)

Sea ice models in short-term and subseasonal forecasting

Important for:

  • Navigation:
    • ice conditions
    • ice pressure
  • Emergency response:
    • SAR
    • Oil spills
  • Planning of human activities
  • Weather forecasting:
    • Traditionally use a static ice cover
    • Coupled forecasting: Atm-Ocn, Ice-Ocn, soon global Atm-Ice-Ocn, already have GSL


  • GIOPS (Global Ice Ocean Prediction System): ~15km resolution in the Arctic
  • RIOPS (Regional Ice Ocean Prediction System): ~2-8km resolution in the Arctic
  • ENGIOPS (ENsemble GIOPS): 21 models Only have a concentration analysis, no thickness but working on it.

Verification methods

  • Short term forecast, you can assess shortly, no wait
  • Forecast vs Persistence Challenging in the melting season because initialization has difficulty distinguishing melt ponds and open water. Point by point metrics are often unreliable
  • overly penalize high resolution
  • sensitive to double penalty

Modeling challenges for sea ice

  • Ice parameterizations: ridging scheme, ice strength, rheology
  • Better representation of MIZ processes
  • Is the problem well formulated as resolution increases?
  • Numerical issues and coupled framework

Hunke et al., 2010 for a good review of sea ice modeling NSIDC data for comparison