A **P**an-Arctic **I**ce-**O**cean **M**odeling and **A**ssimilation **S**ystem (**PIOMAS**) is used for this project. PIOMAS is a coupled Parallel Ocean and sea Ice Model (POIM, Zhang and Rothrock 2003) with capabilities of assimilating ice concentration and velocity data. It is formulated in a generalized orthogonal curvilinear coordinate (GOCC) system and designed to run on computers with a single processor or massively parallel processors. PIOMAS couples the Parallel Ocean Program (POP) with a thickness and enthalpy distribution (TED) sea-ice model. The POP model is developed at the Los Alamos National Laboratory.

The TED sea-ice model is a dynamic thermodynamic model that also explicitly simulates sea-ice ridging. The model originates from the Thorndike et al. (1975) subgrid-scale ice thickness distribution theory and is enriched by subgrid-scale ice enthalpy distribution theory (Zhang and Rothrock, 2001). It has 12 subgrid-scale categories each for ice thickness, ice enthalpy, and snow. This multicategory TED model consists of seven main components: a teardrop viscous-plastic ice rheology from Zhang and Rothrock (2005) that determines the relationship between ice internal stress and ice deformation (Hibler 1979), a mechanical redistribution function that determines ice ridging (Thorndike et al. 1975; Rothrock, 1975; Hibler, 1980), a momentum equation that determines ice motion, a heat equation that determines ice growth/decay and ice temperature, an ice thickness distribution equation that conserves ice mass (Thorndike et al. 1975; Hibler, 1980), an ice enthalpy distribution equation that conserves ice thermal energy (Zhang and Rothrock, 2001), and a snow thickness distribution equation that conserves snow mass (Flato and Hibler, 1995). The ice momentum equation is solved using Zhang and Hibler’s (1997) ice dynamics model that employs a line successive relaxation technique with a tridiagonal matrix solver, which has been found to be particularly useful for parallel computing (Zhang and Rothrock, 2003). The heat equation is solved over each ice thickness category using a modified three-layer thermodynamic model (Winton, 2000). The latest PIOMAS has the capabilities of simulating 12-category subgrid-scale sea ice floe size distribution (Zhang et al., 2015, 2016) and melt pond distribution (Zhang et al., 2018). The configuration of the finite-difference grid of PIOMAS is shown below.

The model grid is a stretched GOCC grid with the northern grid pole displaced into Greenland. This causes the model to have its highest resolution in the Greenland Sea, Baffin Bay, and the eastern Canadian Archipelago. This lets the model have a reasonably good connection between the Arctic Ocean and the Atlantic Ocean via the Greenland-Iceland-Norwegian (GIN) Sea and the Labrador Sea. The mean horizontal resolution is 22 km for the Arctic, Barents, and GIN (Greenland-Iceland-Norwegian) seas, and Baffin Bay. The model is one-way nested to a global POIM (GIOMAS) by imposing open boundary conditions along the southern boundaries (~ 43^{o}N). Monthly output from GIOMAS is used for the open boundary conditions. The model was driven by the NCEP/NCAR reanalysis data. Additional PIOMAS information and latest analysis can be found at https://psc.apl.uw.edu/research/projects/arctic-sea-ice-volume-anomaly/. PIOMAS sea ice output has been widely used.

## References

Flato, G. M., and W. D. Hibler, III, 1995: Ridging and strength in modeling the thickness distribution of Arctic sea ice. J. Geophys. Res., 100, 18,611-18,626.

Hibler, W. D. III, 1979: A dynamic thermodynamic sea ice model. J. Phys. Oceanogr., 9, 815-846.

Hibler, W. D. III, 1980: Modeling a variable thickness sea ice cover. Mon. Wea. Rev., 108, 1943-1973.

Thorndike, A. S., D. A. Rothrock, G. A. Maykut, and R. Colony, 1975: The thickness distribution of sea ice. J. Geophys. Res., 80, 4501-4513.

Winton, M., 2000: A reformulated three-layer sea ice model. J. Atmos. Ocean. Tech., 17, 525-531.

Zhang, J. and W.D. Hibler: On an efficient numerical method for modeling sea ice dynamics, *J. Geophys. Res.*, *102*, 8691-8702, 1997.

Zhang, J., and D.A. Rothrock: A thickness and enthalpy distribution sea-ice model, *J. Phys. Oceanogr*., *31*, 2986-3001, 2001.

Zhang, J., and D.A. Rothrock: Modeling global sea ice with a thickness and enthalpy distribution model in generalized curvilinear coordinates, *Mon. Wea. Rev*., *131(5)*, 681-697, 2003.

Zhang, J., and D.A. Rothrock, The effect of sea-ice rheology in numerical investigations of climate, *J*. *Geophys. Res., 110*, C08014, doi:10.1029/2004JC002599, 2005.

Zhang, J., A. Schweiger, M. Steele, and H. Stern, Sea ice floe size distribution in the marginal ice zone: Theory and numerical experiments, *J. Geophys. Res. Oceans*, *120*, doi:10.1002/2015JC010770, 2015.

Zhang, J., H. Stern, B. Hwang, A. Schweiger, M. Steele, M. Stark, and H.C. Graber, Modeling the seasonal evolution of the Arctic sea ice floe size distribution, *Elementa*, *4:*000126, doi:10.12952/journal.elementa.000126, 2016.

Zhang, J., A. Schweiger, M. Webster, B. Light, M. Steele, C. Ashjian, R. Campbell, and Y. Spitz, Melt pond conditions on declining Arctic sea ice over 1979-2016: Model development, validation, and results, J. Geophys. Res. Oceans, 123, https://doi.org/10.1029/2018JC014298, 2018.