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1. QAGU PUBLICATIONS Journal of Geophysical Research Supporting Information for Simulation of the Melt Season using a Resolved Sea Ice Model with Snow Cover and Melt Ponds Eric D Skyllingstad Karen M Shell Lee Collins College of Earth Ocean and Atmospheric Sciences Oregon State University Corvallis OR 97331 Chris Polashenski Cold Regions Research and Engineering Laboratory U S Army Engineer Research and Development Center Hanover NH 03755 Contents of this file Text S1 Introduction This supplement provides a detailed description of the sea ice model used in the main paper Text S1 1 Model Description The model combines a three dimensional grid structure for ice brine state variables with a horizontal two dimensional snow and ice height field similar to the Scott and Feltham 2010 model Each grid point is filled with some combination of ice and snow liquid water brine and air depending on the snow ice and water table heights For brine filled ice the ice internal structure is assumed to follow the mushy layer approach presented in Feltham et al 2006 where each ice grid volume is divided into fresh water ice with ice volume fraction brine with salinity S if the volume is below the water line or ice and air Grid cells on the surface that are completely water filled and do not have an ice fraction are considered melt pond cells Snow and ice are treated the same thermodynamically in the model but ha2. ace air temperature relative humidity and wind speed from the ARM site are used to compute sensible and latent heat fluxes from bulk formula 1 p C CyU T ma 1 Fi PaL CnU q q where pa 1 29 kg m is the air density Cp 1004 J K kg is the air heat capacity Cu 1 5 x 10 is the transfer coefficient for heat and moisture U is the measured wind speed Ta is the measured atmospheric temperature from 2 0 m height Ly 2 5 x 10 J kg is the latent heat of vaporization for water gs is the saturation specific humidity corresponding to a temperature of 77 and qa is the measured specific humidity from 2 0 m height see Stull 1988 pg 262 References Hunke E C and W H Lipscomb 2013 CICE the Los Alamos Sea Ice Model Documentation and Software User s Manual version 5 0 Tech Rep LA CC 06 012 Los Alamos National Laboratory Los Alamos New Mexico Notz D and M G Worster 2006 A 1 D enthalpy model of sea ice Ann Glaciol 44 123 128 Skyllingstad E D and C A Paulson 2007 A numerical study of melt ponds J Geophys Res 112 C08015 doi 10 1029 2006JC003729 Taylor P D and D L Feltham 2004 A model of melt pond evolution on sea ice J Geophys Res 109 C12007 doi 10 1029 2004JC002361 Stull R B 1988 An Introduction to Boundary Layer Meteorology 666 pp Kluwer Acad Dordrecht Netherlands Wettlaufer J S M G Worster and H E Huppert 2000 Solidi
3. fication of leads Theory experiment and field observations J Geophys Res 105 C1 1123 1134
4. ll temperature Melting or freezing is then diagnosed by calculating a new grid cell solid fraction using g u 3 which assumes that the mixture of ice and brine are always at the freezing temperature Thus as grid cell heat content changes ice fraction and brine concentration are adjusted to maintain an overall temperature at the freezing point For grid cells with bulk salinity lt 0 02 psu we discard the salinity and consider the grid cell as a mixture of pure ice and water In this case the temperature is held fixed at O C and heating is used to either freeze or melt the ice fraction using OPN yy SE D Eat Fat B 7 ian F V k VT zo Zu z m l 4 Each horizontal grid point consists of N equally spaced Az snow ice levels plus a top snow ice layer of height Aziop which sum to his When the surface is not covered by a pond a slightly different ice budget is used in this top cell where heating is assumed to decrease the total thickness his using Ah F F F oT sh Ih Jla 5 AZ ee ME 7 fian V k VT _ 7 where h NAz Az and Az lt Az The ratio of density accounts for the greater volume per unit mass of ice when converting to thickness change When Azp is less than 0 01Az or is less than 0 02 then the ice volume contained in the top layer Az is added to the ice volume of the Nth grid cell just below the top and the number of vertical grid points N is red
5. reased melt water ponds are assumed to be fresh The pond water temperature is governed by A e eat Oz d x y l 9 where dp x y is the pond depth hp his at each grid point and heat conduction through the pond bottom into the top ice snow grid point is governed by 6 Shortwave flux divergence is calculated across the vertical depth of the pond In this study our primary interest is in modeling the early summer melt season so ponds are typically ice free Consequently we do not model pond ice formation in cases with strong surface cooling but conserve heat by allowing the pond temperature to temporarily fall below freezing As indicated in Skyllingstad et al 2007 wind stirring of pond water typically leads to well mixed pond water and uniform pond side bottom melting Here we use a simple averaging approach to distribute temperature within contiguous pond covered grid points x y l I Sa i j ee x y l gt Y 1 6 Dd ij 10 dl where Tp x y is the depth averaged pond temperature Averaging is over a nine point 3 by 3 stencil and performed for each time step 4 Heating and Cooling Terms The top layer absorbs all downwelling longwave radiation and upwelling longwave radiation is calculated with the Stefan Boltzman equation ale 4 Riy OT g gt 9 where o 5 67 x 10 W m K and T is the surface temperature ice pond or snow simulated by the model at each grid point Input values of surf
6. rface Subscripts s and denote solid and liquid phases respectively The surface fluxes Fsh F n and Fw are zero except in the top layer and are divided by the vertical grid spacing Az we note below that for conditions where the net flux is cooling the surface flux divergence is calculated over 3 vertical grid points to avoid unrealistic cold surface temperatures For simplicity we model the vertical transport of brine through a Darcy velocity and ignore lateral transport of heat and other brine properties Melt water in the model is assumed to move instantly across the domain so that the water table is always at a uniform level Ap with the minimum water table height set to sea level hy When the grid cell below the watertable the grid cell heat capacity cm and conductivity km are set following Wettlaufer et al 2000 pe pe 9 ec 1 4 k k o k 1 2 where pc 1 883 x 10 J m K pc 4 185 x 10 J m K ks 2 W m Kh and ki 0 5 W mt Kt When the ice void fraction is filled with air the second terms in the heat capacity and conductivity equations 2 are zero and these terms are scaled accordingly when the grid cell has a mixture of ice liquid and air Pond cells use only the liquid phase constants For simplicity we hold the heat capacity and conductivity constant over each time step At For grid points that are mixture of ice and brine eq 1 is used to either warm or cool the grid ce
7. uced to N 1 and Az Az If the top grid cell is covered by a pond then 5 is reduced to Pel _ Ah DL Pan V knVT 11 2 6 For grid cells above the water table height decreases in void fraction are added to the grid point melt water budget mw defined in equation 3 in the main text When the net surface flux generates cooling we average the surface flux divergence over the top 3 vertical grid cells to avoid excessive cooling in the top fractional grid cell When internal values of drop below 0 05 then the grid cell and the adjacent grid cell one level above are combined Dei gt 0 5 G1 h Site 0 5 S Sia 7 and the combine cell temperature is set to either the freezing temperature if the cells are brine filled or zero 3 Pond Thermodynamics Melting of sea ice below and adjacent to ponds is calculated using exchange rates following McPhee et al 1987 which yield an ice melting velocity wice dependent on the pond temperature and ice salinity We assume that ponds melt at the same rate both vertically and laterally and we partition the pond temperature change from melting accordingly Melting of sea ice along the pond edge is calculated by reducing the ice fraction of the adjacent grid cell by w w A Ice S At Ice At 8 p 7 e g where As is grid cell side area and Vg is the grid cell volume This term is added to Eq 4 for the adjacent grid cell accounting for inc
8. ve different properties in the radiative transfer scheme We assume that the void fraction 1 of grid cells that are below the water table or sea level when there is no flooding are always filled with brine or fresh water 2 Ice Thermodynamics Different heat budget equations are used in the model depending on the location of the grid cell relative to the water table the salinity of the brine in the cell and if the grid cell vertical location contains the top of the snow ice his For grid cells that are below the water table with bulk salinity S S 1 gt 0 02 psu we use a budget equation derived by Feltham et al 2006 T S Ts Sun OT pL oT _ oo r s r Oh FS Oz 0 F Pr F V k VT zU 2 E 1 where pc m represents the combined densities p and heat capacities c for the ice and brine mixture pc represents the density and heat capacity for the brine T 5 0 0545 C is the freezing temperature for brine km is the mixture conductivity Isw z is the shortwave radiation flux calculated from the CICE radiative transfer scheme see main text ps is the ice density L 3 34 x 10 J kg is the latent heat of fusion Wdarcy 18 a velocity representing vertical brine transport defined in more detail in the main text Fsn Fin and Fiw are surface fluxes of sensible heat latent heat and infrared radiation respectively Positive upward fluxes indicate heat loss from the su
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