Terr. Atmos. Ocean. Sci., Vol. 21, No. 1, 1-15, February 2010 doi: 10.3319/TAO.2009.03.20.01(IWNOP) One-Dimensional Sea Ice-Ocean Model Applied to SHEBA Experiment in 1997 - 1998 Winter Wen-Yih Sun1, 2, 3, * and Jiun-Dar Chern 4, 5 1 Taiwan Typhoon and Flood Research Institute, Taichung, 40763 Taiwan, ROC 2 Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907-1397, USA 3 Department of Atmospheric Sciences, National Central University, Jhongli, Taiwan, ROC 4 NASA/GSFC Code 613.1, Greenbelt, MD 20771, USA 5 Goddard Earth Sciences and Technology Center, University of Maryland, Baltimore County, Baltimore, MD 21228, USA Received 13 July 2008, accepted 20 March 2009 ABSTRACT A one-dimensional sea ice-ocean model with its application in the Arctic Ocean is presented. The model includes a mixed-layer ocean model, a multi-layer snow/ice model, and the interfaces among atmosphere, snow/sea ice, and sea water. The observational data from the measurements at the ice station of the Surface Heat Budget of the Arctic Ocean (SHEBA) field experiment between November 1997 and January 1998 were used to drive and validate the model. The energy budget of the stand-alone simulations shows that the longwave radiative cooling is mainly balanced by the heat released of freezing at the bottom of the sea-ice. The results also show that the effect of ventilation and blowing snow are required to reproduce the detailed observed surface temperature, thickness of the sea ice, sensible heat flux and upward longwave radiation. Key words: SHEBA, Model, Energy budget Citation: Sun, W. Y. and J. D. Chern, 2010: One-dimensional sea ice-ocean model applied to SHEBA experiment in 1997 - 1998 winter. Terr. Atmos. Ocean. Sci., 21, 1-15, doi: 10.3319/TAO.2009.03.20.01(IWNOP) 1. INTRODUCTION In the Polar Regions the energy budgets of atmosphere water. Most numerical models were applied to simulate the and ocean are strongly affected by the presence of snow/ seasonal or annual variation of sea ice instead of the daily sea ice. As a result of high albedo, snow and sea ice dra- evolution due to the limitation of observational data. matically reduce the amount of shortwave radiative energy Recently, SHEBA (Moritz and Perovich 1996) pro- available at the surface. Because of its low thermal conduc- vided daily observations, including upward and downward tivity, snow/sea ice also significantly restricts heat exchange radiative fluxes, precipitation, wind, humidity, air and snow between the ocean and the atmosphere. The variation of temperatures, sensible heat flux, as well as temperature, sa- sea ice distribution, concentration, and thickness has been linity, and density of sea water in 1997 - 1998. The schematic widely recognized as one of the strongest signals in climate diagram of snow and ice sites on SHEBA is shown in Fig. 1. changes (Houghton et al. 1990). In the past, several sea-ice SHEBA also provided data of snow and sea ice depths. Here, models and observational studies (Semtner 1976; Washing- we present a one-dimensional snow/sea ice-ocean model ton et al. 1976; Mellor 1986; Mellor et al. 1986; Price et al. and comparisons between the model simulations and obser- 1986; Josberger 1987; Maykut and Perovich 1987; Morison vations during November 1997 and January 1998, when the et al. 1987; Omstedt 1990; McPhee 1992; Jin et al. 1994; observed temperature, salinity, and density of sea water are Kiehl et al. 1996; McPhee et al. 1999; and others) have been available at UCAR Joint Office for Science Support (JOSS). presented to study the thermodynamics and dynamics of sea The simulations show that the radiative cooling at surface is ice and interactions among the atmosphere, sea ice and sea mainly balanced by the heat released from freezing at the bottom of sea ice. Sensitivity tests show that simulated sea ice thickness and other fields are strongly affected by snow * Corresponding author thickness. Simulations also reveal that ventilation can affect E-mail: [email protected] the heat transfer and temperature in snow. 2 Wen-Yih Sun & Jiun-Dar Chern where T is water temperature, cw is the specific heat capacity of sea water, Δz is the layer-thickness, S is salinity, tw is the density of seawater, H is the heating, wSll is salinity flux, respectively. δ(φ) is defined as dz()kk=-zz-+12//k 12 (4) Here subscripts k - 1/2 and k + 1/2 stand for the value at the top and bottom of the k-layer. Because the advection is not included, we may include the Newtonian forcing in equations for temperature c()TTobs - Dz and salinity $ -3 a ct()SSobs - Dz o = 1000 Kg m , and coefficients of t and bt are as follows: # -6 at =+(77.5 8.75Tc)10 (5) Fig. 1. Schematic diagram of snow and ice sites on SHEBA floe. # -3 bt =-(77.91 16. 6Tc)10 (6) The multi-layer snow/sea ice-ocean model is based where Tc = T - 273.15 K, Hf - m is the net latent heat released on conservation of energy, mass, and momentum (Sun and from freezing or melting. The heat flux inside the water is Chern 2005). The mixed-layer ocean model is used to pre- dict water temperature, salinity, density, and turbulent ki- ,,a .-,. netic energy, while the snow/sea ice model is used to pre- Hs +-HHpR+-(1 w),sR+-Rkfor = 1/2 H = . dict the thickness, temperature, and heat transfer of snow/ ) wwt ll w $ -+cRwT sk,3for /2 (7) sea ice. Mathematical formulation and physical processes of the mixed-layer ocean model are presented in section 2. The where wTll is the eddy heat flux, αw, albedo at the open formulas of the one-dimensional snow/sea ice model are in water, is a function of solar zenith angle, etc. (Kraus and . section 3. A simple parameterization for snow ventilation is Businger 1994) (hereafter KB), and Rsw is downward short- presented in section 4. The comparisons between the mod- wave radiation inside water. The absorption of shortwave eled simulations and observations are discussed in section 5, radiation inside water may be approximated in the form which is followed by Summary. .. bznna bz Rsww==Rs sfcn//aen (1 - w)Rs ae (8) n n 2. ONE-DIMENSIONAL MIXED-LAYER OCEAN aakk MODEL -1 where (a1, a2) = (0.4, 0.6), and (b1, b2) = (15, 0.5) m (Price The models are applied to simulate the response of the et al. 1986). change of snow, sea ice, and sea water due to the atmospher- The downward and upward longwave radiations at the sur- ic forcing. It is noted that the current velocity is excluded face are due to the lack of observational data and the horizontal pres- sure gradient. It is also noted that shortwave radiation is not . RR,,= fsw air (9) calculated due to the high latitude of SHEBA floe in the winter, although equations are included here for complete- and ness. The equations for a one-dimensional ocean model, which includes 27 layers, are - 4 R, = fsw vTsfc (10) 2()TzD . =+dtHc()ww HTfm- +-c()obs TzD (1) , 2t where R air is downward longwave radiance reaching the sea surface, emittance εsw is 0.98, and Stefan-Boltzmann constant σ is 5.67 × 10-8 W m-2 K-4. Hs, H, , and Hp are the 2()SzD =-dc()wSll+ ()SSobs - D (2) surface sensible heat flux, latent heat flux, and heat trans- 2t z fer associated with precipitation at the surface, respectively (Lynch-Stieglitz 1994, hereafter L-S). They follow the simi- tt ab wc= 0 (.10-+ttTS) (3) larity equations: Sea Ice-Ocean Model for SHEBA 3 Hs ==cwaatiaal l -=cuaati** tiaacchaV ()sfca- i (11) the snow/sea ice model, whenever the sea water is frozen, it was automatically taken as sea ice and resulting in the decrease of the top-layer water. On the other hand, melt of HL, ==vattwqaall-Luva**q sea ice increases the mass of water beneath sea ice accord- t ==LEv evapvLcahVas()qqfc - a (12) ing to Ep. (17). The freezing point of the seawater Tsw (fre) is a function where Va is the wind speed near the surface, and of salinity: t $ cTwwaaPr,.forKT 273 15 Tsw (fre) = 273.15 - 55S, S in kg/kg (Maykut 1985) (18) Hp = 1 (13) (cTsn tnews- now aaPs,.forKT 273 15 Similarity equations are applied at the atmospheric surface in which Pr and Ps are precipitation rate for rain and snow layer to calculate u*, θ*, and q*. -1 (in m s ), cw and csn are specific heat capacity of water The heat flux between sea ice and water was proposed and snow, respectively. Ta is the air temperature, qsfc is by Josberger (1987) and McPhee (1992): 0.98 of the saturated mixing ratio at ocean surface, and -3 tnews- now = 170 kg m is the density of the new fallen snow. wTll=-cuhsws* wm[]TTlswf()re (19) From Eq. (3), we obtain the buoyancy -1 -gpl where chsw = 0.006, u*sw = 0.5 cm s is friction velocity under abttll t0 =-gT gS (14) sea ice, Tml is the mixed layer temperature. u*sw varies from 0 -1 to 2 cm s and Tml - Tsw (fre) varies from 0 to 0.32 K according The eddy fluxes wTll and wSll are derived from to the 1984 Marginal Ice Zone Experiment ( MIZEX 84) and the 1988 Coordinate Eastern Arctic Experiment (CEAREX -1 88)(McPhee 1992; Kiehl et al. 1996). u*sw is 0.88 cm s in 2T wTll=-lT (15a) the Weddell Sea during the Antarctic Zone Flux Experiment cm2z (ANZFLUX)(McPhee et al.