Wan-Ling Tseng1,2, Ben-Jei Tsuang3, Noel S. Keenlyside4, Huang-Hsiung Hsu1, & Chia-Ying Tu1

Appendix

Resolving the upper-ocean warm layer improves the simulation of the Madden-Julian Oscillation

Wan-Ling Tseng1,2, Ben-Jei Tsuang3, Noel S. Keenlyside4, Huang-Hsiung Hsu1, & Chia-Ying Tu1

1Research Center for Environmental Changes, Academia Sinica, Taipei, Taiwan.

2GEOMAR | Helmholtz-ZentrumfürOzeanforschung, Kiel, Germany.

3National Chung-Hsing University, Taichung, Taiwan.

4Geophysical Institute and Bjerknes Centre, University of Bergen, Bergen, Norway.

Corresponding author: W.-L. Tseng, Research Center for Environmental Changes, Academia Sinica, Taipei, 115, Taiwan. ()

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The one-column ocean model, Snow-Ice-Thermocline(SIT), is based on Tsuang et al. (2001) thatfollowsthe turbulent kinetic energy (TKE) approach ofGaspar et al. (1990). SIT parameterizesice-formation, the warm-layer effect andthe cool-skin effect,and introducesa surface effective thickness ()to improve the simulation of upper ocean temperature(Tu and Tsuang 2005; Tsuang et al. 2009).The model has been verified at a tropical ocean site(Tu and Tsuang 2005), in the South China Sea (Lan et al. 2010), and in the Caspian Sea (Tsuang et al. 2001).The meltandformation of snow and ice above a water column has been introduced(Tsuang et al. 2001). However, these parts are not utilized in the experiments here.

SIT determines water temperature, salinity, and u, v currents (denoted as variable X) in each depth according to the energy, salinity and momentum budget in a one-column model (e.g., Gaspar et al., 1990) as:

(1)

where (positive upward) is the vertical flux of scalar X, a transport property. It can be temperature (T) (K), horizontal velocities (u, v) (m s-1) or salinity (S) (practical salinity ‰).Variable z is the height (positive upward). The over bar represents a time averaged value. Furthermore, the penetration of solar radiation is parameterized according to a nine-band equation(Paulson and Simpson 1981), where the absorption coefficients of solar radiation are set according to (Fairall et al. 1996).

To simulate the warm layer the vertical resolution of the water column needs to be fine enoughto resolve variations in the upper 10 m of the ocean.Below the cool skin, the vertical flux is parameterized using the classical K approach as:

(2)

wherek and ν are eddy and molecular diffusion coefficients (m2 s-1), respectively. Furthermore k and ν are designated as km and νm for momentum, and as kh and νh for temperature and salinity. The surface net heat flux (latent heat flux + sensible heat flux + net long wave radiation) are used as the upper boundary condition for heat Eq; the wind stress is used as the upper boundary condition for momentum Eq; the net fresh water salinity flux, (evaporation - precipitation - river inflow) multiply by surface salinity, is used as the upper boundary condition for salinity Eq.

To simulate the cool skin effect, the eddy diffusion coefficient for heat, kh, within the cool skin and the eddy diffusion coefficient for momentum, km, within the viscous layer are set to zero: molecular transport is the only mechanism for vertical diffusion of heat and momentum in the cool skin and in the viscous layer, respectively(Hasse 1971; Grassl 1976; Wu 1985). The molecular diffusion coefficient for momentum, , is set at 1.20×10-6 m2 s-1, and that for heat, , is set at 1.34×10-7 m2 s-1, according to (Paulson and Simpson 1981). The thickness of the cool skin δ is determined by (Saunders 1967) as:

(3)

whereλ is a dimensionless constant and is the friction velocity of water (m/s). SIT determines λ according to (Artale et al. 2002).Below the cool skin and the viscous layer, eddy diffusivity is determined according to a TKE-mixing length approach(Gaspar et al. 1990).

To correct bulk SST computed using conventional discretization to skin SST we introduce a surface effective thickness () (Tu 2006; Tu and Tsuang 2014). The effective thickness is a function of the surface layer, which is added to the top of the uppermost numerical layer of the conventional discretization (Fig. A1). This surface layer has a physical thickness d of 0.25 h1, i.e., d = 0.25 h1. The net heat flux absorbed within the surface layer is G0+Rsn[F(z0)-F(z0-d)]+G0,1. To determine the upper skin temperature T0 (not the column-mean temperature) of the surface layer, T0 is parameterized as:

(4)

Where he is the effective thickness (m) for heat of the surface layer. Note that the first term on the right-hand side of the above equation is a cooling term since the non-solar surface heat flux G0 is usually upward (Saunders 1967; Dalu and Purini 1982; Soloviev and Schlüssel 1994; Fairall et al. 1996). The second term is a heating term due to the absorption of shortwave solar radiation (Fairall et al. 1996). The third term is the vertical heat flux due to molecular (if within the skin layer) or eddy (if below the skin layer) diffusivity. Eq. (4) is proposed by this study to calculate the skin temperature T0. The effective thickness is a function of heat conductivity. It is derived analytically to reproduce the diurnal fluctuation of skin temperature if the fluctuation can be described as a cosine function in time (Tsuang et al. 2009). The effective thickness is derived to be:

(5)

where is the angular velocity of the earth with respect to the sun (=2/86400 s-1). Note that the upper temperature T0 of the skin layer is the so-called sea surface temperature (SST). Once SST is determined, we can determine heat fluxes between the atmosphere and ocean for the next model timestep. Then, the error due to incorrect usage of T1 for T0 to determine heat exchange between the atmosphere and ocean in the conventional approach is corrected.

Overall, SIT simulates the SST and upper ocean temperature variations, including the cool-skin and warm-layer mechanisms. In the finest resolution experiments, SIT has 42 vertical layers, and with 12 in the upper 10m. Simulated water temperaturesare at surface,and grid cells with center atdepth of0.05mm,1 m, 2 m, 3 m, 4 m, 5 m, 6 m, 7 m, 8 m, 9 m, 10 m, 16.8 m, 29.5 m, 43.6 m, 59.3 m, 76.9 m, 96.8 m, 119.4 m, 145.3 m, 174.9 m, 208.9 m, 248.3 m, 293.8 m, 346.8 m, 408.4 m, 480.2 m, 564.3 m, 662.6 m, 779.7 m, 913.1 m, 1072 m, 1258.8 m, 1478.6 m, 1737.3m, 2042m, 2401m, 2824.4m, 3323.6m, 3912.4m, 4607.1mand the ocean seabed. The resolution in the upper 10 m is very fine in order to capture the upper ocean warm layer, and there is a layer at 0.05 mm and resolving a corresponding effective thicknessfor reproducing the cool skin of the ocean surface.For the C-17m we deleted layer from 0.05mm to 10 m and C-59m we deleted layer from0.05mm to 43.6 m.

In addition, a nudging technique is used to correct the bias of calculated ocean temperature and salinity (denoted as X) at layers deeper than 10 m depth as:

(6)

where is calculated X at depth k at timestepn+1; is calculated by Eq. (1) at timestep n+1; is observed at timestep n+1; is a relaxation factor. It should be within 0 and 1. When settingat 0, the calculated Xis determined by Eq. 1 only; when settingat 1, the calculated Xis restored back to observed X every time step. The relaxation factor is parameterized as:

(7)

Where is the timescale for nudging; is the timestep. To account for neglected horizontal processes, the ocean is weakly nudged with a 30-day time scale for depths within 10-100 m (i.e., and 1-day time scale for depths > 100 m (i.e., ) to the observed climatological ocean temperature; there is no nudging within the upper 10-m depth.

Reference

Artale V, Iudicone D, Santoleri R, Rupolo V, Marullo S, D'Ortenzio F (2002) Role of surface fluxes in ocean general circulation models using satellite sea surface temperature: Validation of and sensitivity to the forcing frequency of the Mediterranean thermohaline circulation. J Geophys Res 107 (C8):29-21-29-24

Dalu G, Purini R (1982) The diurnal thermocline due to buoyant convection. Quarterly Journal of the Royal Meteorological Society 108 (458):929-935

Fairall C, Bradley EF, Godfrey J, Wick G, Edson JB, Young G (1996) Cool-skin and warm-layer effects on sea surface temperature. Journal of Geophysical research 101 (C1):1295-1308

Gaspar P, Gregoris Y, Lefevre J-M (1990) A simple eddy kinetic energy model for simulations of the oceanic vertical mixing: Tests at station Papa and long-term upper ocean study site. J Geophys Res 95 (C9):16179-16193

Grassl H (1976) The dependence of the measured cool skin of the ocean on wind stress and total heat flux. Boundary-Layer Meteorology 10 (4):465-474

Hasse L (1971) The sea surface temperature deviation and the heat flow at the sea-air interface. Boundary-Layer Meteorology 1 (3):368-379

Lan Y-Y, Tsuang B-J, Tu C-Y, Wu T-Y, Chen Y-L, Hsieh C-I (2010) Observation and simulation of meteorology and surface energy components over the South China Sea in summers of 2004 and 2006. Terrestrial, Atmospheric and Oceanic Sciences 21 (2):325-342

Paulson CA, Simpson JJ (1981) The temperature difference across the cool skin of the ocean. J Geophys Res 86 (C11):11044-11054

Saunders PM (1967) The temperature at the ocean-air interface. Journal of the Atmospheric Sciences 24 (3):269-273

Soloviev AV, Schlüssel P (1994) Parameterization of the cool skin of the ocean and of the air-ocean gas transfer on the basis of modeling surface renewal. Journal of Physical Oceanography 24 (6):1339-1346

Tsuang B-J, Tu C-Y, Arpe K (2001) Lake parameterization for climate models. Max-Planck-Institute for Meteorology Rept 316:72pp

Tsuang B-J, Tu C-Y, Tsai J-L, Dracup JA, Arpe K, Meyers T (2009) A more accurate scheme for calculating Earths-skin temperature. Climate Dynamics 32 (2-3):251-272

Tu C-Y (2006) Sea Surfce Temperature Simulation in Climate Model. National Chung Hsing University,

Tu C-Y, Tsuang B-J (2005) Cool-skin simulation by a one-column ocean model. Geophysical research letters 32 (22)

Tu C-Y, Tsuang B-J (2014) Numerical discretization for sea surface temperature simulation in a turbulent kinetic energy ocean model.

Wu J (1985) On the cool skin of the ocean. Boundary-Layer Meteorology 31 (2):203-207

FigureA1. Left figure is the schema of the surface effective thickness of an ideal surface with depth d. is the skin temperature and is the averaged temperature of the uppermost layer of the water with a thickness of . Note that the shaded area denotes the energy stored from the surface to depth d, which is close to the rectangular area. The mean temperature thus calculated from the rectangular area, the open circle beneath, is representative of the skin temperature. denotes the energy flux between layer i and j. Right figure is the schematic of the conventional discretization with a thickness of for the uppermost layer, representing only the bulk SST.