Influence of topographic interaction and numerical ...

Liyanarachchi Waruna Arampath De Silva and Hajime Yamaguchi, Influence of topographic interaction and numerical diffusion on the Arctic Ocean freshwater modeling, Proc.31st International Symposium on Okhotsk Sea & Sea Ice (Mombetsu-16 Symposium), Mombetsu, Hokkaido, Feb. 21-24, 2016, pp.246-248.

Influence of topographic interaction and numerical diffusion on the Arctic Ocean freshwater modeling Liyanarachchi Waruna Arampath DE SILVA1,2 and Hajime YAMAGUCHI2 1 2

National Institute of Polar Research, Tokyo, Japan The University of Tokyo, Tokyo, Japan

Abstract Liquid freshwater plays a major role in the Arctic Ocean circulation and melting of sea ice. The vertical stratification in the halocline between fresh, cold surface water and salty, warm bottom water limits the upward transfer of heat and thus influence the generation and melting of sea ice. Therefore, reproducing the Arctic freshwater is an important parameter in Arctic Ocean numerical simulations. To reduce the pressure gradient error associated with sigma coordinates numerical models, the bottom topography is smoothed so that the bottom slope between two adjacent grids points less than 0.2. Present study, influence of the smoothness parameter and freshwater content is discussed in details. Further, Eulerian tracers like freshwater fields being subject to advection and mixing by current. Numerical simulation of this advection fields is a difficult task and there are many potential source of errors that can occur. Some numerical advection schemes produced unnecessary numerical diffusion, while other scheme lead to unnecessary numerical oscillations. Therefore, in this study we have investigated the accurate and computationally cheap numerical scheme for simulating the Arctic freshwater. Key words: Arctic Ocean, Freshwater modeling, Topographic interaction INTRODUCTION Past decades of satellite observations have shown a rapid decrease of summer Arctic sea ice extent. Furthermore, the Arctic sea ice cover is now thinner, weaker, and drifts faster. Therefore, the ocean shows an increase in the Arctic freshwater storage and warmer inflows from the Atlantic and Pacific Oceans. Coastal fresh water runoff from Siberia and Greenland has also increased. Liquid freshwater (LFW) plays a major role in the Arctic Ocean circulation and melting of sea ice. The vertical stratification in the halocline between fresh, cold surface water and salty, warm bottom water limits the upward transfer of heat and thus influence the generation and melting of sea ice. Past model studies have shown that LFW influence the large-scale ocean circulations. Therefore, reproducing the Arctic freshwater is an important parameter in Arctic Ocean numerical simulations. However, most of the numerical models cannot reproduce the freshwater behavior in the Arctic Ocean. Therefore, in this study, we analyze the influence of two different numerical factors in the Arctic Ocean freshwater modeling. First, numerical diffusion associated with advection scheme and its influence on freshwater modeling is analyzed. Second, topographic interaction with freshwater modeling is analyzed. To reduce the pressure gradient error associated with sigma coordinates numerical models (Mellor et al. 1998), the bottom topography is smoothed so that the

bottom slope between two adjacent grids points less than 0.2. Present study, influence of the smoothness parameter and freshwater content is discussed in details.

MODEL DESCRIPTION Ice–ocean coupled model used in this study is based on the model developed by De Silva et al. (2015). The ocean model is based on generalized coordinates, the Message Passing Interface version of the Princeton Ocean Model (POM; Mellor et al. 2002). The ice thermodynamics model is based on the zero-layer thermodynamic model proposed by Semtner (1976). The ice rheological model is based on the elastic–viscous–plastic (EVP) rheology proposed by Hunke (2001) and is modified to take ice floe collisions into account, following Sagawa & Yamaguchi (2006). Model domain is constructed using Earth Topography one-minute Gridded Elevation Dataset (ETOPO1). The zonal and meridional grid spacings are approximately 25 × 25 km for the whole Arctic model. To resolve the surface and bottom ocean dynamics, we use the logarithmic distribution of the vertical sigma layers near the top and bottom surfaces. The level-2.5 turbulence closure scheme of Mellor & Yamada (1982) is used for the vertical eddy viscosity and diffusivity. The horizontal eddy viscosity and diffusivity are calculated using a formula proportional to the horizontal grid size and velocity gradients (Smagorinsky 1963); the proportionality coefficient

chosen is 0.2. LFW content is defined (Eq 1.) according to the method proposed by Rabe et al. (2011). Sref − S dz Sref z=0 m h

LFW =

∫

(1)

where S is the observed salinity and Sref =35, h is calculated between the surface and the depth of the 34 isohaline h=z(S=34).

DISCUSSION We demonstrate how the Arctic freshwater is behaved in the numerical model by applying several advection schemes to the icePOM model. Numerical simulation of advection fields is a difficult task and there are many potential sources of errors that can occur. Some numerical advection schemes produced unnecessary numerical diffusion, while other scheme lead to unnecessary numerical oscillations. Therefore, in this study we have investigated the accurate and computationally cheap numerical scheme for simulating the Arctic freshwater. For the comparison we have used four different advections schemes, the first order upstream scheme, the Lax-Wendroff scheme, the Superbee scheme, the Super-C scheme and the central differencing scheme. To explain the freshwater behavior we setup the simple box model with 100m resolutions as shown in Fig1. Initial freshwater field is being advected with prescribed velocity field.

oscillation. By comparing these numerical simulations we have chose the Superbee numerical scheme for icePOM model freshwater advection. We also compared the influence of freshwater accumulation in the Canadian basin by changing the bottom topographic smoothing parameter (r), which defined in Eq. 2. r=

H1 − H 2 H1 + H 2

(2)

where H1 and H2 are the depths of the adjacent two grid points. According to the Mellor et al. (1998) maximum limit of smooth parameter is set to be 0.2. Fig. 2 shows the whole Arctic model bathymetry with different smooth parameter. Lower smooth parameter (0.01) shows very high smoothing of model bathymetry and could not represent the correct steepness of Arctic Ocean basins and coastlines. (b)

(a)

Fig. 2 Whole Arctic model bathymetry (a) smooth parameter r=0.175 (b) smooth parameter r=0.01

To check the influence of both advection scheme and grid smoothness parameter we have conduct four experiments as shown in table 1. Table 1. Experimental setup

Solid boundary

Advection scheme m/s

Distance (km

Central

TVD Superbee

r=0.01

Scenario1

Scenario2

r=0.175

Scenario3

Scenario4

Fig. 1 Numerical domain and velocity field, Green box ) shows the initial freshwater field.

After 9hrs of simulation we have compared the different advection schemes performance. 1st order upstream scheme is extremely numerically diffusive and reduced the amount of freshwater concentration 23%. The lax-Wendrof scheme is less diffusive but shows the numerical oscillation in the freshwater field. The Superbee scheme has no numerical oscillations and shows less diffusive compared to upstream scheme and freshwater concentration reduced to 69% after 9hrs calculation. Super-C scheme produced the similar results to the Superbee scheme but produces numerical

Grid smoothness

Whole Arctic computation is start from PHC3.0 climatological temperature and salinity field. After three years of integration using ERA-interim reanalysis atmospheric data we have compared the freshwater accumulation in Fig 3.

(a)

(b)

grid smoothing associated with sigma coordinate should be done by very carefully.

ACKNOWLEDGEMENTS This study was supported by Green Network of Excellence Program Arctic Climate Change Research Project REFERENCES (c)

(d)

Fig 3. Liquid freshwater content (a) Central advection scheme and r=0.01 (b) TVD and Superbee advection scheme and r=0.01 (c) Central advection scheme and r=0.175 (d) TVD and Superbee advection scheme and r=0.175

After 3 years, Superbee advection scheme and r=0.175 combination give the best freshwater accumulation in the Canadian basin compared to the observation freshwater provide by Rabe et al. (2011).

CONCLUSION This paper has investigated the influence of topographic interaction and advection schemes on freshwater simulation in the Arctic Ocean. TVD scheme with Superbee limiter is the accurate and computationally cheap numerical scheme for simulating the Arctic freshwater. It was also found that

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