NeverWorld2 初始状态与边界条件

# Initial condition

# Ocean

# Temperature

The initial temperature is a function of both latitude ($\phi$, in radians) and ocean depth ($z$, in meters). The surface temperature $SST^*(\phi)$ is defined as a piecewise cubic function that interpolates between the values ($y$) -1.033, 28.3, and -30°C at latitudes ($\phi$) -67.803, -2.803, and 137.197, respectively. The initial temperature is defined as a function of the surface temperature and depth, $T^*(z,\phi)$, which is defined as

$T^*(z,\phi) = 16 - 12 \cdot \tanh\left(\frac{z-400}{700}\right) \cdot \frac{1-\tanh\left(\frac{500-z}{150}\right)}{2} \cdot \frac{1-\left(\frac{\phi}{75}\right)^2}{0.75} + \left(15 \cdot \left(1-\tanh\left(\frac{z-50}{1500}\right)\right) - 1.4 \cdot \tanh\left(\frac{z-100}{100}\right) + \frac{7 \cdot (1500-z)}{1500}\right) \cdot \frac{SST^*(\phi)}{23.5} \cdot \frac{1-\tanh\left(\frac{z-500}{150}\right)}{2}.$

where $SST^*(\phi)$ is the surface temperature defined above.

# Salinity

The initial salinity is uniform at each layer and defined as a function of depth, $S^*(z)$, which is defined as

$S^*(z) = 34.8 + (0.55 + 1.25 \frac{5000-z}{5000} - 1.62 \tanh\left(\frac{z-60}{650}\right) + 0.2 \tanh\left(\frac{z-35}{100}\right) + 0.2 \tanh\left(\frac{z-1000}{5000}\right)) \cdot \frac{0.2}{1.84} \cdot \frac{1-\tanh\left(\frac{z-500}{150}\right)}{2}.$

# Ice

There is no ice in the initial condition.

# Surface boundary condition

# Ocean

# Wind stress

The wind stress is purely zonal. We construct the wind stress from piecewise cubic functions that interpolate between the values ($y$) -0.05, 0.2, -0.1, -0.02, -0.1, 0.1, and 0 Pa at latitudes ($\phi$) -75, -45, -15, 0, 15, 45, and 70, respectively.
Then we add a seasonal cycle to the wind stress, which are
$\phi_t=\phi+3\cos(2\pi t-0.79)$, where $t$ is the time in years (normalized between 0 and 1 within the year) and $y_t=y/144*(\cos(2\pi t-0.79)+12)^2$

# Heat flux

The thermodynamic forcing also follows a meridional structure and is enforced on the model’s surface through a restoring condition to the predefined annual cycle of apparent temperature, $SST_f$ , defined as a piecewise cubic function that interpolates between the values ($y$) -3, 28.3 and -30°C (corresponding index are $i=1,2,3$) at latitudes ($\phi$) -65, 0 and 140, respectively.
Seasonal variations are added, which are
$\phi_t=\phi+3\cos(2\pi (t-0.558))$ and
$y_t=\left\{\begin{matrix} y-0.5\cos(2\pi (t-0.558)),i=1 \\ y,elsewhere \end{matrix}\right.$

Total surface heat flux (i.e., $Q_{tot}$, split into solar part $Q_{sr}$ and non-solar part $Q_{ns}$, both in $Wm^{-2}$) is in proportion to $SST_f-SST$, with SST the model’s instantaneous surface temperature. $Q_{tot}$ is defined in

$Q_{tot}(\phi,t) =-40\cdot(SST_f(\phi,t)- SST(\phi,t))= Q_{sr}(\phi,t)+Q_{ns}(\phi,t)$

where

$Q_{sr}(\phi,t) =\max(230\cdot\cos(0.019\cdot\phi-0.447\cdot\cos(2\pi(t-0.475))),0)$

# Evaporation minus precipitation (EMP) flux

The EMP flux is purely zonal. We construct the EMP flux from piecewise cubic functions that interpolate between the values ($y$) 0, -0.5, 1.1095246481, -1.2, 1, -0.5, and 0 $Kg/m^2/s/(3.16*10^{-5})$ at latitudes ($\phi$) -75, -55, -20, 5, 30, 50, and 80, respectively.
Then we add a seasonal cycle to the EMP flux, which is
$y_t=y*(1-\cos(2\pi(t-0.475))/8)$.

# Ice

# Wind stress

Set as the same as ocean.

# Heat flux

$SST_f$ is set as -1.9°C on the ice, still compare to model’s instantaneous surface temperature. $Q_{tot}$, $Q_{ns}$ and $Q_{sr}$ are set according to the same formula as ocean.

# Evaporation minus precipitation (EMP) flux

Set as the same as ocean. But $Q_{emp}$ is set as 0 on the ice.

# Others

Snow precip and ice sublimation are set as 0 on the ice.