28.2.5 linear_tstar

For restoring the surface buoyancy in idealized ocean models using temperature alone, it is often useful to employ a linear profile. The papers by Cox and Bryan (1984) and Cox (1985) used the density profile

 

$$\sigma^{*} = 23 + \frac{6 \vert\phi\vert}{65}$$ (28.10)

where $\phi$ is latitude in degrees and $\sigma = 1000 \, (\rho - 1)$. The profile is symmetric across the equator. For MOM, it is necessary to translate this density profile into a temperature. For this purpose, assume a linear equation of state as discussed in Sections 15.1.2.4 and 15.1.2.4

$$\rho = \rho_{o} \, [1 - \alpha \, ( T - T_{o})],$$ (28.11)

which implies

$$T_{o} + \frac{\sigma_{o} -\sigma^{*}}{1000 \, \alpha \rho_{o}}.$$ T^* = (28.12)

The following reference values are chosen (see Appendix 3 of Gill 1982)

$$19^{\circ}C$$ T_o = (28.13)

$$35 \mbox{psu}$$ S_o = (28.14)

$$0 \mbox{dbar}$$ p_o = (28.15)

$$\rho_{o} 1.025022 \; g/cm^{3}$$ = (28.16)

$$\sigma_{o} 1000 \, (\rho_{o}-1) = 25.022$$ = (28.17)

$$\alpha 2489 \times 10^{-7} \; \mbox{}^{\circ}K^{-1}.$$ = (28.18)

As a result,

$$26.93 - .3618 \, \vert\phi\vert,$$ T^* = (28.19)

where again, $\phi$ is in degrees latitude, and T^* is in Celcius. With $\sigma^{*}$ given by (28.10), the restoring temperature takes the values

$$T^{*}(\phi = 0) 26.9^{\circ}C$$ = (28.20)

$$T^{*}(\phi = 65) 3.4^{\circ}C.$$ = (28.21)

Figure 28.2 shows the temperature profile across the northern hemisphere obtained with this option. This profile can easily be changed in the model code (routine setvbc.F).