35.1.9.1 dm_taper

Option dm_taper enables the hyperbolic tangent re-scaling for steep slopes by Danabasoglu and McWilliams (1996). The tapering is given by

$$taper = 0.5\left[1-\tanh \left( \frac{\vert S\vert-del^{dm}}{S^{dm}} \right) \right],$$ (35.75)

where S is the neutral direction slope, and del^dm and S^dm are namelist input parameters. These three tunable parameters determine the details of this tapering scheme. One should exercise some care in choosing these coefficients in order to maintain model stability.

Since the $\tanh$ function is so quickly changing, there is no need to provide a slope check if-test with dm_taper. Instead, the diffusivities are always defined according to

$$(A_{I}, \kappa, B)_{effective} = taper * (A_{I}, \kappa, B)_{un-scaled}.$$ (35.76)

With the GFDL Cray T90, a strange code bug is associated with the $\tanh$ function. Whenever $\tanh$ is called with an argument larger than roughly 19, an overflow results and the model is brought down. The $\tanh$ of numbers larger than 19 are quite close to unity, and so a fix for this bug has been implemented so that the argument never gets too large. Those wishing to use option dm_taper who do not share such silly problems are certainly encouraged to remove this fix in order to save in computation time. With the current code, the option dm_taper is slower than gkw_taper.

Note that neither gkw_taper nor dm_taper apply to option full_tensor, which is re-scaled as given in Section .