Sponge layer feedbacks in middle‐atmosphere models

Middle‐atmosphere models commonly employ a sponge layer in the upper portion of their domain. It is shown that the relaxational nature of the sponge allows it to couple to the dynamics at lower levels in an artificial manner. In particular, the long‐term zonally symmetric response to an imposed extratropical local force or diabatic heating is shown to induce a drag force in the sponge that modifies the response expected from the “downward control” arguments of Haynes et al. [1991]. In the case of an imposed local force the sponge acts to divert a fraction of the mean meridional mass flux upward, which for realistic parameter values is approximately equal to exp(−Δ z / H ), where Δ z is the distance between the forcing region and the sponge layer and H is the density scale height. This sponge‐induced upper cell causes temperature changes that, just below the sponge layer, are of comparable magnitude to those just below the forcing region. In the case of an imposed local diabatic heating, the sponge induces a meridional circulation extending through the entire depth of the atmosphere. This circulation causes temperature changes that, just below the sponge layer, are of opposite sign and comparable in magnitude to those at the heating region. In both cases, the sponge‐induced temperature changes are essentially independent of the height of the imposed force or diabatic heating, provided the latter is located outside the sponge, but decrease exponentially as one moves down from the sponge. Thus the effect of the sponge can be made arbitrarily small at a given altitude by placing the sponge sufficiently high; e.g., its effect on temperatures two scale heights below is roughly at the 10% level, provided the imposed force or diabatic heating is located outside the sponge. When, however, an imposed force is applied within the sponge layer (a highly plausible situation for parameterized mesospheric gravity‐wave drag), its effect is almost entirely nullified by the sponge‐layer feedback and its expected impact on temperatures below largely fails to materialize. Simulations using a middle‐atmosphere general circulation model are described, which demonstrate that this sponge‐layer feedback can be a significant effect in parameter regimes of physical interest. Zonally symmetric (two dimensional) middle‐atmosphere models commonly employ a Rayleigh drag throughout the model domain. It is shown that the long‐term zonally symmetric response to an imposed extratropical local force or diabatic heating, in this case, is noticeably modified from that expected from downward control, even for a very weak drag coefficient.