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Empirical parameterization of Tropical Ocean–Atmosphere Coupling: The “Inverse Gill Problem”

Myles R. AllenAtmospheric, Oceanic and Planetary Physics, University of Oxford, United Kingdom

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Michael K. DaveyMeteorological Office Unit, Hooke Institute, Oxford, United Kingdom

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Abstract

A number of linear models of the steady-state response of the tropical atmosphere to sea surface temperature (SST) anomalies have been proposed, all based on the shallow-water equations. Despite their formal similarity, the various models have very different physical interpretations and suggest widely varying values for key parameters, including the mechanical damping rate (or coefficient of Rayleigh friction), the strength of the coupling to SST, and the “effective stability” of the lower troposphere. In order to place empirical constraints on these coefficients, the linear momentum equations are inverted to obtain the scalar forcing fields P′(interpreted as vertically integrated boundary-layer pressure anomalies) that best reproduce observed surface wind anomalies through the period 1984–90. This gives an optimum value for the mechanical damping rate, independent of the coupling parameterization. Direct optimization of a fully linear Gill-type model of ocean-atmosphere coupling reveals that the problem of identifying optimum values for the other two parameters (coupling and stability) is degenerate; if one parameter is fixed, the other is well constrained by the data, but if both are allowed to vary, the cost function (rms error in the model output winds) has no well-defined minimum. Models of this type also suggest a simple relationship between P′ and anomalies of SST and divergence, however. A significant but strikingly different relationship is found between these three quantities derived from the observations. If uniform, linear coupling is assumed, this result suggests that the large-scale response of the tropical atmosphere to SST anomalies is consistent with a moderately moist-unstable boundary layer, with the stability of the response being maintained by turbulent diffusive processes. This may be parameterized most simply by introducing biharmonic diffusion on Pinto the “thermodynamic” equation of a Gill-type model. Simple forms of nonlinear coupling both to SST and to divergence are also investigated. Although the possibility that nonlinear effects are important cannot be excluded, no evidence is found to suggest that either of two widely used nonlinear coupling parameterizations represent an improvement on a fully linear scheme.

Abstract

A number of linear models of the steady-state response of the tropical atmosphere to sea surface temperature (SST) anomalies have been proposed, all based on the shallow-water equations. Despite their formal similarity, the various models have very different physical interpretations and suggest widely varying values for key parameters, including the mechanical damping rate (or coefficient of Rayleigh friction), the strength of the coupling to SST, and the “effective stability” of the lower troposphere. In order to place empirical constraints on these coefficients, the linear momentum equations are inverted to obtain the scalar forcing fields P′(interpreted as vertically integrated boundary-layer pressure anomalies) that best reproduce observed surface wind anomalies through the period 1984–90. This gives an optimum value for the mechanical damping rate, independent of the coupling parameterization. Direct optimization of a fully linear Gill-type model of ocean-atmosphere coupling reveals that the problem of identifying optimum values for the other two parameters (coupling and stability) is degenerate; if one parameter is fixed, the other is well constrained by the data, but if both are allowed to vary, the cost function (rms error in the model output winds) has no well-defined minimum. Models of this type also suggest a simple relationship between P′ and anomalies of SST and divergence, however. A significant but strikingly different relationship is found between these three quantities derived from the observations. If uniform, linear coupling is assumed, this result suggests that the large-scale response of the tropical atmosphere to SST anomalies is consistent with a moderately moist-unstable boundary layer, with the stability of the response being maintained by turbulent diffusive processes. This may be parameterized most simply by introducing biharmonic diffusion on Pinto the “thermodynamic” equation of a Gill-type model. Simple forms of nonlinear coupling both to SST and to divergence are also investigated. Although the possibility that nonlinear effects are important cannot be excluded, no evidence is found to suggest that either of two widely used nonlinear coupling parameterizations represent an improvement on a fully linear scheme.

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