Hierarchical Tropical Cloud Systems in an Analog Shallow-Water Model

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
  • | 2 Center for Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, Massachusetts
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Abstract

Recent observations have revealed an hierarchy of cloud clusters and superclusters within the Madden-Julian oscillation of the equatorial troposphere. The authors here report on the results of simulations with a model based on a simple nonlinear analog of the shallow-water equations. The model consists of a troposphere represented by single values of vertical velocity and temperature and in which the horizontal motions are assumed always to represent the first baroclinic mode. The troposphere overlies a subcloud layer of fixed depth in which the evolution of moist entropy is predicted. The model is driven by specified values of radiative cooling and sea surface temperature, and a Newtonian relaxation of the surface wind toward a specified value. The system is horizontally homogeneous except for an anisotropy owing to the equatorial β effect.

An eastward-propagating low-wavenumber disturbance containing an hierarchy of superclusters and cloud clusters is spontaneously generated from a random initial state using each of three cumulus parameterizations: a Kuo-like scheme and two prognostic schemes. A fourth scheme, which assumes an instantaneous adjustment to convective neutrality, fails to produce an hierarchical structure. Experiments with fixed wind speed in the surface flux formulas demonstrate that the WISHE (wind-induced surface heat exchange) mechanism is responsible for the organized structures in the model field, except when the Kuo-like scheme is used; even in this case the modes are strongly affected by WISHE.

The supercluster resembles a Matsuno-Gill pattern in all three cases, but the horizontal cloud distribution within the superclusters differs substantially among the three schemes. The Kuo-like scheme produces grid-column convection aligned along the convergence zones as a result of its direct coupling of convection with the large-scale convergence. This scheme always produces grid-scale motions. The prognostic schemes, which allow for the finite timescale of convection, are less prone to gridpoint structure, but the degree of such structure depends sensitively on the parameters of the schemes and the presence or absence of time-lagged downdrafts.

The authors find that the wavenumber spectrum of convective updrafts is nearly flat, while the zonal wind spectrum is strongly peaked at low wavenumbers. This behavior exists even if the nonlinear advection terms are switched off, showing that these play little or no role in the final wavenumber selection. Even turning off all of the model nonlinearity except for the “up-only” nature of convection preserves the essential structure of the full solution, although it does weakly flatten the zonal wind spectrum.

The dependence of the behavior of the system on the magnitude and direction of the background surface wind is also explored. A weaker easterly wind forcing leads to a modulation of the superclusters into a yet lower-wavenumber structure; this modulation propagates faster than the superclusters. Westerly wind forcing suppresses the Kelvin-type mode and generates a mixed mode resembling a mixed Rossby-gravity wave. A further increase of the westerly wind forcing induces westward-moving disturbances as well. This model is considered as a framework for interpreting more complicated tropical models.

Abstract

Recent observations have revealed an hierarchy of cloud clusters and superclusters within the Madden-Julian oscillation of the equatorial troposphere. The authors here report on the results of simulations with a model based on a simple nonlinear analog of the shallow-water equations. The model consists of a troposphere represented by single values of vertical velocity and temperature and in which the horizontal motions are assumed always to represent the first baroclinic mode. The troposphere overlies a subcloud layer of fixed depth in which the evolution of moist entropy is predicted. The model is driven by specified values of radiative cooling and sea surface temperature, and a Newtonian relaxation of the surface wind toward a specified value. The system is horizontally homogeneous except for an anisotropy owing to the equatorial β effect.

An eastward-propagating low-wavenumber disturbance containing an hierarchy of superclusters and cloud clusters is spontaneously generated from a random initial state using each of three cumulus parameterizations: a Kuo-like scheme and two prognostic schemes. A fourth scheme, which assumes an instantaneous adjustment to convective neutrality, fails to produce an hierarchical structure. Experiments with fixed wind speed in the surface flux formulas demonstrate that the WISHE (wind-induced surface heat exchange) mechanism is responsible for the organized structures in the model field, except when the Kuo-like scheme is used; even in this case the modes are strongly affected by WISHE.

The supercluster resembles a Matsuno-Gill pattern in all three cases, but the horizontal cloud distribution within the superclusters differs substantially among the three schemes. The Kuo-like scheme produces grid-column convection aligned along the convergence zones as a result of its direct coupling of convection with the large-scale convergence. This scheme always produces grid-scale motions. The prognostic schemes, which allow for the finite timescale of convection, are less prone to gridpoint structure, but the degree of such structure depends sensitively on the parameters of the schemes and the presence or absence of time-lagged downdrafts.

The authors find that the wavenumber spectrum of convective updrafts is nearly flat, while the zonal wind spectrum is strongly peaked at low wavenumbers. This behavior exists even if the nonlinear advection terms are switched off, showing that these play little or no role in the final wavenumber selection. Even turning off all of the model nonlinearity except for the “up-only” nature of convection preserves the essential structure of the full solution, although it does weakly flatten the zonal wind spectrum.

The dependence of the behavior of the system on the magnitude and direction of the background surface wind is also explored. A weaker easterly wind forcing leads to a modulation of the superclusters into a yet lower-wavenumber structure; this modulation propagates faster than the superclusters. Westerly wind forcing suppresses the Kelvin-type mode and generates a mixed mode resembling a mixed Rossby-gravity wave. A further increase of the westerly wind forcing induces westward-moving disturbances as well. This model is considered as a framework for interpreting more complicated tropical models.

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