Identifying convectively coupled equatorial wave structures

Guiying Yang, Brian Hoskins,Julia Slingo
CGAM, Department of Meteorology,
University of Reading

The complete picture of the tropical atmosphere involves the interaction of convection and other physical processes with each other and with the dynamics, both locally and globally. The organization of tropical convection, the interaction of multiple time and space scales, and the development and maintenance of equatorial waves are crucial for prediction in the tropics. The main aim of this study is to increase basic understanding of the physics and dynamics of the tropical atmosphere in the context of convectively coupled equatorial waves, and to use that understanding to evaluate the performance of climate and weather forecasting models. It will be shown that current models have a poor simulation of these waves.

ECMWF Reanalysis (ERA) and satellite observed window brightness temperature (Tb) data have been used to diagnose the relationship between the dynamical structure and convective organization of equatorial waves. In the real atmosphere the complicated space-time dependence of the ambient state can lead to Doppler shifting of the theoretical dispersion curves for equatorial waves, and to variations in the vertical heating profile and hence the equivalent depth h. Consequently, a space-time filter based on theoretical dispersion curves may fail to identify individual modes. Here we develop a new methodology in which, after separation into westward and eastward moving structures, the ERA fields are projected onto the parabolic cylinder functions suggested by the theory. Based on the theory the meridional wind v solution of primitive equations on the equatorial-plane linearized about a resting atmosphere has the form of parabolic cylinder functions Dn(y). The relationship of v to the other variables, zonal wind u and geopotential height Z, is best expressed by the relationship between v and the sum and difference between u and (g/h)1/2Z, namely, q=(g/h)1/2Z + u and r=(g/h)1/2Z -u. The q and r solutions also have the form of these functions. Figure 70 shows the horizontal structures of equatorial waves of meridional wave number n=0,1,2 for v solutions vn=Dn(y/yo)ei(kx-wt) with yo=6° and k=6. It is seen that different equatorial modes have different meridional structure dependent on n. For odd (even) n, v is antisymmetric (symmetric) about the equator and has n+2 nodes, whereas u and the divergence field are symmetric (antisymmetric) about the equator.


When the data are expanded in terms of the parabolic cylinder functions, two key parameters, the trapping scale yo=(c/2b)1/2 and the latitude domain Y, need to be prescribed/identified. Values of the parameters are chosen to minimize analysis errors. A case study for 1992 summer shows that the best fit values are yo=6° and Y=20°. This yo corresponds to a phase speed c= 20ms-1 or h=43m which is close to the preferred values deduced from space and time spectral analysis of the brightness temperature for the season. The methodology has proved very useful for detecting these important characteristics of equatorial modes.

Figures 71 and 72 show examples of westward equatorial wave activity in July 1992. There is a convection (low Tb) moving westward from central America to eastern Pacific, indicated by the blue arrow line in Figure 71.a. It has a mixture of symmetric and antisymmetric components. Comparing with Figure 70 and bearing in mind that convection is often associated with upper (lower) level divergence (convergence), it is clear that there are convectively coupled westward mixed Rossby-gravity (WMRG) waves in the upper and lower troposphere, and n=1 Rossby waves in the lower troposphere. The convection and dynamical fields are consistent with each other and with the theoretical analysis. The evolution of the dynamical fields is closely connected with the convection. In the first few days when the antisymmetric component of the convection is dominant, the WMRG wave is prevalent and has the first baroclinic vertical structure with lower level winds shifting slightly westward relative to the convection.



The upper level WMRG weakens after 16 July and the lower level WMRG wave disappears at this day. At almost the same time, on 15 July, the lower level n=1 Rossby wave develops, replacing the lower level WMRG wave. Associated with this the convection moves poleward and shows an increasing symmetric component near 10°-15° of latitude, in agreement with the development of the n=1 Rossby wave. The consistency between ERA and Tb data from two independent sources further suggests the convectively coupled nature of these equatorial waves.

Extension of this analysis to several years of data will enable statistical assessment of the seasonal and interannual variability in the behaviour of equatorial modes, which can be used for model evaluation. It may also enable assessment of the seasonal and interannual variability in the behaviour of equatorial modes, which can be used for model evaluation. It may also enable key questions to be answered, such as whether convection is forcing or is forced/modulated by these modes, whether there is a positive feedback between the convection and the dynamics of these modes, and how and to what extent the basic state influences the interaction between modes.