The location of the Inter-Tropical Convergence Zone plays an important role in the climatology of tropical regions. Yet, despite its importance, the basic physics that determine the location of the ITCZ are not fully understood. Observational analyses show that, where the cross-equatorial pressure gradient is strong, the maximum convection is not necessarily associated with the highest sea surface temperature,or correspondingly, the lowest sea level pressure. Tomas and Webster (1997) argue that if a strong enough cross-equatorial pressure gradient exists and the system is inertialy unstable, secondary ameliorating circulations will drive strong off-equatorial convection in regions where ITCZ location is determined by low tropospheric dynamics. The observational record is re-examined to test the inertial instability hypothesis using the new ECMWF reanalysis data set. Composite analyses are performed to study the structure of the summer meridional circulation for the tropical Eastern Pacific Ocean and Atlantic Ocean. In agreement with Tomas and Webster theory, we find that the magnitude of the cross-equatorial pressure difference appears to determine the intensity of convection with low values of outgoing longwave radiation always to the north of the zero absolute vorticity line, and the absolute vorticity advection equatorward of the this line. Also the observed oscillation period of the disturbance for the studied regions coincides with theoretical oscillation period of the inertial flow.

We examine the eastern Pacific Ocean Intertropical Convergence Zone (ITCZ) both in its mean state and transient phases using a combined diagnostic, theoretical and numerical modeling approach. We note that the ITCZ is perpetually in a transient state with strong variability occurring on 4-8 day time scales. Transients, about half the amplitude of the mean ITCZ, propagate northwards from the near-equatorial southern hemisphere eventually increasing the convection in the vicinity of the mean ITCZ convection. It is argued that the mean ITCZ is continually inertially unstable with incursions of anticyclonic vorticity advected across the equator resulting in the creation of a divergence-convergence doublet. The low-level convergence generates convection and vortex tube stretching which generates cyclonic vorticity counteracting the northward advection of anticyclonic vorticity. During a cycle, the heating in the mid-troposphere near 10°N oscillated between 6 and 12 K/day at the inertial frequency of the latitude of the mean convection. The shallow meridional circulation, noted in the mean field in other studies, appears to be a result of the transient nature of the ITCZ. It is hypothesized that westward propagating equatorial waves result from the inertial oscillation of the ITCZ. To test that the waves are formed in situ in the eastern Pacific and not remnants of waves propagating from the Atlantic or promoted by the Central and South American orography, several numerical experiments are undertaken using a high-resolution regional model spanning the western Atlantic Ocean and the eastern Pacific. In the control case, the model is initialized at all boundaries with full high-frequency observations. In two additional experiments, these transients are filtered out, and a third experiment is run with the topography over a large part of Central and South America removed. In all experiments, westward propagating waves are formed in the region of high CEPG suggesting that the hypothesis of in situ development may be correct.

Variable resolution method helps to study the local scale phenomenon of interest within the context of global scale atmosphere/ocean dynamics. Global spectral methods based on spherical harmonics as basis functions are known to resolve a given function defined on the sphere, in an uniform manner. Though known for its mathematical elegance and higher order accuracy, global spectral methods are considered to be restrictive for developing mesh-refinement strategies. The only mesh refinement strategy available until now is due to the pioneering work of F. Schmidt. Schmidt transformation can study only one region with higher resolution. The study of tropical dynamics is an interesting theme due to the presence of teleconnections between various phenomena, especially Indian Monsoon and the El-Nino. The Inter-Tropical Convergence Zone (ITCZ)is a continental scale phenamenon. It is in the ITCZ, many monsoon systems and tropical cyclones do occur. To study such phenomena under variable resolution method, high resolution is required in the entire tropical belt. Hitherto such a kind of mesh refinement strategies were not available in global spectral models. In this work, a new variable resolution method is developed that can help to study the tropical sub-scale phenomena with high resolution, in global spectral models. A new conformal coordinate transformation named ’High resolution Tropical Belt Transformation(HTBT)’ is developed to generate high resolution in the entire tropical belt. Mathematical demonstrations are given to show the existence of additional conformal transformations available on the sphere, indicating additional degrees of freedom available to create variable resolution global spectral method. Variable resolution global spectral method with high resolution over tropics is created through HTBT. The restriction imposed by Schmidt’s framework that the map-ping factor of the transformation need to have a finite-decomposition in the spectral space of the transformed domain is relaxed, by introduction of a new framework. The new framework uses transformed spherical harmonics Bnm as basis for spectral computations. With the use of FFT algorithm and Gaussian quadrature, the efficiency of the traditional spectral method is retained with the variable resolution global spectral method. The newly defined basis functions Bnm are the eigenvalues of the transformed Laplacian operator . This property of Bnm provide an elegant direct solver for the transformed Helmholtz operator on the sphere. The transformed Helmholtz equations are solved accurately with the variable resolution method. Advection experiments conducted with variable resolution spectral transport scheme on the HTBT variable grid produces near-dispersion free advection on the tropical belt. Transport across homogeneous resolution regions produce very less dispersion errors. Transport of a feature over the poles result in severe grid representation errors. It is shown that an increase in resolution around the poles greatly reduces this error. Transport of a feature from a point close to poles but not over it, does not produce such representation errors. Fourth-order Runge-Kutta scheme improves the accuracy of the transport scheme. The second order Magazenkov time-scheme proves to be better accurate than the leap-frog scheme with Asselin filter. The non-divergent barotropic vorticity equation is tested with two exact solutions namely Rochas solution and Rossby-Haurwitz wave solutions. Each of the solution tests certain unique and contrasting characteristic of the system. The numerical behaviour of the solutions show non-linear interactions in them. The singularity at the poles, arising due to the unbounded nature of the latitudinal derivative of the map factor of HTBT, triggers Gibbs phenomena for certain functions. However the recent advances in spectral methods, especially spectral viscosity method and Boyd-Vandeven filtering strategy provide ways to control the Gibbs oscillation and recover higher accuracy; make the variable resolution global spectral method viable for accurate meteorological computations.