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A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

An investigation was conducted to find out if sea surface temperature (SST) - African rainfall relationships could be simulated in a global climate model (GCM). If indeed that were possible, researchers generated useful diagnostics that can enable them to understand the physical mechanisms which lead to rainfall fluctuations over Africa in response to sea surface temperature anomalies over global ocean.

The results of this rainfall index-sea surface temperature (SST) correlation analysis suggest that interannual fluctuations in SST, which are dominated by El Nino Southern Oscillation (ENSO) events have a significant influence on the oscillatory behavior of sub-Saharan rainfall anomalies. It is noted that the sub-Saharan rainfall correlates significantly with tropical Pacific as well as with Empirical Orthogonal Functions 1 (EOF1) of the Atlantic SST anomalies.

The relationship between SST and rainfall index anomalies over sub-Saharan Africa for the 1970-1984 period is investigated. Results of an empirical orthogonal function analysis indicate that the most dominant eigenmode, EOF1, is characterized by warming over the central eastern Pacific, cooling over the eastern midlatitude Pacific, and warming over the entire Atlantic and Indian ocean basins. EOF1 is found to have statistically signifiant monthly correlations for the Sahel and Soudan regions, with the warm El Nino-like phases of SST EOF1 corresponding to drought conditions. These results suggest that the large-scale SST anomalies may be responsible for a large component of the observed vacillation of sub-Saharan rainfall.

Application of the bounded-derivative and normal-mode methods to a simple linear barotropic model at a typical middle latitude shows that the two methods lead to identical constraints up to a certain degree of approximation. Beyond this accuracy the two methods may differ from each other. When applied to a global nonlinear barotropic model using real data, again the two methods lead to similar balanced initial states. The gravity oscillations in the unbalanced height field, which have amplitudes of up to 60 m with a dominant periodicity of about 5 to 6 h, are practically eliminated by both initialization methods. The rotational wind component is smooth even for the unbalanced initial state. The small-scale spatial features of the irrotational wind component are drastically reduced by initialization. Both the nonlinear normal-mode and the bounded-derivative initialization methods yield similar divergence fields centered around the areas of highest orography. The comparison shows that there is no significant loss of information in the mass and momentum fields, despite the fact that the bounded-derivative method employs only the original, rotational wind component to construct a balanced initial state compared to the normal-mode method, which, in addition, makes use of the unbalanced divergent wind and height fields.

Browning et al. (1980) proposed an initialization method called the bounded derivative method (BDI). They used analytical data to test the new method. Kasahara (1982) theoretically demonstrated the equivalence between BDI and the well known nonlinear normal mode initialization method (NMI). The purposes of this study are the extension of the application of BDI to real data and comparison with NMI. The unbalanced initial state (UBD) is data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLAS GCM to the 300 mb surface. The global barotropic model described by Takacs and Balgovind (1983) is used. Orographic forcing is explicitly included in the model. Many comparisons are performed between various quantities. However, we only present a comparison of the time evolution at two grid points A(50 S, 90 E) and B(10 S, 20 E) which represent low and middle latitude locations. To facilitate a more complete comparison an initialization experiment based on the classical balance equation (CBE) was also included.

Experiments were performed to examine the impact of adopting various procedures in the assimilation of patches of data during the progress of a numerical forecast. A barotropic model described by Takacs and Balgovind, 1983 is used for the experiments. The model is global and its discretization is similar to the GLA Fourth Order GCM. The effect of orography is included in the model. The experiments are of an identical twin kind. The nature run starts from global fields of wind (u and v) and height (h) at 300 mb. They are real data of January, 1979 OOZ which were interpolated from the adjacent sigma levels of the GLA GCM and then balanced by the bounded derivative method. From this initial state a 6 day forecast is performed. At intervals of 3 hours this information is saved over sectors of 60 width in longitude, from the south pole to the north pole, to simulate data coverage and observational frequency of a polar orbiting satellite.

A barotropic model over an equatorial beta-plane is used to investigate the response when a uniform zonal current crosses an isolated hypothetical mountain centered at the equator. The bounded derivative initialization method is applied to suppress gravity-inertia motions. A quasi-stationary trough is generated at the top of the orography. Its intensity is greater in the easterly case than in the westerly case of the initial zonal current. A diagnostic equation is derived to interpret this difference in the solution. The quasi-stationary orographic divergence field which is positive on the windward slope and negative on the leeward slope (for both easterly and westerly cases of the initial zonal current) is responsible for maintaining the trough. The difference in the intensity of the trough is due to the contribution of the beta-u effect, which changes sign with the direction of the initial zonal flow.

The utility of the bounded derivative method (BDM) as an initialization tool was examined using real data and the GLAS fourth order global barotropic model. Two constraints on initial data were derived. The first constraint based on the BDM is an equation for calculating initial divergence. The second constraint yields an additional equation of elliptic type for computing the initial height field. This equation is more general than the balance equation first proposed by Charney (1955). It also has more terms which include the contributions of initial divergence and orography. The development of a data insertion scheme based on the BDM is discussed.

A system of equations which describe the motion of a barotropic fluid in the presence of bottom topography are presented. The mathematical expression for orography is developed and the bounded derivative initialization method is applied to suppress gravitational oscillations. A stationary orographic trough is simulated. The geopotential and zonal motion have maximum deviation from the mean state at the top of the mountain. Regarding meridional speed, outflow occurs on the windward slope and inflow on the leeward slope. Divergence of order (10(-6)s(-1) is found on the windward slope while convergence of the same order of magnitude resides on the leeward slope. This outcome may have interesting implications regarding real climatology occurring over the equatorial regions of continental land masses.