This study has been spurred by evidence of the interactions of complex but competing dynamical (physical) processes operating on different time scales over the tropical Atlantic, as well as the role of quasi-stationary African orography, which exert significant impacts on the West African climate. The overarching goal of the study was to develop a prototype putative ocean-atmosphere-based phenomenological model to investigate rainfall variability over East Sahel, one of the sub-regions most sensitive to the variability of the global climate system. This approach could have the potential of contributing to enhancing our understanding of the region's climate. The data sources used were (i) NCEP/NCAR reanalysis, (ii) ERSST, (iii) GHCN version 2 Land Precipitation Anomalies, (iv)climate indices obtained from http://www.esrl.noaa.gov/psd/data/climateindices/list/, and (v) authors' indices, generated from NCEP/NCAR reanalysis and ERSST data. With an initial assemblage of 42 time-evolving candidate predictors, selected based on prior knowledge, centered on July-August-September (JAS) East Sahel rainfall, and under five different experimental set-ups, a Lasso multivariate regression was applied to establish the causal relationships between the predictors and the response variable, at different time lags. The regression model, augmented by kappa (k) statistical significance test, retained a total of 19 most prominent predictors, with varying number, depending on each time lag per experimental set-up. These formed the building blocks for the development of a generic putative model. The implementation of a higher level abstraction Environmental Causality Impact Analysis Model (ECIAM), which captured all the causal relationships suggested by the Lasso regression, provided the consolidated results that led to the discovery of three distinct hypotheses linked to East Sahel rainfall variability. The preliminary results suggest (i) an NAO-like driven-hypothesis, which is significant at monthly and seasonal time-scales, (ii) a Mediterranean Sea-like driven-hypothesis, exhibited in two variants, but both operating on monthly time-scales, and (iii)an ENSO-like driven-hypothesis, which operates on seasonal time-scales. The study has given us the opportunity for further exploration and elaboration of the emerging hypotheses and their plausible physical processes.