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Abstract The influence of large bodies of water on convection initiation (CI) and the environment in which convection evolves is highly complex due to the wide range of parameters that control relevant processes. A substantial focus of sea-breeze front (SBF) CI research has focused on the role of mesoscale boundary or organized boundary layer circulation interactions with SBFs; however, less research has focused on heterogeneities in convective parameters and how those may affect CI coverage, timing, and location. In this two-part series, the authors present a parameter study of SBF CI through Cloud Model 1 (CM1) large-eddy simulations across a parameter space varying the cross-shore wind component and radiative forcing and water surface temperatures consistent with June, July, and August in the Great Lakes region. In Part I of this series, simulations under conditions of calm, weak, and moderate offshore flow (0, −2.5, and −5.0 m s⁻¹) are presented. CI occurred in all calm simulations, with decreased coverage and frequency of CI in weak offshore flow. CI was least frequent during moderate offshore flow, despite stronger convergence, due to a shear profile that favored undercutting by the SBF under conditions of moderate offshore flow. Surface-based convective available potential energy (SBCAPE) maxima developed on the cool side of the SBF, with convection occurring on the cool side of the SBF in some cases. Analyses are presented with a focus on the nature of the SBF, distribution of convective parameters, and their implications on CI.