River deltas form where sediment-laden water debouches into a basin. The spatial delineation of a delta is nontrivial and yet is fundamental to systematically evaluating fluxes across its surface. Here we study shoreline dynamics of the Wax Lake Delta (WLD), a naturally developing delta, downstream of the Atchafalaya River, USA. We demonstrate the ability to extract hydrodynamic and morphodynamic shorelines from time series of satellite imagery and topography data, respectively. The hydrodynamic shoreline corresponds to the traditional dry-wet interface, whereas we introduce the concept of a morphodynamic shoreline demarcating the topset-foreset transition of a delta to quantitatively express the degree of inundation of a delta plain. These shorelines enable us to assess environmental controls on inundation of the WLD delta plain, noting the abundance of satellite imagery, whereas time series of bathymetric data from delta plains are scarce. From the analysis of NOAA and U.S. Geological Survey environmental data, we identify the effects of river discharge, tides, wind, and vegetation on shoreline position. In particular, using Delft3D simulations and a simplified momentum balance, we highlight the nonuniform and nonlinear effect of wind on delta plain inundation. Our analyses reveal that wind, riverine discharge, and tides significantly contribute to inundation of the WLD, and hence, incorporating their interaction is essential to the accurate modeling of hydrodynamics and ecodynamics of the WLD delta plain, as well as to the dynamic shape of delta plains in general.