A physically based rainfall forecasting model for real-time hydrologic applications is developed with emphasis on utilization of remote sensing observations. Temporal and spatial scales of interest are lead times of the order of hours and areas of the order of 10 km2. The dynamic model is derived from conservation of mass in a cloud column as defined by the continuity equations for air, liquid water, water vapor, and cloud water. Conservation of momentum is modeled using a semi-Lagrangian frame of reference. The model state is vertically integrated liquid water content in a column of the atmosphere. Additionally, laws of thermodynamics, adiabatic air parcel theory, and cloud microphysics are applied to derive a basic parameterization of the governing equations of model dynamics. The parameterization is in terms of hydrometeorologic observables including radar reflectivity, satellite-infrared brightness temperature, and ground-level air temperature, dew point temperature, and pressure. Implementation and application is described by French et al. (this issue) and involves incorporation of uncertainty analysis and a two-dimensional spatial domain, where the dynamics of the continuous space-time rainfall process are discretized onto a rectangular grid.