The Lagrangian Model (LMODEL) is a new multisensor satellite rainfall monitoring methodology based on the use of a conceptual cloud-development model that is driven by geostationary satellite imagery and is locally updated using microwave-based rainfall measurements from low earth-orbiting platforms. This paper describes the cloud development model and updating procedures; the companion paper presents model validation results. The model uses single-band thermal infrared geostationary satellite imagery to characterize cloud motion, growth, and dispersal at high spatial resolution (;4 km). These inputs drive a simple, linear, semi-Lagrangian, conceptual cloud mass balance model, incorporating separate representations of convective and stratiform processes. The model is locally updated against microwave satellite data using a two-stage process that scales precipitable water fluxes into the model and then updates model states using a Kalman filter. Model calibration and updating employ an empirical rainfall collocation methodology designed to compensate for the effects of measurement time difference, geolocation error, cloud parallax, and rainfall shear.