Methods are derived for the time-continuous four-dimensional assimilation of satellite sounding temperatures. The methods presented include time-continuous versions of direct insertion, successive correction and statistical linear regression. They are applied to temperature sounding data obtained from radiance measurements taken by instruments aboard the polar-orbiting satellites NOAA 4 and Nimbus 6. The data were collected during the U.S. Data System Test in January-March 1976. A comprehensive series of experiments was performed to study the effects of using various amounts of satellite data and differing methods of assimilation. The experiments included the assimilation of data from the NOAA 4 satellite only, from Nimbus 6 only, and of data from both satellites combined. Other experiments involved variations in the application of our time-continuous statistical assimilation methods and of asynoptic successive correction methods. Intermittent assimilation of the sounding data was also tested, and its results compared with those of time-continuous assimilation. Atmospheric states determined in the assimilation experiments served as initial states for a sequence of evenly spaced 3-day numerical weather forecasts corresponding to each experiment. The effects of the satellite data were evaluated according to the following criteria: 1) differences between the initial states produced with and without utilization of satellite data, 2) differences between numerical predictions made from these initial states, and. 3) differences in local weather forecasts resulting from the large-scale numerical predictions. Initial-state differences were evaluated in terms of magnitude and location of large-scale differences between meteorological fields. Numerical prediction differences were evaluated in terms of SI skill scores and rms errors, as well as by synoptic case studies. An automated forecasting model (AFM) based on quasi-geostrophic theory and on subjective forecasting principles was developed to facilitate the objective evaluation of differences produced in local weather forecasts, especially precipitation forecasts. These studies suggest the following conclusions: 1) satellite-derived temperature data can have a modest, but statistically significant positive impact on numerical weather prediction in the 2-3 day range; 2) the impact is highly sensitive to the quantity of data available, and increases with data quantity; and 3) the method used to assimilate the satellite data can influence appreciably the magnitude of the impact obtained for the same data.