New observing systems such as the Oklahoma Mesonet, the NEXRAD Doppler radar network, and high resolution satellite data present the opportunity to make accurate numerical weather predictions on the mesoscale and thunderstorm scale. There is a need for efficient data assimilation techniques that can take full advantage of the new data and be used for prediction on these scales. Two assimilation methods are presented to address this need: a method of directly correcting phase errors in a forecast and a modified Bratseth successive correction scheme which is able to use raw Doppler radial velocity data. It is common for numerical forecasts to have position errors in small scale features such as thunderstorms and fronts. The phase correction data assimilation automatically identifies such position errors and applies a three dimensional field of horizontal translations to correct all the model variables even though a limited number of variables may have been directly observed. The Advanced Regional Prediction System (ARPS) Data Assimilation System, ADAS, is then used to correct any amplitude errors and allows the corrections to be blended into the forecast using analysis increment updates. Tests are done using simple models to show the utility and robustness of the techniques, and the schemes are successfully applied to real data cases. A front in Central Oklahoma is analyzed and forecast, and a complex severe weather outbreak in the Texas Panhandle is successfully simulated using the techniques. The improvement due to the storm-scale data assimilation lasted between 2 and 3 hours for a 3-km forecast, which is at or beyond the generally expected limit of predictability for thunderstorms.