This thesis develops a method for direction dependent calibration of the ionosphere in radio interferometric data. The method uses the physical theory of the propagation of radio waves through a... Show moreThis thesis develops a method for direction dependent calibration of the ionosphere in radio interferometric data. The method uses the physical theory of the propagation of radio waves through a random weakly scattering medium, to construct a Gaussian process prior for differential total electron content. We develop a technique for applying this to real data, and apply the technique to several 8-hour LOFAR HBA observations. We find the method is able to, for the first time, remove the direction dependent effects of the ionosphere using a screen based approach. In the process we discover a direction dependent systematic in the data that places a limit of the efficacy of the method. Show less