Calibration of radio interferometric observations becomes increasingly difficult towards lower frequencies. Below ~300 MHz, spatially variant refractions and propagation delays of radio waves traveling through the ionosphere cause phase rotations that can vary significantly with time, viewing direction and antenna location. In this article we present a description and first results of SPAM (Source Peeling and Atmospheric Modeling), a new calibration method that attempts to iteratively solve and correct for ionospheric phase errors. To model the ionosphere, we construct a time-variant, 2-dimensional phase screen at fixed height above the Earths surface. Spatial variations are described by a truncated set of discrete Karhunen-Loeve base functions, optimized for an assumed power-law spectral density of free electrons density fluctuations, and a given configuration of calibrator sources and antenna locations. The model is constrained using antenna-based gain phases from individual self-calibrations on the available bright sources in the field-of-view. Application of SPAM on three test cases, a simulated visibility data set and two selected 74 MHz VLA data sets, yields significant improvements in image background noise (5-75 percent reduction) and source peak fluxes (up to 25 percent increase) as compared to the existing self-calibration and field-based calibration methods, which indicates a significant improvement in ionospheric phase calibration accuracy.
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