  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 Earth's 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.
