  A fundamental assumption of the data model used in radio interferometric
calibration is that the sky model only consists of compact and discrete radio
sources. This assumption breaks down when there are large scale diffuse
structure such as the Galaxy visible in the observed data. No straightforward
method currently exists to include such large scale diffuse structure in
calibration and only indirect techniques such as excluding short baselines or
filtering are used in practice as a remedy. In this paper, we propose a novel
mechanism to include large scale diffuse sky models into direction dependent
calibration of radio interferometers.
  We extend distributed calibration of radio interferometric data with both
spectral and spatial regularization to include models for diffuse emission. We
use shapelet basis functions to model both the diffuse sky structure as well as
the spatial variation of systematic errors. The application of the direction
dependent errors onto the diffuse sky is done in closed form using specific
properties of shapelet basis functions, avoiding the need for expensive
operations such as convolution.
  We provide extensive simulations showing the efficacy of our proposed method.
We are able to overcome a major problem faced by existing calibration
techniques, i.e., the suppression of large scale diffuse structure by not
properly modeling such structure in calibration.
