Calibration of a typical radio interferometric array yields thousands of parameters as solutions. These solutions contain valuable information about the systematic errors in the data (ionosphere and beam shape). This information could be reused in calibration to improve the accuracy and also can be fed into imaging to improve the fidelity. We propose a distributed optimization strategy to construct models for the systematic errors in the data using the calibration solutions. We formulate this as an elastic net regularized distributed optimization problem which we solve using the alternating direction method of multipliers (ADMM) algorithm. We give simulation results to show the feasibility of the proposed distributed model construction scheme.