Large radio astronomy multi-element interferometers are frequently used as single dishes in a tied-array mode when signals from separate antennas are added. Phase shifts arising during wave propagation through a turbulent atmosphere can significantly reduce the effective area of an equivalent single dish. I aim to give estimates of the impact of the ionosphere and troposphere on the effectiveness of a radio interferometer working in tied-array mode. Statistical estimates of the effective area are calculated and the power-law of turbulent atmosphere irregularities has been used. A simple method of tied-array calibration using optimization techniques is proposed. The impact of phase errors on the effectiveness of tied-arrays are given for low and high frequencies. Computer simulations demonstrate the efficacy of the proposed calibration algorithm.