Some systems such as an outdoor public address system and radio acoustic sounding system create loud sounds. The sounds need to be propagated to the desired location for efficient public address. However, sound is greatly affected by atmospheric conditions particularly for long-distance propagation, and it is important to comprehend atmospheric effects. Numerical methods based on geometric acoustics or linear wave acoustics are widely used today for sound field analysis. However, these methods cannot easily consider atmospheric conditions. In addition, we cannot analyze nonlinear sound fields by these methods. In the present paper, we propose a method for analyzing sound fields considering atmospheric conditions and nonlinearity. Equations for numerical sound field analysis, with which we can consider various atmospheric conditions and nonlinearity, are derived from the equations of continuity in fluid dynamics, the Navier-Stokes equations and the law of the conservation of energy. We present numerical calculations of acoustic radiation characteristics and sound fields based on the equations we have obtained, and we use the finite-difference time-domain method to solve them. The effects of atmospheric conditions such as wind, viscosity and nonlinearity can be seen in the results, and thus, the sound generation and sound wave propagation can be comprehended in detail.