Atmosphere is one of the most important noise sources for ground-based cosmic microwave background (CMB) experiments. By increasing optical loading on the detectors, it amplifies their effective noise, while its fluctuations introduce spatial and temporal correlations between detected signals. We present a physically motivated 3D-model of the atmosphere total intensity emission in the millimeter and sub-millimeter wavelengths. We derive a new analytical estimate for the correlation between detectors time-ordered data as a function of the instrument and survey design, as well as several atmospheric parameters such as wind, relative humidity, temperature and turbulence characteristics. Using an original numerical computation, we examine the effect of each physical parameter on the correlations in the time series of a given experiment. We then use a parametric-likelihood approach to validate the modeling and estimate atmosphere parameters from the polarbear-i project first season data set. We derive a new 1.0% upper limit on the linear polarization fraction of atmospheric emission. We also compare our results to previous studies and weather station measurements. The proposed model can be used for realistic simulations of future ground-based CMB observations.