In this paper a numerical stochastic model of the joint non-Gaussian periodically correlated time-series of air temperature and relative humidity is proposed. The model is based on the assumption that real weather processes are periodically correlated random processes with a period equal to 1 day. This assumption takes into account the diurnal variation of real meteorological processes, defined by the day/night alternation. The input parameters of the model (one-dimensional distributions of air temperature and relative humidity and the correlation structure of the joint time-series) are determined from long-term real observations at weather stations. On the basis of simulated trajectories, some statistical properties of rare combinations of air temperature and relative humidity are studied. In the future, the model will be expanded by the addition of a third component, atmospheric pressure, and with a model of this three-element meteorological complex, properties of enthalpy of moist air time-series will be studied.