Abstract: This paper provides an algorithm that computes the predictability limit of atmospheric variables by use of observational data, based on the concept of the nonlinear local Lyapunov exponent (NLLE) and related nonlinear error growth dynamics developed by the authors in the recent years. The NLLE and its derivatives can be used to quantify the predictability of chaotic dynamical systems. The algorithm introduced here is practical in the sense that it applies the nonlinear error growth theory to the estimate of actual atmospheric predictability through using observations. As an example, the temporalspatial distributions of the predictability limit of geopotential height fields are calculated and discussed. It is found that for the 500hPa height fields, the annual mean predictability limit (AMPL) appears a zonal distribution with the maximum of around two weeks in the tropics and Antarctic. The AMPL is about 9-12 days in the Arctic, 6-9 days in the middle-high latitudes of the Northern Hemisphere, and 4-6 days in the middle latitudes of the Southern Hemisphere. Moreover, the atmospheric predictability limit varies with season. For most regions of the two hemispheres, especially for the Antarctic, the tropical Indian Ocean, the North Pacific and North Atlantic, the predictability limit in winter is much longer than that in summer. Vertically, the predictability limit increases with height. It changes from below two weeks in the lower troposphere to about one month in the lower stratosphere. This is consistent with the fact that weather patterns in the troposphere tend to alter on a time scale of a few days, and circulation regimes in the stratosphere tend to persist for several weeks or more.