The temporal spatial distributions of weather predictability of different variables

To study the atmospheric predictability from the view of nonlinear error growth dynamics, a new approach using the Nonlinear Local Lyapunov Exponent (NLLE) is introduced by the authors recently. The NLLE and its derivatives can be used to quantify the predictability limit of chaotic dynamical systems. In order to apply the NLLE approach to the study of actual atmospheric predictability, a reasonable algorithm is provided to obtain the estimation of the NLLE and its derivatives by using the observational data. Based on the NLLE approach, the temporal-spatial distributions of weather predictability of different variables including geopotential height, temperature, zonal and meridional wind, are investigated by using the NCEP/NCAR reanalysis data, respectively. The results are summarized as follows: (1) At the 500 hPa level, the temporal-spatial distribution characteristics of the predictability limit are different for different variables. In general, the predictability limit of geopotential height is the largest in most regions, that of temperature and zonal wind the second, and that of meridional wind the smallest. (2) The predictability limits of geopotential height and temperature appear a zonal distribution with the relatively high value over the Antarctic, the tropics and the Arctic, and the relatively low value in the middle-high latitudes of northern and southern hemispheres. The predictability limit of zonal wind is the highest over the tropics, while that over the Antarctic, the Arctic and middle-high latitudes is the lowest. The predictability limit of meridional wind is the highest over the Antarctic and Arctic, while that over the tropics and middle-high latitudes is the lowest. (3) The predictability limits of geopotential height, temperature, and zonal wind are all found to increase with height. The predictability limit is below two weeks in the low troposphere, while the predictability limit is about one month in the low stratosphere. (4) For all variables, the predictability limit is found to vary with the seasons. For the most regions of the northern and southern hemispheres, the predictability limit in winter is higher than that in summer.