The nonlinear local Lyapunov exponent (NLLE) can be used as a quantification of the local predictability limit of chaotic systems. In this study, the phase-spatial structure of the local predictability limit over the Lorenz-63 system is investigated. It is found that the inner and outer rims of each regime of the attractor have a high probability of a longer than average local predictability limit, while the center part is the opposite. However, the distribution of the local predictability limit is nonuniformly organized, with adjacent points sometimes showing quite distinct error growth. The source of local predictability is linked to the local dynamics, which is related to the region in the phase space and the duration on the current regime.

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The distributions of near-surface meteorological elements, such as wind, are greatly affected by the terrain underneath, which makes the power structure of micro geomorphic area more vulnerable to the influence of local climate. Single hills with length are one of typical terrains in microrelief. In this paper, the circulation caused by buoyant flows and temperate within typical single hilly terrain with length is studied. The Detached Eddy Simulation (DES) is used to integrate buoyancy, turbulence and micro-terrain into a single model and it is applied to the special situation of micro-terrain climate. How the wind field is influ-enced by different surface temperature and the model surface roughness is carefully described. The results show that, different surface temperature has a very strong effect on the speedup ratio. Compared with the air temperature, the lower the terrain surface temperature is, the more obvious the speedup ratio effect is, and vice versa. For different roughness surface terrain, the speedup ratio has almost the same characteristics.

Many studies have confirmed that the complexity of a time sequence is closely related to its predictability, but few studies have proposed methods to reduce the time sequence complexity, which is the key to improving its predictability. This study analyzes the complexity reduction method of observed time sequences based on wind speed data. Five sampling methods, namely the random method, average method, sequential method, max method and min method, are used to obtain a new time sequence with a low resolution from a high resolution time sequence. The ideal time sequences constructed by mathematical functions and the observed wind speed time sequences are studied. The results show that the complexity of ideal time series of periodic sequences, chaotic sequences and random sequences increases in turn, and the complexity is expressed by the approximate entropy (ApEn) exponent. Furthermore, the complexity of the observed wind speed is closer to the complexity of a random sequence, which indicates that the wind speed sequence is not easy to predict. In addition, the complexity of sub-time series change with different sampling methods. The complexity of sub-time series obtained by the average method is the lowest, which indicates that the average method can reduce the complexity of observed data effectively. Therefore, the complexity of sub-time series sampled from the high-resolution wind speed data is reduced by using the average method. The method that can reduce the complexity of wind speed substantially will help to choose the appropriate wind speed data, thus improving the predictability.

The impact of the length of the evolutionary window (EW) on the estimation of the predictability limit of the Lorenz-63 model using the nonlinear local Lyapunov exponent (NLLE) method is studied. The structure of the initial errors and error growth dynamics are analyzed. It is found that there exists an optimal EW, at which the estimated predictability limit is closest to its theoretical value. With a shorter EW, the predictability limit is underestimated, while at longer EWs it is overestimated. The optimal EW is approximately equal to the decorrelation time of the system. A preliminary explanation for this link, based on the loss of information from the initial state, is given.(Citation: Huai, X., J. Li, R. Ding, and D. Liu, 2017: Optimal evolutionary window for the nonlinear local Lyapunov exponent. SOLA, 13, 125−129,