The chaotic characteristics of the tall tower wind speed data within Missouri was investigated using both quantitative and qualitative methodologies. The phase space diagrams were constructed using the method of time delay. The two parameters needed in the construction of the attractor are the embedding dimension and the time delay. The former was determined using the Cao Algorithm and the latter by Average Mutual Information (AMI). Qualitatively, the phase portraits display chaos for all the wind speed time series for the various stations and height levels. They did not illustrate periodicity nor were they random motions, rather, they depicted a single attractor representative of chaos. Quantitatively the Largest Lyapunov Exponent (LLE) was evaluated. It was determined that for the Columbia station the wind speeds display chaotic characteristics representative of the positive LLEs. However, the increasing level of chaos characteristics did not coincide with the increasing height levels of the tall tower. Thereafter, a simple non-linear prediction algorithm was used to forecast wind speeds using a moving window. The attractor was constructed using the first 56 days and the subsequent 6 h or 36 (10 min) time steps were predicted. The preceding forecast was done when the attractor was reconstructed using the training data of 56 days starting from a 6-h delay from the previous run. The RMSE, MAE and Correlation were investigated for the model with the errors evaluated cumulatively for all of the 1st through 36^st predictions. It was determined that the errors increase as the forecasting steps increased for all stations and height levels. The RMSE plateaus at higher wind speeds for increasing height levels with the exception of the station, Neosho, where it plateaued at all height levels at approximately 3.0 ${\text{ms}}^{-1}$. For Columbia at all height levels, after the 20th time step or 3.33 h, the model's normalized errors exceeds 1 or 100%. However, using a 50% normalized error cap, it was noted that these values occurred for Columbia's height levels after the 1st, 2nd and 3rd time steps respectively. For Blanchard, this value was given by the 2nd time step for both heights whilst for Neosho, at all heights this percentage occurred after at most, 2 time steps. From the Lyapunov exponent, the prediction horizons or the time limits to obtain accurate predictions from the chaotic system were determined to be 6 time steps for all the height levels in the Columbia station using a 95% confidence band. When a range of confidence bands was used, it was shown that for the 90% confidence, this value was decreased to 4 time steps. This model was compared to the benchmark model of persistence where it was determined that the EDM is comparable to persistence and it beats it in the very short-term range of one time step for Columbia and Blanchard. Seasonality and diurnal cycle analyses were also accomplished. Seasonality was investigated by slicing the results every 6 h or extracting every 36th forecast error. It was shown that four of the eight stations' height levels had the season of summer incurring the lowest magnitude of average errors and standard deviations. The diurnal cycle was examined by extracting every four of the 6 time slices done previously. The time of day was analysed by lagging these slices by 6, 12 and 18 h. It was determined that there was no evident trend where a particular time of day the model incurred more errors and had greater standard deviations for all stations and heights.

使用定量和定性方法研究了密苏里州高塔风速数据的混沌特性。相空间图是使用时间延迟方法构建的。构造吸引子所需的两个参数是嵌入尺寸和时间延迟。前者是使用Cao算法确定的，而后者是通过平均相互信息（AMI）确定的。定性地，相图显示了各个站和高度级别的所有风速时间序列的混乱情况。他们没有说明周期性，也不是随机运动，而是描绘了一个代表混乱的吸引子。定量评估了最大的Lyapunov指数（LLE）。已确定，对于哥伦比亚站，风速显示出代表正LLE的混沌特性。但是，混沌特性的增加与高塔的高度增加并不一致。此后，使用简单的非线性预测算法使用移动窗口预测风速。使用前56天构建吸引子，并预测随后的6小时或36（10分钟）时间步长。先前的预测是在从前一轮运行的6小时延迟开始使用56天的训练数据重建吸引子时完成的。对模型的RMSE，MAE和相关性进行了调查，并对第1至36个阶段的所有错误进行了累积评估 混乱特征的增加水平与高塔的高度水平增加不一致。此后，使用简单的非线性预测算法使用移动窗口预测风速。使用前56天构建吸引子，并预测随后的6小时或36（10分钟）时间步长。先前的预测是在从前一轮运行的6小时延迟开始使用56天的训练数据重建吸引子时完成的。对模型的RMSE，MAE和相关性进行了调查，并对第1至36个阶段的所有错误进行了累积评估 混乱特征的增加水平与高塔的高度水平增加不一致。此后，使用简单的非线性预测算法使用移动窗口来预测风速。使用前56天构建吸引子，并预测随后的6小时或36（10分钟）时间步长。先前的预测是在从前一轮运行的6小时延迟开始使用56天的训练数据重建吸引子时完成的。对模型的RMSE，MAE和相关性进行了调查，并对第1至36个阶段的所有错误进行了累积评估 使用前56天构建吸引子，并预测随后的6小时或36（10分钟）时间步长。先前的预测是在从前一轮运行的6小时延迟开始使用56天的训练数据重建吸引子时完成的。对模型的RMSE，MAE和相关性进行了调查，并对第1至36个阶段的所有错误进行了累积评估 使用前56天构建吸引子，并预测随后的6小时或36（10分钟）时间步长。先前的预测是在从前一轮运行的6小时延迟开始使用56天的训练数据重建吸引子时完成的。对模型的RMSE，MAE和相关性进行了研究，并对第1到36的所有错误进行了累积评估^圣预测。已确定，随着所有站和高度水平的预报步骤的增加，误差也会增加。RMSE高原在较高的风速下会增加高度，但Neosho站除外，Neosho在所有高度均在3.0处达到高原${\text{小姐}}^{-\mathrm{1个}}$。对于所有高度的哥伦比亚，在第20个时间步长或3.33小时后，模型的归一化误差超过1或100％。但是，使用50％的归一化误差上限，应注意的是，这些值分别是在第一，第二和第三时间步长之后出现在哥伦比亚州的身高水平上。对于Blanchard，该值由两个高度的第二时间步长给出，而对于Neosho，在所有高度处，该百分比最多在两个时间步长之后出现。根据李雅普诺夫指数，使用95％置信带，对于哥伦比亚站中所有高度，确定从混沌系统获得准确预测的预测范围或时间限制为6个时间步长。当使用一定范围的置信带时，表明对于90％的置信度，该值减小到4个时间步长。将该模型与持久性基准模型进行了比较，后者确定了EDM与持久性具有可比性，并且在哥伦比亚和布兰查德的非常短的一步范围内击败了它。还完成了季节性和昼夜周期分析。通过每6小时对结果进行切片或每36个预测误差提取一次来调查季节性。结果表明，八个台站的四个高度水平处于夏季，平均误差和标准偏差的幅度最小。通过提取先前完成的6个时间片中的每四个时间片来检查昼夜周期。通过将这些切片延迟6、12和18小时来分析一天中的时间。