Fundamental Studies on the Applications of the Wavelet Analysis to Hydraulic Engineering

20世纪80年代初，J. Morlet提出了一种新的“小波分析”理论，正在迅速扩大其应用领域，特别是在信号处理、信息通信和图像数据压缩方面。传统的随机数据分析方法，即频谱，只是在整个时域内从频率的角度对数据进行解析，而小波分析方法则是在频域和时域对数据进行分析。在本研究中，我们试图将该方法的适用性扩展到水利工程和水文。(1)水文与水文气象：重复季节变化的降水、温度、流量等水文与水文气象时间序列显示了年变化格局。应用小波分析来阐明这些特征。(2)遥感数据分析：植被具有减缓气候变化的作用。利用归一化植被指数（NDVl）和地表温度（GST）对都市区两个大型林区进行了分析。NDVI和GST散点图中点的广泛分散可以用二维小波分析确定的森林和城市化面积的大小来解释。(3)冠层流动的湍流结构：Honami现象不仅从流体力学的角度来看是有趣的，而且从环境和粮食生产的实际角度来看也是有趣的，因为植物的摆动可能极大地促进了动量、物质（CO_2和O_2）和热量的交换。湍流冠层流动三维数值模拟的小波分析显示了冠层流动结构的时间变化。(4)测量误差的去除：通过该技术去除导致严重误差的噪声信号，特别是在反估计问题中，检测出无意义的高频白噪声和脉冲信号。

A new theory of "WEVELET ANALYSIS", proposed in the early 1980's by J. Morlet is rapidly expanding its application fields, especially to signal processing, information communication and compression of image data. While the convential method of random data analysis, spectrum, is the resolution method of data only in terms of frequency for entire time domain, the new method of wavelet analyzes data in both frequency and time domain. In this research, we have tried to extend the applicability of the method to hydraulic engineering and hydrology.(1) Hydrology and Hydrometeorology : Hydrological and hydrometeorological time series, such as rainfalls, temperature, and streamflows repeating the seasonal variation, show the annual changes of the patterns. The wavelet analysis has been applied to elucidate these characteristics.(2) Remote Sensing Data Analysis : Vegetation has the effect of climate mitigation. Two large forest areas in metropolitan area have been analyzed in terms of NDVl (Normalized Difference Vegetation Index) and GST (ground surface temperature). A wide scatter of points in the scatter diagram between NDVI and GST can be explained by the size of forested and urbanized area determined by the 2-dimensional wavelet analysis.(3) Turbulence Structure of Canopy Flow : Honami phenomenon is interesting not only from the view point of fluid mechanics but also from a practical view of environment and food production, since the plant waving may contribute considerably to accelerate the exchange of momentum, matter (CO_2 and O_2) and heat. The wavelet analysis of 3-dimensional numerical simulation of the turbulent canopy flow shows the temporal change of the flow structure.(4) Removal of Measurement Error : Noise signals which cause serious error especially in inverse estimation problems are removed by the technique, detecting meaningless higher frequency white noise and impulse signals.