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

J·莫雷特在20世纪80年代初由S提出的“小波分析”的新理论正在迅速扩展其应用领域，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--谱分析是数据在整个时间域的频率分解方法，而新的小波分析方法是在频域和时间域分析数据。在本研究中，我们尝试将该方法的适用性扩展到水利工程和水文学中。(1)水文和水文气象：水文和水文气象时间序列，如降雨量、温度和径流量的重复季节变化，显示了这些模式的年变化。遥感数据分析：植被具有缓解气候的作用。利用归一化植被指数(NDVl)和地表温度(GST)对大都市地区的两大林区进行了分析。NDVI和GST散点图上的点的广泛散布可以用二维小波分析确定的森林和城市化区域的大小来解释。(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有助于加速动量、物质(CO_2和O_2)和热量的交换。对湍流冠层流动进行三维数值模拟的小波分析显示了流动结构的时间变化。(4)测量误差的消除：利用该技术去除引起严重误差的噪声信号，特别是在逆估计问题中，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.