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

80年代初由J. Morlet提出的一种新的理论--“小波分析”（WEVELETANALYSIS），正在迅速地扩展其应用领域，特别是在信号处理、信息通信和图象数据压缩等方面。传统的随机数据分析方法--谱分析法是在整个时间域上仅从频率上对数据进行分辨的方法，而小波分析法是一种新的随机数据分析方法，它是在频域和时间域上对数据进行分析的方法。本研究尝试将该方法推广到水利工程和水文学领域。(1)水文和水文气象学：水文和水文气象时间序列，如降雨量、温度和流量重复季节变化，显示了模式的年度变化。小波分析已被应用于阐明这些特征。(2)遥感数据分析：植被具有气候减缓效应。本文对北京市两个大型林区的归一化植被指数（NDVI）和地表温度（GST）进行了分析。NDVI和GST之间的散点图中的广泛分散的点可以解释由二维小波分析确定的森林和城市化地区的大小。(3)冠层流的湍流结构：Honami现象不仅从流体力学的角度来看，而且从环境和粮食生产的实际角度来看都是有趣的，因为植物波动可能大大有助于加速动量，物质（CO_2和O_2）和热量的交换。三维湍流冠层流数值模拟的小波分析揭示了流场结构的时间变化。(4)测量误差的去除：噪声信号，特别是在逆估计问题中引起严重的误差，通过该技术被去除，检测无意义的高频白色噪声和脉冲信号。

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.