In this paper, wavelet analysis methods, mainly including wavelet basis function, continuous and discrete wavelet transform and wavelet threshold de-noising, were introduced first. Then, current researches and applications of the wavelet analysis methods to various aspects of hydrology were summarized and reviewed from three points of view: research significance, current researches and applications, and key and difficult problems and the inadequate applications to hydrology. The six aspects of wavelet-based hydrologic analysis include: continuous wavelet-based analysis of hydrologic time series' characteristics under multi-temporal scales, discrete wavelet decomposition and reconstruction different sub-signals of hydrologic time series, quantification of complicated variability of hydrologic processes, wavelet de-noising in hydrologic time series, wavelet cross-correlation analysis of hydrologic time series, and wavelet-based hydrologic time series simulation and forecasting. Finally, several suggestions and opinions on the future researches and applications of wavelet analysis methods in hydrology were discussed. They focus on selection of wavelet basis function, wavelet threshold de-noising, wavelet decomposition, wavelet cross-correlation analysis, and wavelet aided forecasting.

Rainfall data are often obtained by ground-based observatories. However, traditional measurements based on raingauge stations can't reflect the spatial variation of precipitation effectively, especially in the Shiyang River Basin, which is a typical area with complicated terrain and climatic characteristics. There is great potential in making hydrological predictions by using satellite-based rainfall estimation. As a precipitation radar satellite, TRMM has been collecting plenty of fine temporal-spatial precipitation data. However, when applied to local basins and regions, the spatial resolution of TRMM products is too coarse, so it is necessary to develop a method to improve the spatial resolution of TRMM before using it. In this paper, a statistical downscaling algorithm based on the relationship between Tropical Rainfall Measuring Mission (TRMM) 3B43 dataset and the DEM(GTOPO30)from USGS is presented. A multiple linear regression model was established under the scale of 1 km. By applying a downscaling methodology based on 1 km resolution, the TRMM3B43 0.25°×0.25° precipitations were downscaled to 1 km×1 km pixel precipitation for each year from 2001 to 2010. The downscaled precipitation estimates were subsequently validated by using the observations obtained from 34 raingauge stations for the duration of 10 years in the Shiyang River Basin. These results showed that: the downscaling procedure resulted in significant improvement in spatial resolution and data quality for annual precipitation during 2001-2010, as well as for a typical dry year (2001) and wet year (2007), and captured the trends of precipitation in spatial distribution and inter-annual variability of annual precipitation with the coefficient of determination R2 ranging from 0.45 to 0.93 at 34 different raingauge stations.