汉江流域日降水多种小波分解与重构及其时空分布

Multi-wavelet Decomposition and Reconstruction of Daily Precipitation over the Hanjiang River Basin

将汉江流域55个气象站点1981年的日降水数据作为随机信号,借助于小波分析时间变化特征,利用Haar等7种小波函数分解日降水信号,采用Kriging空间内插方法把分解得到的小波系数空间离散化,在每个100m×100m栅格上进行小波的重构,从而实现随机性较高的日降水信息的时空降尺度,以期得到较为准确的日降水时空数据集。利用该流域另外45个气象站点1981年的日降水数据进行时空模拟结果的验证。通过平均误差等指标的定量评估,结果表明,采用Haar小波母函数对日降水信号进行分解与重构能够最准确地表达日降水的时空变化特征,更能充分表达日降水的高度随机性本质特征。

Daily precipitation of 55 meteorological stations over the Hanjiang River basin was regard as stochastic signal in order to express its change characteristics on temporal scale. At first, daily precipitation signal was decomposed using the Haar wavelet, the Daubechies （db2） wavelet, etc. and the wavelet coefficient from decomposition of daily precipitation was regionalized using the Kriging spatial interpolation algorithm. Then the wavelet coefficient in each 100 m X 100 m grid was reconstructed by the Haar wavelet and six other wavelets to get the spatial and temporal mapping of daily precipitation and test the sensitivity of different wavelet functions to the interpolated results. Meanwhile the daily precipitation amount from other 45 meteor- ological stations over the Hanjiang River basin was used to validate the interpolated results quantitatively by five indexes： mean error （ME）, mean absolute error （MAE）, root mean-square error （RMSE）, correlation coefficient, and determinacy coefficient. Results show that the Haar wavelet is the best wavelet to decompose and reconstruct daily precipitation and express the temporal-spatial variation of daily precipitation. The wave profile of the Haar wavelet in the time domain resembles the shape of the precipitation impulses in a given time span, which might be the best way to simulate the temporal variation of daily precipitation. So the interpolated results of daily precipitation amount using the Haar wavelet is perfect in the spatial-temporal interpolation model based on wave over the Hanjiang River basin.