小波变换在河西地区水文和气候周期变化分析中的应用

小波时—频分析由于其局部优化性质而优于傅立叶分析。应用 Meyer小波 ,对甘肃河西地区近 50 a来年径流量、年降水量和年平均气温做周期分析 ,发现河西地区水文气象序列的变化周期基本在 35a、2 2 a、1 1 a、5～ 6a和 2～ 3a左右的时间尺度上浮动。而这些基本周期正是太阳黑子活动周期或海—气相互作用的周期 ,说明河西地区水文、气象序列的周期变化受天体运动变化的影响。天体运动直接影响降水和气温的周期变化 ,进而在一定的下垫面条件下 ,影响径流的周期变化。

APPLICATION OF WAVELET TRANSFORM ON ANNUAL RUNOFF，YEARLY AVERAGE AIR TEMPERATURE AND ANNUAL PRECIPITATION PERIODIC VARIATIONS IN HEXI REGION

Hexi Region lies in the inland area of Northwest China that is semi-arid and arid region.Because of relatively scare precipitation in this area,the main water resources are the runoff from the mountain drainage basin.Precipitation,evapotranspiration and runoff are the dynamic factors of the water resources balance of this region,while precipitation and air temperature are main factors that effect evapotranspiration.Therefore,it is very important to know the variation regularities of the hydrological and meteorological series in this region.For this purpose,we use the Meyer wavelet transform method that has being used extensively in hydrology and in meteorology,to analysis the periodic regularities of the annual precipitation,yearly average air temperature and annual runoff in Hexi region. 　　The Meyer wavelet function is: Ψ(ω)=0　　　　　　　　　　　　　 ｜ω｜［(2)/(3)π，(8)/(3)π］ (2π)-1/2eiω/2sin((π)/(2)v((3)/(2π)｜ω｜-1)) (2)/(3)π｜ω｜(4)/(3)π (2π)-1/2eiω/2cos((π)/(2)v((3)/(4π)｜ω｜-1)) (4)/(3)π｜ω｜(8)/(3)π (1) Where v(x)=x4(35-84 x+70 x2-20 x3)　　0x1 　　To discrete Hydrologic and Meteorological series r(k),the Lagrange A Trous algorithm is: w(i,j)=∫∞-∞r(t)(1)/(a)Ψ((t-b)/(a))dt (2) where a=2－j,and b=a*j,they are scaling coefficient and position coefficient respectively; w(i,j) is wavelet coefficient at level i position j. 　　Using low-pass wave filter,we can get the approximation coefficient CA1,and using high-pass filter,we can get the detail coefficient CD1.Then,we decompose the CA1 into CA2 and CD2 in the same way,and so on.Now we reconstruct the approximation and detail coefficient Ai and Di,i=1,2,…n,where n is decomposed level of the hydrologic or meteorological series.At last,we get the reconstructed hydrologic or meteorological series using the next equation: r(k)=An(k)+Σni=1Di(k) (3) 　　Plot the graph of the reconstructed hydrologic or meteorological series,from which we can find the periods of these series.If the series are long enough,the approximation coefficient An will provide the tendency period.From i=1～5,the periods that Di reflect are from short to long relatively. 　　The results show that the periods of average annual air temperature and yearly precipitation series of Hexi Region are accordant,and they vary at 35 a,22 a,11 a,5～6 a and 2～3 a or 4 a.It agrees with the variation regularities of the mutual action of sea and atmosphere,and of the sunspot.They both affect the climatic change of the globe.Thus they effect the periodic changes of runoff.