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《Advance In Earth Sciences》 2001-03

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

CHEN Ren sheng, KANG Er si, ZHANG Ji shi (Cold and Arid Regions Environmental and Engineering Research Institute, Chinese Academy of Sciences, Lanzhou 730000, China)
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｜[23 π ,83 π ] (2 π ) -1/2 e iω/2 sin ( π 2v(32 π ｜ω｜-1)) 23 π ｜ω｜43 π (2 π ) -1/2 e iω/2 cos ( π 2v(34 π ｜ω｜-1)) 43 π ｜ω｜83 π (1)Where v(x)=x 4(35-84 x+70 x 2-20 x 3) 0x1 To discrete Hydrologic and Meteorological series r(k), the Lagrange A Trous algorithm is:w(i,j)=∫∞-∞r(t)1aΨ(t-ba) d t(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 CA 1, and using high pass filter, we can get the detail coefficient CD 1. Then, we decompose the CA 1 into CA 2 and CD 2 in the same way, and so on. Now we reconstruct the approximation and detail coefficient A i and D i, 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)=A n(k)+ Σ ni=1D i(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 A n will provide the tendency period. From i=1~5, the periods that D i 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.
【Fund】： “九五”国家重点科技攻关项目!“河西走廊黑河流域山区水资源变化和山前水资源转化监测研究”(编号 :96 -12 -0 3-s) ;; 国家自然科学基
【CateGory Index】： P339
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