Advances in Earth Science ›› 2001, Vol. 16 ›› Issue (3): 339-345. doi: 10.11867/j.issn.1001-8166.2001.03.0339

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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   

  1. Cold and Arid Regions Environmental and Engineering Research Institute,Chinese Academy of Sciences,Lanzhou730000,China
  • Received:2000-10-09 Revised:2000-12-14 Online:2001-06-01 Published:2001-06-01

CHEN Ren-sheng, KANG Er-si, ZHANG Ji-shi. APPLICATION OF WAVELET TRANSFORM ON ANNUAL RUNOFF,YEARLY AVERAGE AIR TEMPERATURE AND ANNUAL PRECIPITATION PERIODIC VARIATIONS IN HEXI REGION[J]. Advances in Earth Science, 2001, 16(3): 339-345.

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 |   [23π,83π]
               (2π)-1/2eiω/2sin(π2v(32π ω - 1))23π  ≤ω≤  43π
              (2π)-1/2eiω/2cos(π2v(34π ω - 1))43π  ≤ω  ≤83π                 (1)
Where  v(x)=x4(35-84x+70x2-20x3)           0 ≤x ≤1
     To discrete Hydrologic and Meteorological seriesr(k), the Lagrange A Trous algorithm is:
    w(i,j) =-∞r(t)1 /a1/2 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 CA1into CA2and CD2in the same way, and so on. Now we reconstruct the approximation and detail coefficient Aiand Di,i=1,2,…n, wherenis 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 Anwill provide the tendency period. Fromi=1~5, the periods thatDireflect 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.

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