正規化球帽諧函數展開及其在衛星測高觀測量之應用

Abstract

球諧函數展開應用於區性研究有理論和實質計算的困難，因此有必 要採用區域內相互 正交的函數來作研究。因為正規化球帽諧函數在球帽 內相互正交，所以適用於表現球帽內 的函數，可用於區域性的研究，於 是本文採用正規化球帽諧函數展開球帽內之SST異常。 TOPEX/POSEIDON( T/P)衛星任務為使用測高儀量測精確的海水面，主要的目的為決定大尺 度的海洋表面地形(SST)。而(T/P)週期10天之動態SST異常可視為海水位 的異常變化，這 與赤道太平洋發生之大自然現象ElNino具有相關性。本 研究的主要目的為結合T/P和ERS-1 測高資料，以球帽諧函展開來檢視赤 道東、西太平洋海水位的變動，藉以瞭解其與ElNino 的關係，採用 JGM-3/OSU91A混合大地水準面。 在赤道東、西太平洋各選取一個球 帽，使用最小二乘法求得球帽係數，從球帽係數分 析球帽內東、西太平 洋海水位異常變化。根據T/P與ERS-1資料所作的結果皆顯示1993年6 月 東太平洋海水位發生了極大的正異常，而西太平洋則發生負的海水位異常 ，這與UT/CSR 所作的研究相符合，此時發生了ElNino。球帽諧函數也可 以當作一個濾波器與中數濾波比 較大致相符 Spherical expansion for regional study will enconter theoretical and computational problems, so orthogonal functions over a given region are needed. Due to the orthogonaltity of normalized spherical cap harmonics, they are suitable for representing functions over a spherical cap. In this study, we use normalized spherical cap harmonic expansion to represent SST anomalies. TOPEX/POSEIDON(T/P)is a satellite mission thatuses altimeter to measure precise sea level. The major goal is the determination of large-scale sea surface topography(SST). T/P 10-day dynamic SST anomalies can be regraded as the variations of sea level which is related to ElNino in the tropical Pacific. The goal of this work is to use T/P and ERS-1 altimeter data to examine sea level changes over the eastern and western Pacific to establish the relationship between sea level and ElNino. For this purpose, JGM-3/OSU91A hybrid geoid is used. We choose two spherical caps in the eastern and western trapical Pacific. By least-squares methods, spherical cap harmonic coefficients were determined and the sea surface changes were analyzed with the coefficients. The results show that high positive sea level anomalies occurred in the eastern Pacific and negtive sea level anomalies in the western Pacific during June, 1993. This result is in good agreement with that obtained by UT/CSR. Also, spherical cap expansion can be used as a filter and the filtered SST is equivalent to that by the median filter.