{"responseHeader":{"status":0,"QTime":8,"params":{"q":"{!q.op=AND}id:\"92718\"","hl":"true","hl.simple.post":"","hl.fragsize":"5000","fq":"!embargo_tdt:[NOW TO *]","hl.fl":"ocr_t","hl.method":"unified","wt":"json","hl.simple.pre":""}},"response":{"numFound":1,"start":0,"docs":[{"modified_tdt":"2015-11-02T00:00:00Z","thumb_s":"/f3/a2/f3a2a8c0f377e39e91764a55df3fc6e38fa76e2d.jpg","oldid_t":"compsci 536","setname_s":"ir_computersa","file_s":"/07/97/079771f1cadb25bc2f7f86031273a9e5bd539ec8.pdf","title_t":"Page 37","ocr_t":"26 1 2n-1 ik1r Ak = - L Ui cos - n i=O n 1 2n-1 ik1r Bk =- L uisin-n i=O n (4.8) Equation ( 4. 7) represents a meteorological field around a given latitude circle as a sum of wave functions in the form of one dimensional data. In order to represent the two dimensional data field, the appropriate orthogonal basis functions must be defined as global fitting functions. The functions used in most spectral models are called spherical harmonics. In essence these are combined functions of sine and cosine functions to represent zonal structure and Legendre polynomials to represent meridional structure. The dependent variable V may be represented as J J+lml V(.-\\, ¢>) = L L nr;: p;: sin¢> eim>. (4.9) m=-Jn=lml where m is the zonal wave number, n is total wave number, J is the maximum wave number resolved, n:;: are the coefficients, ¢> is latitude, ,\\ is longitude, and P;:- ·sin¢> are Legendre polynomials of the first kind, which are defined by (4.10) where 11 is colatitude. Horizontal values of multiple levels can be calculated by the same method. In grid point models there are truncation errors associated with the finite dif-ference approximation used to evaluate the derivatives and the errors become larger if grid lengths increase. However, there is no difference approximation needed in the horizontal domain, since all of derivatives are evaluated analytically. Analytical computation of derivatives is possible because functions derivatives are known exactly. Hence this model provides better numerical stability and it guides","restricted_i":0,"id":92718,"created_tdt":"2015-11-02T00:00:00Z","format_t":"application/pdf","parent_i":92762,"_version_":1642982584347525120}]},"highlighting":{"92718":{"ocr_t":[]}}}