splegend.f File Reference

Compute Legendre polynomials. More...

Go to the source code of this file.

Functions/Subroutines
subroutine	splegend (I, M, SLAT, CLAT, EPS, EPSTOP, PLN, PLNTOP)
	Evaluates the orthonormal associated Legendre polynomials in the spectral domain at a given latitude. More...

Detailed Description

Compute Legendre polynomials.

Author

IREDELL

Date

92-10-31

Definition in file splegend.f.

Function/Subroutine Documentation

splegend()

subroutine splegend	(		I,
			M,
			SLAT,
			CLAT,
		real, dimension((m+1)*((i+1)*m+2)/2)	EPS,
		real, dimension(m+1)	EPSTOP,
		real, dimension((m+1)*((i+1)*m+2)/2)	PLN,
		real, dimension(m+1)	PLNTOP
	)

Evaluates the orthonormal associated Legendre polynomials in the spectral domain at a given latitude.

Subprogram splegend should be called already. If l is the zonal wavenumber, N is the total wavenumber, and EPS(L,N)=SQRT((N**2-L**2)/(4*N**2-1)) then the following bootstrapping formulas are used:

 PLN(0,0)=SQRT(0.5)
 PLN(L,L)=PLN(L-1,L-1)*CLAT*SQRT(FLOAT(2*L+1)/FLOAT(2*L))
 PLN(L,N)=(SLAT*PLN(L,N-1)-EPS(L,N-1)*PLN(L,N-2))/EPS(L,N)
 

Synthesis at the pole needs only two zonal wavenumbers. Scalar fields are synthesized with zonal wavenumber 0 while vector fields are synthesized with zonal wavenumber 1. (Thus polar vector fields are implicitly divided by clat.) The following bootstrapping formulas are used at the pole:

 PLN(0,0)=SQRT(0.5)
 PLN(1,1)=SQRT(0.75)
 PLN(L,N)=(PLN(L,N-1)-EPS(L,N-1)*PLN(L,N-2))/EPS(L,N)
 

PROGRAM HISTORY LOG:

• 91-10-31 MARK IREDELL
• 98-06-10 MARK IREDELL GENERALIZE PRECISION

Parameters

	I	- INTEGER SPECTRAL DOMAIN SHAPE (0 FOR TRIANGULAR, 1 FOR RHOMBOIDAL)
	M	- INTEGER SPECTRAL TRUNCATION
	SLAT	- REAL SINE OF LATITUDE
	CLAT	- REAL COSINE OF LATITUDE
	EPS	- REAL ((M+1)*((I+1)*M+2)/2) SQRT((N**2-L**2)/(4*N**2-1))
	EPSTOP	- REAL (M+1) SQRT((N**2-L**2)/(4*N**2-1)) OVER TOP
[out]	PLN	- REAL ((M+1)*((I+1)*M+2)/2) LEGENDRE POLYNOMIAL
[out]	PLNTOP	- REAL (M+1) LEGENDRE POLYNOMIAL OVER TOP

Definition at line 44 of file splegend.f.

Referenced by sptgpm(), sptgpmv(), sptgps(), sptgpsv(), sptgpt(), sptgptsd(), sptgptv(), sptgptvd(), and sptranf0().