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**********************************************************************************************
****************** Overview of the CDAT interface to the NCAR SPHEREPACK 3.0 *****************
**********************************************************************************************
None
************************************************************************************
************************** Sphere class documentation ******************************
************************************************************************************
--------------------------------------------------------------------------------------
To make an instance x of the Sphere class type
x = sphere.Sphere(lonArray , latArray, numberLevels = nlev, numberTimes = ntime,
computed_stored = 'computed')
where nlev and ntime are the actual number of levels and times respectively and the
keywords are
lonArray = longitude vector (required)
latArray = latitude vector (required)
numberLevels = number of levels (optional)
numberTimes = number of times (optional)
computed_stored (optional) : 'computed' -- computed Legendre polynomials
'stored' -- stored Legendre polynomials
This choice involves a 30% storage/speed tradeoff
As an example, for a 2D field using 'computed Legendre polynomials' type
x = sphere.Sphere(lonArray , latArray)
As an example, for a 4D field with 3 levels, 120 times using 'stored Legendre polynomials' type
x = sphere.Sphere(lonArray , latArray, 3, 120, 'stored')
or using the keywords explicitly
x = sphere.Sphere(lonArray , latArray, numberLevels = 3, numberTimes = 120,
computed_stored = 'stored')
where the order of the keyword entries is immaterial.
-----------------------------------------------------------------------------------
**************************** Sphere class functions ********************************
--------------------------------------------------------------------------------------------------------
routine: div
purpose: computes the divergence of a vector function
usage: div = x.div( u, v, missingValue) where x is an instance of Sphere
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: div -- the divergence of the vector function
definition: div(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: idiv
purpose: computes an irrotational vector function with given divergence
usage: u, v = x.idiv(div, missingValue)
passed: div -- divergence function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: u -- zonal vector function
v -- meridional vector function
definition: idiv(self, div, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: vrt
purpose: computes the scalar vorticity of a vector function
usage: vort = x.vrt(u, v, missingValue)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: vort -- the vorticity of the vector function
definition: vrt(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: ivrt
purpose: computes a divergence-free vector function whose vorticity is
given
usage: u, v = x.ivrt(vort, missingValue)
missingValue -- an optional number requesting a check for missing data
passed: vort -- vorticity on a global grid
returned: u -- zonal vector function
v -- meridional vector function
definition: ivrt(self, vort, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: idvt
purpose: computes a vector function with given divergence and vorticity
usage: u, v = x.idvt(div, vort, missingValue)
passed: div -- divergence function on a global grid
vort -- vorticity function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: u -- zonal vector function
v -- meridional vector function
definition: idvt(self, div, vort, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: vts
purpose: computes the derivative of the vector function with respect
to latitude
usage: ud, vd = x.vrt(u, v, missingValue)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: ud -- zonal vector function
vd -- meridional vector function
definition: vts(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: grad
purpose: computes the gradient of a scalar function
usage: u, v = x.grad(sf, missingValue)
passed: sf -- scalar function on a global grid
returned: u -- zonal vector function
v -- meridional vector function
missingValue -- an optional number requesting a check for missing data
definition: grad(self, sf, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: igrad
purpose: computes a scalar function whose gradient is a given vector
function
usage: sf = x.igrad(u, v, missingValue)
passed: u -- zonal vector function
v -- meridional vector function
missingValue -- an optional number requesting a check for missing data
returned: sf -- a scalar function
definition: igrad(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: slap
purpose: computes a scalar Laplacian of a scalar function
usage: slap = x.slap(self, sf, missingValue)
missingValue -- an optional number requesting a check for missing data
passed: sf -- scalar function on a global grid
returned: slap -- scalar function
definition: slap(self, sf, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: islap
purpose: computes a scalar function whose scalar Laplacian is given
usage: sf, ierror = x.islap(slap, missingValue):
passed: slap -- scalar Laplacian on a global grid
missingValue -- an optional number requesting a check for missing data
returned: sf -- a scalar function
definition: islap(self, slap, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: vlap
purpose: computes the vector Laplacian of a given vector function
usage: ulap, vlap = x.vlap(u, v, missingValue)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: ulap -- zonal vector Laplacian function
vlap -- meridional vector Laplacian function
definition: vlap(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: ivlap
purpose: computes a vector function whose Laplacian is a given vector
vector function
usage: u, v = x.ivlap(ulap, vlap, missingValue)
missingValue -- an optional number requesting a check for missing data
passed: ulap -- zonal Laplacian vector function on a global grid
vlap -- meridional Laplacian vector function on a global grid
returned: u -- zonal vector function
v -- meridional vector function
definition: ivlap(self, ulap, vlap, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: sfvp
purpose: computes the stream function and the velocity potential of a
vector function
usage: sf, vp = x.sfvp(u, v, missingValue)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: sf -- stream function
vp -- velocity potential
definition: sfvp(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: isfvp
purpose: computes a vector function with a given stream function and
velocity potential
usage: u, v = x.isfvp(sf, vp, missingValue):
passed: sf -- stream function on a global grid
vp -- velocity potential on a global grid
missingValue -- an optional number requesting a check for missing data
returned: u -- zonal vector function
v -- meridional vector function
definition: isfvp(self, sf, vp, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: truncation
purpose: performs a triangular truncation of a scalar or a vector function with
or without tapering. For example, a request for T42 entails eliminating all
values for the total wavenumber above 42. The remaining values are tapered
by default.
usage: u, v = truncation(42, u, v)
u, v = truncation(wave, u, v)
u, v = truncation(wave, u, v, 'no', missingValue):
or
sf = truncation(42, sf):
sf = truncation(wave, sf):
sf = truncation(wave, sf, v, 'no', missingValue):
passed: wave - the truncation wave number. For example, a request for T42 is wave set
to 42 whick entails eliminating all values for the total wavenumber above 42.
u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
or
sf -- a scalar with v = None instead of u, v
taper - (optional) the values remaining after truncation are tapered if the default 'yes'
is not changed to 'no'.
missingValue -- an optional number requesting a check for missing data
returned: u, v or sf
definition: truncation(self, wave, u, v = None, taper = 'yes', missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: sha
purpose: computes analysis coefficients for a scalar function
usage: a, b = x.sha(sf, missingValue)
missingValue -- an optional number requesting a check for missing data
passed: sf -- scalar function on global grid
returned: a -- coefficients
b -- coefficients
definition: sha(self, sf, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: shs
purpose: computes a scalar function from the coefficients
usage: sf = x.shs(a, b)
passed: a -- coefficients
b -- coefficients
returned: sf -- scalar function
definition: shs(self, a, b):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: vha
purpose: computes the vector harmonic analysis
usage: br, bi, cr, ci = x.vha(u, v, missingValue)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
missingValue -- an optional number requesting a check for missing data
returned: br -- coefficients
bi -- coefficients
cr -- coefficients
ci -- coefficients
definition: vha(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: vhs
purpose: computes the vector harmonic synthesis
usage: u, v = x.vhs(br, bi, cr, ci)
passed: br -- coefficients
bi -- coefficients
cr -- coefficients
ci -- coefficients
returned: u -- zonal vector function
v -- meridional vector function
definition: vhs(self, br, bi, cr, ci):
--------------------------------------------------------------------------------------------------------
************************************************************************************
**************************** Regrid class documentation ****************************
************************************************************************************
--------------------------------------------------------------------------------------
To make an instance x of the Regrid class type
x = sphere.Regrid(lonArrayOut, latArrayOut, lonArrayIn, latArrayIn, numberLevels = nlev,
numberTimes = ntime)
where nlev and ntime are the actual number of levels and times respectively and the keywords are
lonArrayOut = output grid longitude vector (required)
latArrayOut = output grid latitude vector (required)
lonArrayIn = input grid longitude vector (required)
latArrayIn = input grid latitude vector (required)
numberLevels = input grid number of levels (optional)
numberTimes = input grid number of times (optional)
-----------------------------------------------------------------------------------
****************************** Regrid class functions ******************************
--------------------------------------------------------------------------------------------------------
routine: regridScalar
purpose: transfers scalar data from one global spherical grid to
another. The grids may be gaussian or equally spaced.
usage: sfregrid= x.regridScalar(sf)
passed: sf -- scalar function on a global grid
returned: sfregrid -- regridded scalar function
definition: regridScalar(self, sf, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: regridVector
purpose: transfers vector data from one global spherical grid to another.
The grids can be gaussian or equally spaced.
usage: uregrid, vregrid = x.regridVector(u, v)
passed: u -- zonal vector function on a global grid
v -- meridional vector function on a global grid
returned: uregrid -- zonal regridded vector function
vregrid -- meridional regridded vector function
definition: regridVector(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
************************************************************************************
*************************** Shiftgrid class documentation **************************
************************************************************************************
--------------------------------------------------------------------------------------
To make an instance x of the Shiftgrid class type
x = sphere.Shiftgrid(lonArray, latArray, numberLevels = nlev, numberTimes = ntime)
where nlev and ntime are the actual number of levels and times respectively and the keywords are
lonArray = longitude vector (required)
latArray = latitude vector (required)
numberLevels = number of levels (optional)
numberTimes = number of times (optional)
-----------------------------------------------------------------------------------
***************************** Shiftgrid class functions ****************************
--------------------------------------------------------------------------------------------------------
routine: shiftScalar
purpose: transfers scalar data on the sphere between an equally spaced
grid that includes the poles and a grid which is offset by a
half grid increment in both longitude and latitude (which
excludes the poles)
usage: sfshift = x.shiftScalar(sf)
passed: sf -- an evenly spaced scalar function on a global grid
returned: sfshift -- the shifted evenly spaced scalar function
definition: shiftScalar(self, sf, missingValue = None):
--------------------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------------------
routine: shiftVector
purpose: transfers vector data on the sphere between an equally spaced
grid that includes the poles and a grid which is offset by a
half grid increment in both longitude and latitude (which
excludes the poles)
usage: ushift, vshift = x.shiftVector(u,v)
passed: u -- zonal evenly spaced vector function on a global grid
v -- meridional evenly spaced vector function on a global grid
returned: ushift -- zonal evenly spaced vector function
vshift -- meridional evenly spaced vector function
definition: shiftVector(self, u, v, missingValue = None):
--------------------------------------------------------------------------------------------------------
************************************************************************************
**************************** Utility documentation *********************************
************************************************************************************
-----------------------------------------------------------------------------
routine: gridGenerator
purpose: generate the grid vectors
usage: lonvals, latvals = sphere.gridGenerator(nlon, nlat, firstLongitude,
typeLatitudes, directionLatitudes)
passed: nlon - size of longitude vector
nlat - size of latitude vector
firstLongitude -- first vector element
typeLatitudes -- 'even' or 'gaussian'
directionLatitudes -- 'north_to_south' or 'south_to_north'
return: lonvals, latvals - the double precision grid vectors
definition: gridGenerator(nlon, nlat, firstLongitude, typeLatitudes, directionLatitudes):
-----------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------
routine: truncate
purpose: perform a triangular truncation of the coefficients in the arrays a and b with
or without tapering. For example, a request for T42 entails eliminating all
values for the total wavenumber above 42. If taper is not None, the remaining
values are tapered.
usage: a,b = truncate(wave, a, b) -- use tapering
a,b = truncate(wave, a, b, taper = 'no') -- turn off tapering
passed: a, b - the arrays
wave - the truncation wavenumber
taper - request for tapering the coefficient values
returned: a, b - the truncated coefficient arrays
definition: truncate(wave, a, b, taper = 'yes'):
note: a, b have indices (nt, n, m)
note: the formula for the exponential tapering was taken from John C. Adams. It is described
in Sardeshmukh P. D. and Hoskins B. J., 1984, Spatial Smoothing on the Sphere. Mon. Wea.
Rev., 112, 2524-2529.
-------------------------------------------------------------------------------------------
|
