Dynlib diag functions: Difference between revisions

Revision as of 18:32, 29 January 2013

Dynlib diagnostic functions

The functions generally operate on real arrays with dimension (nz,ny,nx) where nz is number of times or levels, and ny and nx are the number of latitudes and longitudes, respectively. The function descriptions below contain detailed descriptions of arguments and returns where there is any deviation from this pattern; otherwise they may be assumed to be of the form:

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	Zonal velocity
v	real	(nz,ny,nx)	Meridional velocity
pv	real	(nz,ny,nx)	Potential vorticity

Returns:
	Type	Dim	Description
res	real	(nz,ny,nx)	output data

The ubiquitous inputs dx and dy are all of the form

	Type	Dim	Description
dx	real	(ny,nx)	dx(j,i) = x(j, i+1) - x(j, i-1) (in metres)
dy	real	(ny,nx)	dy(j,i) = y(j+1, i) - y(j-1, i) (in metres)

Typically, the results for each level or time are computed individually in 2-D fashion, though they are returned as a 3-D array of the same size as the input.

dynlib.diag.vor : 2-D vorticity

res=vor(u,v,dx,dy)

Calculates the z component of vorticity of (u,v), using centred differences.

dynlib.diag.div : 2-D divergence

res=div(u,v,dx,dy)

Calculates the 2-D divergence of (u,v), using centred differences.

dynlib.diag.def_shear : shear deformation

res=def_shear(u,v,dx,dy)

Calculates the shear (antisymmetric) deformation of (u,v), using centred differences.

dynlib.diag.def_stretch : stretch deformation

res=def_stretch(u,v,dx,dy)

Calculates the stretch (symmetric) deformation of (u,v), using centred differences.

dynlib.diag.def_total : total deformation

res=def_total(u,v,dx,dy)

Calculates the total (rotation-independent) deformation of (u,v), using centred differences.

dynlib.diag.def_angle : deformation angle

res=def_angle(u,v,dx,dy)

Calculates the angle between the x-axis and the dilatation axis of the deformation of (u,v).

dynlib.diag.isoline_angle : iso-line contour angle

res=isoline_angle(pv,dx,dy)

Calculates the angle between the x-axis and the iso-lines of (for example) PV.

dynlib.diag.isoline_to_deformation_angle : angle between dilatation axis and iso-lines

res=isoline_to_deformation_angle(u,v,pv,dx,dy)

Calculates the angle between the dilatation axis and the iso-lines of (for example) PV.

dynlib.diag.stretch_stir : fractional stretching rate and angular rotation rate of grad(PV)

(stretch,stir)=stretch_stir(u,v,pv,dx,dy)

Returns real arrays, dim (nz,ny,nx):

stretch 
= fractional PV gradient stretching rate 
= 1/|gradPV| * d/dt(|gradPV|)
= gamma, 'stretching rate' (Lapeyre Klein Hua)^[1]
= -1/|gradPV| * Fn (Keyser Reeder Reed)^[2]

Fn = 0.5*|gradPV|(D-E*cos(2*beta))
   =  1/|gradPV| * F (Markowski Richardson)^[3]

stir 
= angular rotation rate of grad(PV) (aka stirring rate)
= d(theta)/dt (Lapeyre Klein Hua)^[1]

= 1/|gradPV| * Fs  (Keyser Reeder Reed)^[2] 
 Fs = 0.5*|gradPV|(vort+E*sin(2*beta))

dynlib.diag.geop_from_montgp : geopotential

res = geop_from_montgp(m,theta,p,dx,dy)

Calculates geopotential (res) from montgomery potential (m), potential temperature (theta) and pressure (p)

dynlib.diag.grad_rev : PV gradient reversal

(resa,resc,resai,resci,resaiy,resciy,tested) = grad_rev(pv,highenough,latitudes,ddythres,dx,dy)

Finds the reversals of PV y-gradient (where the negative y-gradient exceeds some threshold) and classifies them as c (cyclonic) or a (anticyclonic). Three measures of c and a reversals are returned (6 in total). Only points flagged in highenough are tested.

Arguments:
	Type	Dim	Description
pv	real	(nz,ny,nx)	potential vorticity
highenough	int*1	(nz,ny,nx)	array of flags denoting whether to test the point for reversal
latitudes	real	(ny)	vector of latitudes
ddythres	real	0	Cutoff y-gradient for pv

highenough is typically the output of the dynlib.diag.highenough function, which returns 1 where the surface is sufficiently above ground level and 0 elsewhere.

ddythres is the cutoff y-gradient for pv. The magnitude of (negative) d(pv)/dy must be above ddythres for reversal to be detected; this applies to revc, reva, revci,revai. Typical value: 4E-12.

Returns:
	Type	Dim	Description
revc	int*1	(nz,ny,nx)	Flag =1 for cyclonic reversal (threshold test applied)
reva	int*1	(nz,ny,nx)	Flag =1 for anticyclonic reversal (threshold test applied)
revci	real	(nz,ny,nx)	Absolute PV gradient where reversal is cyclonic (threshold test applied)
revai	real	(nz,ny,nx)	Absolute PV gradient where reversal is anticyclonic (threshold test applied)
revciy	real	(nz,ny,nx)	Absolute PV y-gradient where reversal is cyclonic (no threshold test applied)
revaiy	real	(nz,ny,nx)	Absolute PV y-gradient where reversal is anticyclonic (no threshold test applied)
tested	int*1	(nz,ny,nx)	flag to 1 all tested points: where highenough==1 and point not on grid edge

dynlib.diag.contour_rwb : detects RWB events, Riviere algorithm

(beta_a_out,beta_c_out) = contour_rwb(pv_in,lonvalues,latvalues,ncon,lev,dx,dy)

Detects the occurrence of anticyclonic and cyclonic wave-breaking events from a PV field on isentropic coordinates.

Reference: Riviere 2009 ^[4]: See the appendix C.

Arguments:
	Type	Dim	Description
pv_in	real	(nz,ny,nx)	isentropic pv. Should be on a regular lat-lon grid and 180W must be the first longitude. (If 180W is not the first longitude, the outputs will have 180W as the first, so must be rearranged)
lonvalues	real	(nx)	vector of longitudes
latvalues	real	(ny)	vector of latitudes
ncon	int	0	number of contours to test, normally 41 or 21
lev	real	0	potential temperature of the level

Returns:
	Type	Dim	Description
beta_a_out	int	(nz,ny,nx)	flag array, =1 if anticyclonic wave breaking
beta_c_out	int	(nz,ny,nx)	flag array, =1 if cyclonic wave breaking

dynlib.diag.v_g : geostrophic velocity

(resx,resy) = v_g(mont,lat,dx,dy)

Calculates geostrophic velocity. Returns zero on equator.

dynlib.diag.okuboweiss : Okubo-Weiss criterion

res = okuboweiss(u,v,dx,dy)

Calculates Okubo-Weiss criterion lambda_0=1/4 * (sigma^2-omega^2)= 1/4 W, where sigma is total deformation and omega is vorticity.

This is the square of the eigenvalues in Okubo's paper^[5] (assumes divergence is negligible).

dynlib.diag.dot_uv : Lagrangian acceleration

(resx,resy) = dot_uv(u,v,mont,lat,dx,dy)

Calculates Lagrangian acceleration on the isentropic surface, based on Montgomery potential.

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	zonal velocity
v	real	(nz,ny,nx)	meridional velocity
mont	real	(nz,ny,nx)	Montgomery potential
lat	real	(ny)	vector of latitudes

dynlib.diag.accgrad_eigs : Lagrangian acceleration gradient tensor eigenvalues

(respr,respi,resmr,resmi) = accgrad_eigs(u,v,mont,lat,dx,dy)

Calculates eigenvalues of the lagrangian acceleration gradient tensor.

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	zonal velocity
v	real	(nz,ny,nx)	meridional velocity
mont	real	(nz,ny,nx)	Montgomery potential
lat	real	(ny)	vector of latitudes

Returns:
	Type	Dim	Description
respr	real	(nz,ny,nx)	Real part of positive eigenvalue
respi	real	(nz,ny,nx)	Imaginary part of positive eigenvalue
resmr	real	(nz,ny,nx)	Real part of negative eigenvalue
resmi	real	(nz,ny,nx)	Imaginary part of negative eigenvalue
ncon	int	0	number of contours to test, normally 41 or 21
lev	real	0	potential temperature of the level

dynlib.diag.dot_def_angle : Lagrangian time derivative of the deformation angle

res = dot_def_angle(u,v,mont,lat,dx,dy)

Calculates Lagrangian time derivative of the deformation angle from deformation and Lagrangian acceleration tensor. That quantity corresponds to

d(gamma)/dt (Spensberger and Spengler 2013^[6]) and
-d(phi)/dt (Lapeyre et. al 1999^[1] ).

<bibtex> @article{SpeSpe2013,

  author = {Spensberger, C. and Spengler, T.},
  title = {Deformation: A new diagnostic for large-scale flow},
  journal = {J. Atmos. Sci.},
  volume = {},
  number = {},
  pages = {in preparation},
  year = {2013},
  url = {},

} </bibtex>

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	zonal velocity
v	real	(nz,ny,nx)	meridional velocity
mont	real	(nz,ny,nx)	Montgomery potential
lat	real	(ny)	vector of latitudes

dynlib.diag.accgrad_eigs : Lagrangian acceleration gradient tensor eigenvalues

(respr,respi,resmr,resmi) = accgrad_eigs(u,v,mont,lat,dx,dy)

Calculates eigenvalues of the lagrangian acceleration gradient tensor.

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	zonal velocity
v	real	(nz,ny,nx)	meridional velocity
mont	real	(nz,ny,nx)	Montgomery potential
lat	real	(ny)	vector of latitudes

Returns:
	Type	Dim	Description
respr	real	(nz,ny,nx)	Real part of positive eigenvalue
respi	real	(nz,ny,nx)	Imaginary part of positive eigenvalue
resmr	real	(nz,ny,nx)	Real part of negative eigenvalue
resmi	real	(nz,ny,nx)	Imaginary part of negative eigenvalue
ncon	int	0	number of contours to test, normally 41 or 21
lev	real	0	potential temperature of the level

dynlib.diag.rotation_strain_ratio : ratio of effective rotation to strain rate

res = rotation_strain_ratio(u,v,mont,lat,dx,dy)

Calculates the r disgnostic of Lapeyre et al (1999)^[1]; r is the ratio of effective rotation to strain rate, where effective rotation comprises both vorticity and strain-axes rotation.

Arguments:
	Type	Dim	Description
u	real	(nz,ny,nx)	zonal velocity
v	real	(nz,ny,nx)	meridional velocity
mont	real	(nz,ny,nx)	Montgomery potential
lat	real	(ny)	vector of latitudes

References

↑ ^1.0 ^1.1 ^1.2 ^1.3 <bibtex> @article{LapKleHua1999, author = {Lapeyre, G. and Klein, P. and Hua, B. L.}, title = {Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence?}, journal = {Physics of Fluids}, volume = {11}, number = {12}, pages = {3729-3737}, year = {1999}, url = {<Go to ISI>://000083495900013 http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHFLE6000011000012003729000001&idtype=cvips&doi=10.1063/1.870234&prog=normal}, } </bibtex>
↑ ^2.0 ^2.1 <bibtex> @article{KeyReeRee1988, author = {Keyser, D. and Reeder, M. J. and Reed, R. J.}, title = {A Generalization of Petterssen Frontogenesis Function and Its Relation to the Forcing of Vertical Motion}, journal = {Monthly Weather Review}, volume = {116}, number = {3}, pages = {762-780}, year = {1988}, url = {<Go to ISI>://A1988N255100017}, } </bibtex>
↑ <bibtex> @book{Mar2010, author = {Markowski, Paul}, title = {Mesoscale meteorology in midlatitudes}, publisher = {Chichester, West Sussex, UK ;Hoboken, NJ : Wiley-Blackwell, 2010}, url = {http://books.scholarsportal.info/viewdoc.html?id=/ebooks/ebooks2/wiley/2011-12-13/2/9780470682104}, year = {2010}, } </bibtex>
↑ <bibtex> @article{Riv2009, author = {Riviere, G.}, title = {Effect of Latitudinal Variations in Low-Level Baroclinicity on Eddy Life Cycles and Upper-Tropospheric Wave-Breaking Processes}, journal = {Journal of the Atmospheric Sciences}, volume = {66}, number = {6}, pages = {1569-1592}, year = {2009}, url = {<Go to ISI>://000267263300006}, } </bibtex>
↑ <bibtex> @article{Oku1969, author = {Okubo, A.}, title = {Horizontal Dispersion of Foreign Particles in Vicinity of Velocity Singularities Such as Convergences}, journal = {Transactions-American Geophysical Union}, volume = {50}, number = {4}, pages = {182-&}, year = {1969}, url = {<Go to ISI>://A1969C982700332}, } </bibtex>
↑ Cite error: Invalid <ref> tag; no text was provided for refs named SpeSpe2013

[LapKleHua1999-1] 1.0 ^1.1 ^1.2 ^1.3 <bibtex> @article{LapKleHua1999, author = {Lapeyre, G. and Klein, P. and Hua, B. L.}, title = {Does the tracer gradient vector align with the strain eigenvectors in 2D turbulence?}, journal = {Physics of Fluids}, volume = {11}, number = {12}, pages = {3729-3737}, year = {1999}, url = {<Go to ISI>://000083495900013 http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PHFLE6000011000012003729000001&idtype=cvips&doi=10.1063/1.870234&prog=normal}, } </bibtex>

[KeyReeRee1988-2] 2.0 ^2.1 <bibtex> @article{KeyReeRee1988, author = {Keyser, D. and Reeder, M. J. and Reed, R. J.}, title = {A Generalization of Petterssen Frontogenesis Function and Its Relation to the Forcing of Vertical Motion}, journal = {Monthly Weather Review}, volume = {116}, number = {3}, pages = {762-780}, year = {1988}, url = {<Go to ISI>://A1988N255100017}, } </bibtex>

[Mar2010-3] <bibtex> @book{Mar2010, author = {Markowski, Paul}, title = {Mesoscale meteorology in midlatitudes}, publisher = {Chichester, West Sussex, UK ;Hoboken, NJ : Wiley-Blackwell, 2010}, url = {http://books.scholarsportal.info/viewdoc.html?id=/ebooks/ebooks2/wiley/2011-12-13/2/9780470682104}, year = {2010}, } </bibtex>

[Riv2009-4] <bibtex> @article{Riv2009, author = {Riviere, G.}, title = {Effect of Latitudinal Variations in Low-Level Baroclinicity on Eddy Life Cycles and Upper-Tropospheric Wave-Breaking Processes}, journal = {Journal of the Atmospheric Sciences}, volume = {66}, number = {6}, pages = {1569-1592}, year = {2009}, url = {<Go to ISI>://000267263300006}, } </bibtex>

[Oku1969-5] <bibtex> @article{Oku1969, author = {Okubo, A.}, title = {Horizontal Dispersion of Foreign Particles in Vicinity of Velocity Singularities Such as Convergences}, journal = {Transactions-American Geophysical Union}, volume = {50}, number = {4}, pages = {182-&}, year = {1969}, url = {<Go to ISI>://A1969C982700332}, } </bibtex>

[SpeSpe2013-6] Cite error: Invalid <ref> tag; no text was provided for refs named SpeSpe2013

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