Dynlib diag functions

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.

ddx : partial x derivative

res=ddx(dat,dx,dy)

Calculates the partial x derivative of dat, using centred differences. For a non-EW-cyclic grid, 0 is returned on the edges of the x domain.

ddy : partial y derivative

res=ddy(dat,dx,dy)

Calculates the partial y derivative of dat, using centred differences. For a non-EW-cyclic grid, 0 is returned on all edges of the x,y domain. For an EW-cyclic grid, 0 is returned on the first and last latitudes.

grad : 2-D gradient

(resx,resy)=grad(dat,dx,dy)

Calculates the 2-D gradient of dat, using centred differences in x and y. For a non-EW-cyclic grid, 0 is returned on all edges of the x,y domain. For an EW-cyclic grid, 0 is returned on the first and last latitudes.

lap2 : 2-D laplacian

res=lap2(dat,dx,dy)

Calculates the 2-D laplacian of dat, using centred differences. For a non-EW-cyclic grid, 0 is returned on all edges of the x,y domain. For an EW-cyclic grid, 0 is returned on the first and last latitudes.

vor : 2-D vorticity

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

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

div : 2-D divergence

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

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

def_shear : shear deformation

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

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

def_stretch : stretch deformation

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

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

def_total : total deformation

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

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

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).

isopv_angle : iso-PV contour angle

res=isopv_angle(pv,dx,dy)

Calculates the angle between the x-axis and the iso-lines of PV.

beta : angle between dilatation axis and iso-PV contours

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

Calculates the angle between the dilatation axis and the iso-lines of PV.

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)LapKleHua1999 
= -1/|gradPV| * Fn (Keyser Reeder Reed)KeyReeRee1988 
Fn = 0.5*|gradPV|(D-E*cos(2*beta))
   =  1/|gradPV| * F (Markowski Richardson)Mar2010

stir 
= angular rotation rate of grad(PV) (aka stirring rate)
= d(theta)/dt (Lapeyre Klein Hua)LapKleHua1999

= 1/|gradPV| * Fs  (Keyser Reeder Reed)KeyReeRee1988 
 Fs = 0.5*|gradPV|(vort+E*sin(2*beta))

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)

rev : PV gradient reversal

(resa,resc,resai,resci,resaiy,resciy,tested) = 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 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

prepare_fft : make data periodic in y for FFT

res = prepare_fft(thedata,dx,dy)

Returns the data extended along complementary meridians (for fft). For each lon, the reflected (lon+180) is attached below so that data is periodic in x and y. NOTE: Input data must be lats -90 to 90, and nx must be even.

Arguments:
	Type	Dim	Description
thedata	real	(nz,ny,nx)	input data

Returns:
	Type	Dim	Description
res	real	(nz,2*ny-2,nx)	output data

sum_kix : sum along k for flagged k-values

(res,nres) = sum_kix(thedata,kix,dx,dy)

Calculates sum along k dimension for k values which are flagged to 1 in kix vector (length nz).

Arguments:
	Type	Dim	Description
thedata	real	(nz,ny,nx)	input data
kix	int	(nz)	index flag for summation

Returns:
	Type	Dim	Description
res	real	(ny,nx)	(summed) output data
nres	int	0	Number of data summed = sum(kix)

Sum_kix is typically used for calculating seasonal means. To do this, kix is set to 1 for times in the relevant season and 0 elsewhere. After (further) summing res and nres over all years, res/nres gives the mean for the season for all years.

high_enough : flags points which are sufficiently above ground

res = high_enough(zdata,ztest,zthres,dx,dy)

Arguments:
	Type	Dim	Description
zdata	real	(nz,ny,nx)	geopotential of gridpoints
ztest	real	(1,ny,nx)	geopotential of topography
zthres	real	0	threshold geopotential height difference

Returns:

Type

Dim

Description

res

int*1

(nz,ny,nx)

Flag array set to:

1 if zdata(t,y,x) > (ztest(1,y,x) + zthres)

0 otherwise

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 ^[1] : 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

v_g : geostrophic velocity

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

Calculates geostrophic velocity. Returns zero on equator.

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 paperOku1969 (assumes divergence is negligible).

laccel : Lagrangian acceleration

(resx,resy) = laccel(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

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

dphidt : Lagrangian derivative of compression axis angle

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

Calculates Lagrangian time derivative of compression axis angle: d(phi)/dt (ref Lapeyre et. al 1999LapKleHua1999 ), from deformation and Lagrangian acceleration 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

References

KeyReeRee1988 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},

}

LapKleHua1999 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> <bibtex>

Mar2010 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>

Oku1969 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> <bibtex>

Riv2009 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>

↑ Riv2009

[1] Riv2009

[1]