Dynlib diag functions: Difference between revisions

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</bibtex>
</bibtex>
</ref>
</ref>
= -1/|gradPV| * Fn (Keyser Reeder Reed)<ref name="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},
}
</bibtex>
</ref>


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


  stir  
  stir  
  = angular rotation rate of grad(PV) (aka stirring rate)
  = angular rotation rate of grad(PV) (aka stirring rate)
  = d(theta)/dt (Lapeyre Klein Hua)<cite>LapKleHua1999</cite>  
  = d(theta)/dt (Lapeyre Klein Hua)<ref name="LapKleHua1999" />  


  = 1/|gradPV| * Fs  (Keyser Reeder Reed)<cite>KeyReeRee1988</cite>  
  = 1/|gradPV| * Fs  (Keyser Reeder Reed)<ref name="KeyReeRee1988" />  
   Fs = 0.5*|gradPV|(vort+E*sin(2*beta))
   Fs = 0.5*|gradPV|(vort+E*sin(2*beta))


Line 346: Line 367:
Detects the occurrence of anticyclonic and cyclonic wave-breaking events from a PV field on isentropic coordinates.
Detects the occurrence of anticyclonic and cyclonic wave-breaking events from a PV field on isentropic coordinates.


Reference: Riviere 2009 <ref>Riv2009</ref> : See the appendix C.
Reference: Riviere 2009 <ref name="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>
</ref>: See the appendix C.


{| border="1" class="wikitable" style="text-align:center;"
{| border="1" class="wikitable" style="text-align:center;"
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Calculates Okubo-Weiss criterion lambda_0=1/4 * (sigma^2-omega^2)= 1/4 W, where ''sigma'' is total deformation and ''omega'' is vorticity.
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<cite>Oku1969</cite> (assumes divergence is negligible).
This is the square of the eigenvalues in Okubo's paper<ref name="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>
</ref> (assumes divergence is negligible).


=== ''dynlib.diag.laccel'' : Lagrangian acceleration===
=== ''dynlib.diag.laccel'' : Lagrangian acceleration===
Line 511: Line 558:
==References==
==References==
<references />
<references />
<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>

Revision as of 10:35, 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.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.

dynlib.diag.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.

dynlib.diag.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.

dynlib.diag.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.

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.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.

dynlib.diag.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.

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.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

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

dynlib.diag.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.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

dynlib.diag.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)

dynlib.diag.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.

dynlib.diag.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

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.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

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.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

  1. ↑ 1.0 1.1 <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. ↑ 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>
  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>
  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>
  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>
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