Dynlib diag functions: Difference between revisions

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== Dynlib diagnostic functions ==
{{db-author}}
 
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:
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || Zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || Meridional velocity
|-
! width="80" | pv
| real || (nz,ny,nx) || Potential vorticity
|}
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Returns:
|-
|
! width="60" | Type
! width="120" | Dim
! width="300" | Description
|-
! width="80" | res
| real || (nz,ny,nx) || output data
|}
 
The ubiquitous inputs ''dx'' and ''dy'' are all of the form
{| border="1" class="wikitable" style="text-align:center;"
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | dx
| real || (ny,nx) || dx(j,i) = x(j, i+1) - x(j, i-1) (in metres)
|-
! width="80" | 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 ===
 
<code>res=vor(u,v,dx,dy)</code>
 
Calculates the z component of vorticity of (u,v), using centred differences.
 
=== ''dynlib.diag.div'' : 2-D divergence===
 
<code>res=div(u,v,dx,dy)</code>
 
Calculates the 2-D divergence of (u,v), using centred differences.
 
=== ''dynlib.diag.def_shear'' : shear deformation ===
 
<code>res=def_shear(u,v,dx,dy)</code>
 
Calculates the shear (antisymmetric) deformation of (u,v), using centred differences.
 
=== ''dynlib.diag.def_stretch'' : stretch deformation ===
 
<code>res=def_stretch(u,v,dx,dy)</code>
 
Calculates the stretch (symmetric) deformation of (u,v), using centred differences.
 
=== ''dynlib.diag.def_total'' : total deformation ===
 
<code>res=def_total(u,v,dx,dy)</code>
 
Calculates the total (rotation-independent) deformation of (u,v), using centred differences.
 
=== ''dynlib.diag.def_angle'' : deformation angle ===
 
<code>res=def_angle(u,v,dx,dy)</code>
 
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 ===
 
<code>res=isoline_angle(pv,dx,dy)</code>
 
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 ===
 
<code>res=isoline_to_deformation_angle(u,v,pv,dx,dy)</code>
 
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)===
 
<code>(stretch,stir)=stretch_stir(u,v,pv,dx,dy)</code>
 
Returns real arrays, dim (nz,ny,nx):
 
stretch
= fractional PV gradient stretching rate
= 1/|gradPV| * d/dt(|gradPV|)
= gamma, 'stretching rate' (Lapeyre Klein Hua)<ref name="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>
</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>
 
Fn = 0.5*|gradPV|(D-E*cos(2*beta))
    =  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
= angular rotation rate of grad(PV) (aka stirring rate)
= d(theta)/dt (Lapeyre Klein Hua)<ref name="LapKleHua1999" />
 
= 1/|gradPV| * Fs  (Keyser Reeder Reed)<ref name="KeyReeRee1988" />
  Fs = 0.5*|gradPV|(vort+E*sin(2*beta))
 
=== ''dynlib.diag.geop_from_montgp'' : geopotential ===
 
<code>res = geop_from_montgp(m,theta,p,dx,dy)</code>
 
Calculates geopotential (res) from montgomery potential (m), potential temperature (theta) and pressure (p)
 
=== ''dynlib.diag.grad_rev'' : PV gradient reversal ===
 
<code>(resa,resc,resai,resci,resaiy,resciy,tested) = grad_rev(pv,highenough,latitudes,ddythres,dx,dy)</code>
 
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. 
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | pv
| real || (nz,ny,nx) || potential vorticity
|-
! width="80" | highenough
| int*1 || (nz,ny,nx) || array of flags denoting whether to test the point for reversal
|-
! width="80" | latitudes
| real || (ny) || vector of latitudes
|-
! width="80" | 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.
           
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Returns:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | revc
| int*1 || (nz,ny,nx) || Flag =1 for cyclonic reversal (threshold test applied)
|-
! width="80" | reva
| int*1 || (nz,ny,nx) || Flag =1 for anticyclonic reversal (threshold test applied)
|-
! width="80" | revci
| real  || (nz,ny,nx) || Absolute PV gradient where reversal is cyclonic (threshold test applied)
|-
! width="80" | revai
| real  || (nz,ny,nx) || Absolute PV gradient where reversal is anticyclonic (threshold test applied)
|-
! width="80" | revciy
| real  || (nz,ny,nx) || Absolute PV y-gradient where reversal is cyclonic (no threshold test applied)
|-
! width="80" | revaiy
| real  || (nz,ny,nx) || Absolute PV y-gradient where reversal is anticyclonic (no threshold test applied)
|-
! width="80" | 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 ===
 
<code>(beta_a_out,beta_c_out) = contour_rwb(pv_in,lonvalues,latvalues,ncon,lev,dx,dy)</code>
 
Detects the occurrence of anticyclonic and cyclonic wave-breaking events from a PV field on isentropic coordinates.
 
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;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | 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)
|-
! width="80" | lonvalues
| real || (nx) || vector of longitudes
|-
! width="80" | latvalues
| real || (ny) || vector of latitudes
|-
! width="80" | ncon
| int || 0 || number of contours to test, normally 41 or 21
|-
! width="80" | lev
| real || 0 || potential temperature of the level
|}
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Returns:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | beta_a_out
| int || (nz,ny,nx) || flag array, =1 if anticyclonic wave breaking
|-
! width="80" | beta_c_out
| int || (nz,ny,nx) || flag array, =1 if cyclonic wave breaking
|}
 
=== ''dynlib.diag.v_g'' : geostrophic velocity ===
 
<code>(resx,resy) = v_g(mont,lat,dx,dy)</code>
 
Calculates geostrophic velocity. Returns zero on equator.
 
=== ''dynlib.diag.okuboweiss'' : Okubo-Weiss criterion===
 
<code>res = okuboweiss(u,v,dx,dy)</code>
 
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<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.dot_uv'' : Lagrangian acceleration===
 
<code>(resx,resy) = dot_uv(u,v,mont,lat,dx,dy)</code>
 
Calculates Lagrangian acceleration on the isentropic surface, based on Montgomery potential.
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || meridional velocity
|-
! width="80" | mont
| real || (nz,ny,nx) || Montgomery potential
|-
! width="80" | lat
| real || (ny) || vector of latitudes
|}
 
=== ''dynlib.diag.accgrad_eigs'' : Lagrangian acceleration gradient tensor eigenvalues ===
 
<code>(respr,respi,resmr,resmi) = accgrad_eigs(u,v,mont,lat,dx,dy)</code>
 
Calculates eigenvalues of the lagrangian acceleration gradient tensor.
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || meridional velocity
|-
! width="80" | mont
| real || (nz,ny,nx) || Montgomery potential
|-
! width="80" | lat
| real || (ny) || vector of latitudes
|}
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Returns:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | respr
| real || (nz,ny,nx) || Real part of positive eigenvalue
|-
! width="80" | respi
| real || (nz,ny,nx) || Imaginary part of positive eigenvalue
|-
! width="80" | resmr
| real || (nz,ny,nx) || Real part of negative eigenvalue
|-
! width="80" | resmi
| real || (nz,ny,nx) || Imaginary part of negative eigenvalue
|-
! width="80" | ncon
| int || 0 || number of contours to test, normally 41 or 21
|-
! width="80" | lev
| real || 0 || potential temperature of the level
|}
 
=== ''dynlib.diag.dot_def_angle'' : Lagrangian time derivative of the deformation angle ===
 
<code>res = dot_def_angle(u,v,mont,lat,dx,dy)</code>
 
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<ref name="SpeSpe2013" />) and
* -d(phi)/dt (Lapeyre et. al 1999<ref name="LapKleHua1999" /> ).
<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>
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || meridional velocity
|-
! width="80" | mont
| real || (nz,ny,nx) || Montgomery potential
|-
! width="80" | lat
| real || (ny) || vector of latitudes
|}
 
 
 
=== ''dynlib.diag.accgrad_eigs'' : Lagrangian acceleration gradient tensor eigenvalues ===
 
<code>(respr,respi,resmr,resmi) = accgrad_eigs(u,v,mont,lat,dx,dy)</code>
 
Calculates eigenvalues of the lagrangian acceleration gradient tensor.
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || meridional velocity
|-
! width="80" | mont
| real || (nz,ny,nx) || Montgomery potential
|-
! width="80" | lat
| real || (ny) || vector of latitudes
|}
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Returns:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | respr
| real || (nz,ny,nx) || Real part of positive eigenvalue
|-
! width="80" | respi
| real || (nz,ny,nx) || Imaginary part of positive eigenvalue
|-
! width="80" | resmr
| real || (nz,ny,nx) || Real part of negative eigenvalue
|-
! width="80" | resmi
| real || (nz,ny,nx) || Imaginary part of negative eigenvalue
|-
! width="80" | ncon
| int || 0 || number of contours to test, normally 41 or 21
|-
! width="80" | lev
| real || 0 || potential temperature of the level
|}
 
=== ''dynlib.diag.rotation_strain_ratio'' : ratio of effective rotation to strain rate ===
 
<code>res = rotation_strain_ratio(u,v,mont,lat,dx,dy)</code>
 
Calculates the r disgnostic of Lapeyre et al (1999)<ref name="LapKleHua1999" />; r is the ratio of effective rotation to strain rate, where effective rotation comprises both vorticity and strain-axes rotation.
 
 
{| border="1" class="wikitable" style="text-align:center;"
|+ style="text-align:left"| Arguments:
|-
|
! width="60" | Type
! width="80" | Dim
! width="300" | Description
|-
! width="80" | u
| real || (nz,ny,nx) || zonal velocity
|-
! width="80" | v
| real || (nz,ny,nx) || meridional velocity
|-
! width="80" | mont
| real || (nz,ny,nx) || Montgomery potential
|-
! width="80" | lat
| real || (ny) || vector of latitudes
|}
 
 
==References==
<references />
 
[[Category:Dynlib]]

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