# Dynlib

## Contents

- 1 Documentation
- 2 Obtaining dynlib
- 3 Quick start to developing with dynlib
- 4 Dynlib functions
- 4.1
*ddx*: partial x derivative - 4.2
*ddy*: partial y derivative - 4.3
*grad*: gradient of a scalar - 4.4
*lap2*: 2-D laplacian of a scalar - 4.5
*vor*: 2-D vorticity - 4.6
*div*: 2-D divergence - 4.7
*def_shear*: shear deformation - 4.8
*def_stretch*: stretch deformation - 4.9
*def_total*: total deformation - 4.10
*def_angle*: deformation angle - 4.11
*isopv_angle*: iso-PV line angle - 4.12
*beta*: angle between dilatation axis and iso-PV lines - 4.13
*stretch_stir*: fractional stretching rate and angular rotation rate of grad(PV) - 4.14
*geop_from_montgp*: geopotential - 4.15
*rev*: PV gradient reversal - 4.16
*prepare_fft*: make data periodic in y for FFT - 4.17
*sum_kix*: sum along k for flagged k-values - 4.18
*high_enough*: flags points which are sufficiently above ground - 4.19
*contour_rwb*: detects RWB events, Riviere algorithm - 4.20
*v_g*: geostrophic velocity - 4.21
*okuboweiss*: Okubo-Weiss criterion - 4.22
*laccel*: Lagrangian acceleration - 4.23
*accgrad_eigs*: Lagrangian acceleration gradient tensor eigenvalues - 4.24
*dphidt*: Lagrangian derivative of compression axis angle

- 4.1

## Documentation

The steps necessary to obtain dynlib are described below. A more thorough documentation is compiled in the main documentation page.

## Obtaining dynlib

- Copying the source code repository
`git clone /Data/gfi/users/tsp065/lib/dynlib.git`

- Change into the dynlib folder
`cd dynlib`

- Compile the library
`./compile`

## Quick start to developing with dynlib

### Editing the Fortran code

The fortran code lives in the main source code directory. At the moment there are six source code files

`$ ls *.f95`

`dynlib_config.f95 dynlib_const.f95 dynlib_conv.f95 dynlib_diag.f95 dynlib_kind.f95 dynlib_stat.f95`

```
```

The most important are `dynlib_diag.f95`

which contains subroutines that calculate various diagnostics, and `dynlib_stat.f95`

which contains statistical functions. Changed Fortran sources need to be recompiled, again using

`./compile`

### Version control

The changes you made to the source code files can be listed by

`git status`

or viewed in detailed diff-comparisons by

`git diff`

or for one file only

`git diff [filename]`

Commit your changes from time to time and give a sensible and brief description of your changes in the editor that is opened (automatically)

`git commit -a`

The commit is then stored in your copy of the source code repository, but not yet available for others, which allows you to also commit work-in-progress.

A more thorough introduction to the version control system is given here or on the official documentation.

### Using the Fortran functions

An example python script which calculates deformation using the Fortran function is provided with `deformation.py`

.

## Dynlib functions

The functions operate on real arrays with dimension (nz,ny,nx) where nz is number of times or levels, and ny and nx are number of latitudes and longitudes, respectively. Typically, the results for each level or time are computed individually as a 2-D slice of the 3-D data.

*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*: gradient of a scalar

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

Calculates the gradient 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.

*lap2*: 2-D laplacian of a scalar

`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 line 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 lines

`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)`

where:

stretch

= fractional PV gradient stretching rate

= 1/|gradPV| * d/dt(|gradPV|)

= gamma, 'stretching rate' (Lapeyre Klein Hua)

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

stir

= angular rotation rate of grad(PV) (aka stirring rate)

= d(theta)/dt (Lapeyre Klein Hua)

= 1/|gradPV| * F_s (Keyser Reeder Reed) where 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)`

Gradient reversal: At each (i,j,k) grid point, finds the reversals of PV y-gradient and classes them as c (cyclonic) or a (anticyclonic)

Arguments:

pv: Potential vorticity pv(k,j,i) on (time, lat, lon) grid. highenough: array of flags, highenough(k,j,i) = {0 or 1} (type int*1) denoting whether to test the point for reversal. This is typically the output of highenough() funtion, which returns 1 where the surface is sufficiently above ground level and 0 elsewhere. latitudes: vector of latitudes of the pv array ddythres: Cutoff y-gradient for pv. The magnitude of (negative) d(pv)/dy must be above ddythres for reversal to be detected; applies to revc, reva, revci,revai.

Returns:

int*1 :: revc, reva (reversal flag) (threshold test applied) real :: revci, revai (reversal absolute gradient) (threshold test applied) real :: revciy, revaiy (reversal absolute y-gradient) (no threshold test applied) int*1:: tested (flag to 1 all tested points: where highenough==1 and not on edge of grid)

*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.

*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 in kix vector (length nz)

returns:

res(ny,nx) - thedata summed over k where kix==1 nres - sum(kix)

Typically used for calculating seasonal means. To do this, kix is set to 1 for times in the relevant season and 0 elsewhere. After 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)`

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 |

Type | Dim | Description | |
---|---|---|---|

res | int*1 | (nz,ny,nx) | border="0" |

3-D 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: RiviÃ¨re (2009, hereafter R09): Effect of latitudinal variations in low-level baroclinicity on eddy life cycles and upper-tropospheric wave-breaking processes. J. Atmos. Sci., 66, 1569â€“1592. See the appendix C.

Arguments:

pv_in(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(nx) : vector of longitudes latvalues(ny) : vector of latitudes ncon : number of contours to test, normally 41 or 21 lev : potential temperature of the level

Returns:

beta_a_out(nz,ny,nx) : flag array, =1 if anticyclonic wave breaking beta_c_out(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

This is the square of the eigenvalues in Okubo's paper (assumes negligible divergence)

*laccel*: Lagrangian acceleration

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

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

Arguments:

u(nz,ny,nx) : zonal velocity v(nz,ny,nx) : meridional velocity mont(nz,ny,nx) : Montgomery potential lat(ny) : latitude

*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:

u(nz,ny,nx) : zonal velocity v(nz,ny,nx) : meridional velocity mont(nz,ny,nx) : Montgomery potential lat(ny) : latitude

Returns:

respr(nz,ny,nx) : Real part of positive eigenvlaue respi(nz,ny,nx) : Imaginary part of positive eigenvlaue resmr(nz,ny,nx) : Real part of negative eigenvlaue resmi(nz,ny,nx) : Imaginary part of negative eigenvlaue

*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 1999), from deformation and Lagrangian acceleration tensor.

Arguments:

u(nz,ny,nx) : zonal velocity v(nz,ny,nx) : meridional velocity mont(nz,ny,nx) : Montgomery potential lat(ny) : latitude