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# shear_stretch_deform

Using spherical harmonics, estimate the kinematic shear-deformation, stretch-deformation and total-deformation of a global horizontal (east-west) wind field.

Available in version 6.6.2 and later.

## Prototype

```load "\$NCARG_ROOT/lib/ncarg/nclscripts/csm/contributed.ncl"  ; This library is automatically loaded
; from NCL V6.2.0 onward.
; No need for user to explicitly load.

function shear_stretch_deform (
u            : numeric,
v            : numeric,
lat      [*] : numeric,
gridType [1] : integer,
opt      [1] : integer
)

return_val [dimsizes(lat)] :  float or double
```

## Arguments

u

Zonal wind component. Must be on a global rectilinear grid ordered South-to-North.

v

Meridional wind component. Same size and shape as u.

lat

Latitudes (degrees).

gridType

Grid type. gridType=0 means gaussian grid; gridType=1 means regular or fixed grid.

opt

option.

• opt=0 means return the shear, stretch and total deformation [3 variables]
• opt=1 means return the shear, stretch, total deformation and the four gradient fields: du/dx, du/dy, dv/dx and dv/dy [7 vriables].

## Return value

```A variable of type list containing variables of the same size and shape as u.
The returned variables do not include any explicit negative (or positive) sign or coefficient (eg:  0.5).

shear   = dvdx + dudy
stretch = dudx - dvdy
deform  = sqrt(shear^2 + stretch^2)

Description

Divergence and vorticity are commonly used kinematic fields.
Less commonly used are the shear-deformation (SHD) and stretch-deformation (STD).
SHD = dv/dx + du/dy
STD = du/dx - dv/dy

When the stretch-deformation is negative/positive the flow is confluent/diffluent.
Typically, the individual shear- and stretch-deformation components are less useful
than the total-deformation (TD):

TD = sqrt(SVD^2 + STD^2)

The advantage of using spherical harmonics over centered-finite-differences
(shear_stretch_deform_cfd)
is that the spherical harmonic derived gradients are "highly accurate."

This function should be used only on high frequency 3-, 6-hrly or daily mean data.

References:
Kinematic Propeerties: Synoptic Meteorology I: 2014

Spensberger, C. and T. Spengler (2014)
A New Look at Deformation as a Diagnostic for Large-Scale Flow
J. Atmos. Sci

uv2vrG,uv2dvG,
uv2vrF,uv2dvF,
uv2vr_cfd,uv2dv_cfd,
shear_stretch_deform_cfd,
qvector_isobaric,
qvector_isobaric_cfd

Examples

Example 1:  See
shear_stretch_deform

Example 2:  Output from Example 1:

u       = f->U
v       = f->V

grdTyp  = 1    ; =1 fixed
cyclic  = True
opt_ssd = 0    ; shear, stretch and total deformation

ssdList = shear_stretch_deform(u,v, u&lat, grdTyp, opt_ssd)

stretch_sph = ssdList[0]    ; _sph only to express that spherical harmonics
shear_sph   = ssdList[1]    ; were used to estimate the gradients
deform_sph  = ssdList[2]
delete(ssdList)           ; not required;   just not needed anymore

printVarSummary(stretch_sph)
printMinMax(stretch_sph,0)

printVarSummary(stretch_sph)
printMinMax(shear_sph,0)

printVarSummary(deform_sph)
printMinMax(deform_sph,0)

The (edited) output:

Variable: stretch_sph
Type: float
Total Size: 5003712 bytes
1250928 values
Number of Dimensions: 4
Dimensions and sizes:   [time | 7] x [level | 17] x [lat | 73] x [lon | 144]
Coordinates:
time: [1823280..1823424]
level: [1000..10]
lat: [-90..90]                  NOTE: the grid is global and ordered S->N
lon: [ 0..357.5]
Number Of Attributes: 2
long_name :   (dudx-dvdy): SPH
units :       1/s

(0)     (dudx-dvdy): SPH (1/s) : min=-0.000355005   max=0.000355005

----

Variable: shear_sph
Type: float
Total Size: 5003712 bytes
1250928 values
Number of Dimensions: 4
Dimensions and sizes:   [time | 7] x [level | 17] x [lat | 73] x [lon | 144]
Coordinates:
time: [1823280..1823424]
level: [1000..10]
lat: [-90..90]
lon: [ 0..357.5]
Number Of Attributes: 2
long_name :   (dvdx+dudy): SPH
units :       1/s

(0)     (dvdx+dudy): SPH (1/s) : min=-0.000355005   max=0.000355005

----

Variable: deform_sph
Type: float
Total Size: 5003712 bytes
1250928 values
Number of Dimensions: 4
Dimensions and sizes:   [time | 7] x [level | 17] x [lat | 73] x [lon | 144]
Coordinates:
time: [1823280..1823424]
level: [1000..10]
lat: [-90..90]
lon: [ 0..357.5]
Number Of Attributes: 3
long_name :   deformation
units :       1/s
information : sqrt[shear^2 + stretch^2 ]

(0)     deformation (1/s) : min=1.04094e-08   max=0.000355055

```