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# beta_dfdy_rossby

Compute the Rossby parameter [beta=df/dy] which is the meridional variation of the Coriolis parameter.

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 beta_dfdy_rossby (
lat [*] : numeric,
opt [1] : logical
)

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

## Arguments

lat

Latitudes (degrees).

opt

opt=False means use default value for the radius of the earth [6.37122e06 meters]. If opt=True and the attribute "rearth" is present, its value in meters will overwrite the default radius of the earth.

## Return value

A variable of the same size and shape as lat.

## Description

The Rossby parameter is the meridional variation of the coriolis_param. It is important in the generation of Rossby waves.

## Examples

Example 1:

```  nlat = 37
lat  = latGlobeF(nlat, "lat", "latitude", "degrees_north")

beta = beta_dfdy_rossby(lat, False)
print(beta)

corp = coriolis_param(lat)
print(sprintf("%7.2f", lat) +" "+sprintf("%10.6f", corp)+" "+sprintf("%10.6f", beta))

```
The (edited) output:
```
Variable: beta
Type: float
Total Size: 148 bytes
37 values
Number of Dimensions: 1
Dimensions and sizes:	[lat | 37]
Coordinates:
lat: [-90..90]
Number Of Attributes: 4
long_name :	Rossby parameter: beta=df/dy
units :	1/(s-m)
info :	meridional variation of the Coriolis parameter
www :	https://en.wikipedia.org/wiki/Rossby_parameter

(0)	-1.000589e-18
(1)	1.995066e-12
(2)	3.974947e-12
(3)	5.924576e-12
(4)	7.829115e-12
(5)	9.67407e-12
(6)	1.14454e-11
(7)	1.312962e-11
(8)	1.471392e-11
(9)	1.618624e-11
(10)	1.753537e-11
(11)	1.875105e-11
(12)	1.982401e-11
(13)	2.074611e-11
(14)	2.151032e-11
(15)	2.211081e-11
(16)	2.254304e-11
(17)	2.280369e-11
(18)	2.28908e-11
(19)	2.280369e-11
(20)	2.254304e-11
(21)	2.211081e-11
(22)	2.151032e-11
(23)	2.074611e-11
(24)	1.982401e-11
(25)	1.875105e-11
(26)	1.753537e-11
(27)	1.618624e-11
(28)	1.471392e-11
(29)	1.312962e-11
(30)	1.14454e-11
(31)	9.67407e-12
(32)	7.829115e-12
(33)	5.924576e-12
(34)	3.974947e-12
(35)	1.995066e-12
(36)	-1.000589e-18

(0)	========
lat       coriolis       beta
(0)	 -90.00   -1.458400e-04  -1.000589e-18
(1)	 -85.00   -1.452850e-04   1.995066e-12
(2)	 -80.00   -1.436243e-04   3.974947e-12
(3)	 -75.00   -1.408706e-04   5.924576e-12
(4)	 -70.00   -1.370448e-04   7.829115e-12
(5)	 -65.00   -1.321759e-04   9.674070e-12
(6)	 -60.00   -1.263012e-04   1.144540e-11
(7)	 -55.00   -1.194651e-04   1.312962e-11
(8)	 -50.00   -1.117199e-04   1.471392e-11
(9)	 -45.00   -1.031244e-04   1.618624e-11
(10)	 -40.00   -9.374414e-05   1.753537e-11
(11)	 -35.00   -8.365038e-05   1.875105e-11
(12)	 -30.00   -7.292000e-05   1.982401e-11
(13)	 -25.00   -6.163464e-05   2.074611e-11
(14)	 -20.00   -4.988021e-05   2.151032e-11
(15)	 -15.00   -3.774617e-05   2.211081e-11
(16)	 -10.00   -2.532485e-05   2.254304e-11
(17)	  -5.00   -1.271079e-05   2.280369e-11
(18)	   0.00    0.000000e+00   2.289080e-11
(19)	   5.00    1.271079e-05   2.280369e-11
(20)	  10.00    2.532485e-05   2.254304e-11
(21)	  15.00    3.774617e-05   2.211081e-11
(22)	  20.00    4.988021e-05   2.151032e-11
(23)	  25.00    6.163464e-05   2.074611e-11
(24)	  30.00    7.292000e-05   1.982401e-11
(25)	  35.00    8.365038e-05   1.875105e-11
(26)	  40.00    9.374414e-05   1.753537e-11
(27)	  45.00    1.031244e-04   1.618624e-11
(28)	  50.00    1.117199e-04   1.471392e-11
(29)	  55.00    1.194651e-04   1.312962e-11
(30)	  60.00    1.263012e-04   1.144540e-11
(31)	  65.00    1.321759e-04   9.674070e-12
(32)	  70.00    1.370448e-04   7.829115e-12
(33)	  75.00    1.408706e-04   5.924576e-12
(34)	  80.00    1.436243e-04   3.974947e-12
(35)	  85.00    1.452850e-04   1.995066e-12
(36)	  90.00    1.458400e-04  -1.000589e-18
```