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# mjo_cross

Calculate space-time cross spectrum over multiple segments. Available in version 5.1.0 and later.

## Prototype

```load "\$NCARG_ROOT/lib/ncarg/nclscripts/csm/gsn_code.ncl"        ; These three libraries are automatically

function mjo_cross (
x    [*][*][*] : numeric,
y    [*][*][*] : numeric,
segLength   : integer,
segOverLap  : integer,
opt         : logical
)

return_val  :  float or double
```

## Arguments

x

A three-dimensional variable array. Nominally: (time,lat,lon). The longitudes should be global; the latitudes should span just the south-north region of interest; and, the 'time' should span the entire period of interest.

y

A three-dimensional variable array similar to x. Nominally: (time,lat,lon).

segLength

Length of the segment.

segOverLap

Overlap of the segment.

opt

Currently, not used. Set to False.

## Return value

The return variable will be a three-dimensional array (16,wavenumber,frequency) containing the 16 cross spectral quantities averaged over all segments.

```         ( 0,:,:)  -  symmetric power spectrum of x
( 1,:,:)  -  asymmetric power spectrum of x
( 2,:,:)  -  symmetric power spectrum of y
( 3,:,:)  -  asymmetric power spectrum of y
( 4,:,:)  -  symmetric cospectrum
( 5,:,:)  -  asymmetric cospectrum
( 6,:,:)  -  symmetric quadrature spectrum
( 7,:,:)  -  asymmetric quadrature spectrum
( 8,:,:)  -  symmetric coherence-squared spectrum
( 9,:,:)  -  asymmetric coherence-squared spectrum
(10,:,:)  -  symmetric phase spectrum
(11,:,:)  -  asymmetric phase spectrum
(12,:,:)  -  symmetric component-1 phase spectrum
(13,:,:)  -  asymmetric component-1 phase spectrum
(14,:,:)  -  symmetric component-2 phase spectrum
(15,:,:)  -  asymmetric component-2 phase spectrum
```
The returned variable will have the following attributes:
```   segmentLength - segment length
segmentOverLap - segment overlap
segmentRepeat - repeat overlap
dof - degrees of freedom
prob - (/0.80, 0.85, 0.90, 0.925, 0.95, 0.99/)
prob_coh2 - coherence-squared levels corresponding to prob
```
and the following coordinate variables:
```   freq - frequencies [ 0.0 to 0.5 cycles per day ]
wave - wave number [-M/2 to M/2 where M is the number of longitudes ]
```

## Description

See the Level 2 diagnostics description: US-CLIVAR MJO diagnostics website. Click on "Description"; then the Level 2 "See more specific discussion"