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# omega_to_w

Convert omega vertical velocity (Pa/s) to (m/s).

Available in version 6.2.0 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 omega_to_w (
omega  : numeric,  ; float, double, integer only
p      : numeric,
t      : numeric
)
```

## Arguments

omega

A variable of any dimensionality containing omega (Pa/s) Array size and shape must match p and t.

p

A variable containing pressure values (Pa). Array size and shape must match omega and t.

t

A variable containing temperature (K). Array size and shape must match omega and p.

## Return value

A double array is returned if omega is double, otherwise a float array of the same size and shape as omega is returned.

## Description

Converts vertical velocity (Pa/s), commonly denoted as omega to vertical velocity (m/s), commonly denoted as w. The approximate relationship used is:

```
rgas = 287.058            ; J/(kg-K) => m2/(s2 K)
g    = 9.80665            ; m/s2
rho  = p/(rgas*t)         ; density => kg/m3
w    = -omega/(rho*g)     ; array operation

```

## Examples

Example 1: If (a) omega[*], p[*] and t[*]; (b) omega[*][*][*], p[*][*][*] and t[*][*][*]; (c) omega[*][*][*][*], p[*][*][*][*] and t[*][*][*][*] and all have the desired units then

```       wa = omega_to_w(omega, p, t)         ; wa[*] (m/s)
wb = omega_to_w(omega, p, t)         ; wb[*][*][*] (m/s)
wc = omega_to_w(omega, p, t)         ; wc[*][*][*][*] (m/s)
```

Example 2: Let omega(time,lev,lat,lon) and t(time,lev,lat,lon) and plevel(lev) have units hPa/day, degC and hPa, respectively.

```                                         ; change units: hPa/day to Pa/s
omega = omega*100./86400.         ; hPa=100Pa, day=86400s ; (hPa/day)(day/86400s)(100Pa/hPa)
omega@units = "Pa/s"

t       = t + 273.15              ; degC -> degK
t@units = "degK"
; make p[*] conform to omega[*][*][*][*]
P       = conform(omega, p, 1)   ; P(:,:,:,:)
P       = P*100                   ; hPa -> Pa
P@units = "Pa"

w       = omega_to_w(omega, P, t)      ; w[*][*][*][*] (m/s)

delete(P)                          ; no longer needed
```