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# wgt_vertical_n

Calculates a weighted vertical average and/or sum (integral). Available in version 6.4.0 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 wgt_vertical_n (
x       : numeric,
dp      : numeric,
iopt    : integer,
dim  : integer
)

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

## Arguments

x

Array to be integrated or averaged. No missing data allowed.

dp

Pressure thicknesses computed by dpres_hybrid_ccm or dpres_plevel. These are the 'weights' associated with each level. This should have the same dimensionality as x.

iopt

• iopt=0 weighted vertical average
• iopt=1 weighted vertical sum
• iopt=2 return a variable of type 'list' containing the weighted vertical sum, vertical average and the weights used.
The dimension(s) of x on which to calculate the vertical sum or average.

## Return value

If opt=0 or 1, an array of of one less rank than the input x. If opt=2, a of type 'list' containing the weighted vertical sum and vertical average. The output will be double if x or dp is of type double. Appropriate metadata are also returned.

## Description

Calculate the weighted vertical average and/or sum along a specific dimension.

```             vertical_average__X = SUM[x*dp]/SUM[dp]      ; iopt=0
vertical_integral_X = SUM[x*dp]              ; iopt=1
```
NOTE: This function is documented as weighted vertical sum/average but it can be used for any weighted quantity along any coordinate. It was developed to isolate vertical sum/average so it is documented as such.

## Examples

Example 1: A sounding with specific humidity at standard pressure levels.

```
ptop = 0            ; integrate ptop==>psfc at each grid point
; user could specify (say) 525 hPa.
psfc = 1008.0
plev = (/1000.,950.,900.,850.,800.,750.,700.,650.,600.  \
, 550.,500.,450.,400.,350.,300.,250.,200.       \
, 175.,150.,125.,100., 80., 70., 60., 50.       \
,  40., 30., 25., 20. /)
plev@units = "hPa"

q    =(/ 19.03,16.14,13.71,11.56,9.80,8.33,6.75,6.06,5.07 \
,  3.88, 3.29, 2.39, 1.70,1.00,0.60,0.20,0.00,0.00 \
,  0.00, 0.00, 0.00, 0.00,0.00,0.00,0.00,0.00,0.00 \
,  0.00, 0.00 /)
q@units = "g/kg"

; layer thickness

dp   = dpres_plevel(plev, psfc, ptop, 0)

;Integrate:

vopt  = 0     ; vertically weighted average
vavg  = wgt_vertical_n(q, dp, vopt, 0)
;print("vavg="+vavg)
;print("========")

;or
vopt  = 1     ; vertically weighted sum (integral)
vsum  = wgt_vertical_n(q, dp, vopt, 0)
;print("vsum="+vsum)
;print("========")

;or
vopt  = 2     ; vertically weighted sum (integral) and average
vAvgSumWgt = wgt_vertical_n(q, dp, vopt, 0)
; extract from list variable [convenience only]
vAvg  = vAvgSumWgt
vSum  = vAvgSumWgt
vWgt  = vAvgSumWgt
```

Example 2: Similar to Example 1 but q(time,lev,lat,lon) and, psfc(time,lat,lon). Note the psfc could also be constant. Here, set ptop to the highest level (lowest pressure).

```     f    = addfile("...", "r")
psfc = f->PSFC                                      ; psfc(time,lat,lon)
q    = f->Q                                         ; q(time,plev,lat,lon) ; dimension (0,1,2,3)
plev = f->plev                                      ; q&plev

ptop = min(plev)    ; 300==>psfc at each grid point

; layer thicknesses
dp   = dpres_plevel_Wrap(plev, psfc, ptop, 0)  ; dp(time,plev,lat,lon)

vopt = 0     ; vertically weighted average over the level (1-th dimension)
vavg = wgt_vertical_n(q, dp, vopt, 1)  ; (time,lat,lon)
vavg@long_name = "Q: vertically weighted average"
vavg@long_name = q@units

vopt = 1     ; vertically weighted sum
vavg = wgt_vertical_n(q, dp, vopt, 1)  ; (time,lat,lon)
vavg@long_name = "Q*DP: vertically weighted sum"
vavg@long_name = "("+q@units" - "+psfc@units+")"
```

Example 3: Let q(time,lev,lat,lon) and the data be on constant pressure levels.

```  f    = addfile("...", "r")

ptop= 300
pbot= 1000
x   = f->q(:,{pbot:ptop},:,:)

dp   = dpres_plevel_Wrap(q&level,psfc,pbot,0)   ; dp[*]

vopt = 0
DP   = conform(x,dp,1)                         ; dp(time,plev,lat,lon)
xint = wgt_vertical_n(x,DP,vopt,1)
xint@long_name = "x wgt sum: vopt="+vopt)
xint@units     = "..."
copy_VarCoords(x(:,0,:,:),xint)
```