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static_energy_atm
Compute the atmospheric moist and dry static energy.
Available in version 6.5.0 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 static_energy_atm (
t : numeric, ; float, double, integer only
q : numeric,
z : numeric,
iounit [2] : integer
)
return_val [dimsizes(z)] : float or double
Arguments
tA scalar or array containing temperature (units: degC, degK, degF). If t, q and z are arrays they must be the same size and shape.
qA scalar or array containing specific humidity (units: kg/kg, g/kg).
zA scalar or array containing height (m).
iounitAn integer array of length 2 which specifies the units of the input t and q.
- iounit(0)=0 input t are degrees Celcius (degC)
- iounit(0)=1 input t are degrees Kelvin (degK)
- iounit(0)=2 input t are degrees Farenheit (degF)
- iounit(1)=0 input q are kg/kg
- iounit(1)=1 input q are g/kg
Return value
A variable of type 'list' which comtains 3 derived variables: [/MSE, DSE, LSE /] The returned units are J/kg.
Description
The static energy is a combination of an air parcel's :
Latent heat: Lv*q ; Lv - latent heat of vaporization of water
Dry Air Enthalpy: Cp*t ; Cp - specific heat of dry air at constant pressure
Potential Energy: g*z ; g - gravity
The atmosphere's total static energy is composed of two components: Dry Static Energy (DSE) and Latent Static Energy (LSE). Specifically:
DSE = Cp*t + g*z
and
LSE = Lv*q
-
The sum of (DSE+LSE) is commonly called Moist Static Energy (MSE):
- The MSE is a thermodynamic variable that describes the state of an air parcel.
It is similar to the equivalent potential temperature. As noted in Yano and Ambaum (2017):
"MSE is conserved under moist adiabatic processes and under hydrostatic balance,
thus it is a useful quantity to understand moist convection."
- The DSE [aka: Montgomery Streamfunction] is a thermodynamic variable similar to potential temperature, except that the concept of static energy assumes that any kinetic energy is locally dissipated into heat.
MSE = DSE + LSE
Reference: Holton, J. R. (1992): An Introduction the Dynamic Meteorology. Academic Press. Wikipedia: Moist Static Energy Yano, J.-I. and Ambaum, M. H. P. (2017): Moist static energy: definition, reference constants, a conservation law and effects on buoyancy Q.J.R. Meteorol. Soc, 143: 2727-2734.
Examples
Example 1:
t = 27.3 ; C iounit(0)=0
q = 14.4 ; g/kg iounit(1)=1
z = 275 ; m elevation above the ground
SE = static_energy_atm(t, q, z, (/0,1/)
; clarity: explicitly extract each variable from list
MSE = SE[0] ; MSE = 341007 J/kg
DSE = SE[1] ; DSE = 304858 J/kg
LSE = SE[2] ; LSE = 36149.8 J/kg
delete(SE) ; no longer needed
printVarSummary(MSE)
printVarSummary(DSE)
printVarSummary(LSE)
Example 2:
a = addfile("cam35.h0.0008-07.nc", "r") T = a->T ; K iounit(0)=1 (time,lev,lat,lon) Q = a->Q ; kg/kg iounit(1)=0 ZG = a->Z3 ; m Geopotential Height (above sea level) PHIS = a->PHIS ; m2/s2 Surface geopotential (time,lat,lon) PHIS = PHIS/9.8 ; m phis = conform(ZG, PHIS, (/0,2,3/)) ; (time,lev,lat,lon) Z = ZG-phis ; m Height above the surface copy_VarCoords(ZG, Z) SE = static_energy_atm(t, q, z, (/1,0 /) ; for clarity: explicitly extract each variable from list MSE = SE[0] DSE = SE[1] LSE = SE[2] delete(SE) ; no longer needed printVarSummary(MSE) printMinMax(MSE,0) printVarSummary(DSE) printMinMax(DSE,0) printVarSummary(LSE) printMinMax(LSE,0) ;--- print an arbitrary location and time hyam = a->hyam ; read from a file the mid-layer coef hybm = a->hybm ; read from a file ps = a->PS ; surface pressure [Pa] p0 = 100000. ; since ps is in Pa or [ f->P0] pm = pres_hybrid_ccm(ps,p0,hyam,hybm) copy_VarCoords(T, pm) pm = pm*0.01 ; convert to hPa pm@long_name = "pressure level" pm@units = "hPa" nt = 0 LAT = 5 LON = 120 print(sprintf("%8.1f", pm(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.1f", T(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.6f", Q(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.1f", Z(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.1f",MSE(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.1f",DSE(nt,:,{LAT},{LON}))+" " \ +sprintf("%8.1f",LSE(nt,:,{LAT},{LON})) )The edited output is:
Variable: MSE
Type: float
Total Size: 1437696 bytes
359424 values
Number of Dimensions: 4
Dimensions and sizes: [time | 1] x [lev | 26] x [lat | 96] x [lon | 144]
Coordinates:
time: [3132..3132]
lev: [3.54463800000001..992.5560999999998]
lat: [ -90..89.99999999999999]
lon: [ 0..357.5]
Number Of Attributes: 4
long_name : Moist Static Energy
units : J/kg
info : MSE = (Cp*t + g*z)+Lv*q
short_name : MSE
(0) Moist Static Energy (J/kg) : min=487256 max=915394
(0) =========
Variable: DSE
Type: float
Total Size: 1437696 bytes
359424 values
Number of Dimensions: 4
Dimensions and sizes: [time | 1] x [lev | 26] x [lat | 96] x [lon | 144]
Coordinates:
time: [3132..3132]
lev: [3.54463800000001..992.5560999999998]
lat: [ -90..89.99999999999999]
lon: [ 0..357.5]
Number Of Attributes: 4
long_name : Dry Static Energy
units : J/kg
info : DSE = (Cp*t + g*z)
short_name : DSE
(0) Dry Static Energy (J/kg) : min=487256 max=915394
(0) =========
Variable: LSE
Type: float
Total Size: 1437696 bytes
359424 values
Number of Dimensions: 4
Dimensions and sizes: [time | 1] x [lev | 26] x [lat | 96] x [lon | 144]
Coordinates:
time: [3132..3132]
lev: [3.54463800000001..992.5560999999998]
lat: [ -90..89.99999999999999]
lon: [ 0..357.5]
Number Of Attributes: 4
long_name : moist static energy
units : J/kg
info : lse = Lv*q
short_name : mse
(0) latent static energy (J/kg) : min=0.00124475 max=55.3337
P T Q Z MSE DSE LSE
3.5 230.3 0.000002 37852.7 602605.8 602601.1 4.7
7.4 222.1 0.000002 32957.0 546323.9 546319.2 4.7
14.0 224.2 0.000002 28764.5 507375.8 507371.1 4.7
23.9 220.1 0.000002 25230.7 468661.8 468657.1 4.6
37.2 215.2 0.000002 22394.1 435906.7 435902.1 4.5
53.1 208.9 0.000002 20171.9 407830.0 407825.5 4.5
70.1 201.2 0.000002 18495.8 383577.0 383572.3 4.7
85.5 192.2 0.000002 17339.5 363277.1 363272.3 4.8
100.6 191.3 0.000002 16424.7 353367.9 353363.8 4.2
118.4 194.4 0.000003 15504.9 347460.5 347454.1 6.4
139.3 200.1 0.000005 14564.2 344022.9 344009.2 13.7
164.0 207.8 0.000013 13591.6 342251.0 342218.3 32.7
192.9 216.5 0.000035 12580.3 341127.1 341040.4 86.6
227.0 225.6 0.000084 11526.9 340020.2 339809.9 210.3
267.1 234.9 0.000174 10430.0 338845.9 338408.2 437.7
314.3 244.2 0.000310 9288.8 337416.7 336637.8 778.8
369.8 253.1 0.000601 8104.0 335519.8 334011.3 1508.5
435.1 262.0 0.001239 6876.7 334030.8 330920.5 3110.3
511.9 269.0 0.003729 5610.5 334897.1 325536.5 9360.6
602.3 275.4 0.005283 4311.0 332521.2 319258.8 13262.4
698.9 281.7 0.007350 3091.8 332011.0 313559.5 18451.5
790.1 286.4 0.009778 2065.1 332812.6 308266.9 24545.6
869.9 291.6 0.011405 1245.7 334101.3 305470.9 28630.4
932.6 295.1 0.015777 642.6 342658.3 303051.3 39607.0
973.6 298.1 0.017377 264.7 346017.2 302394.7 43622.5
995.7 299.8 0.017613 66.3 346386.1 302169.2 44216.9