pot_temp_equiv
Compute the equivalent potential temperature using an approximation which does not use the lifting condensation temperature.
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 pot_temp_equiv (
p : numeric, ; float, double, integer only
t : numeric,
w : numeric,
dim [1] : integer,
humVarType [1] : string
)
return_val [dimsizes(t)] : float or double
Arguments
pArray containing pressure levels (Pa).
tArray containing temperatures (K).
wArray containing the humidity related quantity. See the humVarType argument description.
dimThe dimension of t which corresponds to p. NOTE: If the rank and sizes of t are the same as those of p this argument is ignored. A suggested placeholder is dim=-1.
humVarTypeIdentifies the quantity associated with the w argument.
- "q" for specific humidity (dimensionless: kg/kg)
- "r" for mixing ratio (dimensionless: kg/kg)
- "rh" for relative humidity (%)
- "td" for dew point depression (K)
Return value
A multi-dimensional array of the same size and shape as t. The output will be double if t or p is of type double. All approprate meta data is returned.
Description
Calculate the equivalent potential temperature (theta_e). Over the years there have been numerous methods used to estimate equivalent potential temperature. Some are appropriate only for limited ranges. None agree 'perfectly.'
This function uses the formulation described in the Wikipedia reference:
Wikipedia: Equivalent Potential Temperature
As noted in www.atmo.arizona.edu/students/courselinks/.../EquivalentPotentialTemperature.doc:
"The problem with this approximate equation is that it assumes all of the water vapor is condensed out and converted to sensible heat at the present pressure of the air parcel. This is incorrect because the water condenses out as the air parcel is lifted into the uppermost troposphere where the pressure is lower such that the adiabatic compression when the air is brought to the surface will be larger. So we can anticipate this equation will systematically underestimate theta_e."
A weakness of this formulation is that it does not use the "lifting condensation temperature." For researchers analyzing buoyancy differences among tropical disturbances this simplification (omission) can be lead to significantly different theta_e.
It is recommended to use pot_temp_equiv_tlcl available in NCL 6.5.0.
See Also
pot_temp_equiv_tlcl, wrf_eth, Meteorology functions,
Examples
Example 1: Compare with the WRF function, wrf_eth. Differences may be due to different algorithms and/or constants. Note that extra coding is necessary to 'broadcast' the one-dimension (1D) array to 3D for use by the WRF function.
; pressure (Pa)
p = (/ 97067.80, 96040.00, 94825.50, 93331.30, 91371.40, 88947.80, 86064.70, 82495.50 \
, 78140.20, 73035.40, 67383.70, 61327.50, 54994.70, 48897.30, 43034.60, 37495.20 \
, 32555.80, 28124.40, 24201.00, 20693.00, 17600.60, 14877.30, 12477.20, 10400.20 \
, 8553.98, 6984.69, 646.18 /)
; temperature (K)
t = (/ 291.15, 291.60, 292.05, 292.13, 292.06, 291.17, 289.11, 287.49 \
, 286.25, 282.14, 277.42, 272.91, 266.99, 261.64, 254.40, 246.38 \
, 238.10, 229.76, 220.88, 213.65, 212.42, 212.58, 212.91, 213.34 \
, 213.73, 214.55, 216.59 /)
; specific humidity (kg/kg; dimensionless))
w = (/0.012258, 0.012111, 0.011914, 0.011483, 0.010575, 0.008992, 0.006021,0.002559 \
,0.005169, 0.005746, 0.001608, 0.001645, 0.001382, 0.000235, 0.000094,0.000178 \
,0.000136, 0.000079, 0.000050, 0.000025, 0.000023, 0.000023, 0.000014,0.000010 \
,0.000008, 0.000007, 0.000007 /)
; Compute
dim = 0
ept = pot_temp_equiv(p, t, w, dim, "q")
; Compare with WRF function (different algorithm)
; The wrf_eth requires 3D or 4D input. Use conform_dims to force desired dimensionality.
; compare with 'wrf_eth' ... this requires 3D or 4D
klvl = dimsizes(p)
p3 = conform_dims((/klvl,1,1/), p, 0)
t3 = conform_dims((/klvl,1,1/), t, 0)
w3 = conform_dims((/klvl,1,1/), w, 0)
ept_wrf = wrf_eth ( w3, t3, p3 ) ; [klvl] x [1] x [1]
ept_dif = ept-ept_wrf(:,0,0) ; difference
print(sprintf("%8.2f", p) +" " \
+sprintf("%8.2f", t) +" " \
+sprintf("%9.6f", w) +" " \
+sprintf("%7.2f", ept)+" " \
+sprintf("%7.2f", ept_wrf(:,0,0)) \
+sprintf("%9.2f", ept_dif))
would yield
P T W ept ept_wrf diff
(0) 97067.80 291.15 0.012258 324.91 328.77 -3.86
(1) 96040.00 291.60 0.012111 325.97 329.91 -3.94
(2) 94825.50 292.05 0.011914 327.10 331.12 -4.01
(3) 93331.30 292.13 0.011483 327.55 331.53 -3.98
(4) 91371.40 292.06 0.010575 327.09 330.91 -3.82
(5) 88947.80 291.17 0.008992 324.52 327.91 -3.40
(6) 86064.70 289.11 0.006021 317.57 320.08 -2.51
(7) 82495.50 287.49 0.002559 310.51 311.95 -1.43
(8) 78140.20 286.25 0.005169 321.08 323.34 -2.26
(9) 73035.40 282.14 0.005746 324.44 326.65 -2.21
(10) 67383.70 277.42 0.001608 315.05 316.00 -0.95
(11) 61327.50 272.91 0.001645 318.56 319.47 -0.91
(12) 54994.70 266.99 0.001382 320.83 321.58 -0.75
(13) 48897.30 261.64 0.000235 321.71 321.95 -0.24
(14) 43034.60 254.40 0.000094 323.99 324.13 -0.14
(15) 37495.20 246.38 0.000178 326.67 326.86 -0.19
(16) 32555.80 238.10 0.000136 328.58 328.74 -0.16
(17) 28124.40 229.76 0.000079 330.41 330.54 -0.13
(18) 24201.00 220.88 0.000050 331.47 331.59 -0.12
(19) 20693.00 213.65 0.000025 335.21 335.32 -0.11
(20) 17600.60 212.42 0.000023 349.03 349.16 -0.13
(21) 14877.30 212.58 0.000023 366.49 366.63 -0.15
(22) 12477.20 212.91 0.000014 385.95 386.11 -0.16
(23) 10400.20 213.34 0.000010 407.35 407.53 -0.18
(24) 8553.98 213.73 0.000008 431.53 431.73 -0.20
(25) 6984.69 214.55 0.000007 459.00 459.23 -0.23
(26) 646.18 216.59 0.000007 914.70 915.57 -0.87
Example 2: Consider p, t and w with dimensionality (ntim,klev,nlat,mlon) and appropriate units. Here w contains mixing ratio (humVarType="r"). Since all variables conform, the dim argument is ignored (set to -1 for convenience or 1)
theta_e = pot_temp_equiv(p, t, w, -1, "r") ; dim=-1 or 1
Example 3: Consider t and w with dimensionality (ntim,klev,nlat,mlon) and p(klev). Here w contains relative humidity (%; humVarType="rh"). This is commonly encountered for isobaric analyses. Here, NCL's dimension numbering is (0[ntim],1[klev],2[nlat],3[mlon]) so dim=1.
theta_e = pot_temp_equiv(p, t, w, 1, "rh")