relhum
Calculates relative humidity given temperature, mixing ratio, and pressure.
Prototype
function relhum ( t : numeric, w : numeric, p : numeric ) return_val [dimsizes(t)] : numeric
Arguments
tA scalar or multi-dimensional array containing the temperature in K.
wA scalar or multi-dimensional array containing the mixing ratio in kg/kg. Must be the same size and shape as t.
pA scalar or multi-dimensional array equal to the pressure in Pa. Must be the same size and shape as t.
Return value
A multi-dimensional array of the same sizes as t. The output will be double if any of the input is double, and float otherwise.
NOTE: 6.2.0: The return missing value is whatever the default missing value is for the type being returned, and *not* t@_FillValue, as it was in the past.
Description
Calculates relative humidity given temperature, mixing ratio, and pressure, using a table look-up procedure. The algorithm and tables can yield some very high relative humidities (> 100%) at high pressures and very low temperature.
Relative Humidity between 0C and -20C are calculated with respect to a mixed phase between ice and water. Below -20C the returned humidities are calculated with respect to ice. Below -20C the results will be very similar to those from relhum_ice and above 0C the results will be very similar to relhum_water.
oLow temperatures and very dry conditions can yield relative humidities greater than 100% (super saturation). In all NCL versions through v5.1.1, any value greater than 100% was set to 100%. Beginning with v5.2.0, the returned relative humidities will be allowed to be greater than 100%. If the pre-v5.2.0 results are desired the user can use the NCL clipping operator ( < ).
rh = relhum (t, w, conform(t,p,1)) rh = rh < 100 ; change all rh values greater that 100 to 100.
The returned values are similar to the results obtained using the algorithm in:
Murray (1967), On the computation of saturation vapor pressure, J. Applied Met., pp 203-204 http://dx.doi.org/10.1175/1520-0450(1967)006<0203:OTCOSV>2.0.CO;2
See Also
relhum_ttd, relhum_ice, relhum_water, dewtemp_trh, mixhum_ptrh
Examples
Example 1
Wallace and Hobbs (Atmospheric Science: An introductory Survey, Academic Press [p73]) state that at p=1000 [hPa], t=18 [C] and q=6 [g/kg] the relative humidity is approximately 45.6%.
p = 1000.*100. ; hPa ==> Pa t = 18.+273.15 ; C ==> K q = 6./1000. ; g/kg ==> kg/kg rh = relhum (t, q, p) ; rh = 46.4 %Example 2
Consider a sounding with the following values:
begin
p =(/ 1008., \ ; hPA (mb)
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. /)
t =(/ 29.3, \ ; C
28.1,23.5,20.9,18.4,15.9,13.1,10.1, 6.7, 3.1, \
-0.5,-4.5,-9.0,-14.8,-21.5,-29.7,-40.0,-52.4, \
-59.2,-66.5,-74.1,-78.5,-76.0,-71.6,-66.7,-61.3, \
-56.3,-51.7,-50.7,-47.5 /)
q =(/ 20.38, \ ; g/kg
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 = q/1000.
tk = t+273.15
pPa = p*100.
rh = relhum(tk, q, pPa)
print(pPa+" "+tk+" "+q+" "+rh)
end
The (edited) output is:
P T Q RH
(Pa) (K) (KG/KG) (%)
------ ------ ------- -------
(0) 100800 302.45 0.02038 79.8228
(1) 100000 301.25 0.01903 79.3578
(2) 95000 296.65 0.01614 84.1962
(3) 90000 294.05 0.01371 79.4898
(4) 85000 291.55 0.01156 73.989
(5) 80000 289.05 0.0098 69.2401
(6) 75000 286.25 0.00833 66.1896
(7) 70000 283.25 0.00675 61.1084
(8) 65000 279.85 0.00606 64.21
(9) 60000 276.25 0.00507 63.8305
(10) 55000 272.65 0.00388 58.0412
(11) 50000 268.65 0.00329 60.8194
(12) 45000 264.15 0.00239 57.927
(13) 40000 258.35 0.0017 62.3734
(14) 35000 251.65 0.001 62.9706
(15) 30000 243.45 0.0006 73.8184
(16) 25000 233.15 0.0002 62.71
(17) 20000 220.75 0 0
(18) 17500 213.95 0 0
(19) 15000 206.65 0 0
(20) 12500 199.05 0 0
(21) 10000 194.65 0 0
(22) 8000 197.15 0 0
(23) 7000 201.55 0 0
(24) 6000 206.45 0 0
(25) 5000 211.85 0 0
(26) 4000 216.85 0 0
(27) 3000 221.45 0 0
(28) 2500 222.45 0 0
(29) 2000 225.65 0 0
Example 3
Let t, w and p be four-dimensional of size (ntim,nlvl,nlat,nlon). The returned value (rh) will be the same size. Every grid point will use the local pressure values.
rh = relhum (t, w, p)Example 4
Let t and w be four-dimensional of size (ntim,nlvl,nlat,nlon). Let p be a one-dimensional of size (nlvl) in units of Pascals. Use conform to expand p to the same dimensions as t and w. Placing the conform directly into the call to relhum has the advantage that the temporary array created lasts only as long as the function.
rh = relhum (t, w, conform(t,p,1))Example 5
Let t and w be four-dimensional of size (ntim,nlvl,nlat,nlon). Derive p using various model output quantities.
p0 = 1000. ps = a->PS ; 3D (time,lat,lon) variable [sfc pressure] hyam = a->hyam ; needed for interpolation hybm = a->hybm pres = new ( dimsizes(t), typeof(t) ) do n=0,nlvl-1 pres(:,n,:,:) = p0*hyam(n) + hybm(n)*ps end do rh = relhum (t, q, pres) ; rel humidity delete (pres)Example 6
An example of very high relative humidities returned by relhum, consider the following data:
P T Q RH
(Pa) (K) (KG/KG) (%)
------ ------ -------- -------
(0) 10000 223.961 6.3001e-08 0.0232985
(1) 12500 223.74 4.0001e-08 0.0189869
(2) 15000 222.816 3.0001e-08 0.0191538
(3) 17500 221.682 4.0001e-08 0.0343044
(4) 20000 220.958 5.00001e-07 0.537078
(5) 22500 219.778 3.00001e-06 4.20652
(6) 25000 218.297 7.70006e-06 14.5205
(7) 27500 217.017 1.49002e-05 36.4838
(8) 30000 216.814 2.34198e-05 64.1835
(9) 35000 220.258 3.80014e-05 78.0791
(10) 40000 226.401 6.99829e-05 76.9895
(11) 45000 231.785 0.000116013 76.3989
(12) 50000 236.517 0.000180032 77.4502
(13) 55000 240.872 0.000239057 70.6865
(14) 60000 244.73 0.000310096 66.8574
(15) 65000 247.981 0.000453205 76.1782
(16) 70000 250.727 0.000620385 85.5402
(17) 72500 251.972 0.000680463 86.1031
(18) 75000 253.466 0.000750563 84.7697
(19) 77500 255.406 0.000850723 81.1474
(20) 80000 257.311 0.00101102 82.192
(21) 82500 258.765 0.00119142 86.6692
(22) 85000 256.656 0.00107913 99.4496
(23) 87500 238.462 0.000260503 158.623 <====
(24) 90000 240.861 0.000369483 179.003
(25) 92500 246.884 0.000539779 144.127
(26) 95000 248.407 0.000600361 141.323
(27) 97500 249.947 0.000675252 140.065
(28) 100000 250.6 0.00070049 139.722 <====
The algorithm allows relative humidities >100 to allow for
supersaturation. In the case where the relhum
yields values above some maximum (say, MaxRh),
the user can use the where function:
rh = where(rh.gt.MaxRh, MaxRh, rh) ; MaxRh=105 (user specified)