Surf. pressure: 1024hpa; surface temperature: -33.1 degree C ; dew point: -36.9

Question

Surf. pressure: 1024hpa; surface temperature: -33.1 degree C ; dew point: -36.9 degree C

a>Calculate the vapour pressure e (note: use this v.p. table)

b>Calculate the Relative Humidity

c>Use the ideal gas law for water vapour e = vRvT (where Rv=462 J kg-1 K-1) to deduce absolute humidity v

d>From the gas law for dry air, p-e (="pd") = dRdT (where Rd=287 J kg-1 K-1), deduce the dry air density d

e>Calculate the total density =d+v

f>Deduce the mixing ratio r=v/d, and compare with the value given on the sounding data. Compare, also, with the value given more directly by the formula r= e/p (=0.622, ratio of molar mass of water vapour to molar mass of dry air).

g>Compare the specific humidity q=v/(v+d) with the mixing ratio

h>The surface potential temperature is given as =243.2K. Recalling that =T (p0/p)Rd/cp = T (p0/p)0.287, deduce what value has been adopted for the reference pressure p0

351 TABLE 94 SATURATION VAPOR PRESSURE OVER WATER (Explanation on p. 350.) Metric units .4 Tem- .0 .3 .8 ture mb.mb. mb. mb. mb. -50 0.06356 -49 -48 -47 -46 0.07124 0.07044 0.06964 0.06885 0.06807 0.06730 0.06654 0.06578 0.06503 0.06429 0.07975 0.07886 0.07797 0.07710 0.07624 0.07538 0.07453 0.07370 0.07287 0.07205 0.08918 0.08819 0.08722 0.08625 0.08530 0.08435 0.08341 0.08248 0.08156 0.08065 0.09961 0.09852 0.09744 0.09637 0.09531 0.09426 0.09322 0.09220 0.09118 0.09017 -45 0.1111 0.1099 0.1087 0.1075 0.1063 0.1052 0.1041 0.1030 0.1018 0.1007 -44 0.1239 0.1226 0.1213 0.1200 0.1187 0.1174 0.1161 0.1149 0.1136 0.1123 -43 0.1379 0.1364 0.1350 0.1335 0.1321 0.1307 0.1293 0.1279 0.1266 0.1252 -42 0.1534 0.1518 0.1502 0.1486 0.1470 0.1455 0.1440 0.1424 0.1409 0.1394 -41 0.1704 0.1686 0.1669 0.1651 0.1634 0.1617 0.1600 0.1583 0.1567 0.1550 -40 0.1891 0.1872 0.1852 0.1833 0.1815 0.1796 0.1777 0.1759 0.1740 0.1722 -39 0.2097 0.2076 0.2054 0.2033 0.2013 0.1992 0.1971 0.1951 0.1931 0.1911 -38 02323 0.2299 0.2276 0.2253 0.2230 0.2207 0.2185 0.2162 0.2140 0.2119 37 0.2571 0.2545 0.2520 0.2494 0.2469 0.2444 0.2419 0.2395 0.2371 0.2347 36 0.2842 0.2814 0.2786 0.2758 0.2730 0.27030.2676 0.2649 0.2623 0.2597 -35 0.3139 0.3108 0.3077 0.3047 0.3017 0.2987 0.2957 0.2928 0.2899 0.2870 -34 0.3463 0.3429 0.3396 0.3362 0.3330 0.3297 0.3265 0.3233 0.3201 0.3170 -33 0.3818 0.3781 0.3745 0.3708 0.3673 0.3637 0.3602 0.3567 0.3532 0.3497 -32 0.4205 0.4165 0.4125 0.4085 0.4046 0.4007 0.3968 0.3930 0.3893 0.3855 -31 0.4628 0.4584 0.4541 0.4497 0.4454 0.4412 0.4370 0.4328 0.4287 0.4246 0 0.5088 0.5040 0.4993 04946 0.4899 0.4853 0.4807 04762 0.4717 0.4672 29 0.5589 0.5537 0.5485 0.5434 0.5383 0.5333 0.5283 0.5234 0.5185 0.5136 -28 0.6134 0.6077 0.6021 0.5966 0.5911 0.5856 0.5802 0.5748 0.5694 0.5642 27 0.6727 0.6666 0.6605 0.6544 0.6484 0.6425 0.6366 0.6307 0.6249 0.6191 -26 0.7371 0.7304 0.7238 0.7172 0.7107 0.7042 0.6978 0.6914 0.6851 0.6789 -25 0.8070 0.7997 0.7926 0.7854 0.7783 0.7713 0.7643 0.7574 0.7506 0.7438 -24 0.8827 0.8748 0.8671 0.8593 0.8517 08441 0.8366 0.8291 0.8217 0.8143 -23 0.9649 0.9564 0.9479 0.9396 0.9313 0.9230 0.9148 0.9067 0.8986 0.8906 -22 1.0538 1.0446 1.0354 1.0264 1.0173 10084 0.9995 0.9908 0.9821 0.9734 21 1.1500 1.1400 1.1301 1.1203 1.1106 1.1009 1.0913 1.0818 1.0724 1.0631 20 12540 1.2432 1.2325 1.2219 12114 20101.1906 1.1804 1.1702 1.1600 -19 1.3664 1.3548 1.3432 1.3318 1.3204 1.3091 1.2979 1.2868 1.2758 1.2648 18 14877 1.4751 14627 1.4503 14381 1.4259 1.4138 14018 13899 1.3781 -17 1.6186 16051 1.5916 1.5783 1.5650 1.5519 1.5389 1.5259 1.5131 1.5003 -16 1.7597 1.7451 17306 1.7163 1.7020 1.6879 1.6738 16599 1.6460 1.6323 -15 1.9118 18961 1.8805 1.8650 1.8496 1.8343 1.8191 18041 1.7892 1.7744 -14 2.0755 2.0586 2.0418 2.0251 2.0085 1.9921 1.9758 19596 1.9435 1.9276 -13 2.2515 2.2333 2.2153 2.1973 2.1795 2.1619 2.1444 21270 2.1097 2.0925 -12 2.4409 2.4213 2.4019 2.3826 2.3635 2.3445 2.3256 2.3069 2.28832.2698 -1 2.6443 2.6233 2.6024 2.5817 2.5612 2.5408 2.5205 2.5004 2.4804 2.4606 -10 2.8627 2.8402 2.8178 2.7956 2.77352.7516 2.7298 2.7082 2.6868 2.6655 93.071 3.0729 3.0489 3.0250 3.0013 778 2.9544 29313 29082 2.8854 8 3.3484 3.3225 3.2967 3.2711 3.2457 3.2205 3.1955 3.1706 3,1459 3,1214 7 3.6177 3.5899 3.5623 3.5349 3.5077 3.4807 3.4539 3.4272 3.4008 3.3745 -6 3.9061 3.8764 3.8468 3.8175 3.7883 3.7594 3.7307 3.7021 3.6738 3.6456 4.2148 4.1830 4.1514 4.1200 4.088840579 4.0271 3.9966 3.9662 3,9361 4.5451 4.511 4.4773 4.4437 4.4103 4.3772 4.3443 43116 4.2791 4.2468 3 4.8981 4.8617 4.8256 4.7897 4.7541 47187 4.6835 4.6486 4.6138 4.5794 2 5.2753 5.2364 5.1979 5.1595 5.1214 50836 5.0460 5.0087 49716 4.9347 15.6780 5.6365 5.59535.5544 5.5138 5.4734 5.4333 5.3934 5.3538 5.3144 0 6.1078 6.0636 6.0 5.9759 5.9325 5.8894 5.8466 5.8040 5.7617 5.7197

Explanation / Answer

a) Since the temperature is, -33.1oC, the vapor pressure as given by the table would be 0.3781 mb (value corresponding to -33 vertically and 0.1 horizontally).

b) The relative humidity can be calculated using the formula,

RH = 100 - 5 (T-Tdp)

Where T is the actual temperature and Tdp is the dew point temperature.

This is because, for every 1 °C difference in the dew point and dry bulb temperatures, the relative humidity decreases by 5%, starting with RH = 100% when the dew point equals the dry bulb temperature.

Therefore, RH = 100 - 5 (-33.1 - (-36.9) ) = 81%

c) e = v Rv T

Where, Rv = specific gas constant = 462 J kg-1 K-1

e = partial pressure of water vapour = 1024 hpa

and T = -33.1 degree C = 240.05 K

Therefore, v = e / Rv T = 1024 / (462*240.05) = 0.009

d) Since p = 1013 hpa

p-e = 1013 - 1024 = 11

Therefore, for p we can use the same formula, with dew point temperature

d = pd / Rv Tdp = 11 / (287 * 240.05) = 0.00016

e) total density, = v + d = 0.009 + 0.00016 = 0.00916

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.