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http://www.ventideal.ru/ventilyaciya_basseina/ras_ven_bas/index.php

 

         1  
   

Handbook for the  Meteorological Observation

Koninklijk Nederlands Meteorologisch Instituut KNMI

September 2000

http://www.knmi.nl/samenw/hawa/pdf/Handbook_H01_H06.pdf

 .

5.2 Calculation of the saturation vapour pressure

The most accurate calculation of the saturation vapour pressure eS(t) is done using what is

known as the Goff-Gratch polynomial (ref. 5). The WMO has adopted this polynomial as the

standard formula. Because of the complexity of this formula and the highly intensive

calculation it requires, the WMO advises using the following approximations:

For water vapour in equilibrium with (or possibly supercooled) a flat water surface:

eS(t) = 6.112 * e {17.62 t/(t+243.12)}                                                                                    (1)

Above ice:

eS(t) = 6.112 * e {22.46 t/(t+272.62)}                                                                                     (2)

(ref. 1)

The above formulae are applicable to pure water vapour. If the situation involves humid air,

i.e. both air and water vapour, then a small correction should be applied. However, given the

required accuracy, this deviation is negligible. The conclusion is then that using formulae 1

and 2 achieves a very good approximation in the range -40 to +35C for the parameter to be

derived. These items meet the accuracy requirements.

Alternative approximation formulae (Magnus, Tetens, Bolton, Sprung) also provide the

required accuracy. These are described in KNMI-TR 153 (ref. 5) and KNMI-TR 140 (ref. 11).

The KNMI has adopted its own formula for derivation of the dew point temperature in the

SYNOP and the METAR:

eS(t) = 6.11 * e {17.504 t/(t+241.2)}                                                                                     (3)

This formula is used both for the water and the ice conditions, since the relative humidity

sensor provides a measurement relative to the water saturation. This formula has been

implemented in the software of the SIAM (ref. 13). The Insa calibration laboratory uses the

following formula, providing close agreement with (3):

eS(t) = 6.11213 * e {17.5043 t/(t+241.3)}                                                                            (4)

Using formulae (3) and (4) for the calculation also produces a derived parameter that meets

the accuracy requirements.

When the SYNOP data is archived in the Climatological Information System (KIS), the dew

point temperature is treated as a basic parameter from which the synchronous value of the

relative humidity is derived. This process is the inverse of the process described above. The

derivation is based on Sprungs formulae.

Above water:

eS(t) = 6.107 * e {17.27 t/(t+237.3)}                                                                                   (5)

                                                                           .  67

Above ice:

eS(t) = 6.107 * e {21.87 t/(t+265.5)}                                                                                   (6)

(ref. 6)

Summary:

Standard formula:

eS(t) = A * exp {B t/(t+C)} 
                                                                                                 (7)

Water surface
 

                                                                                             A                       B                      C

WMO                                                                                6.112                 17.62               243.12

KNMI (SYNOP, METAR, SIAM)                                     6.11                   17.504             241.2

KNMI (Insa Calib.Lab.)                                                    6.11213             17.5043           241.3

KNMI (KIS)                                                                      6.107                 17.27               237.3

Ice surface
 

                                                                                             A                        B                      C

WMO                                                                               6.112                  22.46              272.62

KNMI (SYNOP, METAR, SIAM)                                                          not applicable

KNMI (Insa Calib.Lab.)                                                                         not applicable

KNMI (KIS)                                                                      6.107                  21.87              265.5

5.3 Calculation of the vapour pressure: e

Given that RH = {e / eS(t)} * 100%,

it follows that e = {RH * eS(t)} / 100%                                                   (8)

5.4 Calculation of the dew point temperature Td

Given that eS(Td) = e and using the standard formula (7), we obtain:

A * exp {B Td /(Td +C)} = e                                                                     (9)

Conversion of this formula produces:

Td = C * {ln e - ln A} / {B - ln e + ln A}                                                    (10) or

Td = C / [{B / (ln e - ln A)} - 1]                                                                 (11)

5.5 Calculation of RH from t and Td

- eS(t) is calculated using (7)

- e is then obtained by filling in t = Td in (7): e = eS(Td)

- RH is calculated using RH = {e / eS(t)} * 100%.