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WORLD METEOROLOGICAL ORGANIZATION

TECHNICAL NOTE No. 61

NOTE ON THE STANDARDIZATION OF PRESSURE

REDUCTION METHODS IN THE INTERNATIONAL NETWORK

OF SYNOPTIC STATIONSReport of a working group of the Commission for Synoptic Meteorology

(prepared by M. Schiiepp, Chairman· F. W. Burnett - K. N. Rao - A. Rouaud)

PRICE: Sw. fr. 3.-

I WMO· No. 154. TP. 74 ISecretariat of the World Meteorological Organization • Geneva • Switzerland

1964

TABLE OF CONTENTS

Foreword ......•......

SU1llIl1ary (English, French, Russian, Spanish).

Introduction . . .

1.

2.

3.3·13.23·33.44.

5·

6.

7.8.

The problem

Criteria for testing-reduction methods

Analysis of different reduction methodsGeneralities ..•.Temperature influenceHumidity influenceComputation of reduction, practical aspects of the procedure.

Pressure in a horizontal plane, or height of a standard pressure surface.

Reduction to standard pressure levels and computation of heights forthe isobaric surfaces (850, 700 mb etc.)

Pressure reduction using isothermal atmospheres

Conclusions . .

Recommendations for the practical use of pressure reduotion methods

Page

V

VII

XI

1

2

336

1616

19

19

20

22

22

List of references

Annexes

27

lb - Values of

la - Values of

lc Values of

0.12· (es = Vapour pressure at station level) .

0.15· (es Vapour pressure at station level) .

0.20· (es Vapour pressure at station level) .

29

31

332. - Practical use of pressure reduction methods Computation of tmv from T and

T12 for the Swiss region. • • • • 35

3. - Values of 0.12 es as functions of T + T12 for the Swiss region. 362

4. - Reduction of atmospheric pressure to mean sea level . . ....... 37

v

FOREWORD

At its second session (New Delhi, 1958), the WMO Commission for Synoptic Meteorology (CSM) established a Working Group on Pressure Reduction Methods. The group was re~

quested to select certain methods of pressure reduction which, after appropriate trials,might be recommended for use in various regions of the world.

The group consisted of Dr. M. SchUepp (Switzerland), chairman, Mr. F.W. Burnett(United States of America), Dr. K.N. Hao (India) and Mr. A. Rouaud (France). The chairmanof the previous working group, Mr. L.D. Harrison (U.S.A.), and a member of that groupMr. J.D. Torrance (Rhodesia and Nyasaland) although not members of the working group nevertheless continued to collaborate with the new group.

The final report of the group was considered by CSM at its third session inWashington in 1962. The commission noted the report and showed great interest and appreciation, recommending that it be published as a WMO Technical Note.

I am glad to have this opportunity of expressing to the members of the workinggroup and all those who have contributed to the preparation of this valuable report thesincere appreciation of the World Meteorological Organization for the time and effort theyhave expended.

(D.A. Davies)Secretary-General

VII

THE STANDARDIZATION OF PRESSURE REDUCTION METHODS

Summary

The aim of this Technical Note is to suggest certain selected methods of pressurereduction which after appropriate trials may be recommended for use in various regions ofthe world.

It starts with a short historical review and some general remarks on the importance.of this problem in synoptic meteorology, and then gives a brief discussion of thecriteria for testing reduction methods. The main part of the Note is devoted to the consideration of different methods of pressure reduction to mean sea-level and other levelsboth below and above the station level. This consideration is supported by a number ofexamples with figures showing, in particular, the comparative results of using differentmethods. Attention is also given to the question as to when pressure should be reducedto sea-level and when it is better to convert it into heights of 850 mb or 700 mb surfaces.

Chapter 9 suggests recommendations for the practical use of pressure reductionmethods in various cases.

Annex 4 reproduces the proposal submitted by the United Arab Republic to the thirdsession of the Commission for Synoptic Meteorology.

VIII

LA NORMALISATION DES METHODES DE REDUCTION DE LA PRESSION

Resume

La presente Note technique a pour objet de recommander certaines methodes de reduction de la pression qui, apres avoir ete dUment experimentees, peuvent etre appliquees dansdiverses parties du globe.

La Note commence par un court apergu historique suivi de quelques remarques generales sur l'importance que ce probleme presente pour la meteorologie synoptique; elle passeensuite brievement en revue les criteres a appliquer pour la mise a l'epreuve des methodesde reduction. La plus grande partie de la Note est consacree a l'examen de differentesmethodes de reduction de la pression au niveau moyen de la mer et a d'autres niveaux, audessous et au-dessus du niveau de la station. Cette partie comprend un certain nombred'exemples et de figures comparant notamment les resultats obtenus a l'aide des diversesmethodes. La Note technique indique egalement quand il convient de reduire Jes pressionsau niveau de la mer et quand il est preferable de les convertir en altitudes des surfacesde 850 ou 700 mb. .

Le chapitre 9 contient quelques recommandations concernant l'application pratiquedes methodes de reduction de la pression dans divers cas.

L'annexe 4 reproduit la proposition presentee par la Republique Arabe Unie a latroisieme session de la Commission de meteorologie synoptique.

IX

CT~APTH3AqHHMETOAOB ITPlrn~EHHH AABnEHHfl

PearoMe

B AaHHO~ TeXHH~eCKOH 3anHCKe npeA~araroTcH HeKOTOpae MeTOAN npHBeAeHH&AaB~eHHH,KOTOpNe noc~e COOTBeTcTByromHX HCllaTaHHH MoryT ONTb peKOMeHAOBaHHA~X HcnO~baOBaHHH B paa~H~HaX pa~oHax MHpa o

3anHCKa OTKpHBaeTCH KpaTKHM HaTopH~eCKHM OOSOpOM H HeKOTopNMH 3aMe~a

HHHMH oomero xapaKTepa OTHOCHTe~bHO B~HOCTH STOH npoo~eMN A~H cHHonTH~ecKoH

MeTeopo~orHH; aaTeM AaeTcH KpaTKoe Hs~o~eHHe KpHTepHeB A~H o~eHKH pa3~H~HHX

MeToAOB npHBeAeHHH AaB~eHHH.OCHOBHaH ~aCTb 3anHcKH nOCBHmeHa paccMoTpeHHropa3~H~HNX MeTOAoB npHBeAeHHH AaB~eHHH K cpeAHeMy ypOBHro MOpH H K ~pyrHM

ypoBHHM,KaK BNme TaK H H~e ypOBHH CTaH~HH.B STOH ~aCTH npHBoAHTCH PEA npHMepoB H ~H~POBNX AaHHNX,xapaKTepHsyromHx B ~aCTHOCTH cpaBHHTe~bHNe pe3Y~bTaTH

npHMeHeHHH pas~H~HHX MeTOAOB.B 3anHcKe pasoHpaeTcH Ta~e Bonpoc 0 TOM,B KaKHXc~y~aHX ~e~ecoo6paaHO npHBoAHTb AaB~eHHe K ypOBHro MOpH,H B KaKHX npeArro~TH

Te~bHee nepeBoAHTh era AO Be~H~HHN,COOTBeTcTByromeH 850 H~H 700 MH~~HoapoBoH

nOBepxHOCTH.

B r~.9 AamTCH peKoMeHAa~HH no npaKTH~ecKoMY HcnO~b30BaHHro MeTOAoBnpHBeAeHHH AaB~eHHH B pas~~HaX C~y~aHX.

B ITpH~o~eHHH 4 H3~araroTcH npeA~o~eHHH,BHeceHHHe Oo~eAHHeHHoH ApaocKoHPecnyo~HKOH Ha TpeTbeH ceCCHH KOMHCCHH no CHHonTH~eCKOH MeTeopo~orHH.

x

NORMALlZACION DE LOS METODOS DE REDUCCIONDE LA PRESION

ResUmen

El objeto de esta Nota Tecnica es recomendar ciertos metodos de reducci6n de lapresi6n que, despues de haber sido debidamente comprobados, se pueden utilizar en variasregiones del globo.

"La Nota comienza con un breve resUmen hist6rico seguido de algunas observacionesgenerales sobre la importancia de este problema en meteorologia sin6ptica, y expone despuesde manera concisa los criterios empleados para comprobar los metodos de reducci6n. Lamayor parte de la Nota esta dedicada al estudio de distintos metodos de reducci6n de lapresi6n al nivel medic del mar y a otros niveles, superiores 0 inferiores al de la estaci6n. Este estudio esta ilustrado con varios ejemplos y figuras que muestran especialmente los resultados comparativos obtenidos por medic de metodos distintos. Tambien setrata del problema de decidir cuando se debe reducir la presi6n al nivel del mar y cuandoes mas conveniente convertirla alas alturas de las superficies de 850 6 700 mb.

El capitulo 9 contiene algunas recomendaciones sobre la aplicaci6n practica delos metodos de reducci6n de la presi6n, en varios casos.

En el Anexo 4 se reproduce la propuesta presentada por la Republica Arabe Unidaen la tercera reuni6n de la Comisi6n de Meteorologia Sin6ptica.

XI

INTRODUCTION

A CSM working group was called to life to study the problems of pressure reductionat the New Delhi session in 1958. It was composed of the following members :

Dr. SchUepp, ZUrich, Switzerland, chairmanMr. Burnett, Washington, USADr. Rao, Bombay, IndiaMr. Rouaud, Paris, France

No other members participated in the same official capacity. But the chairman ofthe former working group, Mr. Harrison of Washington, contributed new proposals, as didMr. Torrance of Rhodesia and Nyasaland, a member of the former group; both these correspondenlB continued to lend the group their valuable collaboration. For financial reasons,no plenary meeting of the group took place; it met in sub-groups and with the personalhelp of Mr. Kutschenreuter, president of CSM at the time, there were exchanges of ideasamong the members.

The task of the working group was defined as follows :

(1) To select the pressure reduction methods for testing;

(2) To examine the results of tests with the aim of reporting to the president of CSMbefore the end of 1959 on the pressure reduction method best suited to meet therequirements of synoptic meteorology.

A preliminary report was sent to the president of CSM at the end of 1959. Thefollowing paper is a slightly modified and completed version of the final report of thegroup, issued in November 1961 for the CSM meeting held in Washington in 1962.

the mdment of observation, he is notThe same applies for Busold's methodpressure in high regions, e.g. in

NOTE ON THE STANDARDIZATION OF PRESSURE REDUCTION METHODS

IN THE INTERNATIONAL NETWORK OF SYNOPTIC STATIONS

1 • THE PROBLEM

The problem of reducing atmospheric pressure to sea-level is one of the oldestproblems of synoptic meteorology. Its solution enabled meteorologists to draw weather mapsfrom the second half of the nineteenth century onwards. The fundamental equation of statics(cf. Technical Note No. 7, pp. 2-3, 20-21) introduces fictitious values of temperature andhumidity between station and sea-level. In Europe, the actual surface air temperature wasgenerally taken as a starting point, and a constant lapse-rate of 0.5°/100 m was assumedin most cases (cf. ;-17Technical Note No. 7). In certain countries, such as Norway (cf. ;-27Eliassen), the meth;d-was improved, as far as possible, to eliminate spurious pressure dif-ferences between neighbouring stations.

In the United States, where atmospheric pressure has to be reduced to sea-levelfrom stations as high as 1900 m, Bigelow (1901 L-i!) developed a reduction method usingthe arithmetical mean of the actual temperature T and the temperature observed 12 hoursbefore as a starting point instead of plain T. By this method, the influence of daily temperature variation was practically subdued. A second correction depending on T was addedto eliminate the influence of different annual temperature variation between continentaland coastal stations (cf. ~!7 pp. 12-13). .

Since that time, the density of the meteorological network has increased to sucha degree that spurious differences in reduced pressure between neighbouring stations havebecome a drawback in certain regions, giving new immediacy to the problem of pressure reduction. Then again, the aerological network created in the last 25 years has enabled us totreat the problem on a three-dimensional basis.

Harrison (U.S.A.) has dealt with the problem in a very radical way; his views arelaid dO~TI in several extensive publications L-4, 5, 6, 170n the different possibilities andprinciples of pressure reduction. The other element influencing pressure reduction, thehumidity of the fictitious air column, has been examined by Rao ~§7 L-27. This influenceis particularly important in tropical countries. Rao recommends a simplified version ofthe method developed in ~!7on pp. 20-21.

On the basis of these publications and of some recent investigations by Rouaud /107and Schuepp ;-117 - ;-13] the CSM Working Group on Pressure Reduction had to choose the-most adequate solutions and to propose their introduction as universal standard methods. Itbecame evident that the problem is a very intricate one even today, in spite of aerologicalprogress.

In Li~- L-l§7 Klauser and Scherhag test a method based on aerological measurements,but as these data are not available to the observer atable himself to codify the definite reduced pressure.described in ~l17, for the reduction to sea-level, ofthe South African region.

Another attempt by Gasser ~l§7, introducing the altimeter setting values used inaviation practice instead of the reduced pressure obtained with the actual methods, leadsto appreciable results only when mean temperature conditions prevail.

No ideal method seems to exist which might easily be put into practice. It is evendoubtful whether any method satisfying all reasonable conditions is conceivable. Nevertheless,

2 THE STANDARDIZATION OF PRESSURE REDUCTION METHODS

it seems that we should adopt a universal method according to which spurious pressure differences between stations of the same country - or frontier stations of neighbouring countries could be avoided.

2. CRI1'ERIA FOR TESTING REDUCTION MlIDIODS

The fact that no universally recognized method has been found so far must be attributed to the multiplicity of requirements demanding satisfaction.

(a) Isobars constructed on reduced pressure values ought to be made a basis for thedetermination of the gradient wind above the surface layer, i.e. some hundreds ofmetres aloft. This criterion is of special importance on sea and in flat country,where no local circulations occur.

(b) A second function of weather map analysis is following up the displacement anddevelopment of pressure centres. As cyclones and anticyclones in higher latitudesare thermally asymmeUdc their axes are generally far from vertical. If the pressure pattern is projected vertically from a higher level to a lower level or viceversa, it will not represent a IItrue ll pressure distribution at that level; askewprojection ought to be adopted. Figure 1, IIPressure reduction to sea-level", illustrates that in cases of vertical projection of the pressure distribution from surface to sea-level a pressure system with inclined axis shows a variable velocityof displacement in the plan if it crosses a high level plateau. This path distortion of the pressure centre is observed when a uniform horizontal temperature distribution is employed for pressure reduction, i.e. if the horizontal temperaturegradients between the different sectors of the system in the free atmosphere areneglected. In spite of the linear displacement of the low pressure system thecentre of the depression seems to be delayed in position 3 due to the projectionfrom the upper l~vel Hp to sea-level (Hp = 0).

Profile I

The axis of the low-pressure system is inolined oonseoutively toasymmetrio temperature distribution.

IPath of the systemof low pressure (T)(straight line) overthe island plateau.

T4

IPlateau, height Hp

TS

Figure 1. Pressure reduotion to sea-level.

THE STANDARDIZATION OF PRESSURE REDUCTION METHODS 3

The first criterion however is fulfilled in the case of vertical projection, provided all stations are situated more or less on the same level, whereas skew projectionwould not fulfil the gradient wind criterion. This drawback is unimportant in a mountainousregion, the wind field being subject to orographical influences and far from obeying thegradient wind law; there is no possibility and no need to relate local circulations due toorography to the reduced pressure pattern.

Figure 2 shows direction and force of the wind at Berne and Interlaken in Switzerland as functions of the pressure gradients in the two nearJ;y- perpendicular directions Interlaken-Berne (abscissa) and Berne-ZUrich (ordinate),. 1 July to 31 December 1961.

It wili be seen from this general survey of criteria derived from practical synoptical requirements that no reduction method can be expected to satisfy both criteria (representation of gradient wind above surface-layer and true location of centres) for stationssituated at different altitudes. We must confine ourselves to one of these criteria. Whena representation of the gradient wind field near the ground in a high and relatively flatregion is the object of the analysis, the pressure distribution at mean station level oughtto be conserved by the reduction process. When its object is to compare the pressure distribution of a relatively small mountainous region with that of surrounding lower regions,the reduction has to take into account the horizontal temperature (and humidity) differencesas revealed by aerological soundings.

In the following sections we shall examine the different methods with respect tothese criteria and from,the point of view of practicability, which is equally important.

3. ANALYSIS OF DIFFERENT REDUCTION METHODS

3.1 Generalities

We refer to WMO Technical Note No. 7,pp. 15-32, where Harrison has given a detailedand very clear account of the problem. The hypsometric equation, discussed in TechnicalNote No. 7, pp. 2-3 can be written in the form :

(0.0148275)ern

(1 - 0.378 -)Pm

(1)

where Po

Ps

HpTsa

ern

Pm

Pressure reduced to sea-level in mb

Station pressure in mb

Station elevation in geopotential metres

Station temperature argument in OK

Assumed lapse rate in the fictitious air column extending from sea-level tothe level of the station elevation in °C/gpm

Mean vapour pressure of the fictitious air column

Mean pressure of the fictitious air column

For our discussions, we start With the modified equation given in Technical NoteNo. 7, p. 20; formula (14)

(2)


Figure 2 shows direction and force of the wind at Berne and Interlaken in Switzerlandas functions of the pressure gradients in the two nearly perpendicular directionsInterlak9n-Berne (abscissa) and Berne-ZUrich (ordinate). 1 July to 31 December 1961.The various symbols in the diagram give the conditions at 0730 h and 13.30 h for thedifferent pressure gradients in the three stations, situated all at nearly the sameheight (.£.. 570 m) .

• = caJm.

For explanation of the symbols see the following legend :

Legendslightstrong

S SW WI •m @ I!l

NW•

NDI!!I

NEoo

Ea

IQ]

SE

o

o

-1.0

iJp'Bern-ZUrich:l0.5 1.0 t

1.0

oo 0

•

11

I

8 <-·D il

•• I •• 0 0

• • · 001 • 0

0 . 0 01 .11 0 <to <f0 0 -.01 . •. 0 o· .., . ..1111 •.. • <10 IO!I 11 0 •

0 IQ '0 ca. .i ... 101 00 -. • ·f a o· III .61 D

00 c .!I> <10' 0 · 0 D

0 .. a • •0 • a ~

0

iJp /nter/olcen-Bern -----1.0 -0.5 0

Cl

o '"o a

J@

Figure 2a. Wind conditione in Berne 0730 h MEZ

a •0 • ,.

• III .. ..Iil 0 c • IIi

• •• • 0 . 0 0

• Do 0 .. 0 0 0 D

0 0 D 11 D 0 .. .. •.01(1 D co • .III D «> .. OD · .. . 11 D

a 0 0 01> ~- .,.. 00 0 ... a• olII 0 «> •.. 000 0 ~ a

0 • a Do ca 00 0 0 oa o:lI D

0 0 0' 0 0 0

Ap /nter/o/ren - 8ern-----1.0 ;0.5

••

coco

~p Bern-ZUrich 10.5 1.0

1.0

~.-1.0

a

o

IJIo

Iil

CD

o

Figure 2b. Wind conditions in Berne 1330 h MEZ *)

*) MEZ - Mean CentraL European Time

'!'HE STANDARDIZATION OF PRESSURE REDUCTION METHODS 5

Berne is situated in hilly country, but exposed to different winds; consequently thegeneral pressure distribution, represented by the chosen gradients, has a marked influence on the wind conditions. If we look at the symbols denoting strong NE-winds,we find that they are situated in the lower left corner of diagrams 2a and 2b, thestrong SW-winds in the upper right corner.

If we look at Figures 2c and 2d, the general view is different. At Interlaken,in a deep alpine valley 40 km from Berne, no distinct relation between wind and general pressure distribution is recognizable. The local orographic influences and theassociated mountain-valley winds dominate. The general pressure gradients as represented in the large-scale weather maps, are insufficient for fixing the local windconditions with the big distances between the stations. Consequently it is not necessary to postulate that the direction of the isobars gives an exact picture of thepressure distribution at ground level in mountainous regions, especially where thereare deep valleys. The local conditions, not represented in the scale of normal weather maps, are determinant for the valley stations.

oLJp 8ern-Ziirich-:l

O.S 1.0 t,--------<_---.--------.---------------,--------0 f.O

/Jp Inter/alien-Bern---..../.0 -0.5

. ~ .'t-------It-------t------t------j 0

•.. '1'.... .. ~i'

.:e ...

@

t· .,•j

'-------'--------...1.--------'-------'-1.0

Figure 2c. Wind canditions in Inter1aken 0730 h MEZ

.!Jp Inter/alren-8ern - /Jp Bt/rn-Ziirich.,-f.0 -0,5 0 0,5 f.O t,-------·;-1,------,---------,-------, f.O

@<!l

@ c III [].. @J .0

@Ill 0 []

I!I . l1:li~

III. ..' . l> 0[]

@ . ~ .. '. .. . .• • .. ..' ... oo .. . • (j) ·4 ... ....

c III -lii :-• III

• <ilt'----------'-----_+_.L..---------.L-- ..J-f.O

'.

Figure 2d. Wind conditions in Inter1aken 1330 h MEZ


where K Hypsometric constant; = 0.0148275oK/gpm

Vapour pressure argument at the station, in mb

A function of H (expressed in °C/mb) see Technical Note No. 7, pp. 20/21p

Since the publication of Technical Note No. 7, Harrison has elaborated new proposalsas mentioned on its p. 32. We shall consider them more in detail in section 6; for themoment, let us take (2) as a basis of discussion. It contains the variables which must bedetermined from.meteerol.'Ogical (or aerological) data

The first and second refer to the vertical temperature distribution in the fictitious air column below station level, the third to humidity conditions. We are going totreat temperature and humidity separately. Humidity is important in tropical and subtropicalregions only; in all other regions, the influence of temperature is predominant.

The denominator on the right of (2) represents the mean virtual temperature of thefictitious air column :

Ts

Tmv

. Thus, for a given height Hp, Tmv

+ aHp +2

is a function of

e Cs h

(2a)

(b)

(a)

In this section we confine ourselves to reduction of pressure to lower levels, sothat only the fictitious air column is considered.

If a gradient wind representation on mean station level H is desired, T oughtmvto be uniform in the whole region.

If the scope of the analysis lies in the comparison of the pressure distributionof the region under consideration with the pressure distribution of the surroundinglower regions, T ought to vary geographically over the region so as to allowcontinuity at th~Vborder of the region with respect to the actual temperature distribution in the surrounding regions.

In the case of a mountain barrier, Tmv will normally be different on both sides.The pressure reduction methods actuall~~sed observ~!he second principle, whereas Harrison'smethod observes the first principle (LlI, p. 32; L.II).

3·2 Temperature influence

Terms T and a in equations (2) and (2a) :s

aBPTs and a determine the mean temperature Tm T + """2 (3)s

of the fictitious air column.

For a, the m~~ adopted temperature lapse-rate, values between 0 and 0.65°/100 mare being used. In L 11 p. 25, the value 0.65°/100 m is recommended; this value approximately equalling the mean temperature lapse-rate in'the troposphere, there is much supportfor its general adoption, though the lapse-rate is generally smaller than 0.65°/100 m inthe lower part of the troposphere.

Figure 3 shows an example of temperature lapse-rates in the free atmosphere between2,000 and 4,000 m (January 1960). The hatched areas have lapse-rates ~ 0.6°C/100 m, i.e.,the lapse-rate is approximately equal to the value of the interrlational atmosphere (0.65°C/100 m). The values diminish considerably in Siberia, where they do not even reach 0.4°C/100 m.

THE STANDARDIZATION OF PRESSURE REDUCTION MEllIODS 7

In the regions where 0.65°C/IOO m is generally considered too high, a simple correction of

the term ; can be obtained by neglecting the hurnidity influence eSCh

in formula (2)

(see paragraph 3.3).

Figure 3. An example of temperature lapse-rate in the freeatmosphere between 2,000 and 4,000 m (January 1960).

The choice of a suitable Ts is much more difficult and of wider implication. Thedifficulties arise from the great variability of temperature in the air layer near the ground(cL Llil). While the daily variation is very slight in the free atmosphere. it j s of cons;derable amplitude in the ground layer, especially in subtropical continental regions. Ifthe actual temperature is substituted for Ts ' Tm will vary in consequence. This daily variation of Tm implies a considerable daily variation of reduced pressure for high-level stationsdue entirely to the reduction calculus and not corresponding to any real phenomenon.

The amplitude of this daily variation is of the order of 10 mb in the case of atemperature amplitude of 20° and a station height of about 1100 to 1200 m! The daily temperature variation, then, ought to be eliminated as far as possible. This is very convenientlydone by taking for Ts the arithmetical mean between the actual surface air temperature andits value 12 hours before observation time;

Ts

(4)

The relevant examples appear in Figures 4 to 6.

If necessary, and at the expense of a more lengthy computation,

Ts

T + T6

+ T12

4

+

may be substituted to (4), T6 and T18before observation time.

being the temperature 6 and 18 hours, respectively,

Even these corrections do not prevent pressure from showing very large differencesbetween stations situated at approximately the same.level, if for orographic reasons theground layer is exposed to differential heating or cooling. This lack of homogeneity occursespecially in the case of pronounced inversions in more or less closed valleys. Though formulae (4) or (5) eliminate the daily temperature variation at each station, pressure

8 THE S'l'ANDARDlZATION OF PRESSURE REDUCTION METHODS

January

Departure of T and

Ta from the dailymean Tm July

................./ .... / \\

I<I.UTEN

" ....i·.............................

I00 r---...- I...--r--.

..........V;SIUN !_3 0

-1.20~ ih·······".,.. /. "f---( "~.....·;;otr..·.. .. ,..

Tmr------.----.-------.-----,I ..' , " ". To.~ol.-------.. ,/~ .... '"- ~ rJ ..

I<LOTEN 7S

IZJQ 6 () lZJQ 1830

Time (MEZ)

Figure 4a. Daily variation of temperature, unsmoothed and smoothed by the formula Ts T + T12 at a station in the region north of the Alps (Kloten Airport,

2ZUI'ich) and in an alpine valley (Sion). Unsmoothed = dotted lines, smoothed = fulllines. The smoothed Ta is more efficient in summer-time (right diagram) than inwinter (left diagram), because in summer the daily variation has a sinusoidal form,while in winter a large flat minimum is connected with a sharp maximum.

January JU~

72- -126- .. 8

4- QfF.r!!jB .. 4

0- .. 0

-4-Ilfi" .........

--4-,- Klolen - -8-12- - -12

- 1612- • 128- - 8~- - ,.o- D

-4- .. -4'8- S/on .. ·8-12- --12·(6- llFF .. -16-211- .. -20t .. - -M

~gJ4 630 lZJQ 1830 OM 030 640 lZJQ 18JQ OM ~

Figure 4b. The scale on the ordinate shows the variation in height of the constantpressure surfaces in metres.

Abscissa = Time (MEZ).

The figure shows the daily variation of pressure at station level (Q,FE) andreduced to sea level (Q,FF) when T or T + T12 is used in the reduction method to get

2the Q,FF values. The compilation with T + T12 leads to a daily variation not much

2differing from the Q,FF feature, while with the T value above, the daily variation hasincreased amplitude.


1ft /lHm

+0.6 ·'5

0164.3mb -0

liiilsdi ·-5-0.6 2286m

+0.6-+5

0

:-5-0.6 --7

-l2

lZJO /830 030 OJQ 5JQ /2 30 /8JQ OJQ

+7·-5· f----t----t~Ir_+---_t--__j

-5·

Figure 4c. Daily variation of pressure in the alpine region I January.

Ordinate Deviation (Lf p) from the mean daily pressure and variation ( Lf H) ofthe constant pressure surface respectively.

Abscissa Time (MEZ).

APm6t

-5 0.6

-5- --5 -tJ.6

;'l:-50.6 --- ---5- ...... /

........"...

0- 96lU-m6 0S/on481m

-5- --5 -0.6

-10- ~-IO -12

-15-g3D 630 0 30 03!! 530

6684mb

AH{11-5

-0

~-5

-5

0.

-5

-10

Figure 4d. Daily variation of pressure in the alpine region I July


Figure 5. Pressure distribution at sea-level in the region1957, 06 GMT. (Weather situation with small pressure gradients.)represent the results of four different reduction methods.

of the Alps, 5.July,Figures 5a to 5d

Figure 5a. Reduction with the extrapolated temperature curve in the free atmosphere at a radiosonde-station (Eliassen method). This method eliminates the localinfluences to a large extent but is not convenient in daily practice.

Figure 5b. Reduction using the actual temperature T at the ground stations. Asimportant ground inversions occur at ear:].y hours, this method gives slightly increasedpressure values in. mountain regions in the morning compared with Figure 5a, whilevalues are lower in the afternoon because of the greater heat in surruner.

Figure 5c. Reduction with T + T12 temperatures. This map shows approximately2

the same features as Figure 5a. The compilation of the reduced values is somewhatmore difficult than in Figure 5b, because two T values are necessary instead of one.however, the additional work for the observer is little.

Figure 5d. Reduction with a global mean temperature according to a fonner proposall made by Mr. Harrison (Logbar Function). Using a uniform global temperature forreduction, e.g., reduotion aooording to the international atmosphere, brings outstrong orographio influenoes (high temperature oorresponding to high·pressure overthe mountains, low temperature corresponding to low pressure centres).


Figure 6. Comparison of three maps for 24 March 1956 (06 h) established intropical regions and constructed according to different methods t Figures 6a, 6b and6c. cf I Rouaud ~1Q1.

The real pressure gradients are small in the regions and consequently light windsprevail. Figures 6b and especially 6c show marked virtual pressure gradients, simulated by local temperature anomalies (Figure 6b) with differences in the stationheight (Figure 6c, see high pressure 1022 mb over the elevated parts of the continent).The sharp' gradients are mainly due to these relief effects and are not realistic. Thetemperatures have to be smoothed on a regional basis T + T12 and not completely

2equalized on a global scale, if we wish to avoid unrealistic values.

Figure 6a.

Corresponding to Figure 5a(Eliassen method).

Figure 6b.

Corresponding to Figure 5b(Actual -t~eratlH'e).

Figure 6c.

Corresponding to Figure 5d(Global mean temperature).


Figure 7 - Comparison of the daily variationof temperature in July (1956-1961) at a slopestation (ZUrich, Central MeteorologicalOffice, 560 m on a southern slope, reducedwith 0.55 C/100 m to an elevation of 430 m)with a valley station (ZUl'1ch-Kloten Airport,flat Valley at 430 m wi th frequent layers ofcold air during the night).

The ordinate shows the temperature in °c,the abscissa the time (MEZ). The full curverepresents the slope station, the broken onethe valley conditions. The latter has a morepronounced daily variation, and in particulara deeper night minimum. The differences arein the order of lOCI they are more appreciablewith clear sky, especially over snow-coveredground. The lower daily mean of the broken

curve (lower values of ~) leads to a

higher value for the reduced pressure in thevalley station, if no correction F is applied.

2116Its'2o

16

'" '--"'".L..._ .'.J -_.... 6

p

-? 't

Figure 8 - Mean vertical temperature distribution over the central station of Greenland(approx. 3,000 1l1) in December. (Results of theFrench Expedition 1949-1950 by Paul-EmileVictor.) An oblique system of co-ordinates isused for showing the temperature conditions,the abscissa giving the temperature in OoC,the oblique straight lines the pressure in alogarithmic scale, as indicated on the leftside.

The portion A-B of the temperature curve givesthe lapse-rate in the troposphere. T-B showsthe strong inversion near ground level. Thisinversion is connected Witll the surface, inthe case of a lower ground level it would betransferred to T'-B'. Consequently, we shoulduse the portion C-C' of the curve for thereduction of pressure to sea-level instead ofT-T' (1.e., in the case of inversions continuing the whole day). An additional term Fshould be added to the observed temperature Tto give an appropriate Ts Value in formula (2).

The inversion, very apparent in the wintermonths (October-March) as demonstrated byFigure 8 disappears during the two monthsJune and July, that is, during the period ofconstant daylight and relatively intensesunshine.


+15~

- 5°1'------+-----" -----~--

\:\ ..

Figure 9. F values (OrdinatesJ, as functions of the temperature T + 12, deter-----:r--mined for the period January-July 1956 forZUrich - K10ten Airport. F values areobtained by comparing the aerologicalascents in the neighbourhood as indicatedin Figure 8. The figure also shows theF curve found by Eliassen for the Norwegian region. The figure indicates theimportant scattering of points at thepre-alpine station} a mean value of F isdifficult to obtain. If conditions arenot very different from those at surrounding stations, an F value = ° can be adoptaiin temperate regions. But a positive Fvalue is often required ~;der polar andsUbpo1ar conditions, especially in Valleystations with extreme temperature inversions.

"' •••• 1•• ,

•.•.1.., ...

,' ..., .. ".• '1"" .,

• 0"

_._- --0 __ 1_O·

+5'

-10° ---------+-------j-------+

-20° -10' o'

_ 7+-7,2-2-

10° 20' C

Figure 10. Weather map ofthe South African Union for8 April, 1960 L2q. Thedotted lines represent thepressure distribution atsea-level (equidistance ofisobars = 2 rob). The fulllines over the African Continent show the height ofthe 850 mb level (at intervals of 10 metres). Thetwo curve systems indicatemarked differences in thegeneral features, thoughthe 850 mb level lies only1500 m above the sea. Thetwo systems are not strictly comparable from the pointof view of gradient windconditions} 2 mb pressuredifference would corres~

pond to 16 m height difference for the 850 mb standardpressure surface.


Figure 11

Example of an Antarctic weather map (from the WMO Bulletin, July1958 ~1-7. The full lines at sea-level and the broken lines ofthe 700 mb standard surface have corresponding intervals (5 mbpressure difference and 40 m height difference). The centres oflow pressure (n) near the Ross Sea have inclined axes. The isohypses of the continental anticyolone (A) demonstrate the gradientwind conditions over the ice-cap, as confirmed by the wind dataat the weather stations.


Figure l2a. Isobars at sea-level over Asia in January(winter anticyclone) and pressure distribution at the 3000 mlevel (broken lines, over Tibet, pressure in mb). The pressuredistribution in the high-level parts of Asi~ differs completelyfrom that at sea-level} it is almost the opposite. Under theseconditions the separation in two maps at different levels asrepr~sented in Figure 8 and Figure 9 is of advantage in avoiding false interpretation of wind conditions near the ground.

Figure l2b. Pressure distribution at sea-level (fulllines) and height of 300 mb standard surface (broken lines)over Europe with cold air advection ~ 2 February 1956. Underthese circumstances the differences between the various levelsare nearly as appreciable as in Figure l2a, but in the alpineregions they are unusual, while in the AsiatiC' mountain rangesthese oonditions are normal.


differences in the reduced value~ result from differences in the daily mean temperature between stations in valleys and those situated on slopes (Figure 7).

To smooth out these inhomogeneities we may introduce an additional correction F :

Ts

T + T12

2+F (6)

Methods to determine F are given in section 3.4 (see Figures 8 and 9). The effectof formulae (4), (5) and (6) is to smooth local temperature differences without changing thetemperature distribution on a synoptic scale. Reduced pressure distribution may be interpreted as a result of extrapolation to sea-level of the pressure distribution in the freeatmosphere. In the case of horizontal temperature gradients (on a synoptic scale), thepressure patterns aloft and at sea-level are not identicaL If the stations are less than600 m above sea-level, the differences between the two pressure patterns are generally insignificant. In the central parts of the Rocky Mountains, however, they may be quite considerable, with the effect that the gradient wind in the ground layer may not be determinedfrom the reduced pressure chart. To represent the gradient wind over high plains, a uniformtemperature should be used in pressure reduction. Harrison's last proposal of an isothermalatmosphere is a step in this direction (cf. section 6). One drawback in this method is thatsuch a uniform temperature should be determined in each case by a meteorological centre;another difficulty arises when the mountain region under consideration extends through different climatic zones as do the Rocky Mountains (from Alaska to Mexico!); in such a regiona uniform temperature is inconvenient, and the best solution would be to renounce any pressurereduction. This solution has, for example, been adopted by the South African Union : aftermany unsuccessful trials to reduce pressure to sea-leVel, the pressure indications of thePlateau stations are used to construct the 850 mb contours (Figure 10), and sea-level isobarsare drawn for coastal stations only, the weather map being thus composed of two differentparts. An untrained user may find it difficult to interpret such a composite map, but it iscertainly preferable to a reduction which would necessarily be unsatisfactory. This separation may actually represent the best solution for regions such as the Antarctic region(Figure 11), Greenland, Tibet (Figure 12a) and Bolivia.

3.3 Humidity influence

In most climates, the influence of humidity on pressure reduction is relativelyunimportant. Even when e (water vapour pressure) amounts·to 20-30 mb - these are maximumvalues, e.g. in the Alps ~ the term es~ will not exceed 2-3°C. It is therefore quite unnecessary to specify this term as a function of altitude, and a mean value will suffice. Raohas shown L-g; that the vertical water vapour pressure lapse-rate varies according to theseason from 0.8 to 2.3 mb/300 m. For~, a constant value of 0.12°C/mb may be taken; thisvalue differs from Hannls formula by not more than 10 per cent for all heights between 0 and800 m above sea-level. It may be used even above this level, since at higher altitudes muchgreater errors arise from the uncertainty in the choioe of Ts and a.

Taking ~ 0.12°C/mb, tables may be computed which show esCh as a function ofobserved quantities, e.g. temperature and relative humidity at the station (Annex la). Sincethe daily variation of es is unimportant, there is no need to average es similarly to Ts ' asindicated by (4).

3.4

3.4.1

Computation of reduction, practical aspects of the procedure

The general reduction formula-----------------------------If we define Ts ' a and Ch as specified in sections 3.2 and 3.3, the reduction for

mula (2) takes the following form :


Po K Hlog P

T + T12 ~+Ps +F + 0.325 0.12 es2 100

For explanation of symbols, see 3.1, 3.2, 3·3.

Except for special orographical situations, F vanishes.

17

(7)

A value = 0 must be attributed to F in regions with persistent ground inversions(i.e. inversions not disappearing in the day-time) or very marked differential heating, thecriterion being the non-representativity of T + T12 on a synoptic scale. As to the deter-

2 __mination of F, we follow a method indicated by Bessemoulin (cf. Rouaud /10/: after tracingmaps of mean monthly reduced pressure Po (assuming F = 0), the "correct"-value of Po ata given station is inferred by interpolation from the values in the vicinity.

T + T12Substituting for the monthly mean temperature T of the station, we obtain2

F

K. ~

log~ / ps)- T - 0.325 Hp - 0.12 e

s100(8)

Thus F is known as a function of T; as T varies only within relatively narrow limits,it is recommended to compute F also for groups of very cold and very hot days to avoid unreliable extrapolation.

This method gives generally not very exact values for F, but ensures good controlof the following basic data for the station in question :

(1) Station pressure

(2) Reading of the pressure by the observer

(3) Station height.

If the F value obtained by (8) differs considerably and systematically from reasonable intervals suggested by the thermal situation of the station, one of the three pointsmay be incorrect.

An easier method for obtaining F values, but without the above-mentioned controlof basic data, is to reduce the climatological monthly means of temperature (Tm) for the wholenetwork (~ ~ 800 m) to sea level

T + 0.65m~

100+ 0.12 e

s

Representative (slope) stations serve to draw isotherms of the reduced temperatureTom over the whole region. Stations situated in big towns or on southern slopes show toohigh values, generally (+ 1/2) - (+ 1°C), while stations in troughs show sometimes very lowtemperatures.

The F values are obtained by a comparison of the reduced temperatures observed atthe station in question (Tom) and the interpolated values from the isobars T~rf

18

3.4.2


As a regular three-hourly observation interval is not ensured by all stations,there are cases where T12 is unknown through lack of observation. In all such cases, T12should be determined from a temperature record (thermogram); it is then recommended to readT12 - T from the temperature record and to substitute

T12 - TT +

2

for T + T12 in the reduction formula, since by this procedure a shift of the temperature2

s,cale on the thermogram is eliminated. In default of a thermograph, take the daily meantemperature for the preceding period of 24 hours according to national standards, e.g.

min. + max.2

(From 0 to 12 h : Minimum of preceding night, maximum of preceding day; in the afternoonMinimum of preceding night, maximum of current day).

3.4.3

The formula (7) may be simplified at stations or in whole regions where the differences between the pressure obtained by the exact and the simplified formula do not exceed0.3 mb at the outside. The following simplifications are recommended :

3.4.3.1 The denominator on the right side of (7) I

( T + T12 + F2

+ 0·325 l\ 0.12 es )100

can be replaced by a constant C for ships and low-level land stations with heights up toapproximately 20 m (stations with medium temperature range), 10 m (stations with high temperature range) or 30 m (stations with low temperature range). In this case the formulae (13)of Technical Note No. 7, P. 19 can be used I

where

C Additive reduction constant = 34.68

Station elevation in gpm

~Tav

(10)

Tav Mean annual normal value of. virtual temperature at the station in OK

3.4.3.2 For land stations at lower altitudes (9) can be replaced by the following formula

( T + T122

+ 0.325 ~100

+ 0.12 em (11)

where em = mean value of vapour pressure, em beingannual mean according to the climatic conditions ofsmall interdiurnal temperature variations T + T12

2value Tm + Tm12 •

2

determined as a function of T or as anthe region involved. In regions withcan be replaced by the monthly mean

2

In polar regions or at high level stations with small daily temperature range (butstrong interdiurnal variations) T + T12 can be replaced by T, and 0.12e can be neglected

m

THE STAND.ARDIZATION OF PRESSURE REDUCTION f.1ETHODS 19

as it is very small at low temperature values. On the other hand attention must be paid toF, which may be important in the case of big inversions (cf. 3.4.1).

3.4.3.3 The reduction to sea-level should be restricted to stations with heights up to 800 m.As regards stations situated between 600 and 800 m, the pressure can either be reduced tosea-level or it can be converted into height for the 850 mb level (for the latter case cf.chapter 5). If, exceptionally, the pressure is reduced to sea-level at stations above 800 m,it may be necessary, in climates with strong diurnal temperature variation, to replaceT + T12 by T + T6 + T12 + T18 (f 3 2)

2 4 c. . .

4. PRESSURE IN A HORIZONTAL PLANE, OR HEIGHT OF A STANDARD PRESSURE SURFACE

From the development of three dimensional analysis with 850 mb, 700 mb and otherconstant pressure surfaces the following question arises : should we prefer constant pressureanalysis (e.g. of the 1000 mb surface) to sea-level isobars?

The representation would be the same for all maps; we could use the same gradientwind rules and the computation of the thickness layers would be facilitated. The reductionerrors would be notably diminished in the case of the strong winterly anticyclones, wherethe most important difficulties arise from pressure reduction. On the other hand the reductions would be somewhat more complicated on ships and lovy-level land stations. Negative valueswould occur in lows and the errors of compilation would probably increase slightly. The correlation between pressure distribution and wind at sea is slightly more marked for sea-levelisobaIJS than for 1000 mb contours, the latter representing the conditions some 100 m abovesea-level in regions with high pressure, some 100 m below sea-level in the case of low pressure.

Comparing the advantages and disadvantages of the two systems, we think that it ispreferable to maintain the conventional representation (isobars at sea-level). It is easyto draw contour-lines at the 1000 rub surface using the temperature values and the sea-levelmap, as the isobars at sea-level and the contours of the 1000 mb surface are more or lessparallel. It is recommended to use corresponding intervals : 2 mb isobars - 16 m contours,or 5 mb isobars - 40 m contours etc.

The aerological stations should use ~he corresponding method for computing theheight of the 1000 mb surface, i.e. (4) T; 12 should be employed for Ts ' This leads

to formula (12) in the following chapter 5.

5. REDUCTION TO STANDARD PRESSURE LEVELS AND COMPUTATION OF HEIGHTS FOR THE ISOBARICSURFACES (850, 700 mb)

5.1 Reduction to standard levels below station level

A formula analogous to (7) ought to be used in this case (cf. L-iJ p. 29 formula(27))

2-log Ps2 (12)

where P3 Pressure at geopotential H3

Ps2 Pressure at station level ~

Ts2T + T12 (+F) at station level

2


Lapse-rate between H2 and H3 (= 0.65°C/IOO m)

Vapour pressure at station level

Function corresponding to ~ in the reduction to sea-level

The value 0.12 can be adopted for C23 when H2 .( 2000 m (see table, Annex la)

The value 0.15 can be adopted for C23

when H2 = 2000-4000 m (see table, Annex Ib)

The value 0.20 can be adopted for C23

when H2

'> 4000 m (see table, Annex lc).

The same rules for simplification of the formula (12) apply in reductions to standard levelsand to sea-level.

Formula 12 is useful for reduction to constant geopotential levels. For the more important cases of computing the heights of pressure surfaces (850, 700 mb etc.) it has to bereplaced by a mOdified equation. This will be dealt with in the recommendations for practical use (paragraph 8.4.1).

5.2 Reduction to standard levels above the station level

Here, we are dealing with real layers, not fictitious ones as in formulae (7) and(12), and verification of the accuracy of the reduction is possible. The problem is todetermine the mean virtual temperature of the layer between the station level HI and thestandard ~eyel H

3as precisely as possible by the reduction formula. We start with formula

(26) of LlI, p. 29 with the same symbols as in formula (12) of 5.1.

(PsI and Tsl = pressure and temperature at station level) :

Ps1 K (H3

- HI)(13)log P

3 (H3

- HI)(Tsl -

a13 eslC

13)+

2

In computing the heights of pressure surfaces, formula (13) has to be replaced by a modifiedequation, see paragraph 8.4.2.

6. PRESSURE REDUCTION USING ISOTHERMAL NIMOSPHERES

As a result of his extended studies Harrison proposes in L-17 to use the followingformula (14) for computing the height of the 1000 mb surface

log (14)

where HlOHsR

go

Tro

Ps

Height of 1000 mb surface

Station level

Constant of gas equation of dry air

Mean acceleration of gravity at sea-level

Estimated mean virtual temperature between Hs and HIO for the region

Pressure at station level

Temperature Tro is supposed to be constant in the whole region at the time of observation. In this case the reduced pressure gives the vertical projection of the pressure


distribution in the elevated region on the 1000 mb surface. The gradient wind distributionin the elevated region can be determined from the HIO values. To ensure easy computationthe following two conditions must be fulfilled

The stations must be on approximately the same level because :

1. The value Tro corresponds to the real temperature in the free atmosphere only formedium values of Hs in the case of a non-isothermal atmosphere. If the differences inheight are considerable, the topography of the region has an influence on the HIO values,causing a field to be superimposed on the pressure field of H

IO~alues.

2. The mean temperature of the region must coincide more or less with the actualobserved values in different parts of it, i.e. the horizontal temperature differences shouldnot exceed a certain amount, otherwise even little differences in station height betweenneighbouring stations will have considerable influence on the topography of the H

IOvalues.

In small countries these suppositions can be fulfilled by a convenient value of Tro 'but it is difficult to find appropriate values when dealing with a far-extending mountainregion as with the Rocky Mountain or the Asiatic mountain ranges. Very considerable temperature differences prevail, often between different regions of the same chain of mountainsas in Alaska and Mexico. The same Tro cannot apply in the two regions. If we wish toavoid inconsistent values of Hro at the boundaries of two regions with different T values,

. ro .we are obliged to use glidlng values of Tro ' Such a system seems only practicable wltha two-way communications system linking the analysis centre and the observer if the observerhas to use the Tro value himself. The two-way communications would complicate the transmission of meteorological messages.

These considerations lead to the conclusion that formula (14) is not advantageousfor use on a world-wide scale, and we think that the methods described in chapters 3 and 5are at present more appropriate for practical use. If we wish to know exactly what windconditions prevail over high plateaux with heights above 1000 m, it is more convenient todetermine them from contour lines of the 850 mb or 700 mb surface than to compute the heightfor the 1000 mb surface or reduce pressure to sea-level. (Composite charts, Figures 10 to12).The 850 mb surface is convenient for the Rocky Mountains, South and East Africa and the highregions of West and Central Asia (Figure 10). The 700 mb surface is recommended for Bolivia,Greenland, Tibet and Antarctica (Figures 11 and 12).

The disadvantage which the more complicated picture of the two sets of curves represents is more than counterbalanced by the good representation of wind conditions in thehigher portions of the continent, and the spatial representation is facilitated by comparingthe differences in the pressure field at both levels in the boundary zone. These compositecharts separate clearly the two levels instead of combining them by a complicated system,using appropriate Tro values communicated by two-way transmission.

If, for purpose of numerical analysis or forecasting, a computation of the heightfor the 1000 mb surface using a regional Tro value is desired, the supplementary code group6ajhhh or possibly a QFE group should be used.

The use of a supplementary group 6ajhhh on a regional basis is recommended forobtaining further information on the suitability of the HIO system developed by Harrison.The group could be added to the normal message. This could be done either for all observations or for a selected number (or a selected period) if the actual conditions of transmission did not allow continuous communications, which would be preferable.

For high-level stations the coded value PPP gives the height of the 850 or 700 mbstandard surface; these data effectively increase the density of stations in constant pressurechar+'s based otherwise on aerological observations. In this case the additional group 6ajhhhwould give the hhh value for the height of the 1000 mb surface for stations up to 1500 m or2000 m, using the HIO reduction formula.

22

7.

7.3

7·5

8.


CONCLUSIONS

A comparison of the different methods of pressure reduction to sea-level usedhitherto leads to the proposal that formula (7) in section 3.4.1 of this reportshould be used. This formula has been quoted from WMO Technical Note No. 7, p. 20;it makes use of T + T12 where T is the actual surface air temperature at the

2moment of observation, T12 the temperature 12 hours before the moment of observa-

tion. As humidity parameter it includes the water vapour pressure.

Low-level stations may use an abbreviated form of this equation as mentioned insection 3.4.3.1 within an intermediate altitude range, and provided that there isno excessive daily water vapour pressure variation, the procedure is as indicatedin section 3.4.3.2; for great altitudes, see section 3.4.3.3.

The representation of the pressure pattern by sea-level isobars as practised hitherto is, on the whole, to be preferred to representation by 1000 mb contours.

Radiosonde stations should use formula (12) in section 5.1 of the report for computing the height of the 1000 mb surface. This formula is analogous to formula (7).

As a general rule, pressure reduction to sea-level is feasible only for stationsbelow 600-800 m. Pressures of stations situated above this upper limit should beconverted into heights of 850 mb or 700 mb surfaces respectively. If a pressurereduction using isothermal atmosphere according to formula (14) in section 6 is"to be practised in specified regions, a special group 6ajhhh should be included inthe coded message; the same additional group might be used for the purpose of numerical analysis and forecasting.

Pressure reduction to a standard level above station level should be computed usingformula (13) in section 5.2. Special investigations on the best choice of theparameters Tsl' a13 and C13 are desirable in cases where this kind of reduction iscarried out in far-extending regions.

RECOMMENDATIONS FOR THE PRACTICAL USE OF PRESSURE REDUCTION METHODS

8.1 The general equation of pressure reduction given in Technical Note No. 7, p. 20,should be used for pressure reduction to sea level I

a. Hp-2-

0.0148275. Hp

(tm~ + 273.2)(2)

where Po

Ps

K

Hp

Ts

a

Pressure reduced to sea-level in mb

Station pressure in mb

Constant

0.0148275

Station elevation in geopotential metres

Station temperature argument in ~

Assumed lapse-rate in the fictitious air column extending from sea-levelto the level of the station elevation in °C/gpm


em Mean vapour pressure of the fictitious air column

Pm Mean pressure of the fictitious air column

es Vapour pressure argument at the station, in mb

~ A function of ~ expressed in °C/mb (see Technical Note No. 7, pp. 20/21)

8.1.1 In this formula for the variables a and ~, uniform values are adopted

a = 0.0065 ~ = 0.12

8.1.2 The variable Ts is generally determined by the following formula

where T

T + T122

Station temperature at the moment of observation

(6)

T12 Station temperature 12 hours before the moment of observation

F A function, in OK, of parameters found to give Ts the desired propertiesfor special orographic situations (see 8.1.2.3).

If in some months the month-

more than 2° from the monthly mean tempera-

500 m and asymmetric daily temperature varia-

gives an approximation of the actual daily mean of tempera

~

ly values of T + T122

ture Tm, the formula (6) has to be replaced by

8.1.2.1 The first term T + T122

ture at the station. In locations with ~

tion the climatolog:ical means of T + T12 should be calculated.2

(T = 0,3,6,9 GMT) differ

T =s +F (6a)

temperatures 6 and 18 hours respectively before observation time.

8.1.2.2the T12to read

If T12 values are not available due to lack of regular three-hourly observations,values ought to be determined from a thermogram. In this case it is recommended

T12-T from the temperature record and to substitute T + T12-T for T + T122 2

In default of a thermograph, the daily mean temperature for the preceding periodof 24 hours is substituted for T + T12, according to national standards, e.g. min. + max.

2 2

8.1.2.3 The second term F in formulae (6) and (6a) compensa~es the effect of frequent persistent ground inversions (i.e. inversions not disappearing in the day-time).

The value of F is obtained as a function of T by comparing the monthly means andseries of very cold and hot days at stations without extreme inversions occurring nearby,both reduced to sea-level by adding 0.65'1~ + 0.12es ' As a check, the F value is obtained

as a function of T by the following formula :

F = K Hp

109 (pjPs)T - 0.325. Hp _ 0.12 es100

(8)

where Mean monthly reduced pressure obtained by interpolation with a map from thevalues in the vicinity

24

Ps


Mean monthly station pressure

T Mean monthly station temperature = mean value of T + T122

es Mean monthly station vapour pressure

The different monthly F values are determined by (8); and those for series of verycold and very hot days are determined in an analogous manner. By this procedure we obtainF as a function of the T + T12 values by a regression line through the different points.

2

F is supposed to be 0 in subtropical and tropical regions. It is similarly discounted in temperate and polar regions if the values of (8) do not exceed 2°.

8.1.3 With these specifications the formula (2) has generally the following form

Po 0.0148275 ~log10Ps T + T12 H

(2a)+F+ 0.325.2 + 0.12 e

2 100 s

or

Po 0.0148275 H(2b)log10 P

Ps T+T6+T12+T18 0.325 -~ ++F+ 0.12 e2 100 s

8.1.3.1 The following table (Annex la) gives the fourth term of the denominator 0.12 esin function of the temperature T and the relative humidity U.

8.2 The general formula (2) can be simplified for lower regions when the differencebetween (2) and the simplified form given in the following formula (10) does not exceed0.2 mb at the outside.

Po Ps + C

C 34.68 HpTav

~ Station elevation in gpm

Tav Mean annual, monthly (or seasonal) normal values of virtual temperatureat the station, in OK.

Generally, in the case of medium temperature range the accuracy will be sufficientfor ~ = 20 m in the case of uniform annual value, ~ = 40 m in the case of monthly valuesof Tmv '

8.3 As a general rule, pressure reduction to sea-level is feasible only for stationsbelow 600-800 m. Pressures of stations situated above this upper limit ought to be convertedinto heights of 850 mb or 700 mb surfaces, respectively (see 3). (Composite charts forregions with high level plateaux.)

8.4 Computing of heights for standard pressure surfaces.

8.4.1 When pressure is lower than at a standard pressure surface (ps ~ 1000 mb orZ. 850 rob or < 700 mb), the following formula (16) is recommended: (see Technical NoteNo. 7. p. 30 (29))-

where H4

H2

Ps2'

Ts2

a24

e24

C24


(K - 14 log P4)Ps2

Geopotential height of the isobaric surface, characterized by thepressure P4

Geopotential (in gpm) of the station (~> H4)

P4 Pressures at geopotentials H2 and H4

T +2 T12 (+F) at the station level

Lapse-rate between H4 and H2

Vapour pressure at the geopotential H2

Function corresponding to Ch in the reduction to sea-level

0.12 for H2 < 2000 m (see table, Annex la)

0.15 for H2 2000-4000 m (see table, Annex Ib)

0.20 for H2 > 4000 m (see table, Annex le).

25

(16)

8.4.2 When pressure is lower than at a standard pressure surface, the following formula(17) is recommended: (see Technical Note No. 7, p. 30 (28))

with the same symbols as in 8.4.1; the index

C13 0.12°C/mb for HI ~ 4000 m

0.15°C/mb for HI ) 4000 m

H = H +4 1

(log~) (Tsl + eSlC14)

( a14 log PsI + K)2 Plj.

1 corresponding to the index 2 in 8.4.1.

(see table, Annex la)

(see table, Annex Ib).

(17)

In the case of upward reduction the F values are generally not negligible and shouldbe determined for large values of H4 - HI by means of aerological soundings giving the realmean temperature Tmv of the layer between station and standard surface. If no appropriatesoundings are available, it may be recognized that for the greater part of the day-time ~3

can be taken as 1.OoC/IOO m in low latitudes, and applied directly to the current T toobtain a value very close to the probable virtual temperature (T ) of the actual air column.

myThe F values are determined by the formula

Instead of using Ts1 = + F and a = 0.65°C/IOO m,13

other formula~better suited to the prevailing conditions in a region may be developed usingthe actual temperature alone or in combination with the maximum temperature (Tmax) of theday, with or without some additional factor and an appropriate value of a

13•


If the values for es differ

two or several seasonal

Generally it is not necessary to use actual values of es ' except in humid climateswith high temperature and frequent changes in the water vapour content from day to day. Inthe normal case the term 0.12 es is compiled as a function of the temperature argumentT+T( 12), using a regression line based on climatological means.

2noticeably as a function of the temperature for various seasons,regression lines may be used for compilation.

value, and with this final value heThe observer adds this sum to the

If an F value is necessary for a particular station under consideration the termsF and 0.12 e

sare combined in the same table, giving the sum F + 0.12 es '

T + T122

records the table of reduction compiled for HP and the different values of Ps'

A special example of a suitable table for the observer based on the climatologicalmeans of 0.12 es (Annex 2) is given in Annex 3 for the Swiss region.


REFERENCES

27

1. World Meteorological Organization - Reduction of atmospheric pressure. TechnicalNote No. 7, WMO-No. 36, TP.12, Geneva, 1954.

2. Eliassen, A. - On the correction and reduction of barometer reading. GeofisiskePublikasjoner, Vol. XIII, No. 11, 1944.

3. Bigelow, F.H. - Report on the barometry of the United States, Canada and West Indies.(Report of the Chief of the Weather Bureau. 1900-1901, Vol. 11), Washington 1902.

4. Harrison, L.P. - Report on the problem of reduction of pressure. Report of the Work-ing Group on Barometry to the WMO Commission for Instruments and Methods ofObservation (CIMO-II) Paris, June 1957.

5. Harrison, L.P. - Addendum to I1Report on the problem of reduction of pressure". Sub-mitted in September 1958 to the Working Group on Pressure Reduction Methods ofthe Commission for Synoptic Meteorology, WMO.

6. Harrison, L. P. - Communication I 11 On the problem of reduction of pressure 11. U. S. WeatherBureau, Washington, 9 October 1959.

7. Harrison, L.P. - Reduction and analysis of pressure data for surface charts. WMO,CCl Ill, London, December 1960. (Working paper No. 50.)

8. Rao, K.N. - Regression of vapour pressure with height, latitude and longitude, Bombay,1957.

9. Rao, K.N. - Contribution of the humidity term in the formula for reduction of pressureto sea-level, Bombay, 1958.

10. Rouaud, A. - Rapport interne sur les methodes de reduction de la pression atmosphe-rique au niveau de la mer. (Not pUblished.)

11. SchUepp, M. - Vergleich der verschiedenen Methoden der Luftdruckreduktion auf dasMeeresniveau. Wetter und Leben, Jahrg. 5, Heft 1 - 2. 15-18. 1953.

12. SchUepp, M. - Das Problem der Luftdruckreduktion auf das Meeresniveau. VI. Interna-tionale Tagung fUr Alpine Meteorologie, Institut Hydro-Meteorologique federal dela Republique Populaire federative de Yougoslavie, Belgrad 1962. S.355-365.

13. SchUepp, M. - Die Reduktion des Luftdrucks auf das Meeresniveau. Vierteljahrsschriftder Naturforschenden Gesellschaft in ZUrich, Jahrgang 107, Heft 2,s.65-100.

14. Klauser, L., Scherhag R. - Eine Verbesserung der Luftdruckreduktion auf das Meeresni-veau - Berliner Wetterkarte 28.2.1963, Beilage 18/63.

15. Klauser, L. - Zur Luftdruckreduktion im deutschen Alpenvorland. Geofisica e Meteoro-logia, Genova, XI, 69-74. 1963.

16. Klauser, L. - Beispiele verbesserter Luftdruckanalysen in Deutschlandkarten. BerlinerWetterkarte 10.7.1963 Beilage 59/63.

17. Busold, W. - Ein Verfahren der Luftdruckreduktion bei hohergelegenen Stationen SUd-afrikas. Berliner Wetterkarte 22.3.1963, Beilage 28/63.

18. Gasser, O. - Einfache Luftdruckreduktion fUr synoptische Wetterkarten. Geofisica eMeteorologia, Genova, XI, 67-68. 1963.

19. Schneider-Carius, K - Die Grundschicht der Troposphare. LeipZig, Geest und Portig,1953, 168 S. (Probleme der Kosm. Physik, 26.).


20. South African Weather Bulletin 8.4.1960-(see Figure 10).

21. Bulletin de I' ClvlM, Geneve, Vo1. VII, No. 3, jui11et 1958 (see Figure 11).

ANNEX la 29

Values of 0.12.(es = Vapour pressure at station level)

rel.humidity% 00.09 10-19 20-29 30-39 40-49 50- 59 60-69 70-79 80-89 90 -100Ts-13 0.5-12 0.5-11 0.5 0.5-10 0.5 0.5 0.5

- 9 0.5 0.5 0.5

- 8 0.5 0.5 0.5 0.5

- 7 0.5 0.5 0.5 0.5

- 6 0.5 0.5 0.5 0.5 0.5

- 5 0.5 0.5 0.5 0.5 0.5

- 4 0.5 0.5 0.5 0.5 0.5

- 3 0.5 0.5 0.5 0.5 0.5 0.5

- 2 0.5 0.5 0.5 0.5 0.5 0.5

- 1 0.5 0.5 0.5 0.5 0.5 0.50 0.5 0.5 0.5 0.5 0.5 0.5 0.51 0.5 0.5 0.5 0.5 0.5 0.5 0.52 0.5 0.5 0.5 0.5 0.5 0.5 1.0

3 0.5 0.5 0.5 0.5 0.5 1.0 1.0

4 0.5 0.5 0.5 0.5 0.5 1.0 1.0

5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.06 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0

7 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.08 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0

9 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.510 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.511 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.512 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.513 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.514 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.0

15 0.5 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.016 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.0 2.0

17 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.0 2.018 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5

19 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5

30 ANNEX la

00-09 10-19 20-29 30-39 40-49 50,-59 60-69 70-79 8)-89 90-100

20 0.5 0.5 1.0 1.5 1.5 2.0 2.0 2.5 3.021 0.5 0.5 1.0 1.5 1.5 2.0 2.0 2.5 3.022 0.5 1.0 1.0 1.5 1.5 2.0 2.5 2.5 3.023 0.5 1.0 1.0 1.5 2.0 2.0 2.5 3.0 3.024 0.5 1.0 1.0 1.5 2.0 2.5 2.5 3.0 3.525 0.5 1.0 1.5 1.5 2.0 2.5 3.0 3.0 3.526 0.5 1.0 1.5 2.0 2.0 2.5 3.0 3.5 4.027 0.5 1.0 1.5 2.0 2.5 3.0 3.0 3.5 4.028 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.529 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.530 0.5 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.031 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.032 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 5.533 0.5 1.0 1.5 2.0 2.5 3.5 4.0 4.5 5.0 5.534 0.5 1.0 1.5 2.0 3.0 3.5 4.0 5.0 5.5 6.035 0.5 1.0 1.5 2.5 3.0 3.5 4.5 5.0 5.5 6.536 0.5 1.0 2.0 2.5 3.0 4.0 4.5 5.5 6.0 7.037 0.5 1.0 2.0 2.5 3.5 4.0 5.0 5.5 6.5 7.038 0.5 1.0 2.0 3.0 3.5 4.5 5.0 6.0 6.5 7.539 0.5 1.0 2.0 3.0 3.5 4.5 5.5 6.5 7.0 8.040 0.5 1.5 2.0 3.0 4.0 5.0 5.5 6.5 7.5 8.541 0.5 1.5 2.5 3.0 4.0 5.0 6.0 7.0 8.0 9.042 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.543 0.5 1.5 2.5 3.5 4.5 5.5 6.5 7.5 9.0 10.044 0.5 1.5 2.5 4.0 5.0 6.0 7.0 8.0 9.0 10~5

45 0.5 1.5 3.0 4.0 5.0 6.5 7.5 8.5 9.5 11.046 0.5 1.5 3.0 4.0 5.5 6.5 8.0 9.0 10.0 11.547 0.5 2.0 3.0 4.5 5.5 7.0 8.0 9.5 11.0 12.048 0.5 2.0 3.5 4.5 6.0 7.5 8.5 10.0 11.5 12.549 0.5 2.0 3.5 5.0 6.5 7.5 9.0 10.5 12.0 13.550 0.5 2.0 3.5 5.0 6.5 8.0 9.5 11.0 12.5 14.051 0.5 2.0 4.0 5.5 7.0 8.5 10.0 11.5 13.0 15.052 1.0 2.5 4.0 5.5 7.5· 9.0 10.5 12.0 14.0 15.5

ANNEX Ib 3l.

Values of O.lS·(es = Vapour pressure at station level)

rel. humidity %00-09 10-19 20...29 30-39 40-49 50-59 60-69 70-79 8:.1-89 90-100

TB-16 0.5-15 0.5-14 0.5 0.5-13 0.5 0.5 0.5-12 0.5 0.5 0.5-11 0.5 0.5 0.5 0.5-10 0.5 0.5 0.5 0.5

- 9 0.5 0.5 o.? 0.5 0.5

- 8 0.5 0.5 0.5 0.5 0.5

- 7 0.5 0.5 0.5 0.5 0.5- 6 0.5 0.5 0.5 0.5 0.5 0.5

- 5 0.5 0.5 0.5 0.5 0.5 0.5

- 4 0.5 0.5 0.5 0.5 0.5 0.5

- 3 0.5 0.5 0.5 0.5 0.5 0.5 0.5- 2 0.5 0.5 0.5 0.5 0.5 0.5 1.0- 1 0.5 0.5 0.5 0.5 0.5 0.5 1.0

0 0.5 0.5 0.5 0.5 0.5 1.0 1.01 0.5 0.5 0.5 0.5 0.5 1.0 1.02 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0

3 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0

4 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0

5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.06 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.57 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.58 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.59 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.5

10 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.011 0.5 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.012 0.5 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.013 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.0 2.014 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.515 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5

32 ANNEX Ib

00-09 10-19 20-29 )0-39 40-49 50 ~59 00....69 70-79 80-89 90-100

16 0.5 0.5 1.0 1.0 1.5 2.0 2.0 2.5 2.517 0.5 0.5 1.0 1.5 1.5 2.0 2.0 2.5 3.018 0.5 1.0 1.0 1.5 1.5 2.0 2.5 2.5 3.019 0.5 1.0 1.0 1.5 2.0 2.0 2.5 3.0 3.020 0.5 1.0 1.0 1.5 2.0 2.5 2.5 3.0 3.521 0.5 1.0 1.5 1.5 2.0 2.5 3.0 3.0 3.522 0.5 1.0 1.5 2.0 2.0 2.5 3.0 3.5 4.023 0.5 1.0 1.5 2.0 2.5 2.5 3.0 3.5 4.024 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.525 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.526 0.5 1.0 1.5 2.5 3.0 3.5 4.0 4.5 5.027 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.028 0.5 1.0 1.5 2.0 2.5 3.0 '3.5 4.0 5.0 5.529 0.5 1.0 1.5 2.0 2.5 3.5 40 0 4.5 5.0 5.530 0.5 1.0 1.5 2.0 3.0 3.5 4.0 5.0 5.5 6.0

31 0.5 1.0 1.5 2.5 3.0 3.5 4.5 5.0 5.5 6.532 0.5 1.0 2.0 2.5 3.5 4.0 4.5 5.5 6.0 7.0

33 0.5 1.0 2.0 2.5 3.5 4.0 5.0 5.5 6.5 7.0

34 0.5 1.0 2.0 2.5 3.5 4.5 5.0 6.0 6.5 7.535 0.5 1.0 2.0 3.0 4.0 4.5 5.5 6.5 7.0 8.0

ANNEX le 33

Values of 0.20· (es = Vapour pressure at station level)

rel.humidity% 00-09 10-19 20-29 ~-39 40-49 50-59 60-69 70-79 00-89 ~ -100

Ts-19 0.5

-18 0.5 0.5

-17 0.5 0.5

-16 0.5 0.5 0.5

-15 0.5 0.5 0.5

-14 0.5 0.5 0.5 0.5

-13 0.5 0.5 0.5 0.5

-12 0.5 0.5 0.5 0.5 0.5

-11 0.5 0.5 0.5 0.5 0.5

-10 0.5 0.5 0.5 0.5 0.5 0.5

- 9 0.5 0.5 0.5 0.5 0.5 0.5

- 8 0.5 0.5 0.5 0.5 0.5 0.5

- 7 0.5 0.5 0.5 0.5 0.5 0.5

- 6 0.5 0.5 0.5 0.5 0.5 0.5 0.5

- 5 0.5 0.5 0.5 0.5 0.5 0.5 1.0

- 4 0.5 0.5 0.5 0.5 0.5 1.0 1.0

- 3 0.5 0.5 0.5 0.5 0.5 1.0 1.0

- 2 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0

- 1 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0

0 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0

1 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0

2 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.5

3 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5

4 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5

5 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 1.56 0.5 0.5 0.5 1.0 1.0 1.0 1.5 1.5 2.0

7 0.5 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.0

8 0.5 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0

9 0.5 0.5 1.0 1.0 1.5 1.5 1.5 2.0 2.0

10 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.5

34 ANNEX le

00-09 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100Ta

11 0.5 0.5 1.0 1.0 1.5 1.5 2.0 2.0 2.512 0.5 0.5 1.0 1.5 1.5 2.0 2.0 2.5 2.513 0.5 0.5 1.0 1.5 1.5 2.0 2.0 2.5 3.014 00 5 1.0 1.0 1.5 1.5 2.0 2.5 2.5 3.015 0.5 1.0 1.0 1.5 2.0 2.0 2.5 3.0 3.016 0.5 1.0 1.5 1.5 2.0 2.5 2.5 3.0 3.517 0.5 1.0 1.5 1.5 2.0 2.5 3.0 3.5 3.518 0.5 1.0 1.5 2.0 2.0 2.5 3.0 3.5 4.019 0.5 1.0 1.5 2.0 2.5 3.0 3.5 3.5 4.020 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

ANNEX 2 35

Eigure 13 I Practical use of pressure reduction methods : Computationof t mv from T and T12 for the Swiss region

Polog - =

Ps

Directions for use:The intersection of the vertical lines for t and thehorizontal lines for t 12 gives the desired value oft mv (oblique lines) for the station level withoutadditional P value.

If the trny value has to be determIned for the meanheight between station and sea-level (t~v) and forP values J 0, the diagram has to be slightly transformed. In this case, the oblique t~v lines are

shifted to tre right so that the 0 point in the leftupper edge corresponds to the 11> value. (The amountof change in the t~v values is

0.325. Hp 0C.)100

The shift is only roughly linear because of the term0.12es ' but the accuracy is practically sufficient.If P J 0, the t

rnvscale is also modified, the amount

of change being P (p is a function of t+tl~2).

In the case of P J 0, the distance> between the ~v

lines are modified and the shifting is generallynot linear.

Calculation of Po - see Smithsonian Tables p.204-2l3·

diagram represents the t rnv values for

level 11>' not for the height~. To

latter value for a given stationtmv lines have to be -1-ih......................to the right accord- j", i i ~~'"

-np

0.0148275' Hp(~v + 273.2)

Calculation of ~v starting with t=temperaturein °c at the time of observation, t 12=temperature 12 hours before, and the Swiss mean valuesfor 0.12es '

BI Pressure reduction to sea-level

Values for the denominator:

t I = t + t12 + P+O. 325 ~ + 0 12mv -2-- 100' e s

in the general formula

get theheight,shifteding tothe 11> scale.

A: Thisstation

36 ANNEX 3

Figure 14 : Values of 0.12 es as functions of

Swiss region

for the

2 1/7 [7't/ t- T~Z;7;- / /2 / ",2

1// VI /

/ / ~2

/ VI/ ~/

.2 I V /

~I /~

/,

I /I /

1 ~1/ ."1.'

if ) / "'. . (IS'';.2 1 /

/ 'S/¥fS/(/fI

/ 1I MNnI I M~eo.12Jj

"I J 1/

,2 / 1/ IV

I~

/JI,

/2 /,4 I~

J,<I

1/ iII I

~ .// IJ

2 '/ UI I - ~-T", fo,Ies

ANNEX 4

REDUCTION OF A'lMOSPHERIC PRESSURE TO MEAN SEA LEVEL

(proposals submitted by the United Arab Republic)

1. Introduction

Referring to Technical Note No. 7, issued by WMO, it was found that Members use different formulae and expressions for the reduction of pressure to M.S.L.

Some of these formulae or expressions depend on the original formula of Laplace, onthe basis of which the International Meteorological Tables were computed by Angot; othersfollow the hypsometric equations ..

In some cases the effects of the variation of humidity or the density of the air orboth are rejected, in others different expressions are applied for the temperature argument.

The variation of the temperature of the air with height is considered sometimes, butwith variable values for the lapse-rate, and at other times the atmosphere is assumed to beisothermal.

Consequently it is not easy to compare the pressures reduced to M.S.L. since differffiltmethods are used by Members in computing this reduction.

The aim of this paper is to find one form for these formulae and expressions whichcan be computed from Angot's tables and which we recommend for international use.

2. The hypsometric formula

The most general expression of the hypsometric equation

log (1)Ps Tmv

where Tmv = integral mean virtual temperature of the air column in absolute degrees, to acertain degree of approximation;

this is obtained on the assumption of a fictitious air column extending from the ground atthe station down to sea level which is known not to be representative for the free atmosphere,since the earth temperature and moisture conditions will have a considerable effect upon theair in the shaft.

Consequently (1) becomes

where Ps Station pressure in mb

(2)

Po Pressure reduced to sea-level in mb

Ts Station temperature argument in absolute degrees

ANNEX. 4

K Hypsometric constant = 0.0148275° absolute

a Assumed lapse rate in the fictitious air column from sea-level to the levelof the station elevation in °C/gpm

Hp The height of the station above M.S.L. in gpm

es Vapour pressure argument at the station in mb

~ A function of HP calculated on the same assumption as mentioned in p. 20 ofthe above-mentioned Technical Note.

3. Conversion of the value of HP from geopotential to geometric metres.

z Z1 5

1[g ~o )

2

dZJl\J gdz =r

9.8 9.8 (r+z)20 0

Z

=~ 5 dz g~o r (1- 1 ) (3)9. (1 + ~ )2 9.8 l+~

0 r r

z __ Z1 + !!- "7(l--=+---"~::--'--)

r r

where z Geometric altitude above M.S.L. in metres

Z Geometric altitude corresponding to the station elevation in metres

g Acceleration of gravity at latitude ~ and height Z in metres/sec2

r Radius of the earth in metres = 6370,000

j5 Latitude of the station

Ts To + (ts °C)

#. The new expression of the hypsometric formulae being substituted for l\J in equation,2), and diViding by K, we get

Plog -2-.

Pa

z

Z

tsZ + azKr 2K

z

Z

r

(4)

sinceTo--=K

To =

Kr

273.0148275

184006)70000

18400

0.003

ANNEx: 4 39

= 67.531 1

K .0148275

t s 1 t s x 67·53"./

K r 6370000quantity compared with the other

4 t s Z.10- and the term <::.. 1 which is a very smallKr

terms and can be neglected at a height of 3 kilometres.

Similarly ~ Ch ~ 10-5, and consequently the term ~ ~

neg},ected.

L:.... 0.1, and can also be--5. Laplace I s formula

Referring to p. 3 of the Technical Note we find that Angot's tables depend on theequation :

Polog

Ps

z18400 + 0.003Z + 67.53 Bm

which was derived from the original formula of Laplace neglecting the humidity and latitudecorrection factors.

6. Comparison of formulae

Comparing (4) and (5) we find that both equations are identical with the understanding that the temperature argument

Bm = is + ~ Z + es Ch (6)2

It is apparent that the right-hand side of (6) provides the necessary corrections for thevariation of temperature with height and also the effect of humidity, and therefore givesa much better approximation for the temperature argument.

7. The temperature argument

7.1 Experience has shown that if the current air temperature is taken as t s ' large varia-tions occur in pressure reduced to sea-level especially at elevated stations where a largediurnal variation in surface temperature is common. Comparison of pressure reduced to sealevel in this way with the barometric reading; at coastal stations discloses that the apparent diurnal variation in reduced pressure for the high stations must be physicallyunrealistic.

In order to overcome this effect it is recommended that one should take it that t sstands for the mean of the current air temperature and the temperature of the air 12 hourspreviously, as many Members do at present.

7.2 The same argument also holds for vapour pressure; it is preferable to use es as themean of the vapour pressure at the station at the time of observation and that 12 hoursbefore. The values of ~ mentioned in the Technical Note are used.

40

7.3 The lapse-rate of the standard atmosphere 0.0065 °c gpro is suggested for applicationin practice. Observing the above suggestions the temperature argument becomes

e =t + t12

2+ 0033 z + (e + e12 )• 2

where t 12 and e12 refer to the values 12 hours before the time of observation.

It is clear that the humidity term is independent of the height of the station aboveM.S.L., since it only accounts for the damp air as found in particular on coastal stations.

7.4 Order of magnitude of the effect of humidity

This effect becomes apparent if we take, for example, damp air of approXimate meandew point 20°C and vapour pressure 23 mb.

The correction for the temperature argument due to the humidity term alone will beabout 2.3°C for sea-level stations and 3.1oC for a station at an altitude of one kilometre.

The corresponding corrections for the reduction of pressure to M.S.L. will be lessthan 0.1 mb for stations at altitudes up to 100 metres, but amounts to 1.5 rob at one kilometre.

7.5 Order of magnitude of the effect of the lapse~rate

The increase in the temperature argument at a level one kilometre above M.S.L. willexceed 3°C due to this effect. The reflection of this excess of temperature on the reductionof p~essure to M.S.L. at that height also amounts to about 1.5 mb.

7.6 Conclusion

For stations at altitudes of 100 metres or less, neither the humidity nor the variation of temperature with height necessitates an appreciable correction of the reduction ofpressure to mean sea-level.

For greater heights, the correction increases gradually, exceeding 3 mb one kilometreabove mean sea-level.

WMO TECHNICAL NOTES

• No. I Artificial inducement of precipitation. . . . . . . . . . . . . . . . . .

• No. 2 Methods of observation at seaPart I: Sea surface temperature . . . . . . . . . . . . . . . . . ..Part 11: Air temperature and humidity, atmospheric pressure, cloud height,

wind, rainfall and visibility. .

• No. 3 Meteorological aspects of aircraft icing. . . . . . . . . . . . . .

• No. 4 Energy from the wind . . . . . . . . . . . . . . . . . . . . .

• No. 5 Diverses experiences de comparaison de radiosondes. Dr. L. M. Malet• No. 6 Diagrammes aerologiques. Dr. P. Defrise .

• No. 7 Reduction of atmospheric pressure (Preliminary report on problems involved)

• No. 8 Atmospheric radiation (Current investigations and problems). Dr. W. L.Godson ..' .

• No. 9 Tropical circulation patterns. Dr. H. Flohn. . . . . . . . . . . . . . .

No. 10 The forecasting from weather data of potato blight and other plant diseasesand pests. P. M. Austin Bourke .

No. 11 The standardization of the measurement of evaporation as a climatic factor.G. W. Robertson .

• No. 12 Atmospherics techniques . . . . . . . . . . . . . . . . . . . . . .

• No. 13 Artificial control of clouds and hydrometeors. L. Dufour - Ferguson HallF. H. Ludlam - E. J. Smith .

• No. 14 Homogeneite du reseau europeen de radiosondages. J. Lugeon - P. Ackermann• No. 15 The relative accuracy of rawins and contour-measured winds in relation to

performance criteria. W. L. Godson. . . . . . . . . . . . .• No. 16 Superadiabatic lapse rate in the upper air. W. L. Godson . .

No.17 Notes on the problems of cargo ventilation. W. F. McDonald.

No. 18 Aviation aspects of mountain waves. M. A. Alaka .

• No. 19 Observational characteristics of the jet stream (A survey of the literature).R. Berggren - W. J. Gihbs - C. W. Newton . . . . . . . . . . . . . .

No. 20 The climatological investigation of soil temperature. Milton L. Blanc . . .No. 21 Measurement of evaporation, humidity in the biosphere and soil moisture.

N. E. Rider .

• No. 22 Preparing climatic data for the user. H. E. Landsberg . . . . . . . . .

No.23 Meteorology as applied to the nllvigation of ships. C. E. N. Frankcom - M.Rodewald - J. J. Schule - N. A. Lieurance .

No.24 Turbulent diffusion in the atmosphere. C. H. B. Priestley - R. A. McCormick-F. Pasquill . . . . . . . . . . . . . . . . .

No.25 Design of hydrological networks. Max A. Kohler .No. 26 Techniques for surveying surface-water resources. Ray K. Linsley . . . .

No. 27 Use of ground-based radar in meteorology (Excluding upper-wind measure-ments). J. P. Henderson - R. Lhermitte - A. Perlat - V. D. Rockney - N. P.Sellick - R. P. J ones. . . . . . . . . . . . . . . . . . . . . . . . .

No. 28 Seasonal peculiarities of the temperature and atmospheric circulation regimesin the Arctic and Antarctic. Professor H. P. Pogosjan. . . . . . . . . .

No. 29 Upper-air network requirements for numerical weather prediction. A. Eliassen- J. S. Sawyer - J. Smagorinsky .

No. 30 Rapport preliminaire du Groupe de travail de la Commission de meteorologiesynoptique sur les reseaux. J. Bessemoulin, president - H. M. De Jong - W. J. A.Kuipers - O. Lonnqvist - A. Megenine - R. Pone - P. D. Thompson - J. D.Torrance .

No.31 Representations graphiques en meteorologie. P. Defrise - H. Flohn - W. L.Godson - R. Pone . . . . . . . . . . . . . . . . . . . . . . . . . .

No. 32 Meteorological service for aircraft employed in agriculture and forestry. P. M.Austin Bourke - H. T. Ashton - M. A. Huherman - O. B. Lean - W. J. Maan-A. H. Nagle .......................•.....

• Out of print

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No. 57

Meteorological aspects of the peaceful uses of atomic energy. Part I - Meteorological aspects of the safety and location of reactor plants. P. J. Meade..The airflow over mountains. P. Queney - G. A. Corby - N. Gerbier H. Koschmieder - J. Zierep .. . . . . . . . . . . . . . . . . . . .Techniques for high-level analysis and forecasting of wind- and temperaturefields (English edition) . . . . . . . . . . . . . . . . . . . . . . . .Techniques d'analyse et de prevision des champs de vent et de temperature ithaute altitude (edition fran«;aise). . . . . . . . . . . . . . . .Ozone observations and their meteorological applications. H. Taba

Aviation hail problem. Donald S. Foster. . . . . . . . . . . . jTurbulence in clear air and in cloud. Joseph Clodman. . . . . .Ice formation on aircraft. R. F. Jones . . . . . . . . . . . . .Occurrence and forecasting of Cirrostratus clouds. Herbert S. Appleman.

Climatic aspects of the possible establishment of the Japanese beetle in Europe. }P. Austin Bourke .Forecasting for forest fire services. J. A. Turner - J. W. Lillywhite - Z. Pieslak

Meteorological factors influencing the transport and removal of radioactivedebris. Edited by Dr. W. Bleeker .

Numerical methods of weather analysis and forecasting. B. Bolin - E. M.Dobrishman - K. Hinkelmann - K. Knighting - P. D. Thompson

Performance requirements of aerological instruments. J. S. Sawyer . . . .

Methods of forecasting the state of sea on the basis of meteorological data. J. J'jSchule - K. Terada - H. Walden - G. Verploegh .Precipitation measurements at sea. Review of the present state of the problemprepared by a working group of the Commission for Maritime Meteorology.

The present status of long-range forecasting in the world. J. M. Craddock -H. Flohn - J. Namias. . . . . . . . . . . . . . . . . . . . . . . . .

:N~4,9_ ~(lductiQ~ll!!d use of data @jained by_'!'IRill) mej~rologicalsa~tellites.(~re-_pared by the National Weathel' Satellite Center of the U. S. Weather Bureau)-&Q.lr~-6';-

The problem of the professional training of meteorological personnel of allgrades in the less-developed countries. J. Van Mieghem . . . . . . . . .

Le probleme de la formation professionnelle du personnel meteorologique detous grades dans les pays insuffisamment developpes. J . Van Mieghem

Protection against frost damage. M. L. Blanc - H. Geslin - I. A. Holzberg -B. Mason .

Automatic weather stations. H. Treussart - C. A. Kettering - M. Sanuki -S. P. Venkiteshwaran - A. Mani .

Stations meteorologiques automatiques. H. Treussart - C. A. KetteringM. Sanuki - S. P. Venkiteshwaran - A. Mani .

The effect of weather and climate upon the keeping quality of fruit . . .

Meteorology and the migration of Desert Locusts. R.C. Rainey . . . . .

The influence of weather conditions on the occurrence of apple scab. J. J. Post C. C. Allison - H. Burckhardt - T. F. Preece . . . . . . . . . . . .

A study of agroclimatology in semi-arid and arid zones of the Near East.G. Pen'in de Bl'ichambaut and C. C. Wallen . • . . . . . . . . . . . . . .

Une etude d'agroclimatologie dans les zones arides et semi-arides du ProcheOrient. G. Perrin de Brichambaut et C. C. Wallen . . . . . . . . . . . . .

Utilization of aircraft meteorological reports. P. K. Rohan - H.M. de Jong S. N. Sen - S. Simplicio . . . . . . . . . . . . . . . . . . . . . . . .

Tidal phenomena in the upper atmosphere. B. Haurwitz .

Windbreaks and shelterbelts. J. van Eimern, R. Karschon, L. A. Razumova,G. W. Robertson . . . . . . . . . . . . . . .

Meteorological soundings in the upper atmosphel'e . . . . . . . . . . . . .

No. 58

No. 59

No. 56

* No. 35

* Out of print

note on the standardization of pressure reduction methods ...library.wmo.int/pmb_ged/wmo_154.pdf ·...

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