A method to obtain a wind model for the boundary layer in a representative tropical region

A method to obtain a wind model for the boundary layer in a

representative tropical region

Citation for published version (APA):

Abu Bakr, E. H., Rutten, M., Smulders, P. T., Vossers, G., & Wieringa, J. (1986). A method to obtain a wind

model for the boundary layer in a representative tropical region. (TU Eindhoven. Vakgr. Transportfysica :

rapport; Vol. R-818-D). Technische Hogeschool Eindhoven.

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Published: 01/01/1986

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EINDHOVEN

A METHOD TO OBTAIN A WIND MODEL FOR

THE BOUNDARY LAYER IN A REPRESENTATIVE

TROPICAL REGION

ABu Bakr, E.H.: Rutten,

M.~

Smulders, P.T.*

*

**

Vossers, G., Wiering&,

J~

October 1986

R 818 D

Paper of the 6th European Wind Energy Conference, October 1986, Rome

* TECHNICAL UNIVERSITY EINDHOVEN

Faculty of Physics

Laboratory of Fluid Dynamics and Heat Transfer

WIND ENERGY GROUP

P.O. Box 513, 5600 MB Eindhoven, Netherlands

CONSULTANCY SERVICES

P.O. BOX 85

WIND ENERGY

3800 AB AMERSFOORT

DEVELOPING COUNTRIES

THE NETHERLANDS

**Royal Netherlands Meteorological Institute

De Bilt, Netherlands

I,

A METHOD TO OBTAIN A WINO MODEl. FOR THE BOUNDARY LAYER· IN A REPRESENTATIVE TROPICAl. REGION

S~QRY

A discussion is given of the

c~struction of • r.f~ence data b ••••

~ich c~n be used for develaoing a bound ... y 1 ayer model .for traoi c.l re'9ions. The representative reQion selveted for the investigation is an area of 20.000 s~.k~ around Khartoum (Sud.n).

The asse~bled surface wind data are

cor"'veted for exposure. and the! r

reliability is checked. It is Shown. that due to the seasonal influence of the Inte .. t",ooic:al-Convargence-zone any fult-vear representation of wind frRQuency distribution is mtsleading and that seasonal ~n~lysis i . ",equired.

The average wind profile to 2 km heiaht sh~ a jet-like app •• ",.nce, which

inv~lid.tes the use of si~le ",elation. between large-scale free atmoSPheric wind and s~f.c. wind climate. It t • • hown

that for the wint ... a.on an E~m.n wind p'-0411e with the"~.l wind modification

... j gM: ,,"ove vse~ul.

1. I~ODLICTION

Reli.ble .sses.ment of wind energy Dotential in countries without a

s1.l4ficilmt numb .... of lIIet_oloolcal • tations is .n outst.nding problem. One solution for this probleM is the

d __ V91op~t of s~ Model to interpolate

~orizontally between the few available

~t.tion~ Mith su .. ~ace wind and/or upper _ind data. Such models have been developed in the l.st decade fOl"

t~er.te-latitude countri.s, Denm.rk .nd

t~. Netherland. in particular. However, these Model. are based on oeostrophic si ... ilar lty principles, a.suming

... on.bly hiOh Coriolis forces, while In the tropic • • uch force • • re MUCh . . . 11er.

*

~.H.A8u B.~r. M.~utten. ~.T.Smulders. G.Vossers

IJni V1!!'-si ty of Technol09Y, Eindhoven. Netherlands **J.Wi1!rinq"

~oy.l Netherland. Meteorol09ical Institute,

n.

Bilt

Addition.lly in the tropics the air ~low

is domin.ted by other .ec:;h.nism., such

a.

th.. l.rQ_ di urnal course. or _.oons. Con.equenU y. the

..,.1

ysi. of the boundary laver in the tropics cannot follow quite the same pattern a. temperate-latitude MOdel ••

In 1985 Eindhoven University (The N.therland.) .tarted a research programme to develop a methodology for ""alualing the wind potential in tropical regions; the khartOUM region in Sudian ",as taken as • test Cia,e (1). SOMe reason. for this choice .re,

1. The .urrounding. of Kh.rtouM are ha.ogeneou. and reasonably flat savannah over 1.roe di.tance •• In this region there are four Metaorolooical station.

with useful wind dat., .0 the station density i . acceptable for Quality control.

2. Applic.tion of wind energy in this .rea is e.timated t.o be econOl1llical. and t.he region 1s oouch in need of .. ater

pu~tng for irrioation and drinking .. at.,..

In this article the cllMatoiOQical and Qeooraphlcal Nind characteri.t.ics of the KhartOUM region will be described .nd • prelilllin.ry an.lysts of t.he surfac:e .nd upper at r data is presented •

2. TIE Cl.II'IATOLOGlCAL AND ~APHlCAL

lUND CHARACTERISTICS OF KHARTOUM

BURROUN-DINGS (CENTRAl,. SUDAN)

Sudan is a very targe country labout 2.3xl06 k.·) Nith the broad Nile valley .eross the .iddle .nd on th. border. some hills and MOUnt.alns. on the e •• t near t.he Red Sea coa.t.. on the fIOUt.h ne.r the border Nl th Kenya and Uvanda and in the west near the bord.,. with Chad. __ Hg.

1. The reI i ef of the Khartoum

surrounding. is r.l.tively flat (dz/dxN 1xlo- over 10· kill'" around Khart.oum).

The climate in thl_ region is __

i-des~t. PhYSically, it. is strongly dependent on the lnt.,.-Trapical-Convergence-lone CI.T.C.I.l the high preSl5\.lre bel t . and the low pressure bel ts [21. The Nind regime 1n Sud.n is

controlled by these pre.sure belts. In Central Sudan there are four seasons: a. The wtnt . . . . eason CDec.-Fabr.) where the I.T.C.I. is far south (-3-N)

t~. end of thi, ,.a.on the t.T.C.Z.

oass~ ov.r the Khartoum rwvton taward. t.h .. North.

c. Monsoon (June-s..ot.) I at t.h .. end of

t.his season t~ I.T.C.2. oass . . over the KhartOUM region southwards.

d. Retreating monsoon (Oct.-Nov.) where the I.T.C.Z. is south of KhartOUM rwvion.

Sanch.tor_ "habootn,- are encountered during the whole ~r. Their occurrence

.. i th QUst. ""cl!<ll!ding 30 111/. [2l, 1iIhould be taken into account for wind turbine risk analyais.

4

500Km

r

1

25

Fig. 1 Relief ",ap of the Sudan (Fro", the Sudan Survey Tooogrltohy)

• )2000M, l1li )1:500.

lID )1000, a )SOO,

c

~o

~. DATA REPRESENTATION

To obtain sufficiently detailed information about the wind r..,i_ in

K~artoum region hourly .. ind data are needed. Hourly _teOf"oloqical data frOlll Khartoum airport (391m ••••• 1.' .nd W.d-Madani station (which is about 180 kill

south of Khartoum) for two years 11983,84) _re compiled in • Burrough. Computer. The data h.ve been corrected for writino and systematic error. by compariSon bet .. een the two set. of dat •• Obviously erroneous data were removed and cOO'IDiled as not-rec:orded. Also _ used datil from nearby stations (where f _

hours of wind observations are recorded) to check the Quality of the data (e.g. Wadi Saidna .nd Shambat).

From the roughn . . s characteristics of the surrounding terrain of each station [4], u.ing the Davenport terr.in-classification, the data were further corrl!cted for the roughness. The potl!ntial wind speed is calculated for each set of data by the help of thv exoosvre formulas [5J. Also thv standard dvviation for the .. ind spved is

calculated. The data art! r.pr.,.nt.d in

~DMthly matrix tabulations (hours versus wind).

airport data and Shamb.t

agrometl!oroloqical data (Shambat is about B km north of Khartoum) is shown in fig.

2. Objective t.errain corrections have be.n m.de for the two set. of data. It i • .

clear from t.he figure that th. data are reliable ( .. ith correl.tion Coefficient.

(r) • 0.94), and they are in gaod

agr~t on the average. Wind data of

this level of accuracy ar. Quite useful m.terial, both for wind energy potential .sU_tell .. nd for lIIOdel dt!velop_nt.

Utling them I . more ltConomical than to put in • new network of .... suring .ouip~t

to estimate tht! wind potential.

Fig. 2

8

COIIIOarison of ~thly aver.Qe. of the _ind potential data from KhartOUM and Shambat (Shambat is

about 9 km North of Khartoum)

~ ____ • ~ 0.7 mI • • 1.00 ~

0.17) U ... ~ .. _

Corr.latton coefficient (I"" A 0.84

4. DATA ANALYSIS

4.1 Frequency distributign

Frequency di.tributions for the KhartOUlll data <1983,84) _ e plotted on

cumul.tive Nalbul! paper and the average distribution shape para . . ter K was obt.ined by lin •• r aver.ging (6). A K-valu. in the ranoe 3-4 is Obt.ined for

~er. December. Janu.ry and February which i . due to the con.t.ant. north trade wind. May, June. July .nd S!!pt.-ber give a K-valu. bel.,. 2 Mhlc:h i . ,:Iue to 1.rqt! wind variations. The other Month. give. K-value in the r.nge 2-3.

FiO. 3 shO!lOS the large variation of

the distribution bet.ween t.he season •• Obviously for .. ind energy .pplication it ts .dvisable not to restrict analysis to the annual distribution. The application of wind energy will be .are efficient in the winter than jn other s.ason ••

Fortunately, in the winter the demand for .. ater pUlIIPing is very high for winter crop irrig.tion.

30

t~

22

10 4

.

·

·

·

.

2

,.

.

"'''9''''

.

_..

_.

_.

_....

.

Fig. ~ 'Percentage fr~uency distribu-tion of potential wind speed . t J<hartOUIII for det. of 1983 and 1984 cOIIIbined.

---Annual distribution.

The Welbull distribution shape factor (K) - 1.7S

••• Janua~ distribution. K - 3.2

---May di.tribution. K - 1.5

4.2 piurnal ~9Urle ~stablli~y

Th. day-to-day variation. present in the data are avwraged out by t.king the .verage of the hourly data for every "'anth. The hourl y average ill presented graphically

.1I

diurn.l plots. Fig. 4 is an .x.mole of the diurnal course of the wind lIpved.

The ratio vu/U in which U i . the monthly avwr.ge for .ach hour of the d.y

''''-St!) ...

calcul.ted for- Cl984,B3)

~artou. airport end Wad-H.deni d.te. While fig. 4 shows the . t •• din . . . of the Minter regime '.mall ... ind speed devi.tion barll). very larg. '~u/U) r.tios Mere found for the Hay and Septtlfllbwr data ( -b01.). Moreover the diurn.l wind direction cou .. se for these _ t h s .... _ larve variations. This can be ~pl.ined by two .. easO".1

e. The low ... ind speed rlPCorded in these ",ant"s.

b. The influence of the I.T.C.Z. which pallS . . over this region in May northward. and in SlIOt_btrl'" southward ••

W. conclude th.t the d.t. of the •• two months are difficult m.teri.l for b •• ic physical modelling because of their l.rve variation •• However. it can be UBed to indicate the p.ssag. of the I.T.C.Z.

The diurnal wind course ShOMlI a ... rk.bl. unst.ble charecter during the daytime (see fig. 4) which originat.s

fr~ the hi9" sensible heat flux

received. The sensible heat flux !HI iSI

\ol .. Q - S - L (0

3.

where Q is the net radiant flux den5itv. L the latent heat of evaporation .nd 5 represents the soil heat flux. The l~tent

heat of ev.poration in Khartoum is so low that it can be neglected. For a land surface S is small in comparison with Q.

A aood estimation for S [73 is S .. 0.1 Q

.. hieh 1 "",li eSJ

H • 0.9 Q (2) From the hourly values of Q averaged over

10 years obt.ined from reference tBJ. it follows that for example the noontime January values of H are about 600 W/m2.

FiV. 4 shows a large difference between the day and night wind sp.-ds • Thhs resul ts frOflll a 15-C tll!fllPeratur. difference between the day and night which is a characteristic of semi-d.s~t

r!!!9ions.

A Mare complete

physical-meteoro-logical analysis of the stability should be based on values of the Monin-Obukhov IvnVth (Ll and related p .... amet ... s. e.g. the frictional velocity CO-) [9J. They can be calcul.ted frOM the available station date of surf.ce wind, roughness 1enVth.

temp ....

ture data and sky cover. Thes. calculations are executed by an iteration proc . . s u.ino the energy balance ~uation, and t.he

9usingar-t)yer-~uations t71.

1"1-.oec.1983

• JIft. 1984

• Feb.

1984 'iii

I

2

2

e

12

1.

LOCAL T1ME

Fig. 4 The potentl.l Mind versus local

U_~ II. Dec:l!'IIIber 1983,

• Januarv 1984, • Fllbruary 1984 The bars show typical _xitllUlII and ~inimua .tand.r4 deviation for the threw MOnths

4.3 Badiopond. protH. behaviwr In our investigation ~ also analys.d the 11.15 G.M.T. uPper air data

(pr.ssur., te~eratur., Mind and

humidity) of 1983 and 1984 frOli J<hartwm airport (surf.ce .levation 381m. •••• 1.). The monthly averav. data were plotted as vertical prafiles . . e fig. 5. Th. r.lativ. humidity is not plotted: it is very low (less tha~ 50X) and not directly r.levant to our argument her ••

'-

100 ;;

..

!

no

..

"

::

!IGO

::

...

!ISO

,-

_•

.

HO !IO Fiq. 5

•

2

.

-,

.

ISS

,"

"

.-; ' : ; '

...

~

.;.

• • • 10 "'''OIruo ,w,s, a • • t I JlO no no 2'0 "Of, fl~"fUIt( .... e t • • , • • ln nil II. ,.. _ < . .

• ,_,.-ru ....

'OR'

..

The vertical data p~ofile ob-tained f~om the upp~ .t~ data, of K"a~toum at~pert., .:Janu.ry 83. Th. sta"d.~d devi.t.ion of the

.V~.~~ (v/~N) is indiceted by

b.~s hchich fer the temp .... atur.

p~Dfile .~. not broad .... than the points)

Fro- the vertical profile. the uop~ li~it of the pl.net.ary Boundary L.yer

(PlILl _ . d .. t. .... mined. It. is ch.r.ct. .... i.ed bv incr ... in potent.i.l temp ... t~.. (th ..

o~tenti.l t.mp .... atur .. is constant in the convective layer i.e. below the UDP ....

limit of the PeL) and. cl •• r ch.nge in the .. ind direction. F~ .,. • ...,1 •• frOft! the

lqg3 data in th .. winter .nd the .dv.ncing "'on.oon .".'!!Ions the upp.... 1 h,t t. of tM

PBL h. Ob.erved around S150 IIIb

<_ ...

g. fio. 5>. ~ere •• in the monsoon .nd r.tr.atin9 monsoon the upp~ limit . . . to be above 800 1IIb.

Throughout the y.ar II'ltcept in H.y, ,June, Seot_ber and Dct.ob~. the •• daytime .. ind orofiles show .. J.t-lik ..

struct.u~e .~ound 900 IIIb which gives the profile a very .pecial shape, diff .... ent from the inland .. ind profil.s u.ually observed .1.eMh ...

Recently similar p~ofil.s have b.en observed in the Arabian Se. t I l l and ... e exol.ined a • • n ,influence of the Somalia-jet. Howwver, this .xolanat.lon i . not valid at the nort.h .... t side of t.h. Ethiopian highl.nd. We r.~her suppose that ~h. Jet-lik • • tructur. ob . . . . ~ in

Kh.~tou.. coul d be the rl!!lUl t. of ~h ... al convection and th~mal .. ind. resulting from the .. agnitud. of the horizon~.l

tempvrature 9r.dien~f which around Kha .. toufOl i s .bou~ O.7'"C/l00 kill. Thermal Nind variation of t.he free at.~sphere

wind profile might account for the strong variation Nith height of t.he wind speed in the lower Kilometer. This might partly explain the ph.nomenon i.e. from the surface to the maximum .. ind speed le~l.

The decrease of wind speed above 1

k ... e.mnot be explained by one radio.onde and surface wind data. gyantit.at.iv. comparison!> of upoer-.ir flow above 1 km over • large reQicn is reouired and for the ouroose of .uch analysi'!!l more data from 5udan.s. radiosonde !>tat.ions are

Using the u.ual free atmospheriC wind equ.tion tl0J Me can write;

au.

9

r:.

1 <lP 1 ilT}

;;- • - ; \c, ;

<ly +

T

Iy (3)

where U" i . t.he horizontal free wind cOlllponll'nt. and f i,. t.he cor! 011 spar .",eter

(0;39x10-4 .-1 for Khartoum). R, C, are .tandard phy.ical constants. Using the t.1!IIIp ... tur • • nd, pressur. data (frOlft the Khartou", rtl!9i on' ec:rrected to a stand .. rd height the aP/ly and ITlly were

calculated for diff .... ent pertod. in the day. Sub.tituting'th. Obt.ained values in equation 13), it .. a. faund that the third

t~1II i . about 15 t t _ the .ecand t .... "' • Th .... for. a . . . first .pproxi_tion _ nl!9lec:t the second terlll. Th. vector forlll of equation (3) 1.1

9

- V T

fT

Intl!9ratlng (4) ... obt.ain U"lz) - U.(0) + Uy(z)

(4)

(5) wh ... O.(e'_i. the free .tmospheric wind at ~.o and Uy is t.h. t.her •• l wind. U'!!Iing

~h. v.lu. of

D.

(z-hl (wh~e h is the Might. of the PeL) frOft! the _.sured upper air data and c.lcul.ting

OT

using the surface isoth .... chart (considered to

b. rep~esent.t.iVtl! far the enUre deoth of the PeL), we can then c.lculate 0.(0) using equation C~). _

A relat.ion between u.ce, and the .urface _sured .. ind speed (Us' at 13 m

Is required. Such .. relation can be fermutated bYI

(6)

Th • • laborat.ion of t.hi. equ.tion is

pr-.nU y bei ng i nYellti gat.ed • _ Our purpose i . to calcul.t.e U.(z) for 188 !ll(z(h u.ing ttqUation (15)'. The _king .ssumption i . that. the lay ... i s

... ll-.ixed between the surfac. and h t.t typically 1 k. height). In the Kh.rtoum ca.e this a.sumption of .trong convective mixing I . quit.e accept.abl. In daytime. Th. diffu.ion c~ficlent in .uch a very un.tabl. tropical bounda,.y layer should b • • pproxl . . ~.ly constant. ~ ,.easonable description far such. ca •• could be the ela •• ical Eklll8n boundary laYl!t" <9L) .olution tlch!;:h is ba.ed on constant diffu.ion coefficient over the who1. bound.ry laYl!t") cerrected fer thermal Mind effects. Thi. MOd.1 can be achieved

by substituting the values of U.Cz) for 188 !ll(z(h. in the Ek.an 9L solution.

Ulz) •

O,,(z)

U - e-"-cot! "Z) (7)

v(z) • U.(z) (e-"· sin "zl

un

Nhere Y C (#/2 K

M, i f 2

In ca.e of a profile at the l~titude

of Kh.rtou~. ~ - 10m-'s is a typical v<tllue for trooical convect.ive layers t12J. With this value the st~ wind profile between the surface and 1 km hqight in fig. S might be reasonably well d9.cribed, Chec~i"g the accuracy of such

~.thodology need. more upper wind speed data than available in the Khartoum orofile. Such detailed information i . under investigation.

S. CO/IICLUStONS

Too oft.en. the Meteorological data

fro~ .ome country are considered to be unr9liable without. orooer checks. In t.he ea.e of Sudan the wind data fr~ the Khartoum "-tvorological office were investigated, corrected for _pO'ISUre, and th'J! re'ISUlts _ . found to bl! of

sufficient. Qualitv for wind energy analysis. It is concluded that such an .oo"oach - v often bl! more econ_ical than _a'Suring a n_ set of wind d"ta for e.timating the wind potential.

From the frequency di.tribution plot. in fig. 3 one observes, that t.hl!

monthly distribution are much more

i~ortant than the annual distribution in considering wind energy application for the Sudan. For two reason. the wint.r .eason i . recOlll-.nded for wind enervy application:

a. The high wind .pRPds and the 1argl! K-value (between 3 and 4).

b. The high dlPflland of ",at.,. PUlllPinO for ... int_ crop irrigation in the Sudan_ The .urf.c. wind data for KhartoulII "'lPQion .hows that th. t.T.C.Z. plav • • ",ajor role in cla •• ifying the •• ason. and conswauently the variation in the wind rI!9

i_ .

The diurnal "'ind course shows a notic.able unstable ch .... cter (.eI! fig.

4) Nhich i . due to tn. la .. ge sensible he.t flux r.ceiv.d. AI.o a laro.

differenctr bl!twwen the day and nioht Mind so-.d. result. f .. ~ the t.~erature

differancl! between the d-V and night labout lS'"C).

The uopwr-.ir data (at noonti_) shows II remarkable Jet-like .tructure in

most month •• This jet-like .tructure i .

assumed to be related to the t".,. . . l wind. A d . . crlpticn for .uch profile i .

found to bl! a cla.sical Ekaan 8L .olution corrected for therMal wind effect ••

The main conclusion i . that i t is definitely not possible to relate Sudanese .urface wind

CU.)

data to the frwe at.osohertr wind

co.)

data in a

si~le fa.hl2"' Comelet. mod.l1tng of the "el.tion of U. and U. reQuir . . additional data and investigation. Further det.iled .... ult. of this re.earch will bl!

• ubmitttrd for publication in an aooroorlat. journal.

5.

ACKNOWLEDGEMENTS

The author. wish to thank the $t~f~

of the KhartoulII Meteorology Offi~e {or their help in the data extraction frpm the t'll!!!h.orology Archive. in Kha .. toum, and th. WOTRO (N1totherland. FoundaHon fo'- the Advancement of Tropical Research) for their financial support for phas. I of th . . . rch program. W. also thank Prof. Dr. C. A.plid.,.. and Prof. Dr. H. Flohn far their encouraQRMent. ~o ~he pro;.ct and Dr. J. Reiff for his useful comments on the draft of this paper.

REFERENCES

[13 a.vosser., P.T.Smulders (1985) "Proposal to devl!loo a _thodolo9Y to mvaluate the wind potential in tropical rttgions" - Report no. R n2

D - Wind Entrr"gy Group - Laboratorv of Fluid Dynamics and Heat Transfe .. - Physics Depart.-nt - University of EindhoVen - The Ntrtherland.

[23 E.H. ABu Sekr (1986) "Preli~inarv

survl!Y of the Sudan Mind regime" -Report no. R 77B D - Wind Energy GrOUP - Laboratory of Fluid Dyna~ics

and Heat Transfer - Physics

Depart-~t - Univer.ity of Eindhoven - Th.

Netherlands '

[31 E.H. ABu Bakr (1985) "Trav.l reoort Bracknl!ll (U.K.)" - Report no. R 7b7

D - Wind Energy Group - Laboratory of Fluid Dynamic. and Heat Transfer

- Physics o.part-.nt - University of Eindhovwn - The Netherlands

[4J E.H. ABu Bakr (1986) "Travl!l reoort KhartoulII (Sudanl" - Report no. R 7b8 D - Wind Energy Group, LaboratorY of Fluid DynaMi~. and Heat Transfer -Physic. DepartMent - Univer.ity of EindhoVen - The Netherland.

[3] J.Wieringa (l986l

"Roughne.s-dep.ndent geographical inter-polation of surface wind speed 'averav . . " - Quart.J.Roy."-teor.Soc ••

112, B67~

t63 E.H.Lyswn (1983) "Introduction to "ind energy" - CWD 82-1 - P.O.Sox B5 - AMersfoort - Th. Netherlands

(7) A.A.M. Holt.lag, A.P. van Uldl!n (983) "A ,itllJ/le sch_ for d.yti~\!!!'

_ti_t:._ of the .urfac. <flu,. •• f .. 0<'11

routine .... th.,. data"

-J'.Cllftl.Appl."-t._. 22. 517-529 eel E.H.ABu Bakr (1982) "Study of

cylindrical pa .. abolic concentrat.or" - B.Be. thesis - Univer.ity of KhartOUllO - Sudan

t9] 9.A.~Bean . t al C19~) "The

PI anetory Boundary L • .,.,. - wt10

- No. 530 (Techn. Note lOS)

(10) A.S.Montn_ A.M. YavlOlll (1971) "Stati.tical fluid mechanic., 'Mechanic. of Turbulenc.· " - Vol. 1 - MIT Pre •• t i l l T.Ho1t. 9.Sethura . . n (1983)

"Aircraf~ and .hip Obsvrvation of

thl! mean stru~~ure of the ~arin.

boundary layer over the Arabian Sea during Monex 79 - Boundary lay.,. "-tl!orO. 33 - 25'9-282

t12] B.M.st. F.A~enfeld (1978) "8eitrage

zu~ Metl!orologie .ine. Steppen- ' gebietes (Tusumb S.W.A.) Met.orol. Rdsch. 31, 97-111 and lbl-179