Short Term Prediction

8/2/2019 Short Term Prediction

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S H O R T- T E R M P R E D I C T I O N O F L O C A L W I N D C O N D I T I O N S

L A R S L A N D B E R GDepartment of Meteolv logy and Wind Energy, RisO National Laboratory, DK -4000 R oskilde,

Denmark

and

S I M O N J . WAT S O NRuthelford Appleton Laboratory, Chilton, Didcot, OX ON , O X ll OQ X, United Kingdom

(Received in final form: 7 January, 1994)

Ab stra ct. Using Num erical W eather Prediction (NWP) m odels it has been shown that they, com -bined with models (either physical or statistical) taking local effects into account, can be usedto predict the wind locally better than the models commonly used today (as eg persistence). By"local" is meant at one distinct spot, as eg the location of a meteorological mast. The physicalmodel of local effects takes the following into account: shelter from near-by obstacles, the effectof roughness changes and the effect of the local orography. The large-scale flow is linked to thesurface flow by the geostrophic drag law , and the logarithmic wind profile. Th e predictions aremade up to 36 hours ahead. The model is tested on data from 50 meteorological stations scatteredall over Europe.

1 . I n t r o d u c t i o n

I n m o r e a n d m o r e a p p l i c a t i o n s i t h a s b e e n f o u n d u s e f u l t o b e a b l e to p r e d i c t th ew i n d a t a s p e c if i c si te . T h e s e a p p l i c a t i o n s r a n g e f r o m f o r e c a s t i n g t h e p o w e r o u t p u t

f r o m w i n d f a r m s , t o c a l c u l a t in g t h e t r a j e c t o r ie s o f h a z a r d o u s g a s e s , t o v e r if i c a t io no f N u m e r i c a l W e a t h e r P r e d i c t i o n ( N W P ) m o d e l s . I n t h is a rt ic l e, m e t h o d s t o d ot h e s e p r e d i c t i o n s w i l l b e d e s c r i b e d a n d e v a l u a t e d . T h e m a i n p a r t o f th i s a r ti c le w i l lb e d e d i c a t e d t o a m o d e l b a s e d o n t h e t r a n s f o r m a t i o n a n d c o r r e c t i o n o f o u t p u t

f r o m N W P m o d e l s t o a su r f a c e w i n d i n f lu e n c e d b y l o c a l e f fe c ts . S o m e o t h e r( m o r e s i m p l e ) m o d e l s w i ll a l s o b e t ri e d in o r d e r t o c r e a t e a f r a m e o f r e f e re n c e .

2 . T h e p h y s i c a l m o d e l

T h e i d e a b e h i n d t h e p h y s i c a l m o d e l is t h a t t h e p r e d i c t e d w i n d f r o m a N W Pm o d e l , w h i c h i s a w i n d s p e c i f i c t o a g r i d c e l l o f s a y 5 0 5 0 k m 2, i s t r a n s f o r m e dt o t h e s u r f a c e u s i n g t h e g e o s t r o p h i c d r a g l a w

G = In u , - A + / 3 2 (1 )

w h e r e G i s t h e g e o s t r o p h i c w i n d , u , t h e fr i c t i o n v e l o c i t y, t~ t h e Vo n K ~ r m ~ nc o n s t a n t ( = 0 . 4 ), f t h e C o r i o l i s p a r a m e t e r , a n d z0 t h e a e r o d y n a m i c r o u g h n e s sl e n g t h . A a n d / 3 a r e c o n s t a n t s h e r e s e t e q u a l t o 1 . 8 a n d 4 . 5 , r e s p e c t i v e l y, i n

a c c o r d a n c e w i t h Tr o e n a n d P e t e r s e n ( 1 9 8 9 ) . T h e s e v a l u e s a r e c l o s e to th e o n e ss u g g e s t e d b y Z i l i t i n k e v i t c h ( 1 9 8 9 ) : 1 .7 a n d 4 .5 .

Boundary-Layer Meteorology70: 171-195, 1994.(~ 1994K luw er Academ ic Publishers. Printed in the Netherlands.


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17 2 L. LANDBERGAND S.J. WATSON

To ge t a ve loc i ty in the su r face boundary l aye r, t he loga r i thmic wind p ro f i l e

u ( z ) = - - u * I n~ 0 0 ) ~ ( 2 )

i s used . Here u(z) i s the ve loc i ty a t he igh t z . T he d i rec t ion o f the w ind a t thesur face , a , i s ca lcu la t ed f rom

- Btan a - . (3)

In ?-~

These equa t ions a re in the i r neu t ra l fo rm. We t r i ed to use thepredicteda t m o -spher i c s t ab il i ty f rom the NW P in the s t ab i l i ty -dependen t ve r s ion o f the abov e

ment ioned equa t ions ( eqs . 1 -3 ) ; t h i s gave no improvement ; on the con t ra ry theneu t ra l ve r s ion pe r fo rmed s ign i f i can t ly be t t e r. Th i s i s mos t l ike ly due to the f ac ttha t i t i s ve ry ha rd , even fo r s t a t e -o f - the -a r t NWP mode l s , t o pa ramete r i se thef luxes a t the surface .

The wind ca lcu la ted so f a r i s s t i l l va l id fo r qu i t e a b ig a rea and i t mus t nowbe cor rec ted to t ake loca l e ffec t s in to accoun t .

2 .1 . LOCAL EFFECTS

In th i s s tudy the fo l lowing i s cons ide red as a ffec t ing the wind loca l ly. The idea

i s t aken f rom the European Wind At la s (Troen and Pe te r sen , 1989) , bu t a s imi la ra p p r o a c h w a s t a k e n b y Wa l m s l e y a n d Ta y l o r ( 1 9 8 7 ) :

- She l t e r f rom ob s tac les , such as houses , row s o f t r ees, e tc . The c o r rec t ionsa re made accord ing to the approach by Pe re ra (1981)

- The e ffec t o f roughne ss changes , eg the change f rom wate r to l and . Thet h e o r y o f th e g r o w t h o f I n te r n al B o u n d a r y L a y e r s ( I B L s ) d e v e l o p e d b yLarsen e t a l . (1982) and Semprev iva e t a l . (1990) has been used .

- The e ffec t o f the o rography, eg the speed-up a t hi ll tops . Here the theory fo rf l o w o v e r c o m p l e x t e rr a in o r ig i n a ll y d e v e l o p e d b y J a c k s o n a n d H u n t ( 1 9 7 5) ,

b u t i n a n i m p r o v e d v e r s i o n b y Tr o e n ( 1 9 9 0 ) t h e B Z - m o d e l , h a s b e e n u s e d .Al l o f these m ode l s a re incorpora ted in WAsp (W ind At la s An a lys i s and A ppt i -

ca ion Program) (Mor tensen e t a l . , 1993) and i t i s th i s p rogram tha t has beenused in th i s s tudy. The ou tpu t f rom the d i ff e ren t mode l s i s pu t in to a ma t r ix ( aWAsp-mat r ix ) and used to co r rec t each p red ic ted geos t roph ic wind in tu rn .

Th i s way o f ope ra t ing d i rec t ly on the t ime se r i e s i s no t the normal way o fus ing WASP, s ince ea ch se t of speed and di rec t ion i s corre c ted a t a t ime and no td i s t r ibu t ions o f seve ra l yea r s o f da ta . Th i s has the con sequ enc e tha t one o f theassumpt ions in the theory beh ind WAsp ( tha t s t ab i l i ty e ffec t s can be t r ea ted in

a s imple manner fo r long t ime se r i e s ) has been v io la t ed . As can be seen in thefo l lowing , th i s v io la t ion does no t l ead to e r roneous r e su l t s - on the con t ra ry.

I t shou ld be no ted tha t i t i s poss ib le fo r o the r loca l e ffec t s to ru le , an exa mp leof th i s i s the loca l c i r cu la tions genera ted by d i ff e rences in hea t ing as sea -b reezes ,


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SHORT-TERM PREDICTION OF LOCAL WIND CONDITIONS 173

and anaba t i c and ka taba t i c winds . I f the a rea in ques t ion i s domina ted by thesee ffec t s , the co r rec t ions f rom WAsp a re no t r igh t . As can be se en l a te r, t hese e ffec t sa re con t r ibu t ing fac to r s to the poor r e su l t s found in pa r t s o f sou the rn Europe .

2.2. D E S C R I P T I O N O F T H E M O D E L

In th i s sec t ion , the mode l wi l l be desc r ibed in some de ta i l ; fo r fu r the r de ta i l s seeLan dberg (1993) . The f ir s t s t ep is to ge t the fo recas t l a rge - sca le w ind rep resen t ingthe geos t roph ic wind . To ob ta in the r e s t o f the va r i ab les in the geos t roph ic d raglaw ( ie z0 and f ) for the s ta t ion in que s t ion , the W Asp - ma tr ix i s read to get theroughness . The WAsp-matr ix conta ins the resul ts f rom the ca lcula t ions (performedby W ASp) o f the loca l e ffec t fo r each 30 deg sec to r, p lus a ca lcu la ted m eso-s ca leroughness . To ca lcu la te f , t he l a t itude o f the s t a t ion i s a l so inpu t.

Al l the va r i ab les in the geos t roph ic d rag l aw have now been de te rmined , andi t i s poss ib le to ca lcu la te the f r ic t ion ve loc i ty, u . . ~ . i s no t g iven exp l i c i t ly in thegeos t roph ic d rag l aw; hence i t i s no t poss ib le to so lve the d rag l aw ana ly t i ca l ly,a n d a n u m e r i c a l i t e ra t iv e m e t h o d , b a s e d o n a c o m b i n a t i o n o f th e N e w t o n - R a p h s o nmethod and bisec t ion , i s used; see Press e t a l . (1986) . S ince z0 (and the res t ofthe quant i t ies in the WAsp-matr ix) are g iven in the 12 sec tors , a funct ion us ingl inea r in t e rpo la t ion i s used to p rov ide va lues fo r any d i rec t ion .

Assuming neu t ra l cond i t ions , i t i s now poss ib le to ca lcu la te the wind a t thes i t e by us ing the loga r i thmic wind p ro f i l e . To in t roduce the loca l e ffec t s , t he

cor rec t ions f rom the WAsp-mat r ix a re app l i ed to the wind speed and d i rec t ion .We have now go t the p red ic ted loca l wind a t the s i t e .

The co r rec t ions in the WAsp-mat r ix have been ca lcu la ted by WAsp once andfor a l l fo r each s t a t ion us ing the in fo rmat ion in the European Wind At la s (Troenand Pe te r sen , 1989). As an exam ple o f the magn i tud e o f these co r rec tions , i t canbe men t ioned tha t they typ ica l ly va ry f rom 0 .7 to 1 .3 t imes the uncor rec ted wind .

Hav ing the fo recas t l a rge - sca le wind , the p rogram runs fo r a f ew seconds pe rfo recas t t ime pe r s t a t ion on a 386-PC, i e the whole 36-hour fo recas t fo r one s i t ein 3-hour s teps i s done in less than hal f a minute .

2 . 3. T H E N W P M OD EL

I n t h i s s t u d y t h e H i g h R e s o l u t i o n L i m i t e d A r e a M o d e l ( H I R L A M ) h a s b e e n u s e das the NWP mode l , i n the ve r s ion run by the Dan i sh Meteoro log ica l Ins t i tu t e .Th i s m ode l has a g rid po in t spac ing o f 56 km and p rodu ces fo recas t s a t m idda yand midn igh t (UT C) in 3 -hour ly st eps up to 36 hours ahead (M achenhaue r, 1988) .H I R L A M i s a w i d e l y u s e d f o r e c a s t i n g m o d e l , b a s e d o n t h e p r i m i t i v e e q u a t i o n sand co vers a l l o f Europe , m os t o f the At lan t i c ( inc lud ing Green land) and pa r t so f Nor the rn Amer ica . Forecas t s fo r a g iven loca t ion a re de r ived by b i - l inea r

in te rpo la t ion o f the four nea res t g r id po in t s .I t i s o b v i o u s t h a t t h e f o r e c a s t s p r o d u c e d b y t h i s N W P m o d e l c a n n o t t a k e

accou n t o f loca l s i t e cond i t ions and c l im a to logy . The fo recas t s a re the re fo rem a d e s i t e s p e c i f i c b y t h e m e t h o d d e s c r i b e d a b o v e .


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174 L. LANDBERG AND S,J . WATSON

2 . 4 . F I N D I N G T H E R I G H T G

Ti l l now i t has been assumed tha t the geos t roph ic wind , G , was a t hand . Th i s

is a p r io r i t rue , bu t a f t e r hav ing t r i ed the geos t roph ic wind a t the su r face f romH I R L A M , i t w a s f o u n d th a t a n o th e r w i n d s o u t p u t f r o m t h e m o d e l h a d t o b e u s ed ,b e c a u s e t h e a c c u r a c y o f th e r e s u lt s o b t a i n e d w a s f a r b e l o w t h a t e x p e c t e d .

T h e r e a r e t w o d i f f e re n t t y p e s o f w i n d s i n H I R L A M : g e o s t ro p h i c a n d a c tu a l.Each o f these i s g iven a t seve ra l mo de l l eve l s , i e at d i ff e ren t he igh ts . T he f ir st pa r to f th i s ana lys i s wi l l be to find which o f these winds approx im ates the theore ti ca lgeos t roph ic wind bes t . Th i s i s to be unders tood in the sense tha t i t i s t he windtha t r e su l t s in the smal l e s t mean e r ro r and s t andard dev ia t ion when inse r t ed asG in the geos t roph ic d rag l aw and then used in the mode l to p red ic t the wind a t

50 me teoro log ica l s t a t ions . These p red ic t ions a re compared to the obse rva t ionsf r o m t h e s t at io n s w h i c h s p a n o n e y e a r fr o m D e c e m b e r 1 9 9 0 t o N o v e m b e r 1 99 t .

The p a ram ete r s fo r th is f i rs t coa r se eva lua t ion a re the me an o f the mea n e r ro rfor a ll s ta t ions , {e) , the s tandard devia t ion ( take n ov er a l l s ta t ions) of the mea nerror O-e, and the m ea n of the s ta ndard dev ia t ion for a l l s ta t ions {cry) . Al l the sep a r a m e t e r s g i v e a ro u g h i d e a o f t h e g e n e ra l p e r f o r m a n c e o f t h e m o d e l s , s i n c ethey ave rage over a l l t he s t a t ions . La te r in th i s sec t ion , a more de ta i l ed ana lys i swi l l be ca rr i ed ou t when m os t o f the d i ff e ren t cand ida te winds ha ve bee n ru ledou t . An exa m ple o f the r e su l ts o f runn ing the mo de l w i th the d iff e ren t cand ida te

winds i s shown in F igure 1 . The re su l t s fo r the o the r months a re quan t i t a t ive lysimilar.

Theore t i ca l cons ide ra t ions ind ica te tha t the geos t roph ic wind a t the su r face i sthe bes t candidate , s ince i t i s a t the surface tha t the f r ic t ional force i s ba lanced bythe pressu re gradient . Lo oki ng a t F igure 1 i t i s seen, how eve r, tha t th is is far f romthe case he re : the wors t r e su l t s a re ob ta ined by us ing the mode l geos t roph ic winda t the su r face . Genera l ly, i t can be seen tha t any geos t roph ic wind , no ma t t e r thehe igh t , i s no t a good approx imat ion . Th i s impl i e s tha t ac tua l mode l winds f romHIRLAM mus t be used ; look ing a t the f igure i t can be seen tha t the r e su l t s o f

us ing the mo de l w inds a t the d i ff e ren t he igh t s a re ve ry s imi la r. There fo re , a morede ta i l ed ana lys i s has to be ca r r i ed ou t .

Ru l ing ou t mos t o f the l eve l s , a c lose r ana lys i s ( the r e su l t o f which i s shownin Tab le I ) r evea led tha t the ac tua l HIRLAM wind a t the 137 m leve l gave thesmal l e s t me an e r ro rs and roo t m ean square ( rms) e r ro r s ; t h is w ind wi l l t he re fo reb e u s e d a s G i n t h e H I R L A M / WA S p m o d e l .

Note , tha t the under ly ing conc lus ion in th i s sea rch fo r the bes t l eve l to t akethe wind f rom, i s tha t the use o fa n y o f t h e a ct u a l m o d e l w i n d s w o u l d o u t p e r f o r mpers i s t ence , c f F igure 1. W i th ano the r se t o f s t a t ions and ano the r N W P m ode l ,

the bes t wind cou ld be f rom ano the r l eve l . The reason why the geos t roph icw i n d p e r f o r m e d s o b a d l y c o u l d b e t h a t i t i s c a l c u l a t e d f r o m d i f f e r e n c e s b e t w e e nq u a n ti t ie s o f a l m o s t t h e s a m e m a g n i t u d e .


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9-

8 -

7 -

6 -

5 -

4 -

3 -

2-

I-

13-

+ 36 h

p h l h2 h3 h4 h5 h6 gO g l g2 g3 g4 g5 g6

Fig . 1 . The 36 hour p red ic t ions fo r June 1991 ( the sum me r case ) us ing the neu t ra lH I R L A M / WA S p - m o d e l w i th a c t ua l m o d e l w i n d s ( h l - h 6 ) a n d g e o s t ro p h i c w i n d s ( g 0 - g 6 ) f r o mthe HI R LA M m odel . Le ve l 0 i s a t the sur face , 1 i s a t 30 m , 2 a t 137 m, 3 a t 359 m, 4 at 729m , 5

a t 1266 m and 6 a t 1979 m ag l . The p red ic t ions a re com pared to pers i s tence (p) . The f ir s t co lum n( in e a c h g r o u p o f 3 ) in c o n n e c t i o n w i th e a c h m o d e l i s th e m e a n v a l u e o f th e m e a n e r r o r a v e r a g e dove r a l l s t a tions , the second i s the s tandard dev ia t ion o f the mean e r ro r t aken o ver a l l st a t ions , andthe th ird i s the mean of the s tandard dev ia t ions fo r the ind iv idua l s t a tions. Bars ex ten d ing o u t s idethe hor izon ta l boundar ies s ign i fy tha t the va lues they represen t a re beyond the ex t reme va lues o fthe y -ax i s .

TA B L E I

The resu l t o f comp ar ing the two bes t mode ls , i e the mo de ls us ing the ac tua lHIRLAM wind a t 137 ( f i r s t row) and 359 m ( second row) , r espec t ive ly. Forre fe rence , t i l e fo recas t us ing the 729 m ( th i rd row) wind i s a l so inc luded .The tab le con ta ins the resu l t s o f the e~ and RMSE ana lys i s , r espec t ive ly.The sc or ing schem e i s such tha t a h igh num ber i s a good score ; see Land berg(1993) for detai ls .

M o d e l l e v e l H e i g h t ( m ) S c o r e e ~ ( p oi nt s) S c o m R M S E ( po in ts )

2 137 287 331

3 359 200 173

4 729 163 146


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176 L . L A N D B E R G A N D S .J . WAT S O N

Others have reached resu l t s a long the same l ines : C la rke and Hess (1974)u s e d t h e ac t u al w i n d i n z = 0 . 1 5 u , / f , w h i c h i s a p p r o x i m a t e l y 4 5 0 m f o r t y p ic a lva lues ; th i s l eve l i s the l eve l wi th the s t ronges t winds , and where the wind i s

geos t roph ic on ave rage under neu t ra l cond i t ions . In ano the r s tudy (Z i l i t i nkev ichand Cha l ikov, 1968) the ac tua l wind a t a fixed he igh t ( ap prox im ate ly 1 km ) wa sused as G in the geos t roph ic d rag l aw.

3 . R e s u l t s

T h e m o d e l s e l e c t e d a n d d e v e l o p e d i n t h e p r e c e d i n g s e c t i o n i s n o w r u n a n dc o m p a r e d t o a c t u a l o b s e r v a t i o n s a s r e p o r t e d t o t h e G T S ( G l o b a l Tr u n k S y s t e m )ne twork fo r a l l s t a t ions in the pe r iod f rom December 1s t , 1990 to November

30 th , 1991 , g iv ing one yea r ' s wo r th o f da ta. The se lec ted mod e l wi l l be ca l l edt h e ' ne u t ra l H I R L A M / WA S p m o d e l ' o r j u s t th e ' H I R L A M / W A S p m o d e l ' , a n da b b r e v i a t e d ' H / W ' .

One o f the t a sks thi s s tudy se t ou t to under t ake , w as to see whe the r i t wa sposs ib le to make fo recas t s tha t pe r fo rmed be t t e r than pe r s i s t ence . Hav ing th i s inm i n d , w e h a v e d e f in e d a' good ' s t a t i on , as a s t a t ion where the fo recas t s p roducedby the mode l a re be t t e r than pe r s i s t ence a f t e r 6 hours , and a' b ad '* s t a t ion asa s t a t ion where pe r s i s t ence pe r fo rmed be t t e r than the mode l fo r a l l l ook-aheadt imes . The reason fo r the 6 hour low er l imi t i s tha tn o n e o f t h e f o r e c a s ts p e r f o r m e d

be t t e r than pe r s i s t ence un t i l f rom be tween 3 and 6 hours ahead . Look ing a t a l lthe s t a t ions , i t has been found tha t 80 % can be l abe l l ed a s ' good ' fo r the +18hour fo recas t . For shor t e r r ange fo recas t s , t h i s pe rcen tage i s r educed and fo rlonger inc reased . Th e +36 h our fo recas t y i e lds 88 % and the +3 hour O %. Thep e r f o r m a n c e a s a f u n c t io n o f l o o k - a h e a d t i m e o f a ' g o o d ' s t at io n c a n b e s e e nin F igure 2 . For ' good ' s t a t ions the abso lu te mean e r ro r and the rms e r ro r a rea round 60 to 80 % o f the pe r s i s t ence m ode l ' s e r ro r fo r the +18 hour fo recas t s ,c f F igure 3 .

Re tu rn ing to F igure 2 , two in te res t ing fea tu res a re seen :

1. The rms e r ro r and the mea n e r ro r o f the HIRLA M/W ASp mode l a re cons tan tfo r the ' goo d ' s t a tion . Th i s i s seen genera l ly fo r al l o f the 50 se lec ted s t a t ions .Th i s i s qu i t e d i ff i cu l t t o exp la in , s ince i t wou ld be expec ted tha t i t wou ld beharde r and ha rde r to p red ic t co r rec t ly a s the look-ahead t ime inc reases ; th i si s found to be the case fo r the pe r s i s t ence mode l . One poss ib le exp lana t ioncou ld b e tha t on ly the leve l o f the wind speed i s p red ic ted r igh t and no t thevar i a tion . I f t h is w as the case , the rms e r ro r o f the p red ic t ion shou ld m oreor l e s s be equa l to the s t andard dev ia t ion o f the obse rva t ions themse lves .Th i s i s seen no t to be the case . As an example , cons ide r the fo recas t fo r

B i r m i n g h a m ( F i g u re 2 ) w h e r e t h e r m s e r r o r o f t h e H I R L A M / WA S p m o d e l i sapprox imate ly 1 .8 m/s , a s compared wi th 2 .2 m/s fo r the t ime se r i e s i t s e l f ,

* o r n o t s o g o o d


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"~" 1.0

3 , 0 . . . . . . . . . i . . . . . . . ,, i . . . . . , , , , i . . . . , , , ,

2.o~ ~ . ~ _ _ _ o . ~

i , , , * ,1 , , i , , ~ , , , , , i t i i , , l l l l l l , l l l l , i i

I0 20 30

Look-ahead t ime (hour s )

-1.0 40

Fig. 2. The mean error (in m/s, denoted by circles) and rms error (in m/s, denoted by squares) of theHIRLAM/WAsp-model (open symbols) compared to persistence (solid symbols) for Birmingham(station 57, a 'good' station) for the entire period (December 1990 to November 1991). Thelook-ahead time (in hours) is along the z-axis.

which is a difference of 18 per cent; furthermore, is it seen using the UKMet. Office Mesoscale model (UKMESO) that models with higher resolutionhave smaller - but still constant - rms errors, cf Figure 11.

Another explanation is that the area covered by HIRLAM (which includesthe Atlantic Ocean) is so big that within a 36 hour period, generally mostof the large-scale weather systems affecting any site in Europe are presentin the initial analysis, with the result that major developments within the36 hour time-frame are know equally well, and therefore predicted equallywell. This of course assumes that the physical model keeps the atmosphereon 'the right track' during the integration. This is confirmed by studying theresult of the UKMESO model (covering a significantly smaller area) whichshows the expected behaviour of a constant and then increasing rms errorwith time, even within the 18 hour range. The reason for the variability inthe first 6-9 hours is probably due to the error induced by the initialisationof the fields in HIRLAM.

There is no doubt, though, that the limited variability of atmospheric windspeeds (ie from 0 to typically around 15 m/s) puts an upper limit on the rmserror of any physical model.

2. The mean error of the persistence model is always close to zero. This is dueto the definition of the persistence model, where most terms cancel each other

in the calculation of the mean error (see Landberg (1993) for a derivation).In Figure 4 the selected stations have been labelled according to their per-

formance relative to the persistence model. As can be seen from this figure,the majority of the good predictions are found for stations located in Northern


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178 L. LANDBERG AND S.J. WATSON

Fig. 3 . The accum ulated dis t r ibut ion of the re la t ive rms error ( ie the rms error of theHIRLAM/WASp model re la t ive to that of the pers is tence model) for a l l s ta t ions for the +18 hourforecast . The c lass i f icat ion (* , + , = , and - ) appl ied in Figure 4 is show n at the top of the figure .

Europe; this is very much in l ine with the experience gathered from using theWAsp program, since the f low at these locations is mainly gove rned b y the large-scale atmospheric f low, ie a non-locally generated f low, As we get nearer to the

Mediterrane an Sea, the quali ty of the forecasts decreases, b ut note that even herethe model general ly outperforms persistence. Note also, as is shown in Section 4,that using MO S improv es the quali ty of the predict ions for the 'ba d' s tations.The improvement is such that these stat ions, after MOS has been applied to theH/W-forecas t , can be label led 'good ' .

Since the amou nt of data p rodu ced is quite large (12 sets of predict ions (+3 .... ,+36h) twice a day for 50 stat ions for one year) , we have chosen to look in somedetai l at one stat ion: Birmingham representing the 'good' s tat ions. For a morecomplete assessment, refer to Appendix ??, where two error measures are l is ted

for al l s tat ions for the +18 hour forecast for the HIRLAM/WAsp model as wetlas for the persistence model. An even more comprehensive l is t ing can be foundin Landberg (1993).

In Figures 5 and 6 scatter-plots of the observed versus the forecast wind speedand direct ion, respectively, for the 'good' s tat ion are shown.

It can be seen from these that the speed and direct ion are predicted quite well ;this holds true for all the stations labelled 'good'.

I t is also useful to look at the distr ibution of the forecast versus the observedwind, s ince in many applicat ions a wind cl imate is represented solely by i ts

(Weibull) distribution. The distributions are shown in Figure 7 and 8. Com-paring the distr ibution of the forec ast to the ob serv ed wind, a quite interest ingfeature leaps to the eye: the expected distr ibution for the 'good' s tat ion is actu-al ly predicted better ( ie more smoothly and accurately) by the forecast than by


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SHORT-TERM PREDICTION OF LOC AL WIND CONDITIONS 179

czz,

F i g. 4. T h e p e r f o r m a n c e o f th e n e u t r a l H I R L A M / WA S p m o d e l r e la t i ve to th e p e r s i s te n c e m o d e lf o r a l l t h e s e l e c t e d s t a t i o n s . A n * i n d i c a t e s t h a t t h e a b s o l u t e e r r o r a n d t h e r m s e r r o r o f t h e m o d e la r e l e s s t h a n 0 . 7 t i m e s t h a t o f t h e p e r s i s t e n c e m o d e l f o r t h e + 1 8 a n d + 3 6 h o u r f o r e c a s t , a + t h a tt h e y l i e b e t w e e n 0 . 7 a n d 1 .0 , = t h a t t h e y a r e e q u a l , a n d - t h a t t h e p e r s i s t e n c e m o d e l p e r f o r m e db e t t e r. S t a t i o n s m a r k e d w i t h o a r e s t a t i o n s o r i g i n a l l y s e l e c t e d b u t r e j e c t e d b e c a u s e o f l a c k o f d a t a( t y p i c a l l y t h e y r e p o r t e d o n l y t w i c e a d a y t o t h e G T S - n e t w o r k ) .

the observations, cf Figure 7. This fact calls for some explanation: experience

has shown that most observations of the wind speed can be represented by the2-parameter Weibull distribution (Weibull, 1951), but as can be seen from thefigure, there seem to be patches o f missing data in the observations (eg 3, 10and 17 knots), these patches are not present in the forecast, for which reasonthe distribution appears smoother. Here is also found another explanation of whythe 'bad' stations are not well predicted when using the mean error and the rmserror as the measure. It is obvious that measurements within the entire intervalspanned should be present when looking at 1 year of data. So quite some doubtcan be raised concerning the quality of some of the observations. The gaps might

stem from a conversion from m/s to knots and back.Studying the distribution of the enor, it was found that it could, to a good

approximation, be labelled Gaussian, cf Figure 9. The dependence of the erroron the time of year has also been examined, as it could be expected that seasons


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1 8 0 L. LAND BERG NDS.J.WATSON'1 5 , i , , I , , . . , I , , , , -

~

10 * tg

O

q . . . . . . . . . . . . . . . . . ~ . . . . l b . . . . i sM o d e l ( m / s )

Fig. 5. A scatter-plot of the forecast wind speed versus the observed, for the +lS h forecast forthe ' good ' station (Birmingham) for the entire period. The existence of the horizontal lines in theplot is due to the resolution of the observations (which is 1 knot).

,-, : " i " " i . . . . . . . . . . . . . . . . .

v70"~ * ]

" ~ 1 8 C

,>

n0 9 0

. . . . . . . . . . , . . . . " , ," ~ao ' ' ' : ~ d ' ~6o

M o d e l ( o )

Fig. 6. A scatter-plot of the forecast win d direction versus the observed for the' g o od ' station(Birmingham).

d o m i n a t e d b y s t o r m s / s t r o n g w i n d s w o u l d b e e a s i e r t o p r e d i c t t h a n s e a s o n s w i t hl o w w i n d s , c f S e c t i o n 4 . 2 . T h i s h a s b e e n f o u n d n o t t o b e t h e c a s e a t a ll . T h e o n l ym o n t h d i f f e r e n t f r o m t h e o t h e r s w a s S e p t e m b e r , a n d t h i s w a s d u e t o t h e f a c t t h a tt h e r e w a s o n e d a y w h e r e a l l H I R L A M f o r e c a s t s w e r e b a d .

T h e d e p e n d e n c e o f t h e e rr o r o n t im e o f d a y h a s n o t b e e n e x a m i n e d , s i nc e i t i s

n o t p o ss i b le t o m a k e a fa i r c o m p a r i s o n , b e c a u s e t h e pr e d ic t io n m o d e l ( H I R L A M )i s o n l y r u n t w i c e a d ay. W h a t c a n b e s a i d i s t h a t, j u d g i n g f r o m e g F i g u r e 2 , t h e r ed o e s n o t s e e m t o b e a n y s i g n i f i c a n t v a r i a b i l i t y, s i n c e t h e m e a n a n d r m s e r r o r a r ec o n s t a n t .


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SHORT-TERM PREDICTION OF LOC AL WIND CONDITIONS 18 l

2 5 ~ ,

2 0

13) 15L)r -

oo

O

0 i . . . . . . . . - , ~ : , ~ - ~ - ~ ,o 5 l O 1 5

Model (m/s)F i g . 7 . T h e d i s t r i b u ti o n o f t h e fo r e c a s t w i n d s p e e d ( l i n e s) v e r s u s t h e o b s e r v e d f o r B i r m i n g h a m( a ' g o o d ' s t at i o n ) ( b ar s ). T h e l o o k - a h e a d t i m e i s + 1 8 h a n d t h e p r e d i c t io n s a r e ta k e n f o r t h e e n t ir e1 year pe r iod . T he b in wid th i s 1 kno t .

25 f' '

i11 150cQ)

~ 1 000

O5

00 5 1 0 1 5

Model (m/s)

F i g . 8 . T h e d i s t r i b u t i o n o f t h e f o r e c a s t w i n d s p e e d ( l in e s ) v e r s u s t h e o b s e r v e d ( b a rs ) f o r th e + 1 8h f o r e c a s t f o r S a l a m a n c a ( ' b a d ' ) .

4 . M ode l ou tp u t s t a t is t ic s (M OS)

W h e n a p p l y i n g a p h y s i c a l m o d e l t o r e a l s i t u a t i o n s , e r r o r s w i l l i n e v i t a b l y o c c u r.T h e s e e r ro r s c a n h a v e d i f f e re n t ca u s e s. T h emodel c a n h a v e s o m e i n h e r e n t e r ro r s,b e c a u s e t h e p h y s i c a l m o d e l d o e s n o t e x a c t l y m a t c h r e a li ty. I n t he c a s e o f th e n e u -

t ra l H I R L A M / WA S p m o d e l , t h e d e f e c t s o f t h e m o d e l a re t h a t it is n e u tr a l, w h i c hm e a n s t h a t t h e s t a b i l i t y - d e p e n d e n t e f f e c t s a r e n o t t a k e n i n t o a c c o u n t , a n d t h a t t h es p a t i a l r e s o l u t i o n i s l o w. F u r t h e r m o r e , t h e m o d e l a s s u m e s t h a t t h e a t m o s p h e r e i sb a r o t r o p i c , w h i c h i t g e n e r a l l y i s n o t . T h i s c o n s t r a i n t i s p a r t i a l l y c i r c u m v e n t e d b y


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Fig. 9 . The dis t r ibut ion of the error (mod el - observed) , comp ared to the Gauss ian curve havi ngthe mean and va r i ance o f the d is t r ibu tion , for the +18h fo recas t fo r B i rmi ngham (a ' good ' s t a tion ).The bin-width is 0 .1 m/s .

the fact that the wind used as the geostrophic wind, is in fact the real wind (ofa baroclinic model) . The condit ions at thesite may have been changed s ince theWAsp analys is of the station w as carried out; this is not at all unc om mo n: the

mast may have been moved (this was found for one stat ion (f irst Exeter and thenDunkesw el l ) ) and the surroundings o f the mast may have be en changed, typica l lybuildings buil t or demolished. Finally, the analysis can ini t ial ly be erroneous. Inthis s tudy i t is l ikely that i t is the spatial resolution of HIRLAM that contributesmostly to the error.

The data can also be incorrect , ei ther because the instrument is not cal ibratedproperly, or because the instrument simply is old. Remember here, that part ofthe variance of the error is caused by the inexacti tude (as compared to presentday mea suring capabil i t ies) of the reported observa tions, s ince the observations

are reported in integer knots c omp ared to accuracies of 0. l m/s. This results inan added contribution to the rms error of 0.15 m/s on average.

Anoth er im portant cau se of error related to the model, is that there is a 'gap 'be tween the sca les of HIRLAM and WAsp, s ince HIRLAM covers a tmospher icphe nom ena on scales from the semi-planetary dow n to scales of the order of100s of ki lometres. WASP, on the other hand, covers p hen om ena related solely tothe stat ionary f low on scales of the order of 10 km dow n to 1 m. So atm osphericphenomena on the meso-scale, such as local thermally driven circulat ions (sea-breezes, anabatic and katabatic winds), are not modeled by any of the models.

To see if i t is possible to correct so me (or all) of these errors, the outpu t fromthe physical model is corrected usingM OS (Model Output Statistics), which basi-cal ly puts the output from the physical model through a non-physical (stat is t ical)post-processor. Normally, this procedure is used to predict parameters not fore-


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cas t d i r ec t ly by the mode l , a s eg the min imum tempera tu re a t a spec i f i c loca t ion .See Glahn and Lowry (1972) fo r an in t roduc t ion to t r ad i t iona l MOS. Two d i f -f e ren t types o f M O S a re used he re : a ze ro -o rde r l inea r m ode l tha t co r rec t s on ly

sys tem at i c under /over-p red ic t ion and sca l ing on a sec to r-by -sec to r bas i s , and an e u ra l n e t w o r k w i t h d i ff e r en t c o m b i n a t i o n s o f th e o u t p u t f r o m t h e p h y s i c a l m o d e la n d m e a s u r e m e n t s a s i n p u t .

To t e s t the e ffec t o f these tw o M O S approaches , 6 s t a tions (ou t o f o r ig ina l ly50) have been se lec ted : 3 ' good ' s t a t ions where the neu t ra l mode l pe r fo rmedwel l* , and 3 ' bad ' ones where the neu t ra l mode l d id no t pe r fo rm we l l** . Thep a r a m e t e r s o f t h e M O S s y s t e m s a r e o p t im i s e d u s i ng f o r e c a s ts a n d o b s e r v a t i o n sf rom D ec em be r 1990 to Ma y 1991 ( the f ir s t ha l f o f the pe r iod) and t e s t ed on theda ta f rom June 1991 to No ve m be r 1991 ( the l a st ha l f o f the pe r iod) .

Be fo re p resen t ing the r e su lt s , two asp ec t s o f the fo recas t ing p rob lem wi l l beana lysed : Wha t i s the e ffec t o f no t us ing the loca l co r rec t ions ( i e no t us ing theWAsp mat r ix )? And wha t i s the inhe ren t va r i a t ion o f the obse rv ed wind speeds ?

4 . 1 . S E N S I T I V I T Y T O TH E L O C A L C O R R E C T I O N S

To see whe th e r the inc lus ion o f the loca l co r rec t ions f rom WAsp ac tua l ly im provesthe fo recas t in t r ans fo rming the HIRLAM forecas t down to the su r face l aye r, i thas been t r i ed to run the neu t ra l mode l wi thou t app ly ing the loca l co r rec t ions( i e wi thou t the WAsp-mat r ix ) on the 6 se l ec ted s t a t ions . No t us ing the loca l

co r rec t ions means in "WASp language" tha t the s t a t ions a re no t in f luenced byobs tac les and o rography, and have a hom oge neo us roughn ess l eng th o f 0 .03 min a l l d i rec t ions . The resu l ts of th is analys is are sh ow n in Figure 10. I t app eare dtha t the loca l co r rec t ions d id indee d im prove the fo recas t s fo r the ' goo d ' s t a tions ;ma in ly by reduc ing the m ean e r ro r. For the ' ba d ' ones , the loca l co r rec t ionssomet imes inc reased the mean e r ro r and somet imes the rms e r ro r. I t was seentha t some s t a tions cou ld no t be ' s a ved ' ( ie the va lue o f the eva lua t ion pa ram ete r so f t h e m o d e l b r o u g h t u n d e r t h o s e o f t h e p e r s is t e n c e m o d e l ) b y e i t h e r m e t h o d .

T h e r e a s o n w h y t h e ' b a d ' s t a t i o n s i n s o m e c a s e s a r e m o r e p o o r l y p r e d i c t e d

when us ing WAsp i s due to the f ac t tha t the d i r ec t ion a l so i s p red ic ted wrong lyby HIRLAM, and tha t , a s a consequence , the co r rec t ion fo r the loca l e ffec t s i st aken f rom the wrong sec to r. As an example , cons ide r a mas t loca ted a t a l akes ide: i f t he wind i s ac tua l ly com ing f rom land bu t is p red ic ted as comin g f romthe lake , the resul t ing local wind wi l l be too h igh.

4 . 2 . S TAT I S T I C A L P R O P E RT I E S O F T H E O B S E RV E D DATA

To ge t a be t t e r idea o f the e r ro r s g iven in the fo l lowing sec t ions, a l i s t o f thes ta t i s t ica l pro per t ies of each of the 6 se lec ted s ta t ions i s g iven in Table , I I. As

can be seen f rom th i s t ab le , t he ' bad ' s t a t ions have qu i t e low mean wind speeds ,* Meani ng that the model forecast rms errors were better than 0.7 times the persistence errors

for the +18 and +36 hour forecast.** Meani ng that the model forecast rms errors were greater than the persistence errors.


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184 L. LANDBERG AND SJ. WATSON

' g o o d ' ' b a d '4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . " . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I

1

j ........................o i

19 56 57 29 35 41

Stat ion

F i g . 1 0. A c o m p a r i s o n b e t w e e n u s i n g th e f ul l n e u tr a l H I R L A M / WA S p m o d e l a n d u s in g t h e m o d e lwi thou t the WAsp cor rec t ions fo r the 6 se lec ted s ta t ions . For each s ta t ion 6 bars a re d i sp layed ingroups o f 3 : the f i r st th ree a re the m ean e r ro r ( in m/s ) o f the mo de lwithout WA s p c o r re c t i o n s ( ' N ow a s p ' ) , t h e f u ll n e u tr a l H I R L A M / WA S p m o d e l ( ' w a s p ' ) a n d p e r s is t e n c e ( ' p e r s i s t ' ) , r e s p e c t i v e ly ; th e

las t th ree bars fo r each s ta t ion a re the rms e r ro r ( in m/s ) fo r the 3 d i ffe ren t mode ls . The compar i soni s m a d e f o r th e + 1 8 h f o r e c a st f o r d a ta f r o m t h e l a st h a l f o f t h e p e ri o d ( J u n e 1 9 9 t t o N o v e m b e r1991).

and the standard deviations (from the mean) are of the same magnitude as themean value. The ' goo d' stations - on the other hand - have higher means andthe standard deviation has a smaller magnitude than the mean. This is a generalfeature: 'good' stations have means that are higher than the standard deviation,and 'bad' ones have lower or equal values. As a rule, one would place wind

turbines at sites with high wind speeds. In these cases, the neutral HIRLAM/WASpmodel is seen to perform well.

4.3. LINEAR SYSTEM

The linear MOS model used here takes output from the HIRLAM/WASp mode]and calculates the linear relationship between it and the observations. This isdone sector by sector for the twelve 30 degree sectors:

nob s = a (O i) + b ( O i ) u H / w ( O i ) (4)

where Uob s is the observed wind, UH /w the forecast wind from the HIRLAM/ -WAsp model from the direction sector 0i, and a(Oi) and b ( O i )are the regressioncoefficients of the twelve 30 deg sectors. The relationship is established using


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SHORT-TERM PREDICTION OF LOCAL WIND CONDITIONS 18 5

TA B L E II

A l i s t o f d i ffe ren t s t a t i s t i ca l p roper t i es o f the observa t ionsf rom the 6 se lec ted s ta t ions . The f i r s t co lumn i s the name,

t h e s e c o n d t h e c a t e g o r y, t h e t h i rd t h e m e a n o f t h e w i n dspeed ( in m/s ) , the four th the s tandard dev ia t ion ( in m/s ) ,a n d t h e f i f th t h e n u m b e r o f o b s e r v a t io n s .

S ta t ion M ean S td . dev. No . obs .

A b b e v i l l e ' b a d ' 4 . 57 2 .6 2 2 7 7 9

S a l a m a n c a ' b a d ' 2 . 9 6 2 . 4 8 2 7 4 7

Bragan ~a 'ba d ' 2 .81 2 .32 2631

M t i n c h e n ' g o o d ' 3 .0 1 2 .0 1 2 8 3 0

M a n c h e s t e r ' g o o d ' 4 .11 2 . 7 0 2 8 6 3

B i r m i n g h a m ' g o o d ' 3 .7 6 2 .2 0 2 8 6 3

d a t a f r o m t h e f ir st h a l f y e a r (i e f r o m D e c e m b e r 1 9 9 0 to M a y 1 9 9 1 ) a n d t e s te d o nda ta f rom the second ha l f yea r. The r e su l t i s shown in Tab le I I I fo r the +18 hourfo recas t . The re i s no quan t i t a t ive d i ff e rence be tween th i s l ook-ahead t ime andt h e o n e s n o t s h o w n . A s c a n b e s e e n , t h e r e i s a n i m p r o v e m e n t w h e n u s i n g t h i s

me thod : ' good ' s t a t ions a re a s a ru l e l e f t un touched , w i th a s l igh t b i a s toward ani m p r o v e m e n t , a n d t h e p e r f o r m a n c e o f t h e p r e d i c ti o n s f o r th e ' b a d ' s ta t io n s a r ew i t h o u t e x c e p t i o n i m p r o v e d . T h e ' b a d ' s t a t i o n s a r e a c t u a l l y i m p r o v e d t o s u c han ex ten t t ha t a f t e r hav ing app l i ed MOS, they can a l l be c l a s s i f i ed a s ' good ' ( i epe r fo rming be t t e r t han pe r s i s t ence ) .

I t i s l ike ly tha t th is me tho d - in the l imi t - wi l l per fo rm b et ter or a t leas t asw e l l a s a n o p t i m a l WA s p a n a l y s i s w i t h o u t M O S , p a r t i c u la r l y s i n c e t h e d a t a a r eb inned in d i r ec t iona l b ins . The r eason i s t ha t - l ook ing a t t he two me thods a sb l a c k - b o x e s - t h e y b o t h h a v e ( i f w e c o n s i d e r s p e e d o n l y ) o n e s c a l e - fa c t o r p e r

sec to r. Ac tua l ly, t he l inea r me thod has the theore t i ca l poss ib i l i t y o f be ing be t t e rs ince th is me thod a l so has an o ff - se t , ie tw o deg rees o f f r eedom .

4 . 4 . N E U R A L N E T W O R K S

I n s t e ad o f u s i n g t h e l in e a r M O S s y s t e m , s e v e r a l (7 ) n eu r a l n e t w o r k s h a v e b e e nu s e d . A n e u ra l n e t w o r k is a n e t w o r k o f m a n y m a s s i v e l y c o n n e c t e d s i m p l e c o m -p u t a t io n a l u n i ts , t ra i n e d b y a d j u s t i n g t o e x a m p l e s ( s e e e g L a p e d e s a n d F a r b e r(1987) and L and berg (1992) fo r re fe rence ) . The r e su l t s o f u s ing the neura l ne t -

w o r k s w e r e e q u a l i n p e r fo r m a n c e t o t h e li n e a r M O S m o d e l , s o th e y, t o o , a c h i e v e da s ign i f ican t imp rovem ent . S ince the t r ain ing o f neura l ne tw orks i s m uch m oret i m e - c o n s u m i n g a n d c o m p l i c a t e d t h a n t h e e s t im a t i o n o f t h e p a r a m e t e r s i n t h e li n-e a r m o d e l , i t m u s t b e c o n c l u d e d t h a t f o r M O S , o n l y t h e l i n e a r m o d e l i s n e e d e d .


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17/25


6 . U s i n g th e U K M e s o -s c a le m o d e l

To see the effect of the resolution (mainly spatial, but also temporal) of the weath-

er prediction model on the performance of the model predicting local wind con-ditions, the British Meteorological Office's UK MESO (United Kingdom Meso-Scale) model is used instead of HIRLAM. The model is non-hydrostatic andhas a spatial resolution of 15 km (HIRLAM: 57 km). The UK-MESO coversonly the United Kingdom, Ireland, and minor parts of continental Europe andcan therefore only be used for the stations situated in the United Kingdom. SeeGolding (1990) for further information on the UK MESO model.

The output used from the model is the 10 m wind. The model we then develop,takes this wind and corrects it for the local effects. The assumption is that the

10 m wind output from the UK MESO model is completely unaffected by localconditions. This is of course not true, since the United Kingdom orography ispresent and taken into account in the model. But because of the reso lut ion of UKMESO, the orography is not resolved on the same scale as in WASR Compari ngthe forecast using UK MESO and WAsp to the HIRLAM/WASp model for all theselected stations in the UK, we see, without any exceptions, that the rms erroris reduced to typically 70 - 80 per cent. The mean error is typically of the samemagnitude as when using the HIRLAM model. An example of this is shown inFigure 11. There are, however, a few stations where the mean error is quite big,

typically around 1 m/s. Note that no MOS was applied to either of the models,so biases like these would have been removed if MOS had been used. As wasmentioned earlier, the forecasts from UKMESO are used only to see the effectof the higher resolution. The goal of this study is to develop a model that canbe used all over Europe.

In conclusion it can be said that - as expected - the higher spatial resolutiongives improved forecasts. Note that the 'price' paid for this improvement is asignificant reduction of the area covered. This fact can only be changed with theuse and development of more powerful computers.

7 . U s in g M O S w i t h U K M E S O F o r ec a st s

To see whether it was possible to correct the 10 m wind from the UK MESOmodel using MOS, a MOS model more sophisticated than the one mentionedabove has been developed.

The MOS approach used to predict UK MESO wind speeds adjusted for localeffects is the following: The predicted value of wind speed tb was assumed tobe a linear function of the forecast value of wind speed output by the mesoscalemodel w:

= r w (5)


18/25

188 L. LANDBERG A ND S.J. WATSON

2 . 0 . . . . . , , , , i , , . . . . , , , z ; . . . . . . , , i , , , , ,

Itl

E

1.0

0.0

- 1 . o . . . . . . . . . 1 'o . . . . . . . 2 'o . . . . . ~ o

L o o k - a h e a d t i m e ( h o u r s )

Fig . 11 . The m ean e r ro r ( in m/s , deno ted by c i rc les ) and rms e r ro r ( in m/s , deno ted by squares )o f th e H I R L A M / WA S p m o d e l (o p e n s y m b o ls ) c o m p a r e d t o th e U K M E S O m o d e l c o m b i n e d w i thWAsp ( so l id symbols ) fo r Manches te r fo r the en t i re pe r iod (December 1990 to November 1991) .The look-ah ead time (in hou rs) is a long the :c-axis.

wh ere r i s a r eg ress ion cons tan t w hich dep ends on the l eve l s o f pa ram ete r s fo rw h i c h f o r e c a s t i n g a c c u r a c y i s f o u n d t o v a r y s y s t e m a t i c a l l y f o l l o w i n g a n A N C O -VA ( a n a l y si s o f c o v a r ia n c e ) p r o c e d u r e w h e r e t h e o b s e r v e d w i n d s p e e d i s t h e

v a r i a t e a n d t h e U K M E S O w i n d s p e e d i s t h e c o v a r i a t e . A n a l y s i n g 2 3 U . K . m e t .s t a t ions ind ica ted tha t the f ac to r s which a ffec ted the fo recas t ing accuracy mos t ,in a sys temat i c m anner were : season , t ime o f day, fo recas t wind d i rec t ion andforecas t p rec ip i t a t ion as we l l a s the in te rac t ion be tween season and d i rec t ion andbe tween p rec ip i t a t ion and d i rec t ion . These f ac to r s a lmos t ce r t a in ly r e f l ec t loca ltopography and s t ab i l i ty e ffec t s . For each pa ramete r l eve l (o r combina t ion o fpa ramete r l eve l s ) such as r a in o r no ra in fo r p rec ip i t a t ion , day o r n igh t fo r t imeo f d a y e tc . , t he r eg ress ion cons tan t r was ca lcu la ted f rom the r a t io o f the mea no b s e r v e d t o t h e m e a n U K M E S O f o r e c a s t w i n d s p e e d s o t h a t E q . 5 b e c o m e s :

@ (i , j , k , l )= r~ jk l x w ( i , j , 1~, l ) (6)

w h e r e t h e r e g re s s i o n o f t h e U K M E S O o u t p u t w i n d s p e e d o n t o th e p r e d ic t e d w i n dspeed va r i e s depe nd ing on the p reva i l ing l eve l s o f the four s ign i f ican t f ac to r si , j , k , 1 me n t ioned above , such tha t seaso n i i s ove r win te r, sp r ing , su m m er andau tumn, t ime o f day j i s ove r day and n igh t , d i r ec t ion k i s ove r N , NE , E , SE ,S , SW , W and N W and p rec ip i ta t ion l is ove r r a in and no ra in . Th e reg ress ioncons tan t s r i j k l n o w f o r m a m a t r ix o f v a l u e s w h i c h d e p e n d o n t h e p a r a m e t e rlevels .

The abo ve p rocedu re was r epea ted fo r t en U .K. s i t e s and the appropr ia t er i j k lr a t ios ca lcu la te d fo r each s i t e us ing hou r ly da ta fo r the pe r iod A pr i l 1988 to Ma rch1989 . These r a t ios were then app l i ed to the pe r iod o f da ta Apr i l 1989 to March1990. Tab le IV sh ow s the me an and s t andard dev ia t ion o f the r e s idua l o bse rv ed


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SHORT-TERM PREDICTION OF LO CAL W IND CONDITIONS 189

TA B L E I V

M e a n a n d s t a n d a rd d e v i a t i o n o f o b s e r v e d m i n u s f o r e -

c a s t w i n d s p e e d r e s i d u a l s i n m / s f o r t h e p e r i o d o f d a taA p r i l 1 9 8 9 t o M a r c h 1 9 90 c o m p a r i n g U K M E S O a n dU K M E S O / M O S f o r e c a s t s .

S i t e

F o r e c a s t M e t h o d

U K M E S O U K M E S O / M O S

M e a n S .D . M e a n S . D .

Ab erpo r th 1 .78 2 .64 -0 .02 2 .56

Bel fas t -1 .37 1 .99 - l .5 4 2 .13

Be nbe cu la -1 .07 2 .33 -0 .28 2 .22

Bi r m ing ham -0 .89 1 .79 -0.01 1 .59Bla ckp oo l -0 .76 2 .22 0 .27 1 .99

C a i r n g o r m 8 . 8 0 6 . 2 2 0 . 4 7 7 . 2 0

Co lt ish al l - 1 .50 2.02 -0.26 1.87

Ro na ld sw ay -1 .33 2 .51 0 .13 2 .25

St . M aw gan 0 .13 2 .24 0 .15 2 .21

W i c k - 1 .5 2 2 . 3 4 0 . 1 4 2 .1 3

m i n u s f o r e c a s t w i n d s p e e d o v e r a ll h o u r l y f o r e c a s t s d u r i n g t h e A p r il 1 9 8 9 / M a r c h1 9 9 0 p e r i o d f o r b o t h ' r a w ' U K M E S O f o r e c a st s a n d f o r t h e ' c o r r e c t e d ' U KM E S O / M O S f o r e c a s t s f o r m u l a t e d u s i n g th e A p r il 1 9 8 8 / M a r c h 1 9 8 9 s ta t is ti c s.W i th t h e e x c e p t i o n o f t w o s i te s , th e m e a n o f th e r e si d u a l s h a s b e e n r e d u c e d b ythe app l i ca t ion o f the M O S pos t -p roce sso r. S imi l a r ly, i n al l bu t tw o cases , t hes t a n d a rd d e v i a t i o n o f th e r e s id u a l s h a s b e e n r e d u c e d b y t h e u s e o f M O S .

8 . S u m m a r y a n d c o n c lu s io n s

The e igh t d i f f e ren t mode l s used in th i s s tudy, a re l i s t ed in F igure 12 ; fo r mored e t ai l, s e e L a n d b e rg ( 1 9 9 3 ). T h e m o d e l s c a n b a s i c a l ly b e g r o u p e d i n t o t w o c l a s s -es :

1 . M o d e l s t h a t u s e n u m e r i c a l w e a t h e r p r e d i c t i o n m o d e l s ( N W P ) ( s u c h a s H I R -L A M a n d t h e U K M E S O m o d e l ) .

2 . M o d e l s t h a t a r e b a s e d s o l e l y o n o b s e r v a t i o n s .T h e f ir st g r o u p c a n b e s u b d i v i d e d i n to m o d e l s t h a t u s e p h y s i c a l m o d e l s o n l y

( th e H I R L A M / WA S p in i ts n e u tr a l a n d s t a b i l i t y - d e p e n d e n t v e r s i o n s a n d t h e U K

M E S O / WA S p m o d e l s ) a n d m o d e l s t h a t ar e b a s e d o n s o m e s ta t is ti c al k n o w l e d g e o fp a s t o b s e r v a t i o n s ( t h e t w o M O S ( M o d e l O u t p u t S t a t i s t i c s ) m o d e l s , o n e b a s e d o na l inea r r e l a t ion and ano the r based on a r e l a t ion gene ra t ed by a neura l ne twork) .L i k e w i s e , t h e s e c o n d g r o u p c a n b e s u b d i v i d e d i n t o t w o c l a s s e s : o n e t h a t d o e s


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190 L. LAND BERG AND S.J. WNFSON

I I } O

~ [ L in ea r M odel ] l inear

' - - - N e ura l N e tw o rk ~ - - - ~ n n , p r e d

. . . . . . . - - 0 H/W

0 ,nosO

0 mo.~ (nn )

O K M E S O n] . . . . . . . . " - - [ M O S , r eg r es s io n Aq w m e s o + M O S

" ' ~ . . . . . ~ m e s a + W A s P

Fig. 12. An ov erv iew of the different mo dels used to predict the local wind condit ions.

no th ing to the obse rva t ions ( the pe r s i s t ence mode l ) and one tha t pe r fo rms somesor t o f t rans fo rmat ion o f the obse rva t ions ( the l inea r and the neura l ne tw orkm o d e l s ) .

The em phas i s in th is paper has been on the deve lopm ent o f the neu t ral m ode lus ing ou tpu t f rom HIRLAM, t r ans fo rming th i s to the su r face l aye r, and conec t ingthe re su l t ing w ind fo r loca l e ffec t s us ing ou tpu t f rom the WAsp mode l ; The neu t ra lmode l has a l so been ex tended to inc lude s t ab i l i ty dependence .

8 . 1 . C O M PA R I N G T H E 8 M O D E L S

In F igures 13 and 14 the mean e r ro r and the rms e r ro r o f the e igh t mode l s a reg iven fo r 2 s ta t ions . B i rming ham , ca tegor i se d as ' goo d ' , i e the s t a t ions ' s obse r-va t ions a re we l l p red ic ted (a s compared to pe r s i s t ence ) by the neu t ra l ve r s ion o fthe HIRL AM /WA Sp mo de l , and Sa lamanca , a ' bad ' s t a tion . Th i s ra t io o f ' good 'to ' bad ' i s no t r ep resen ta t ive o f the 50 s t a t ions s tud ied , s ince a t l eas t 80 pe r cen to f these a re l abe l l ed a s ' go od ' . I t i s we l l know n, how ever, t ha t one l ea rns , no tf rom the successes , bu t f rom the f a i lu res .

To ma ke a f a ir compa r i son o f the d i ff e ren t mod e l s , on ly da ta f rom the la s tha l f o f the pe r iod ( i e f rom June 1991 to N ov em be r 1991) have been used in theeva lua t ion fo r a l l t he mode l s .

8 . 2 . C O N C L U S I O N S

A n u m b e r o f c o n c l u s i o n s c an b e d r a w n :


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SHORT-TERM PREDICTION OF LOCA L WIND CONDITIONS 19 1

. . . . S . a . . n c a

i i : i : : iii i'! 1 1 l ] iii iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiI:::' , [ ] ~ N I - ' : "

m o s O m e s o ~WA s P n n, p re d ~ t s i s l

Fig . 13 . The com par ison of the e ight mod els for Sa lamanca . The f ir st bar (of the two for eachmodel ) i s the mean er ror ( in m/s) and the second i s the rms er ror (a l so in m/s) . An explanat ionof the d i fferent abbrevia t ions of the d i fferent mo dels can be fou nd in Figure 12. 'N /A ' means tha tthe UK M ESO forecas t i s not ava i lab le , because the s ta t ion i s not wi th in the area covered by themodel . Sa lam anca i s a 'bad ' s ta t ion meaning tha t the HIRLAM/WASp m odel does n ' t p redic t i t verywel l (as com pared to pers i s tence) .

E

41Birmingham

+18h

6 , j . . . . " ~ " "

- 11 i. , w ' , . ~ l = . i , ; ~ o . , - , ~ ' J i ~ '

r n o s 0 r n e s e* WA s P n n ,p r ed p e r s is t

Fig . 14 . The com par ison of the e ight mo dels for Bi rmingham . See Figure 13 for explanat ion .Birmingham is a 'good ' s ta t ion .

- T h e p e r f o r m a n c e o f e x i s t in g fo r e c a s t m e t h o d s ( m a i n l y p e r s i s t e n c e ) h a s b e e n

s u r p a s s e d s i g n i f i ca n t l y b y t h e m e t h o d s d e v e l o p e d a n d p r e s e n t e d i n t h is s tu d y .

- A t s i t e s w i t h h i g h m e a n w i n d s p e e d s , th e n e u tr a l H I R L A M / W A S p m o d e l i s

f o u n d to p e r f o r m p a r t i c u l a r l y w e ll .- I f n o d a t a a r e a v a i l a b l e a t t h e s i te ( t h e t y p i c a l c a s e ) , t h e n e u t r a l v e r s i o n o f

t h e H I R L A M / W A S p m o d e l s h o u l d b e u s ed . I f a n N W P m o d e l e x is t s w i th

a h i g h e r r e s o l u t i o n t h a n H I R L A M , i t s h o u l d b e u s e d i n s t e a d . I f t h e s it e i s


22/25


d o m i n a t e d b y s t r o n g l o c a l t h e r m a l l y - d r i v e n c i r c u l a t i o n s , t h e m o d e l s h o u l dbe used wi th g rea t cau t ion .

- Fo r look -ahea d t imes sho r t e r t han 3 to 6 hours , t he pe r s i s t ence m ode l shou ld

b e u s e d , s i n c e n o n e o f t h e m o d e l s p e r f o r m s a s w e ll .- I f on - s i t e da ta a re ava i lab le , tw o app roach es can b e taken :

= I f o u t p u t f r o m N W P m o d e l s i s a t h a n d , t h e f o r e c a s t u s in g t h e n e u t r alv e r s i o n o f th e H I R L A M / W A S p m o d e l s h o u l d b e u s ed , c o r r e c t e d w i t h t h el i n e a r M O S m o d e l .

= I f n o o u t p u t f ro m N W P s i s a t h a n d , t h e l in e a r c o r r el a ti o n m e t h o d b a s e do n o b s e r v a t i o n s o n l y s h o u l d b e u s e d .

- T h e s t a b i li t y - d e p e n d e n t v e r s i o n o f t h e n e u tr a l m o d e l f a i le d t o p r o d u c e a n yi m p r o v e m e n t o v e r t h e n e u tr a l m o d e l , m a i n l y b e c a u s e o f t h e d i ff i cu l ty f o r

the NWP mode l in p red ic t ing the hea t f luxes a t t he su r face .- T h e n e u r a l n e t w o r k s p e r f o r m e d q u i t e w e l l , o f t e n b e t t e r t h an t h e n e u t ra l

H I R L A M / WA S p m o d e l , b u t s i n c e t h e m u c h s i m p l e r li n e ar m o d e l s p e r f o r m e de q u a l l y w e l l ( f o r t h e M O S v e r s i o n a n d f o r t h e p r e d i c t i o n b a s e d o n o b s e r -va t ions on ly ) , i t mu s t be conc lu ded tha t neura l ne tw orks - i n th is s tudy -h a v e n o t s h o w n a n y o u t s t a n d i n g p e r f o r m a n c e . T h i s i s m o s t l i k e l y d u e t o t h efac t t ha t, even th oug h the p rob lem of p red ic t ing the wind loca l ly i s a ha rdone , pe r s i s t ence pe r fo rms qu i t e we l l , and the re i s no t much fo r the neura ln e t w o r k t o ' l e a r n ' .

A c k n o w l e d g e m e n t s

T h i s s t u d y h a s b e e n f u n d e d b y t h e D a n i s h R e s e a r c h A c a d e m y a n d t h e E E CJ O U L E - p r o g r a m m e u n d er co n tr ac t J O U R - 0 0 9 1 - C ( M B ) . T h e H I R L A M d a ta a ndt h e o b s e r v a t i o n s h a v e b e e n p r o v i d e d b y t h e D a n i s h M e t e o r o l o g i c a l I n s t i t u t e .T h e B r i t is h M e t e o r o l o g i c a l O ff i c e h a s t h ro u g h R u t h e r f o r d A p p l e t o n L a b o r a t o r yp r o v i d e d t h e d a t a f r o m t h e U K M E S O m o d e l .

W e w o u l d l i k e t o t h a n k D r A k s e l W a l l 0 e H a n s e n , U n i v e r s i t y o f C o p e n h a g e n ,

G e o p h y s i c a l I n st it u te , D r E r ik L u n d t a n g P e t e r se n , D r S 0 r e n E . L a r s e n , N i e l sG . M o r t e n s e n a n d J a k o b M a n n , a l l f r o m D e p a r tm e n t o f M e t e o r o l o g y a n d W i n dE n e rg y, R i s e N a t i o n a l L a b o r a t o r y f o r h e l p f u l d i s c u s s i o n s .

W e w o u l d a l s o l ik e t o t h an k M r. G i l R o s s o f th e U . K . M e t . O f f i c e f o r a d v i c eo n a p p l y i n g M o d e l O u t p u t S t a t i s t i c s t o t h e m e s o s c a l e m o d e l w i n d f o r e c a s t s .

A t t h e m e t . s t a t i o n a t R A F D u n k e s w e l l , w e w o u l d l i k e t o t h a n k M r J o h nP a w l e y f o r b e i n g v e r y h e l p f u l . F i n a l l y, w e w o u l d l i k e t o t h a n k R a s m u s P o u l s e nf o r d i g i t i s i n g t h e m a p s o f D u n k e s w e l l .


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SHORT-TERM PREDICTION OF LOC AL W IND CONDITIONS 193

Appendix: Ta ble VA l i st o f t h e re s u l t s o f t h e n e u t r a l H I R L A M A VA S p m o d e l f o r t h e 5 0 s t a ti o n s u s e d i n t h is s t u d y,e x e m p l i f i e d b y t h e + 1 8 h o u r f o r ec a s t . T h e f o r e c a s t s a re c o m p a r e d t o t h e + 1 8 h o u r p e r s i s t e n c e

f o r e c a s t. T h e c o l u m n m a r k e d ' e , H / W ' g i v e s t h e m e a n e r r o r ( in m / s ) f o r t h e s ta t io n f o r th e + 1 8h o u r f o r e c a s t , t h e c o l u m n m a r k e d ' e , p e r s ' g i v e s t h e m e a n e r r o r ( i n m / s ) f o r t h e p e r s i s t e n c em o d e l fo r t h e + 1 8 h o u r f o re c a st . T h e c o l u m n s m a r k e d ' R M S E , H / W ' a n d ' R M S E , p e r s ' g i v e t h er o o t - m e a n - s q u a r e e r r o r f o r t h e H I R L A M / W A S p m o d e l a n d p e r s i s te n c e f o r th e + 1 8 h o u r f o r e ca s t ,r e s p e c t i v e l y.

N a m e H e i g h t H e i g h t L a t. L o n g . e , e , R M S E , R M S E ,

s t a ti o n a n e m . H / W p e r s H / W p e t s

M i d d e l k e r k e , B 4 . 0 1 2 .7 5 1 . 2 2 . 9 - 0 . 3 6 - 0 . 0 2 2 . 43 3 . 6 2

F l o r e n n e s , B 2 8 0 . 0 6 . 4 5 0 . 2 4 . 7 - 0 . 5 5 - 0 . 0 1 1 .8 4 2 . 5 8

L i s t / S y l t , D 2 6 . 0 1 2 . 1 5 5 . 0 8 . 4 - 0 . 7 4 - 0 . 0 1 2 . 9 9 3 .6 1

Bre me n, D 3 .0 10 .0 53 .1 8 .8 0 .38 -0 .0 0 1 .87 2 .54

Ha nno ver, D 51 .0 10 .0 52 .5 9 .7 0 .25 -0 .0 1 1 .64 2 .39

Ber l in , D 48 .0 10 .0 52 .5 13 .4 -0 .1 8 0 .01 1 .60 2 .39

M t i n c h e n , D 5 2 7 . 0 1 0 .0 4 8 .1 11 .7 - 0 . 7 6 - 0 . 0 0 2 . 2 8 2 . 3 6

~ l b o rg , D K 3 . 0 1 0 . 0 5 7.1 9 . 9 0 . 1 2 - 0 . 0 1 2 . 1 2 3 . 0 9

Beld r inge , D K 17 .0 8 .0 55 .5 10 .3 -0 .7 2 0 .03 2 .11 2 .76

K a s t ru p , D K 5 . 0 1 0 .0 5 5 . 6 1 2.7 - 0 . 4 6 - 0 . 0 0 2 . 07 2 . 80

R 0 n n e , D K 1 6 .0 1 0 .0 5 5.1 1 4.8 - 0 . 3 7 0 . 0 2 2 . 35 2 . 9 8

Za rag oza , E 247 .0 23.0 41.7 - 1 .0 - 1 .22 0.0 4 3.91 3.67

S a l a m a n c a , E 7 9 0 . 0 1 0.3 4 0 . 9 - 5 . 5 2 . 5 7 - 0 . 0 1 4 . 3 0 2 . 9 3A l b a c e t e , E 7 0 0 . 0 5 . 7 3 8 . 9 - 1 . 9 - 0 . 3 9 0 . 01 3 .5 1 3 . 55

Alm er ia , E 20 .0 6 .7 36 .9 -2 .4 - 1 .58 0 .02 3 .76 3 .71

Va l en t ia , E I 1 8.0 1 2.0 5 1 .9 - 1 0 . 3 - 0 . 4 6 - 0 . 0 2 2 . 64 4 . 07

S h a n n o n , E I 8 .0 1 2.0 5 2 .7 - 8 . 9 - 0 . 0 7 - 0 . 0 0 2 . 26 3 .5 5

B e l m u l l e t , E I 9 . 0 1 2 .0 5 4 . 2 - 1 0 .0 - 0 . 2 3 0 . 0 0 2 . 6 2 4 . 2 6

M a l i n H e a d , E I 2 4 .0 2 1 .0 5 5 .4 - 7 . 3 - 0 . 7 2 - 0 . 0 1 3 .0 8 4 .7 3

A b b e v i l l e , F 7 7 . 0 11.0 5 0.1 1 .8 - 0 . 2 7 - 0 . 0 3 2 . 03 3 . 0 9

B r e s t, F 1 0 3 .0 1 0.5 4 8 . 5 - 4 . 4 - 0 . 2 0 - 0 . 0 1 1 .8 8 2 . 9 0

Lyo n , F 201 .0 12 .0 45 .7 5 .0 -1 .9 1 0 .03 3 .44 3 .17

B o r d e a u x , F 5 1 . 0 11.0 4 4 . 8 - 0 . 7 - 0 . 2 0 0 . 0 0 1 .9 6 2 . 4 6Carc asson ne , F 130 .0 11 .2 43 .2 2 .3 -2 .8 6 0 .01 4 .03 3 .72

Istres , F 24.0 10.0 43.5 4.9 - 1 .11 0.04 2.86 3.75

B e n b e c u l a , G B 6 . 0 1 0.0 5 7 .5 - 7 . 4 - 0 . 9 9 0 . 0 0 3 . 04 4 .2 4

E s k d a l e m u i r, G B 2 4 9 .0 1 0 .0 5 5 .3 - 3 . 2 - 0 . 4 5 - 0 . 0 2 2 . 42 3 .2 7

Val ley, GB 10 .0 16 .0 53 .3 -4 .5 0 .06 - -0 .03 2 .86 4 .21


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194

Table V eontinued.

L. LANDBERG AND S.J. WATSON

Name Height Height Lat. Long. e, e, RMSE, RMSE,

station ahem. H/W pers H/W pers

Blackpool, GB 10.0 12.0 53.8 -3 .0 -0 .6 0 -0 .0 5 2.34 3.26Manchester, GB 70.0 10. 0 53.4 -2 .3 -0 .0 9 0.00 1.89 2.88Birmingham, GB 94.0 10 .0 52 .5 - 1.7 0.26 0.01 1.76 2.53London, GB 24.0 10.0 5 1 . 5 -0 .5 0.43 0.00 1.89 2.55Exeter, GB 31.0 12. 0 50.7 -3 .4 0.74 -0 .0 1 2.23 3.42Bournemouth, GB 10.0 13.0 50.8 -1 .8 0.48 -0 .0 1 1.91 3.10Wick, GB 35.0 10.0 58.5 -3 .1 -0 .0 7 -0. 01 2.25 3.6lKerkyra, GR 2.0 4.0 39.6 19.9 0. 11 -0 .0 1 2.70 3.44

Athina, GR 28.0 10.0 37.9 23.7 -0 .36 -0 .0 1 2.58 3.42Naxos, GR 9.0 10 .0 37.0 25.4 - 1.29 -0 .1 2 4.3 l 4.77Rodos, GR 4.0 7.0 36.4 28.1 - 1.53 -0 .0 3 3.09 3.10Pisa, I 2.0 6.0 43.7 10.4 - 1.27 0.02 2.46 2.69Brindisi, I 15.0 6.0 40.7 18. 0 -0 .28 -0 .0 1 2.64 3.I7Alghero, I 40.0 10.0 40.6 8.3 1.12 0.01 2.37 3.17Cagliari, I 18.0 6.5 39.3 9.1 -1.52 -0 .0 1 2.90 3.24Schiphol, NL -4 .0 10.0 52.3 4.8 -0.1 1 -0 ,0 1 2.04 3.25Eelde, NL 5.0 10 .0 53 .1 6.6 0.2 l 0.00 1.83 2.72Eindhoven, NL 20.0 10 .0 51.5 5.4 0.68 0.00 1.78 2.53

Sagres, P 40.0 6.0 37.0 -9 .0 2.29 -0 .0 1 3.80 2.97Viana do Castelo, P 16.0 11.0 41.7 - 8 .8 -0.48 0.00 1.97 2.55Braganga, P 1.0 9.1 41.8 -6 .7 2.54 -0 .04 4.85 2.61Lisboa, P 103.0 7.0 38.8 -9 .1 -0 .19 0.03 2.26 3.15

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