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192 A.S. OMOLAYO

r e t u r n p e r i o d y i e ld s t h e c o r r e s p o n d i n g a r e a l m e a n d e p t h f o r t h e d u r a t i o n a n dr e t u r n p e r i o d .T h e n e e d f o r a r e a l r e d u c t i o n f a c t o r i n e s t i m a t i n g c a t c h m e n t r a i n f a l l f r e -q u e n c i e s f r o m p o i n t r a i n f a l l f re q u e n c i e s h a s l o n g b e e n r e c o g n i z e d . E f fo r ts t oh a v e t h e c o n c e p t a d o p t e d f o r u s e i n d e s i g n f l o o d e s t i m a t i o n b e g a n i n t h eU n i t e d S t a t e s ( U .S . W e a t h e r B u r e a u , 1 95 7). S i m i l a r e f fo r ts w e r e m a d e t w od e c a d e s l a t e r i n t h e U n i t e d K i n g d o m ( N a t u r a l E n v i r o n m e n t a l R e s e a r c hC o u n c i l ( N E R C ) , 1 97 5). H e r s h f i e l d ( 19 6 2 ) i d e n t i fi e d t w o t y p e s o f r e d u c t i o nf a c t o rs , s t o r m - c e n t r e d a n d f i x e d -a r e a , w h i c h a r e b r i e fl y d e s c r i b e d b e l o w , w h i l ea n a t t e m p t w a s m a d e b y B e l l (1 97 6) t o c l a r if y th e m e a n i n g , s i g n i fi c a n c e a n dt h e n e e d f o r a r e a l r e d u c t i o n f a c t o r s ; b u t t h e r e s t i l l r e m a i n s o m e p r o b l e m s i nt h e i r r e c o g n i t i o n a n d a p p l i c a t i o n . O n e s u c h p r o b l e m i s t h e t r a n s p o s i t i o n o fa r e a l r e d u c t i o n f a c t o r s c o m p u t e d f o r a c e r t a i n r e g i o n t o o t h e r r e g i o n s . F o ri n s ta n c e , th e U n i t e d S t at es r e d u c t i o n f a c to r s h a v e b e e n r e c o m m e n d e d f o r u sei n A u s t r a l i a ( I n s t i t u t i o n o f E n g i n e e r s , A u s t r a l i a , 1 98 7) w h i l e t h o s e o f t h eU n i t e d K i n g d o m h a v e b e e n a d o p t e d i n N o r w a y f o r e s ti m a t in g a r e al r ai n fa llf o r c a t c h m e n t s u p t o 5 0 00 k m 2 ( F o r l a n d a n d K r i s t o f f e r s o n , 1 98 9). T h e p r e s e n ts t u d y i n v e s t i g a t e s t h e s u i t a b i li t y o f t h e U n i t e d S t a t e s v a lu e s t o t h e A u s t r a l i a ne n v i r o n m e n t .Storm -centred areal reduction facto rs

T h e a r e a i n w h i c h t h e r a i n f a l l s i s n o t f i x e d b u t c h a n g e s w i t h e a c h s t o r m .T h e r e p r e s e n t a t i v e p o i n t f o r c a l c u l a t i n g th e a r e a l r e d u c t i o n f a c t o r i s t h e c e n t r eo f t h e s t o rm , d e f in e d t o b e t h e p o i n t o f m a x i m u m r a in f a ll . T h i s a ls o c h a n g e sw i t h e a c h s t o r m . T h e a r e a l r e d u c t i o n f a c t o r i s g i v e n b y :A R F = R / P (1)w h e r e R i s t h e a r e a l s t o r m r a i n f a l l e n c l o s e d b y a s e l e c t e d i s o h y e t a n d w i t h i nw h i c h t h e r a i n f a l l is e v e r y w h e r e e q u a l t o , o r g r e a t e r t h a n , t h e v a l u e f o r t h ei s o h y e t , a n d P i s t h e m a x i m u m p o i n t r a i n f a l l ( a t s t o r m c e n t r e ) . S i n c e t h ep o s i ti o n o f t his m a x i m u m p o i n t m e a s u r e m e n t o n th e g r o u n d c a n n o t b ep r e d i c t e d a h e a d o f th e s t o r m a r ri v a l, t h e a r e a is c h o s e n o n l y a f t er t h e s t o r mh a s a r r iv e d . T h e a v e r a g e o f C o v e r m a n y e v e n t s m a y b e r e g a r d e d a s t h e ' t r u e 's t o r m - c e n t r e d a r e a l r e d u c t i o n f a c t o r f o r t h e r e g i o n . S t o r m - c e n t r e d a r e a lr e d u c t i o n f a c t o r s c a n b e u s e d i n p r o b a b l e m a x i m u m r a i n f a l l s t u d i e s b u t a r ei n c o r r e c t f o r e s t i m a t i n g a r e a l r a i n f a l l o f a p a r t i c u l a r f r e q u e n c y f r o m p o i n tr a in f a l l s . I t w i l l , t he r e f o r e , no t be dea l t w i th f u r the r i n t he p r e sen t s tudy .Fixed-area reduction fac tor s

T h e f i x e d - a r e a r e d u c t i o n f a c t o r i s u s e d i n o r d e r t o d e r i v e c r i t i c a l s t o r m s

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TRANSPOSITION OF AREAL REDUCTION FACTORS FOR RAINFA LL FREQUENCY ESTIMATION 195The significance of fixed-a rea reduction fac tor s

F l o o d f r e q u e n c y e s t i m a t i o n u s i n g t h e f i x e d - a r e a r e d u c t i o n f a c t o r i sr e q u i r e d n o t o n l y f o r e n g i n e e r i n g d e s i g n o f d a m s p i ll w a y s b u t a l so a s a b a s is f o rm e a s u r e s t o m i t ig a t e f l o o d h a z a r d s , w h e t h e r t h e s e m e a s u r e s i n v o l v e s t ru c t u r a lw o r k s , d r a i n a g e , l a n d - u s e r e g u l a t i o n o r f l o o d w a r n i n g s y s t e m s . S t r e a m f l o wd a t a g e n e r a l l y p r o v i d e t h e m o s t r e l i a b le e s ti m a t e s o f f l o o d f re q u e n c i e s . B u tr a in f a ll d a t a a r e u s u a l l y m o r e w i d e ly a v a i la b l e t h a n s t re a m f l o w d a t a , b o t ha r e a l l y a n d t e m p o r a l l y . I t is a ls o a n a c c e p t a b l e e n g i n e e r i n g p r a c t i c e , ins i t u a t i o n s w h e r e s t r e a m f l o w d a t a a r e u n a v a i l a b l e o r g r o s sl y i n a d e q u a t e , t o u s ea r e a l r a i n f a l l d a t a a s i n p u t i n t o a n a l y t i c a l p r o c e d u r e s f o r e s t i m a t i n g f l o o dp e a k s ( I n s t i t u t i o n o f E n g i n e e r s , A u s t r a l i a , 1 98 7).T h e ' R a t i o n a l ' m e t h o d o f f lo o d e s t im a t i o n , e x p re s se s fl o o d p e a k a sQ r = K I r A (3)w h e r e Q r r e p r e s e n t s t h e f l o o d p e a k w i t h a v e r a g e r e t u r n o f T y e a r s , I r is a r e aR r / d u r a t i o n ( w h e r e R r is a r e a l r a in f a l l w i t h r e t u r n p e r i o d o f T y e a rs ) w h i l e Ais t h e c a t c h m e n t a r e a . T h e c o n s t a n t K d e p e n d s o n t h e u n i t s u s e d , t h e t y p e o fc a t c h m e n t a n d r e t u r n p e r i o d . IT a n d R r s h o u l d b e e s ti m a t e d f r o m w e i g h te da v e r a g e p o i n t r a i n f a l l P r a d j u s t e d b y a n a r e a l r e d u c t i o n f a c t o r .THE TRANSPOSITION OF AREAL REDUCTION FACTORS

N o t m u c h w o r k h a s b e e n d o n e t o e s t im a t e v a l u es o f a re a l re d u c t i o n f a c t o r si n c o u n t r i e s o t h e r t h a n t h e U n i t e d S t a t es o f A m e r i c a ( U S ) , th e U n i t e dK i n g d o m ( U K ) a n d N e w Z e a l an d ( A .I . T o m l i n s on , p e rs o n a l c o m m u n i c a t io n ,1 9 8 3 ) . T h i s i s b e c a u s e o f t h e s p a r s e n e t w o r k s o f r a i n f a l l s t a t i o n s a n d s h o r tr e co r d s . I n A u s t r a li a a n d e l se w h e r e t h e U S v a l u e s a re g e n e r a l ly a s s u m e d w h e nt h e n e e d t o u s e a r e a l r e d u c t i o n f a c t o r s i s r e c o g n i z e d . H o w e v e r , a r e t h e U Sv a l u e s a p p r o p r i a t e t o A u s t r a l i a ? T h e r e i s n o b a s i s f o r u s i n g t h e m o u t s i d e t h eU S o t h e r t h a n t h e a s s u m p t i o n t h a t c l i m a t ic a l ly s i m i la r ar e a s s h o u l d h a v e t h es a m e v a l u e s. I n t h e c a se o f A u s t r a li a , w h i l e p a r t s o f A u s t r a li a a n d t h e U S m a yb e s a i d t o b e c l i m a t i c a l l y s i m i l a r b e c a u s e t h e y h a v e s i m i l a r m e a n a n n u a lr a in f a ll , m e a n a n n u a l t e m p e r a t u r e a n d g e n e r a l t o p o g r a p h y , o r o g r a p h i c e ff ec tso n r a i n f a l l a r e m u c h s t r o n g e r i n t h e U S ( B r u n t , 1 97 0) le a d i n g t o d i f fe r e n ts t o r m t y p e s a n d f r e q u e n c i e s o f o c c u r r e n c e . I t i s , t h e r e f o r e , a r g u a b l e w h e t h e rt h e U S - b a s e d a r e a l r e d u c t i o n f a c t o rs w i ll s u it t h e A u s t r a l i a n e n v i r o n m e n t .METHODOLOGIES

A n u m b e r o f m e t h o d s o f e s t im a t i n g fi x e d -a r ea r e d u c t i o n f a c t or s a r e

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1 9 6 A .S . O M O L A Y O

d o c u m e n t e d . E m p i r i ca l m e t h o d s h a v e be e n a p pl ie d f or t he U S a n d U K a n di n c l u d e t h a t o f B e ll w h i le t h e o r e t i c a l m e t h o d s i n c l u d e t h o s e o f R o c h e ( 19 6 3)a n d R o d r i g u e z - I t u r b e a n d M e j i a ( 1 9 7 4 ) ; a s w e l l a s t h e t h e o r e t i c a l - e m p i r i c a lm e t h o d o f M y e r s a n d Z e h r ( 19 80 ). S o m e o f th e se m e t h o d s a re b ri ef lye x p l a i n e d b e l o w . I n e q n s . ( 4 ) , ( 5 ) a n d ( 6 ) t h a t f o l l o w t h e s y m b o l s h a v e t h ef o l l o w i n g m e a n i n g s : Uu is th e a n n u a l m a x i m u m p o i n t r a i n f a ll a t s t a t i o n i i ny e a r j ; U,~ is th e p o i n t r a i n f a ll a t s t a t i o n i o n t h e d a y t h e a n n u a l m a x i m u m a r e a lr a i n f a l l o c c u r s i n y e a r j ; w is t h e T h i e s s e n w e i g h t i n g f a c t o r f o r t h e s t a t i o n ; Iis t h e n u m b e r o f s t a t i o n s ; J i s t h e l e n g t h o f d a t a r e c o r d ( y e a rs ) ; r i s t h e r a n k .US Weather Bureau method

U s i n g T h i e s s e n ( 1 9 11 ) w e i g h t i n g f a c t o r s, t h e a r e a l r a in f a ll o f e a c h e v e n t o ft h e c h o s e n d u r a t i o n is c a l c u l a t e d a n d t h e h i g h e s t o f th e s e in e a c h y e a r o fr e c o r d i s s e le c te d . T h e m e a n o f th e r e s u l ti n g a n n u a l s er ie s t h r o u g h o u t t h el e n g t h o f re c o r d i s c o m p u t e d . T h i s m e a n c o n s t it u t e s t h e n u m e r a t o r o f e qn . (4).T h e n e x t s t e p is t o p i c k t h e h i g h e s t p o i n t m e a s u r e m e n t s a t e a c h s t a t i o n i n e a c hy e a r . T h e g r a n d m e a n ( o r p o o l e d m e a n ) o v e r a ll st a t i o n s a n d o v e r a ll ye a r s o fr e c o r d is th e d e n o m i n a t o r o f t h e e q u a t i o n . T h e a r e a l r e d u c t i o n f a c t o r i se x p r e s s e d s i m i l a r t o e q n . ( 1 ) a sa R V u s Z Y', w,V;~/Z Z ~ (4)

j i j i

U K me tho dA l t h o u g h a r e a l r a in f al ls n e e d t o b e c o m p u t e d , t h e ir o n l y u se in t h is m e t h o d

is t o i d e n ti f y t h e d a y t h e a n n u a l m a x i m u m e v e n t o c c ur s. T h e p o i n t m e a s u r e -m e n t s , U ,'s , o f t hi s m a x i m u m a r e n o t e d . T h e m a x i m u m p o i n t r e c o rd i n g s, U~,a t e a c h s t a t i o n i n t h e s a m e y e a r a r e i d e n t i f i e d . T h e r a t i o o f U ,; t o U~ a t e a c hs t a t i o n i n t h e y e a r i s f o u n d . T h e g r a n d m e a n o f t h es e r a ti o s o v e r a ll s t a t io n sa n d a ll y e a r s o f r e c o r d i s a d o p t e d a s th e a r e al r e d u c t i o n f a c t o r . T h e U Km e t h o d is n o t a s t r a n s p a r e n t a s th e U S a n d B e ll 's m e t h o d s ; t h e a s s u m p t i o n so n w h i c h i t i s b a s e d d o n o t a p p e a r t o b e d o c u m e n t e d .A R F u K = (1 /IJ ) Z Y . UUU~j (5)

j i

Bell s meth odI n a p p l y i n g t hi s m e t h o d t h e v a l u es in t h e a n n u a l m a x i m u m a r ea l r a i nf a lls er ie s a r e r a n k e d . T h e v a l u e s in t h e a n n u a l m a x i m u m p o i n t r a in f a l l se ri es a t

e a c h s t a t i o n a r e a l s o r a n k e d . T h e T h i e s s e n w e i g h t e d m e a n o f p o i n t r a i n fa l ls

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TRANSPOSITION OF AREAL REDUCTION FACTORS FOR RAINFALL FREQUENCY ESTIMATION 197

of the same rank is then computed, resulting in annual series of weightedmaximum point rainfalls. This is essentially a device for pooling individualfrequency into a single representative one. The areal reduction factor Cr ofrank r is the ratio of the areal rainfall of rank r to the weighted average pointrainfall of the same rank. This indicates the variation in the areal reductionfactor with rank and hence return period. If areal reduction factors areassumed to be independent of the return period, as with the US and UKmethods, then the mean of C r over all ranks estimates the areal reductionfactor for the location:ARFBELL = (1/J)~ C r = ~ - . w i U i j ) r / ~ - ~ w i U t j ) r (6)R o d r i g u e z - I t u r b e a n d M e j i a m e t h o d

This is a correlation approach based on spatial process. It assumes the pointrainfall process to be a stationary time series and its correlation function tobe isotropic and separable into spatial and time-dependent parts. Given thatA is the size of the area being considered the areal reduction factor in thismethod is defined as:A R F R I M = r l A 2 (7)The symbol r A is the expected correlation coefficient between two pointsrandomly selected on the chosen location but separated by the 'characteristicdistance', DA One of the points is usually a key or reference station and thecharacteristic distance depends on the shape and size of the area.

The choice of the key station and the dilemma of which correlation coeffi-cient value to pick if more than one station happens to be positioned at thecharacteristic distance constitute obstacles to the practical application of thisapproach. The assumption o f isotropy implies that the correlation coefficientis a function only of the distance between stations and not their orientationbut this does not appear to apply in the network of stations in the Australiancapital cities. Matern (1960) and Rodriguez-Iturbe and Mejia (1974) showthat the characteristic distance may be expressed bydA = d I D A / D I (8)where dl, with a magni tude of 0.5108, is the characteristic distance for alocation whose area is l km 2 while D A and DI are corresponding distanceswithin area size A and a similarly shaped area size of I km 2, respectively. If thelocation is circular these will be their respective radii so thatd A = 0.9054 D A . (9)The characteristic distance thus approximates 16.2 km for a 1000 km 2 circular

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TRANSPOSITION OF AREAL REDUCTION FACTORS FOR RAINFALL FREQUENCY ESTIMATION 199east of the city. Darwin, on the other hand, receives 1500 mm year ~ duringthe annual wet season. The rain comes mainly from thundersto rms associatedwith the northwest monsoo n which affects the city from November to March.The period from May to September is, however, usually warm and dry.Perth's rainfall is similarly unevenly distributed through the year. January andJune monthly mean rainfalls in Per th are 8 mm and 180 mm, respectively.Long dry spells lasting more than 45 days at a time are not uncommonbetween October and February. In contrast to Perth and Darwin,Melbourne's mean annual rainfall of 660mm is almost evenly distributedthrough the year. Summer rains in Melbourne are generally of thunders tormorigin while winter rains are associated mainly with the passage of frontaldepressions.

Hobart lies at the foot of Mt. Wellington (1270m), 30km from the opensea. Its 600 mmy ear ~ rainfall is almost evenly distributed through the year.However, Mt. Wellington causes large spatial variations in rainfall distribu-tion between the various parts o f the metropol itan area such that The Springswhich lies on the slope of the mountain often receives over 1400mm of rainper year. Brisbane's rainfall is not seriously affected by orography as is thecase with Hobart. The reason being that Brisbane is situated in the coastalplains surrounded by hills generally less than 170m high. Brisbane receivesboth summer and winter rains. Much of the summer rainfall is due toconvective storms within troughs extending southwards from northernAustralia while winter rainfall is largely associated with the passage of coldfronts extending northwards from the mid-latitude depressions. Sydney'srains are associated with cold fronts and thunderstorms. April is usually thewettest month while September is the driest. However, at least 60 mm of rainis received each month. Canberra is located 100 km inland unlike the othe rcapital cities which are located near the coast. Its rainfall, 622 mm year ~, isalmost evenly distributed through the year. And since the city is generallyunder the influence of westerly winds variations in the rainfall are largely dueto variations in the strength and regularity of the westerly winds.Criteria for choosing the locations

Circular areas of 100, 200, 250, 500 and 1000 km 2 were chosen within eachcity. Darwin and Canberra were left out because of their inadequate data. Thestations within the selected cities have long records and the networks ofraingauges are more dense than elsewhere in Australia. The location of thecircular area within each city was adjusted to enclose the maximum numberof current rainfall stations with at least 30 years of data. The distributions ofthe network of stations within each of the six chosen cities are presented in

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200 A S OMOLAYO

F i g . 4 f o r t h e 1 00 0 k m 2 c a se . E a c h c i r c u l a r a r e a w a s d i v i d e d i n t o T h i e s s e np o l y g o n s to c o m p u t e t h e w e i g h t i n g fa c t o r s t o b e u s e d w i t h t h e s t a ti o n s .D a t a s o u r c e s a n d a n a l y s i s

T h e a v a i l a b il i ty o f t h e 1 d a y d a t a is m u c h b e t t e r t h a n f o r o t h e r d u r a t i o n s ,s o t h e y w e r e g e n e r a l l y u s e d i n t h e c a l c u l a t i o n s . D a t a w e r e s u p p l i e d b y t h eC o m m o n w e a l t h B u r e a u o f M e t e o r o l o g y i n M e l b o u r n e a n d S y d n e y a n d f r o mt h e S y d n e y M e t r o p o l i t a n W a t e r, S e w e r a g e a n d D r a i n a g e B o a r d . T h e d a t ac o v e r t h e p e r i o d 1 9 5 4 - 1 9 8 3 . T h e d a t a s i t u a t i o n f o r s h o r t e r d u r a t i o n s w a sm u c h l e ss s a ti s f a c to r y d u e t o s p a r s i t y o f p l u v i o g r a p h s t a t io n s w h i c h a l so w e r em o s t l y u n p r o c e s s e d . 1 h d u r a t i o n d a t a f o r e i g h t s t a ti o n s w i t h in t h e M e l b o u r n em e t r o p o l i t a n ar e a w e r e p ro v i d e d by t h e C o m m o n w e a l t h B u r e au o f M e t e o r o l-o g y i n M e l b o u r n e .

A s i s u s u a l fo r m o s t r a i n f a ll r e c o r d s , th e r e w e r e g a p s i n t h e d a t a . T h e g a p sw e r e f ill ed u s i n g s t a n d a r d m e t h o d s o f m a k i n g e s ti m a t e s o f m i s s in g d a t a( I n s t i t u t i o n o f E n g i n e e r s , A u s t r a l i a , 1 95 8; W i e s n e r , 1 97 0, p . 1 31 ). T h e d a t ap e r i o d f i n a l l y c h o s e n f o r e a c h c i r c u l a r a r e a w a s f i x e d t o e n s u r e m a x i m u mn u m b e r o f s ta t io n s w i t h a c o n c u r r e n t a n d a l m o s t u n b r o k e n r e co r d . T h i sr e d u c e d t h e a m o u n t o f g a p f il li ng , b u t a l s o r e d u c e d t h e l e n g t h o f r e c o r d b e l o w3 0 y e a r s in s o m e c a p ti a l c it ie s. T h e d a t a p e r i o d a n d t h e n u m b e r o f s t a t io n se n c l o s e d w i t h i n t h e 1 00 0 k m 2 a r e a i n e a c h c i t y a r e p r e s e n t e d i n T a b l e 1.

C a r t e s i a n c o o r d i n a t e s w e r e d e t e r m i n e d f o r th e p o s i t i o n o f e a c h s t a t io nr e f e r r e d t o a c o m m o n o r i g i n w i t h i n e a c h c i r c u l a r a r e a . T h e c o o r d i n a t e s w e r en e e d e d t o d e t e r m i n e t h e i n te r s t a ti o n d i s t an c e s a s re q u i r e d f o r t h e c o m p u t a t i o nO f d A . T h e a r ea l r e d u c t i o n f a c to r s e s ti m a t e d b y t h e f o u r m e t h o d s t o g e t h e r w i t ht h e a v e r a g e s a r e g i v e n i n T a b l e s 2 - 5 f o r t h e l d a y r a in f a ll d u r a t i o n . T h e s ea v e r a g e s h a v e b e e n p l o t t e d i n F i g . 2 f o r e a c h m e t h o d . I n t h e f i g u r e A R F u s ,f o r in s t a n c e , r e fe r s to t h e a v e r a g e r e d u c t i o n f a c t o r s g i v e n by t h e U S m e t h o d ,a n d s i m i l a r l y f o r t h e o t h e r m e t h o d s . T h e r e d u c t i o n f a c t o r s f o r t h e h o u r l yr a i n f a l l f o r M e l b o u r n e a r e g i v e n i n T a b l e 6 b u t a r e n o t p l o t t e d i n F i g . 2 .RESULTS

C o n s i d e r i n g t h e 1 d a y r e d u c t i o n v a l u e s f ir st , t h e R o d r i g u e z - I t u r b e a n dM e j i a m e t h o d g a v e g e n e r a l l y s m a l l e r v a l u e s f o r t h e a r e a s s t u d i e d t h a n t h eo t h e r m e t h o d s , a s in d i c a t e d b y T a b l es 2 - 5 . W h i le t h e r e d u c t i o n f a c t o r s s h o u l di n c r e a s e a s t h e si ze o f a r e a d e c r e a s e s , t h e v a l u e s f o r H o b a r t a c t u a l l y s h o w am a x i m u m a r o u n d t h e 2 50 k m 2 a r ea f o r a ll m e t h o d s e x ce p t t h e U S m e t h o d .T h i s a n o m a l y m a y b e d u e t o o r o g r a p h i c e f fe c ts s in c e H o b a r t is a h i ll y c it y . A si n d i c a t e d e a r l i e r e a c h c i r c u l a r a r e a w a s a d j u s t e d t o e n c l o s e t h e m a x i m u m

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202TABLE 1L e n g t h o f d a t a r e c o r d f o r t h e c i t i e s

A.S. OMOLAYO

C i t y S t a t i o n s D a t a p e r i o dA d e l a i d e I I 1955-1983B r i s b a n e 12 1954-1983H o b a r t l0 1962-1981M e l b o u r n e 9 1954-1983P e r t h 11 1962 1981Sydney 1954-1983

n u m b e r o f s ta t io n s : t h e a d j u s tm e n t o f t h e 2 5 0 k m 2 a r ea i n H o b a r t m i g h t h a v ep l a c e d i t u n d e r m o r e d i r e c t o r o g r a p h i c i n f l u e n c e t h a n t h e o t h e r a r e a s .A n a n a l y s i s o f v a r i a n c e w a s p e r f o r m e d t o t e st w h e t h e r t h e s m a l l d i ff e r en c e sa m o n g t h e r e d u c t i o n f a c t o rs f o r t h e s ix ci ti es p r e s e n t e d i n T a b l e s 2 - 5 a r e r e alo r d u e to s a m p l i n g v a r i a ti o n . I n e a c h c a s e t h e c o m p u t e d v a l u e o f v a r ia n c er a t io w a s f o u n d n o t to b e s i g n if ic a n t a t t h e 5 l ev e l f o r 5 a n d 2 4 d e g r e e s o ff r e e d o m . T h e r e d u c t i o n f a c t o r s w e r e , th e r e fo r e , r e p r e s e n te d b y a v e r a g ev a l u e s , g i v e n i n t h e t a b l e s .

B e l l' s m e t h o d g a v e t h e h i g h e s t a v e r a g e v a l u e s . T h i s i s p r o b a b l y a s a r e s u lto f th e r a n k i n g i n c o r p o r a t e d i n t o th e m e t h o d . T h e a v e r a g e s g i v e n b y th e U Sm e t h o d a r e h i g h er t h a n t h o s e b y t h e U K m e t h o d . T h e U S a n d U K a v e r a g esh a v e b e e n p l o t t e d ; t h e y a r e l a b e l l e d A R F u s a n d A R F u K i n F i g . 2 . I t s h o u l db e r e c a ll e d t h a t f o r e s t i m a t i o n o f d e s i g n a r e a l r a i n f a l ls in A u s t r a l i a t h e u s e o ft h e U S - b a s e d r e d u c t i o n f a c t o r s US o f F i g . 2 ) h a s b e e n r e c o m m e n d e d . F i g u r e2 i n d i c a t e s t h a t t h e US c u r v e i s g e n e r a l l y h i g h e r t h a n A R F u s , t h e A u s t r a l i aTABLE 21d a y a r e a l r e d u c t i o n f a c t o r s by US m e t h o dCity Area (kin2)

1000 500 250 200 1O0A d e l a i d e 0.884 0.909 0.908 0.927 0.954B r i s b a n e 0.843 0.956 0.963 0.961 0.960H o b a r t 0.879 0.844 0.908 0.920 0.869M e l b o u r n e 0.901 0.917 0.935 0.927 0.939P e r t h 0.865 0.882 0.982 0.964 0.957Sydney 0.864 0.916 0.936 0.943 0.863A v e r a g e 0.873 0.904 0.939 0.940 0.924U S I 0.91 0.92 0.94 0.95 0.97

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TRANSPOSITION OF AREAL RED UCTION FACTORS FOR RAINFALL FREQUENCY ESTIMATION

TABLE 3I day areal reduction factors by UK method

203

City Area (km2)1000 500 250 200 100

Adelaide 0.834 0.855 0.905 0.928 0.930Brisbane 0.908 0.920 0.932 0.922 0.938Hobart 0.855 0.828 0.863 0.853 0.835Melbourne 0.898 0.9 4 0.937 0.938 0.945Perth 0.863 0.860 0.918 0.915 0.929Sydney 0.881 0.895 0.920 0.902 0.926Average 0.873 0.879 0.913 0.909 0.916UK 1 0.89 0.91 0.92 0.93 0.94

curve. However, comparison of actual A RF values from Table 2 shows thatthe US values and the Australia averages have the same value of 0.94 for the250 km 2 area and are quite close to each ot her between the area range of200-500 km 2. In ot her words, the US -derived reduct ion fa ctors ma y be safelyemployed for design purposes within this range of areas in Australia.

A detailed discussion similar to that on the 1 day reduc tion fact ors cannotbe given at this stage fo r the 1 h re duc tion factor s becaus e the 1 h values areonly computed for Melbourne. However, Table 6 shows that the four com-putational methods gave similar values; and the values fall between 0.75 and0.83. This is a higher range of values compa red with the US- an d the UK -derived values, also shown in Table 6, which vary from 0.67 to 0.76 and from0.62 to 0.79, respectively.

TABLE 41day areal reduction factors by Bell's methodCity Area (km2)

1000 500 250 200 100Adelaide 0.856 0.889 0.945 0.948 0.949Brisbane 0.930 0.947 0.953 0.948 0.964Hobart 0.867 0.889 0.927 0.905 0.881Melbourne 0.917 0.937 0.946 0.946 0.946Perth 0.867 0.882 0.936 0.936 0.940Sydney 0.907 0.923 0.929 0.932 0.939Average 0.891 0.911 0.939 0.936 0.937

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204TABLE 51 d a y a r ea l r e d u c t i o n f a c t o r s b y R o d r i g u e z - I t u r b e a n d M e j ia s m e t h o dC i t y A r e a (km 2)

1000 500 250 200 100

A.S. OMOLAYO

A d e l a i d e 0.768 0.920 0.846 0.792 0.967Brisbane 0.869 0.832 0.875 0.840 0.946H o b a r t 0.809 0.488 0.768 0.642 0.696M e l b o u r n e 0.670 0.820 0.820 0.933 0.918Perth 0.611 0.639 0.470 0.509 0.880S y d n e y 0.549 0.875 0.881 0.893 0.779A v e r a g e 0.713 0.762 0.777 0.768 0.864

CONCLUSIONSA n a t t e m p t h a s b e e n m a d e t o d i s t i n g u i s h b e t w e e n s t o r m - c e n t r e d a n d

f ix e d - a r e a r e d u c t i o n f a c to r s t h u s r e m o v i n g t h e c o n f u s i o n t h a t u s u a l l y a ri se si n u n d e r s t a n d i n g a n d a p p l y i n g t h e c o n c e p t o f a r ea l r e d u c t i o n f a c t o r s i nr a i n fa l l f r e q u e n c y e s t i m a t i o n . T h e j u s t i fi c a t i o n f o r u s i n g th e U S r e d u c t i o nf a c t o r s i n A u s t r a l i a h a s a l s o b e e n i n v e s t i g a t e d e m p i r i c a l l y . T h e r e s u l t s s h o wt h a t t h e U S v a l u e s a r e p r o b a b l y s a t i sf a c t o r y i n A u s t r a l ia f o r e s t i m a t i n g 2 4 ha r e a r a i n f a l ls f o r a r e a l s i z e s b e t w e e n 2 0 0 a n d 5 0 0 k m 2. T h e a r e a l r e d u c t i o nf a c t o r s p r e s e n t e d i n t h i s s t u d y h a v e b e e n b a s e d o n t h e a s s u m p t i o n t h a t t h ea r e a l r e d u c t i o n f a c t o r d o e s n o t v a r y w i t h th e r e t u r n p e r i o d . V a r i a t i o n w i t h th er e t u r n p e r i o d n e e d s t o b e i n v e s t i g a t e d i n o r d e r t o m a k e m o r e v a l i dc o n c l u s i o n s . F u r t h e r m o r e t h e a r e a l r e d u c t i o n f a c t o r s f o r a r e a s s m a l l e r t h a n1 0 0 k m 2 r e q u ir e d f o r u r b a n h y d r o m e t e o r o l o g i c a l s tu d i e s c o u l d n o t b ec o m p u t e d d u e t o th e w i d e s ca t te r o f t h e s t a t io n s . A m o d e l t h a t i n c o r p o r a t e sTABLE 6I h a re a l r e d u c t i o n f a c t o r s fo r M e l b o u r n eM e t h o d A r e a (km 2)

1000 500 250 200 100US 0.790 0.778 0.750 0.800 0.808UK 0.769 0.763 0.756 0.768 0.767Bell 0.756 0.745 0.749 0.748 0.749Rod/Mejia 0.773 0.834 0.815 0.815 0.797US 1 - 0.68 0.73 0.75 0.82UK1 0.62 0.68 0.73 0.75 0.79

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