Wave Information Studies of U S Coastlines
Hindcast Wave Informatio
for the US Atlantic C o a s t
by Jon M. Hubertz, Rebecca M. Brooks,Willie A. Brandon, Barbara A. Tracy Coastal Engineering Research Center U.S. Army Corps of Engineers
Waterways Experiment Station 3909 Halls Ferry Road
Vicksburg, MS 39180-6199
Final report
Approved for public release; distribution is unlimited
PREFACE
In late 1976 a study to produce a wave climate for US coastal waters was
initiated at the US Army Engineer Waterways Experiment Station (WES). The
Wave Information Study (WIS) was authorized by Headquarters, US Army Corps of Engineers (HQUSACE) as part of the Coastal Field Data Collection Program, which is managed by the WES Coastal Engineering Research Center (CERC).
Messrs. John H. Lockhart, Jr.; John G. Housley; James E. Crews; and Robert H. Campbell, HQUSACE, are Technical Monitors for the Coastal Field Data
Collection Program; Ms. Carolyn M. Holmes is Program Manager; and Dr. Jon M. Hubertz is WIS Project Manager.
This report, the 30th in a series, provides revised wave information at 108 nearshore locations along the US Atlantic coastline and 3 stations along
the north coast of Puerto Rico. It supersedes information provided in WIS
Reports 2, 6, and 9. The information is derived from wind fields developed in
a previous hindcast for the period 1956-1975 and the present version of the
WIS wave model, WISWAVE 2.0. This report was written by Dr. Jon M .. Hubertz.
Application of the model and preparation of all the tables and statistical
calculations were done by Ms. Rebecca M. Brooks. Ms. Willie Ann Brandon
conducted the verification studies prior to the hindcast. Ms. Barbara Tracy
was responsible for model tests to assure proper functioning of the computer code.
The study was conducted under the direct supervision of Dr. Martin C. Miller, Chief, Coastal Oceanography Branch (COB), and Mr. H. Lee Butler,
Chief, Research Division; and under the gene~a1 supervision of Dr. James R.
Houston and Mr. Charles C. Calhounl Jr., Director and Assistant Director,
CERC, respectively. Word processing of this report was done by Ms, Jane
Staub1e, COB, CERC. Editing was done by Ms. Janean Shirley, Information
Technology Laboratory, WES.
At the time of publication of this report, Dr. Robert W. Whalin was
Director of WES. COL Leonard G. Hassell, EN, was Commander.
CONTENTS PREFACE Page PART I : PART I I : PART I I I : PART I V : INTRODUCTION WINDS . . . . WAVE MODEL . VERIFICATION PART V: PART V I : REFERENCES FIGURES 1-4 TABLES 1-16 APPENDIX A APPENDIX B APPENDIX C RESULTS
EXPLANATION OF SUMMARY TABLES
SUMMARY TABLES . . RETURN PERIOD TABLES
COMPARISON OF MEASURED AND HINDCAST WIND SPEEDS AND DIRECTIONS . . . . 3 5 6 7 H i n d c a s t f o r 1990 H i n d c a s t f o r 1956-1975 . . . ^ 10 15 16 20 A l B I Gl
HINDCAST WAVE INFORMATION FOR THE US ATLANTIC COAST
PART I : INTRODUCTION
1 . Wave I n f o r m a t i o n S t u d i e s (WIS) have s u p p l i e d wave c l i m a t e
i n f o r m a t i o n a t n e a r s h o r e l o c a t i o n s a l o n g t h e US A t l a n t i c c o a s t f o r t h e 20-year p e r i o d 1956-1975, docxmented i n WIS R e p o r t 2 (Corson e t a l . 1 9 8 1 ) , WIS R e p o r t 6 ( C o r s o n e t a l . 1 9 8 2 ) , and WIS R e p o r t 9 ( J e n s e n 1983). T h i s i n f o r m a t i o n met a c r i t i c a l need f o r wave i n f o r m a t i o n i n c o a s t a l e n g i n e e r i n g s t u d i e s i n t h e 1980's. Wave measurements made b y t h e N a t i o n a l Oceanic and A t m o s p h e r i c A d m i n i s t r a t i o n (NOAA) and t h e Corps o f E n g i n e e r s (CE) d u r i n g t h e 1980's made v e r i f i c a t i o n o f t h e s e WIS r e s u l t s p o s s i b l e by c o m p a r i n g s t a t i s t i c s and t h e d i s t r i b u t i o n s o f wave h e i g h t s and p e r i o d s f r o m t h e two d i f f e r e n t t i m e p e r i o d s
( e . g . M i l l e r and Jensen 1 9 9 0 ) .
2. M i l l e r and Jensen c o n d u c t e d a wave c o m p a r i s o n f o r t h e N o r t h C a r o l i n a c o a s t a t t h e F i e l d Research F a c i l i t y (FRF) o f t h e C o a s t a l E n g i n e e r i n g Research C e n t e r (CERC), US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n (WES). T h i s c o m p a r i s o n i n d i c a t e d t h a t t h e d i s t r i b u t i o n o f h i n d c a s t wave h e i g h t s , p e r i o d s , and d i r e c t i o n s d i f f e r e d f r o m t h e d i s t r i b u t i o n s o f measured d a t a . The r e p o r t c o n c l u d e d f o r wave h e i g h t s t h a t :
Wave h e i g h t d i s t r i b u t i o n s agree w e l l f o r waves o v e r 2 m. However, o n l y 44 p e r c e n t o f t h e h e i g h t s exceed 0.5 m f o r t h e WIS e s t i m a t e s , compared w i t h 76 p e r c e n t f o r t h e FRF measurements. T h i s d i f f e r e n c e i s a t t r i b u t e d , i n p a r t , t o t h e c o a s t a l o r i e n t a t i o n , w h i c h g r e a t l y r e d u c e s t h e f e t c h f o r w i n d s b l o w i n g near s h o r e - p a r a l l e l a t t h e gage s i t e . A l s o , t h e Phase I I I h i n d c a s t method does n o t c o n s i d e r a d d i t i o n a l wind-wave g r o w t h f r o m t h e i n p u t Phase I I p o i n t s .
3. The agreement b e t w e e n d i s t r i b u t i o n s o f t h e p e r i o d was n o t c o n c l u s i v e s i n c e WIS r e p o r t e d t h e mean p e r i o d o f t h e sea o r s w e l l p o r t i o n o f t h e
s p e c t r u m , w h i c h e v e r c o n t a i n e d t h e l a r g e r e n e r g y d e n s i t y , and t h e FRF r e p o r t e d t h e peak p e r i o d o f t h e e n t i r e s p e c t r u m . The mean p e r i o d i s an e n e r g y - w e i g h t e d average a c r o s s f r e q u e n c y bands. I n t h e case o f t h e o r i g i n a l h i n d c a s t r e s u l t s , t h e average was a c r o s s t h o s e f r e q u e n c y bands d e s i g n a t e d sea o r s w e l l and
c o n t a i n i n g t h e l a r g e r amount o f e n e r g y d e n s i t y i n t h e e n t i r e s p e c t r u m . The peak p e r i o d i s t h e i n v e r s e o f t h e f r e q u e n c y a t w h i c h t h e peak e n e r g y i n t h e
s p e c t r u m o c c u r s . I t i s n o t a p p r o p r i a t e t o t r y and compare t h e s e two d i f f e r e n t e s t i m a t e s o f wave p e r i o d .
4. For wave d i r e c t i o n , t h e r e p o r t c o n c l u d e d :
B o t h t h e WIS and FRF d i r e c t i o n s t e n d t o be p r i m a r i l y s h o r e - n o r m a l . A c l e a r d i f f e r e n c e between t h e
d i s t r i b u t i o n s i s t h a t t h e WIS e s t i m a t e s have many more s h o r e - p a r a l l e l low waves. T h i s d i f f e r e n c e a r i s e s because t h e h i n d c a s t method a l l o w s f o r t h e
t r a n s f o r m a t i o n o f w i n d - s e a e n e r g y d e r i v e d f r o m wave c o n d i t i o n s p r o p a g a t i n g i n a l l d i r e c t i o n s .
5. E x a m i n a t i o n o f wave d i r e c t i o n s i n d i c a t e d t h a t improvements i n t h e h i n d c a s t s were, needed. The d i s t r i b u t i o n o f mean wave d i r e c t i o n f r o m WIS Phase I I I r e s u l t s a t s t a t i o n 132 (Giomberland I s l a n d , GA) i s shown i n F i g u r e 1 as t h e c u r v e AP3. There i s a t e n d e n c y f o r a l a r g e p e r c e n t o f wave d i r e c t i o n s t o f a l l w i t h i n c e r t a i n 10-deg bands ( f o r example, t h e 10-, 100-, and 130-deg bands i n
t h i s c a s e ) . T h i s t e n d e n c y i s a l s o p r e s e n t i n r e s u l t s f r o m Phases I and I I s t a t i o n s f a r t h e r o f f s h o r e and a t o t h e r s t a t i o n s a l o n g s h o r e . No e x p l a n a t i o n f o r t h i s b e h a v i o r i s a v a i l a b l e o t h e r t h a n a p o s s i b l e e r r o r i n t h e computer code o r i m p l e m e n t a t i o n o f t h e code on t h e computer used t o p r o d u c e t h e r e s u l t s . Measurements f r o m NOAA d i r e c t i o n a l buoy 41008 a t a n e a r b y s i t e ( K i n g s Bay, GA) a r e a l s o p l o t t e d t o i n d i c a t e what s h o u l d be p r o d u c e d b y
h i n d c a s t v a l u e s . T h i s a t y p i c a l d i s t r i b u t i o n o f d i r e c t i o n s p r o d u c e d b y t h e o l d h i n d c a s t i s t h e most c o m p e l l i n g r e a s o n f o r r e v i s i n g t h e h i n d c a s t r e s u l t s . O t h e r s (Weggel, D o u g l a s s , and T u n n e l l 1988) have a l s o n o t e d " u n r e a l i s t i c " b e h a v i o r i n some o f t h e WIS r e s u l t s , w h i c h i n d i c a t e s t h a t r e v i s i o n i s a p p r o p r i a t e .
6. A 1-year h i n d c a s t f o r t h e A t l a n t i c was done f o r 1988, u s i n g as n e a r l y as p o s s i b l e t h e same t e c h n i q u e and model as i n t h e o r i g i n a l h i n d c a s t
( L i n and Wang 1990). R e s u l t s were compared t o NOAA buoy and n e a r s h o r e GE wave gage measurements. H e i g h t s compared w e l l t o measurements, b u t p e r i o d s and d i r e c t i o n s d i f f e r e d b y r e l a t i v e l y l a r g e amounts.
7. These comparisons l e d t o t h e d e c i s i o n t o r e v i s e t h e WIS i n f o r m a t i o n f o r t h e A t l a n t i c c o a s t f o r t h e p e r i o d 1956-1975. T h i s r e p o r t summarizes t h e p r o c e d u r e used i n t h e r e v i s i o n , v e r i f i c a t i o n o f t h e model p r i o r t o and a f t e r t h e c a l c u l a t i o n s , and p r e s e n t s h i n d c a s t r e s u l t s i n summary t a b l e s i n
PART I I : WINDS
8. The d i s t r i b u t i o n s o f h i n d c a s t (1956-1975) w i n d speeds and d i r e c t i o n s i n v a r i o u s speed and d i r e c t i o n c a t e g o r i e s were compared t o v a l u e s a v a i l a b l e f r o m NOAA buoy measurements made i n t h e 1980's i n o r d e r t o j u d g e t h e a c c u r a c y o f t h e w i n d c l i m a t o l o g y i n t h e o r i g i n a l h i n d c a s t . Some measurements o f w i n d speeds and d i r e c t i o n s f r o m an NOAA buoy o f f N o r t h C a r o l i n a , f o r a s h o r t t i m e p e r i o d c o i n c i d e n t w i t h t h e h i n d c a s t p e r i o d , were a l s o compared t o h i n d c a s t v a l u e s .
9. The l o c a t i o n s o f t h e s i x buoys and model g r i d p o i n t s u s e d f o r w i n d comparisons a r e shown i n F i g u r e 2. The buoys a r e : 41006, 41002, 4 1 0 0 1 ,
44004, 4 4 0 1 1 , and EBOl. Buoy d a t a were o b t a i n e d f r o m G i l h o u s e n e t a l . ( 1 9 9 0 ) . Buoy d a t a were g e n e r a l l y a v a i l a b l e f r o m t h e l a t e 1970's t o t h e l a t e 1980's. WIS w i n d s were a v a i l a b l e f r o m 1956-1975. A l t h o u g h t h e t i m e p e r i o d s a r e d i f f e r e n t , t h e a s s u m p t i o n i s made t h a t t h e w i n d c l i m a t o l o g y f o r t h e two p e r i o d s i s s i m i l a r ; t h u s , t h e d i s t r i b u t i o n o f speeds and d i r e c t i o n s s h o u l d be s i m i l a r . The p l a t e s i n A p p e n d i x G compare t h e d i s t r i b u t i o n s o f measured and h i n d c a s t w i n d speeds and d i r e c t i o n s a t t h e f i v e l o c a t i o n s shown i n F i g u r e 2. A l s o shown i s a t i m e s e r i e s c o m p a r i s o n f o r one month o f measurements d u r i n g t h e same h i n d c a s t p e r i o d . The d i s t r i b u t i o n s o f speeds and d i r e c t i o n s a r e q u i t e s i m i l a r a t a l l l o c a t i o n s . The t i m e s e r i e s comparisons a l s o f o l l o w each o t h e r i n g e n e r a l , w i t h t h e h i n d c a s t c u r v e t e n d i n g t o be smoother t h a n t h e
measured. Since t h e means and d i s t r i b u t i o n s o f w i n d speeds and d i r e c t i o n s i n t h e two p e r i o d s were c o m p a r a b l e , t h e o r i g i n a l w i n d s were j u d g e d a c c e p t a b l e and u s e d i n t h e r e v i s e d h i n d c a s t .
10. The winds u s e d i n t h e o r i g i n a l h i n d c a s t were r e f e r e n c e d t o a s p h e r i c a l o r t h o g o n a l g r i d , whereas t h e g r i d s y s t e m used i n t h e r e v i s e d h i n d c a s t c o i n c i d e s w i t h l a t i t u d e and l o n g i t u d e l i n e s . C o n s e q u e n t l y , an
i n t e r p o l a t i o n scheme was used t o o b t a i n v a l u e s a t 1-deg i n t e r v a l s o f l a t i t u d e and l o n g i t u d e . These were used i n t h e c o m p a r i s o n s i n Appendix C. The good agreement s u p p o r t s use o f t h e i n t e r p o l a t i o n scheme.
PART I I I : WAVE MODEL
1 1 . The l a t e s t v e r s i o n o f t h e CE wave model, WISWAVE 2.0 (WIS R e p o r t 27 ( H u b e r t z 1 9 9 2 ) ) was u s e d w i t h t h e CRAY Y-MP/6 computer system a t WES. T h i s s u p e r - c o m p u t e r a l l o w e d a d o u b l i n g o f t h e r e s o l u t i o n o f t h e o r i g i n a l h i n d c a s t . The n e s t e d g r i d o p t i o n o f WISWAVE was employed u s i n g two l e v e l s o f r e s o l u t i o n . L e v e l 1 c o v e r e d t h e N o r t h A t l a n t i c Ocean w i t h a g r i d s p a c i n g o f 1 deg i n
l a t i t u d e and l o n g i t u d e . T h i s g r i d i s shown i n F i g u r e 3. The c i r c l e d p o i n t s a l o n g t h e US E a s t c o a s t i n F i g u r e 3 r e p r e s e n t l e v e l - 1 g r i d p o i n t s , w h i c h s u p p l y i n f o r m a t i o n t o t h e l e v e l - 2 g r i d . These p o i n t s a r e a l s o shown i n F i g u r e 4, w h i c h shows t h e l e v e l - 2 g r i d . L e v e l 2 c o v e r e d t h e c o n t i n e n t a l s h e l f w i t h a g r i d s p a c i n g o f 1/4 deg. L e v e l - 2 g r i d p o i n t s between t h e c o a s t and b o u n d a r y i n p u t p o i n t s f r o m l e v e l 1 a r e w a t e r p o i n t s w i t h a s s o c i a t e d d e p t h s . G r i d p o i n t s t o t h e e a s t o f t h e boundary i n p u t p o i n t s a r e c o n s i d e r e d l a n d p o i n t s t o reduce t h e number o f c o m p u t a t i o n a l w a t e r p o i n t s ,
12. L o c a t i o n s a t w h i c h wave i n f o r m a t i o n i s a v a i l a b l e a r e shown i n F i g u r e 2 as numbered d o t s a l o n g t h e c o a s t . Deep w a t e r i s assumed i n l e v e l 1 , and b a t h y m e t r y a t mean low w a t e r i s u s e d i n l e v e l 2. The i s l a n d s and s h o a l s o f f t h e s o u t h e a s t c o a s t o f F l o r i d a a r e i n c l u d e d i n t h e d e p t h g r i d f o r t h e r e v i s e d h i n d c a s t . The Bahamas banks and s h o a l s were n o t i n c l u d e d i n t h e o r i g i n a l Phase I I h i n d c a s t and i t i s q u e s t i o n a b l e w h e t h e r d e p t h s were u s e d i n Phase I I a l o n g t h e c o a s t . Thus t h e r e v i s e d h i n d c a s t s h o u l d more a c c u r a t e l y r e p r e s e n t t h e s e f e a t u r e s as w e l l as t h e c o a s t l i n e i n t h e n u m e r i c a l g r i d because o f t h e i n c r e a s e d r e s o l u t i o n .
13. The v a l u e s o f t h e v a r i o u s c o e f f i c i e n t s i n WISWAVE a r e t h e same as t h o s e u s e d i n t h e G r e a t Lakes h i n d c a s t s (WIS R e p o r t s 22 t h r o u g h 2 6 ) . These c o e f f i c i e n t s a r e d e s c r i b e d i n d e t a i l i n P a r t I I I o f any o f t h e G r e a t Lakes h i n d c a s t r e p o r t s ( e . g . H u b e r t z , D r i v e r , and R e i n h a r d 1 9 9 1 ) . The d e e p w a t e r v e r s i o n o f WISWAVE (WISWAVE 1.0 and r e f e r r e d t o as DWAVE i n t h e G r e a t Lakes h i n d c a s t s ) i s i d e n t i c a l t o t h e p r e s e n t v e r s i o n WISWAVE 2.0, b u t l a c k s t h e p r o p a g a t i o n r o u t i n e s , w h i c h can use a r b i t r a r y d e p t h s . The d o c u m e n t a t i o n o f t h e s e a d d i t i o n s i n WISWAVE 2.0 i s p r o v i d e d i n WIS R e p o r t 27 ( H u b e r t z , 1 9 9 2 ) .
PART I V : VERIFICATION
H i n d c a s t f o r 1990
14. A 1-year h i n d c a s t f o r 1990 was c o m p l e t e d p r i o r t o r e c a l c u l a t i n g t h e 20 y e a r s o f wave i n f o r m a t i o n i n o r d e r t o v e r i f y t h e model and p r o c e d u r e s . Model r e s u l t s were compared t o measurements a t 14 l o c a t i o n s a l o n g t h e A t l a n t i c c o a s t ( F i g u r e 2 ) . These comparisons a r e summarized by month i n T a b l e s 1-6.
15. H i n d c a s t w i n d s f o r 1990 were o b t a i n e d f r o m t h e F l e e t N u m e r i c a l Oceanographic Center (FNOC). These 19.5-m e l e v a t i o n w i n d s a r e spaced 2.5 deg a p a r t i n l a t i t u d e and l o n g i t u d e and a r e a v a i l a b l e e v e r y 6 h r . I n t e r p o l a t i o n i n space f r o m t h e 2.5-deg s p a c i n g i s done p r i o r t o p r o v i d i n g i n p u t t o t h e wave model g r i d s . The model i n t e r p o l a t e s i n t e r n a l l y i n t i m e between t i m e s when winds a r e a v a i l a b l e . M o n t h l y v a l u e s o f b i a s and r o o t mean square d i f f e r e n c e f o r h i n d c a s t and measured w i n d speeds a t t h e 14 l o c a t i o n s a r e shown i n T a b l e s 1 and 2, r e s p e c t i v e l y . G e n e r a l l y t h e h i n d c a s t winds t e n d t o be l o w e r by about 1 m/sec t h a n measured a t t h e 14 s i t e s . T y p i c a l r o o t mean square d i f f e r e n c e s
( T a b l e 2) a r e 2-3 m/sec. Buoy and FNOC winds a r e n o t i n d e p e n d e n t s i n c e t h e buoy d a t a a r e a s s i m i l a t e d i n t h e p r o c e s s t o produce w i n d speeds and
d i r e c t i o n s .
16. The d i f f e r e n c e between measured and h i n d c a s t (buoy minus model) m o n t h l y mean s p e c t r a l wave h e i g h t v a r i e d f r o m 0.3 t o -0.8 m, w i t h an average d i f f e r e n c e o f -0.2 m ( T a b l e 3 ) . The d i f f e r e n c e between measured and h i n d c a s t
(buoy-model) m o n t h l y mean peak wave p e r i o d s v a r i e d f r o m 1.8 t o -3.6 sec, w i t h an average d i f f e r e n c e o f -0.6 sec ( T a b l e 4 ) . The range and mean m o n t h l y r o o t mean square d i f f e r e n c e f o r h e i g h t were 0.3 t o 1.1 and 0.5 m and f o r p e r i o d were 0.4 t o 4.8 and 2.5 sec ( T a b l e s 5 and 6, r e s p e c t i v e l y ) .
17. Thus, f r o m t h e r e s u l t s o f t h i s 1-year h i n d c a s t , on a v e r a g e , one
C Q u l d e x p e c t h i n d c a s t wave h e i g h t s t o be s l i g h t l y h i g h (0.2 m) w i t h r e s p e c t t o measurements a l o n g t h e c o a s t , and a t any t i m e t o d i f f e r f r o m measured v a l u e s on average by 0.5 m. The a c c u r a c y o f t h e buoy wave h e i g h t measurements i s ±0.2 m o r 5 p e r c e n t f o r waves above 4,0 m ( G i l h o u s e n e t a l . 1 9 9 0 ) . The average h i n d c a s t wave peak ( d o m i n a n t ) p e r i o d s a r e s l i g h t l y h i g h (0.6 s e c ) w i t h r e s p e c t t o measured v a l u e s a l o n g t h e c o a s t , and a t any t i m e d i f f e r on t h e
average f r o m measured v a l u e s b y 2.5 sec. The a c c u r a c y o f buoy wave peak p e r i o d measurements i s ±1.0 sec ( G i l h o u s e n e t a l . 1990).
18. S p e c t r a l wave h e i g h t s a r e an i n t e g r a t e d q u a n t i t y . T h a t i s , t h e y a r e based on t h e sum o f e n e r g y under t h e d i s c r e t e spectrum. Wave peak mean d i r e c t i o n s a r e s i m i l a r , b u t t o a l e s s e r degree an i n t e g r a l q u a n t i t y , i n t h a t t h e y a r e t h e e n e r g y - w e i g h t e d mean o f a l l wave d i r e c t i o n s i n t h e peak f r e q u e n c y band. Wave peak p e r i o d s , however, a r e n o t an i n t e g r a t e d o r mean v a l u e . They a r e b a s e d o n l y on t h e l o c a t i o n a l o n g t h e f r e q u e n c y a x i s o f t h e peak s p e c t r a l energy. Thus, i f t h e s p e c t r u m i s d o u b l e peaked, r e p r e s e n t i n g sea and s w e l l , f o r example, t h e peak f r e q u e n c y c a n s h i f t f r o m , say, 4 t o 10 sec d e p e n d i n g on t h e r e l a t i v e m a g n i t u d e o f t h e two peaks. T h i s t e n d s t o i n t r o d u c e l a r g e
d i f f e r e n c e s i n p e r i o d c o m p a r i s o n s when, f o r example, a sea peak i s l a r g e s t i n a gage r e c o r d and t h e s w e l l peak i s l a r g e s t i n a h i n d c a s t f o r t h e same t i m e p e r i o d , o r v i c e v e r s a .
19. I n t h e above example, b o t h gage and h i n d c a s t r e s u l t s w o u l d be c o r r e c t . There a r e two m a i n components i n t h e s p e c t r a and t h u s two peak p e r i o d s . I f two p e r i o d s were c a l c u l a t e d f r o m t h e gage s p e c t r u m and two f r o m
the h i n d c a s t s p e c t r u m , t h e c o r r e s p o n d i n g sea and s w e l l p e r i o d s f r o m gage and h i n d c a s t w o u l d most l i k e l y be i n agreement.
20. Peak p e r i o d s i n s i n g l e - p e a k e d s p e c t r a can a l s o v a r y i n t i m e due t o t h e peak s h i f t i n g f r o m one f r e q u e n c y band t o a n o t h e r . The amount o f v a r i a t i o n depends on t h e w i d t h o f t h e f r e q u e n c y bands and i s g e n e r a l l y l a r g e r i n t h e l o w e r f r e q u e n c y bands. For example, f o r a f i x e d band w i d t h o f 0,01 Hz, t h e p e r i o d w i l l v a r y f r o m 14.3 t o 12.5 sec f o r a s h i f t f r o m 0.07 t o 0.08 Hz and f r o m 7.1 t o 6.7 sec f o r a s h i f t f r o m 0.14 t o 0.15 Hz. T h i s c a n l e a d t o r e l a t i v e l y l a r g e d i f : ^ e r e n c e s i n peak p e r i o d s f o r s p e c t r a whose peaks a r e w i t h i n one o r two b a n d w i d t h s o f each o t h e r a t l o w e r f r e q u e n c i e s . The number
and s i z e o f t h e f r e q u e n c y b a n d w i d t h s can a l s o a f f e c t t h e v a r i a b i l i t y o f peak p e r i o d i n t i m e f o r gage o r model r e s u l t s . Peak p e r i o d s c a l c u l a t e d f r o m
s p e c t r a w i t h f e w e r f r e q u e n c y bands t h a t a r e w i d e r more c l o s e l y a p p r o x i m a t e a mean v a l u e t h a n p e r i o d s a s s o c i a t e d w i t h one o f many n a r r o w bands. S p e c t r a p r o d u c e d f r o m t h e a n a l y s i s o f gage d a t a u s u a l l y have more f r e q u e n c y bands t h a n
t h o s e c a l c u l a t e d i n WIS h i n d c a s t s ( t y p i c a l l y 20 b a n d s ) . T h i s may i n t r o d u c e d i f f e r e n c e s on t h e o r d e r o f seconds when c o m p a r i n g peak p e r i o d s . Sometimes t h e gage s p e c t r a a r e "band averaged," t h a t i s , a number o f a d j a c e n t bands a r e
a v e r a g e d t o g e t h e r t o produce one band. I f t h e s i z e and l o c a t i o n i n f r e q u e n c y space o f t h e r e s u l t i n g gage s p e c t r u m i s s i m i l a r t o t h e h i n d c a s t s p e c t r u m , peak p e r i o d s w i l l be comparable.
21. Mean p e r i o d s , w h i c h a r e e n e r g y - w e i g h t e d means o v e r a l l f r e q u e n c i e s , can be compared, b u t f o r a double-peaked s p e c t r u m , t h e mean p e r i o d may be between t h e sea and s w e l l p e r i o d s , say, 7 sec i n t h e example above, and t h u s n o t be r e p r e s e n t a t i v e o f e i t h e r sea o r s w e l l wave p e r i o d . I n a b r o a d s i n g l e -peaked s p e c t r u m , t h e mean p e r i o d w i l l be one v a l u e r e p r e s e n t i n g t h e many p e r i o d s p r e s e n t . The mean p e r i o d w i l l approach t h e peak p e r i o d f o r s i n g l e -peaked n a r r o w s p e c t r a . We have chosen t o use peak p e r i o d t o c h a r a c t e r i z e t h e d i s t r i b u t i o n o f energy d e n s i t y i n f r e q u e n c y , s i n c e t h i s i s now t h e most
commonly used v a r i a b l e f r o m measurements and h i n d c a s t / f o r e c a s t s t u d i e s . Mean p e r i o d s a r e a v a i l a b l e i n t h e o u t p u t r e c o r d s f o r use i f d e s i r e d , b u t peak
p e r i o d s a r e used i n t h e summary t a b l e s . A WIS p o s t - p r o c e s s i n g program, SPECOMP, i s a v a i l a b l e t o i d e n t i f y t h e s p e c t r a l h e i g h t s , peak p e r i o d s , and peak mean d i r e c t i o n s o f t h e two m a j o r e n e r g y - c o n t a i n i n g p o r t i o n s o f t h e WIS
s p e c t r a . T h i s s p e c t r a l component d e c o m p o s i t i o n i s n e c e s s a r y f o r c o a s t a l e n g i n e e r i n g a p p l i c a t i o n s a t t h o s e l o c a t i o n s where t h e wave c l i m a t e has s i m u l t a n e o u s l y o c c u r r i n g m u l t i p l e p e r i o d s and d i r e c t i o n s .
22. Problems s i m i l a r t o t h e v a r i a b i l i t y i n peak p e r i o d s o c c u r i n p i c k i n g one d i r e c t i o n c h a r a c t e r i s t i c o f an e n t i r e s p e c t r u m . The peak mean d i r e c t i o n i s t h e e n e r g y - w e i g h t e d mean o f a l l d i r e c t i o n s a t t h e peak f r e q u e n c y . The mean d i r e c t i o n i s t h e e n e r g y - w e i g h t e d mean o f a l l d i r e c t i o n s i n a l l
f r e q u e n c y bands. U s i n g t h e examples above f o r peak p e r i o d , i t i s a p p a r e n t t h a t t h e mean d i r e c t i o n o f a double-peaked s p e c t r u m may n o t be r e p r e s e n t a t i v e o f e i t h e r m a j o r component o f t h e s p e c t r u m . The mean d i r e c t i o n o f a b r o a d s p e c t r u m w i l l be one v a l u e r e p r e s e n t i n g t h e many p r e s e n t . For c o a s t a l
e n g i n e e r i n g a p p l i c a t i o n s i n w h i c h wave d i r e c t i o n i s a c r i t i c a l p a r a m e t e r , use o f mean d i r e c t i o n . m a y be an u n a c c e p t a b l e p a r a m e t e r i f t h e l o c a l wave c l i m a t e t y p i c a l l y has wave energy a p p r o a c h i n g s i m u l t a n e o u s l y f r o m d i f f e r e n t
d i r e c t i o n s .
23. We.Jiave chosen t o use t h e peak mean d i r e c t i o n t o c h a r a c t e r i z e t h e d i r e c t i o n i n t h e s p e c t r u m . T h i s v a l u e i s more commonly used f r o m measurements and h i n d c a s t / f o r e c a s t s t u d i e s t h a n mean d i r e c t i o n . T e s t s c o n d u c t e d a t CERC t o d e t e r m i n e t h e most a p p r o p r i a t e wave p a r a m e t e r s t o use i n c o a s t a l p r o c e s s e s
m o d e l i n g i n d i c a t e t h a t s p e c t r a l h e i g h t , peak p e r i o d , and peak mean d i r e c t i o n g i v e t h e most m e a n i n g f u l r e s u l t s i f one i s c o n s t r a i n e d t o use j u s t t h r e e wave parameters.* To p r e s e r v e a l l o f t h e i n f o r m a t i o n i n a d i r e c t i o n a l wave
spectrum, one s h o u l d use t h e complete spectrum. However, t h i s i s n o t
p r a c t i c a l , a t p r e s e n t , s i n c e most c o a s t a l e n g i n e e r i n g a p p l i c a t i o n s a r e l i m i t e d t o t h e use o f t h r e e wave p a r a m e t e r s as i n p u t ; h e i g h t , p e r i o d , and d i r e c t i o n . The program SPECOMP, d i s c u s s e d above, can be used t o p r o d u c e two t r i p l e t s o f h e i g h t , p e r i o d , and d i r e c t i o n f o r a spectrum. T h i s i s a b e t t e r a p p r o x i m a t i o n t h a n u s i n g one t r i p l e t f o r wave c l i m a t e s h a v i n g m u l t i p l e components. Mean wave d i r e c t i o n s a r e a v a i l a b l e on t h e o u t p u t r e c o r d s f o r use i f d e s i r e d , b u t peak mean d i r e c t i o n s a r e used i n t h e summary t a b l e s . Next, h i n d c a s t r e s u l t s f r o m t h e p e r i o d 1956-1975 a r e compared t o measured r e s u l t s f r o m buoys a t f i v e l o c a t i o n s a l o n g t h e c o a s t where WIS s t a t i o n s and buoys a r e c l o s e t o t h e same l o c a t i o n and d e p t h .
H i n d c a s t f o r 1956-1975
24. There a r e f i v e buoys a l o n g t h e c o a s t , w h i c h a r e a t l o c a t i o n s c l o s e t o p o i n t s where WIS r e s u l t s a r e saved f r o m t h e 20-year h i n d c a s t f o r b o t h t h e o l d and new h i n d c a s t s . The buoy and WIS s t a t i o n l o c a t i o n s a r e l i s t e d i n T a b l e 7, a l o n g w i t h depths a t t h e buoys and WIS s t a t i o n s f r o m t h e r e v i s e d h i n d c a s t . T a b l e 8 p r o v i d e s s i m i l a r i n f o r m a t i o n f o r t h e o l d h i n d c a s t .
F i g u r e 2 shows t h e l o c a t i o n o f t h e buoys w i t h r e s p e c t t o t h e WIS s t a t i o n s , t h e a c t u a l c o a s t l i n e , and t h e l a n d / w a t e r boundary as r e p r e s e n t e d i n t h e model. Measured and h i n d c a s t wave c o n d i t i o n s c a n be a f f e c t e d b y l o c a l f e a t u r e s , e s p e c i a l l y n e a r t h e c o a s t . Examples o f t h e s e f e a t u r e s a r e d e p t h d i f f e r e n c e s between measurement and model s i t e s , d i f f e r e n c e s i n a c t u a l l o c a t i o n o f t h e c o a s t l i n e and i t s r e p r e s e n t a t i o n i n t h e model, and t h e p r e s e n c e o f c u r r e n t s i n n a t u r e t h a t a r e a b s e n t i n t h e model. Such f e a t u r e s , w h i c h may a f f e c t
comparisons a t t h e f i v e buoy s i t e s , a r e d i s c u s s e d n e x t .
25. Buoy 41008 i s a p p r o x i m a t e l y 8 n.m. (14.82 km) f a r t h e r o f f s h o r e t h a n WIS s t a t i o n 28 and i s i n 18 m o f w a t e r v e r s u s 1 1 m a t t h e WIS s t a t i o n . B o t h
P e r s o n a l Communication, J u l y 1992, Mark Cravens, C o a s t a l E n g i n e e r , US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
l o c a t i o n s are open and u n s h e l t e r e d b y e i t h e r t h e a c t u a l c o a s t l i n e o r model r e p r e s e n t a t i o n o f t h e l a n d / w a t e r boundary. B o t h s h o u l d be u n a f f e c t e d b y c u r r e n t s s i n c e t h e y are away f r o m t h e G u l f Stream, w h i c h i s t h e major c u r r e n t i n t h i s r e g i o n . The e f f e c t s o f t h e G u l f Stream o r l o c a l t i d a l c u r r e n t s n e a r bays and i n l e t s a r e n o t i n c l u d e d i n t h e h i n d c a s t .
26. C o a s t a l - M a r i n e Automated Network (CMAN) S t a t i o n CHLV2 (Chesapeake Bay L i g h t h o u s e , V i r g i n i a ) i s c l o s e s t t o WIS s t a t i o n 59. Waves a t t h e CMAN
s t a t i o n are measured b y an i n f r a r e d l a s e r wave h e i g h t s e n s o r , s a m p l i n g t h e sea s u r f a c e i n a d e p t h o f 12 m o f f t h e n o r t h e a s t c o r n e r o f t h e l i g h t h o u s e . The d e p t h a t t h e WIS s t a t i o n i s 14 m. B o t h l o c a t i o n s are open and u n s h e l t e r e d b y e i t h e r t h e a c t u a l c o a s t l i n e o r model r e p r e s e n t a t i o n o f t h e l a n d / w a t e r
boundary. The CMAN s t a t i o n i s s h e l t e r e d f r o m t h e west t o t h e s o u t h b y t h e l i g h t h o u s e . The l i g h t h o u s e , w i t h i t s l a s e r wave-measuring d e v i c e , i s near t h e e n t r a n c e t o Chesapeake Bay and t h u s may be exposed t o t h e ebb and f l o o d
c u r r e n t s f r o m t h e bay and ocean, r e s p e c t i v e l y . These c u r r e n t s have a maximum magnitude o f about 1 m/sec i n t h e e n t r a n c e . No c u r r e n t s were used i n t h e h i n d c a s t . Thus, any measurable e f f e c t s o f t h e ebb and f l o o d c u r r e n t s on waves, ( e . g . s t e e p e n i n g and b r e a k i n g f o r o p p o s i n g f l o w , o r l e n g t h e n i n g and f l a t t e n i n g f o r f l o w i n t h e same d i r e c t i o n as wave p r o p a g a t i o n ) are n o t
r e p r e s e n t e d i n t h e h i n d c a s t r e s u l t s . No q u a n t i t a t i v e measure o f t h e e f f e c t o f c u r r e n t s such as t h e s e on wave c l i m a t e a t t h e s e s i t e s i s a v a i l a b l e , so t h e i r p o s s i b l e e f f e c t s a r e unknown.
27. Buoy 44012, a t a d e p t h o f 24 m, i s l o c a t e d i n t h e e n t r a n c e t o Delaware Bay c l o s e s t t o WIS s t a t i o n 66 a t a d e p t h o f 18 m. The c u r r e n t s i n t h e bay e n t r a n c e are a g a i n on t h e o r d e r o f 1 m/sec and may i n f l u e n c e l o c a l wave c o n d i t i o n s . Buoy 44012 i s a Large N a v i g a t i o n a l Buoy (LNB), w i t h a
d i s c u s - s h a p e d h u l l , 12 m i n d i a m e t e r . These buoys do n o t f o l l o w t h e s l o p e o f t h e s h o r t e r l e n g t h ( h i g h e r f r e q u e n c y ) s u r f a c e waves as w e l l as t h o s e o f
s m a l l e r s i z e . For example, t h e buoy w o u l d p r o b a b l y n o t r e s p o n d w e l l t o a 4-sec wave w i t h a l e n g t h o f a b o u t 24 m, s i n c e t h e l e n g t h o f t h e buoy i s o n l y o n e - h a l f t h e w a v e l e n g t h . A t r a n s f o r m a t i o n i s a p p l i e d b y t h e N a t i o n a l Data Buoy C e n t e r (NDBC) i n p r o c e s s i n g t h e d a t a f r o m a l l LNB's t o c o r r e c t f o r t h i s l a c k o f r e s p o n s e .
28. Buoy 44013 i s near M a s s a c h u s e t t s Bay a t a d e p t h o f 30 m. WIS s t a t i o n s 94 and 95 a r e c l o s e by. S t a t i o n 94 was chosen f o r c o m p a r i s o n s i n c e
i t i s a t a d e p t h o f 27 m and t h e d e p t h a t s t a t i o n 95 i s 55 m. The l o c a t i o n o f 44013 i s s h e l t e r e d by t h e c o n f i g u r a t i o n o f t h e c o a s t l i n e ( F i g u r e 2, Sheet 4 ) . The g r i d s p a c i n g i n t h e model does n o t a l l o w r e s o l u t i o n o f f e a t u r e s such as Cape Ann, w h i c h i s t h e s m a l l cape t o t h e n o r t h o f buoy 44013. S t a t i o n 94 i s n o t s h e l t e r e d f r o m t h e n o r t h as t h e l a n d / w a t e r b o u n d a r y o f t h e model ( s o l i d l i n e i n F i g u r e 2) i s c o n f i g u r e d . Thus, one m i g h t e x p e c t l e s s wave e n e r g y t o be p r e s e n t a t buoy 44013 t h a n a t s t a t i o n 94 f o r c e r t a i n w i n d and wave
p r o p a g a t i o n c o n d i t i o n s . Buoy 44013 i s an LNB 12-m d i s c u s h u l l and t h u s s u b j e c t t o p o s s i b l y u n d e r e s t i m a t i n g wave c o n d i t i o n s f o r s h o r t e r l o w - p e r i o d waves.
29. F i n a l l y , buoy 44007 i s a t a d e p t h o f 4,7 m and i s c l o s e s t t o WIS s t a t i o n 99 a t a d e p t h o f 18 m. S h e l t e r i n g f r o m t h e a c t u a l c o a s t l i n e and model r e p r e s e n t a t i o n i s n e a r l y e q u i v a l e n t and s h o u l d n o t i n t r o d u c e any b i a s i n
c o m p a r i s o n s . T h i s buoy i s a l s o an LBN w i t h a 12-m d i s c u s - shaped h u l l . 30. T a b l e 9 p r e s e n t s a summary o f average and maximum v a l u e s o f s p e c t r a l wave h e i g h t and peak p e r i o d f r o m measurements and new h i n d c a s t r e s u l t s a t t h e f i v e l o c a t i o n s d i s c u s s e d above. T a b l e 10 p r e s e n t s s i m i l a r i n f o r m a t i o n f r o m t h e o l d h i n d c a s t , b u t f o r wave h e i g h t s o n l y , s i n c e p e r i o d s a r e n o t comparable t o o l d v a l u e s f r o m t h e r e v i s e d h i n d c a s t . T a b l e s 11-15 c o n t a i n t h e m o n t h l y i n f o r m a t i o n summarized i n T a b l e 9. Note t h a t t h e t i m e p e r i o d s f r o m w h i c h t h e averages and maximum v a l u e s a r e d e r i v e d a r e d i f f e r e n t . The h i n d c a s t v a l u e s a r e f r o m t h e 20-year p e r i o d 1956-1975, w h i l e t h e
measurements a r e f r o m 4 t o 9 y e a r s , d e p e n d i n g on t h e buoy, i n t h e p e r i o d f r o m 1982-1991. The h i n d c a s t r e s u l t s a r e c o n t i n u o u s i n t i m e e v e r y 3 h r . The buoy d a t a may have gaps i n t h e r e c o r d o f v a r i o u s l e n g t h s o f t i m e t h r o u g h o u t t h e y e a r s . The buoys measure a l l waves p a s s i n g , w h i l e t h e h i n d c a s t o n l y g e n e r a t e s waves w i t h i n t h e model g r i d , and t h e w i n d f i e l d s used e x c l u d e t r o p i c a l storms
and h u r r i c a n e s . Thus, s w e l l p r o p a g a t i n g f r o m t h e South A t l a n t i c and waves g e n e r a t e d by t r o p i c a l storms and h u r r i c a n e s a r e n o t p r e s e n t i n t h e h i n d c a s t r e s u l t s .
3 1 . Mean wave h e i g h t s f r o m t h e r e v i s e d h i n d c a s t and measurements ( T a b l e 9) a t t h e f i v e s i t e s g e n e r a l l y a g r e e , c o n s i d e r i n g t h e b i a s o f 0.2 m d e t e r m i n e d f r o m t h e h i n d c a s t f o r 1990 and t h e a c c u r a c y o f t h e buoy measurements o f 0.2 m, or 5 p e r c e n t . The l a r g e s t d i f f e r e n c e o f 0.5 m i s a t buoy ^4013 i n
h i n d c a s t v a l u e s . P e r s o n n e l a t NDBC* b e l i e v e h e i g h t s f r o m t h i s buoy may
u n d e r e s t i m a t e a c t u a l c o n d i t i o n s based on o b s e r v a t i o n s f r o m l o c a l p e o p l e i n t h e r e g i o n . T h i s may be due t o t h e s i z e o f t h i s buoy (LNB, 12 m) and t h e
p e r c e n t a g e o f h i g h e r f r e q u e n c y waves i n t h i s embayment v e r s u s t h e open ocean. The d i f f e r e n t i a l s h e l t e r i n g d i s c u s s e d above may a l s o c o n t r i b u t e t o t h i s t r e n d . The e f f e c t o f c u r r e n t s n e a r t h e e n t r a n c e s t o Chesapeake and Delaware Bays may a f f e c t t h e wave c l i m a t e a t t h e s e l o c a t i o n s . Mean peak p e r i o d s a g r e e , on average, w i t h i n 1 sec o r c l o s e t o t h e a c c u r a c y o f t h e buoy measurements
(±1.0 s e c ) .
32. Maximum wave h e i g h t s g e n e r a l l y agree w i t h i n 1.0 m. There i s no t r e n d f o r t h e maximum h i n d c a s t v a l u e s t o be h i g h e r o r l o w e r t h a n measured maximum v a l u e s . The l a r g e s t d i f f e r e n c e i s a t t h e M a s s a c h u s e t t s Bay s i t e , where t h e buoy v a l u e i s l o w e r t h a n t h e h i n d c a s t by 2.6 m. The d i f f e r e n t i a l
s h e l t e r i n g d i s c u s s e d above may be r e s p o n s i b l e f o r t h i s d i f f e r e n c e . Maximum measured and h i n d c a s t peak p e r i o d s agree on t h e average w i t h i n 2 sec.
33. The r e s u l t s f r o m t h e o l d h i n d c a s t i n T a b l e 10 i n d i c a t e t h a t t h e o l d h i n d c a s t mean wave h e i g h t r e s u l t s a r e g e n e r a l l y i n agreement w i t h buoy
measurements, b u t b i a s e d l o w on t h e average b y about 0.4 m, w h i l e maximum v a l u e s a r e c o n s i s t e n t l y l o w b y a b o u t 1 m. No c o m p a r i s o n o f p e r i o d s i s
p o s s i b l e because o f t h e way i n w h i c h t h e o r i g i n a l p e r i o d s were c a l c u l a t e d (see p a r a g r a p h 3 ) .
34. Mean and maximum v a l u e s o f s p e c t r a l wave h e i g h t s and peak p e r i o d s f r o m t h e new 20-year h i n d c a s t agree w e l l w i t h measured v a l u e s a t f i v e s i t e s a l o n g t h e c o a s t f r o m G e o r g i a t o Maine ( T a b l e s 9 and 11-15) . These
c o m p a r i s o n s , and t h e r e s u l t s f r o m t h e 1-year h i n d c a s t d i s c u s s e d above, v e r i f y t h a t t h e new h i n d c a s t v a l u e s o f wave h e i g h t and peak p e r i o d a r e c o n s i s t e n t w i t h t h e c l i m a t o l o g y o f t h e s e wave p a r a m e t e r s a l o n g t h e c o a s t . Next, h i n d c a s t wave d i r e c t i o n s a r e compared t o d i r e c t i o n a l wave measurements.
35. There a r e few d i r e c t i o n a l wave measurements o f l o n g d u r a t i o n i n deeper w a t e r o f f s h o r e away f r o m n e a r s h o r e r e f r a c t i o n e f f e c t s . One s e t o f such measurements f o r t h e p e r i o d 1988-1991 i s a v a i l a b l e f r o m NOAA buoy 41008 (30.7 N, 81.1 W) a b o u t 20 s t a t u t e m i l e s (32.2 Km) o f f t h e c o a s t o f G e o r g i a
* P e r s o n a l Communication, May 1992, D a v i d Wang, Oceanographer, NDBC, S t e n n i s , MS.
( F i g u r e 2, Sheet 2 ) . The d i s t r i b u t i o n o f peak mean d i r e c t i o n i n 10-deg
i n c r e m e n t s f r o m t h i s s e t o f measurements i s shown i n F i g u r e 1 . A l s o p l o t t e d a r e v a l u e s o f t h e same p a r a m e t e r f r o m t h e r e v i s e d h i n d c a s t f o r t h e p e r i o d 1956-1975 a t WIS s t a t i o n 28 ( R e v i s e d A t l a n t i c L e v e l 2 (RAL2), 30.75 N,
81.25 W). The d i s t r i b u t i o n o f mean wave d i r e c t i o n s f r o m Phase I I I (30.81 N, 81.45 W, d e p t h 10 m) o f t h e o r i g i n a l h i n d c a s t a r e a l s o p l o t t e d ( A t l a n t i c Phase 3, AP3). Note t h a t t h e Phase I I I r e s u l t s a r e mean d i r e c t i o n s v e r s u s peak mean d i r e c t i o n s , and o n l y wave energy w i t h a component t o w a r d s h o r e i s p r e s e n t . The mean d i r e c t i o n s were d e t e r m i n e d i n t h e same manner as t h e mean p e r i o d . That i s , sea and s w e l l p o r t i o n s o f t h e s p e c t r a were d e t e r m i n e d and t h e p o r t i o n c o n t a i n i n g t h e l a r g e r amount o f energy d e n s i t y was used t o d e t e r m i n e mean d i r e c t i o n , e x c l u d i n g t h e r e m a i n i n g p o r t i o n .
36. The d i r e c t i o n a l d i s t r i b u t i o n f r o m t h e r e v i s e d h i n d c a s t r e s u l t s
agrees r e a s o n a b l y w i t h t h e shape o f t h e c u r v e f r o m t h e buoy d a t a . D i f f e r e n c e s a r e g e n e r a l l y l e s s t h a n 5 p e r c e n t . Note t h a t t h e buoy d a t a a r e f r o m t h e
p e r i o d 1988-1991, w h i l e t h e WIS r e s u l t s a r e f r o m 1956-1975. To c o n c l u d e t h a t t h e new WIS r e s u l t s a r e a c c u r a t e f r o m t h i s i n f o r m a t i o n , one must assume t h a t t h e d i r e c t i o n a l wave c l i m a t e i s t h e same f o r b o t h p e r i o d s o f t i m e . T h i s d i r e c t i o n a l c o m p a r i s o n , t h o u g h l i m i t e d , shows t h a t t h e r e v i s e d WIS r e s u l t s a c c u r a t e l y r e p r e s e n t t h e d i r e c t i o n a l wave c l i m a t e a t t h i s l o c a t i o n .
PART V: RESULTS
37. H i n d c a s t r e s u l t s a r e a v a i l a b l e a t t h e l o c a t i o n s shovm i n F i g u r e 2, as w e l l as a t t h r e e l o c a t i o n s n o r t h o f P u e r t o R i c o a l o n g 19 deg N a t 65, 66, and 67 deg W. R e s u l t s a r e a v a i l a b l e as t i m e s e r i e s f o r t h e 20-year p e r i o d o r as t a b u l a r summaries s i m i l a r t o p r e v i o u s WIS r e p o r t s . Time s e r i e s r e s u l t s a r e a v a i l a b l e e v e r y 3 h r . Each r e c o r d c o n t a i n s , i n o r d e r : s t a t i o n number, d a t a -t i m e (UTC), s p e c -t r a l wave h e i g h -t ( m e -t e r s ) , peak and mean p e r i o d ( s e c o n d s ) , mean d i r e c t i o n ( d e g r e e s " f r o m " i n a compass s e n s e ) , w i n d speed and d i r e c t i o n
( m e t e r s p e r second, same d i r e c t i o n a l c o n v e n t i o n as w a v e s ) , t h e f r e q u e n c y
s p e c t r u m ( p e r c e n t a g e o f m**2/hz), and t h e mean d i r e c t i o n i n each f r e q u e n c y b a n d ( p e r c e n t o f 360 d e g ) . The f o r m a t and d o c u m e n t a t i o n o f t h e o u t p u t r e c o r d s a r e d e s c r i b e d i n d e t a i l i n WIS R e p o r t 27 ( H u b e r t z 1992) o r i n an A S C I I f i l e
accompanying t h e d a t a . The r e c o r d f o r m a t was d e s i g n e d t o p r o v i d e b a s i c wave i n f o r m a t i o n such as h e i g h t , p e r i o d , and d i r e c t i o n , as w e l l as a more c o m p l e t e s p e c t r a l d e s c r i p t i o n o f wave c o n d i t i o n s . The e n t i r e 20-year t i m e s e r i e s a t a s t a t i o n c a n be p r o v i d e d i n a compressed f o r m a t on two h i g h - d e n s i t y 3-1/2 i n . d i s k s f o r use on p e r s o n a l computers.
38. A l s o a v a i l a b l e a r e two p e r s o n a l computer p r o g r a m s , VIEWTSAT (View Time S e r i e s A t l a n t i c ) and VIEWSPAT (View S p e c t r a A t l a n t i c ) , w h i c h c a n be u s e d t o v i e w t i m e s e r i e s o f wave p a r a m e t e r s o r wave f r e q u e n c y s p e c t r a ,
r e s p e c t i v e l y . A n o t h e r p o s t - p r o c e s s i n g program, SPECOMP, was used t o d e t e r m i n e t h e two m a j o r components i n f r e q u e n c y and d i r e c t i o n o f t h e d i r e c t i o n a l
s p e c t r a . T h i s a l t e r n a t i v e f o r m a t i s u s e f u l when an a p p l i c a t i o n r e q u i r e s b e t t e r r e s o l u t i o n o f d i r e c t i o n a l s p e c t r a l wave e n e r g y t h a n t h e r e s o l u t i o n p o s s i b l e u s i n g o n l y t h e s p e c t r a l h e i g h t , peak p e r i o d , and peak mean d i r e c t i o n , b u t s t i l l c o n f i n i n g i n f o r m a t i o n t o t r i p l e t s o f h e i g h t , p e r i o d , and d i r e c t i o n . Each s t a t i o n ' s 20year parameter/component f i l e c a n be p r o v i d e d on one h i g h -d e n s i t y 3 - 1 / 2 - i n . -d i s k . Less -d i s k space, a p p r o x i m a t e l y 4.5 Mb as oppose-d t o 8 Mb f o r t h e s p e c t r a l f i l e , i s r e q u i r e d t o r e s t o r e t h i s a l t e r n a t e d a t a f i l e t o t h e h a r d d i s k . The t i m e s e r i e s o f r e s u l t s ( i n e i t h e r f o r m a t ) , t h e programs t o v i e w t h e s p e c t r a , and t h e t a b u l a t e d s t a t i s t i c a l summaries a r e a v a i l a b l e . F o r more i n f o r m a t i o n , c o n t a c t t h e WIS p r o j e c t o f f i c e (601-634-2028).
PART V I : EXPLANATION OF SUMMARY TABLES
39. The r e v i s e d h i n d c a s t wave r e s u l t s a r e summarized and t a b u l a t e d i n a f o u r - p a g e f o r m a t f o r each s t a t i o n . These summary t a b l e s a r e p r e s e n t e d i n
Appendix A. The t h r e e s t a t i o n s n o r t h o f P u e r t o R i c o a r e a t t h e end o f t h e appendix. The f i r s t page c o n t a i n s t h e d i s t r i b u t i o n o f s p e c t r a l wave h e i g h t , peak p e r i o d , and peak mean d i r e c t i o n i n 0.5-m h e i g h t , 1-sec p e r i o d , and 22.5-deg d i r e c t i o n c a t e g o r i e s by month f o r t h e 20-year p e r i o d . These t a b l e s a r e u s e f u l i n showing t h e d i s t r i b u t i o n o f h e i g h t , p e r i o d , and d i r e c t i o n
t h r o u g h t h e range o f t h e i r v a l u e s and i n t i m e t h r o u g h t h e y e a r . As an example o f u s i n g t h e t a b l e , a t s t a t i o n 1 (page A3) f o r a l l J a n u a r i e s f r o m 1956 t o 1975, i n c l u s i v e , t h e r e were 2,073 o c c u r r e n c e s o f h i n d c a s t waves w i t h a h e i g h t between 0.50 and 0.99 m, i n c l u s i v e . Model o u t p u t i s e v e r y 3 h r on t h e h o u r i n UTC t i m e . The t o t a l number o f p o s s i b l e o c c u r r e n c e s f o r each month i s shown a t
t h e b o t t o m o f each m o n t h l y column. The t o t a l f o r F e b r u a r y d i f f e r s f r o m t h e o t h e r months due t o t h e l e n g t h o f t h e month (28 days) p l u s an e x t r a day i n t h e month e v e r y 4 y e a r s , o r l e a p y e a r . The t o t a l ntimber o f o c c u r r e n c e s i n each
c a t e g o r y i s shown i n t h e l a s t column on t h e r i g h t s i d e o f t h e page. The t o t a l p o s s i b l e number o f o c c u r r e n c e s i s 58,440. Note t h a t number o f o c c u r r e n c e s i s r e p o r t e d , whereas p r e v i o u s WIS r e p o r t s have used p e r c e n t o c c u r r e n c e s . T h a t i s , t h e number o f o c c u r r e n c e s , d i v i d e d b y t h e t o t a l p o s s i b l e , t i m e s 100. The number o f o c c u r r e n c e s i s used t o e x p l i c i t l y a c c o u n t f o r each o c c u r r e n c e . The t r u n c a t i o n o f p e r c e n t a g e v a l u e s c a n o m i t i n d i c a t i o n o f r a r e o c c u r r e n c e s and p o s s i b l y y i e l d c u m u l a t i v e t o t a l s l e s s t h a n 100 p e r c e n t .
40. The n e x t s e t o f t a b l e s shows t h e number o f o c c u r r e n c e s b y 1-m
h e i g h t and 2-sec p e r i o d c a t e g o r i e s f o r e i g h t d i f f e r e n t d i r e c t i o n bands each 45 deg i n w i d t h , and a f i n a l t a b l e f o r a l l d i r e c t i o n s . These t a b l e s a r e u s e f u l t o f i n d t h e dominant d i r e c t i o n f r o m w h i c h wave energy i s a p p r o a c h i n g a l o c a t i o n and how i t i s d i s t r i b u t e d i n h e i g h t and p e r i o d . For example, a t s t a t i o n 1 (page A4) t h e r e were 149 o c c u r r e n c e s o f waves w i t h a h e i g h t b e t w e e n 2.00 and 2.99 m and p e r i o d between 9.0 and 10.9 sec f r o m t h e d i r e c t i o n band b e t w e e n 67.50 and 112.49 deg c e n t e r e d a b o u t 90.0 deg. Column and row
summations a r e shown a l o n g t h e b o t t o m row and r i g h t - h a n d column, r e s p e c t i v e l y , as i n t h e o c c u r r e n c e s - b y - m o n t h t a b l e s d i s c u s s e d above. Note t h a t a t t h i s
between t h e compass d i r e c t i o n s o f ENE and ESE, and most o f t h e s e a r e l o w i n h e i g h t and p e r i o d .
4 1 . The d i s t r i b u t i o n o f w i n d i n 2.5-m/sec and 45-deg speed and d i r e c t i o n c a t e g o r i e s , on a m o n t h l y b a s i s , i s shown i n t h e n e x t two t a b l e s . These t a b l e s a r e u s e f u l f o r u n d e r s t a n d i n g t h e c l i m a t o l o g y o f w i n d s a t a s i t e . L o c a l sea c o n d i t i o n s and w i n d - d r i v e n c u r r e n t s can be i n f e r r e d f r o m t h e w i n d c l i m a t o l o g y . Note t h a t a t t h i s s t a t i o n , w i n d s a r e g e n e r a l l y l e s s t h a n 7.5 m/sec and a r e f r o m t h e e a s t o r n o r t h e a s t .
42. The l a s t two t a b l e s , page A6, summarize mean and maximum wave h e i g h t s by month f o r each o f t h e 20 y e a r s h i n d c a s t . The maximum wave h e i g h t
t a b l e a l s o i n c l u d e s t h e peak p e r i o d and peak mean wave d i r e c t i o n a s s o c i a t e d w i t h t h e maximum wave h e i g h t o c c u r r e n c e . Means and maxima by month f o r a l l y e a r s and by y e a r s f o r a l l months a r e summarized on t h e b o t t o m row and r i g h t -hand column, r e s p e c t i v e l y . A s s o c i a t e d peak p e r i o d s and peak mean d i r e c t i o n s a r e i n c l u d e d i n t h e summary row and column o f t h e maximum t a b l e .
43. As an example, t h e maximum h e i g h t i n 1956 a t s t a t i o n 1 was 2.4 m, had a peak p e r i o d o f 9 sec, and was coming f r o m a b o u t 70 deg f r o m t h e ENE. S i n c e t h e peak d i r e c t i o n s o f t h i s t a b l e a r e d i v i d e d by 10, t h e t a b u l a t e d v a l u e i s t h e mid-range o f a 10-deg d i r e c t i o n band. The a c t u a l v a l u e f o r t h e peak d i r e c t i o n , r e p r e s e n t e d b y a 7, c o u l d have been f r o m any d i r e c t i o n f r o m 65 t o 74 deg. The l a r g e s t h e i g h t o c c u r r i n g a t t h i s s t a t i o n i n any o f t h e J a n u a r i e s o f t h e 20-year p e r i o d i s 3.1 m, and o c c u r r e d i n b o t h 1957 and 1968, w i t h r e s p e c t i v e peak p e r i o d s o f 9 and 7 sec and peak d i r e c t i o n s o f 80 and 90 deg.
44. The l a s t two l i n e s o f t h e summary t a b l e s f o r each s t a t i o n c o n t a i n t h e maximum h e i g h t a t t h e s t a t i o n f o r t h e e n t i r e 20-year p e r i o d and t h e
a s s o c i a t e d peak p e r i o d , peak mean d i r e c t i o n , and d a t e o f o c c u r r e n c e , and t h e maximum w i n d speed, a s s o c i a t e d d i r e c t i o n , and d a t e o f o c c u r r e n c e . A t t h i s p a r t i c u l a r s t a t i o n , t h e maximum h e i g h t o c c u r r e d on June 3, 1968 and was due t o t h e i n f l u e n c e o f H u r r i c a n e Abby s o u t h o f Cuba. Note t h a t h u r r i c a n e s a r e n o t modeled as e n t i t i e s , b u t t h e y can i n f l u e n c e t h e l a r g e r s c a l e p r e s s u r e f i e l d s f r o m w h i c h t h e w i n d f i e l d s a r e c a l c u l a t e d and t h u s r e s u l t i n h i g h w i n d and wave energy.
45. A p p e n d i x B c o n t a i n s e s t i m a t e d wave h e i g h t s f o r r e t u r n p e r i o d s o f 2, 5, 10, 20, 25, and 50 y e a r s b a s e d on t h e 20 y e a r s o f h i n d c a s t r e s u l t s and t h e F i s h e r T i p p e t t Type I and I I d i s t r i b u t i o n s . The v a l u e s were c a l c u l a t e d u s i n g
t h e methods employed i n t h e s i g n i f i c a n t wave h e i g h t a n a l y s i s module o f t h e Automated C o a s t a l E n g i n e e r i n g System (ACES) package ( L e e n k n e c h t , S z u w a l s k i ,
and S h e r l o c k 1990) . Note t h a t t h e s e v a l u e s do n o t r e p r e s e n t t h e e f f e c t s o f t r o p i c a l s t o r m s o r h u r r i c a n e s . WIS R e p o r t 19 ( A b e l e t a l . 1989) s h o u l d be used f o r e s t i m a t e s r e l a t e d t o t h o s e e v e n t s . The l o c a t i o n s a t w h i c h
i n f o r m a t i o n i s a v a i l a b l e i n t h e two s t u d i e s d i f f e r , due t o t h e d i f f e r e n t model g r i d s used.
46. T a b l e 16 p r e s e n t s a c o m p a r i s o n o f wave h e i g h t s f o r v a r i o u s r e t u r n p e r i o d s a t t h e f i v e l o c a t i o n s where t h e o r i g i n a l h i n d c a s t s t a t i o n s a r e c l o s e t o t h e r e v i s e d h i n d c a s t l o c a t i o n s . The o r i g i n a l h i n d c a s t v a l u e s a r e d e n o t e d by AP3 f o r A t l a n t i c Phase 3, and t h e r e v i s e d h i n d c a s t v a l u e s by RAL2 f o r R e v i s e d A t l a n t i c L e v e l 2. F i s h e r T i p p e t t Type I and Type I I e s t i m a t e s were c a l c u l a t e d f r o m b o t h t h e o r i g i n a l 20-year t i m e s e r i e s and t h e r e v i s e d 20-year t i m e s e r i e s . The e s t i m a t e s p u b l i s h e d i n WIS R e p o r t 9 ( J e n s e n 1983) a r e a l s o shown. These were c a l c u l a t e d u s i n g p r o b a b i l i t i e s d e t e r m i n e d by t h e number o f events p l u s one, d i v i d e d b y t h e r a n k o f t h e e v e n t . Wave h e i g h t s were r a n k e d u s i n g o n l y one h e i g h t p e r e v e n t , where e v e n t s were d e f i n e d as storms s e p a r a t e d by a t l e a s t 5 days.
47. The e s t i m a t e d h e i g h t s f o r a l l r e t u r n p e r i o d s a r e u n i v e r s a l l y h i g h e r f o r t h e r e v i s e d h i n d c a s t t h a n f o r t h e o r i g i n a l h i n d c a s t . The h i g h e r v a l u e s a r e c l o s e r t o t h e h i g h e s t v a l u e s measured b y t h e buoys c l o s e t o t h e s e
l o c a t i o n s . Note t h a t t h e d u r a t i o n o f buoy measurements i s s h o r t e r t h a n t h e 20 y e a r s o f h i n d c a s t r e s u l t s and f o r a d i f f e r e n t p e r i o d o f t i m e . I n summary, t h e r e v i s e d v a l u e s o f wave h e i g h t f o r v a r i o u s r e t u r n p e r i o d s a r e l a r g e r t h a n t h e o r i g i n a l h i n d c a s t v a l u e s and more a c c u r a t e , s i n c e t h e y more c l o s e l y c o r r e s p o n d t o maximum measured v a l u e s .
48. These summary t a b l e s and t h e model o u t p u t r e c o r d s f r o m w h i c h t h e y were d e r i v e d a r e a v e r i f i e d source o f i n f o r m a t i o n f o r t h e w i n d and wave
c l i m a t e a l o n g t h e US East c o a s t . T h i s i n f o r m a t i o n can be u s e d t o g a i n a b a s i c u n d e r s t a n d i n g o f w i n d and wave c o n d i t i o n s a t a s i t e and may be used as i n p u t t o more s p e c i f i c m o d e l i n g a s s o c i a t e d w i t h c o a s t a l e n g i n e e r i n g p r o j e c t s . P r e s e n t c o a s t a l e n g i n e e r i n g p r a c t i c e r e q u i r e s s i t e - s p e c i f i c i n v e s t i g a t i o n s w i t h p o s s i b l e m o d e l i n g o f a l t e r n a t i v e d e s i g n s . Thus, h i g h - r e s o l u t i o n wave
i n f o r m a t i o n c l o s e t o t h e s h o r e i s more e f f i c i e n t l y p r o d u c e d , as r e q u i r e d f o r s i t e - s p e c i f i c p r o j e c t s , b y making use o f t h i s o f f s h o r e wave i n f o r m a t i o n r a t h e r
t h a n a p p l y i n g a h i g h e r r e s o l u t i o n l e v e l o f m o d e l i n g a l o n g t h e e n t i r e
c o a s t l i n e . T h i s one s e t o f r e v i s e d h i n d c a s t r e s u l t s r e p l a c e s t h e t h r e e phases o f t h e p r e v i o u s s t u d y summarized i n WIS R e p o r t 2 (Corson e t a l . 1 9 8 1 ) , WIS R e p o r t 6 (Corson e t a l . 1 9 8 2 ) , and WIS R e p o r t 9 (Jensen 1 9 8 3 ) .
REFERENCES
A b e l , C. E., T r a c y , B. A., V i n c e n t , C. L., and Jensen, R. E. 1989 ( A p r ) . " H u r r i c a n e H i n d c a s t Methodology and Wave S t a t i s t i c s f o r t h e A t l a n t i c and G u l f H u r r i c a n e s f r o m 1956-1975," WIS R e p o r t 19, US Army E n g i n e e r Waterways
E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
Corson, W. D., R e s i o , D. T., Brooks, R. M., E b e r s o l e , B. A., Jensen, R. E., Ragsdale, D. S., and T r a c y , B. A. 1981 ( J a n ) . " A t l a n t i c Coast H i n d c a s t Deepwater S i g n i f i c a n t Wave I n f o r m a t i o n , " WIS R e p o r t 2, US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
. 1982 ( M a r ) . " A t l a n t i c Coast H i n d c a s t , Phase I I : Wave I n f o r m a t i o n , " WIS R e p o r t 6, US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
G i l h o u s e n , D. B., M e i n d l , E. A., Changery, M. J . , F r a n k s , P. L., B u r g i n , M. G., and M c K i t t r i c k , D. A. 1990 ( F e b ) . " C l i m a t i c Summaries f o r NDBC Buoys and S t a t i o n s , Update 1 , " N a t i o n a l Data Buoy C e n t e r , S t e n n i s , MS.
H u b e r t z , J . M. 1992 ( J u n ) . "A Users Guide t o t h e WIS Wave Model, V e r s i o n 2.0," WIS R e p o r t 27, US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
Jensen, R. E. 1983 ( J a n ) . " A t l a n t i c Coast H i n d c a s t , S h a l l o w - W a t e r , S i g n i f i c a n t Wave I n f o r m a t i o n , " WIS R e p o r t 9, US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
Leenknecht, D., S z u w a l s k i , A., and S h e r l o c k , A. 1990 ( D e c ) . "Automated C o a s t a l E n g i n e e r i n g System," US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
L i n , Li-Hwa, and Wang H. 1990 ( D e c ) . " A p p l i c a t i o n s o f WIS Wave Models i n V e r i f i c a t i o n Study," UFL/COEL-90/013, C o a s t a l and Oceanographic E n g i n e e r i n g Department, U n i v e r s i t y o f F l o r i d a , G a i n e s v i l l e , FL.
M i l l e r , H. C.', and Jensen, R. E. 1990 ( O c t ) . "Comparison o f A t l a n t i c Coast Wave I n f o r m a t i o n Study H i n d c a s t s w i t h F i e l d Research F a c i l i t y Gage
Measurements," CERC-TR-90-17, US Army E n g i n e e r Waterways E x p e r i m e n t S t a t i o n , V i c k s b u r g , MS.
Weggel, J . R., D o u g l a s s , S. L., and T u n n e l l , J . E. 1988 ( M a r ) . "Sand-B y p a s s i n g S i m u l a t i o n U s i n g S y n t h e t i c Longshore T r a n s p o r t Data," J o u r n a l o f Waterway. P o r t , C o a s t a l , and, Ocean E n g i n e e r i n g . V o l 114, No. 2.
KINGS BAY, GEORGIA
RAL2 28 V S AP3132 V S NOAA 41008
30-,Wave Direction (degrees)
^ RAL2 (56-75) AP3 (56-75) - Q - BUOY (88-91)
F i g u r e 1 . D i s t r i b u t i o n o f wave d i r e c t i o n s f r o m o r i g i n a l h i n d c a s t (AP3) and r e v i s e d h i n d c a s t (RAL2) f o r 1956-1975 and measurements f r o m Buoy 41008 d u r i n g 1988-91
F i g u r e 2. L o c a t i o n o f WIS S t a t i o n s ( s o l i d d o t s ) , NOAA buoys ( c i r c l e d d o t s ) , l a n d / w a t e r b o u n d a r y ( s o l i d t h i n l i n e , a c t u a l ; s o l i d wide l i n e ,
ATLANTIC
OCEAN
30 O 4 1 0 0 6 28 F i g u r e 2. (Sheet 2 o f 4 )Atlantic Revision - Grid Level 1
82° W 62° W 42° W 22° W L o n g i t u d e
F i g u r e 3. One-degree l a t i t u d e / l o n g i t u d e g r i d f o r l e v e l 1 o f h i n d c a s t ( c i r c l e d p o i n t s a r e b o u n d a r y i n p u t p o i n t s f o r l e v e l 2)
Atlantic Revision - Grid Level 2
L o n g i t u d e
F i g u r e 4. O n e - q u a r t e r - d e g r e e l a t i t u d e / l o n g i t u d e g r i d f o r l e v e l 2 o f h i n d c a s t ( c i r c l e d p o i n t s a r e i n p u t p o i n t s f r o m l e v e l 1)
T a b l e 1
Wind Speed B i a s . Buoy - Model, 1990*
Buoy J a n Feb Mar A p r May J u n J u l Aug Sep Oct Nov Dec Average
41006 0. 8 0. .8 0. 3 0. ,6 1. .0 0. 6 1. ,0 1. 0 1. ,6 0. .9 1.0 0.9 41008 0. ,1 0. 3 0, .3 0. 4 1, ,0 1. .4 1. 3 1. ,7 1. 2 1. .6 1. .2 1.1 1.0 41002 0. ,3 0. 9 0. .9 0. .9 0. 9 1. ,2 0. 6 0. ,6 0. ,6 0.9 0.8 41001 2, ,1 1. 9 1. ,3 1 . 8 1. ,5 1. .1 1. 6 1. ,0 0. 8 2. ,0 2. ,3 2.9 1.7 44014 -0.3 -0.3 44015 1. .3 1. ,2 - 1.2 44009 1. 3 1. 2 1. ,6 0. 9 1. ,1 0. .0 1. 6 1 . 6 1. ,9 1. ,1 1.3 1.2 44001 0.4 0.4 44004 1. ,7 1. 3 1. .0 0. 5 -0. .3 0, .2 0. 6 0. ,9 1. 4 1. .9 2. .3 1.4 1.1 44012 - -44008 1. 8 1. 6 1. .6 1 . 3 2, .0 1. .2 2. 1 1. ,0 1. 0 2. .0 2. .3 2.2 1.7 44011 1. 1 0. 6 0. ,0 -0. 1 0. ,4 -0, .9 0. 3 1. ,2 1. 4 1. .1 - 1 . .2 -1.2 0.2 44005 1. 7 I . 5 0.
.9
1 . 1 0. ,7 0, .4 0. 4, 1. ,3 1. 4 1. .0 1. ,6 1.2 1.1 44007 -0. 1 0. 8 0. ,9 0. 3 1. ,0 0, .6 0. 5 0. 8 1. 2 0. .7 0. .9 0.3 0.6 V a l u e s i n meters p e r second.T a b l e 2
Wind Speed RMSD'. 1990'
Buoy J a n Feb Mar Apr May J u n J u l Aug Sep Oct Nov Dec Average
41006 2. 2 1.8 1 . 6 1. ,5 2, .0 1. 7 2. ,0 1.8 2. .7 1. ,7 1.7 1.9 41008 1. .9 2. 2 1.9 2. 0 2. 0 2. .2 2. 3 2. ,4 2.1 2. ,5 2. .3 2.3 2.2 41002 1.0 2. 0 1. 7 2. ,6 2. 0 1. ,9 1.5 2. ,3 1. .5 2.0 1.8 41001 3. .1 2. 5 2.6 2. 8 2. 2 2. ,1 2. 2 2. ,0 2.1 3. .1 2. ,9 3.5 2.6 44014 - - - -44015 - - 3. .1 2. ,4 - 3.0 44009 3. .0 3. 0 3.0 2. 8 3. 1 2. ,4 3. 0 2. ,8 2.2 3. .1 2. ,6 2.8 2.8 44001 - - - -44004 3. .4 2. 9 2.6 2. 6 2. 6 2. ,0 1. 7 2. ,3 2.3 3. ,8 3. ,2 2.8 2.7 44012 - - - -44008 3. .0 2. 8 2.5 2. 5 3. 1 2. .2 3. 0 2. ,1 2.3 3. ,4 3. ,3 3.1 2.8 44011 2. ,9 2. 4 2.1 2. 3 2. 5 2. ,4 2. 0 2. ,9 2.8 2. ,7 2. ,6 2.3 2.5 44005 2. ,8 2. 5 2.1 2. 3 2. 2 1. ,7 1. 7 2. 0 2.4 2. ,3 2. .5 2.2 2.2 44007 3. .0 2. 4 2.8 2. 0 2. 8 2. ,2 2. 1 2. 0 2.3 2. ,5 2. ,8 2.8 2.5
Root Mean Square D i f f e r e n c e V a l u e s i n m e t e r s p e r second.
T a b l e 3
Wave H e i g h t B i a s . Buoy - Model. 1990'
Buoy J a n Feb Mar A p r May J u n J u l Aug Sep Oct Nov Dec Average
41006 -0. 1 -0. 1 -0. 5 -0. 3 -0, .2 -0. 2 -0. 3 -0. 3 -0. 1 -0. ,2 -0. 5 -0.2 41008 -0. 2 -0. 1 -0. 1 -0. 4 -0. 1 -0. .1 -0. 1 -0. 3 -0. 2 -0. 2 0, .0 -0. 3 -0.2 41002 - -0. 4 -0. 4 -0. 2 -0. .1 -0. 2 -0. 4 -0. 5 -0. 6 -0.4 41001 0. 0 -0. 1 -0. 1 -0. 2 -0. 1 -0. .1 0. 0 -0. 3 -0. 3 -0. 1 0, .1 -0. 1 -0.1 44014 - - -0. 1 -0.1 44015 - - -0. 3 -0, .3 -0. 8 -0.5 44009 -0. 4 -0. 4 -0. 4 -0. 5 -0. 3 -0. .2 -0. 1 -0. 3 -0. 4 -0. 4 -0. .2 -0. 4 -0.3 44001 - - -0. 1 0. .1 -0. 1 -0.0 44004 0. 2 -0. 1 -0. 2 -0. 3 -0. 1 -0. .3 -0. 3 -0. 2 -0. 3 0. 0 0. .3 0. 0 -0.1 44012 - - -0. 3 0, .0 -0. 4 -0.2 44008 0. 0 -0. 2 -0. 3 -0. 3 -0. 1 -0. .4 -0. 3 -0. 3 -0. 2 -0. 2 -0. .1 -0. 2 -0.2 44011 0. 1 -0. 2 -0. 4 -0. 3 0. 0 -0. .3 -0. 2 -0. 2 -0. 1 -0. 1 0. .0 -0. 4 -0.2 44005 0. 1 -0. 1 -0. 2 -0. 3 -0. 1 -0. .4 -0. 3 -0. 4 -0. 2 -0. 4 0. .0 -0. 2 -0.2 44007 -0. 3 -0. 3 -0. 3 -0. 3 -0. 1 -0. .2 -0. 2 -0. 3 -0. 3 -0. 6 -0, .5 -0. 5 -0.3 V a l u e s i n m e t e r s . No d a t a a v a i l a b l e .
T a b l e 4
Wave Peak P e r i o d B i a s . Buoy - Model. 1990*
Buoy J a n Feb Mar Apr May J u n
41006 0. 4 -0. 5 - 1 . 5 - 1 . 9 -0.8 41008 - 1 . 5 -0. 1 - 1 . 1 - 1 . 1 -2. 7 -1.6 41002 - 1 . 0 -2. 3 - 1 . ,4 -0.5 41001 -0. ,9 -0. 3 - 1 . 1 - 1 . 9 -0. ,8 -0.4 44014 -44015 -44009 -0. ,6 -0. 1 -0. ,7 -0. 2 0. ,5 -0.1 44001 -44004 -0. ,6 -0. 1 - 1 . 3 - 1 . 5 0. 2 -0.2 44012 -44008 -0. ,3 0. 3 -0. 4 0. 0 0. 7 -0.1 44011 0. 5 -0. 1 - 1 . ,3 -0. 9 0. ,2 -0.4 44005 -0. .4 -0. 7 - 1 . ,6 - 1 . 5 0. ,3 -0.6 44007 0, ,7 1 . 1 0. ,0 -0. 3 1. ,8 -0.4
J u l Aug Sep Oct Nov Dec Average -0. .5 -0. .9 - 1 . ,0 -0. 8 -0. 7 - 1 . .7 -0. .9 - 1 . .0 - 1 , ,2 - 1 . .6 - 1 . 8 - 1 . 4 -2. .7 - 1 , .5 0. .1 - 1 . .1 -0, .3 - 1 . .9 - 1 . .0 -0. .2 -0. .5 -0. .6 -0. 8 -0. 8 - 1 . ,3 -0. .8 -0. .5 -0. .5 - 1 . 1 - 1 . 4 -2. .8 - 1 , .8 -0. .9 0, .6 0, ,0 -0. 2 -0. 9 -2. .1 -0. .4 -0. .4 -0. .4 -0. .5 -0. .4 -0, ,6 -0. 5 -0. 8 - 1 , .7 -0. .7 -0. 7 -0. 2 -3. .6 - 1 . .5 0, .1 0. .4 0, .3 0. 0 -0. 1 -0. ,3 0. .0 0, .0 -0. .6 -0, ,5 0. 1 -0. 3 -0, .9 -0, ,4 -0. .5 -0. .5 -0, .4 -0. 8 - 1 . 0 - 1 . .7 -0. .8 0. .4 0. .2 0, .8 0. 5 -0. 1 0. ,8 0. .4 * V a l u e s i n seconds.
T a b l e 5
Wave H e i g h t Root Mean Square D i f f e r e n c e . 1990'
Buoy J a n Feb Mar Apr May J u n J u l Aug Sep Oct Nov Dec Average
41006 0. 5 0. .4 0. .6 0. .4 0. .4 0.4 0. .4 0. .5 0 .6 0. 4 0, .7 0. .5 41008 0, .4 0. 4 0. .3 0. .5 0. .3 0. .3 0.3 0, .4 0. .4 0 .5 0. 3 0. .5 0. ,4 41002 0, .5 0. .6 0. .5 0. .3 0.4 0. .5 0. .7 0, ,8 0. .5 41001 0, .8 0. 5 0. .4 0, .5 0. .4 0. .3 0.3 0. .5 0, .7 0 .9 0. 5 0. .6 0. .5 44014 - 0, ,5 0. .5 44015 - 1 .1 0. 8 1. .0 1. .0 44009 0. .6 0. 6 0. ,7 0. .7 0. .5 0. .4 0.4 0. .5 0. .6 0 .8 0. 5 0. ,6 0. .6 44001 - 0. ,5 0. .5 44004 0. .7 0. 5 0, .5 0. .5 0. .6 0, .5 0.4 0. .5 0. .6 1 .0 0. 7 0. .7 0, .6 44012 - 0 .7 0. 7 0. .7 0. .7 44008 0, .5 0. 8 0. .6 0. ,5 0. .5 0. .6 0.5 0. .5 0. .5 0 .9 0. 5 0. .5 0. .6 44011 0. .7 0. 7 0. .7 0. .6 0. .6 0, .6 0.4 0. .6 0. .5 0 .8 0. 5 0. .8 0. .6 44005 0. .6 0. 6 0. .5 0. .4 0, ,4 0. .6 0.4 0. .6 0. .5 0 .8 0. 6 0. ,6 0. .6 44007 0, .6 0. 6 0. .5 0. .6 0. .4 0. .5 0.4 0. .4 0. .5 0 .7 0. 7 0. .7 0. .6 V a l u e s i n m e t e r s .
T a b l e 6
Wave Peak P e r i o d Root Mean Square D i f f e r e n c e . 1990'
Buoy Jan Feb Mar A p r May J u n J u l Aug Sep Oct Nov Dec Average
41006 1 . 3 1. 5 3. 1 3. .4 2, .0 2.3 2. ,3 2. ,6 3.5 2. .3 3.4 2.5 41008 3. ,5 0. 4 2. 2 2. 0 4. .4 3, ,0 3.0 3. ,9 3. ,4 3.5 3. .1 4.0 3.0 41002 1 . 3 3. 6 2. .7 1, ,6 1.8 2. ,8 1. ,7 - 3.4 2.4 41001 1. ,9 1 . 8 2. 3 3. 1 2. .2 1. .4 1.4 3. ,5 2. ,5 2.8 2. ,6 3.3 2.4 44014 - - 2.4 2.4 44015 - 2.8 2. ,7 4.3 3.3 44009 3. .1 2. 8 2. 7 2. 8 2. .7 1. .6 2.6 3. ,7 2. ,6 2.9 3. ,2 4.2 2.9 44001 - - 2.4 2.4 44004 2. .4 1 . 6 2. 7 2. 9 2. ,4 1. .3 1.4 4. ,8 2. .4 2.6 2. ,5 3.4 2.5 44012 - 3.0 2. 8 4.6 3.5 44008 2. .4 1 . 9 2. 6 2. 0 2. .0 1. ,3 1.8 4. ,3 2. ,0 2.2 2. ,1 2.5 2.2 44011 1. ,9 1. 7 2. 7 2. 1 2. ,3 1. .5 1.7 3. 9 2. ,3 2.4 1. .7 3.0 2.3 44005 1. ,7 2. 1 3. 0 2. 8 1. ,8 1, .7 1.9 3. 1 2. ,4 2.5 2. ,5 3.3 2.4 44007 3. ,1 3. 0 2. 9 1 . 8 3. ,1 1. .8 2.8 3. ,4 3. ,2 2.9 2. 8 3.4 2.8 V a l u e s i n seconds.
