UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Wave hindcast sensitivity to wind forcing Hodgins, Sandra Leella Margaret 1986

You don't seem to have a PDF reader installed, try download the pdf

Item Metadata

Download

Media
[if-you-see-this-DO-NOT-CLICK]
[if-you-see-this-DO-NOT-CLICK]
UBC_1986_A7 H62.pdf [ 7.26MB ]
Metadata
JSON: 1.0062938.json
JSON-LD: 1.0062938+ld.json
RDF/XML (Pretty): 1.0062938.xml
RDF/JSON: 1.0062938+rdf.json
Turtle: 1.0062938+rdf-turtle.txt
N-Triples: 1.0062938+rdf-ntriples.txt
Original Record: 1.0062938 +original-record.json
Full Text
1.0062938.txt
Citation
1.0062938.ris

Full Text

WAVE HINDCAST SENSITIVITY TO WIND FORCING by SANDRA LEELLA MARGARET HODGINS B.A.Sc, University of Waterloo, 1970  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE  in THE  FACULTY OF GRADUATE STUDIES  DEPARTMENT OF CIVIL ENGINEERING  We accept t h i s thesis as conforming to the required standard  THE  UNIVERSITY OF BRITISH COLUMBIA October 1986  © Sandra Lee11a Margaret Hodgins, 1986  In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements advanced Library agree  degree at THE UNIVERSITY s h a l l make i t freely  that  purposes  OF BRITISH COLUMBIA, I agree  a v a i l a b l e f o r reference and study.  permission f o r extensive copying  may be granted  representatives.  by the Head  of t h i s  thesis  that the I further  f o r scholarly  of my Department or by h i s or her  I t Is understood that copying or publication of t h i s thesis  f o r f i n a n c i a l gain s h a l l not be allowed without my written permission.  Department of C i v i l Engineering THE UNIVERSITY OF BRITISH COLUMBIA 2075 Wesbrook Place Vancouver, Canada V6T 1W5  Date:  of an  October 1986  Abstract E f f i c i e n t planning and safe operation of marine vessels and coastal structures require  good  statistical  understanding  terras.  of wave  properties,  In the absence of very  u s u a l l y expressed  in  long direct measurement records,  spectral wave hindcasting i s r o u t i n e l y used to d e r i v e design and o p e r a t i n g criteria.  The method i n v o l v e s s o l u t i o n of a time-dependent energy balance  equation i n c l u d i n g s p a t i a l propagation, growth due to l o c a l wind, non-linear t r a n s f e r s between frequency  components and d i s s i p a t i o n processes.  The most  important source of e r r o r s i n a c a r e f u l h i n d c a s t i s the input wind which i s normally derived from h i s t o r i c a l surface pressure data. models generate a sea-state that i s almost  Since spectral wave  i n balance with l o c a l winds, wind  sea i s l a r g e l y independent of the preceding storm history. the other hand, propagates  f r e e l y at off-wind angles perpetuating any errors  that occurred i n i t s generation. modelled  Shallow water near-shore  with a small-area, nested  the surrounding  Swell energy, on  large-area model.  zones are u s u a l l y  subgrid that receives boundary data from Since the wave energy solution within the  submodel can be dominated by the boundary conditions, errors i n the large-area model must be minimized. The purpose of this study was to i n v e s t i g a t e the s e n s i t i v i t y of hindcast wave f i e l d s to p r e s c r i b e d e r r o r s i n the e v o l u t i o n of the wind p a t t e r n s .  Using a  r a d i a l l y symmetric model of s u r f a c e p r e s s u r e , f i v e parameters were used to define storm e v o l u t i o n : storm trajectory, minimum central low pressure, rate of storm i n t e n s i f i c a t i o n , advection rate and storm size. of each parameter were used variation  to o b t a i n the l i k e l y  i n the s i g n i f i c a n t  c o n s i d e r i n g wind sea o n l y ,  wave  height  S e n s i t i v i t y analyses maximum  field.  the three most important  attributable  On t h i s  b a s i s , and  parameters are (1)  trajectory, (2) minimum central pressure and (3) advection rate.  With careful  wind f i e l d re-construction, wave hindcasts of s p e c i f i c events can be performed to acceptable engineering standards f o r extreme value analysis. the present, c l i m a t o l o g i c a l (continuous multi-year) wave databases  However, f o r constructed  by s p e c t r a l h i n d c a s t i n g w i l l be too i n a c c u r a t e to warrant t h e i r cost. The most  promising  advance  f o r wave  hindcasting  (and f o r e c a s t i n g ) i s the  p o s s i b i l i t y of a c q u i r i n g h i g h - r e s o l u t i o n wind and wave data with s a t e l l i t e sensors to eliminate the need for inherently inaccurate surface pressure data.  - iii Table of Contents  Page  Abstract T a b l e of  ii Contents  iii  List  of  Tables  v  List  of  Figures  vi  Acknowledgement  xii  1.0  Introduction  1  2.0  Sea-State Description:  for  Wave M o d e l l i n g  The E n e r g y B a l a n c e E q u a t i o n  10  2.2  Wave M o d e l P a r a m e t e r i z a t i o n s  11  2.2.1  Wave D i r e c t i o n a l i t y  11  2.2.2  The E n e r g y S o u r c e F u n c t i o n  13  2.2.3  The E n e r g y S p e c t r u m  15  Parametric  15  2.3  Forms  Forms  16  Other  Considerations  16  2.3.1  W i n d - S e a and S w e l l  16  2.3.2  S h a l l o w Water E f f e c t s  18  2.3.3  Wind I n p u t  18  S p e c t r a l Wave M o d e l s  23  3.1  Parametric  24  3.2  Discrete  S p e c t r a l Wave M o d e l s  S p e c t r a l Wave M o d e l s  26  3.2.1  The ODGP M o d e l  27  3.2.1  The ADWAVE M o d e l  30  Propagation  .  S o u r c e Terms 4.0  10  2.1  Discrete  3.0  The B a s i s  Wind F i e l d S e n s i t i v i t y : the  30 33  An A p p l i c a t i o n Sensitivity  of  ADWAVE  Analysis  39  4.1  S t r u c t u r e of  4.2  Wind F i e l d S p e c i f i c a t i o n  40  4.2.1  The S u r f a c e P r e s s u r e F i e l d M o d e l  42  4.2.2  Gradient  47  and S u r f a c e W i n d F i e l d s  39  4.3  Wave M o d e l a n d G r i d S e t up  47  4.4  Pressure Parameter  51  Specification  4.4.1  Trajectory  53  4.4.2  Central  53  4.4.3  Storm Speed  53  4.4.4  R a d i a l S c a l i n g Parameter  55  Pressure  -  iv  -  T a b l e of Contents (Continued) Page 4.5  Summary o f M o d e l T e s t C a s e s  56  4.5.1  S t o r m 1: The M e d i a n B a s e S c e n a r i o  56  4.5.2  Storm 2: E x p l o s i v e Deepening  57  4 . 5 . 3 Storm 3: E a s t e r l y S h i f t e d Northward 4.5.4  Storm 4:  4.5.5  Storm 5: A d v e c t i o n Rate ( S t a l l e d Weather System  6.0  of  59 in  Alaska)  60  4.5.6  S t o r m 6 : D e e p e s t C e n t r a l Low  61  4.5.7  Storm 7: H i g h e s t Minimum C e n t r a l P r e s s u r e  62  4.5.8  Storm 8:  D i s c u s s i o n of  Idealization  Sensitivity  of  the February 5 - 7 ,  Analysis Results  1960 S t o r m  63 66  5.1  The B a s e S c e n a r i o  66  5.2  Storm I n t e n s i t y V a r i a t i o n s  73  5.3  Storm T r a j e c t o r y  91  5.4  A d v e c t i o n Rate of  5.5  The I d e a l i z a t i o n  Summary o f 6.1  6.2  the of  C e n t r a l Low  the February 5 - 7 ,  95 1960 S t o r m  R e s u l t s and C o n c l u s i o n s  Summary o f 6.1.1  Sensitivity  99 104  Test Results  104  Storm I n t e n s i t y  105  Radial Extent  105  L o w e s t M i n i m u m C e n t r a l Low P r e s s u r e  106  H i g h e s t M i n i m u m C e n t r a l Low P r e s s u r e  107  Rate of  108  Intensification  6.1.2  Storm T r a j e c t o r y  109  6.1.3  Storm A d v e c t i o n Rate  110  6.1.4  Comparison of  111  Maximum E r r o r s  Conclusions  113  6.2.1  The M e t e o r o l o g i c a l P e r s p e c t i v e  113  6.2.2  Wave H i n d c a s t i n g P e r s p e c t i v e  113  6.2.3 Engineering Applications 7.0  58  Increased Radial Extent  the Gulf  5.0  Trajectory  References  Perspective  114 116  - v -  List  of Tables Page  T a b l e 3.1  Comparison  of P r e d i c t e d  and Observed Wave Heights  as a  F u n c t i o n of M o d e l l e d Energy Source Terms  38  T a b l e 4.1  Storm 1 S c e n a r i o Parameters  56  T a b l e 4.2  Storm 2 S c e n a r i o Parameters  57  T a b l e 4.3  Storm 3 S c e n a r i o Parameters  58  Table 4.4  Storm 4 S c e n a r i o Parameters  59  T a b l e 4.5  Storm 5 S c e n a r i o Parameters  60  T a b l e 4.6  Storm 6 S c e n a r i o Parameters  61  T a b l e 4.7  Storm 7 S c e n a r i o Parameters  62  T a b l e 4.8  Storm 8 S c e n a r i o Parameters  63  T a b l e 6.1  Summary of S e n s i t i v i t y  T a b l e 6.2  Summary  of  to Radial Extent  Sensitivity  t o Lowest  105 Minimum  Central  Pressure Table 6.3  Summary  106 of S e n s i t i v i t y  to Highest  Minimum  Central  Pressure  107  T a b l e 6.4  Summary of S e n s i t i v i t y  to I n t e n s i f i c a t i o n  108  Table 6.5  Summary of S e n s i t i v i t y  t o Storm T r a j e c t o r y  109  T a b l e 6.6  Summary o f S e n s i t i v i t y  t o Storm Advection. Rate  109  Table 6.7  Maximum Sea-State V a r i a b i l i t y Parameter S e n s i t i v i t y T e s t s  Attributable  to Pressure 112  - vi -  L i s t of Figures Page Fig.  1.1  The west  coast  o f Canada  f e a t u r e s as w e l l Fig.  1.2  are  landform  as wave m o n i t o r i n g s t a t i o n s .  A  0.2 mm,  where 0.1016 mm  below mean sea l e v e l  level. 1.3  the major  2  L e v e l l e d contour a n a l y s i s of the ocean s u r f a c e . interval  Fig.  showing  = 1 foot.  Contour  Shaded areas  and c l e a r areas a r e above sea  (From Cote et a l . , 1960).  directional  measured  wave  spectrum  4 calculated  o f f the west c o a s t of Canada.  The  from  data  presentation  i s F ( f ,9) i n t h e l o w e r p a n e l and E ( f ) d i r e c t l y a b o v e the Fig.  1.4  same frequency s c a l e .  A c o n t o u r map the  F i g . 2.1  (From Hodgins et a l . , 1985).  6  of s i g n i f i c a n t wave h e i g h t as h i n d c a s t f o r  west c o a s t o f B r i t i s h C o l u m b i a .  Nikleva,  on  ( F r o m H o d g i n s and  1986).  7  The c o s i n e - p o w e r s p r e a d i n g f u n c t i o n .  The  left  panel  i l l u s t r a t e s the shape v a r i a t i o n w i t h s (from Sarpkaya and  Isaacson,  distribution Hasselmann F i g . 2.2  1981);  of  s as  the a  function  panel of  shows  the  f r e q u e n c y (from  et a l . , 1980).  12  A s c h e m a t i c i l l u s t r a t i o n of the t h r e e terms  that  together  redistribution  of  are  wave  frequency. (From Hasselmann F i g . 2.3  right  A c o m p a r i s o n of s p e c t r a l  energy source  responsible  energy  as  a  for  function  the of  et a l . , 1973)  14  frequency d i s c r e t i z a t i o n i n  e q u a l f r e q u e n c y and e q u a l p e r i o d i n c r e m e n t s f o r N=15, f  F i g . 2.4  min= ' 0  0 5  H  z  a  n  d  f  max= 0  2  H z  «  1 7  A c o a r s e deep water h i n d c a s t g r i d w i t h a nested water model g r i d as used f o r a h i n d c a s t west  coast  Nikleva, F i g . 2.5  British  Columbia.  of waves on the  (From  Hodgins  and  1986).  Variations 10-m  of  shallow  19  i n the drag c o e f f i c i e n t  e l e v a t i o n wind speed.  as a f u n c t i o n of the  (From Hsu,  1986).  21  -  vii  -  L i s t of Figures (Continued) Page Fig.  3.1  M e a s u r e d and h i n d c a s t series  at  three  Hurricane grid  Cardone Fig.  3.2  stations  Camille.  points et  of  in  to  the  site  panel  increments  Mexico  during  numbers  designate  sites.  (From 29  a two-dimensional  three-dimensional  shows  time-  measurement  the of  relief  discretization  frequency  and  spectrum.  The u p p e r  1 9 8 1 ) shows a  ( f r o m S a r p k a y a and I s a a c s o n , in  of  height  1975).  al.,  F(f,6)  wave  the G u l f  The h i n d c a s t  close  R e p r e s e n t a t i o n of panel  significant  of  and  that  direction  portion  the  lower  spectrum  in  as a p p l i e d  in 31  ADWAVE. Fig.  Fig.  Fig.  3.3  3.4  4.1  The b i l i n e a r  interpolation  water  in  a n d (b)  Energy  regimes  growth.  (From  The  scheme i n  ADWAVE ( a )  in  deep 32  s h a l l o w water. within  a spectrum  during  active  wave  1982).  Resio,  inter-relationship  of  34  meteorological  and  sea-state 41  parameters. Fig.  4.2  S u r f a c e p r e s s u r e as a f u n c t i o n from measurements Camille.  Fig.  4.3  panel)  the  Fig.  4.5  calculated  passage of  Hurricane  1975). for  and an a c t u a l  both at  43  a moderately  intense  surface pressure  approximately  the  chart  same s c a l e  for 44  same l o w p r e s s u r e s y s t e m .  Parameters d e f i n i n g a  the  al.,  An i d e a l i z e d p r e s s u r e f i e l d  (bottom p a n e l ) ,  4.4  during  (From Cardone e t  storm (upper  Fig.  made  of d i s t a n c e  sphere.  A typical  d i s t a n c e between a r b i t r a r y  (From P e a r s o n ,  on  1984).  i d e a l i z e d pressure f i e l d  corresponding surface  points  wind  46 (upper  (U^Q) f i e l d  panel)  (lower  and  panel).  its 48  -  viii  List  of  -  Figures  (Continued) Page Fig.  4.6  The w i n d and w a v e m o d e l g r i d longitude special  Fig.  4.7  grid,  the  output  coastline  southwest  l°xl°  latitude-  representation  ,  and  the  points.  50  The s t o r m t r a j e c t o r i e s (b)  showing the  cold  of  (a) s o u t h w e s t  lows.  frontal  lows  and  (Adapted f r o m L e w i s and M o r a n ,  1985). Fig.  4.8  52  The t h r e e  segments  of  an i d e a l i z e d  b a s e d on t h e s o u t h w e s t cold Fig.  4.9  the  peak of  pressures  the  storm  (lower  5.1  southwest  (kPa).  Idealization  of  the  the  storm data field  panel)  with  and. t h e  12-hourly  and M o r a n ,  for  at  in  roughly  Fig.  storm  the  storm  central 64  corresponding  12Z ( u p p e r p a n e l ) a n d t h e  panel)  12Z  1985).  surface pressure chart  (lower  Peak wind  (upper  (From L e w i s  trajectory actual  f o r F e b r u a r y 6, 1960 at  panel)  to F e b r u a r y 6, 1960 a t  Fig.  lows and the  54  trajectory  4.10  trajectory  lows.  The s u r f a c e p r e s s u r e c h a r t at  Fig.  frontal  storm  storm  same s c a l e s  as  4.9.  65  1 s h o w i n g maximum w i n d s o f  60  knots. Fig.  5.2  67  Six-hourly storm  1 along  The peak of hour hours Fig.  5.3  significant legs  B - C and C-D of  at  T i m e - s e r i e s of  fourth panel;  significant  the entrance to  ordinates Fig.  5.4  of  during P  Q  fields  p r o d u c e d by  storm  trajectory.  8 6 0 1 0 2 1 8 ( d a y 02  maximum w a v e s a r e  six  03 h o u r 0 0 ) .  wave h e i g h t at  storm  i n storms  68  (H ), g  peak  the s p e c i a l output  Queen C h a r l o t t e  (31,13))  The e v o l u t i o n  the  86010300 (day  (Tp) and mean w a v e d i r e c t i o n at  the  the storm winds occurs at  18) i n t h e later  wave height  period point  Sound (model g r i d  1.  1 and 2.  co72 74  -  List  ix  -  of  Figures  (Continued) Page Fig.  5.5  Contoured f i e l d s 1 for  5.6  G  75  significant  wave h e i g h t  (Tp) and mean w a v e d i r e c t i o n  5.7  at  (31,13))  T i m e - s e r i e s of  during  north  of  (26,17)) 5.8  significant  period point  storms  is  at  of  53°N  storm  1  points  north  (26,17)  and at  the  of  (H„), s  peak  Islands  (grid  period point  coordinates  2.  78 1, 6 a n d 7.  In a l l  cases  145°W. and  e x e m p l i f i e d by s i g n i f i c a n t output  77  the s p e c i a l output  i n storms  Q  imposed a t  Comparison  1 and  co-  2.  wave h e i g h t  Queen C h a r l o t t e  The e v o l u t i o n of P Q  5.9  the  during  P (min) Fig.  peak  the s p e c i a l output  storm  (Tp) and mean w a v e d i r e c t i o n  Fig.  ( H ), s  t h e e n t r a n c e t o Queen C h a r l o t t e Sound (model g r i d  ordinates Fig.  6-  time s t e p s .  T i m e - s e r i e s of  at  storm  t h e p e r i o d d a y 02 h o u r 06 t o d a y 03 h o u r 00 i n  hourly Fig.  A H c a l c u l a t e d as s t o r m 2 l e s s  of  80  storm  6  wave h e i g h t  the  entrance  response at the  Queen C h a r l o t t e to  as  special Islands  Queen C h a r l o t t e  Sound  (31,13). Fig.  5.10  The f i e l d  5.11  5.12  G  the  time  of  maximum w a v e h e i g h t s -  1 ( d a y 03 h o u r  00) d i f f e r e n c e d  storm  1 (upper  and t h e  The f i e l d  panel)  in  as s t o r m 6 minus  corresponding f i e l d  of  H  G  1.  82  of AH  a  t  the  time  of  maximum w a v e h e i g h t s  storm  1 ( d a y 03 h o u r  00) d i f f e r e n c e d  storm  1 (upper  and t h e  from storm Fig.  of A H at  storm  from storm Fig.  81  panel)  in  as s t o r m 7 minus  corresponding f i e l d  of H  G  1.  Time-series  84 of  H  and T i n the e n t r a n c e to Queen s p C h a r l o t t e S o u n d and a t t h e c o a s t a l s i t e t h a t i s n o r t h o f t h e Queen C h a r l o t t e  Islands.  85  -  List  x  of  -  Figures  (Continued) Page Fig.  5.13  C o m p a r i s o n of i s o b a r r a d i i as a f u n c t i o n  rggo f °  scale Fig.  5.14  The f i e l d hour  18;  the case of  r  of  AH  at  g  the  upper panel)  s e q u e n c e ( d a y 03 h o u r s t o r m 4 minus Fig.  5.15  5.16  5.17  the westernmost  1 (upper  Comparison direction due west  Fig.  5.19  Comparison  in 5.20  in  of  modelling  field  panel).  The  AH  s  field  b e g i n n i n g of  of  the  panel)  and  minus  Maximum d i f f e r e n c e s near  the  the  H  g  is  g  coast.  Tp  point 93 mean  s p e c i a l output  point 94  after  after the  the stall  12.5 m on d a y 03 h o u r  00.  hours  and 1 t o  92  mean  Sound.  12 h o u r s  96 at  s g  d a y 03 h o u r 00  12 h o u r s later  a r e on t h e o r d e r  storm centre  The  and  g  a n d 24 h o u r s  minus H  24  H ,  in  Sound.  field  c a l c u l a t e d as H the s t a l l )  90  H„, T_ a n d s p s p e c i a l output  the  3 and 1 a t  12 a n d 13.5 m o n d a y 04 h o u r  4 and 1  of  time-series  The maximum H  89  panel).  5° c l o s e r to  3 and 1 at  panel)  4 and 1  u n d e r maximum w i n d s  time-series  wave h e i g h t  (upper  as 88  H and T from storms s p output s i t e .  the  storms  02  differenced  t h e e n t r a n c e t o Queen C h a r l o t t e of  (day  1.  the  The s i g n i f i c a n t  (lower  5.21  the  lower panel)  t h e e n t r a n c e t o Queen C h a r l o t t e  storm s t a l l  Fig.  the end of  i n storm 3 i s  i n storms of  direction  Fig.  maximum w i n d s  p a n e l ) and i n s t o r m 3 ( l o w e r  storm t r a j e c t o r y 5.18  and at  S i g n i f i c a n t wave h e i g h t storm  Fig.  of  T i m e - s e r i e s comparison of at  Fig.  86  H and T from storms s p e n t r a n c e t o Queen C h a r l o t t e Sound.  the  radial  Q  T i m e - s e r i e s comparison of at  Fig.  storm  the  P = 9 5 8 mb.  time  12;  of  of  later  (lower 6 to  (the  (upper panel).  nearly  8 m  3 m a l o n g t h e B.C. c o a s t .  97  -  List  xi  of  -  Figures  (Continued) P a  Fig.  5.22  The  AH  g  field  calculated  s t o r m 5 minus H times the Fig.  5.23  preceding  5.25  04 h o u r  12 i n s t o r m 1.  H , &  T  At  in  these  and h a v e b e e n  for  and mean w a v e  Aside from the in a l l  very  intervals  intervals  direction  p  early  spinup  storms  1, 6  period,  the  s t o r m s I s e s s e n t i a l l y t h e same. g  i n s t o r m 8 at  b e g i n n i n g on day 02 h o u r  The s e a - s t a t e p a t t e r n i n t e r m s o f H hourly  12  98  The s e a - s t a t e p a t t e r n i n terras o f H hourly  Fig.  day  12 h o u r s .  response of  mean d i r e c t i o n 5.24  at  t h e e n t r a n c e to Queen C h a r l o t t e Sound f o r  and 8.  Fig.  a t d a y 03 h o u r  g  the storm systems are e q u i v a l e n t  Time-series in  as H  §  g  12-  18.  i n storm 6 at  b e g i n n i n g on d a y 02 h o u r  101  12.  102 12103  e  -  xii  -  Acknowledgement All  computer  were p r o v i d e d  and s u p p o r t i n g  software  resources,  by S e a c o n s u l t M a r i n e R e s e a r c h L t d .  including of  the  ADWAVE m o d e l ,  Vancouver, B.C.  -  1.0  1 -  INTRODUCTION  Every  y e a r between O c t o b e r and M a r c h t h e B r i t i s h  C o l u m b i a c o a s t l i n e ( F i g . 1.1)  comes u n d e r t h e i n f l u e n c e o f one o r more s e v e r e n o r t h e a s t (Lewis and M o r a n , 1985). inland, the  w i t h i n a broad  Queen C h a r l o t t e  north, the  typically  well  offshore,  potential  coast:  that  aboard, these  ships  and about storms.  attributed  northern  More commonly,  and e n t e r s  schemes.  Vancouver  the t r a j e c t o r y  the G u l f of A l a s k a .  impact  a r e known  l o w p r e s s u r e s y s t e m s move  band between  directly  to  barge t r a f f i c ,  was w a s h e d  The s e v e r i t y  of  Between to have  reports  with  coastal  although  coast  of  a s many  forecasting  Island  during  a severe  damage  f o r B.C. c o a s t a l  since  ( F i g . 1.1). June  limited water  of  t h e buoy  (40 m), and p r i o r (MEDS,  at  Tofino  Environmental  and Oceans.  is  located  continued  sea-state  o n Hood C a n a l  the  o f 1984  northwest  event  led  to  a  i n w e a t h e r and  specification  to  on  i s a semi-permanent non-  Data  The u t i l i t y  close  to January  coast  of  Vancouver  Service of  the coast  these in  (MEDS) data  of  is  relatively  here the quite  shallow  1981 t h e s e d a t a w e r e g e n e r a l l y  1982 a n d May 1984 MEDS s p o n s o r e d a m a j o r w a v e c l i m a t e  British  Columbia coast  Entrance at the l o c a t i o n s only  This  on t h e west  (Seakem,  of  poor  through  Sound, Hecate S t r a i t  shown i n F i g 1.1. R e l i a b l e d i r e c t i o n a l  at the Mclnnes I s l a n d May 1985 u n d e r  R e v o l v i n g F u n d (ESRF) a n d w i l l  site.  Six  and D i x o n data  were  T h i s p r o g r a m o f d a t a c o l l e c t i o n was  the support  be r e p o r t e d  study of  1985; H o d g i n s et a l . , 1985).  wave buoys were d e p l o y e d i n Queen C h a r l o t t e  obtained  damage h a s  1984).  Between O c t o b e r the n o r t h e r n  usually  A W a v e r i d e r buoy h a s been p o s i t i o n e d and m a i n t a i n e d  Fisheries  since  quality  station  1970 by t h e M a r i n e  Department  are  waters.  of Canada a r e v e r y meagre.  wave measuring  off  1984) recommending i m p r o v e m e n t s  There  Island  bridge  lost  storm.  the  directional  members  again i n October  crewmembers were  for  coast  report  e x t e n s i v e damage i n  o c c a s i o n a l l y wave  For engineering purposes, the data r e s o u r c e s west  the  offshore  a s 60 c r e w  property  s e a - s t a t e was h i g h l i g h t e d  Commission of E n q u i r y ( L e B l o n d , sea-state  along  away.  v e s s e l s and f o u r  Vancouver  and  to the  1957 a n d 1 9 8 3 , L e w i s a n d M o r a n  sunk  of  the winds,  the l o c a l  when s i x f i s h i n g  shifts  l o g booming o r  o c c u r r e d a s i n F e b r u a r y 1979 when a s e c t i o n o f a f l o a t i n g (Washington)  Island  Each of these e v e n t s has  t h e same number o f v e s s e l s h a v e s u f f e r e d  The r a r e r  directly  o n some a s p e c t o f m a r i n e a c t i v i t y  shipping, fishing,  development  eight  Islands.  to s e r i o u s l y  international  resource  Some o f t h e s e  P a c i f i c Ocean s t o r m s  of the E n v i r o n m e n t a l  by D o b r o c k y S e a t e c h ( 1 9 8 6 ) .  Studies  Fig.  1.1  The w e s t c o a s t of C a n a d a s h o w i n g f e a t u r e s as w e l l as wave m o n i t o r i n g  the major stations.  landform  -  The wave c l i m a t e a t most of  are  available  particular  have  coastal structure  hindcasting. surface  relief.  limited  p r o b l e m i n most m a r i t i m e  years over  fields  large  As a r e s u l t ,  regional  locations  i n f l u e n c e d by  e v e n the  applicability  or harbour f a c i l i t y .  This approach i s  pressure  -  these s i t e s is s t r o n g l y  l a n d f o r m s and by b a t h y m e t r i c that  3  This  f e w months o f  to  the  that is t r a d i t i o n a l l y  which wind  r e g i o n s of  the g l o b e and b e c a u s e the  of  aerial  images i s  a common  winds  extend  (or  for  many  p h y s i c a l mechanisms well-known.  the ocean,  shown i n F i g .  a  o v e r c o m e by w a v e  maps c a n be d e r i v e d )  To g a i n a n i m p r e s s i o n o f how w a v e s u s u a l l y a p p e a r i n one s t e r e o p a i r  is  p o s s i b l e because the d a t a a r c h i v e s of  from  data  d e s i g n e r of  limitation  g o v e r n i n g s e a - s t a t e e v o l u t i o n by w i n d f o r c i n g a r e s u f f i c i e n t l y  of  adjacent  1.2.  a contour  This p l o t ,  plot  in  which  t h e w h i t e a r e a s a r e w a v e c r e s t s a n d t h e d a r k a r e a s t r o u g h s , was d r a w n f r o m a regular  9 0 b y 60 p o i n t  images.  The w a v e s shown h e r e w e r e i n t h e g e n e r a t i o n a r e a w i t h a mean o v e r -  water  wind of  discernible at about pattern  18 k n o t s  alignment  30° to is  If  the  from of  a great  of  d e a l of as the  spot  crests  of  the  of  implying  fine  structure  wave p a t t e r n  derived  the  from  about  of  20 m i n  at d i f f e r e n t  average  length)  is  F i g . 1.2),  l e n g t h a l o n g a c r e s t o n l y a few  the  after  wave  length.  It  is  only  waves have  t h e a c t i v e g e n e r a t i o n a r e a t h a t t h e y become s o r t e d o u t  propagated  into  of  wide,  and  wind waves are s h o r t - c r e s t e d w i t h the dominant  which  wind.  wave p a t t e r n s  a p p e a r s d i s o r d e r e d (as i n  a  propagation  wave p a t t e r n s  a n g l e s to the  individual  stereo  There i s  S u p e r i m p o s e d on t h i s  a l a r g e number o f  the  the  photographs.  a mean d i r e c t i o n  (down t o  s u p e r p o s i t i o n of  angles associated with  then the o v e r a l l  time  the wind v e c t o r .  wave l e n g t h s t r a v e l l i n g  range of  wave h e i g h t s  330°T a t  the  the r i g h t  c a n be i n t e r p r e t e d different  grid  times  away  long-crested  the  from swell  waves. The  variability  significance is  to  for  illustrated most c o a s t a l  Fig.  ( s u c h as s i g n i f i c a n t  direction; state  is  may be  in  this  manner  developed over  1.2  does  not  have  engineering applications.  d e s c r i b e s u c h an e n s e m b l e of  height  w a v e s by a s i n g l e  wave h e i g h t ,  a reliable  time  any  practical  The t y p i c a l  characteristic  H ) , wave p e r i o d and ( i f  from which normal  representation  and e x t r e m e  wave  possible)  g  statistical  approach  of  design  the  sea-  conditions  derived.  The v a s t  majority  1.2,  are time-series  fixed  in  but  point.  of  Such  wave d a t a  data  of  collected  are not  spatial  sea surface e l e v a t i o n  are  routinely  and  (and  snapshots perhaps  conveniently  like  tilt)  analyzed in  Fig. at  a  the  -  Fig.  1.2  4  -  L e v e l l e d contour a n a l y s i s of the ocean s u r f a c e . Contour i n t e r v a l 0.2 mm, where 0.1016 mm = 1 f o o t . Shaded areas are below mean sea l e v e l and c l e a r areas are above sea l e v e l . (From Cotg et a l . , 1960)  -  5  -  f r e q u e n c y d o m a i n by F o u r i e r t r a n s f o r m i n g in  a distribution  called  of  a variance  wave energy  (or  energy or  the  E as a f u n c t i o n  power)  spectrum.  be c a l c u l a t e d w i t h c o n f i d e n c e f r o m a b o u t 4 Hz.  If  t i l t  calculated. F(f,0)  and,  time domain s i g n a l .  A sample measured d i r e c t i o n a l by i n t e g r a t i n g  over direction,  t h e mean d i r e c t i o n  a l s o to  The p r i m a r y  product  most u s e f u l height  (of  w h i c h F i g . 1.3 i s  secondary product  which  is  direction.  readily  1986)  secondary  obtained  shows a c o n t o u r  data  array  at  by  Traditional by s p a t i a l  Such wave h e i g h t  schemes,  of  the  each of  of  and  production  hindcasting.  contain  and  single  element).  The  significant  wave  and  H  which  g  time.  F(f,0)  of  B.C. c o a s t a l h i n d c a s t s t u d y (Hodgins  errors,  and  of  is  s  at  over  a space plane  A time-series  of  of  this  such  plots  that can n o r m a l l y  particular  points  are  important  some o f  be  readily  thorough  wave  most  problems  model  features,  serious  usually  be i n  the f o r c i n g wind d a t a ,  address  the  characteristics the  of  fields  p r o d u c e d by  of  Canadian M e t e o r o l o g i c a l  and  error  and s e v e r a l  these e r r o r s . numerical  by  in hindcast recent  stage  effects problem prior  wave f i e l d s  to  will  s t u d i e s h a v e begun  Statistical weather  physical  The  careful  verification  the  propagation  of  and w h i t e c a p i n g .  c a n be m i n i m i z e d  s o u r c e of  operational  omission  in  inadequate  i n a c c u r a t e wave  frequencies,  calibration  the  w h i c h may be i n h e r e n t  wave growth c o e f f i c i e n t s ,  landform  Nevertheless,  N i k l e v a (1986),  frequency  to the n o r t h ,  a r r a y of  of  shows a  and t e m p o r a l a r r a y  regional sea-state evolution  these p o t e n t i a l  definition  the  to  interpolation.  bathymetric  a  2  north.  a typical  processes a s s o c i a t e d w i t h wave-wave i n t e r a c t i o n s of  can  and  t i m e - s e r i e s of H  fields  omission  is  frequency  map o f  wave m o d e l : i n a c c u r a t e c a l i b r a t i o n resolution  The wave  is travelling  integration  a particular  d e p i c t s the best e s t i m a t e of obtained.  11 s .  the e q u i v a l e n t  F i g . 1.4 f r o m a r e c e n t  Nikleva,  extracted  is  about  This i l l u s t r a t i o n  of wave h i n d c a s t i n g i s a s p a t i a l  energy s p e c t r a F(f,0)  which  e n e r g y s p e c t r u m F ( f ,0) c a n b e  9 to  (fp)  frequencies is  d a t a sampled at  as E ( f ) .  component w i t h the peak e n e r g y c o n t e n t all  f  s p e c t r u m i s s h o w n i n F i g . 1.3 a s  s e a s t a t e d o m i n a t e d by w a v e s w i t h p e r i o d s o f  at  frequency  results  G e n e r a l l y one s p e c t r u m  20 m i n o f  is a l s o measured, a d i r e c t i o n a l  of  This  assessments of  prediction  C e n t r e (CMC) h a v e b e e n r e p o r t e d  to  wind  (NWP) m o d e l s  by H o d g i n s and  H o d g i n s and H o d g i n s (1986) and M a c L a r e n P l a n s e a r c h ( 1 9 8 5 ) .  Cardone et a l . (1980) h a v e c o n d u c t e d a s i m i l a r s t u d y of U.S. m e t e o r o l o g i c a l data.  - 6 -  8214 28  Mclnnes Island at 03:00:00 10/19/83 20 16  13  1110 9  P  .T V 0  s e C ,  4  5  6  _i  '''  Deg. of Freedo»» 64. Banduidth«0.0200 H2 Hs« 4.33 • . Tp« 3.59 sec  fsi  X  a  in c cu  cu 3 O 0_  Max. Contour-10.97 (95x of Peakl Contour interval »0.744. Theta « 9.  a c z•  ao  ' 'I' ' I i i ' i i' ' ' 0.04 0.06 0.08 0.10 0.12 0.14  -i—i—]—i—r—r—r—r-t  1  i  0.16  0.18  0.20 0.22  0.24  Frequency (Hz)  Fig.  1.3  A directional wave s p e c t r u m c a l c u l a t e d from d a t a measured o f f the west c o a s t of Canada. The p r e s e n t a t i o n i s F ( f ,9) i n t h e l o w e r p a n e l and E ( f ) d i r e c t l y a b o v e on the same frequency s c a l e . (From Hodgins et a l . , 1985)  - 7 -  Fig.  1.4  A c o n t o u r map o f s i g n i f i c a n t w a v e h e i g h t a s h i n d c a s t f o r the west c o a s t of B r i t i s h C o l u m b i a . (From Hodgins and N i k l e v a , 1986).  -  H o d g i n s and N i k l e v a ( 1 9 8 6 ) northeast coast  Pacific  regional  of  8  -  investigated  the  effects  on e r r o r  t h e CMC a n a l y s i s t i m e ( " n o w - c a s t " )  surface  pressure  C e n t r e (PWC) f r o m w h i c h t h e  re-analysis  authors  derived  prepared  are  calibration analytical  improved  data in  analysis  regional  weather  forecaster.  winds  e x c e e d i n g 10 k n o t s ,  the  reported  bias  2 to  (rms)  speed e r r o r  7 knots  Cardone winds  et  al.  (1980)  generated  also  by a NWP m o d e l  " o b j e c t i v e " wind f i e l d s  Bias  had c o n s i s t e n t l y  was  less  than  direction error  and k i n e m a t i c  1 knot,  was 3 0 ° ,  error  bias  and rms  rms w i n d  including  wind  field  by i n p u t by  of the  kinematic  root-mean-square 20° to  fields,  28°.  of  Pacific included  w i n d s w e r e b l e n d e d by  computer  errors  than  but  NE  also  speed e r r o r a l l  wind  For the  is  These r e s e a r c h e r s found that  lower  west  Weather  extent  characteristics  i n which s h i p - r e p o r t e d  w i t h t h e NWP m o d e l w i n d s . fields  error  a l l  3 knots,  and rms d i r e c t i o n  investigated  and o f  a lesser  the  5 to  Pacific  of  experience of  is  the  the  a r e c a l i b r a t e d by h a n d  most  and to  is  of  in  On a v e r a g e , t h e NWP m o d e l  by human i n t e r v e n t i o n ,  the k i n e m a t i c  the  a surface wind,  to m a r i n e o b s e r v a t i o n s r e p o r t e d by s h i p s a t s e a . fields  winds,  by  k i n e m a t i c a n a l y s i s i n which n u m e r i c a l model wind f i e l d s  wind  statistics  the k i n e m a t i c  the  other  was a b o u t  observations  wind  6 knots  wind types.  and  irrespective  of  rms wind  speed. All  of  t h e s e s t u d i e s were l i m i t e d  or f o r e c a s t wind w i t h a p o i n t to r e l a t e  the e r r o r  Golding  (1983),  to consequences f o r  s u c h as C l a n c e y  and most  i n t e r c o m p a r i s o n of a h i n d c a s t  w i n d m e a s u r e m e n t , and none o f  parameters  Other i n v e s t i g a t o r s  to s t a t i s t i c a l  other  et  al.  E u r o p e and N o r t h A m e r i c a h a v e p u b l i s h e d s i m i l a r based  on  wave  attributed made a t  to  modelling  known o r  results  in  suspected wind  the m o d e l l e d s e a - s t a t e .  (1986),  wave f o r e c a s t i n g  which  J a n s s e n et  wave  currently  s t a t e s t o w i t h i n +1 m i n h e i g h t input winds. and o t h e r s  of  (1984),  Because  error  these  is  study  Of t h e  largely  comparisons  effects  i n the  space or  time.  on wave m o d e l  f o r c i n g wind i n p u t ,  the s t r u c t u r e  can g e n e r a l l y  field  results  of  a set  end o b j e c t i v e  this of of  accurate systematic  investigation  is  common s y s t e m a t i c identifying  on wave model p e r f o r m a n c e .  and e v o l u t i o n o f  to  hindcast sea-  e r r o r s , some a r e  The p u r p o s e o f  w i t h the  these e r r o r s have s e r i o u s e f f e c t s  controlling  wind  are  unlikely.  a n d +2 s i n p e r i o d g i v e n s u f f i c i e n t l y  s e v e r a l s o u r c e s of  a r e random i n the  state-of-the-art  in  analyses  i s o l a t e d p o i n t s w i t h i n complex weather systems, the o p p o r t u n i t y  Wave m o d e l s w h i c h a r e  errors  statistical  field  i d e n t i f y more s p e c i f i c c a u s e - a n d - e f f e c t c o n n e c t i o n s i s  to  al.  and h i n d c a s t i n g g r o u p s  types of  errors.  them h a s b e e n a b l e  By  the f o r c i n g wind f i e l d s ,  which  carefully variations  - 9 -  in  the  time-series  linked  to  the  of  the  causative factors  Reporting  of  theory  wave m o d e l l i n g  of  this  may  be  the wind  and  the  terms,  considerations  that  effects  and w i n d  Chapter  3 is  is,  and are  wave  form  included  of  fairly  distinct  generation,  variations  in  terms of wave energy at  application  hindcast  energy  models.  provide a preliminary tolerable  spectra.  elements: one  the  particular evolution  heart  Important  energy p r o p a g a t i o n ,  and  of  this  peripheral  shallow  water  configurations.  the  input  discrete  wind  Emphasis i s  as i n p u t  of  in  the  and o u t p u t e r r o r  problem,  generalized  this  research.  were  quantified  domain.  results  in  The i n p u t detail  Chapter  i n C h a p t e r 6.  5.  in  of in  These  characteristics  the range of a c c e p t a b l e wind  followed  a n a l y s i s are reported  in  solution  in sea-state statistics.  output  total  p l a c e d o n t h e ADWAVE  function  are described i n  the  the  that  a n a l y s i s i n which the e f f e c t s  forcing  locations  i n d i c a t i o n of  by d i s c u s s i o n o f  of  the e x p e r i m e n t a l p a r t  a sensitivity  uncertainty  t h r e e wave m o d e l s  dissipation  the wave model s e t - u p c o n f i g u r a t i o n  drawn from t h i s  of  The  approaches to s o l u t i o n  propagation  have been i n t e r p r e t e d  for  essential  t o a more s p e c i f i c d e s c r i p t i o n o f  The e x p e r i m e n t was c o m p r i s e d o f  errors  two  the p h y s i c s of s e a - s t a t e  are s w e l l  m o d e l w h i c h was u s e d e x c l u s i v e l y i n  effects  directly  parameterization.  devoted  three  the  g e o g r a p h i c a l and b a t h y m e t r i c  systematic  into  experimental  wave  h a v e been  g  the e n e r g y b a l a n c e e q u a t i o n i n c l u d i n g e n e r g y s o u r c e and s i n k  propagation  illustrate  in  (H )  history.  r e s e a r c h has been d i v i d e d  parameterized  discussion is  that  in  energy f i e l d  Chapter 2 d e s c r i b e s the elements of  model. that  integrated  to  parameter winds Chapter  and 4,  The c o n c l u s i o n s  -  2.0  10  -  SEA-STATE DESCRIPTION: THE BASIS FOR WAVE MODELLING  Virtually  all  wave  prediction  models  are  b a s e d on e q u a t i o n s  c o n s e r v a t i o n of wave e n e r g y at s p e c i f i e d l o c a t i o n s . system d e s c r i b e s the t i m e - s p a c e e v o l u t i o n illustrated averaged of  t i m e (on t h e  order  of  a r e assumed to  1 to  3 h) a n d c h a r a c t e r i s t i c  a d i s c r e t e a r e a (up  2.1  The Energy Balance Equation  The p r o c e s s e s t h a t  must  and away f r o m t h e  point,  processes  that  to  be  2.5° of  latitude  considered are  g r o w t h due  redistribute  d i s s i p a t i o n due t o  The s p e c t r a a r e  that  over  to  energy  whitecapping  The s o l u t i o n  of wave s p e c t r a F ( f , 0 ) ,  i n F i g . 1.3, a t s e l e c t e d p o i n t s .  representations  describing  be v a l i d  and  for of  of  the this  s u c h as  that  statistically  some f i n i t e  sea-state  period  conditions  longitude).  propagation local  of  winds,  between  wave energy  non-linear  frequency  and b o t t o m f r i c t i o n .  toward  transfer  components,  The e n e r g y  and  balance  d e s c r i b i n g t h e s e p r o c e s s e s i s w r i t t e n as ± 3t  F(f,9)  where F  is  c ^ ( f ) . V F ( f , 9 ) = S ( f , 6)  -  wave e n e r g y as a f u n c t i o n  (2.1)  of  frequency (f)  Cg i s t h e w a v e g r o u p v e l o c i t y a s a f u n c t i o n V  is  the g r a d i e n t  S  is  the  Understanding of  energy source  the  p a r a m e t e r i z a t i o n of  The two most  (JONSWAP).  1968 a n d 1971 a t  ODGP w a s a j o i n t  six  and m e t e o r o l o g i c a l JONSWAP  was  institutes  an to  locations  result  of  the wave  s t u d i e s , both s t a r t e d  oil  i n the G u l f of  international the  undertaking structure  The l a t t e r e x p e r i m e n t  in  program conducted between  Mexico to c o l l e c t  the  record during  evolution  of  t h e wave e n e r g y s p e c t r u m and t h e r e b y  Although  offshore  but  terms  in  research  the  energy  1968 and 1969 w i t h  winds  to  facilitate  elucidate  The  studying  the  physical  evolution.  ODGP a n d JONSWAP w e r e s o d i f f e r e n t  e a c h was a n i m p o r t a n t ,  in hurricanes.  13 l o c a t i o n s i n t h e N o r t h S e a .  to  that  oceanographic  cooperating  source  was  mechanisms r e s p o n s i b l e f o r  steady  of  between  l a s t e d 10 weeks i n  c o m p r e h e n s i v e d a t a c o l l e c t i o n a t up t o objective  industry  d a t a w i t h e m p h a s i s on s e v e r e c o n d i t i o n s  determine  balance equation.  of  important  and  a r e t h e O c e a n D a t a G a t h e r i n g P r o g r a m (ODGP) a n d t h e J o i n t ] J o r t h S e a Wave  Project  the  S(f,9)  the p r o c e s s embodied i n  i n wave m o d e l s has e v o l v e d as a d i r e c t  measurement e x p e r i m e n t s . 1968,  dy)  function.  physics governing it  frequency  o p e r a t o r / _ 3 _ , _3_ \ a n d  \9x net  of  (9)  and d i r e c t i o n  again very  in  purpose,  different,  the e v e n t u a l advance i n  outcome  wind-wave  -  11 -  modelling.  T h e ODGP d a t a s e t a l l o w e d ,  a  wave m o d e l — t h e  verified  ODGP m o d e l  become t h e b a s i s o f v i r t u a l l y States.  which  wave  highlighted  from  European o p e r a t i o n a l  t h e ODGP m o d e l  the development  forecasting  the importance  p r o c e s s e s between wave f r e q u e n c i e s  are omitted  time,  of  by C a r d o n e e t a l . (1975) w h i c h h a s  a l l commercial  T h e JONSWAP e x p e r i m e n t  energy t r a n s f e r  f o r the f i r s t  and i t s  i n the United of  (wave-wave successors.  f o r e c a s t i n g wave m o d e l s , i n a d d i t i o n  non-linear  interaction), Many o f  the  to Hasselmann's  r e s e a r c h models (Hasselmann e t a l . , 1976; Gunther e t a l . , 1979a,b) and R e s i o ' s (1981,  1982) h i n d c a s t m o d e l ,  utilize  2.2  Wave Model Parameterizations  2.2.1  Wave D i r e c t i o n a l i t y  In  many m o d e l s  equation  t h e JONSWAP  (2.1) i s i n t e g r a t e d  results.  with respect  energy e q u a t i o n , w r i t t e n here i n one s p a t i a l  to 6 to y i e l d  the  dimension (Hasselmann et a l . ,  1976) a s _3_ E ( f ) + c ( f ) . 3 E ( f ) g  F(f,8)  = S(f)  (2.2)  9x  o-t  c a n t h e n be o b t a i n e d  solution  o f (2.2) such  by a p p l y i n g  a spreading function  G(f,0)  that  F ( f , 0) = E ( f ) . G ( f , 6 ) w h e r e G must  fa,  to the  (2.3)  satisfy 0)d  = 1  (2.4)  —TT The  most w i d e l y  and  Pierson,  used f u n c t i o n a l  = \ * ( 0  ,  G(0)  (2.5)  otherwise  G i s independent  Higgins  G are the cosine-squared (St. Denis  | 0| ITT/2  2  where  of  1953): / 2 cos 0,  G(6)  forms  of wave  frequency;  and the c o s i n e - p o w e r  e t a l . , 1961) = C(s) c o s  2 s  /  6 -  6\  where C(s) i s t h e n o r m a l i z i n g  (2.6)  factor  needed t o e n s u r e t h a t  (2.4) i s  s i s a f u n c t i o n o f f r e q u e n c y , a n d 0 i s t h e mean w a v e d i r e c t i o n . power s p r e a d i n g f u n c t i o n and  (Longuet-  as a f u n c t i o n  satisfied,  The c o s i n e -  i s shown i n F i g . 2.1 f o r v a l u e s o f s b e t w e e n 1 a n d 10  of frequency.  This figure  shows t h a t  the largest  values  of  -  Fig.  2.1  The c o s i n e - p o w e r i l l u s t r a t e s the and I s a a c s o n , distribution of Hasselmann et a l .  12  -  spreading function. The l e f t p a n e l shape v a r i a t i o n w i t h s (from Sarpkaya 1981); the r i g h t p a n e l shows the s as a f u n c t i o n of f r e q u e n c y (from , 1980).  -  s,  which are about  10, o c c u r a t  the  13  -  peak f r e q u e n c y  w e l l - f o c u s s e d a l o n g t h e mean w a v e d i r e c t i o n wave f r e q u e n c i e s propagation.  2.2.2  The E n e r g y S o u r c e F u n c t i o n  The n e t field  energy source f u n c t i o n  "  S  S  in  +  S  nl  +  w i t h the f o l l o w i n g S^  n  = the  S  input  of  energy  processes net  energy from  are  energy  shown  of  at  The n e t  the  frequencies  at  high  very  included  of  forward  processes: 7  (whitecapping) in  is  the  S ^  Fig. of  2.2,  f a c e of  dominant  d o e s S^  energy  only  S ^ at n  the  are  n  to  are  about  than the  S^  n  energy  from f r e q u e n c i e s  has an a n a l y t i c  this  computations  figure  mechanism  energy  contribute  s  i  the  above  spectrum.  present  Although  input  n  more  with  This  S ^ and S  therefore  the wave  together  frequency.  removes  n  energy i s  integral).  analytically,  the  S ^ t e r m was e v a l u a t e d n  w i t h the data f o r  S to  functional too  complex  formulation  form of to' be  but  energy  transfers  of  that  accordance w i t h  all  remaining  between  n  has  linear  2 . 2 c a n be i n f e r r e d .  a similar wave  S ^  can  routinely  The p a r t i t i o n  h o w e v e r , be d e r i v e d d i r e c t l y  from  S^  c a s e s and  n  + Sj^.  combined  The  theories,  the  to  components  the  such  spectrum  p r o c e s s model  of energy between S ^  t h e JONSWAP d a t a .  n  latter  whitecapping,  waves (Hasselmann et a l . ,  distribution  growth  terms  spectral  l o n g w a v e s by damped s h o r t S.,  two  test  d i s s i p a t i o n mechanisms, p r i m a r i l y  for  attenuation  individual  the  account  for  for  examine  was a s s u m e d t o  Assuming  three  i n wave m o d e l s .  I n JONSWAP,  also  of  wave  process  frequencies  redistribution  Boltzmann  be e v a l u a t e d  terms  function  higher  t h o s e b e l o w on t h e  as  in  p  Of t h e s e e n e r g y s o u r c e t e r m s , (known  of energy to the  N e a r and j u s t b e l o w f ,  p  Only  a  n  balanced,  to  as  S ^ which  lower than f .  balance.  input  of  wind  schematically  at f r e q u e n c i e s  contributes.  the  transfer  curve  importance  but  the  (1973)  d i s s i p a t i o n process  transfer  emphasizes the  a r o u n d t h e mean d i r e c t i o n  meanings:  = the  resultant  other  2  S^ These  is  < ' >  = the n o n - l i n e a r  s  al.  At  ds  S ^ n  fp  S which governs  was d e s c r i b e d by H a s s e l m a n n e t  the wave e n e r g y  ( w i t h i n about +45°).  the e n e r g y i s more s p r e a d o u t  wave  and t h a t  as  1973).  itself,  shown i n  and S ^  g  the  could  in Fig. not,  -  Fig.  2.2  14  -  A s c h e m a t i c i l l u s t r a t i o n of the t h r e e energy s o u r c e terms that together are responsible for the redistribution of wave e n e r g y as a f u n c t i o n of f r e q u e n c y . (From Hasselmann et a l . , 1973)  -  15  -  approaches  to  the  2 . 2 . 3 The E n e r g y S p e c t r u m P a r a m e t r i c Forms There  are  equation  two  general  (2.1).  approximated  The  by  first  method  a universal  related  spectral  all  from e m p i r i c a l  laws.  The b e s t - k n o w n  forms  Moskowitz,  1964)  (Hasselmann et growing  of  for  assumes  that  parametric  parameters a^ are u s u a l l y shape f u n c t i o n s ,  solution every  spectrum  to wind speed,  of  the  energy  spectrum  E(f,a^).  can  be  governing  frequency,  and  o f w h i c h must be r e a d i l y d e t e r m i n e d f r o m d a t a o r  E a r e t h e P i e r s o n - M o s k o w i t z (PM) s p e c t r u m ( P i e r s o n and fully-developed  wind  seas  and the  JONSWAP  a l . , 1973) w h i c h was d e v e l o p e d by a n a l y s i s o f  wind-sea  E(f)  The  peak s p e c t r a l  balance  spectrum  fetch-limited  spectra.  The PM s p e c t r u m i s g i v e n by E(f)  = ag (27T)- f- exp[-0.74/_g_\ /f ] 4  2  5  4  (2.8)  4  \27TU / i n which  a is  Phillips'  The JONSWAP p a r a m e t r i c  constant  (=0.0081) a n d U i s  spectral equation  my  5  4  4  than a  f  = frequency at c(f)  Y  = the  c(f)  the p o i n t  2  2  b  spectral (if  of  f  maximum e n e r g y  peak enhancement  factor 2  ])  s h a p e p a r a m e t e r d e f i n e d by o  (if  &  f<fp)  a n  d  f>f ) p  The p e a k e n h a n c e m e n t f a c t o r , PM a n d JONSWAP f o r m s , limited  of  p  o  now a f u n c t i o n  constant  = exp([-(f-f ) ]/[2a f  o = the  (2.9)  c ( f )  where a = t h e P h i l l i p s ' s c a l i n g p a r a m e t e r , rather  speed.  is  E(f) = a g ( 2 T r ) ~ f - e x p / - 5 Tf " T \ . Y 2  wind  which  heightens  largely  accounts for  and s h a r p e n s  seas to model the " o v e r s h o o t " e f f e c t  the  the d i f f e r e n c e  spectral  between  peak i n  m e a s u r e d i n JONSWAP.  fetch-  The t e r m  overshoot d e s c r i b e s the o b s e r v a t i o n that under steady wind c o n d i t i o n s , energy at  and n e a r f  in developing  seas  can exceed the e v e n t u a l  energy l e v e l a t t a i n e d at those f r e q u e n c i e s . reduces  to  the  PM s p e c t r u m w h i c h  t h e maximum e f f e c t increasing  |f-f  |.  is  at  f fp =  imposes  F o r Y=l,  f =0.14(g/U) p  Hasselmann et  al.  (1976)  report  equilibrium  t h e JONSWAP and a=0.0081.  ( s i n c e c ( f ) = l ) and d i m i n i s h e s  the  equation For  exponentially  t h a t most w i n d - s e a  Y>1. with  spectra  -  adhere to  16  -  t h e JONSWAP f o r m w i t h a v e r a g e p a r a m e t e r  a =0.09,  independent  f e  of  fetch.  This  form of  v a l u e s of  E is  Y=3.3,  called  03=0.07  and  t h e m e a n JONSWAP  spectrum.  Discrete Forms The  second g e n e r a l  The  directional  such  that  solution  dependence i s  MA8 =  2-rrand  often  done  typically  in  0.05  always  typical  corresponding resolutions is  technique  of  Hz ( T = 2 0  22.5°,  way:  s),  f  m  o  TO  d i s a d v a n t a g e of in  the  lower  spectral  this  method i s  frequencies.  energy  w i l l  logical  alternative  For  same  the  elements,  the  divided  values  30°,  a similar  involves  NAf  that  this  M  are  2.3  of  12,  0.2  of  16,  f  H z (T=5  i  n  s),  w  n  and  i  or  c  n  (period)  T h i s means t h a t  importance  24  sectors to  give  frequency  case  £ ± m  n  Af=0.01 Hz.  is The  x  the  resolution  of  the spectrum i s  coarsest  and s e v e r e s e a - s t a t e s , most  poorly  defined  limits  spectral  for  F(f,0).  equal  part  of  the  and  the  same  c a n be g r e a t l y resolution  the m o d e l l i n g  (  the  number  m a x  of  i m p r o v e d as  spectrum i n  A  ~T ^ ).  T  m  n  discrete  illustrated  c a n , a n d s h o u l d , be the  of  spectrum.  i s t o i m p o s e e q u a l p e r i o d e l e m e n t s : NAT =  frequency  most  number  of  D i s c r e t i z a t i o n of  t o more p r e c i s e l y s p e c i f y t h e s h a p e and p e a k o f states  a  and 1 5 ° . f  low frequency r e s o l u t i o n  i n F i g . 2.3.  of  In moderate  be i n  into  discretization  = ^ max~ min^»  is  v  ci  the  tailored  those s e a -  application.  Other Considerations  2.3.1 Wind-Sea and Swell One i m p o r t a n t (2.1)  is  energy  the that  context, exceeds can  consideration in parameterization  propagates  into  of  the  that  the  there  either  of  the  energy  is  local  wind,  the energy balance  generated  interest  these  since it  conditions.  conservation  dispersion) or  which  refractive  differencing  is  effects  a  ray  set  are r e a d i l y  Because  to  is  equation  w i n d - s e a and of  from a f a r .  assumed t h a t  In  the  these  reduced  swell  modelling velocity  no a t m o s p h e r i c  are to  freely only  an  input  propagating advection  zero.  swell,  approach (to  the method of tracing  is  equation  no p a r a m e t r i c m o d e l o f  a finite  numerical scheme,  locally  a r e a of  e q u a t i o n w i t h energy source terms Since  a model of  a s w e l l w a v e may be d e f i n e d a s a n y s e a c o m p o n e n t whose p h a s e  be a b s o r b e d u n d e r  waves,  building  the  solution  high-order  characteristics.  technique,  is  incorporated.  employed  technique chosen i s  a c c u r a c y to Frequently  control  the  because s h a l l o w  latter water  - 17 -  Period (s)  28 20 16 13 1110 9 8 7 6 5 I y-1• i • i -1 • i • itt>11• 1111. • . . t . . . . . . . . . 1 1 1 1 1 1 1 1 1 i i*  0.04  0.06  0.08  0.10  0.12 0.14 0.16 0.18 Frequency (Hz)  Period (s)  1  *  *  0.20 0.22  *  '  •  0.24  7  6  5  A  . i . • . . i  i  i  i  28 20 1 6 1 3 1 1 1 0 9 8 • m i l i u m 11 I . I . I . i . I . I .  '  in c  cu  Oo _  O  -  1  0.04  Fig.  2.3  0.06  0.08  0.10  0.12 0.14 0.16 0.18 Frequency (Hz)  0.20 0.22  0.24  A comparison of s p e c t r a l frequency d i s c r e t i z a t i o n i n e q u a l f r e q u e n c y a n d e q u a l p e r i o d i n c r e m e n t s f o r N=15, f  min= 0  0 5  H  z  a  n  d  f  max  = 0  -  2  H z  -  -  In p r i n c i p l e , model  swell  boundaries,  available.  the i n f o r m a t i o n  represents  contrasted  with  that  be g e n e r a t e d  would  domain  significant  be  c o a s t s of  of  swell  waves i s  is  It  therefore,  important,  meteorological equal period  2 . 3 . 2 S h a l l o w Water In  the  interests  deep w a t e r  are  In  s  n  o  outside  wave m o d e l l i n g  the  this  generally  t  applications)  cases  low.  can c o n t a i n  resolve  since  model's  omission  (as  swell  physical  may  cause  On b o t h t h e e a s t a n d w e s t  significant  this  accurately  discretization  (Fig.  intense  is  in  the  range  if  The a d v a n t a g e  evident  in  T=20  storm systems.  frequency  modelled.  2.3)  energy  this  such of  the  case.  Effects  of  computational  approximations  required.  be  i  wave  results.  to  to  time a l o n g the  n(f>9)»  a s s o c i a t e d w i t h the p a s s a g e of  events  spectral  some  generally  Canada wave measurements  of  on l i m i t e d - a r e a  systems  In  i n wave h i n d c a s t  s w e  ocean b a s i n  storm  for.  t o 30 s r a n g e t h a t is  global  other  accounted  errors  The f r e q u e n c y  by  or  F  t o do s o ,  a restriction  hemispheric  cannot  -  e n e r g y c o u l d be i n p u t a s a f u n c t i o n  but  This  18  that  unless  event,  efficiency, accurate  the  usual  most  wave h i n d c a s t s  near-shore  approach  is  sea-state to  solve  are  run  conditions the  deep  are  water  e q u a t i o n s on a c o a r s e g r i d whose p r i m a r y d o m a i n i s t h e deep o c e a n and to these r e s u l t s solution for  as b o u n d a r y c o n d i t i o n s  domain.  the west  An e x a m p l e o f  coast hindcast  for  a nested, fine-grid  a nested g r i d  arrangement  refraction,  wave  shoaling,  and s h a l l o w w a t e r wave b r e a k i n g . describe  the  evolution  wave c r e s t s . saturated  critical  to  give  Spectral refraction  is modelled  effect  better  of a f i n e - g r i d  modelling  of  Fig.  2.4  models  by b o t t o m  are  friction  and s h o a l i n g  models  rays"orthogonal of  Sound o r  Hecate  nested model i s  sheltering  consideration in hindcasting  Queen C h a r l o t t e  by i m p o s i t i o n  water  a  to  depth-limited  form.  A secondary b e n e f i c i a l resolution  dissipation  use  1986).  i n s h a l l o w water  of wave energy a l o n g c h a r a c t e r i s t i c  Wave b r e a k i n g  spectral  energy  shallow  shown i n  by S e a c o n s u l t ( H o d g i n s a n d N i k l e v a ,  P h y s i c a l m e c h a n i s m s t h a t may b e a c c o u n t e d f o r bathymetric  is  as  improved  conditions.  This  landform c a n be a  near-shore sea-states in areas  like  Strait.  2 . 3 . 3 Wind I n p u t All  wave growth models expect wind i n p u t  s p e e d and d i r e c t i o n surface  pressure  (or data,  vector or  p r e d i c t i o n m o d e l , and e i t h e r  components).  they of  may  be  as a t i m e - s e r i e s These winds  generated  by  t h e s e may i n c o r p o r a t e  of  near-surface  may be d e r i v e d a numerical direct  from  weather  measurements.  - 19 -  Fig.  2.4  A c o a r s e deep w a t e r h i n d c a s t g r i d w i t h a n e s t e d s h a l l o w w a t e r model g r i d as used f o r a h i n d c a s t of waves on t h e west c o a s t of B r i t i s h C o l u m b i a . (From Hodgins and N i k l e v a , 1986).  -  20  -  T h e r e a r e two k e y a s p e c t s t o s p e c i f i c a t i o n o f r e s o l u t i o n (both temporal  and s p a t i a l )  the wind  forcing  and t h e a c t u a l  term: s c a l e s  p a r a m e t e r i z a t i o n of  of  wind  force. Generally  hindcast  a gradient interval  wind  winds are d e r i v e d from 6 - h o u r l y  that  implies  rapidly  of  increments  that  of  the  turning  then reduced to a n e a r - s u r f a c e  an i n t e r p o l a t i o n  which i s t y p i c a l l y interpolation  is  wind v e c t o r U i s  wind f i e l d s .  If  a r e much l e s s  common, b u t  Attempts  actual gradients Since  the  friction  velocity  input  S  i  n  This  time  time  step  be v e r y a c c u r a t e in  400 km) i s  is  length fine  the wind f i e l d s  will  gridded wind f i e l d s  as  typically  i n a d e q u a t e t o embody  the  direction).  normally  at the sea s u r f a c e u * ,  In  and w i t h f a i r l y  v e r y u n s u c c e s s f u l because the  the order of  term  of  as  vectorial  digitized  scale  interpolation  i n wind speed (and p o s s i b l y  energy  are  to use h i s t o r i c a l  a r c h i v e d f r o m a NWP m o d e l a r e u s u a l l y r e s o l u t i o n (of  may n o t  the model g r i d  i s o b a r s p a c i n g (1 t o 4 mb), t h e n s p a t i a l  coarse s p a t i a l  In the time domain,  pressure charts  than  vector.  down t o t h e m o d e l i n t e g r a t i o n  t h e o r d e r of one h o u r .  be r e a s o n a b l y a c c u r a t e .  surface pressure charts  formulated  the i n p u t  in  terms  of  the  w i n d U m u s t be c o n v e r t e d  by  t h e wave m o d e l t o u * as u£ = C U  (2.10)  2  D  where the drag c o e f f i c i e n t g e n e r a l dependence of C Thus are  u*  with  several  this other  Q  0  D  the  formulations  111U£25 m / s . (1986)  and h i s  Prior  to about  constant. speeds, i t  If  wind  U.  Garratt  on wind speed of  (1977)  the  found  a  form  is  proportional  with  different  to  approximately  U ^  4  .  There  d e p e n d e n c i e s on U s u c h as  the  (1981): (2.12)  3  speed at  10 m e l e v a t i o n  R e c e n t l y a number of findings  of  (2.11)  formulation  = (0.49 + 0.065U)*10~  where U i s  a function  4 6  one p u b l i s h e d by L a r g e and P o n d C  is  the drag c o e f f i c i e n t  = 0.51xlO~ U ' 3  D  C  and  is  defined  in  the  range  t h e s e f o r m u l a e h a v e b e e n c o m p a r e d by Hsu  are i l l u s t r a t e d  in Fig.  1970, wave model f o r m u l a t i o n s  2.5. may h a v e a s s u m e d t h a t C p w a s a  such a model were w e l l - c a l i b r a t e d  for  l o w and m o d e r a t e  w o u l d i n c r e a s i n g l y u n d e r - e s t i m a t e wave growth  as winds  wind  strengthen.  - 21 -  1 Kondo.1975 2 Qarratt,1977 3 Smith, 1980 4 Amorocho and 0aVrtas,19S1 5 Large and Pond, 1981 6 Don*lan,1982 7 Wu.1982 8 Graf at al.,1984 9 Thl« atudy  >8  10  15  20  25  30  U ,(nM-') 10  F i g . 2.5  V a r i a t i o n s i n the drag c o e f f i c i e n t as a f u n c t i o n o f the 10-m e l e v a t i o n wind speed. (From Hsu, 1986).  -  Because the wind model w i l l  vector  22  varies with  be c a l i b r a t e d  -  elevation  to accept input at  10 m a n d 1 9 . 5 m a r e common s t a n d a r d s . other  than  the  reference  an a t m o s p h e r i c relationship  level,  boundary  layer  it  model.  the  sea surface,  a particular  If  must  above  wind  first  input  reference is  only  be c o n v e r t e d  The s i m p l e s t  of  a  given  elevation—  available  at  by a p p l i c a t i o n  of  these  is  an  empirical  s u c h as  (2.13)  w h e r e U"M  is  the measured wind  speed at  UR  is  the wind speed at  the  A  is  an e m p i r i c a l  elevation h  reference  constant  ,  level h ,  and  r  a p p r o x i m a t e d by D e t n o r s k e V e r i t a s  (1982)  as  0.15. Accurate  hindcasting  s u c h as the method  requires used i n  1985).  The  same p r o c e d u r e  surface  pressure data  velocity  u*  wind u ,  the  air  and  sea  surface  Q  the  roughness is  length  assumed,  length, the  is  to  as  via  the as  gradient  a function  case,  0  = (U*/K)  g  is  the g r a v i t a t i o n a l  thickness.  free-atmosphere  CQ).  to  the  form  for  required  gradient)  temperature the  surface  profile  and s u r f a c e  reference  friction  (or  air  A logarithmic  column s t a b i l i t y at  upper  the  of  boundary l a y e r roughness  of  U  roughness  elevation  z.  For  from  (0.4)  s u r f a c e roughness l e n g t h  rotation  the  (2.14)  the  surface  method,  from  0  is  and  s u r f a c e winds  this  empirical  (Delage,  ln(ln(z/z ))  z  frictional  an  model  models  1  von Karman's c o n s t a n t  angular  the  layer  0  is  The  With  the s o l u t i o n i s determined  where < Q  and  air  w i n d s p e e d U(z)  derive  wind  w h i c h d e p e n d s on t h e  equivalent  of  of  boundary  spectral  to  wind.  a function  (conceptually  atmospheric  required  temperature,  u* = K u { l n ( l n ( z / z ) ) } U(z)  also  column s t a b i l i t y  stability  precise  C M Cforecast  the is  determined  extract  neutral  more  (0.35  u*/g)  constant  the  wind  vector  at  the  sea  surface  due  i s a l s o c a l c u l a t e d and d e p e n d s o n t h e same length  parameters  as  well  as  the  to  the  stability  boundary  layer  -23  3.0  -  SPECTRAL WAVE MODELS  S p e c t r a l models have e v o l v e d w i t h improvements of wave g e n e r a t i o n . are d i s c r e t e independent  spectral  of  interactions but of  that  between the  on t h e  generation"  of  step.  the  was  mechanism f o r modelling they  method.  h a v e had  accurate  to  of  wind  spectral  difficulty  i n c l u d e ji  too  priori the  g e n e r a t i o n " model  on a c o m p l e t e  representation  equation  removes a l l  that  preliminary Komen, b u t In  this  results  full  of  a particular  the  mimick  the  gave  these  to  non-linear  of  all  a priori  this  three model wave m o d e l .  source  The " s e c o n d  time  parametric  spectral  however,  in  that  shape because  interaction  process  available.  source  terms  in  restrictions  the  1984) i s  energy  on s p e c t r a l  based  conservation shape.  Some  t h i r d g e n e r a t i o n model have been p r e s e n t e d is  still  a few y e a r s  by  away.  c l a s s e s are described w i t h s p e c i f i c d e t a i l s The m o d e l s r e p r e s e n t e d a r e a s  drawn  follows:  Reference(s)  second g e n e r a t i o n parametric spectral  The HYPA M o d e l  Hasselmann et a l . (1976) Gunther et a l . (1979a,b)  f i r s t generation discrete spectral  The ODGP M o d e l  Cardone et  second g e n e r a t i o n discrete spectral  The ADWAVE M o d e l  Resio  Class  an  that  M o d e l Name  Model  by  redistribution  on s p e c t r a l  wave-wave  important,  each m o d e l l i n g  are "second generation", restrictions  be  that  interactions  energy the  to  only  principal  spectrum.  this  impetus  are  p r o p o s e d by t h e WAM G r o u p (Komen,  implementation  chapter,  f a c e of  are  1960»s,  bins  h a v e shown n o t  they  generalizing  that  These models  seas,  models  c a n be e v a l u a t e d e c o n o m i c a l l y i s n o t The " t h i r d  frequency  the frequency b i n s a f t e r  of  spectra  of  a l . (1973)  forward  the energy o v e r  representation  c o n s i d e r the  from the  f r e q u e n c i e s (wave-wave i n t e r a c t i o n s )  frequency  arbitrary  that  Hasselmann et  growth stage  discrete of  It  the  low  redistribution  generation" models, dating  formulations  each other.  during  energy  The " f i r s t  i n u n d e r s t a n d i n g of the p h y s i c s  al.  (1981,  (1975)  1982,  1985)  -  3.1  24  -  P a r a m e t r i c S p e c t r a l Wave M o d e l s  There  are  many p a r a m e t r i c  research, best  operational  known  are  (Hasselmann discussion is  on  al.,  the  1976;  work  Gunther  b a s e d on t h e i r  The  equation  by  parametric  parameters  a.^  measurement  experiments.  To  solutions  obtain  assumptions.  that  are  of  K.  et  H a s s e l m a n n and  al.,  (2.1)  H a s s e l m a n n et  form f o r  expressed  readily  in  naturally  al.  (1976)  spectral  form for  to  for  equations  of  9 a  i  +  D  i j  k  set  =  of  T  based  on  a  set  the  spectrum of  over  This  of  wave  simplifying direction  a n d u s e d t h e JONSWAP E(f).  E(f).  spectral  results  several  (2.1)  energy  to  parametric  substitution  yields  i  ^-> 3  five  JONSWAP p a r a m e t e r s  D j j k = the wave p r o p a g a t i o n T^ = t h e  following  form  - ^ i 3x  where a ^ = t h e  substitute  of  integrated  (2.2)  3t  the  co-workers  the  energy  involves  i n the form of  the  for  these,  his  and  the  terms  specified  obtain model equations E(f)  1979a,b)  Of  s p e c t r a l wave m o d e l l i n g i s to s o l v e the  E is  to  h a v e been d e v e l o p e d  and w a v e h i n d c a s t i n g .  assuming a p a r a m e t r i c  spectrum  that  techniques.  The b a s i c c o n c e p t i n p a r a m e t r i c balance  wave m o d e l s  wave f o r e c a s t i n g ,  based  et  spectral  s o u r c e terms  (functions  p  a  (functions  of  a^)  a^)  al.  first  and cx, a r e n e c e s s a r y a s m o d e l l i n g v a r i a b l e s b e c a u s e o f t h e s h a p e  f  i n v a r i a n c e of for  wave  the spectrum.  energy  in  terras  with equations s i m i l a r five In  JONSWAP p a r a m e t e r  order  wind table  to  input of  E(f;a^). only  the  argued that of  of  {f , a , y , 0" , o^}  Hasselmann et two,  (1976)  velocities  1  of  v=  fpU/g  parameterizations:  results  parameters  only  in a prognostic peak f r e q u e n c y )  the  model and  G u n t h e r et a l . (1979) i n c l u d e d  ot a l l  spaces.  solutions  mean  spectral  (non-dimensional  i n form to (3.1).  and d i s s i p a t i o n  In p r a c t i c e ,  five  This s i m p l i f i c a t i o n  s o l v e these equations,  exact  the  this  JONSWAP  empirical  processes, to  the  and  formulae  S ^  is  parameterized  Boltzman integral  approach i s s i m p l i f i e d spectrum.  The  are substituted  result  for  by  a  a range of  for  the  look-up spectra  by u s i n g t h e s o l u t i o n is  quite  simple  of S  n  ^  -  S  -0.54  v  S =  -5.0  a  S  =  y  So  a  Sa  b  2  a f 3  p  2  -  0.5(a -0.09) ]a f  - -[25.5(a -0.09)  -  0.5(a -0.07)]a f  a  b  coefficient  of  of  -0.586 f o r  coefficient a.  In  the  (1979b),  S  = 5.022xl0"  and o c c u r s i n  only  is  2  b  i  p  2  a  of  S  v  is  c a l i b r a t e d by e m p i r i c a l  non-dimensional fetch.  The e x p r e s s i o n f o r S. in  p  = -[25.5(a -0.07)  as f u n c t i o n s  a value  -  2  -16.0(Y-3.3)a f  The c o n s t a n t a  a f  25  Gunther et  is  n  v  3  the  g i v e n by G u n t h e r e t  4 / 3  af  r e g i o n of  a e q u a t i o n of  a l s o determined  S^  The  equations  g  influence  are  the set  from the  reported  to  criterion  requires  than the  largest  the  so t h a t  solved  predictor-corrector  (1979b)  f  and  p  report  using  al.  (1979b)  s p e c i f i e d by ( 3 . 1 ) .  empirical  on  a  domain of  grid  as  a  be s e c o n d o r d e r the  group  accurate  ratio  of  velocity  of  in  grid  interest  waves i n  the  f  and  p  lies  al.  below  omitted.  function  of  time  by  and the  stability  t i m e s t e p A x / A t be solution  domain.  larger In  G u n t h e r e t a l . ( 1 9 7 9 a ) a p p l i c a t i o n , a 2 km g r i d a n d a 5 m i n i n t e g r a t i o n were used to model s e l e c t e d p e r i o d s of squared d i r e c t i o n a l  spreading function,  the  five  p a r a m e t r i c model i s parametric  spectrum E(f) function  provides  One s e v e r e swell  is  spectral  specified,  limitation  wind-sea  of  model  parametric s p e c t r a l model. known ( G u n t h e r large  et  al.,  computational  characteristics  step  independent  of  f,  was assumed t o  a straightforward  unknowns a . , .  s e t of  Once t h e s e  and a p p l i c a t i o n  of  the  five  a^ are  apply  direction.  equations  determined,  directional  in the  spreading  F ( f , 9).  energy c o n t r i b u t i o n s  spectral  thus  the  t h e JONSWAP e x p e r i m e n t . T h e c o s i n e -  and t h e mean w a v e d i r e c t i o n was s p e c i f i e d b y t h e a v e r a g e l o c a l w i n d The e n t i r e  a  The s o l u t i o n scheme i s  s p a c e and t i m e spacing to  constant  and Gunther et  d i s s i p a t i o n t e r m was  spatial  The  dependence of  a l . (1976)  spectral  this  fetch  method (Gunther et a l . , 1979a).  that  as  p  has been assumed t h a t  the  al.  of  the North Sea.  m o d e l s d e s c r i b e d by H a s s e l m a n n e t  it  relations  parametric to  models  is  that  they  t h e w a v e s p e c t r u m . The c o u p l i n g  and  a  swell  model  is  referred  e x c l u d e any  of  a  parametric  to  as  a  hybrid  The d i s a d v a n t a g e s w i t h t h e h y b r i d m o d e l s a r e  1979b;  Janssen et  housekeeping  and the  spectral  al.,  1984).  requirement  wind-sea fixed  The f i r s t to  convert  well-  problem i s  the  between  ray  g r i d mesh t o i n c o r p o r a t e  appropriate  - 26 contributions chiefly of  of s w e l l energy to the c a l c u l a t e d E ( f ) s o l u t i o n — b u t  an i n c o n v e n i e n c e .  somewhat a r b i t r a r y  and t o d e a l w i t h fundamental  The o t h e r  assumptions  and r a t h e r  poor  model has been a t t r i b u t e d For example,  Gunther  d i s a d v a n t a g e a r i s e s from the l a r g e  required  the i n t e r a c t i o n  If  for  then  wind)  frequency)  maintain  t h e same t o t a l  energy  absorbed i n s t a n t a n e o u s l y  (3)  Swell  subject i.e.  energy  t o wave g r o w t h ,  f <f<0.9f Q  swell  into  With  (where  is  to  conserve  energy at f<f  determined and a f t e r  numerically  swell  by a d j u s t i n g  Q  exceeds 0 . 9 f  f  to  then  p  swell  regard  to  w i t h a and Y f i x e d .  S w e l l may e x i s t  at  frequencies  t h e range of n o n - l i n e a r  interaction,  a s g/2TTUcos^ directions);  S ^ = 2irf [ ( f - f n  p =density  (a  separation;  the wind-sea spectrum without  but outside  Q  i s included.  frequency  Wind-Sea:  f  adjusted  of f  the  angle  the M i l e s - P h i l l i p s  growth  )/f  air,  Q  ] [c  is  p / p ^ ] a  p =density  f o r f>f  and  T h e s e a s s u m p t i o n s by G u n t h e r e t a l . ( 1 9 7 9 b ) a r e d e s c r i b e d as i n t u i t i v e ,  and  w  of  Q  and  a  of  Q  where  water  i n  =0  f  i n E(f) before  mechanism i s assumed s u c h t h a t S  is  p  where  s e p a r a t i o n between wind and s w e l l  otherwise  p  t h e PM v a l u e  p  If  (defining  p  forecasting  assumptions.  of E ( f ) above f ( P M ) ;  i s conserved  Interacting  f =f (PM);a  spreading of s w e l l  (2) S w e l l B e c o m i n g W i n d - S e a :  direction;  swell  i s much more  operational  ( i . e . below  p  becomes s w e l l  cosine-squared d i r e c t i o n a l  is  f <0.13g/U  i n the wind-sea p o r t i o n  cut-off  the Dutch  made t h e f o l l o w i n g  (1) W i n d - S e a B e c o m i n g S w e l l :  energy  of  number  wind-sea from  This d i f f i c u l t y  is  ( J a n s s e n e t a l . , 1984).  e t a l . (1979b)  a 10 m e l e v a t i o n  to d i s t i n g u i s h  of the two.  performance  to i t  this  c=0.05).  h a v e no d o u b t to parametric 3.2  been r e f i n e d ,  but they  do i l l u s t r a t e  the fundamental  objection  s p e c t r a l wave m o d e l l i n g .  D i s c r e t e S p e c t r a l Wave M o d e l s  Discrete  spectral  difference frequency  wave  models  are solutions  (2.1) a c h i e v e d  t e c h n i q u e s i n w h i c h t h e s p e c t r u m F ( f ,9) i s d i v i d e d and d i r e c t i o n  (1) t h e y do n o t r e l y e n e r g y by d i r e c t i o n ,  domains.  These models have t h r e e  on e m p i r i c a l  sea and s w e l l wave  spreading functions  (2) t h e y d o n o t i m p o s e a u n i v e r s a l  s h a p e e x c e p t when e n e r g y s a t u r a t i o n  different  of  types.  into  obvious  finite  discrete  advantages:  to r e d i s t r i b u t e parametric  i s a c h i e v e d , and (3) they  a s a c o m b i n e d phenomenon r a t h e r  by  treat  than as a h y b r i d  wave  spectral local  wind  combination of  -  The v a r i o u s  operational  and  f r o m one a n o t h e r p r i m a r i l y S(f,8), these,  and two  empirical  pressure f l u c t u a t i o n s instability  by t h e i r  to at  in  this  class  p a r a m e t e r i z a t i o n of  different  by t h e ODGP m o d e l  formulations  -  r e s e a r c h models  fundamentally  exemplified  27  describe  formulations  (Cardone et  wave  distinguished  t h e e n e r g y s o u r c e terra  have developed.  al.,  initiation  are  1975),  by  bases  turbulent  including  Furthermore,  contributor  each of  S(f,9) S,  the  +S  on  d g  atmospheric  the  Cardone model  assumes t h a t  ' p a r a m e t e r i z a t i o n of  i n  of  t h e s e a s u r f a c e and w a v e g r o w t h by t h e M i l e s - P h i l l i p s  mechanism.  negligible  S  One  to  the  is  much more  S  ±n  d  g  energy  and S  S -i i s  n  n  l  balance.  closely terms,  The  other  b a s e d on t h e  and R e s i o ' s  approach  JONSWAP  (1981,  a  l to  results  1982) ADWAVE  m o d e l i s t h e most w e l l - d e v e l o p e d , w e l l - p u b l i s h e d e x a m p l e . 3.2.1  T h e ODGP M o d e l  The ODGP m o d e l was d e v e l o p e d by C a r d o n e e t  al.  (1975) under  the  s p o n s o r s h i p of the Ocean Data G a t h e r i n g Program i n the G u l f impetus  for  the  study  was  to  monitor  wind  and  wave  of  oil  Mexico.  conditions  h u r r i c a n e s w i t h a v i e w to b u i l d i n g a - c a l i b r a t e d wave h i n d c a s t i n g describe  the e v o l u t i o n  of  m o d e l i s d e s c r i b e d by i t s calibration (1966).  of  h u r r i c a n e waves throughout authors  as " a r a t h e r  Because the wave model  the p u b l i s h e d d e t a i l s  of  its  came t o  code and c a l i b r a t i o n  S  the e m p i r i c a l  during  model  to  The ODGP w a v e and  p u b l i s h e d by P i e r s o n e t  al.  exploited  by C a r d o n e ,  procedure are sketchy.  down-wind  spectral  components  formulae  A ( f , 0 , U ) + B ( f , 6 , U ) . F ( f ,9)  in  to  The  application  be c o m m e r c i a l l y  Wave g r o w t h and d i s s i p a t i o n a r e a p p l i e d according to  the G u l f .  straightforward  t h e P i e r s o n - T i c k - B a e r (PTB) m o d e l " ,  industry  1 -  /  F(f,9)  \  2-  (3.2)  wf,e,u); where A  is  the  gravity  linear  growth  instability U  is  the wind  F^  is  the  initiates  growth term i n c o r p o r a t i n g  the  excitation  of  of  the M i l e s - P h i l l i p s  mechanism, speed,  s a t u r a t e d PM s p e c t r u m f o r  directional  relatively  which  w a v e s on a c a l m s e a s u r f a c e ,  B.F i s t h e e x p o n e n t i a l  The f o r m u l a t i o n s  coefficient  spreading function the  unimportant,  a g i v e n wind speed m u l t i p l i e d  by a  G(f, 9).  A and B c o e f f i c i e n t s  are unpublished.  s e r v i n g o n l y to i n i t i a t e s p e c t r a l energy  The A t e r r a growth.  is  -  D i s s i p a t i o n of  upwind  (1975),  the o r i g i n a l  F  but  in  diss F  That  spectral  components  ra  dissipation  was  the i n i t i a l  is  0  al.  form: (3.3)  applied  N  is the  ) of  of  the  the  the and  l o c a l wind  Gulf  of  for  the  spectral  by  1265  points  a discrete  between  large  computer  memory  to  (2.1).  points  The G u l f  arranged  al.  a  Mexico  triangular  i n which s t r a i g h t  lines  The n o m i n a l  grid  s p e c t r u m was  calculated bands.  c o m p u t e r memory and i n p u t / o u t p u t  limitation  to  implementation  of  at to  s u c h wave  computers. results  the p e r f o r m a n c e of  three  in  of  13 f r e q u e n c y b a n d s a n d 24 d i r e c t i o n  the primary  from p u b l i s h e d  illustrates  directional  T h i s demand f o r  devices is  m o d e l s on s m a l l  other (1975)  maximum w a v e h e i g h t  generally  of  the  ODGP h u r r i c a n e C a m i l l e h i n d c a s t  this model.  B a s e d on t h e h u r r i c a n e  h u r r i c a n e h i n d c a s t s and one t r o p i c a l report is  that  4.9 f e e t  s e a s t a t e s o f maximum w a v e h e i g h t represent  difference  the  solutions  discrete  another  4x10^ components of s p e c t r a l e n e r g y were d e t e r m i n e d  time s t e p .  3.1 i s  from  miles.  grid  then, almost  Cardone et  illustrate  on a n i c o s a h e d r a l - g n o m o n i c map p r o j e c t i o n  and s t o r e d t h a t was c o m p r i s e d o f  mass s t o r a g e  half-  t h e w a v e component d i r e c t i o n  models,  difference  represented  these  each h o u r l y  to  direction,  finite  s p a c i n g was 20 n a u t i c a l  results,  of  c i r c l e s and hence a r e d e e p w a t e r wave t r a j e c t o r i e s .  each of  calibrated  direction,  Mexico hindcast  parametric  a r e a was  are great  upwind  W  is  grid pattern  is  the  l o c a l w i n d d i r e c t i o n and c a l c u l a t e d a s N = 4 - [ | Q , - 6 | - 1 8 0 ] / 1 5 ,  6w  requirements  E q u a t i o n (3.3)  on  the wind sea spectrum ( i . e . the  deviation  t h e u p w i n d w a v e component  discrete  function  spectrum),  is  of  damping  where  6^  Details  a  Q  down-wind  a function  as  spectrum F ( f , 6 ) .  t h e z e r o t h moment ( f t  plane  Fig.  the  d e s c r i b e d by C a r d o n e e t  N  be a p p l i e d a t 2 - h o u r l y i n t e r v a l s  In a l l  not  0  components of  At  is  o  is,  study  -  PTB m o d e l i t . h a d  [exp(-78v^ fJ)]  =  28  the  root-mean-square  ( 1 . 5 m) a n d t h e  a c c u r a c i e s , but  comparison p a i r s are almost c e r t a i n l y without  bias  is  +1.5  in  the  Camille hindcast,  the feet  r a n g i n g b e t w e e n 20 a n d 80 f e e t .  satisfactory  p r e d i c t e d wave h e i g h t s ,  error  storm  predicted ( 0 . 5 m)  the  time  of  in  Such v a l u e s  measurement-prediction  t h e maximum m e a s u r e d and t h e  regard to  and  o c c u r r e n c e of  maximum  either.  -  29  -  /  STATION 2  32  1 / 1  x 2  • 002 8  —  "2" • 801  0  UJ X  Hindcoit 801 Hindcoit 802  -  _  _  V  a ?  i A  .  T  2  A  OOGf>  > •I  0  S T A T I O N S  so  100  SCA.t N.Ml.  /  ; »  -  9URW0OD-1T».B 5  noMtDA  T  R  A  RIG  N  S  W  50  O  E 32 z  \ »  t t f  CAMIUP  * 7 5  3  I 0900  1 1000  1  1100  1  1200  1 1300  i 1400  Hindcoit Hindcoit i 1500  874 875 I 1600  l?0O  TIME (COT)  Fig.  3.1  ^  "  \  \  v  \  T  *" * • 8M  D  \  24  IC  L  \\  STATION 3  19  R  \  STOK-M  < o  G/O'S.'.t  1 1 \  l  T I  \  7  ALABAMA  .  LOUISIANA  u. 16  1  DlSSHHfH  1  24  1 1 I  t .  Measured and h i n d c a s t s i g n i f i c a n t wave h e i g h t times e r i e s at t h r e e s t a t i o n s i n the G u l f of M e x i c o d u r i n g Hurricane C a m i l l e . The h i n d c a s t s i t e numbers d e s i g n a t e grid points c l o s e to the measurement s i t e s . (From Cardone et a l . , 1975).  T R A C K  -  -  3.2.1  30  -  ADWAVE  T h e ADWAVE h i n d c a s t (1981, 1982). solution terras  to  Its the  present  complete  i n c l u d e wind  (wave-wave  model  formulation  from  (Resio,  non-linear  energy  and d i s s i p a t i o n .  F(f,8)  spectrum  1985) i s  is  d e s c r i b e d by a finite  s c h e m a t i c a l l y i n F i g . 3.2)  applied over  the m o d e l l i n g domain.  in  at  between wave  source  frequencies  d o n e by t h e m e t h o d  of  calculations.  The  and  (as  frequency  each point  Resio  difference  i n which the  s h a l l o w water  discretized  illustrated  are c a l c u l a t e d as changes i n  transfer  Propagation is  c h a r a c t e r i s t i c s which i s g e n e r a l i z e d for energy  precursors  energy b a l a n c e e q u a t i o n (2.1)  input,  interaction)  has e v o l v e d  direction  on a r e g u l a r  x-y  grid  P r o p a g a t i o n and the s o u r c e / s i n k mechanisms  energy  in  each of  and 6 e l e m e n t s .  these f  Propagation The p r o p a g a t i o n  of  wave energy  frequency-direction solution  grid  location F(f9  d i s c r e t i z e d element (i+6x,j+6y)  at  time  characteristic invariant  c  level  3.3a)  and  Fig.  3.3a).  The  same  the  have  6)  ray  case  first ray  at  the  is  content  have  quantity  determined  by  the  done i n s m a l l  to vary  c and c  Since  the  directions constants  as f u n c t i o n s  model  is  written  with depth (location  of  points  each g r i d  pre-processing  adds  speeds the  time  very  terms  of  at  in  the  position along  the  conserved, f shallow The  point  (i.e.  energy  B in  at  i n F i g . 3.3b. incremental  0  but  in  the  The b a c k steps i n  of Fig.  point  case,  is  water.  interpolation  depth  (i,j)  of  discrete time,  all  p h a s e and g r o u p  at  significantly  stepping  fixed  independently  B and 0 ) ,  point  c At  fixed  ray  order  depth.  in  specified  calculated for  but  of  (i.e.  generalized  to  &  the  F i g . 3.3a.  (i+6x,j+6y)  point  tracing  0 and B i s  from  bilinear  intersection  as d e p i c t e d  points  n+At  F.c.c„ i s  in  At a  time  a distance  c h a r a c t e r i s t i c rays are c u r v i l i n e a r location  at  originated  illustrated  grid  for  location.  ray moves from deep i n t o  origination  applies  deep w a t e r  travelled the  ( i + 6 x , j + 6y) i s  n,  a  energy  and w i l l  at  principle  n  can o n l y  m  c h a n g e s as t h e  the  i  ;i,j)  m  then at  r e a d i l y u n d e r s t o o d i n terras o f a s i n g l e  P ^ k * ^ )  (i,j)  (constant  F(fj ,9 )  most  Along this  and 0 o n l y  of  F at time  n,  ray.  The deep w a t e r content  element  is  frequencies the  velocities  interpolation may be  e a c h f r e q u e n c y and d i r e c t i o n . to  t h e c o m p u t e r memory  c a l c u l a t i o n phase of  the  model.  and  preThis  requirements,  -  31  -  F(f,9)  centre of frequency-direction element F ( f , 9 )  Fig.  3.2  R e p r e s e n t a t i o n of a t w o - d i m e n s i o n a l s p e c t r u m . The u p p e r p a n e l ( f r o m S a r p k a y a a n d I s a a c s o n , 1981) shows a p o r t i o n of F ( f , 0 ) i n t h r e e - d i m e n s i o n a l r e l i e f and the lower p a n e l shows t h e d i s c r e t i z a t i o n of t h a t s p e c t r u m in i n c r e m e n t s of f r e q u e n c y and d i r e c t i o n as a p p l i e d in ADWAVE.  -  32  -  B position of wave | component at j beginning of time step  position of wave component at end of time step  I I I  interpolation along ray  i  Fig.  3.3  The b i l i n e a r i n t e r p o l a t i o n s c h e m e i n w a t e r and (b) i n s h a l l o w w a t e r .  ADWAVE ( a )  in  deep  -  Source Terms:  S  Hasselmann  al.  et  empirically involves There that of  +S  n l  in  primarily also  this  is  +S  a growing  1984-85.  somewhat  as  shown  in  intermediate  energy Fig.  (Bouws e t  to  give  al.,  recent  study  empirical  evidence  Further  evidence  1985).  formulation  for  s p o n s o r e d by  The t r a n s f o r m a t i o n  Bank w i t h a d i r e c t i o n a l results  10% i n  spectrum  3.4:  the  range where S ^  The h i g h  times  and g o v e r n e d  input  is  n  frequency  energy spectrum i s energy  1986).  terms  of  the  wave-wave  the  ESRF Waves  deep water  waves  into  wave buoy d u r i n g w i n t e r  indicate  total  that  the  agreement  e n e r g y and s i g n i f i c a n t  storms  is  quite  wave h e i g h t  but  i n peak p e r i o d .  ADWAVE t h e  a l l  Island  w i t h i n about  In  at  al.,  source/sink  n  (1985)  a  the  and the w a v e - w a v e i n t e r a c t i o n s S ^ .  measurements  Resio from  Preliminary  low  spectrum.  the  n  among  and  a s p r e d i c t e d by ADWAVE was c o m p a r e d w i t h m e a s u r e m e n t s i n 12 m of  on S a b l e  acceptable,  S^  of  1982) h a v e shown t h e o r e t i c a l l y  balance  s h a l l o w water  of  Committee (Hodgins et  in  the  resource  m e c h a n i s m comes  s h a l l o w water  (1981,  the wind input  a l s o so i n  interaction  water  and R e s i o  deep w a t e r  suitability  -  d s  (1973)  that  is  the  i n  33  also  is  c o n s i d e r e d to  forward is  tail by  by  (region  the  segments  frequencies  below  f ,  III)  is  power  -  as the  r e g a r d e d as f u l l y  Phillips'  dissipation  through  law.  This  of  of  range  whitecapping  the  saturated  part  equilibrium  an  p  and the h i g h f r e q u e n c y ' t a i l  E(f) = f ^  to  three  at  operational  referred  balanced  face  be c o m p o s e d o f  and  the where wave  breaking. Modern hypotheses ( R e s i o , energy  to  region  III  is  1985; K i t a i g o r o d s k i i ,  not  wave-wave  interactions  regimes II  and I I I  from  the  originating  i n deep w a t e r  is  local from  1983) a r g u e t h a t  wind,  but  region  approximately  II.  from  the s o u r c e  resonant  nonlinear  The t r a n s i t i o n  (Kitaigorodskii,  (3.4)  U  a  a  6  u  w h e r e ot  is  approximately  4.4x10  ,  B  is  approximately  1.5x10  , and  U„ i s Thus f „  g  is  is  about  frequency 50 k n o t s . regime) i n  the average wind about  0.5  5.32/U„. a  Hz o r  cutoff  between  1983)  *g " g a = JL 27Tf  of  T =2  speed.  For a moderate wind of s.  For  i n wave m o d e l l i n g  the  20 k n o t s  transition  (T =5 s ) ,  U  to  must  be a t  (U =10 m/s) a  the  then  normal  f_  g  high  b e 26.6 m/s o r j u s t o v e r -5 I t w o u l d t h e r e f o r e be r a r e t o h a v e a r e g i o n I I I ( i . e . an f slope a h i n d c a s t wave s p e c t r u m .  - 34 -  ENERGY GAINED ON FORWARD FACE OF SPECTRUM DUE TO WAVEWAVE INTERACTION SOURCE  DYNAMIC EQUILIBRIUM MAINTAINED BETWEEN ATMOSPHERIC INPUT AND WAVEWAVE INTERACTION SINK  m ENERGY INPUT FROM WAVEWAVE INTERACTIONS LOST TO VISCOUS AND TURBULENT DISSIPATION  ATMOSPHERIC SOURCE OF ENERGY  WAVE SPECTRUM lEtf)]  z  $ ° ° > o £  UJ  a >• a  < cc  E  WA VE-WAVEINTER ACTION SOURCE/SINK  Fig.  3.4  Energy growth.  regimes w i t h i n a spectrum (From R e s i o , 1982).  during  active  wave  -  Resio  (1985)  and K i t a i g o r o d s k i i  equilibrium  35  -  (1983) h y p o t h e s i z e t h a t  s h a p e c h a r a c t e r i z e d by a p o w e r  f o u n d by K i t a i g o r o d s k i i i n e x p e r i m e n t a l E(UJ) = a g U u  where  is  A  is  of  angular frequency the s a t u r a t e d  range are  depend, for energy  f  Kolmogoroff's  -1/30),  a  shape of  and  this  part  of  the  spectrum i s  on mean l o c a l w i n d  on l o c a l wind s p e e d .  been d e s i g n a t e d  transfer  theory  ),  (2Trf).  e q u i l i b r i u m range i n r e c o g n i t i o n energy  4.4x10  speed.  invariant, The  limits  , and as s u c h t h e y h a v e d y n a m i c d e f i n i t i o n s  t h e most p a r t ,  of  (-  depends d i r e c t l y  and f  spectrum has  theories  f o r which has been  constant, A  the energy c o n t e n t the  an  (3.5)  t h e mean w i n d s p e e d ( u / U "  In other words,  a l s o has  4  the g r a v i t a t i o n a l  wis  but  "  support  II  data from s e v e r a l s o u r c e s :  a non-dimensional constant  g is U  a  law,  region  from  of  a  of  This central  by K i t a i g o r o d s k i i the  low  parallels  to high  turbulent  (1983)  between  frequencies  energy  that  r e g i o n of  as  Kolmogoroff's  Kitaigorodskii's  i n wave s p e c t r a  cascade  the  from  low  to  and high  frequencies. I n ADWAVE, t h e w i n d e n e r g y i n p u t S  i  n  =  fa  X  C  A is  «  P  a  is  P  w  i s water  coefficient  g is  the  into  the  transfer is  wave  the wave  reasonably  of  wind  field,  coefficient,  10-m e l e v a t i o n w i n d s p e e d ,  al.  (1973)  field  is  concluded that of  Resio  about  60%.  (1985)  and  constant.  the  order  a c r o s s the a i r - s e a i n t e r f a c e ,  important.  expressing the f r a c t i o n  density,  the g r a v i t a t i o n a l  Hasselmann et  as  density,  the s u r f a c e drag  UJQ i s  defined  .  momentum t h a t e n t e r s air  is  (3.6)  a partitioning  is  region II  D ^10  Pw where  to  argues  t h e minimum a t m o s p h e r i c momentum of  but  that  10 t o It  the  40% o f  may be up t o partitioning  the  total  100% i f  flux  momentum dissipation  coefficient  is  more  - 36 -  The d r a g c o e f f i c i e n t slightly C  different  (1985)  with  coefficients:  = (0.75 + 0.054 U  D  Resio  h a s t h e f o r m p r o p o s e d by L a r g e a n d Pond (1981)  1 0  )xl0  (3.7)  - 3  has assumed t h a t  where  bottom  effects  are  negligible  S^  is  n  e x a c t l y b a l a n c e d by S ^ when t h e e n e r g y s p e c t r u m i s s a t u r a t e d i n r e g i o n Based on t h i s collision  n  E  tanh where  £ is  g is  3 / 4  of  (k d)  of  1981;  1982;  to  the  is  not  constant,  or net  the  not  from  the  energy  discussed  on t h e  transfer forward  equilibrium frequencies  where 6 i s  to face  form is  conductivity. E(f)  forward  i n deep w a t e r ) ,  (hii f^/g  in balance,  S^ -S ^  Kolmogoroff  range  among  the  by R e s i o  in  f a c e of of  S ^, n  the permanently is  presumed  (Resio,  and  n  wave  p r o v i d e s a net  n  although  numbers  any of  the  or  the  source method  frequencies  referenced  works  the  or of  (and  (Resio,  the  s p e c t r u m ( r e g i o n I i n F i g . 3.4) remainder  have  The  an  rate heat  I n deep w a t e r ,  yields  = E(f ) p  dissipated  idea  energy  transfer  in  rather  transfer  than  among  a medium o f  an the  (3.9)  4  performed  by  constant  p  bottom i n t e r a c t i o n e f f e c t s ,  is  The s h a p e  exp{-6(f/f )~ }  a dimensionless  tests  which i s  evolutionary of  viewed as an a n a l o g u e of this  of  saturated s p e c t r a l region III.  to  1985).  constant.  O t h e r e n e r g y s o u r c e - s i n k terras  deep w a t e r  <f<°°,  depth.  d e f i n e d as a f i x e d p r o p o r t i o n  of  the  1985).  Energy growth  implicit  t o be o f  100),  l o c a l water  energy  directions)  (evaluated numerically  t o t a l s p e c t r a l energy i n the domain f  the  distributing  rate  (3.8)  When t h e w i n d - w a v e s y s t e m i s sink  energy f l u x  the  5  t h e p e a k wave number  d is  total  of  p  the  kp i s  the  integration  P  the g r a v i t a t i o n a l  is  Q  an a p p r o x i m a t e  g i v e n as  a non-dimensional constant  order  E  * -  3  and  the e x p r e s s i o n f o r  s p e c t r a l parameters i s  = ^  l  balance  (Boltzmann) i n t e g r a l ,  i n terms of  S  equilibrium  II.  i n c l u d e d i n ADWAVE a r e s h o a l i n g , r e f r a c t i o n  a l t h o u g h none of as p a r t  of  this  these f a c t o r s research.  are i n c l u d e d i n  and the  -  Using h i s t o r i c a l Carolina; South  Seaconsult, water  Table  for  input  growth.  four  also  of  s  included  ADWAVE f o r  give  negligible  the  wind  input  and the  in  Hodgins  et  al.,  variety  summary o f  each s p e c t r a l  diminishes with to  s h o r e w a r d s h a l l o w H2 s i t e . to  H It  the  g  the  the  values  shallow  The  In  S ^ term  S(f)  case  s o u r c e of the  terms  1,  quickly  n  wave  d e e p e r H^  the d i f f e r e n c e  various  four  refraction,  case.  at  and  source-sink  shoaling,  dominant  is  North  1986  cases.  test  time,  be t h e  simultaneous  being a t t r i b u t e d  of  of  energy  these test  importance  in  of  (Duck,  and M e l k b o s s t r a n d ,  a wide  and s h o a l i n g b e g i n s  values that i s  Japan;  the performance  relative  the  locations  verify  Resio's  interactions  Columns 2 and 3 g i v e  location these H  (1985;  and n o n l i n e a r  e x a m p l e , as the  becomes  Nishikinohama Coast,  3.1 p r e s e n t s  columns  different  Japan;  1986a) has been a b l e to  righthandmost wind  Resio  implementation  conditions.  -  wave measurements from f o u r  Hiezu Coast,  Africa),  37  between  i n the  last  columns.  T h e ADWAVE p r e d i c t i o n a l w a y s w i t h i n 10% o f examples  that  terras i s a b o u t  of  H  g  at  site  H2 i s  given  the measured v a l u e w i t h o u t  exceed the t h e same b u t  10% d e v i a t i o n , certainly  not  the  in  c o l u m n 4 and i s  any a p p a r e n t  relative  uniquely  so.  bias.  importance  In of  These r e s u l t s  v e r y a c c e p t a b l e p e r f o r m a n c e by ADWAVE o v e r a b r o a d r a n g e o f p h y s i c a l conditions.  almost the the  two S(f)  indicate prototype  -  38 -  Table Comparison of  3.1  P r e d i c t e d a n d O b s e r v e d Wave H e i g h t s as a F u n c t i o n of  M o d e l l e d E n e r g y S o u r c e Terms  Date-Time  «1  H  8210100100 8210101300 8210110100 8210111300 8210120100 8210121300 8210121900 8210241300 8210251300 8410060700 8410061900 8410070700 6412021405 6412021434 6412021527 6410021546 6401311620 6401311710 6901160000 6905130000 6905290000 6908190000 6910070000 6911180000 7001270000  1.8 2.4 2.1 2.0 2.0 2.4 2.2 4.1 3.6 1.1 1.4 1.5 1.9 2.4 2.0 1.9 .8 .8 1.7 3.4 2.7 3.4 2.1 4.4 2.7  1.8 2.6 2.7 2.6 2.4 3.1 3.1 3.4 3.2 1.0 1.2 1.4 1.8 2.1 2.0 1.9 .7 .8 1.5 3.1 2.4 3.0 2.2 3.5 2.6  2  H  pred  Dev  1.8 2.8 2.6 2.4 2.5 3.0 2.8 3.5 3.6 1.0 1.3 1.5 2.0 2.4 2.1 1.9 .6 .8 1.5 3.3 2.6 3.0 2.3 3.6 2.5  .0 .2 -.1 -.2 .1 -.1 -. 3 .0 .4 .0 .1 .0 .1 .3 .1 -.1 .0 .0 .1 .2 .2 .0 .1 .2 -.1  % Dev -.1 7.8 -3.7 -6.1 5. 3 -3.3 -9.9 1.1 13.5 -3.0 5.7 2.1 6.1 12.0 4.3 -2.9 -2.2 6.6 4.0 6.4 8.4 -.5 3.4 4.5 -3.6  %  *1 -4.5 54.1 59.0 83.7 91.9 93.1 94.9 .9 50. 4 -.9 -12.2 -18.3 59.1 61.4 69.6 -63.5 -.9 -.5 -44.6 27. 4 17. 4 -59.3 81.9 17.4 -7.7  2  .0 .0 .0 .0 .0 .0 .0 -.9 -11.7 .0 -.4 -.9 -22.2 -16.4 -14.6 -18.8 -.2 -.6 -31.3 -13.6 -49.3 -2.2 -5.4 -15.7 -69.8  • *3 49.7 30.6 31.7 10.5 1.9 .6 .7 42.5 .1 48.0 41.8 50.0 .0 . 1 .2 .3 37. 6 52.6 15. 3 .3 .1 1.4 7.1 6.3 5.9  KEY H  H  l  pred  .. ••  % Dev . .  predicted H  pred " 1  0  0  x  <  H  P  (m) a t s i t e  1 (deeper)  height  (m) a t s i t e  2  wave h e i g h t  2  H  height  (m) a t s i t e  (shallower) 2  <> m  red "  H )/H 2  2  %1  c h a n g e due t o  %2  c h a n g e due t o  %3  c h a n g e due t o w i n d  7.4  c h a n g e due t o n o n l i n e a r  shoaling refraction input interactions  »4 -45.8" -15.3 -9.3 -5.8 -6.2 -6.3 -4.4. -55.7 " -37.9 -51.1 " -45.5 -30.9 -18.7" -22.1 -15.6 -17.4. -61.4" -46.4 -8.9" -58. 8 -33.2 -37.0 -5.6 -60.6 -16.6.  —  -  -  -  4.0  -  WIND F I E L D S E N S I T I V I T Y : AN A P P L I C A T I O N OF ADWAVE  To  investigate  hindcasting, choice  of  the  effects  that  ADWAVE  for  the  wave  and f a m i l i a r i t y .  equation i n arbitrary physics  than  found  errors  model  was it  s o l u t i o n method f o r  in  may  cause  Since  a first  it  dictated  e a c h new s i t u a t i o n .  coast  of  1986b)  is  contains  Seaconsult,  Island  1986),  in  Bank on C a n a d a ' s  i s a complex computer program,  resources:  CPU t i m e ,  important  hindcasting applications  east  it  parameterizations  model  like  (Resio  and V i n c e n t ,  errors  are g e n e r a l l y  automatically  1979).  its  a bias  frequency d i s t r i b u t i o n to  is  ODGP,  (Hodgins  et  in  so t h a t  total total  in  (peak p e r i o d ) .  justified  wind f i e l d note  that  most  cases  rms e r r o r . energy  mass s t o r a g e .  1986;  of  variations  in  this  investigation  errors  is  to  (T ),  interest  spectral  period  F(f,9)).  The p h y s i c a l d e t e r m i n a n t s fetch  p  mean w a v e  and  duration.  conditions  pressure system ( r a d i a l the  of  may b e  large  and wave  model  reducing  either  one  wave h e i g h t )  and/or  For engineering a p p l i c a t i o n s , i t  the m e t e o r o l o g i c a l f o r c i n g  meteorological  for  on t h e g r o u n d s  input  (significant  quantify  i n t h e B.C. c o a s t a l w a t e r s  The s e a - s t a t e p a r a m e t e r s of  speed,  computer  and t h e n  safety  In t h i s  is to way  factors.  the S e n s i t i v i t y A n a l y s i s  s e a - s t a t e parameters  of  al.,  However,  r e m o v e a s much b i a s a s p o s s i b l e f r o m a w a v e h i n d c a s t  S t r u c t u r e of  The p u r p o s e  path  west  The c h a r a c t e r i s t i c w a v e m o d e l  safe, economical designs are achieved w i t h optimal  wind  is  Sea ( S e a c o n s u l t ,  u n d e r s t a n d t h e p r o b a b l e n a t u r e of any r e m a i n i n g random e r r o r s .  4.1  it  of  calibration  v e r y demanding of  use i s  These authors  additive,  reduces the  usually  important  Beaufort  coast  v i r t u a l memory and p e r i p h e r a l  minimizing modelling errors, e s p e c i a l l y if  is  energy  1986a).  Because i t  error  the  by  a good c h o i c e b e c a u s e  the c o n s e r v a t i o n of  generation  The  ADWAVE h a s b e e n s u c c e s s f u l l y a p p l i e d o n t h e  C a n a d a ( H o d g i n s and N i k l e v a ,  and o n S a b l e  wave  largely  e x p e c t e d t o more a c c u r a t e l y m o d e l d i v e r s e i n p u t c o n d i t i o n s w i t h o u t for  in  a n a l y s i s has been c o n s t r u c t e d .  hindcast  water depths.  is  field  On t h e o t h e r h a n d ,  represents a very up-to-date  more  wind  a systematic s e n s i t i v i t y  availability it  39  of  storm passage along i t s  that  to  of  hindcast to  known  parameters.  direction  In  in  are a t t r i b u t a b l e  are s i g n i f i c a n t  of  variations  (0)  wave h e i g h t  and s p e c t r a l  (H ),  peak  g  shape (E(f)  or  t h e s e p a r a m e t e r s ( i n deep w a t e r ) turn  these  factors  the s u r f a c e p r e s s u r e f i e l d :  extent  low i n r e l a t i o n  the  governed  intensity  the s y s t e m and d e p t h of  the c o a s t l i n e or to  are  s i t e s of  are  of  the  the c e n t r a l interest,  by low  low),  rate  t r a j e c t o r y and r a t e of s t o r m i n t e n s i f i c a t i o n .  of  Fig.  -  4.1 i l l u s t r a t e s most  surface  control  of  how t h e s e f a c t o r s  pressure  the wind  To s y s t e m a t i c a l l y utilized  in  function  of  field,  alter  and  a  hindcasting  the  r in  radial  influence  In p a r t i c u l a r the  fetch,  surface pressure patterns, symmetric  terms  of  scale  conventions,  pressure  the c e n t r a l  R.  In  P is  with  the  to  trajectory  select of  trajectory  storms  central the  Q  calculated  reasonable  the  AX /At,  and f i l l i n g  of  the  p r e s s u r e map was c o n s t r u c t e d  output  s h a l l o w water Hindcast (E(f)  results  and  Q  within  the  Wind F i e l d  specified in the  -  central  -  a radial  of  the  of  was u s e d  modelling every point  of  the  of  well  the  rates  as  low  of  latter  deep water  input  spectral  (1985)  for  along  the that  intensification  vector  were  winds  sea-state.  were  boundary  l°xl°  The p r e s e n t  conditions  of o n e - and t w o - d i m e n s i o n a l H „ , T^ and 8 a t  domain as w e l l  as  on the  grid.  solution  are derived  for  complete  spectra selected  fields  from s u r f a c e p r e s s u r e p a t t e r n s  t i m e a n d s p a c e by a t h r e e of  scaling  of  the  that  are  the  central  p a r a m e t e r model based on  low p r e s s u r e of  time,  position, and  parameter 1015 mb.  c a l c u l a t i o n was a p p l i e d t o t h e s u r f a c e p r e s s u r e maps t o  atmosphere wind. to  An a n a l y s i s  step.  a s s u m i n g a mean b a c k g r o u n d p r e s s u r e e q u a l t o  the f r e e  R as  the  time-series  low p r e s s u r e as a f u n c t i o n  wind  6-  hindcasting.  fields  time h i s t o r y  A gradient  each  Specification  The i d e a l i z e d w i n d  -  for  was d e s i g n e d t o p r o v i d e a v e r y d e t a i l e d  provide  consist  d e r i v e d parameters at  fully  and  Q  velocity  the wave model time  would  P  P (min),  a  wind-wave  by L e w i s a n d M o r a n  and F ( f , 6 ) ) and d e r i v e d s e a - s t a t e p a r a m e t e r s  -locations  4.2  for  the  Q  specification  coastal  Pacific  p r e s s u r e maps and t h e s e  The h i n d c a s t m o d e l c o n f i g u r a t i o n  application  X ,  as  G r a d i e n t and n e a r - s u r f a c e w i n d f i e l d s  Q  surface  latitude-longitude  values  of  AP /At.  i n time to  northeast  low  position  low  from the  interpolated  the  defined  usual  in  used  through  p r e s s u r e P , t h e mean p r e s s u r e  accordance  one s u r f a c e  field  27 y e a r s was  that  a n i d e a l i z e d m o d e l was  o f a 2.5 t o 3.5 d a y s t o r m d u r a t i o n .  severe  shows  primarily  hourly hindcast interval of  it  curvature.  a radially  radius  -  are r e l a t e d .  parameters  field  which  40  calculate  h i n d c a s t wave m o d e l .  The b o u n d a r y  surface  winds  layer  suitable  model for  described in direct  input  derive  Section to  the  2.3.3  ADWAVE  derived sea-state parameters  H  -  41  s  = EL  P 6 T  modelled sea-state  -  =  Fkm.Af.A9 k m l/f(max(F ))  =  0(max(F  4  k m  F(f,0)  k m  ))  Wf^f  max  O°<0<36O°  governing physical parameters  controlling meteorological conditions  surface pressure parameters  Fig.  4.1  duration  storm intensity  traj ectory of s t o r m  P AP/Ar R  The i n t e r - r e l a t i o n s h i p parameters.  X  of  Q  velocity of storm  deepening & filling  AX /At  AP /At  Q  meteorological  Q  and  sea-state  -  42  -  4 . 2 . 1 The S u r f a c e P r e s s u r e F i e l d M o d e l The m o d e l u s e d h a s b e e n a d a p t e d f r o m one by C a r d o n e e t applied  to  symmetric field  hurricanes  storm  (P) o f  governs  in  the  Gulf  pressure f i e l d  (P)  constant gradient.  the  free  of  is  Mexico.  In  this  wind  model  s u p e r i m p o s e d on a l a r g e  The c o m b i n e d s u r f a c e  atmosphere  a l . (1975)  field  from  the  was  an  axially  scale  pressure  pressure  which  that  distribution  surface  wind  is  determined. The a x i a l l y  symmetric  as a f u n c t i o n P = P where P  is  Q  radius  + AP e ~  Q  the  Ap i s R  of  the  is  pressure b e t w e e n r-*=°  s c a l e parameter  such that  P was a s s u m e d e q u a l  those  ±  where I P  by  the  isobars is  = INT((AP-l)/4), = 4i  ±  + P  T h i s mapping of surface  field  actual  that  the  in  i  the eye of  Q  i  the  In  this  and R were s p e c i f i e d f o r  Q  Q  4 mb i s o b a r  increment,  of  (4.1)  then  the  as (4.2)  those isobars  are (4.3)  is  equivalent  p r e p a r e d by A E S .  of  will  for  will  chart P.  The  is  to  the  format  of  F i g . 4.3a i l l u s t r a t e s Ap=60 m b ,  proportional  maximum v e l o c i t y pressure  a  P .  5 mb i n c r e m e n t s  The r e s u l t  a storm.  = 1,1  pressure f i e l d  observations  determined  Q  = 1,1  c o n c e n t r a t e d near the c e n t r e of periphery.  P )  how P , Ap a n d R a r e  and t h e p r e s s u r e v a l u e s o f  for  Q  hand-drawn  available  P -  = R  the p a s s a g e of  AES s t a n d a r d  Since wind speed i s i n v e r s e l y provides  r  = 0 (i.e.  e x p r e s s e d by r e a r r a n g e m e n t for  pressure chart  pressure  at  1015 mb, and P  Q  = -R/ln(4i/AP)  v  to  l o c a t i o n , X , of  represented  r a d i u s of  and r  + 0.37AP  Q  given geographical AP i s  as (4.1)  from s u r f a c e p r e s s u r e measurements d u r i n g  If  isobars P  R / r  Hurricane Camille i l l u s t r a t e s  application,  d e f i n e d by t h e s e t o f  from the storm c e n t r e  pressure gradient  P = P for  r  central  is a radial  F i g . 4.2  storm pressure f i e l d  P =955 Q  mb,  a a  and  standard synthetic  R=479  km.  to d P / d r , e v a l u a t i n g d P / d r  be f o u n d a t shown i n  idealized  R/2.  F i g . 4.3b, pressure  For comparison, b a s e d on t h e contours  are  t h e s y s t e m and much more d i s p e r s e d n e a r  be somewhat s t r o n g e r w i n d s  the s t o r m and a b r o a d s u r r o u n d i n g a r e a of  in a small  region  v e r y weak w i n d s .  =0 an few  more its near  Neither  -  43 -  I O I C  -  S rOA. - * *  1000  A V -  3I—  ^  X AO BILOXI G U L F PORT NEW ORLEANS ( N A S ) N E W O R L E A N S ( WSO) B A Y ST. LOUIS  x  930  O • A O  /o  980  •  MINIMA  ALONG  DELTA  o/ Ap« 105 R = 10  /  970  / / .  .o 9 6 0 6  / / /  ui  3 cc o.  950  CAMILL.E  PRESSURE  HISTORICAL  r i  / *  9'10  lOVlSIA  930  "  PROFILE  DATA  usisstrri  • 7 I  MA  . - — TRANS WORLD _3URWOt5ETr£\«j R i o JO 2  920  OOG? STATIONS  \ 910  SCi.t  soo O  20  40  60  N.MI.  80 D I S T A N C E  Fig.  4.2  100  V CAMIUF STO«M TRACK  120  140  160  ISO  ( n- m i . )  S u r f a c e p r e s s u r e as a f u n c t i o n of d i s t a n c e c a l c u l a t e d f r o m m e a s u r e m e n t s made d u r i n g t h e p a s s a g e o f H u r r i c a n e C a m i l l e . (From Cardone et a l . , 1975).  -  At  86010:1  lit arm  P<i> P<i) P(i) P(:L) P(i) P<i) P<i) P<:i) P<i)  Fig.  00  44  -  hours  c e n t r e d at 50.00 degrees N 145.00 degrees W Central Pressure = 9 5 5 . mb Mean G e o s t r o p h i c P r e s s u r e 1 0 1 5 . mb P r e s s u r e D i f f e r e n c e -• 6 0 . mb Radial Scale = 4 7 9 . 4 6 km  = = = = ~  =  960. 965. 970. 975. 980. 985. 990. 995. 1000.  4.3  mb mb mb mb mb mb mb mb mb  R(i) = 193. R(i) = 268. RCi) = 346. R(.i) = 436. R(i) = 548. R(:L) = 692. R(i) = 890. R ( i ) = 1182. R ( i ) = 1667.  km km km km km km km km km  An i d e a l i z e d p r e s s u r e f i e l d f o r a m o d e r a t e l y i n t e n s e s t o r m (upper p a n e l ) and an a c t u a l s u r f a c e p r e s s u r e c h a r t ( b o t t o m p a n e l ) , b o t h a t a p p r o x i m a t e l y t h e same s c a l e f o r t h e same l o w p r e s s u r e s y s t e m .  -  of  these differences  model  for  should  45  -  restrict  i d e a l i z e d wind f i e l d  the u s e f u l n e s s of  l o c a t e d on the  central  is  and  A  is  Q  the  longitudes  longitude  (or  great  d defined  in  <> f  relative  are negative).  orthodrome length  where  X Q C ^ Q . ^ Q )  the  to  earth's  latitude  the  surface  relative  Greenwich  arc)  from X  to  Q  to  field  an a r b i t r a r y  with  the  meridian  Assuming the e a r t h i s a p e r f e c t  circle  pressure  generation.  The s t o r m p r e s s u r e map i n F i g . 4 . 3 a i s p r e s s u r e at  the  the  equator  (hence  west  sphere, then  point  X.2^2'^2^  n  the a  (4.4)  cos  o  earth's  The p r o b l e m , g i v e n X the azimuth (the from the  0  radius  ( 6 3 7 1 km) a n d A X =  and d=r^,  Q  is  A ) must  also  ^2~\)*  to determine  angular d e f l e c t i o n  meridian  a of  the  X2.  For a unique  orthodrome  latitude <j>2  be i m p o s e d . is (4.5)  cosines for  of  X  the  = A  law of  Q  may t h e n be i n v o k e d t o s p e c i f y  the  as  2  -  longitude  2  a spherical triangle  s i n ' ' ' [cos6sin<{>  =  Applying  A  clockwise  = d a  The l a w o f  the  solution,  measured  W i t h r e f e r e n c e t o F i g . 4 . 4 , t h e a n g l e S s u b t e n d e d by t h e a r c d 6  a  F i g . 4.4 a s  d = a c o s * [sincf> sin4>2 + cos<)> cos<}>2 AX] where a i s the  s  0  sines  + sin0cos<J> cosa]  (4.6)  o  to  the  azimuth  angle a yields  the  specification  of  o f X2 a s +  s i n.-1 r .s i n a s i n G  (4.7)  COS<f>n  In  other  in  latitude-longitude  In  this  into  words,  an i s o b a r  application,  2M e l e m e n t s  e x c e e d a minimum  A ,  a was  varied  additional  points  points  were  chosen to  the  from  required  the  Act t o  arc  MAa  length  radians  a =0  define  correspond roughly  C of  to  r^  the  and  rate  of  Q  may be  azimuth  isobaric  of  cx =TT.  of  At  the  contour  In  digitization  was  divided  points the  a l l  same t i m e ,  contour.  discretized  a n g l e ct.  symmetry about  w h e r e A a = Tr/M.  each i s o b a r i c the  from X  between d i s c r e t i z a t i o n  Taking advantage  added at to  distance  as a f u n c t i o n  circumference  length.  were  radial  coordinates  such that  not 0  at  meridian  cases at  two  least  These numbers of  could  12  were  a s t a n d a r d AES  -  Fig.  4.4  46  -  Parameters d e f i n i n g d i s t a n c e between a r b i t r a r y p o i n t s a s p h e r e . (From P e a r s o n , 1984).  on  -  surface  pressure  The t r a j e c t o r y longitude  of  the  -  chart. X  was d e f i n e d  Q  positions.  segment o f  47  as a f u n c t i o n  The s p e e d o f  of  translation  path as v=d/At u s i n g  (4.4)  to  time  is  at  discrete  readily  calculate  latitude-  calculated  for  any  d.  4.2.2 Gradient and Surface Wind F i e l d s The g r a d i e n t  wind  field,  a l s o known as the  c a l c u l a t e d from the g r a d i e n t of  the  computation  is  of  a force  the  surface  force  t e r m due t o c u r v a t u r e  assumed  be a t  500 m e l e v a t i o n ,  boundary  boundary  wind  layer  is  Centre  method d e t e r m i n e s temperatures, elevation  reference  isobars.  above  the  influence  u* as a f u n c t i o n  on  air is  column  in  of  The  of  is  basis  C o r i o l i s and a  This gradient  surface  the  the  the  the  wind  is  atmospheric  each f u l l  to  (1985)  In  this  wind,  length.  drawn  profiles,  is  imposed.  in  the  standard  50 k n o t s .  means 60 k n o t s  from  the  specific  the  form  vector.  Thus,  of  near-surface  T h i s wind  Isobars  is a shorthand for  the west  a  field  grid  F i g . 4.5 shows an e x a m p l e  10 k n o t s ,  from  and s e a  latitude-longitude  represents  the  the  the  air  Wind at  application  stability  means 25 k n o t s  Canadian  upper  roughness  the head of  at. t h e  gradient  using empirical  feather  z using a  S e c t i o n 2.3.3,  c o r r e s p o n d i n g U^Q f i e l d . are  elevation  As d i s c u s s e d i n  wave m o d e l .  vectors  feathers  Delage  c a l c u l a t e d on a l ° x l °  domain of  which  near-surface  of  the  stability.  5 k n o t s and the " v " f e a t h e r from  work  z=10 m a n d n e u t r a l  mb s p a c i n g a n d t h e w i n d convention  the  and Yamada ( 1 9 7 6 ) .  s u r f a c e p r e s s u r e map and t h e  4.3  the  then c a l c u l a t e d from u*  level  encompasses  wind i s  distribution.  of  an a r b i t r a r y  b a s e d on  d e n o t e d by U^Q i s  which i s  to  and a n e m p i r i c a l  z is  depend  reduced  model  Meteorological  is  pressure  field,  layer.  The g r a d i e n t  which  atmosphere wind  b a l a n c e among p r e s s u r e g r a d i e n t ,  centrifugal to  free  that of  a  a r e drawn a t  1  meteorological each h a l f  feather  D i r e c t i o n of for  the  example,  and  east.  Wave Model and Grid Setup  The s t u d y on the  area for  north,  discretization  modelling  b y 160°W o n t h e is  in  west  1° l a t i t u d e  which  is  37 b y 22 e l e m e n t s .  F(f,0)  is  determined  on a p o l a r  purposes i s  at  stereographic  At  each model projection  b o u n d e d by 39°N o n t h e s o u t h , b y  and by  124°W o n t h e  and 1° l o n g i t u d e each of time of  these  step.  east.  spatial  increments g i v i n g a  points  the  The m a p p i n g o f  the northeast  The  Pacific  energy  grid  spectrum  the model Ocean i s  60°N  domain  shown  in  F i g . 4.5  A t y p i c a l i d e a l i z e d p r e s s u r e f i e l d (upper p a n e l ) and i t s c o r r e s p o n d i n g s u r f a c e wind (U^Q) f i e l d (lower p a n e l ) .  -  Fig.  4.6.  The r e s o l u t i o n  be s u i t a b l e  for  of  hindcasting  Because the m a j o r i t y of c a l c u l a t i o n of  although  hindcast  modelling  values  is  of  the  for  Modelling require  in  wave c l i m a t e  effects  typical  very  have  mesh,  finer  resolution  Af=0.0113  Hz a n d f  the s h e l f  shallow  water  =0.2  U s i n g l i n e a r wave t h e o r y wave of  33 s w i l l  smallest  grid  or  at  computational result,  a convenient  Time-series points  designated  location of  output  in  in  locations  of  the  is  in  F i g . 4.6:  points  (including  of  on a  spectral boundary  the  coast.  complex bathymetry  such that f i  at  =  m  n  may  F r e q u e n c y was  0.030  about  c  of  57  km,  four  E(f)  gT/47T o r the  scheme i s  1800 s ( 0 . 5 h )  the  Hz ( T = 3 2 . 8  26 m / s .  the  each running  off  Since  the  step  for  time  57x10/26=2192  and F ( f , 6 ) was o b t a i n e d a t  along  period  s.  As a  was s e l e c t e d .  coast  S o u n d m a r k e d by a s t a r  hourly  longest  maximum  southwest  (including  symbol),  11 s p e c i a l  one w a v e  buoy  two p a r a l l e l  rows  from the c e n t r a l  a U.S.A. deep o c e a n m e t e o r o l o g i c a l  obtained  along  16 a n g l e s (A8=2TT/ 1 6 = 2 2 . 5 ° ) .  and a s e c o n d d e e p o c e a n d a t a b u o y s i t e time-series,  accurate  configuration  calculation  regions  propagation  H , T , 6, s p  Queen C h a r l o t t e  three a d d i t i o n a l  for  b r e a k become the i n p u t  water  velocity  time step of of  included  and deep w a t e r a p p r o x i m a t i o n s ,  length  stability  be  Hz (T=5.0 s ) .  have a group  element  to  grid.  was f i x e d  m o  i n s h a l l o w water have been  The d e e p w a t e r  p a r a m e t e r i z e d i n 16 e q u a l f r e q u e n c y c l a s s e s s),  optional  s t e p i n c o a s t a l wave m o d e l l i n g ;  the edge of  not  coast.  a r e i n deep w a t e r ,  effects  would  first  shallow  yet  n e c e s s a r i l y c o a r s e and w o u l d near the  nearshore s e a - s t a t e s .  a finer  a third,  Directional  coastline is  the c a l c u l a t i o n p o i n t s  these  c a l c u l a t e d at  conditions  of  -  s h o a l i n g and r e f r a c t i v e  omitted,  coarse grid  the  49  d a t a buoy  coastal station),  the Washington-Oregon coast.  intervals,  provide  the  first  These  level  of  comparisons between the v a r i o u s case s t u d i e s . H o u r l y o u t p u t of the e n t i r e f i e l d of H T a n d 0 w a s a l s o made f r o m w h i c h c o n t o u r e d maps o f H „ w e r e s p s constructed  to  state.  compare  To  contoured  to  significantly  illustrate  the  between  highlight different.  overall certain  regions  development input  where  the  and e v o l u t i o n  scenarios, sea-state  fields  of of  the AH  sea-  g  were  development  was  special  - 51 -  4.4  Pressure Parameter S p e c i f i c a t i o n  Recently,  L e w i s and M o r a n ( 1 9 8 5 )  northeast  Pacific  Ocean.  realistic  mean o r  median  prepared a catalogue  From t h i s  document,  and e x t r e m e  it  values  evolution.  classes  frontal  as  were c o n s i d e r e d : the  defined  Both  southwest  the  s e v e r e storms  in  possible  derive  occurred  between  October  somewhat more common w i t h 21 e v e n t s generated  concurrent  pressure  between  l o w and the  by  these  storms  in  and M a r c h ,  the  southwest  Many of the  the storm c e n t r e s  4 0 ° a n d 45°N p a r a l l e l s as  indicated  Charlotte  sketched  by  the  Islands  A l a s k a they u s u a l l y There were  are  but  reportedly  as  the  of  offshore  less,  the  forcing  be  quite  c a n be  of  very  the  frequently,  derived.  21  west 145°W,  intensification,  offshore  27 y e a r s  of  enter  the  the  studied  Queen  Gulf  by L e w i s  t r a j e c t o r y to the  are g e n e r a l l y  less  severe  of  ship-reported  and  frontal in  c a u s e 20 m w a v e s .  storm t y p e , but  terms  One s h i p  wave  heights  be a c o n c e r n t o C a n a d a ' s w e s t  Fortunately,  climate  important  Ship  these  north along  storm  with  from the  they are g e n e r a l l y  t h a t s e r i o u s damage a l o n g t h e c o a s t d o e s n o t o c c u r . wave  m  large.  industries.  design purposes, e s p e c i a l l y for  istics  in  These storms  this  the  1983.  10 m.  five  is  rapidly.  a l t h o u g h one d i d r e p o r t e d l y  nearshore  will  recorded  low  low  25  are 8 to  storms  these have a s i m i l a r  to  to  is  As t h e  t h e s e a r e s e v e r e s t o r m s w h i c h must  s h i p p i n g and f i s h i n g far  pressure,  storms  as  consistently  The g r e a t e s t  and 55°N.  low  time were not e s p e c i a l l y  Clearly  fairly  4.7a.  central  cold  s i n k i n g has been a t t r i b u t e d the  track  begin to d i s s i p a t e q u i t e  F i g . 4.7b.  of wave g e n e r a t i o n ,  at  cold  frontal  great  reports  and t u r n s h a r p l y  Fig.  between 50°  About h a l f  a s shown i n  in  lowest  14 s o u t h w e s t  Moran (1985). lows  storm  27 y e a r d a t a b a s e f r o m 1957 t o  1 6 . 5 ra s w e l l , a l t h o u g h m o r e t y p i c a l  approximately, as  parameters  Two m e t e o r o l o g i c a l  s i n k i n g o r s e v e r e damage i s known t o h a v e h a p p e n e d d u r i n g storms.  to  the  by L e w i s and M o r a n .  usually  Waves  was  for  g o v e r n i n g the s u r f a c e p r e s s u r e f i e l d  of  resulting  in  from  such  a comprehensive  the exposed o u t e r  reasonable  statistics  strong  sea-state coast. of  their  coast  sufficiently Neverthe-  meteorological description  for  Because they  are  major  character-  - 52 -  4.7  The s t o r m t r a j e c t o r i e s o f ( a ) s o u t h w e s t f r o n t a l l o w s a n d (b) s o u t h w e s t c o l d l o w s . ( A d a p t e d from L e w i s and M o r a n , 1985).  - 53 4.4.1  Trajectory  These s t o r m s were i d e a l i z e d i n terras of 4.8:  a spin-up  where  the  leg  trajectory  n o r t h to the  turns  western model  north  (B),  the  edge o f  central  the  model  segments i l l u s t r a t e d  boundary  a storm  l o c a t i o n o f minimum c e n t r a l  leg over which northern  between the  three  (point  in Fig.  A) and t h e  intensification  leg  point  proceeding  l o w p r e s s u r e ( C ) , and a s t o r m  filling  p r e s s u r e i n c r e a s e s as the s t o r m a p p r o a c h e s domain (D).  The mean t r a j e c t o r y  path  was  the  imposed  f r o m t h e w e s t a l o n g 4 2 ° N ( A t o B ) a n d t h e n c e n o r t h a l o n g 145°W (B t o C t o D ) . V a r i a t i o n s w i t h i n +5° of  the  145°W l o n g i t u d e  are a l s o  realistic.  4.4.2 C e n t r a l P r e s s u r e The a v e r a g e minimum c e n t r a l cold  lows  sketched i n  r e c o r d of this  l o w p r e s s u r e b a s e d o n t h e 21 s o u t h w e s t f r o n t a l  F i g . 4.7 i s  944 mb and t h e  largest  l o w p r e s s u r e was i m p o s e d a t  958 mb f o r value  of  data  ranging  970 mb.  5 3 ° N 145°W,  between the  and  minimum  The m e d i a n p o s i t i o n (C)  due w e s t  of  the  Queen  of  Charlotte  Islands. At  the w e s t e r n  data ranging  edge (A),  t h e mean p r e s s u r e of  b e t w e e n 954 and  1 0 1 0 mb.  At  t h e 21 s t o r m s w a s 9 8 4 mb  the  northern  edge (D),  from  the  mean  c e n t r a l p r e s s u r e w a s 9 7 0 mb w i t h a m i n i m u m o f 9 5 2 mb a n d a m a x i m u m o f 9 8 2 mb. The v a l u e s a t p o i n t  B a r e more d i f f i c u l t  ( F i g . 4.7) v a r y g r e a t l y  in this  area.  Instead,  b e t w e e n A and C was u s e d t o e s t i m a t e rate  of  deepening  approximately storm 4.4.3  of  -0.6  the  was  Ap /At Q  P = 9 6 9 mb a t Q  B.  The  typical  Q  average  determined  B for  P  to  be  rates  of  translation. Storm Speed  There are  two a s p e c t s t o s t o r m s p e e d :  centre AX /At  through  Q  development  (or  the  segments  deepening) of  the  The f i n a l  system w i l l  from the coast.  order  of  latitude During  of  42°N.  highest  about  the  the e a r l y  typical  averaging  study  translation area  and  pressure system Ap /At. Q  stage of  in  this  area for  35 t o 40 k m / h w h i c h i s  study area, The  the  of  development  of  the  the  storm  rate  of  The s p e e d w i t h  ( l e g A - B , B-C o r  C-  s t a g e u s u a l l y h a s t h e s l o w e s t movement and o c c a s i o n a l l y a s t o r m  become s t a t i o n a r y  a r e on t h e  the rate of  low  w h i c h the s t o r m moves depends on i t s D).  pressure  implies  trajectories  t h e mean r a t e of c h a n g e of  a r e a s o n a b l e v a l u e at  central  mb/h w h i c h  to s p e c i f y s i n c e the  Queen C h a r l o t t e storm formation  up t o 24 h o u r s .  the e q u i v a l e n t Islands  to  the  of  Average speeds 18 h o u r s  southern  to  Alaskan  i n the s o u t h w e s t e r n r e g i o n of  s p e e d s a r e 4 5 t o 55 k m / h b e t w e e n 160°W a n d 145°W velocities  70 k m / h .  occur  move  during  These speeds cannot  the  intensification  be c a l c u l a t e d  very  the  along stage,  accurately  - 54 -  4.8  The t h r e e s e g m e n t s of b a s e d on t h e s o u t h w e s t cold lows.  an i d e a l i z e d s t o r m t r a j e c t o r y f r o n t a l lows and the s o u t h w e s t  -  from the 1 2 - h o u r l y c e n t r a l development The  of  average  -  p r e s s u r e p o s i t i o n s , but  the i d e a l i z e d wind f i e l d rate  Occasionally, period,  55  in  of  8 of  and t h i s  central  situation  pressure system.  is  this  known  Since the winds  deepening  severe  affecting  events  containing  rab/h.  During  by r e p o r t s  a period  one o f  of  of  these  AP /At  as " e x p l o s i v e  or  -0.6  d e e p e n i n g " of  rab/h.  outer  coastal  location. the  low  sea-state  be among For  average  - 3 . 3 mb/h i n t e n s i f i c a t i o n  10 m l o c a l w i n d w a v e s a n d 12.5 m s w e l l  the  a very high  these storms w i l l  e x p l o s i v e deepening,  storms  is  Q  s t r e n g t h e n so q u i c k l y ,  an o f f s h o r e  the  r a t e e x c e e d s . - 1 m b / h o v e r a 12 h o u r  c a n d e v e l o p w i t h o u t m u c h w a r n i n g a n d many o f most  for  time-series.  pressure  t h e 21 s t o r m s ,  t h e y do s u f f i c e  the  rate  the  eight  was  occurred  -1.8  followed  waves.  4.4.4 Radial Scaling Parameter Of  all  the storm c h a r a c t e r i s t i c s ,  subjectively storms. (1985)  d e t e r m i n e d due t o  From i n s p e c t i o n o f and  the  evolution  the  radial  limitations  the f u l l y in  was d e t e r m i n e d  time  in  the  available  and  i s more o r l e s s c o n s t a n t f r o m t h e c e n t r e  km),  while  a g i v e n system.  this  radial  the other  dimension r^gg  selected for  s i n c e by  substitution  in  to  for  the  21  latitude. (4.1)  to  low  pressure  these  pressure  t h e 9 9 0 mb i s o b a r  over  d e v e l o p e d p r e s s u r e maps,  was a b o u t  d a t a maps w h i c h w e r e o f  other  d i m e n s i o n of  F o r t h e 21 f u l l y  r<jgg c o u l d be a s s m a l l a s 3 o r 4 ° o f was  physical  a few  patterns  the a v e r a g e of  the  space of  it  of  data  most  d e v e l o p e d s t o r m maps i n L e w i s a n d M o r a n  systems,  the time h i s t o r y  that  s c a l i n g p a r a m e t e r R was t h e  8 ° of  latitude  very i n t e n s e storms A compromise of  determine  R for  6° of  (or  890  suggested latitude  each s p e c i f i c P  Q  rearrangement  R = -r  9  9  Q  In  990 - P  (4.8)  c  AP~ In essence then, because the throughout  radial  a s t o r m as a f u n c t i o n  o n l y be t e s t e d i n d i r e c t l y  through  of  dimension r^gg  P . Q  As a r e s u l t ,  adjustment  of  rg Q. Q  w  a  s  specified, R varies  the s e n s i t i v i t y  to R can  -  4.5  56  -  Summary of Model Test Cases  4.5.1 Storm 1: The Median Base Scenario A b a s e l i n e s t o r m was c o n s t r u c t e d cases.  It  was c o m p o s e d o f  turning  north along  145°W w i t h  p o i n t A , 9 6 9 mb a t p o i n t mb a t  point  D.  of  the other  representative  (1985).  average P  of  Table 4.1  of  compare most o t h e r from  point  the west of  along  test 42°N  9 8 4 mb i m p o s e d  at  C ( 5 3 ° N 145°W) a n d 9 7 0  o f d e e p e n i n g A P / A t = - 0 . 6 m b / h was s e l e c t e d Q  filling  with  21 s t o r m s  AP /At=+0.7 Q  trajectory  v a r i a b l e s are  the  to  values  Q  9 5 8 mb a t  storm advance a l o n g the  parameter a f t e r are  the  Q  rate  which  median t r a j e c t o r y  B, P ( m i n ) of  The a v e r a g e r a t e  f o l l o w e d by a t y p i c a l The r a t e  the  against  imposed.  that  summarizes the storm  were  path  mb/h. is  not  an  The r e s u l t i n g  independent speeds A X / A t Q  a n a l y z e d from Lewis  and  Moran  parameters.  Table 4.1 Storm 1 Scenario Parameters  Point  Leg  A A-B B B-C C C-D D  Latitude Longitude 42°N 160°W 42°N 145°W 53°N 145°W 59°N 145°W  Length (km)  Time YYMMDDHH  Duration (h)  AX /At (km/h) Q  24  52  18  -0.6 958  18 86010312  Q  -0.6  68  86010218 667  AP /At (mb/h)  969  86010200 1223  P  984  86010100 1238  o (mb)  37  +0.7 970  - 57 4.5.2 Storm 2; Explosive Deepening The c e n t r a l 2,  but  AP /At Q  preceding mb/h.  pressures  storm  was a d j u s t e d  1 at  along Q  in  the p r e s s u r e  average  S e c t i o n 4.4.3.  points legs  the a c h i e v i n g of P ( m i n )  T h i s was t h e  discussed  of  C and D were unchanged i n  A - B and B-C so t h a t  at p o i n t C the  explosive Table  A,  4.2  deepening  contains  in  the  storm  12  hours  r a t e o f d e e p e n i n g was rate  the  in  the  complete  8 case  -1.8  storms  specification  of  parameters.  Table 4.2 Storm 2 Scenario Parameters  Point  Leg  A-B  B-C  C-D  Latitude Longitude 42°N 160°W 42°N 145°W 53°N 145°W 59°N 145°W  Length (km)  Time YYMMDDHH  Duration (h)  AX /At (km/h) Q  24  52  86020200 1223  -0.2  68  86020218  958 18  86020312  Q  980 18  667  AP /At (mb/h)  984  86020100 1238  o (mb) P  37  -1.2 -1.8 +0.7  970  (avg.) (max.)  -  -  S t o r m 3: E a s t e r l y S h i f t e d N o r t h w a r d  4.5.3 As  58  illustrated  in F i g . 4.7,  Trajectory  the B-C-D p o r t i o n  e a s i l y be 5 ° c l o s e r t o t h e B . C . c o a s t l i n e . the  effect  of  this  eastward  translation  the  resulting  the  storm trajectory  S t o r m 3 was u s e d t o by  pressure parameters  140°W i n s t o r m 3 .  and c o n f i r m s  that Q  Table  B and  the  Table  4.3  the o n l y  c o n s e q u e n t i a l v a r i a t i o n from storm 1 i s a s m a l l i n c r e a s e i n Ax /At  can  investigate  simply moving point  s u b s e q u e n t s t o r m p a t h f r o m 145°W i n s t o r m 1 t o summarizes  of  in  other  leg A-B.  4.3  Storm 3 Scenario Parameters  Point  Leg  A A-B B B-C C C-D D  Latitude Longitude 42°N 160°W 42°N 140°W 53°N 140°W 59°N 140°W  Length (km)  Time YYMMDDHH  Duration (h)  AX /At (km/h) Q  86030100 1649  69  86030200  Q  -0.6  68  86030218  -0.6 958  18 86030312  AP /At (mb/h)  969 18  667  Q  984 24  1223  P (mb)  37  +0.7 970  - 59 -  4 . 5 . 4 Storm 4 : Increased Radial Extent Storm  4 has  t h e same t r a j e c t o r y ,  central  t r a n s l a t i o n as storm 1, but the r a d i a l of l a t i t u d e . hence  extent was  radius  speeds.  of the 990 mb  As d i s c u s s e d  isobar  repeated  and  speed of  i n c r e a s e d from r g Q = 6 ° to 8° Q  from T a b l e 4.1 i n T a b l e  i n Section  i n the 21 f u l l y  from Lewis and Moran (1985) that were s t u d i e d . are  history  The e f f e c t of t h i s change i s , on a v e r a g e , t o r e d u c e Ap/Ar and  r e d u c e t h e wind  average  pressure  4.4.4, 8° was  the  d e v e l o p e d p r e s s u r e maps  The storm s c e n a r i o parameters  4.4.  Table 4 . 4 Storm 4 Scenario Parameters  Point  Leg  A A-B B B-C C C-D D  Latitude Longitude 42°N 160°W 42°N 145°W 53°N 145°W 59°N 145°W  Length (km)  Time YYMMDDHH  Duration (h)  ^ ^ (km/h) 1  0  86040100 1238  52  86040200  Q  -0.6  68  86040218  -0.6 958  18 86040312  AP /At (mb/h)  969 18  667  0  (mb) 984  24  1223  p  37  +0.7 970  - 60 -  4.5.5 Storm 5: Advection Rate ( S t a l l e d Weather System In the Gulf of Alaska) Storm 5 i s i d e n t i c a l  to storm 1 u n t i l  p o i n t C i n the t r a j e c t o r y . constant  At t h i s  i n c h a r a c t e r and s t a t i o n a r y  the same manner as storm 1.  Table  day 03 h o u r 00 w h i c h i s 6 h o u r s p a s t  point  (55°N  145°W) the system remains  f o r 24 hours. 4.5 d e s c r i b e s  I t then proceeds n o r t h i n  the c h a r a c t e r i s t i c s  of t h i s  storm.  Table  4.5  Storm 5 Scenario Parameters  Point  Leg  A A-B B B-C C  Latitude Longitude 42°N 160°W 42°N 145°W  stall  Time YYMMDDHH  1238  0  1223  86050412  Q  -0.6  68  86050218  445  AP /At (mb/h)  969 18  86050300 86050400  (mb)  52  86050200  55°N 145°W  59°N 145°W  p  (km/h)  984 24  222  stall-D  Duration (h)  86050100  53°N 145°W C-stall  D  Length (km)  -0.6 958  6  37  24  0  12  37  +0.7 962  0.0 +0.7  970  -  this  (53°N  s c e n a r i o t h e minimum c e n t r a l 145°W)  illustrated and t h e at  -  S t o r m 6: D e e p e s t C e n t r a l Low  4.5.6 In  61  rate  points  was  set  to  the  pressure imposed at  minimum  recorded  i n F i g . 4.7 w h i c h was 944 mb. of  filling  a l o n g l e g C-D were a d j u s t e d  B and D n e a r l y  mb/h.  a very  The c h a r a c t e r  intense  described  equal  to  of  this  storms  deepening along  l e g B-C  to  t h o s e i n s t o r m 1.  storm  is,  rate  therefore,  low pressure system f o l l o w e d  by T a b l e  of  by  same p o i n t C the  Q  The r a t e  d e e p e n i n g was - 1 . 3 m b / h b e t w e e n B and C and t h e +1.4  P (min)  the  very  among  keep the  values  The r e s u l t i n g of  of  P  Q  rate  of  doubled  to  development  of  rapid dissipation  as  f i l l i n g  a rapid  4.6.  Table  4.6  Storm 6 S c e n a r i o Parameters  Point  Leg  Latitude Longitude 42°N 160°W  A  A-B B B-C C C-D D  Length (km)  Time YYMMDDHH  53°N 145°W 59°N 145°W  52  86060200  -0.7  68  86060218  -1.3 944  18 86060312  Q  968 18  667  AP /At (mb/h)  984 24  1223  P (mb) Q  (km/h)  86060100 1238  42°N 145°W  Duration (h)  37  +1.4 970  -  4.5.7  62  -  Storm 7: Highest Minimum Central Pressure  I n s t o r m 7 t h e minimum c e n t r a l  p r e s s u r e d e e p e n s o n l y a s f a r a s 9 7 4 mb.  This  w a s t h e h i g h e s t v a l u e a m o n g t h e 21 s t o r m s i l l u s t r a t e d  i n F i g . 4.7. However,  the prototype  creating storm  s t o r m s y s t e m was s t i l l  responsible for  force  w i n d s w h i c h a r e d e f i n e d by L e w i s a n d M o r a n ( 1 9 8 5 ) a s a w i n d s p e e d e x c e e d i n g 48 knots  (i.e.  Beaufort  system d i d not mb/h  to  details  the of  scale  10 o r  deepen at a l l  9 7 4 mb m i n i m u m  this  in at  greater).  In  the  l e g A - B and t h e n P point  scenario are l i s t e d  in  Table  C and  did  Table  4.7.  Q  not  idealized  scheme,  d e c r e a s e d by a b o u t f i l l  in  leg  C-D.  the -0.6 The  4.7  Storm 7 Scenario Parameters  Point  Leg  A  Latitude Longitude 42°N 160°W  A-B B B-C C C-D D  Length (km)  Time YYMMDDHH  53°N 145°W 59°N 145°W  AX (km/h) / A t  0  86070100 1238  42°N 145°W  Duration (h)  52  86070200  Q  0.0  68  86070218  -0.6 974  18 86070312  AP /At (mb/h)  984 18  667  P  984 24  1223  o (mb)  37  0.0 974  - 63 -  4.5.8 Storm 8: I d e a l i z a t i o n of the February 5-7, 1960 Storm The  storm of  February 5-7,  1960 i s  the  one I n w h i c h P ( m i n )  reached the  Q  lowest  r e c o r d e d v a l u e o f 9 4 4 mb a m o n g t h e 21 s t o r m s e x t r a c t e d f r o m L e w i s a n d M o r a n (1985).  It  constitutes  quite  a s e v e r e storm, e s p e c i a l l y s i n c e the  p r e s s u r e was r e a c h e d v e r y e a r l y s y s t e m on F e b r u a r y of X  Q  and P  same terras  at  Q  6 at  12Z and t h e  i n F i g . 4.10.  idealized  throughout One  other  its  trajectory.  history  trajectory  pressure  its  central  of  at  this  system is  fairly  difference  between s t o r m 8 and the  change i s  only  2 0 mb o f  other  deepening i n  the  is  other hand, P (min) Q  1 d e e p e n s by 26 mb b u t  t o be a t 3 ° of  followed  fills  storm 8 i s  t h e same t i m e  latitude  at  point  24 h a s  The r a t e  test  deepened at the w e s t e r n edge of  of  a  0  steady  already significantly  duration  P (rain) at  the  of  the  advance  about  50  km/h  h i s t o r y as seen i n T a b l e 4.8.  maximum p r e s s u r e  The  terras  presented in  low v a l u e f o r  s t o r m 1 (and 6).  weather  pressure in  v e r s i o n reaches i t s  B and r e m a i n s c o n s t a n t  low  of  F i g . 4.9 shows t h e  The i d e a l i z e d s t o r m i s  The s y n t h e t i c  storm p r o g r e s s e s a l o n g the the  the  12 h o u r I n t e r v a l s .  6 hours west of p o i n t  of  in  minimum  further  in  by 20 mb o f  by o n l y 6 hours  filling.  is  that  the  storm 8 since i t  is  the study domain.  On  By c o m p a r i s o n ,  storm  12 mb.  longer  than storm  1 and p o i n t  t h e two s t o r m s ( d a y 02 h o u r  south i n storm  cases  18) b u t  it  C is is  defined  positioned  8.  Table 4.8 Storm 8 Scenario Parameters  Point  Leg  Latitude Longitude  Length (km)  42°N 160°W 0  42°N 149°W  0  0  B-C  C-D  42°N 145°W 50°N 145°W 59°N 145°W  A  / (km/h) x  A  0  A  / (rab/h) p  A  t  0  -l.Havg.) -1./(max.)  0.0  55  944  86080200 18  49  0.0  944  86080218 24 86080318  P  944 6  1001  o (mb)  50  86080118  890  t  964 18  331  P (min)-B  Duration (h)  86080100 908  A-P (min) P (min)  Time YYMMDDHH  42  +0.8  964  - 64 -  12Z 6th February 1960 (+6)  IM'  .  4.9  N  1»t'  Hi*  U»*  T h e s u r f a c e p r e s s u r e c h a r t f o r F e b r u a r y 6 , 1 9 6 0 a t 12Z at t h e peak of the s t o r m (upper p a n e l ) and the s t o r m trajectory (lower panel) with 12-hourly central pressures (kPa). (From L e w i s a n d M o r a n , 1 9 8 5 ) .  -  65  -  Storm 8  Fig.  4.10  I d e a l i z a t i o n of t h e s u r f a c e p r e s s u r e c h a r t c o r r e s p o n d i n g t o F e b r u a r y 6 , 1 9 6 0 a t 12Z ( u p p e r p a n e l ) a n d t h e s t o r m t r a j e c t o r y ( l o w e r p a n e l ) a t r o u g h l y t h e same s c a l e s a s the a c t u a l storm data i n F i g . 4 . 9 .  - 66 -  5.0  D I S C U S S I O N OF S E N S I T I V I T Y A N A L Y S I S RESULTS  5.1  The B a s e S c e n a r i o  Storm 1 i s  t h e b a s e s c e n a r i o a g a i n s t w h i c h most o t h e r  characteristics conditions event  for  are  its  knots  as  m are present 12.  are  A l o n g the west a result, gradient  the  fields  later  is  g  about  coast of  (H  shows  the  s Sound.  At  will  not  with unrestricted increase  corresponding generation  B of  the peak of  the  time-series  of  the storm t r a j e c t o r y )  centred at  point  the end of  D).  the  the  to the end  of  Sea-states exceeding 9 s e q u e n c e on d a y 03  00 w h i c h i s  hour  6 h after  the  region  o v e r a 24 h o u r  of  g  at  the  site  in  the  on  on t h e  day  H  g  is  03  at  due  to  southeastern  the c o r r e c t  1.0 m t o  entrance  to  about  nomogram i n  swell  propagating  s i d e of  This  h i n d c a s t i n g of  hours  the  finding  in  storm  Queen  wind  speed  Under such  light  U.S. Army,  03  12.  knots  thereafter  about  a  15  1.5 m a s s u m i n g a s t e a d y w i n d f o r  (Bretschneider  As  the n o r t h end of  speed i s  12 t o d a y 0 3 h o u r 0 0 ;  exceed about  T  0.5 t o  p e r i o d b e g i n n i n g on d a y 01 h o u r  t h e maximum w i n d  15 h o u r s p r e v i o u s l y .  s w e l l energy to  uniform H  p r o g r e s s i v e l y more s o u t h w e s t e r l y .  fetch in  from the southwest.  1.8 m n e a r T o f i n o t o 4 . 5 m a t  location,  increase in  p o s i t i o n e d about of  6-hourly  average  i s p r e s e n t e d i n F i g . 5.2 f r o m t h e e n d o f  >T ,"§) h i s t o r y p  this  d i m i n i s h e s and s h i f t s  abrupt  The  10 m o n d a y 0 3 h o u r  t h e s o u t h f r o m d a y 02 h o u r  g  5.1.  s e a - s t a t e e v o l v e s from a f a i r l y  Fig.  forcing, H  Fig.  B r i t i s h C o l u m b i a , waves a r r i v e  Islands  Charlotte  Maximum w i n d s p e e d s a t  12 t o  i n c r e a s i n g from about  5.3  represent  The  maximum.  t h e Queen C h a r l o t t e  from  (P  f r o m d a y 02 h o u r  The maximum H  storm winds  in  c e n t r e d at p o i n t  s i m u l a t i o n 36 h o u r s  were s e l e c t e d to  storm.  shown  wave h e i g h t  s p i n - u p p e r i o d (P the  pressure f i e l d  a severe winter  60  significant  of  cases are compared.  Fig.  12 h o u r s  1977).  The  5.3  and  the  from  the  shoreward  s y s t e m as i t  highlights  t h e c o a s t a l wave  the  was  importance  regime.  73  - 67 -  f r r f r f r 1111 f f f r f t f t»f * (  ( f f ( (  J  <'  I  «itvg  sVl0 A  ?ig'  5  \s.tiot8.  d  tot  storm  - 68 -  Fig.  5.2  S i x - h o u r l y s i g n i f i c a n t w a v e h e i g h t f i e l d s p r o d u c e d by s t o r m 1 a l o n g l e g s B - C and C - D o f t h e s t o r m t r a j e c t o r y . T h e p e a k o f t h e s t o r m w i n d s o c c u r s a t 8 6 0 1 0 2 1 8 ( d a y 02 h o u r 18) i n t h e f o u r t h p a n e l ; t h e maximum w a v e s a r e s i x h o u r s l a t e r a t 8 6 0 1 0 3 0 0 ( d a y 03 h o u r 0 0 ) .  Fig.  5.2  Continued.  Fig.  5.2  Continued.  Fig.  5.2  Continued.  - 72 -  5.3  T i m e - s e r i e s of s i g n i f i c a n t wave h e i g h t ( H ) , peak p e r i o d (Tp) and mean w a v e d i r e c t i o n a t t h e s p e c i a l o u t p u t p o i n t a t t h e e n t r a n c e t o Queen C h a r l o t t e Sound ( m o d e l g r i d c o o r d i n a t e s ( 3 1 , 1 3 ) ) d u r i n g s t o r m 1. g  -  5.2  Storm I n t e n s i t y  Storm 2 t e s t s as  by  illustrated state  If  the d i f f e r e n c e  should  not  be v e r y  be  the  winds,  retarded  the b e g i n n i n g of  hours  after  the  o f maximum H  H (storm  2) m i n u s  g  wherein the  the  the d i f f e r e n c e s  regions.  the  1) i s  on t h e  largest  m lower is  is  g  significant  illustrated  by  1 to  At t h e c o a s t a l s i t e n o r t h o f in  the  5.7).  is  because  the  This  storm development  energy  order  of  arriving  at  the  12 h o u r s  that than  of  site  is  with  weaker,  local  coastal  g  corresponds  5 m.  indicate In  a  region  this  case,  Comparison w i t h  w i t h the h i g h e s t  8.0 m.  results  later  sea-state  this  in Fig.  well-sheltered  until  winds) the  and t h e r e  storm  has  is  energy of  coast.  This  a  broad  about  2  finding  5.6. there i s v i r t u a l l y  scenarios  during  g  i n the a r e a of  latitude  in swell  response between storm  hour  c o i n c i d e n t w i t h peak H  a l o n g the  Sound s i t e  Fig.  As s t o r m 2 d e v e l o p s ,  no d i f f e r e n c e  South of  to  i s c a l c u l a t e d as  s t o r m 1.  t h e Queen C h a r l o t t e I s l a n d s  (i.e. offshore  this  high  d a y 03 h o u r 00 w h i c h i s 6  a r e no l o n g e r  This  is  be l e s s  3 . 5 m b y t h e s t o r m p e a k o n d a y 02 a t  2 m less.  site  sea-  t h e s l o w m o v i n g C-D l e g  differences  7.5 t o  -^°N.  a  early  equilibrium  The d i f f e r e n c e A H  about  time-series  the  and w h i c h  Q  than  of  e v e r y 6 h o u r s f r o m d a y 02 h o u r  are coincident  t h e Queen C h a r l o t t e  difference  in  P (min)  greater  differences  wave h e i g h t  spin-up  1.  By d a y 03 h o u r 0 0 , t h e r e i s v i r t u a l l y  i n which H  that  development  negative  somewhat  l o c a l wind g e n e r a t i o n n o r t h of region  field  less  d i m i n i s h to about  Futhermore,  early  g  that  these d i f f e r e n c e s  g  a  storm  e x p l o s i v e d e e p e n i n g as  b y t h e end o f  g  deepening to  storm 2 i s are  has  therefore,  as i n s t o r m  i n the H  1) s o  g  that  is,  v a l u e s i n s t o r m 1.  g  H (storm  areas where H ( s t o r m  18.  the  differences  5.2 i n d i c a t e s  p e r i o d of  the e x p l o s i v e deepening u n t i l  s e a - s t a t e of  largest  H  the  be a s g r e a t  end of  the time  an e q u a l l y i n t e n s e  scenario  are roughly  of  Because  F i g . 5.5 s h o w s t h e d i f f e r e n c e  of  and maximum s e a - s t a t e s w i l l  seas  the f i e l d  great.  06 a t  by a s h o r t  local  in  energy s h o u l d not  this  The e x p e c t a t i o n  will  I.  essence,  followed  F i g . 5.4.  development  swell  In  Q  in  than i n storm  o f more r a p i d d e v e l o p m e n t  P (min).  diminished intensity  -  Variations  the e f f e c t  measured  73  the  1 and 2 ( F i g .  early  stages  c a n be l i t t l e  passed  no  this  of  swell  northerly  latitude.  79  -  940  -i  ;  00  : —  12 Day  Fig.  5.4  74  -  i  i  00  12  01  The e v o l u t i o n o f  Day  P  Q  00 02  i n storms  12 Day  1 and 2 .  03  - 75 -  Fig.  5.5  C o n t o u r e d f i e l d s o f AH p e r i o d d a y 02 h o u r 06  G  c a l c u l a t e d as storm 2 l e s s s t o r m 1 f o r the t o d a y 03 h o u r 00 i n 6 - h o u r l y t i m e s t e p s .  - 76 -  - 77 -  Storm 2  Queen  Charlotte  Sound (31,13)  Fig.  5.6  T i m e - s e r i e s of s i g n i f i c a n t wave h e i g h t ( H ) , peak p e r i o d (Tp) and mean w a v e d i r e c t i o n a t t h e s p e c i a l o u t p u t p o i n t a t t h e e n t r a n c e t o Queen C h a r l o t t e S o u n d ( m o d e l g r i d c o ordinates (31,13)) during storm 2. g  Storm  1  North  of  Queen  Charlotte  Islands  Storm  2  North  of  Queen  Charlotte  (26,17)  Fig.  5.7  Islands (26,17)  T i m e - s e r i e s o f s i g n i f i c a n t w a v e h e i g h t ( H ) , p e a k p e r i o d (T ) a n d m e a n w a v e d i r e c t i o n a t t h e s p e c i a l o u t p u t p o i n t n o r t h o f t h e Queen C h a r l o t t e I s l a n d s ( g r i d c o o r d i n a t e s ( 2 6 , 1 7 ) ) d u r i n g s t o r m s 1 and 2. g  -  Storms 6 and 7 t e s t intensity  sensitivity  of  c r e a t e d by t h e d i f f e r e n c e s  Fig.  5.8.  the  maximum  In  storm 6 the winds  consequence f o r 14 m ( o r Along  the  79  the  -  the wave f i e l d in central  14 mb d i f f e r e n c e  are  strengthened  wave f i e l d  is  from  coast  the  differences  are  Charlotte  Islands  and Queen C h a r l o t t e  deviation  appears  at  progressively builds Queen C h a r l o t t e Islands.  of the  nearly  relative history  the  it  the  time  storm  75  important  knots  the  (or H  from  exemplified  by  northern  Sound s i t e s  in  g  in  since  25%).  largest  of  to an i n c r e a s e of  Sound and a b o u t  P (min)  for  Q  area of  dominated  60% r e s u l t i n g t o P = 1 0 1 5 mb.  i n terms of  least  this  5 m i n about  Since the r a t e fact,  about  model, e r r o r s of at  differences of  to  quite  peak  about  1.5 m i n  winds  of  type  (day  1.0 m o v e r  5 m n o r t h of  The  10 m t o  by  storm  local  from  hour  3 m for  to a f i n e  Q  development  in  reach i t s  Fig.  by s t o r m  1,  P (min) Q  against  18)  and  storm  1 in  grid  nested  5.10 or  shows  a potential  which i s  than  respect), there w i l l for  maximum error  calculated in  the  storm  l a r g e sea-state changes.  s t o r m 6 i s more r a p i d  maximum p o t e n t i a l  first  from a s e r i o u s under  T h e r e a r e , of c o u r s e , a l s o d i f f e r e n c e s  i s s i m i l a r to storm 2 i n t h i s  l o c a l sea to  sea,  a 25% c h a n g e i n  AP /At which mitigate  The  trajectory.  wind  9 m as p r e d i c t e d  02  Queen  the Queen C h a r l o t t e  30% c o u l d e a s i l y r e s u l t of  the  F i g . 5.9.  In terms of s p e c i f y i n g a boundary c o n d i t i o n  estimate Within  is  Q  an i n c r e a s e i n  in  p r e s s u r e t h a t a r e shown  P (min) 60  variations  40%).  the  coastal  in  to  in storm  1  be l e s s t i m e  the g i v e n wind  (in for  forcing.  .  .  . 83  -  Day  Fig.  5.8  01  80  Day  -  02  T h e e v o l u t i o n o f P i n s t o r m s 1, 6 a n d 7 . P ( m i n ) i s i m p o s e d a t 5 3 ° N 145°W. Q  Q  Day  In a l l  03  cases  -  Storm  6  north  of  81 the  Queen C h a r l o t t e  Islands  (26,17)  Storm  6  Queen C h a r l o t t e  Sound  (31,13)  .  5.9  C o m p a r i s o n of storm 1 and s t o r m 6 response as e x e m p l i f i e d by s i g n i f i c a n t wave h e i g h t a t t h e s p e c i a l o u t p u t p o i n t s n o r t h of the Queen C h a r l o t t e Islands ( 2 6 , 1 7 ) and at the e n t r a n c e t o Queen C h a r l o t t e Sound (31,13).  -  82  -  Dashed l i n e s i n d i c a t e n e g a t i v e d i f f e r e n c e s Heavy s o l i d l i n e s i n d i c a t e a d i f f e r e n c e of z e r o Light solid lines indicate positive differences  Fig.  5.10  The f i e l d o f A H a t t h e t i m e o f maximum w a v e h e i g h t s i n s t o r m 1 (day 03 h o u r 00) d i f f e r e n c e d as s t o r m 6 m i n u s s t o r m 1 (upper p a n e l ) and the c o r r e s p o n d i n g f i e l d of H f r o m s t o r m 1. g  g  -  -  83  Storm 7 has c o n s i d e r a b l y weaker winds than storm 1 s i n c e i t s 974 mb I s  16 mb h i g h e r  r e p r e s e n t i n g a change of  28% i n P  w i n d s r e a c h o n l y 35 k n o t s , j u s t a l i t t l e more t h a n h a l f i n s t o r m 1.  The l a r g e s t d i f f e r e n c e  relative  Q  of  i n the s i g n i f i c a n t  the  storm  1 H  throughout The  Fig.  field  indicates  a general  t h e r e g i o n d o m i n a t e d by t h e  coastal  due to  g  swell  climate  is  also  illustrates  Charlotte  Islands  Queen C h a r l o t t e  this  trend  greatly  and t h e o t h e r  Sound.  at  two  Peak  maximum field  is  Comparison with  on the  reduced i n in  of  the  order  of  50%,  both height  and  period  s t a g e s of  the  storm.  early  stations:  s o u t h e a s t of  A difference  60 k n o t  of  local wind-sea.  the weaker s e a - s t a t e development  5.12  reduction,  low  to P.  wave h e i g h t  b e t w e e n 5 a n d 6 m i n 10 m f o r s t o r m 1 a s s h o w n I n F i g . 5 . 1 1 . the  central  one n o r t h w e s t  these i s l a n d s  2 m in H  in  of  the  the  Queen  entrance  to  combined w i t h a 6 s l o w e r T s  is predicted i n storm 7 for which is H  g  18 h a f t e r  difference  just  before  Storm 4 i s r  990 ^  This the  s  is  t h e more n o r t h e r l y  the storm peak.  almost  as g r e a t ,  t h e end o f  the model  also a test  of  site  by t h e  end of  the  test  At t h e Queen C h a r l o t t e Sound s i t e ,  but  some l o n g p e r i o d s w e l l  begins  to  the  arrive  run.  storm i n t e n s i t y  i n c r e a s e d to 8° of  p  latitude  in  that  the  radial  extent  f r o m 6 ° i n s t o r m 1 (and a l l  defined  other  storms).  r e p r e s e n t s a n i n c r e a s e i n s t o r m s i z e o f 2 2 2 km (33%) f r o m t h e c e n t r e 990 mb i s o b a r .  Since the d e r i v a t i o n  wind speeds are expected. change i n  behaviour example,  is  scaling seen at  there  is  of  increase for pressure.  radial  300 km f o r  essentially  the  In  the  larger  Fig.  5.13  d i s t a n c e s between about no d i f f e r e n c e  a b o u t 300 a n d 800 km a n d a s l i g h t to about  wind speed depends on d P / d r ,  larger  in  the  storm this  somewhat  to  of the  anomalous  800 a n d 1000 km.  In  pressure gradient  between  decrease i n the g r a d i e n t storm  s y s t e m due  to  lower  H o w e v e r , as shown i n F i g . 5.13, the l o c a l r a t e  P may a c t u a l l y  logarithmic  of  by  from the c e n t r e  this  out  system.  .  . 87  - 84 -  Heavy s o l i d l i n e s i n d i c a t e a d i f f e r e n c e of z e r o Light solid lines indicate positive differences  Fig.  5.11  The f i e l d o f A H a t t h e t i m e o f maximum w a v e h e i g h t s i n s t o r m 1 ( d a y 03 h o u r 00) d i f f e r e n c e d a s s t o r m 7 m i n u s s t o r m 1 ( u p p e r p a n e l ) and t h e c o r r e s p o n d i n g f i e l d o f H f r o m s t o r m 1. g  g  Storm  7  Queen  Charlotte  Sound  Storm  7  North  of  (31.13)  Fig.  5.12  Queen  Charlotte  Islands (26,17)  T i m e - s e r i e s of H and T i n the e n t r a n c e to Queen C h a r l o t t e Sound and a t t h e c o a s t a l s i t e t h a t i s n o r t h o f t h e Queen C h a r l o t t e I s l a n d s . g  p  - 86 -  Fig.  5.13  C o m p a r i s o n of i s o b a r r a d i i as a f u n c t i o n of the s c a l e r^gQ f o r t h e c a s e o f P = 9 5 8 mb. Q  radial  - 87 -  Fig.  5.14  shows  the  AH  g  field  (storm 4 minus  w i n d s i n t h e u p p e r p a n e l and a t t h e end of These r e s u l t s coast  is  indicate  slightly  that during  greater  in  storm  1) a t  than i n  the  storm development  storm 4 than  no d i f f e r e n c e  s m a l l e r base storm.  in  s u p p o r t e d by t h e Charlotte storm  H  at  Sound ( F i g . 5.15).  1 periods  are  equal  numerically  larger.  storm periphery the  of  t i m e - s e r i e s of  essentially  At  most  centre  early  storms  1 and 4.  H  in  the wave f i e l d  by  coastal  storm  1 although  the  2 to  10 s i n  storm  storm,  s p e c i a l output  on day 0 2 , t h e  point,  first  H o w e v e r , as t h e  in  the  the area  is  almost is  e n t r a n c e t o Queen on d a y 03  the  The wave h e i g h t s  are  storm 4 r e s u l t s  are  the  wind i n t e n s i f i c a t i o n  at  the  5.13. which  42 h o u r s  overall  panel.  conclusion  storm e a r l y  although  the s l i g h t  e x p l a i n e d by F i g .  This  1.  peak,  v a l u e s a r e up t o 2 m  comparisons i n the  peak of  the  g  stations.  the  T h i s i s due t o is  p  of  along  By t h e end of: t h e s t o r m t h e r e  and T  g  At  throughout  that  westernmost  longer  the  time  the model run i n the l o w e r  d o m i n a t e d by l o c a l w i n d - s e a t h e l a r g e r s t o r m s y s t e m H less  the  of  is  within  results  380 km o f are n e a r l y  storm wave f i e l d  00) and d e c a y s , the m o d e l r e s u l t s a t t h i s  the  storm  equal  peaks (day  03  in  hour  s i t e ( F i g . 5.16) show t h a t t h e s e a -  s t a t e i s 0 . 5 t o 1.0 m l e s s w h e n f o r c e d b y t h e l a r g e r s t o r m 4 . Of  the  three  central  intensity  to  parameter  that  the v a l u e of difficult  changes i n were  d i s c u s s i o n of  tested  is  extent, quite  of the  to  determine  s e a and t h e storm  although  small.  Of  development,  minimum  the the  range  of  remaining and i t  is  values two  least  of  this  parameters,  an e x c e e d i n g l y  a c c u r a t e l y from the s c a t t e r e d measurements  few m e t e o r o l o g i c a l  development  i d e a l i z a t i o n of  of  the wave r e s u l t s are c e r t a i n l y  Q  parameter  speed  radial  (speed  P ( m i n ) a p p e a r s t o be t h e more c r i t i c a l  made by s h i p s a t the  tested  p r e s s u r e , and r a d i a l e x t e n t ) ,  sensitive  on  parameters  w i l l  be  buoys. drawn  the February 5-7,  Further in  1960  Section  observations 5.5  in  the  storm.  91  -  .  5.14  88  -  T h e f i e l d o f A H a t t h e t i m e o f m a x i m u m w i n d s ( d a y 02 h o u r 18 ; u p p e r p a n e l ) a n d a t t h e e n d o f t h e m o d e l l i n g s e q u e n c e (day 03 h o u r 1 2 ; l o w e r p a n e l ) d i f f e r e n c e d as s t o r m 4 m i n u s s t o r m 1. g  - 89 -  Fig.  5.15  T i m e - s e r i e s c o m p a r i s o n o f H and T from storms a t t h e e n t r a n c e t o Queen C h a r l o t t e S o u n d . s  p  4 and  1  - 90 -  Fig.  5.16  T i m e - s e r i e s comparison of at the westernmost output  H and Tp f r o m s t o r m s site. s  4 and 1  -  5.3  Storm  test  of  the  storm t r a j e c t o r y  is  a reasonable alternate  the southwest of  difference  cold  the  effects  by 5 ° o f  lows  trajectory  considered in  to  the e f f e c t  a similarity a s i d e from  is a l i t e r a l clearly  Percentage Charlotte  the  the  this  shows t h a t  the northward  part  F i g . 4.7 shows t h a t  this  southwest  study.  in Fig.  in  the  H  of  site  Because  towards  t h e end o f  s e a - s t a t e parameters at This i s  of  from  a shifting  this  is  of  the H  spatial is  convergence  the  end of  wave f i e l d  along  near  a  will  the  test.  the  by 5 ° towards  1 m  to  the  coast,  the  coast.  Queen C h a r l o t t e  coast  the  Queen  18 ( F i g .  Sound s i t e .  10 m i n s t o r m 3 .  results  12,  H  g  all  three  t h e s a m e i n t h e two  storm  c o n s i d e r i n g the  i n the v i c i n i t y  of  the s p e c i a l  sea-state is  latitude  at  H o w e v e r , F i g . 5.18  1:  the  of  Here  storm  in  by 5 ° o f  At  3 m o n d a y 02 h o u r  s i t e are very n e a r l y  gradient  field  the  northward  longitude  s t o r m s e q u e n c e o n d a y 03 h o u r  c l e a r that  the s p a t i a l  5 ° of  and  i n s e a - s t a t e near the storm peak i s the  c o n s i s t e n t w i t h the  F i g . 5.2, i t  output points  the  toward  the  lows  the a b s o l u t e  42°N,  the wave f i e l d  greatest  increase is  due w e s t  in  frontal  5.17.  are  g  At  sea-states  f r o m 3.5 m i n s t o r m 1 t o a l m o s t  p a n e l of  both  distortions  translation  differences  Sound s i t e ,  in  small  apparent  s p e c i a l output  cases.  140°W.  of  i s o n l y 286 km, and t h i s  The most d r a m a t i c d i f f e r e n c e  changes  to  diminishes with increasing latitude.  Nevertheless,  the  for  translation  t h e s t o r m 1 and s t o r m 3 p a t h s a r e c o n v e r g e n t ,  contribute  5.17).  of  longitude  d i s t a n c e of 413 km, b u t a t 59°N i t  which i s  -  Trajectory  S t o r m 3 was d e s i g n e d t o  portions  91  not  very  final  offshore  large  so  that  c a n o n l y m a k e a b o u t 0 . 5 t o 1.5 m  difference. For  the  coastal  sites,  continuity  must s t e e p e n when t h e s t o r m t r a c k F i g . 5.17 a l o n g V a n c o u v e r I s l a n d . Sound i n F i g . 5 . 1 9 , coast  about  it  18 h o u r s  appears that earlier  i n s t e a d o f d a y 03 h o u r 0 0 ) . there  i s an i m p o r t a n t  well-developed the  At the c o a s t , intensity  is  this  tests,  is  that  closer  From the the  to  the the  gradient coast.  wave  This  is  height seen  in  t i m e - s e r i e s i n Queen C h a r l o t t e  s e a - s t a t e begins i t s  storm  in  3 than  in  The d e v e l o p m e n t o f T  p  storm  sharp r i s e 1 (day  at  the  02 h o u r  in storm 3 indicates  06  that  l o c a l w i n d - s e a c o m p o n e n t d u r i n g d a y 0 2 , w h i c h was n o t  i n s t o r m 1,  storm centre  in  dictates  b e c a u s e t h e c o a s t a l w i n d s a r e somewhat h i g h e r  c l o s e r to  the  coast.  scenario produces greater  including  when  i m p o s i t i o n of  changes t h a n any of  the deepest c e n t r a l  the  storm  low.  95  Fig.  5.17  S i g n i f i c a n t w a v e h e i g h t f i e l d u n d e r maximum w i n d s i n s t o r m 1 ( u p p e r p a n e l ) and i n s t o r m 3 ( l o w e r p a n e l ) . The storm t r a j e c t o r y i n storm 3 i s 5° c l o s e r to the c o a s t .  - 93 -  Storm 3 (25,13)  5.18  Comparison o f Che t i m e - s e r i e s o f H , T a n d mean d i r e c t i o n i n storms 3 and 1 a t the s p e c i a l output p o i n t due w e s t o f t h e e n t r a n c e t o Queen C h a r l o t t e S o u n d . g  - 94 -  Storm 3  Queen  Charlotte  Sound (31,13)  .  5.19  C o m p a r i s o n of the t i m e - s e r i e s of H , T a n d mean d i r e c t i o n i n s t o r m s 3 and 1 a t t h e s p e c i a l o u t p u t p o i n t i n t h e e n t r a n c e t o Queen C h a r l o t t e S o u n d .  - 95 -  5.4  Advection Rate of  In t h i s  t h e C e n t r a l Low  s e c t i o n o n l y one i m p o r t a n t  L e w i s and M o r a n ( 1 9 8 5 ) in  there  case i s c o n s i d e r e d : the s t a l l e d  are four  e x a m p l e s among t h e  w h i c h a l o w p r e s s u r e s y s t e m became s t a t i o n a r y  n o r t h of states  the  in  Queen C h a r l o t t e  these storms  Islands  are i n v a r i a b l y  s i n k i n g was r e c o r d e d i n  two o f  after  the  h i g h (8 t o  the f o u r  storms.  e x p l o s i v e deepening i n the development  for  21 s t o r m s  up  to  insertion  55°N 145°W.  of  At  north gradient  of  time  10 t o  A t d a y 03 h o u r 00 t h e at  the  same t i m e  s t o r m peak..  00 t o j u s t  over  Two o f  these events  hour  the  coast  southerly  stall  1 m or  (Fig.  less  for  panel).  The c o n d i t i o n s g  t h e end o f  5 m) u n d e r  5.21).  this  At  the  half  of  the G u l f of A l a s k a ,  over  that  this  difference  storm  increase  the coast are  offshore  s p e c i a l output  132°W a n d 2 m f o r  points, the  F i g . 5.22 shows t h e n e t  t h a n +1  ra.  day 03 h o u r  24  change  is  two s o u t h e r l y difference 12 l e s s  the  preceding storm h i s t o r y .  In  sites  in H  g  at  s t o r m 1 day  the  12  northwest  t h e s t o r m 5 s e a - s t a t e i s g e n e r a l l y e l e v a t e d by 1 m  can the  the  the  t h e two s t o r m s a r e t h e same a n d h a v e b e e n f o r is  an  l o w i n a r e g i o n t h a t was  H, of  is  the moving storm system.  be  attributed  study In  largely  domain, the  the  two  to  the  the c o a s t .  12 i n s t o r m 1 a n d t h e  from the w e s t s o u t h w e s t , most of  fact this  g  time  stall.  is  In  the the  e l e v a t e d by 1 t o  Based on the  final  panel  that waves a r r i v i n g  at  predicted increase in H  a r i s e s from propagating s w e l l energy that would a l s o a r r i v e t h e e x t r a 24 h o u r s o f m o d e l l i n g  anticlockwise,  scenario sea-states are  southeast, however, H  and somewhat more c l o s e r t o  i n F i g . 5.2 f o r  pattern  The l a r g e s t d i f f e r e n c e  Because t h e wind and wave c i r c u l a t i o n i s  southwestern quarter  2 m offshore  hour  1.  in  same w i t h i n l e s s  10 m on d a y 03  b a s e s t o r m ( s t o r m 5 d a y 04 h o u r  point,  hours:  of  the  longitude.  At t h i s only  are  The c h a n g e i n the s e a - s t a t e  the c e n t r a l  5.2  later  s e a - s t a t e i n c r e a s e s by more t h a n 2 m by t h e end o f  s t o r m 5 and t h e  03 h o u r 1 2 ) .  storm 1 i n F i g .  12 a n d 24 h o u r s  has i n c r e a s e d from  later.  t h o s e s i t e s west of  t h a t are e a s t of  a r e u s e d w i t h a 24  w i n d s a l o n g t h e B.C. c o a s t .  p e r i o d i s shown i n F i g . 5.21.  the  had  to  i n c r e a s e of more t h a n 7 m due s o u t h of  Along  also  t h e maximum w i n d s a r e 50 t o 55 k n o t s w i t h a s o u t h  The maximum H  w e a k l y d e v e l o p e d (4 t o  Reported s e a -  at  1 3 . 5 m 24 h o u r s  d u r i n g the s t a l l  usually  10 m l o c a l w i n d s e a ) and s h i p  s e a - s t a t e h a s d e v e l o p e d as shown f o r  p r e s e n t e d i n F i g . 5.20.  4.7  b e g i n n i n g o n d a y 03 h o u r 00 c e n t r e d  20 k n o t  (fifth  Fig.  stages.  c o n s t a n t wind p a t t e r n  this  In  24 h o u r s ,  In the i d e a l i z e d storm 5 e x a m p l e , the storm 1 wind f i e l d s hour  in  low.  t h a t was a v a i l a b l e  for  storm  g  1 within  t n s t o r m 5. . . .  99  - 96  Fig.  5 . 2 0  n  The s i g n i f i c a n t w a v e h e i g h t f s t o r m s t a l l ( u p p e r p a n e l ) and ( l o w e r p a n e l ) . The maximum H 1 2 and 1 3 . 5 m on d a y L ) 4 h o u r 0 U g  i e l d 1 2 hours a f t e r the 2 4 hours a f t e r the s t a l l i s 1 2 . 5 m on day 0 3 hour .  - 97 -  Fig.  5.21  The A H f i e l d c a l c u l a t e d as H a t d a y 03 h o u r 00 ( t h e b e g i n n i n g o f t h e s t a l l ) m i n u s H G 12 h o u r s l a t e r ( u p p e r p a n e l ) and minus H 24 h o u r s l a t e r (lower panel). Maximum d i f f e r e n c e s a r e on t h e o r d e r o f 6 t o n e a r l y b m n e a r t h e s t o r m c e n t r e and 1 t o 3 m a l o n g t h e B . C . c o a s t . g  g  - 98 -  Fig.  5.22  T h e AH f i e l d c a l c u l a t e d as H a t d a y 04 h o u r 12 i n s t o r m 5 m i n u s H a t d a y 0 3 h o u r 12 i n s t o r m 1. A t t h e s e t i m e s t h e s t o r m s y s t e m s a r e e q u i v a l e n t and h a v e b e e n f o r t h e p r e c e d i n g 12 h o u r s . g  g  -  The  location  additional  of  the  wave e n e r g y .  consequence i t  will  have  the  north  of  wind-sea i n southeast  5.5  stall  will  99  determine  which  The more n o r t h e r l y  have for  the  southern  Queen C h a r l o t t e  that  r e g i o n and t h e  s i d e of  a stationary  potential weather  the  coast,  Islands  sites stall  the  most  position,  the  less  it  will  and t h e more i m p a c t  from g r e a t e r for  receive  development  much more s w e l l  of  energy  local  from  the  system.  The Idealized Storm of February 5 to 7, 1960  The a c t u a l and i d e a l i z e d v e r s i o n s of and  4.10.  It  has  hindcasting.  others.  been i n c l u d e d  Even  qualification,  if  -  that  There  is  for  to  storm are i l l u s t r a t e d  e m p h a s i z e an  idealized  a n y one o f  ample  this  cases,  it  important cannot  i n F i g . 4.9  point  be  in  said,  without  t h e s t o r m p a r a m e t e r s i s more i m p o r t a n t  scope w i t h i n  the n a t u r a l  variability  of  wave  than  these  (factors,  combined i n u n f a v o u r a b l e w a y s , t o g e n e r a t e a more s e v e r e s e a - s t a t e  t h a t p r o d u c e d by a n y o f Storm 8 has but  they  central  a number  occur low  in  the extreme cases a l r e a d y  of  characteristics  unique  pressure  combinations.  of  944  mb a s  d e e p e n i n g segment p r e c e d i n g P ( m i n )  common w i t h  storm at  h a s t h e same t r a j e c t o r y  Lt  other  it  test  has the a  12 h o u r  -1.7 mb/h,  is  about  as s t o r m 1 (and a l l  scenarios,  same minimum  has  6;  than  investigated.  For example,  that,  Q  as i n s t o r m 2; i t  in  the  explosive  t h e same others  rate  except  n u m b e r 3). The i m p o r t a n t others  are  (1)  characteristics  Q  a  is  reached i n  result,  will  the  be more  P (min) Q  winds  It  is  are.  is  storm enters  slower  s e c t i o n which w i l l Another  especially  for  what  in  for  the  of  reaching  the  T h i s means t h a t  the  the  model g r i d .  southern  As  B.C. c o a s t  lower,  and h e n c e t h e  from the study  the  effect  exact  B-C l e g higher,  of  the  northern  is  1)  winds  are  in  stronger,  the  which w i l l  is also a l i t t l e  the that  promotion the  maximum  as  area.  differences  trajectory  then  case.  storm  tend  faster  the s e a - s t a t e somewhat on the  offsets  coast,  of  but i t  tend to d i m i n i s h which  the d u r a t i o n of  than i n the average (storm  and e x i t s  a bit  factor the  swell  quadrant  24 h o u r s a s t h e s t o r m a d v e c t s e a s t w a r d and  pressure i s  t h e maximum w a v e f i e l d  coast.  8 more s e v e r e t h a n any o f  energetic.  i s much l o n g e r  more u n c e r t a i n It  southwest  (see F i g . 4.10).  The c e n t r a l the  the  southwesterly  persists  northward  (3)  make s t o r m  threefold: P (min)  (2)  which  filling  of  high  to  speed build  i n t h e C-D northern  sea-states,  process begins 3°  of  -  latitude  further  Because  this  latitudes  of  storm the  is  much s t r o n g e r  model  grid,  Vancouver Island  greater  than i n  other  the  and e v o l u t i o n  as a r e f e r e n c e . 18  gradually  propagates northeast  of  higher  fields  test  is  case.  centred  swell  energy  Sound ought  H and s  in  to  longer T . p  the  southerly  that  propagates  be  This  coastal  swell  from s t o r m 8,  energy  is  using the h i g h l i g h t e d  the  east  independent  from  o n e s , and e n e r g y i s  already  that  confirmed  in Fig.  7 m contour  T h e w a v e p a t t e r n n e a r t h e s o u t h e r n g r i d e d g e a t d a y 02 h o u r  the  of  region  the  active  centred  storm  around  f r o m a r e a s on t h e s o u t h e a s t e r n s i d e of  mechanism  is  illustrated  the  cascades  d i s s i p a t e d through  energy  to  higher  the  and  and  to  the  At  the  storm centre.  f a s t e r than  wave-wave  frequencies  centre  145°W  same t i m e e n e r g y i s d i s p e r s e d w i t h t h e h i g h e r w a v e s t r a v e l l i n g smaller  considerably  Sound.  the  becomes more  to  it  southwesterly  scenarios:  12-hourly H  while  a n d Queen C h a r l o t t e  i n F i g . 5 . 2 3 i n Queen C h a r l o t t e  5.24 w i t h  -  s o u t h i n s t o r m 8 t h a n i n any o t h e r  towards  The o r i g i n  100  where  the  the  interaction s p e c t r u m may  be s a t u r a t e d .  Based on t h e H  g  pattern  o n d a y 03 h o u r  18 a n d t h e w e s t s o u t h w e s t e r l y mean w a v e  d i r e c t i o n ( F i g . 5 . 2 3 ) , t h e s e a - s t a t e c o u l d be e x p e c t e d t o p e a k a t a b o u t 8.5 m in  Queen  Charlotte  trajectory about for  roughly  this  less  of  the  to  the  using  the  trajectory,  g  in  storm  low pressure) w i l l  5.25 shows t h e the  patterns  frora  (with  as  the  p r o b a b l y not  evolutionary  5 m contour  7 ra c o n t o u r  6  storm  8  same exceed  pattern  a reference (Fig.  of  that  5.24).  H  g  is The  i n t h e s e two s t o r m s e m p h a s i z e s , f o r  in  the s w e l l  that w i l l  arrive  d e t e r m i n e d by t h e e a r l y s t o r m h i s t o r y ,  propagation  Charlotte  H  that  energy content  almost t o t a l l y (2)  contrast,  Fig.  the s w e l l f i e l d  particular (1)  location.  severe storm  equivalent  similarity this  By  a n d t h e same minimum c e n t r a l  6.5 ra a t  this  Sound.  onto  Islands,  is  the  coast,  particularly  at  the c o a s t and  s o u t h of  e s s e n t i a l l y i n d e p e n d e n t of  Ls  the  the Queen later  low  pressure system e v o l u t i o n .  104  -  Storm  101  -  8  Queen  Charlotte  Sound  (31,13)  31  ,  1  ,  2  ,  3  ,  STORM  /STORM / / / STORM  x  1  1  1  l  1  (  STORM  —  8  1;  STORM  5  8  6 1  1  " ^  ,  4  1  6  .  1 l! 1 STORM  1  1  1  J 1  JULY 19BG  Fig.  5.23  !  1  AUGUST 1986  T i m e - s e r i e s r e s p o n s e of H , T and mean w a v e d i r e c t i o n i n t h e e n t r a n c e t o Q u e e n C n a r l o t t e Sound f o r s t o r m s 1, 6 and 8. A s i d e from the v e r y e a r l y s p i n u p p e r i o d , the mean d i r e c t i o n i n a l l s t o r m s I s e s s e n t i a l l y t h e same.  Fig.  5.24  The s e a - s t a t e p a t t e r n i n t e r m s of H in storm 8 at 1 2 - h o u r l y i n t e r v a l s beginning o n d a y 02 h o u r 1 8 . g  Fig.  5.25  The s e a - s t a t e p a t t e r n i n t e r m s of H in storm 6 at 12-hourly i n t e r v a l s b e g i n n i n g o n d a y 02 h o u r 1 2 . g  -  104  6.0  SUMMARY OF RESULTS AND CONCLUSIONS  This  analysis  deep  ocean  has  west  meteorological chapter parameter  investigated  the in  of  the  the  coast  parameters  for  sensitivity  of  a particular  findings  turn.  Thereafter,  general  discussed in  terms  is  are  of  British  study  each parameter  -  hindcast  Columbia  class  summarized  of  and  the  variations  in  to  storm t r a j e c t o r y .  quantified  c o n c l u s i o n s on the of  s e a - s t a t e s on  for  In  this  each  relative  deep o c e a n and c o a s t a l  storm  effect  of  sea-state  hindcasting. 6.1  Summary o f  S e n s i t i v i t y Test Results  To c h a r a c t e r i z e t h e maximum l o c a l l y comparative (1)  situations  the  maximum  value  t h e maximum H height;  (3)  of  While  these  changes, the  negative AH 1  do  importance  differences  at  g  of  are  the  in  g  the  base  sensitivity  following  do n o t  characterize the  or  (storm  1)  case  and  the  case;  test  the  and i t s  c o r r e s p o n d i n g base  s t o r m p e a k a n d t h e minimum b a s e  various  reported  the  necessarily sea-state  pressure  isolate  as s e n s i t i v i t y  the  per  cent  to  rank  wave h i n d c a s t i n g .  All  variations  parameters  v a l u e s mean t h e s e n s i t i v i t y  g  three  region.  comparisons  they  differences,  and  within this  g  H  i n the s e n s i t i v i t y  g  the greatest AH H  sea-state  were c o n s i d e r e d :  corresponding value i n (2)  generated  for  storm minus test  results  largest  sufficiently  the  base storm;  are lower  hence  than the  storm  predictions.  The c o a s t a l terms. examined  swell  The at  variations  changes three  were c o n s i d e r e d s e p a r a t e l y i n s l i g h t l y  between  specific  the  base  locations:  H  g  the  and  special  i n t h e e n t r a n c e t o Queen C h a r l o t t e  Sound and j u s t  Islands.  difference  determined,  At  these  sites,  independent  the  the  sensitivity output  n o r t h of  between  of the t i m e of o c c u r r e n c e of  t h a t most m o d e l p e r f o r m a n c e  characteristics  are  points  cases near  were  Tofino,  t h e Queen C h a r l o t t e  hindcast either  reported.  different  maxima  one, i n the  were way  - 105 -  6.1.1 Storm I n t e n s i t y Radial rate  extent  o f t h e l o w p r e s s u r e s y s t e m , t h e minimum c e n t r a l  of i n t e n s i f i c a t i o n  are the key f a c t o r s  p r e s s u r e and t h e  considered here.  R a d i a l Extent The  s t o r m s i z e was d e f i n e d  and  as s u c h i t  i n terms  may v a r y w i d e l y  f r o m 3° o f  km) w i t h a m e a n o f 8° (890 k m ) . (667 km) a n d t h e s e n s i t i v i t y  of a constant  In t h i s  radius  latitude study  o f t h e 990 mb i s o b a r ,  (334 km) t o a b o u t  13° (1445  t h e b a s e v a l u e was s e t a t 6°  t o a c h a n g e t o 8° was i n v e s t i g a t e d .  The r e s u l t s  a r e s u m m a r i z e d i n T a b l e 6.1  T a b l e 6.1 Summary o f S e n s i t i v i t y  to Radial Extent  Base V a l u e :  6° o f l a t i t u d e (667 km)  Sensitivity Value:  8° o f l a t i t u d e (890 km)  Per Cent Change:  33% i n c r e a s e i n r a d i u s 78% i n c r e a s e i n a r e a  Wind F i e l d Variations  n e a r s t o r m c e n t r e , d e c r e a s e s ~ 5 t o 10 k n o t s remote f r o m s t o r m c e n t r e ( i n t h e v i c i n i t y mb i s o b a r ) , i n c r e a s e s ~ 5 k n o t s no change i n between  of t h e 990  Maximum Local Wind-Sea Difference Maximum Base V a l u e :  10 ra o n day 03 hour 00 A H = -1 m (-10%)  Maximum S e n s i t i v i t y T e s t : 9 m on day 03 hour 00 A H = -1 m (-1J Maximum D i f f e r e n c e :  -2 m on day 02 hour 18 m i n . base H = 8.5 m (-24%) ( v e r y l o c a l i z e d under t h e maximum w i n d s )  Coastal Swell  s t o r m maxima t o end of t e s t r u n  Tofino  Base H (m) 1.3  Queen C h a r l o t t e Sd N Queen C h a r l o t t e  I  g  g  Sensitivity H (m) 1.6  Difference  g  (m) 0.3  23%  3.1  3.3  0.2  6%  4.7  4.7  0.0  0%  - 106 -  Lowest Minimum C e n t r a l Low The  minimum  central  had  t h e mean P ( m i n )  p r e s s u r e was value  Q  reduced system.  to  944 mb.  Pressure  This  The s e n s i t i v i t y  of  9 5 8 mb a n d  latter test  imposed at  value  results  in  145°W.  the  represents  In  the  sensitivity  a very  intense  are summarized i n Table  Table Summary of S e n s i t i v i t y  53°N  base case test low  it  6.2.  Pressure  Base V a l u e :  958 mb a t 53°N 145°W  S e n s i t i v i t y Value  944 mb a t 53°N 145°W  Per Cent Change:  25% deeper r e l a t i v e t o P = 1015 mb  Wind F i e l d Variations  n e a r s t o r m c e n t r e , i n c r e a s e s ~ 10 t o 15 k n o t s 5 k n o t i n c r e a s e out t o about 600 km from s t o r m c e n t r e  Maximum Local Wind-Sea Difference 10 m  on day 03 h o u r 00  AH  Maximum S e n s i t i v i t y T e s t : 1 4 m  on day 03 h o u r 00  A H = +5 m (36%)  +5 m  on day 02 hour 18  m i n . base H  Maximum Base V a l u e :  Maximum D i f f e r e n c e :  = +1.5 m (15%) S  g  = 6 . 5 m (77%)  ( v e r y l o c a l i z e d under t h e maximum w i n d s ) Coastal Swell  s t o r m maxima t o end o f t e s t  Tofino  Base H (m) 1.3  Queen C h a r l o t t e Sd N Queen C h a r l o t t e  I  g  Sensitivity H (m) 1.7  g  A  run  «s (m) 0.4  Difference 31%  3.1  4.0  0.9  29%  4.7  5.9  1.2  26%  was  pressure  6.2  t o Lowest Minimum C e n t r a l  it  -  H i g h e s t Minimum C e n t r a l Low The  highest  value  the s t o r m d i d not domain.  Its  of  intensify  characteristic  -  Pressure  P (min) 0  107  imposed at  5 3 ° N 145°W was 974 mb.  very greatly  during  its  sea-state differences  Table Summary of S e n s i t i v i t y  In  passage through  this  case,  the  model  are presented i n Table  6.3.  6.3  t o H i g h e s t Minimum C e n t r a l P r e s s u r e  Base V a l u e :  958 mb a t 53°N 145°W  S e n s i t i v i t y Value:  974 mb a t 53°N 145°W  P e r Cent Change:  28% l e s s deep r e l a t i v e t o P = 1015 mb  Wind F i e l d Variations  n e a r s t o r m c e n t r e , d e c r e a s e s - 15 t o 25 k n o t s 5 t o 10 k n o t i n c r e a s e out t o about 600 km f r o m s t o r m centre  Maximum Local Wind-Sea Difference 10 m  on day 03 hour 00  A H = - 5 m (-50%)  Maximum S e n s i t i v i t y T e s t : 5 m  on day 03 h o u r 00  AH  5 m  on day 03 hour 00  m i n . base H  Maximum Base V a l u e :  Maximum D i f f e r e n c e :  g  = - 5 m (-100%)  S  g  = 8 m (-38%)  ( v e r y l o c a l i z e d under t h e maximum w i n d s ) Coastal Swell  s t o r m maxima t o end of t e s t  Tofino  Base H (m) 1.3  Queen C h a r l o t t e Sd N Queen C h a r l o t t e  I  Sensitivity H (m) 0.5  run  *s (m) -0.8 A  Difference -62%  3.1  1.5  -1.6  -52%  4.7  2.7  -2.0  -43%  -  108 -  Rate o f I n t e n s i f i c a t i o n Occasionally  storms  that  travel  at t y p i c a l  rates  along their  i n c l u d e a 12 t o 24 h o u r s e g m e n t d u r i n g w h i c h t h e c e n t r a l 1  rab/h  or more.  Such a h i g h  rate  deepening.  In the l a s t  1984), west  coast storms w i t h t h i s  weather  forecasters  deepen at rapidly  modelling  of  peak.  the d u r a t i o n  it  of  The r e s u l t s  the  rate  affects each wind  the f i s h i n g  will  low pressure f a l l s is called  boat  losses  to p r e d i c t  I n many c a s e s ,  which  i n November from  storms  will  the e x p l o s i v e c y c l o g e n e s i s  system i n t o a severe one. of  both  deepening  for  storm  is  also  important  the wind  field  f o r up t o a d a y p r e c e d i n g t h e  storm  the shape (hence f e t c h )  pattern  o f one i n t e n s i f i c a t i o n  rate  sensitivity  of  test  are presented  i n T a b l e 6.4.  Table 6 . 4 Summary o f S e n s i t i v i t y t o Rate o f I n t e n s i f i c a t i o n Base V a l u e :  - 0 . 6 mb/h f r o m day 02 hour 06 t o day 02 hour 18  S e n s i t i v i t y Value:  - 1 . 8 mb/h from day 02 hour 06 t o day 02 hour 18  P e r Cent Change:  200% i n c r e a s e i n r a t e o f deepening f o r t h e 12 hours p r e c e d i n g t h e s t o r m peak  Wind F i e l d Variations  none a t t h e s t o r m peak up t o 25 k n o t s weaker near the storm c e n t r e 12 hours b e f o r e t h e s t o r m peak  Maximum Local Wind-Sea Difference 10 m on day 03 hour 00  A H = 0 m (0%)  Maximum S e n s i t i v i t y T e s t : 1 0 m on day 03 hour 00  A H = 0 m (0%)  Maximum D i f f e r e n c e :  m i n . base H  Maximum Base V a l u e :  - 5 m o n day 02 hour 06  G  G  G  = 7 m (-71%)  - 5 ra on day 02 h o u r 12 m i n . base H = 7 m (-71%) ( v e r y l o c a l i z e d under the maximum winds) G  Coastal Swell  s t o r m maxima t o end o f t e s t r u n  Tofino  Base H (m) 1.3  Queen C h a r l o t t e Sd N Queen C h a r l o t t e  I  by  explosive  c h a r a c t e r h a v e r e c e i v e d more a t t e n t i o n is difficult  a m i l d weather  hindcasting i n that and  because i t  intensification  (since  these a c c e l e r a t e d r a t e s .  transforms  Correct  two y e a r s  of  trajectory  Sensitivity H (m) 0.7  AH (m) -0.6  Difference -46%  3.1  2.2  -0.9  -29%  4.7  4.0  -0.7  -15%  - 109 -  6.1.2 Storm Trajectory As  clearly  this  illustrated  i n F i g . 4.7, w i t h i n  a n a l y s i s , the northward  the c l a s s  of  l e g of the storm t r a j e c t o r y  storms  can vary w i d e l y .  a v e r a g e p a t h a l o n g 145°W c a n e a s i l y be d e f l e c t e d 5 ° o f l o n g i t u d e coast,  and t h i s  summarized  was t h e s e n s i t i v i t y  t h e more  The  results  general  hindcasting  are sensitive  determine  with  satellite  imagery.  more  c a s e t h a t was t e s t e d .  in  The  c l o s e r to the  The r e s u l t s  are  i n T a b l e 6.5.  In  be  considered  certainty,  to  context,  its  especially  tracked  is  specification  Those weather  accurately  this  for  as t h e y  and i t  storms  systems  that  near  a very  that  is  quite  parameter.  difficult  network.  Summary of S e n s i t i v i t y to Storm Trajectory Base V a l u e :  n o r t h e r n t r a j e c t o r y a l o n g 145°W  S e n s i t i v i t y Value:  n o r t h e r n t r a j e c t o r y a l o n g 140°W  P e r Cent Change:  26% l e s s d i s t a n c e t o c o a s t a t 49°N 42% l e s s d i s t a n c e t o c o a s t a t 55°N  Wind Field Variations  none i n r e l a t i o n t o t h e s t o r m c e n t r e a l o n g t h e c o a s t , peak winds s t r e n g t h e n by ~5 k n o t s on t h e s o u t h c o a s t and - 1 0 k n o t s on t h e n o r t h c o a s t a t day 02 h o u r 18 change i n d i r e c t i o n i s n e g l i g i b l e  Maximum Local Wind-Sea Difference 10 m on day 03 h o u r 00 AH  Maximum S e n s i t i v i t y T e s t : 1 0 m on day 03 h o u r 00 Maximum D i f f e r e n c e :  AH  g  = - 4 m (-40%)  g  = +6 m (60%)  +6 m on day 03 hour 00 m i n . base H = 3 . 5 m (171%) - 5 m on day 02 h o u r 18 m i n . base H = 8 m (-63%) ( v e r y l o c a l i z e d under t h e maximum w i n d s ) g  g  Coastal Swell  s t o r m maxima t o end o f t e s t r u n Base H  g  Sensitivity H (m) 3.3  g  s (m) 2.0  A H  Difference  Tofino  (m) 1.3  Queen C h a r l o t t e Sd  3.1  4.8  1.7  55%  4.7  8.2*  3.5*  74%*  4.7  5.8  1.1  23%  N Queen C h a r l o t t e  I  to  by t h e more d e n s e and  Table 6.5  Maximum Base V a l u e :  to  a r e n o t w e l l - m a p p e d by  cross the coast are l i k e l y  the coast  systematic land-based meteorological reporting  important  154%  *due t o l o c a l wind s e a  - 110 -  6.1.3  Storm A d v e c t l o n Rate  The most s i g n i f i c a n t  change  that  can o c c u r i n the storm a d v e c t i o n r a t e i s  a s s o c i a t e d w i t h low p r e s s u r e s y s t e m s t h a t s t a l l  ( i . e . become s t a t i o n a r y i n  space) without change i n any other p r e s s u r e c h a r a c t e r i s t i c s . last  Typically  stalls  24 h o u r s and o c c u r somewhere i n t h e n o r t h e r n G u l f o f A l a s k a a f t e r  storm has peaked and begun to d i m i n i s h i n i n t e n s i t y . results  of t h i s s e n s i t i v i t y  T a b l e 6.6 summarizes  test.  Table  6.6  Summary o f S e n s i t i v i t y t o Storm A d v e c t i o n Rate Base Value:  37 km/h  from 53°N to 59°N along 145°W  S e n s i t i v i t y Value:  16 km/h  from 53°N to 59°N along 145°W  Per Cent Change:  57% slower on average  Wind F i e l d Variations  none i n space except as a function of time a f t e r day 03 hour 12  Coastal winds  •Deep ocean  up to 5 knots stronger from Queen Charlotte Sound to northern Queen Charlotte Islands 25 to 30 knots stronger due W of Queen Charlotte I except 10 to 35 knots weaker near storm centre 15 to 25 knots stronger due W of Queen Charlotte Sd 5 to 15 knots stronger due W of Vancouver Island more rapid d i r e c t i o n change with longitude  Maximum Local Wind-Sea Difference Maximum Base Value:  10 m  on day 03 hour 00  Maximum S e n s i t i v i t y Test:12.5 m on day 03 hour 12 (up to end of base)  A H = 0 m (0%) g  AH  G  = 6.2 m (50%)  Maximum Difference:  7 m on day 03 hour 12 min. base H = 3 m (233%) (very l o c a l i z e d under the maximum winds; this difference w i l l increase as the s t a l l continues)  Coastal Swell  storm maxima to end of test run at 0312 (and 0412)  G  s (m)  A H  Difference  Tofino  (m) " 1.3 (3.8)  (m) 1.4 (3.9)  Queen Charlotte Sd  3.1 (4.8)  3.0 (3.7)  -0.1 (-1.1) -3% (-23%)  N Queen Charlotte I  4.7 (5.5)  4.4 (5.8)  -0.3 (0.3)  0.1 (0.1)  8% ( 3%)  -6% ( 5%)  the the  - Ill 6 . 1 . 4 C o m p a r i s o n o f Maximum E r r o r s Based  on  the  sea-state  encapsulated relative most  sea-state  there  the  H  to  errors  over  the  in  about  a linear  10%. less  It  parameter.  widest  area  be c o r r e c t  This  is  6.6  and  t o b e made o n  the  The one w h i c h c a u s e s  the  is  the  per  to  t h a n 1 cm a t  cent  within  storm  especially in historical  the s t a l l e d  the c e n t r a l  longitude  low  to  a meteorological  therefore,  of  reduce  a b o u t 70 km n e a r 5 0 ° N ,  to expect  this  surface  degree  of  surface pressure data.  may be c a u s e d by e x t r e m e c h a n g e s i n  by a s t a l l e d  trajectory.  change as a f u n c t i o n 1° o f  the s c a l e of  seems u n r e a l i s t i c ,  g  through  i n the p a t h of  a p h y s i c a l d i s t a n c e of  accuracy,  sea under  to  must  chart.  (i.e.  6.1  clear distinctions  scaling  analysis  changes i n H  Tables  150% i n b o t h l o c a l w i n d - s e a a n d s w e l l r e s u l t e d f r o m a  trajectory  corresponds to  rate  are  each s e n s i t i v i t y  change  Applying  distance,  Greater  noted  n o t t h e maximum r e a l i z a b l e ) s h i f t  pressure.  but  of  i n excess of  l a r g e (but  g  i n T a b l e 6.7,  importance  Differences  differences  storm system),  but  the storm  these are r e s t r i c t e d  s y s t e m and t o a n y i n c r e a s e d s w e l l  to  advection  local  wind-  the e v o l v e s from  this  area. The minimum limits. the  central  Intensifying  P (min)  about  50%  lower.  under-estimate  It  will of  E r r o r s of  inferred  in  intensification  intensification  20%.  by  Q  same p e r c e n t a g e e x c e p t  Reducing the  be  p r e s s u r e was  is  not  25% ( - 1 4  very  within  mb)  created H  reasonable  change H  measurements  b y more  g  P (min)  It  i s most u n l i k e l y  than  a  i n c r e a s e s of  g  roughly  expect  that  and the d i s t r i b u t i o n  any of  of  that  10%; h o w e v e r ,  a  5  mb  the  equivalent by  g  about  Q  network  c o n s i s t i n g of  lighthouses  try  a  and o t h e r  these data sources w i l l  are  over-  t h e deep o c e a n s i n c e P ( m i n )  reporting  a storm centre since s h i p s ' captains w i l l conditions  historical  can l e a d to u n d e r e s t i m a t i n g H  Q  from  to  few m e t e o r o l o g i c a l b u o y s , s h i p s - o f - o p p o r t u n i t y , stations.  its  l o c a l i z e d p o c k e t s u n d e r t h e maximum w i n d s .  +5 mb a r e v e r y p o s s i b l e o v e r  from  virtually  b y 28% ( + 16 mb) g e n e r a t e d s e a - s t a t e s t h a t  then  the depth of  varied  must very land  be c l o s e  to  to a v o i d s e v e r e wind and wave  the r e m a i n i n g part  of  the network  is  so  changes  in  sparse. Assuming  that  the  of  rate  the  minimum c e n t r a l  intensification  to  pressure  value  value  can have  that  S i n c e the w i n d - s e a w i l l  respond to  wind  will  speed and d i r e c t i o n  and the errors  resulting of  this  type  swell would  the  not  normally  a given, at  l o c a l wind,  be s h o r t e r  energy w i l l  is  for  more  unless  two c o n s e q u e n c e s .  the d u r a t i o n of a g i v e n  rapidly  be d i m i n i s h e d . arise  most  the  deepening  Significant surface  storms,  pressure  pressure  charts  -  112  Table  -  6.7  Maximum Sea-State V a r i a b i l i t y A t t r i b u t a b l e to Pressure Parameter S e n s i t i v i t y Tests  Sensitivity  Parameter  L o c a l Wind-Sea D i f f e r e n c e Max. From Max. From M a x . AH Base Sensitivity  s  Radial Extent  (R)  Minimum C e n t r a l P r e s s u r e minimum P ( m i n ) Q  maximum Rate of  P (min) Q  Intensification  Traj ectory Storm A d v e c t i o n Rate  n/a:  no a p p l i c a b l e c o m p a r i s o n  Swell M a x . AH * &  -10%  -11%  -24%  0 to  23%  15%  36%  77%  26 t o  31%  -50%  -100%  -38%  - 4 3 t o -62%  n/a  n/a  -71%  -15 to  -46%  -40%  60%  55 t o  154%  n/a  50%  -63 to 233%  171%  -23 to  * independent  of  8%  time  -  are  very  inaccurate  intervals  have  unless  they  -  are  only  available  a c c o r d i n g to  on the h i n d c a s t an impact  of  the  results.  not  more  definition  used i n  S m a l l adjustments  t h a n +10%  in  the  this in  wave  g r e a t e r per cent changes are p o s s i b l e i n low l e v e l  6.2  at  widely  spaced  during storm development.  The s t o r m s i z e , effect  or  113  study,  the  has the  radius  field  (±25%)  maxima,  coastal swell  least will  although  energy.  Conclusions  6.2.1 The Meteorological Perspective Two c o n c l u s i o n s a r e a p p a r e n t (1)  With is  the advent  expected  of  that  trajectory  from the routine  this  study:  images of  improvements  positioning w i l l  in  cloud formations, the  have occurred.  a c c u r a c y of  Since this  wave m o d e l l i n g , b e t t e r  wave  on a v e r a g e , s h o u l d be f o u n d when s a t e l l i t e  preparing (2)  of  satellite  significant  s e n s i t i v e parameter for results,  results  the s u r f a c e p r e s s u r e  weather  ships,  hindcasting  network  in  at sea  poor maintenance  buoys which n o r m a l l y  r e l i a b l e guidance to m e t e o r o l o g i s t s ) w i l l accurate pressure f i e l d  i s a most  charts.  ( e s p e c i a l l y decommissioning of of m e t e o r o l o g i c a l  storm  data are used  Any d e g r a d a t i o n i n the s u r f a c e p r e s s u r e m o n i t o r i n g  removal  it  p r o v i d e the  tend to r e s u l t  in  or  most less  specification.  6.2.2 Wave Hindcasting Perspective This  study  demonstrates  t h e same e l e m e n t s o f are l o c a l l y active  that  the  ADWAVE ( a n d p r e s u m e a b l y o t h e r m o d e l s t h a t  p h y s i c s of  in balance with  wave g e n e r a t i o n )  winds  preceding storm h i s t o r y .  As a r e s u l t ,  will  on a n y a r b i t r a r y  not  follow  the  h a v e two (1)  depend s t r o n g l y storm peak.  produces s e a - s t a t e s  the wind i n the sense t h a t  s t o r m c e n t r e and the s t r o n g e s t  is  the H  largely  peak s e a - s t a t e s i n  The w a v e f i e l d ' s  wind  field  "memory" o f  g  field  the  errors a wind  that  under  independent  the  of  the  deep o p e n o c e a n that  precede  field  error  or  will  forms: Through the  temporal  interpolation  from (say) 6 - h o u r l y  ( c o r r e s p o n d i n g to a v a i l a b l e s u r f a c e p r e s s u r e c h a r t s ) model time full (2)  embody  Swell  s t e p , an e r r o r  i n a s i n g l e wind f i e l d  w i n d maps  to the  wave  influences almost a  12 h o u r s o f w a v e h i n d c a s t i n g . energy  perpetuate  that  any e r r o r  propagates that  freely  occurred in i t s  at  off-wind  generation.  angles  will  -  Nested  wave  assessment linked from  of  to  the  model the  the  effects  coarse run  invariably  of  wind  to  the  -  an added errors.  dimension  In  one t h r o u g h  finer  adequate  unless  from  complexity  the  the  supply  of  to  an  nested g r i d  is  boundary  conditions  are  U s u a l l y the open water boundaries  are  points  significant  of  the  interest  swell  energy  boundary  that  the  approximation  can propagate  into  domain from remote storm systems t h a t are not b e i n g m o d e l l e d . hand,  nested grids  are  usually  of  these cases boundary c o n d i t i o n s important In  than the  s h a l l o w water,  and b o t t o m  l o c a l wind  and/or  of  overall  often  physical  model  On t h e  other  dimensions  be a s i m p o r t a n t ,  and a t  period  and  times  in  more  forcing.  are  applications.  boundary s p e c i f i c a t i o n of  a function  In  will  percolation  a r e e x c l u d e d f r o m deep w a t e r  6.2.3  small  is  the  where n e s t e d g r i d s a r e u s u a l l y a p p l i e d , r e f r a c t i o n ,  friction  on c o r r e c t  spectra  n e s t e d one.  to z e r o e n e r g y f l u x .  well-removed  of  such a case,  coarse grid hindcast modelling,  set  sufficiently  present  coarser surrounding  In deep w a t e r  quite  grids  114  (frequency)  additional  terms  Refraction, in particular,  the p a r t i t i o n  and  source/sink  shoaling  of  the  total  that  depends  energy  (H ) g  as  direction.  Engineering Applications Perspective  terms  of  extreme  value  design a p p l i c a t i o n s ,  a n a l y s i s of  the  importance  the a n n u a l extreme e v e n t  (for  sea dominated s e a - s t a t e at ranked importance w i l l  (2)  the v a l u e of  (3)  the advection rate  reanalysis  trajectory  of  key  relatively  the  that  certainly  case,  discounted  since  be a l o c a l  wind-  the p r e s s u r e parameters  and hence the l o c a t i o n of  Q  of  surface  of  P (rain), Q  and P . Q  pressure f i e l d s ,  as p o s s i b l e of  in  important  standards.  demand f o r  w i t h i n the economic c o n s t r a i n t s  of  and w i t h  a kinematic  extreme wave e v e n t s  within engineering  small,  almost  T h u s , w i t h due c o n s i d e r a t i o n o f  to h i n d c a s t a s e t  as ADWAVE t o  In  c a n be l a r g e l y  e x p e c t e d t o be much l e s s  much m e a s u r e d w i n d d a t a feasible  P  Q  as p o s s i b l e .  of•the  peak.  P (min),  deepening i s  i s as c o r r e c t  swell  coastal  be  the  of  of  l o n g - t e r r a wave c l i m a t e f o r  example) w i l l  its  (1)  The r a t e  the  man-time  P (min) Q  the p i t f a l l s , incorporation  analysis,  it  is  with of  as  quite  u s i n g a s p e c t r a l model such  Because  the  and computer  most m a j o r  so l o n g as  projects.  data  requirements  are  r e s o u r c e s c a n be met  -  I n many c a s e s or  climatological  in addition  situations  to,  long  include  installations  installation, phases of  will  tender  gravity-base  construction of  extreme  to  (using a very digital the  at  least  fast  one y e a r o f  attempt  wind  micro-computer  a s much c o m p u t e r considering  future,  the  (satellite)  satellites  short,  towing,  islands.  In  each  these a c t i v i t i e s wave  collection  climate:  of  wave  is  joint and  1500 h o u r s of in  this  weather  or  measurements  and w a v e h i n d c a s t i n g w o u l d  s h a l l o w water  the  number  digital  to  wind  into  the  objectively the  service.  w i t h the a p p r o p r i a t e  to  rig  persistence statistics  require  of  many  c o m p u t e r CPU t i m e  study)  to  generate  nested a p p l i c a t i o n would  of  sources of  fields,  it  significant  does  realization incorporate  numerical  the  require  not  errors  In  the next  remove the  of  seem p r u d e n t  In t h i s  which is  real-time  that  decade or  scatterometer  respect,  s t i l l  in  are  surface pressures,  it  thereby  w a v e h i n d c a s t i n g and surface  of  enough  or p a s s i v e microwave sensors,  begin the m o d e l l i n g process w i t h a c t u a l data-based d i g i t a l  the  remotely-sensed  s o , when t h e r e  r e l i a n c e on p r e s s u r e d a t a f o r  to  until  a n a l y s i s and p r o g n o s i s p r o c e d u r e s  s h o u l d be p o s s i b l e t o a r c h i v e w i n d d a t a i n s t e a d o f gradually  certain  s i t e - s p e c i f i c n e a r s h o r e wave c l i m a t o l o g i c a l d a t a  ability  wind data  the n a t i o n a l  pipeline  and o p e r a t i o n ,  normal  a s was d o n e  promising development, is  as  time as w e l l .  only  into  hindcasting  most  breakwaters;  such  w i n d d a t a c a n be g e n e r a t e d w i t h much g r e a t e r r e l i a b i l i t y . the  coastal  t o p r e p a r e a d e e p w a t e r w a v e h i n d c a s t a n d t o e x a m i n e some  A subsequent  may b e i n t r o d u c e d  These  U n l e s s many s i t e s a r e i n v o l v e d  p r e p a r e wind i n p u t and about  results.  Therefore,  the  than,  to wave h i n d c a s t i n g f r o m b o t h c o s t and a c c u r a c y p o i n t s  wind f i e l d s ,  of  very  fixed  and  artificial  and d i r e c t i o n ,  are  rather  platform construction,  of  value expectations.  For example,  man-months  period  time-frames  routing  and e x e c u t i n g e a c h of  understanding  of  facilities  exploitation  and m a i n t e n a n c e of  planning  height,  and o p e r a t i o n  vessel  production  swell  v a l u e s are required.  exposed b e r t h i n g  and o t h e r  be p r e f e r r a b l e  view.  construction  tanker  of  decision-making  extreme  hydrocarbon  informed  distribution  w i n d - s e a and of  offshore  for  by  short-term  return period  planning,  case the e f f i c i e n c y enhanced  of  of  concrete  and d r e d g i n g  -  statistics  s u c h as h a r b o u r s ,  a n d many a s p e c t s  115  winds.  to  -  7.0  116  -  REFERENCES  B o u w s , E . , H. G u n t h e r , W. R o s e n t h a l a n d C . L . V i n c e n t , 1 9 8 5 . S i m i l a r i t y of the Wind S p e c t r u m i n F i n i t e D e p t h W a t e r . J . Geophys. R e s . , 90(C1), 9 7 5 986. Cardone,  V . J . , W.J. P i e r s o n and E.G. Ward, 1975. H i n d c a s t i n g the S p e c t r a of H u r r i c a n e G e n e r a t e d W a v e s . Offshore C o n f e r e n c e , P a p e r OTC 2 3 3 2 .  Cardone,  V . J . , A . J . B r o c c o l i , C V . Greenwood and J . A . G r e e n w o o d , 1980. Error C h a r a c t e r i s t i c s of E x t r a t r o p i c a l - S t o r m W i n d F i e l d s S p e c i f i e d F r o m H i s t o r i c a l Data. J . P e t r o l . T e c h . , 8, 872-880.  Clancy,  R.M., J . E . K a i t a l a , and L . F . Zambresky, 1986. The F l e e t O c e a n o g r a p h y C e n t e r G l o b a l S p e c t r a l Ocean Wave M o d e l . Meteor. S o c , 67(5), 498-512.  Directional Technology  Numerical B u l l . Am.  C o t e , L . J . , J . O . D a v i s , W. M a r k s , R . J . M c G o u g h , E . M e h r , W . J . P i e r s o n , J . F . R o p e k , G. S t e p h e n s o n a n d R.C. V e t t e r , 1960. The Directional S p e c t r u m o f a W i n d G e n e r a t e d S e a as D e t e r m i n e d F r o m D a t a O b t a i n e d by t h e S t e r e o Wave O b s e r v a t i o n P r o j e c t . M e t e o r o l o g i c a l P a p e r s , New Y o r k U n i v e r s i t y , C o l l e g e of E n g i n e e r i n g , ^ ( 6 ) . D e l a g e , Y . , 1985. Surface Turbulent F l u x Formulation Atmospheric Models. Mon. Wea. R e v . , 1 1 3 . Det n o r s k e  Dobrocky  Golding,  in  Stable Conditions  for  V e r i t a s , 1982. R u l e s f o r t h e D e s i g n a n d I n s p e c t i o n o f Offshore S t r u c t u r e s , A p p e n d i x A: E n v i r o n m e n t a l C o n d i t i o n s . Oslo, Reprint 1982, A l l .  S e a t e c h , 1986. Technical report Studies Revolving Fund, Ottawa.  prepared  for  the  Environmental  B., 1983. A Wave P r e d i c t i o n S y s t e m f o r R e a l - T i m e Forecasting. Q u a r t . J . R. M e t . S o c , 1 0 9 , 3 9 3 - 4 1 6 . Over  O c e a n s and  Sea  State  Garratt,  J . R . , 1977. R e v i e w of Drag C o e f f i c i e n t s Mon. Wea. R e v . , 105, 9 1 5 - 9 2 9 .  Continents.  Gunther,  H . , W. R o s e n t h a l a n d K . R i c h t e r , 1979a. A p p l i c a t i o n of the P a r a r a e t r i c a l S u r f a c e Wave P r e d i c t i o n M o d e l t o R a p i d l y V a r y i n g W i n d F i e l d s D u r i n g JONSWAP 1 9 7 3 . J . Geophys. R e s . , 84(C8), 4855-4864.  Gunther,  H . , W. R o s e n t h a l , T . J . W e a r e , B . A . W o r t h i n g t o n , K. H a s s e l m a n n a n d J . A . E w i n g , 1979b. A H y b r i d P a r a m e t r i c a l Wave P r e d i c t i o n M o d e l . J. G e o p h y s . R e s . , 84_(C9), 5 7 2 7 - 5 7 3 7 .  H a s s e l m a n n , K . , T . P . B a r n e t t , E . B o u w s , H. C a r l s o n , D . E . C a r t w r i g h t , K. E n k e , J . A . E w i n g , H. G i e n a p p , D . E . H a s s e l m a n n , P . K r u s e m a n , A . M e e r b u r g , P . M u e l l e r , D . J . O l b e r s , K. R i c h t e r , W. S e l l a n d H. W a l d e n , 1 9 7 3 . M e a s u r e m e n t s o f W i n d - W a v e G r o w t h and S w e l l D e c a y D u r i n g t h e Joint N o r t h Sea Wave P r o j e c t (JONSWAP). Deutsche Hydrographische Z e i t s c h r i f t , R e i h e A . , Nr. 12. H a s s e l m a n n , K . , D . B . R o s s , P . M u e l l e r a n d W. S e l l , 1 9 7 6 . A Parametric P r e d i c t i o n M o d e l . J . Phys. O c e a n o g r . , 6^,200-228.  Wave  -  117  -  H a s s e l m a n n , D . E . , M. D u n c k e l a n d J . A . E w i n g , 1 9 8 0 . D i r e c t i o n a l Wave S p e c t r a O b s e r v e d D u r i n g JONSWAP 1 9 7 3 . J . Phys. Oceanogr., ^0(8), 1264-1280. Hodgins,  D.O., P.H. L e B l o n d , D.S. D u n b a r and C.T. N i w i n s k i , 1985. A Wave C l i m a t e S t u d y of The N o r t h e r n B r i t i s h C o l u m b i a C o a s t , V o l u m e II. T e c h n i c a l r e p o r t p r e p a r e d f o r F i s h e r i e s and O c e a n s , C a n a d a by Seaconsult Marine Research Ltd., Vancouver.  Hodgins,  D.O. a n d S . N i k l e v a , 1 9 8 6 . On t h e I m p a c t o f New O b s e r v i n g S i t e s o n S e v e r e Sea S t a t e Warnings f o r the B.C. C o a s t . Unpublished technical r e p o r t p r e p a r e d f o r F i s h e r i e s & O c e a n s C a n a d a by S e a c o n s u l t M a r i n e Research Ltd., Vancouver.  Hodgins,  D.O. and S. H o d g i n s , 1 9 8 6 . A n E v a l u a t i o n o f Wave F o r e c a s t i n g M o d e l s and F o r e c a s t Wind F i e l d s i n t h e C a n a d i a n C o n t e x t . Draft report prepared f o r the E n v i r o n m e n t a l S t u d i e s R e v o l v i n g F u n d , Ottawa.  Hodgins,  D . O . , C . T . N i w i n s k i a n d D.T. R e s i o , 1 9 8 6 . C o m p a r i s o n and V a l i d a t i o n o f Two S h a l l o w - W a t e r S p e c t r a l Wave M o d e l s . Draft report prepared f o r The E n v i r o n m e n t a l S t u d i e s R e v o l v i n g F u n d s , O t t a w a by S e a c o n s u l t Marine Research L t d .  Hsu,  S.A.,  Janssen,  1986. A Mechanism for the I n c r e a s e of Wind S t r e s s (Drag) C o e f f i c i e n t W i t h Wind S p e e d O v e r W a t e r S u r f a c e s : A P a r a m e t r i c M o d e l . J . P h y s . O c e a n o g r . , 16(1), 144-150.  P . A . E . M . , G . J . Komen a n d W . J . P . de V o o g t , 1984. An Operational C o u p l e d H y b r i d Wave P r e d i c t i o n M o d e l . J . Geophys. Res., 89(C3), 3635-3654.  K i t a i g o r o d s k i i , S.A., 1983. On t h e T h e o r y o f t h e E q u i l i b r i u m R a n g e i n t h e Spectrum of W i n d - G e n e r a t e d G r a v i t y Waves. J . Phys. Oceanogr., 13(5), 816-827. Komen, G . J . , 1 9 8 4 . T h e W a v e M o d e l l i n g (WAM) P r o j e c t : Proposal for the D e v e l o p m e n t and O p e r a t i o n a l I m p l e m e n t a t i o n o f a T h i r d G e n e r a t i o n Ocean Wave M o d e l . F i r s t d r a f t i s s u e d b y C h a i r m a n WAM G r o u p , De B i l t , The N e t h e r l a n d s . L a r g e , W.G. a n d S . Moderate  Pond, 1981. Open O c e a n Momentum F l u x M e a s u r e m e n t s to Strong Winds. J . Phys. Oceanogr., 11(3), 324-336.  LeBlond, P.H., 1984. F i n a l R e p o r t of t h e I n v e s t i g a t i o n on t h e O c t o b e r 1 1 - 1 2 , 1984 o n t h e West C o a s t o f V a n c o u v e r I s l a n d . o f t h e E n v i r o n m e n t , V i c t o r i a , B.C. Lewis,  in  Storm of Ministry  C . J . a n d M.D. M o r a n , 1 9 8 5 . S e v e r e Storms O f f C a n a d a ' s West C o a s t : A C a t a l o g u e Summary f o r t h e P e r i o d 1957 t o 1 9 8 3 . Canadian Climate C e n t r e U n p u b l i s h e d R e p o r t No. 8 5 - 7 .  L o n g u e t - H i g g i n s , M . S . , D . E . C a r t w r i g h t a n d N.D. S m i t h , 1 9 6 1 . O b s e r v a t i o n s o f the D i r e c t i o n a l S p e c t r u m of Sea Waves U s i n g t h e M o t i o n s of a F l o a t i n g Buoy, i n O c e a n Wave S p e c t r a . P r e n t i c e - H a l l , E n g l e w o o d Cliffs, 111-132.  -  118  -  M a c L a r e n P l a n s e a r c h , 1 9 8 5 . E v a l u a t i o n o f t h e S p e c t r a l O c e a n Wave M o d e l (SOWM) for Supporting R e a l - T i m e F o r e c a s t i n g i n the Canadian East Coast Offshore. Unpublished technical report prepared for the M e t e o r o l o g i c a l S e r v i c e s R e s e a r c h Branch, Atmospheric Environment S e r v i c e , Downsview, Ont. MEDS,  1984. H i s t o r i c a l W a v e M e a s u r i n g S t a t i o n s , S t a t i o n L o c a t i o n s Summary. Dept. of F i s h e r i e s and O c e a n s , M a r i n e E n v i r o n m e n t a l Data S e r v i c e . Updated 2 8 - 0 9 - 8 4 .  Pearson,  F . , 1984. Map P r o j e c t i o n Virginia.  Methods.  Sigma S c i e n t i f i c ,  Inc.,  P i e r s o n , W.J. and L. M o s k o w i t z , 1964. A Proposed S p e c t r a l D e v e l o p e d Wind S e a B a s e d on t h e S i m i l a r i t y Kitaigorodskii. J . G e o p h y s . Res., 69, 5181-5190.  Blacksburg,  Form f o r FullyTheory of S.A.  P i e r s o n , W . J . , L . J . T i c k and L. B a e r , 1966. Computer Based Procedures for P r e p a r i n g G l o b a l Wave F o r e c a s t s a n d W i n d F i e l d A n a l y s e s C a p a b l e o f U s i n g Wave D a t a O b t a i n e d by a S p a c e c r a f t . S i x t h N a v a l Hydrodynamics Symposium, O f f i c e of N a v a l R e s e a r c h , W a s h i n g t o n , D.C., 4 9 9 - 5 3 2 . Resio,  D.T., 1 9 8 1 . The E s t i m a t i o n of W i n d - W a v e G e n e r a t i o n Spectra Model. J . Phys. Oceanogr., 11, 510-525.  Resio,  D.T., 1982. Wave P r e d i c t i o n i n S h a l l o w W a t e r . P r o c . 14th O f f s h o r e T e c h n o l o g y C o n f e r e n c e , OTC 4 2 4 2 , V o l . 2 , 1 4 7 - 1 5 2 .  R e s i o , D.T., 1985. Wave T r a n s f o r m a t i o n s Related M a n u s c r i p t s u b m i t t e d t o ASCE J . o f W a t e r w a y , Engineering. Resio,  St.  in  a  Discrete  Annual  to N o n l i n e a r Fluxes. P o r t , C o a s t a l and O c e a n  D.T. a n d C . L . V i n c e n t , 1 9 7 9 . A C o m p a r i s o n of V a r i o u s N u m e r i c a l Wave Prediction Techniques. P r o c . 11th Annual O f f s h o r e Technology C o n f e r e n c e , OTC 3 6 4 2 , 2 4 7 1 - 2 4 7 8 .  D e n i s , M. a n d W . J . P i e r s o n , 1 9 5 3 . On t h e Seas. T r a n s . SNAME, 6 1 , 2 8 0 - 3 5 7 .  Motion  Ships  in  Confused  S a r p k a y a , T. and M. I s a a c s o n , 1 9 8 1 . M e c h a n i c s of Wave F o r c e s Structures. V a n N o s t r a n d R e i n h o l d C o . , New Y o r k .  on  Offshore  Seaconsult,  1986a.  Unpublished  report  prepared  for  Seaconsult,  1986b.  Unpublished  report  prepared  for  Seakem,  1985.  A Wave C l i m a t e  Study of  of  M o b i l O i l Canada, L t d . E s s o R e s o u r c e s Canada L t d .  the Northern B r i t i s h  Columbia  Coast.  T e c h n i c a l r e p o r t p r e p a r e d f o r M a r i n e E n v i r o n m e n t a l Data S e r v i c e s B r a n c h , D e p a r t m e n t o f F i s h e r i e s a n d O c e a n s , O t t a w a by Seakem O c e a n o graphy L t d . , S i d n e y , B.C. ' U . S . Army,  Yamada, T .  1977. Office,  Shore P r o t e c t i o n Washington.  Manual,  Vol.  I.  U.S.  Government  1976. On t h e S i m i l a r i t y F u n c t i o n s A , B , a n d C o f Boundary L a y e r . J . Atmos. S c i . , 23, 781-793.  the  Printing  Planetary  

Cite

Citation Scheme:

    

Usage Statistics

Country Views Downloads
United States 8 1
China 2 17
City Views Downloads
Ashburn 7 0
Beijing 2 1
Sunnyvale 1 1

{[{ mDataHeader[type] }]} {[{ month[type] }]} {[{ tData[type] }]}
Download Stats

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062938/manifest

Comment

Related Items