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UBC Theses and Dissertations

On the geographic variability of oceanic mesoscale motions Thomson, Keith Alec 1986

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ON THE GEOGRAPHIC VARIABILITY OF OCEANIC MESOSCALE MOTIONS  by  KEITH ALEC THOMSON B.Sc.,.Royal Roads M i l i t a r y  C o l l e g e , 1977  • A THESIS SUBMITTED IN PARTIAL FULFILMENT OF . THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in  THE  FACULTY OF GRADUATE STUDIES  . Oceanography Department  We accept  t h i s t h e s i s as conforming  t o the r e q u i r e d  THE  standard  UNIVERSITY OF BRITISH COLUMBIA June 1986  ©Keith A l e c Thomson, 1986  In  presenting  this  thesis  in partial  fulfilment  of  the  requirements  advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of granted by  the  understood t h a t  Head of my  Department or by  written  Department of Oceanography  The  U n i v e r s i t y of B r i t i s h  6270 U n i v e r s i t y Vancouver, B.C. V6T  Date:  Boulevard Canada  1W5  June 26,  this thesis  c o p y i n g or p u b l i c a t i o n of  not be a l l o w e d without my  1986  Columbia  and  study.  I further  for  Library  agree  her  representatives.  t h i s t h e s i s f o r f i n a n c i a l gain  permission.  that  f o r s c h o l a r l y purposes may  h i s or  an  be  It i s shall  ii  ABSTRACT Quasi-synoptic  expendable  Canadian Armed F o r c e s ,  the  United  Oceanographic Data Center, of these  data  and  s i x geographic Atlantic  and  the  two  f o r the P a c i f i c  results  Northwest  and  data and  and  of p r e v i o u s  Pacific,  Pacific,  variables,  variability,  S t a t e s Navy  r e g i o n s were d e f i n e d :  A t l a n t i c , Northeast of  bathythermograph  the  of  from  the  States National the  basis  studies using climatological  data,  the high-energy the  acquired,  United  Atlantic  the  Oceans.  On  r e g i o n s of the Northwest  low-energy  South A t l a n t i c and  representative  were  regions  of  the  South P a c i f i c .  upper  layer  were o b t a i n e d f o r each s e c t i o n - the mid-  Northeast  Spatial  (400  m)  thermocline  series  mesoscale temperature  and the g e o p o t e n t i a l anomaly (0 - 4000 kPa).  The  central  estimated  moments  f o r the  the combined Atlantic,  and  the  s i x geographic  low-energy a r e a s .  it  was  found  wavenumber r e g i o n s , the  In the  that  spectra  the  temperature between  high-energy  temperature  150  and  200  m  regions  between  in  respectively. 0.26  the  The  m^/s^,  high-  and  in  corresponding  the  The  high-energy  geopotential  baroclinic  anomaly  surface v e l o c i t y  and  5.5  cm/s,  have a g r e a t e r p o r t i o n of wavenumbers The  (i.e.  eddy k i n e t i c  280  geographic  evaluating  the  their  to  and  100  fields  Northeast  and  400  m  s c a l e s of  (B)  and  (M).  calculated  power-laws  temperature  the  300  are  1.40  and  field,  wavelengths),  dominant  300  and  9.6  and  and  170  155 17.5  km  the  high-  km,  with  cm/s.  The  velocity regions  i n the  low-energy  and  and  spectral  with  concentrated  than  the  0.54°C,  In g e n e r a l , the high-energy variance  is  standard d e v i a t i o n s of  have  of  and  higher  regions.  low-energy  regions  36 cm^/s^, r e s p e c t i v e l y .  Rossby waves were of  The  regions  u n i t mass f o r the  quasigeostrophic  parameter  spectral km  variability  (Ro), the Burger number wave steepness  respectively.  energies per  were e s t i m a t e d a t 250  The  350  the  i s more r e p r e s e n t a t i v e of  regions,  low-energy r e g i o n s have dominant wavelengths of s c a l e s of 4.5  and  areas  s t a n d a r d d e v i a t i o n s of the g e o p o t e n t i a l anomaly are 0.67  respectively.  wavelengths  low-energy  v a r i a b l e were  t o the b a r o c l i n i c eddy  eddy v a r i a b i l i t y i n most of the low-energy r e g i o n s . temperature,  each  combined high-energy  r e p r e s e n t a t i v e of the temperature v a r i a b i l i t y due whereas, the  of  of  the  governing  scaling the  dynamics  parameters  ( i . e . the  s p h e r i c i t y parameter  A l s o , the p r o p e r t i e s of with  the  observed  s p e c t r a were  (3*))  free  wavelengths  compared  was  with  inferred Rossby  and  by  number  the  Rossby  linear dispersive and  the  spectral  s e v e r a l models  of  iii nonlinear geophysical turbulence. which  i s consistent  inferred  from  these  with  the  analyses  I t was found scaling  f o r quasigeostrophy.  exhibit  a  Motions w i t h wavelengths g r e a t e r than linear/nonlinear high-energy  Rossby  regions  wave  are, of  km  i n the  turbulence  theory,  three-dimensional than  200  between theory.  high-energy  km  more  theory. course,  Rossby  nonlinear Motions,  are  specifically,  i n the low-energy  dynamics  variability.  with  regions  have  theory,  perturbations than  the  in  with  Charney's Motions w i t h dynamics  that  the  corresponding  with wavelengths l e s s  consistent  turbulence.  wave  geographic  Mesoscale  more  regions,  quasigeostrophic  linear/nonlinear  distinct  The  200 km i n a l l r e g i o n s a r e c o n s i s t e n t w i t h  l e n g t h s c a l e s i n the low-energy r e g i o n s . 200  t h a t Ro<<1, B = 0(1) and 3*<<1,  than  quasigeostrophic (1971)  model  wavelengths are  and q u a s i g e o s t r o p h i c  of less  intermediate turbulence  iv  TABLE OF CONTENTS Page Abstract  i  Table of Contents  i v  L i s t o f Symbols  v  List of Abbreviations  v i  L i s t of Tables  viii  L i s t of Figures  x i  Acknowledgements  Chapter  xiv  I - Introduction  1  Chapter I I - Data S e t  5  A.  Data C o l l e c t i o n  B.  Data P r o c e s s i n g  Chapter  5 11  I I I - D e s c r i p t i v e Analyses  A.  Geographic  Regions  B.  Geographic  Variability  Chapter  i  22 22  o f t h e Thermal S t r u c t u r e  IV - S t a t i s t i c a l Analyses  24  58  A.  Spatial Series  59  B.  C e n t r a l Moments  60  C.  Seasonal V a r i a b i l i t y  74  D.  Horizontal Anisotropy  77  E.  Wavenumber S p e c t r a  79  Chapter V - Dynamical  Inferences  100  A.  Q u a s i g e o s t r o p h i c S c a l i n g Parameters  100  B.  L i n e a r R o s s b y Waves  108  C.  Nonlinear Geophysical Turbulence  113  D.  Summary o f t h e I n f e r r e d D y n a m i c s  118  Chapter VI - Conclusions  121  References  126  LIST OF SYMBOLS  anisotropy  factor  B u r g e r number group  velocity  phase  velocity  g e o p o t e n t i a l a n o m a l y p e r t u r b a t i o n , 0 - 4000 k P a wavenumber  spectrum  C o r i o l i s parameter a t a given  latitude  gravitational acceleration z o n a l wavenumber, p o s i t i v e t o t h e e a s t h o r i z o n t a l wavenumber,  =  k^+l  2  kurtosis m e r i d i o n a l wavenumber, p o s i t i v e t o t h e n o r t h length scale,  A = 2TTL  R o s s b y wave s t e e p n e s s p a r a m e t e r o b t a i n e d  with U  R o s s b y wave s t e e p n e s s p a r a m e t e r o b t a i n e d w i t h Brunt-Vaisala number o f  U*  frequency  observations  number o f i n d e p e n d e n t  observations  s p e c t r a l power-law exponent intermittency factor r a d i u s o f t h e e a r t h , R = 6371 km R o s s b y number i n t e r n a l Rossby deformation standard  radius  deviation  mid-thermocline  temperature p e r t u r b a t i o n , v e r t i c a l l y - a v e r a g e d from  150 t o 200 m o r f r o m 350 t o 400 m baroclinic  (0-400m) v e l o c i t y  scale  upper bound o f t h e t r u e v e l o c i t y  scale  skewness m e r i d i o n a l g r a d i e n t of the C o r i o l i s parameter a t a given sphericity  parameter  latitude wavelength,  A = 2 nL  latitude  vi  LIST OP ABBREVIATIONS  Geographic Regions  NWA  Northwest A t l a n t i c ,  a high-energy region  NWP  Northwest P a c i f i c , a high-energy region  NEA  Northeast Atlantic,  SA  South A t l a n t i c ,  NEP  N o r t h e a s t P a c i f i c , a low-renergy r e g i o n  SP  South P a c i f i c , a low-energy  HIGH  c o m p o s i t e h i g h - e n e r g y r e g i o n c o n s i s t i n g o f t h e NWA a n d NWP  LOW  c o m p o s i t e l o w - e n e r g y r e g i o n c o n s i s t i n g o f t h e NEA, SA, NEP a n d SP  a low-energy  a low-energy  region  region  region  regions  regions  NPSF  N o r t h P a c i f i c S u b t r o p i c a l F r o n t , a s u b r e g i o n o f t h e NEP i n t h e vicinity  NPEC  of thesubtropical  front  N o r t h P a c i f i c E q u a t o r i a l C u r r e n t , a s u b r e g i o n o f t h e NEP i n t h e vicinity  of theequatorial  current  Data Sources and Instruments CAF  C a n a d i a n Armed F o r c e s  USN  U n i t e d S t a t e s Navy  N0DC  N a t i o n a l Oceanographic Data C e n t e r ( U n i t e d  XBT  expendable  SXBT  s h i p - l a u n c h e d expendable  AXBT  a i r - l a u n c h e d expendable  bathythermograph  Oceanographic Parameters  T-S  temperature-salinity  S-Z  salinity-depth  bathythermograph bathythermograph  States)  vii T-Z  temperature-depth  SSS  sea surface  salinity  EKE  eddy k i n e t i c  energy  EPE  eddy p o t e n t i a l  energy  Quasigeostrophic Dynamics  LRW  l i n e a r Rossby  wave  NRW  n o n l i n e a r Rossby  wave  QGT  quasigeostrophic  turbulence  Miscellaneous  UBC  University of B r i t i s h  RRMC  R o y a l Roads M i l i t a r y  RMS ACF  Columbia College  root-mean-square autocorrelation function  viii  LIST OF TABLES  Table II-1  T a b l e IV-1  RMS  differences  for  t h e CAF t r a n s - o c e a n i c s e c t i o n s .  Decorrelation crossings for  Table IV-2  between  scales  bucket  obtained  of t h e averaged  t h e s e c t i o n s i n each  Sample  standard  SSS a n d i n f e r r e d  from  the  autocorrelation  geographic  deviation,  SSS  first-zero functions  region.  skewness,  kurtosis  and  i n t e r m i t t e n c y o f T f o rt h e geographic r e g i o n s from t h e sections.  Table IV-3  Sample  standard  deviation,  skewness,  kurtosis  and  i n t e r m i t t e n c y o f D f o rt h e geographic regions from the sections.  Table IV-4  Sample  standard  intermittency  deviation,  of T  skewness,  f o r the geographic  kurtosis  and  regions, the  NPSF a n d t h e NPEC f r o m t h e s u r v e y s . T a b l e IV-5  Sample  standard  intermittency  deviation,  of D  skewness,  f o r the geographic  kurtosis  and  regions, the  NPSF a n d t h e NPEC f r o m t h e s u r v e y s .  T a b l e IV-6  Summary o f t h e number o f s e c t i o n s b y g e o g r a p h i c r e g i o n and q u a r t e r o f t h e y e a r .  T a b l e IV-7  Summary o f t h e s t a t i s t i c s  o f T a n d D f o r t h e NEP i n  each q u a r t e r o f t h e year. T a b l e IV-8  Isotropic  decorrelation  first-zero  crossings  scales of  the  obtained  from  the  regionally-averaged  autocorrelation functions of the surveys.  Page Table IV-9  The of  anisotropy  the meridional  from of  factor,  scale  (1*2)  meridional to  from  =  g  L /L , M  decorrelation  the averaged the surveys,  A  i s the  Z  length  scale  autocorrelation  the zonal  t h e averaged  (L^)  function  decorrelation zonal  ratio  length  autocorrelation  function.  T a b l e IV-10  81  Variance  of  obtained  T  and  by  wavelengths  D  with  95%  integrating  confidence  the  spectra  limits between  o f 1000 a n d 100 km.  86  T a b l e IV-11  Peak w a v e l e n g t h s  of the T spectra.  89  Table IV-12  Peak w a v e l e n g t h s  of the D spectra.  92  Table IV-13  Two-dimensional  isotropic  eddy  estimates of t h e geographic  Table IV-14  kinetic  regions.  C o n t r i b u t i o n o f each bandwidth  95  of the D spectra t o the  t w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c  Table IV-15  Length and v e l o c i t y eddy  T a b l e V-1  and  99  the  sphericity  (Ro), the Burger (g*)  parameter  f o r the 104 and t h e  dynamics from i t s value. (w,1/s), p e r i o d s  (Cp,  and  m/s),  baroclinic  quasi-synoptic  Summary  number  regions.  Frequencies free  T a b l e V-4  mesoscale  Summary o f t h e R o s s b y wave s t e e p n e s s p a r a m e t e r inferred  T a b l e V-3  97  variability.  geographic  T a b l e V-2  energy.  scales of the baroclinic  Summary o f t h e R o s s b y number (B)  energy  group  wavelengths.  waves  ( C , m/s) g  of  the  of the observed  l e n g t h s c a l e s i n t h e NEP.  of the properties  baroclinic  (T, y r ) , phase v e l o c i t i e s  velocities  Rossby  105  Rossby  of  waves  the linear with  the  111  first-mode observed 112  X  Page T a b l e V-5  T a b l e V-6  Summary  of the spectral  power-law  exponents  of the  mid-thermocline temperature.  117  Summary o f t h e i n f e r r e d d y n a m i c s .  119  xi  LIST OF FIGURES  Figure  II-1  Locations  of  the  XBT  data  used  i n  this  investigation.  Figure  II-2  Anr e x a m p l e o f t h e XBT s p a t i a l s e r i e s each c r u i s e t o check f o r d i g i t i z a t i o n  Figure  II-3  II-4  Plots  of the inferred  III-1  Global  mesoscale  altimeter  Figure  III-2  The  ground  III-3  Eddy  variability  energy  Standard deviation a variable  from  regions  N0DC h i s t o r i c a l s h i p F i g u r e -1.11-4  SSS  for  collinear  SEASAT  tracks.  s i x geographic  kinetic  salinity.  sections.  i n v e s t i g a t i o n a r e shown w i t h Figure  showing t h e  SSS a n d t h e b u c k e t  e a c h o f t h e CAF s i n g l e - s h i p Figure  errors.  Map o f t h e P a c i f i c a n d A t l a n t i c O c e a n s T-S a n d S-Z c u r v e s u s e d t o i n f e r  Figure  produced f o r  as  f o r this  t h e XBT d a t a s e t .  (cm /s ) 2  drift  defined  2  obtained  from  the  file.  o f t e m p e r a t u r e a t 260 m b a s e d o n  grid analysis  o f t h e NODC XBT f i l e  north  o f 10°S. Figure  III-5  Surface  currents  of  the  Atlantic  and  Pacific  Oceans. Figure  III-6  SXBT  section  Preserver,  (PE-071082) i n  October  collected 1982  by  across  t h e HMCS the  North  Atlantic. Figure  III-7  Temperature  (°C) s e c t i o n  t h e USN m u l t i s h i p Figure  III-8  Maps 150  obtained  from  s u r v e y a t 33°N i n t h e NWA.  o f temperature t o 200 m  (72-001276)  (°C) v e r t i c a l l y - a v e r a g e d  i n t h e NWA,  c o l l e c t e d b y t h e CAF.  from  multiship  from  surveys  xii P a  Figure III-9  Temperature  (°C) s e c t i o n s  from  t h e USN  Temperature  36  (°C) s e c t i o n  t h e HMCS S a g u e n a y  (SY-051081)  c o l l e c t e d by  (CAF) a c r o s s t h e N o r t h A t l a n t i c i n  October 1981.  Figure  III-.11  38  Map o f v e r t i c a l l y - a v e r a g e d t e m p e r a t u r e to  200 m  1982  i n t h e NEA o b t a i n e d b y t h e C A F , O c t o b e r 38  F i g u r e 111-12  Temperature  (°C) s e c t i o n s  F i g u r e 111-13  Temperature  (°C) s e c t i o n  t h e HMCS Q u ' A p p e l l e  F i g u r e 111-14  Temperature  CAF  (°C)  temperature  section  Detailed  Figure III-17  North 1979  from  of  vertically-averaged  150 t o 200 m  of t h e North  Pacific  taken  the  Front  1980 a n d May 1 9 8 2 .  temperature eddy  survey  (°C)  found  44  sections  of  i n t h e March  the  1980 CAF  (GU-270380) i n t h e NEP.  46 temperature  150 t o 200 m t a k e n i n t h e v i c i n i t y  Pacific  Subtropical  Front  between  of the  December  a n d F e b r u a r y 1980.  from  Equatorial 1981  i n  Subtropical  47  USN AXBT s u r v e y s o f v e r t i c a l l y - a v e r a g e d (°C)  t h e HMCS  42  USN AXBT s u r v e y s o f v e r t i c a l l y - a v e r a g e d (°C)  Figure III-18  by  November 1 9 8 2 .  (°C) f r o m  anticyclonic multiship  42  collected  surveys  between F e b r u a r y  F i g u r e 111-16  c o l l e c t e d by  ( C A F ) f r o m Samoa t o H a w a i i i n t h e c e n t r a l  multiship  vicinity  (QE-251182)  40  (CAF) i n t h e NEP, f r o m H a w a i i t o  equatorial Pacific,  III-15  f r o m t h e NODC i n t h e SA.  I s l a n d i n November 1 9 8 2 .  Qu'Appelle  Figure  (°C) f r o m 150  (ME-041082).  Vancouver  e  multiship  s u r v e y s i n t h e NWP.  F i g u r e 111-10  9  150 t o 200 m t a k e n  temperature  i n the North  Pacific  C u r r e n t s o u t h o f H a w a i i , between  January  and A p r i l 1981.  50  xiii Page F i g u r e 111-19  CAF  SXBT  survey  temperature North  (°C)  Pacific  (QE-141182)  of v e r t i c a l l y - a v e r a g e d  from  150  100  to  Equatorial  m  taken  across  Countercurrent,  the  November  1982.  F i g u r e 111-20  USN  53  AXBT  survey  temperature Hawaii,  F i g u r e 111-21  CAF  (°C)  16 J a n u a r y  to  vertically-averaged  200  m  taken  north  of  1981.  54  Zealand  to  Samoa, November 55  Temperature  Examples  (°C)  of  section eastern  the  (24-230483)  spatial  the  obtained  from 57  SP.  series  s e c t i o n s i n t h e NWP  Sample p l o t s o f and  of  .  trans-oceanic F i g u r e IV-2  150  f r o m New  t h e NODC i n t h e  F i g u r e IV-1  from  SXBT s u r v e y  1982.  F i g u r e 111-22  (AA-16081)  averaged  of  T  and  and  D  for  NEP.  isotropic,  61 meridional  zonal a u t o c o r r e l a t i o n f u n c t i o n s f o r the  NWP  and  NEP. Figure  IV-3  78  Examples  of  the  normalized  variance-conserving  spectra. F i g u r e IV-4  84  Examples  of  confidence  the  variance-conserving  spectra  with  limits.  85  F i g u r e IV-5  Normalized  variance-conserving  s p e c t r a of  T.  88  F i g u r e IV-6  Normalized  variance-conserving  spectra of  D.  91  F i g u r e V-1  The  dominant  plotted  F i g u r e V-2  length  in relation  (L) to  and  the  i s o p l e t h s of  wave s t e e p n e s s p a r a m e t e r  (M).  Sample  the  plots  representations.  of  velocity  (U)  scales  the  Rossby 107  log-log  spectral 116  xiv  ACKNOWLEDGEMENTS  F i n a n c i a l support acknowledged. contract (UBC)  was r e c e i v e d from a number o f sources and i s g r a t e f u l l y  These  with  include:  t h e Defence  and D.P. K r a u e l  a  research  Research  assistantship  Establishment-Pacific  (RRMC), s e v e r a l  teaching  Science  and E n g i n e e r i n g  Mysak (UBC), K. Groot and  t y p i n g s e r v i c e s f o r the production  a  by W.J. Emery (1981-85)  from  S t r a t e g i c Grant h e l d by L.A.  ( M c G i l l ) , and p a r t - t i m e  of t h i s  from  a s s i s t a n t s h i p (1985-86) from a  Research C o u n c i l  (PBS) and K. Hamilton  held  assistantships  the Department o f Oceanography, UBC, a r e s e a r c h Natural  (1981-85)  thesis  employment  (1985-86) from Dobrocky  Seatech L t d . , Sidney, B.C..  The  ship-of-opportunity  without t h e c o o p e r a t i o n Pacific,  the o f f i c e r s  program c o u l d n o t have been s u c c e s s f u l l y completed  and a s s i s t a n c e  o f t h e Defence Research  and crews o f t h e n i n e t e e n  Canadian Armed F o r c e s  t h a t p a r t i c i p a t e d , P. Nowlan (UBC) and N. S u t h e r l a n d provided  The  access  encouragement and support  i s extended  over the l a s t two y e a r s .  o f t h e t h e s i s and s h o r t  tenure  t o L.A. Mysak  G.  services  Louttit,  o f A.  P. Greisman  Weaver,  on t h e s u p e r v i s o r y  and G. Swaters.  the heroic  typing  for  his  I am g r a t e f u l t o M. Bowman  B e n e f i c i a l d i s c u s s i o n s were h e l d w i t h A. Bennett, A. B l a s k o v i c h , Harper,  supervisory  P.H. L e B l o n d and S. Pond, i s g r a t e f u l l y  A s p e c i a l acknowledgement  h i s review  R. Thomson k i n d l y  s u p e r v i s o r , W. J . Emery, and my  committee, c o n s i s t i n g o f D.P. K r a u e l ,  for  (RRMC).  vessels  t o t h e UBC computing system from Sidney, B.C.  guidance from my r e s e a r c h  acknowledged.  Establishment-  committee.  D. Dunbar, J .  The c o u r i e r and h o s t e l r y  exploits  o f D.  Duncan  and t h e  s u b s t a n t i a l c o n t r i b u t i o n s o f time and e f f o r t by my Mom and Dad t o p r o o f r e a d i n g t h i s t h e s i s were very much  A  very  s p e c i a l thanks  i n s p i r a t i o n and support  appreciated.  i s due t o Joanne,  Keith  and E l i z a b e t h  for their  d u r i n g my s t u d i e s a t UBC and f o r l i v i n g i n p o v e r t y  a t y r a n t f o r t h e l a s t y e a r (or s o ) .  with  1 I.  The  purpose  variability (i.e.  of  100  of  the  this  synoptic  to  1000  bathythermograph  (XBT)  single-ship from  the  the  Pacific  descriptive governing  and  dynamics  will  motions  that  the  exhibit  demonstrated  a  XBT  The  existence of  disturbances 1936  beginnings  noted  a  several  form of  the  south.  Swallow's f l o a t s  similar  North  scales  S t r e a m and  work  isolated  the  eddy  has  Pacific  r i n g s of  (Roden,  with  consistent  number a n d  with  to  1977; trace  the  Ebbesmeyer and the  600  been  evolution  1977)  current  done  km  and  movement o f  general Taft, of  have i n the  several  hydrographic  distribution, respect  National  the  discussed  regions of  the  and  the  models.  of  that  the  It  which  reflect  a  is  baroclinic has  been  perturbations  of  Fuglister,  currents exceeding  since  shown t o  Historical  and  using  geographic  form  b e e n known s i n c e a t  north  i n t h e same d e c a d e c l e a r l y  and  waves.  obtained  dynamics.  c r u i s e s l e d by  w a v e l e n g t h s b e t w e e n 400 be  to  these  to  v a r i a b i l i t y using a wide v a r i e t y of data bases. the  surveys,  variability  scales  mesoscale  quasi-synoptic  s i x geographic  be  the  expendable  the  Gulf  of  least  Stream.  The  i n v e s t i g a t i o n s i n t o t r a n s i e n t o c e a n c u r r e n t s came i n  w i t h d e p t h s o f up t o 4 0 0 0 m a n d  in  mesoscale  dynamical  i n t h e mean f l o w , h a s  strong  1950s w i t h a s e r i e s o f  Extensive  will  variability  that  oceanic  of  Navy  geographic  velocity  of  geographic  dynamic f e a t u r e s of mesoscale dimensions, i n the  of concentrated  Gulf  compiled  and  mesoscale  or d i s c r e t e eddies  when I s e l i n  the  governing  from  the  quasi-synoptic  States  The  length  and  the  multiship/AXBT  statistics  intensity  of  were s o r t e d i n t o  inferred  sets,  determine  was  United  Oceans.  wavenumber be  set and  the  to  from  data  These data  dominant  data  and  sections  Forces,  the  v a r i a b i l i t y of the  A  geographic  for  climatological  dynamics  Atlantic  fields  hypothesized  statistics  surveys.  Armed  and  is  wavelengths)  Oceanographic Data Center. in  investigation  km  trans-oceanic  Canadian  INTRODUCTION  several  thrown o f f t o  10 cm/s  the  (Rhines,  north  region  of  20°  models  of  to  the  Gulf  Stream Rings i n the  Satellite-tracked Stream  Lai  to  linear  quite  were  Rossby  determine  the  Sargasso  Sea  and  buoys have  Rings  with  50°N, w h i c h  free  been u s e d  1971;  surveys  disturbances  have  (Parker,  eddies  mesoscale  C l a s s i c a l hydrographic wavelike  and  1977).  this  data  Gulf  instantaneous  showed d e e p d i s c r e t e  XBT  circulation  1979).  the  investigate  shown  idealized  t o map  Richardson, been  able  to  successfully  2 (Richardson,  1979).  Several  hydrographic  and  d a t a a t Ocean Weather  XBT  Emery  and  Magaard,  study  the  variability  1976). of  the  sea  surface  1976), t h e h i s t o r i c a l h i s t o r i c a l XBT  temperature  Deschamps e t a l . ,  SEASAT  the h i s t o r i c a l  (Cheney  et  (Dantzler,  1977;  a l . , 1983;  Fu,  (White  time  and  t e c h n i q u e s have field  series  Walker,  been  employed  1981; Van W o e r t , 1 9 8 2 ) .  ship  drift  Valuable  1980),  E m e r y , 1983a) a n d s a t e l l i t e and  GOES-3  have  ( W y r t k i et_ a l . ,  ( L u t j e h a r m s and B a k e r ,  1983)  to  1972b;  variability  data f i l e  of  1974;  (Saunders,  of the mesoscale  hydrographic data f i l e  data f i l e  analysed long  stations  of the geographic inhomogeneity  b e e n p r o v i d e d by u t i l i z i n g  from  have  Remote-sensing  H o l l o d a y a n d O ' B r i e n , 1975; descriptions  investigators  the  altimetry  (Robinson  et a l . ,  1983).  In  the  last  decade,  the  capability  coverage o f l a r g e r e g i o n s of the ocean  of  XBTs  to  obtain  has been demonstrated.  quasi-synoptic Saunders  (1971)  o b s e r v e d t h e e v o l u t i o n o f an i s o l a t e d eddy n o r t h o f t h e G u l f Stream w i t h AXBTs. Bernstein several  and  White  sets  of  investigators North  distribution  500  were  South  over space and time  POLYGON  of  A picture one  The  for  of  km  of  this  statement about  subtropical  of  XBT  wavelengths  i n the  Grachev,  with  1981).  of the  c a n be  dynamics  has  of  Basin  surveys of  the  use  XBT  The  same  mid-latitude  in  the  energy Similar  (Schmitz,  1981)  Ship-of-opportunity  and  programs  s u b s t a n t i a l amounts o f  significantly specific  linear  data  1975  and  t o the  data  has  examining  the  mesoscale  Similarly,  surveys  of the s t a t i s t i c s  thesis  At  At  turbulent.  their  has o n l y been t o u c h e d on. XBT  ocean.  emerged.  wave p r o c e s s e s .  for  1978)  knowledge  regions of the  exploited.  quasi-synoptic  geographic v a r i a b i l i t y  the oceanic mesoscale motions.  with  The  170°W.  q u a s i g e o s t r o p h i c dynamics  r e p r e s e n t e d as  to  km  1979).  n o t as y e t been  investigation  gyre.  1 9 7 3 ) , MODE (MODE G r o u p ,  quasi-synoptic  600  i n the  t h e m o t i o n s c a n be c o m p l e t e l y n o n l i n e a r a n d  of  of  decrease east  Newfoundland  have c o n t r i b u t e d  intense  data  magnitude  determining the geographic v a r i a b i l i t y  intent  of  order  (White and B e r n s t e i n ,  the motions  and  set  wavelength  and a r e c o n t i n u i n g t o , y i e l d  dynamics,  potential  statistics  different  (Lutjeharms,  ( R o b i n s o n , 1982)  other extreme,  dominant  Pacific  conducted Africa  a  North  1000  of the d i v e r s i t y  extreme,  a  ( K o s h l y a k o v and  POLYMODE mesoscale  the  an  to  u s i n g XBTs h a v e b e e n ,  and  in  observed  at  investigations to  XBTs  determined  (1977), w i t h  Pacific,  adjacent  (1974)  and  use  I t i s the to  make  a  the  dynamics  comprises s i x chapters.  Chapter  3 II describes The  the  collection  d e s c r i p t i v e analyses  l e n g t h s c a l e s and  and  are  processing  typical  statistical  a m p l i t u d e s of  variability 400  m).  the  variables  c e n t r a l moments a n d  discuss  the  variability  Pacific,  the  quarters  of  region the  of  the  with  year.  length  wavenumber  the  the  The  and  geostrophic and  spectra.  In  the  Rossby waves a r e  scales  Chapter  the  examined  V,  each  the  variability  the  key  terms  Northeast  over  the  four  from  the The  from  the  quasigeostrophic and  free linear baroclinic  are  compared w i t h  conclusions,  of  The  estimated.  of  -  are  s c a l i n g parameters  p r o p e r t i e s of  The  the  determined  applicability  turbulence.  (0  field.  obtained  are  are  quasigeostrophic The  for  are  energies  region  mesoscale  anomaly  eddy  surveys  spectra  t h e wavenumber s p e c t r a  geophysical  geographic  are  for  e v a l u a t i n g the  e x a m i n e d and  nonlinear  fields  of  the  these variables  mesoscale  distribution  examined  the  geopotential of  the  contains  represent  the  eddy k i n e t i c  t h e R o s s b y wave s t e e p n e s s p a r a m e t e r .  summarize  to the  velocity  with different  IV  of  most even  velocity  d y n a m i c s i s i n f e r r e d by  of  used  set.  d e l i n e a t e d and  Chapter  wavenumber s p e c t r a  mesoscale  g e o p o t e n t i a l anomaly s p e c t r a  models  are  data  i n each r e g i o n are  maps.  geographic v a r i a b i l i t y  seasonal  dominant  eddy v a r i a b i l i t y and  XBT  Geographic regions  mesoscale s t r u c t u r e are  sections  Two  quasi-synoptic  - t h e m i d - t h e r m o c l i n e t e m p e r a t u r e and  The  used t o  temperature analyses.  the  i n Chapter I I I .  d e s c r i p t i v e c h a r a c t e r i s t i c s of the with  of  statistics  several  i n Chapter  and  the  VI,  inferred  dynamics.  It The  i s important  oceanic  to  mesoscale  wavelengths) of  define  several  is  high-wavenumber  a  variability  compared t o the  c u r r e n t s , which i s comparable t o the  statistical  to the  (A) al.  of a feature 1982),  X =  circulation origin,  study,  ( B e r n s t e i n and  applies  The  velocity  or  features  property  behavior  mechanical  The and  "eddy"  I t includes  (Emery,  a r o t a t i o n a l motion. (AXBT)  term  or  The  term  individual  to  the  closed  caused  bathythermographs  (SXBT) (MBT).  The  by  a  A  wide  no  list  ocean  (XBT)  a l l  cells  and  variety  of  eddy"  of or  features  with  includes  both  term  the  et  of  connotations  This  Due  (Emery  "discrete  of  km  wavelength  circulation  closed circulation  A  the  description  "eddy" has  probes.  1000  representation  relation  term expendable bathythermograph ship-launched  of  thesis.  radius.  1977). the  the to  a convenient  r o t a t i o n a l motion.  signify  100  deformation  ( L ) by  individual  fluctuations  1983b).  (i.e.  White,  2TTL.  " i s o l a t e d eddy" i s used t o  include  Rossby  scale  dynamical  air-launched  internal  i s r e l a t e d to i t s length  mesoscale p e r t u r b a t i o n s . space/time  band  throughout  l a r g e - s c a l e mean f l o w  methods employed i n t h i s  of length s c a l e s i s the wavelength  used  does  not  symbols  and  a  list  of the abbreviations  immediately  used  a f t e r the Table of  regularly  Contents.  throughout  the  thesis  can  be  found  5  II.  The  collection  described i n this large  States  was  Armed  curves;  analyses  using  Oceans,  10,000  individual  States  Center  83 s e t s  set  Navy  (NODC).  o f XBT d a t a  XBTs a c q u i r e d (USN),  i s  These  temperature-salinity  oceanographic  variables  were  from t h e  and t h e United temperature-depth  subjectively t o delete questionable  o f t h e m e s o s c a l e eddy  data  data;  salinity  (T-S) and s a l i n i t y - d e p t h were  calculated  for  the  variability.  DATA COLLECTION  The  XBT  reasonable  data  set,  coverage  l o c a t i o n s o f these were p r o c u r e d the  Data  historical  and s e v e r a l  over  the United  Oceanographic  XBT  t o examine t h e mesoscale s t r u c t u r e over a  and A t l a n t i c  (CAF),  p r o f i l e s were f i l t e r e d inferred  of the quasi-synoptic  I n order  comprise  Forces  National  (S-Z)  A.  chapter.  These d a t a  Canadian  (T-Z)  and processing  portion of the Pacific  obtained.  THE DATA SET  Canadian  obtained  from  of the Pacific  data  t h e C A F , USN  and A t l a n t i c .  a n d NODC, Figure  pn a M e r c a t o r p r o j e c t i o n o f t h e oceans.  while  t h e USN a n d NODC  data  were  a  I I - 1 shows t h e T h e CAF d a t a  by managing and implementing a s h i p - o f - o p p o r t u n i t y Navy,  provides  acquired  program from  with  archived  files.  The  C a n a d i a n Armed F o r c e s  CAF  destroyer  February  squadrons  1980 t o J u n e  were o b t a i n e d  Data  were  1983 t o c o l l e c t  on a c o n t r a c t  and  North  Eleven  single-ship sections  Atlantic  i n a  ship-of-opportunity  quasi-synoptic  from t h e Defence Research  t o W.J. Emery a n d D.P. K r a u e l . trans-oceanic  used  SXBT  These  data  Establishment  - Pacific  c r u i s e s were conducted, r e s u l t i n g i n t e n  and nine  multiship  surveys  i n the Pacific  Oceans-  overseas  deployments  Canada.  On e a c h  when  t h e course  was, f o r t h e most  c r u i s e , SXBTs a n d s e a s u r f a c e  f r o m one o f t h e s h i p s  salinities  f o r t h e e n t i r e voyage.  S S S p e r 25 km o v e r r a n g e s o f a b o u t 4000 km.  squadrons  part,  from  directly  (SSSs) were  The s q u a d r o n s  c r u i s e d a t s p e e d s o f 13 k n o t s , r e s u l t i n g i n a h i g h s a m p l i n g and  from  data.  D a t a w e r e c o l l e c t e d o n t h e r e t u r n p a s s a g e o f CAF d e s t r o y e r  hourly  program  to  taken  generally  d e n s i t y o f o n e SXBT  Depending on o p e r a t i o n a l and  Figure II-1  Locations of the XBT data used In t h i s investigation. a. A l l of the XBT data. b. CAF data.  Figure II-1  Continued. c. USN data. d. NODC data.  8 t r a i n i n g r e q u i r e m e n t s , m u l t i s h i p s u r v e y s were c o n d u c t e d . surveys v a r i e d  from  40 t o 180 km  three or four ships. this  An  British  Columbia  with  program  on-board  The  of  XBT  (Anderson,  of  19  technician  different  or  student from  on  each  College  cruise.  i s widely  used,  l a u n c h e r were u s e d  were  t h e T-4  p r o v i d e d by  probe  1979; S i p p i c a n ,  so  with  supply  the University  were  the  of  assisted  responsible f o r  details  The  and  5  or  on  using  each  the  servo-amplifier gain,  station.  XBTester  system.  The  Model  A-4  for  Sippican  The  whichever  The  reported  is  greater  and  faulty  o f thumb, no more  systems  were  tested  temperature  be  strip-chart  SXBTs w e r e t a k e n e v e r y h o u r  XBT  used  A MK2A-1  +2%  two p r o b e s were  not  w i t h o u t systems.  supply  m  will  consisting of  the ships  t h e CAF's  i s +_0.2°C 1975).  on  As a r u l e  cruise  i n length  monitored and  They  o r s u s p e c t SXBTs w e r e i m m e d i a t e l y r e p e a t e d .  each  km  d e s t r o y e r s and  r e c o r d e r s and deck-mounted l a u n c h e r s .  (460 m)  of  total  the data  system  and h a n d - h e l d  accuracy  1300  M o s t o f t h e CAF s h i p s h a d SXBT s y s t e m s  MK2A-1 s t r i p - c h a r t  probes  to  c o n t r o l and c o o r d i n a t i o n o f t h e m u l t i s h i p s u r v e y s .  discussed here.  T-4  a  (UBC) o r R o y a l Roads M i l i t a r y  Sippican  recorder  -  scientist,  the c o l l e c t i o n  on-site quality  600  Each o f Canada's f o u r d e s t r o y e r s q u a d r o n s p a r t i c i p a t e d i n  observational  ships.  i n w i d t h and  The c o v e r a g e o f t h e s e  than  prior  to  calibration,  l a u n c h e r i n s t a l l a t i o n r e s i s t a n c e and servo response.  The  c a l i b r a t i o n was s u b s e q u e n t l y c h e c k e d e v e r y s i x h o u r s .  The t e m p e r a t u r e p r o f i l e s traces good  (Department  T-Z  traces  interpolation digitized fall  rate  o f t h e Navy,  were  would  provide  at  the  reasonable  performed  minicomputer.  system on The  a  for failures  returning  inflection  corrected f o r the nonlinearity  linearity  data  response  were  DTR-3036  (GTO  transferred  each  suspect  cruise.  such  that  f o r a l l depths. of the trace  1970).  due  The linear The t o the  These o p e r a t i o n s  Corporation)  to  and  (temperature) a c c o r d i n g t o  equations (Sippican,  Datatizer  from  points,  temperatures  (depth) and t h e s e r v o - a m p l i f i e r XBT  inspected  1978) u p o n  digitized  v a l u e s were  Sippican's were  were v i s u a l l y  UBC's  Amdahl  and  LSI-11/23  V8  mainframe  computer.  SSS  was  obtained from  bucket  samples  The samples were r e t a i n e d i n 4 oz g l a s s analysis.  The  conductivity  ratios  taken  sample  were  immediately  bottles  measured  after  each  SXBT.  a n d r e t u r n e d t o UBC f o r  using  a  Guildline  Autosal  9 Model  8400  Salinity  salinometer.  Scale,  salinometer  The  1978  has  (Pond  salinities and  were  Pickard,  estimated  1983).  a  manufacturer's  reported  equivalent s a l i n i t y .  The s a l i n i t i e s  of the f i r s t  P a c i f i c , were o r i g i n a l l y  x  10  ,  over  corrections  the  were  estimated from,  The  Radar  observed  made.  range  Thus,  used. adjacent  SSSs  employed  to obtain  possible,  ships.  of  used  (32  i n this  during  Overall,  varied  +^.003  10~3  Although the  36  x  .003  10~ ),  the  have  been  3  investigation S c a l e , 1978.  depending  on t h e v e s s e l and t h e and r e l a t i v e f i x .  n a v i g a t i o n , Loran-C  m u l t i s h i p surveys,  the absolute  x  i s l e s s than  to  possible absolute  satellite  Autosal  two c r u i s e s , i n t h e N o r t h e a s t  salinity  the best  on p o i n t s o f l a n d ,  When  accuracy  or corrected to, the Practical Salinity  i n order  fixes  of  Practical  Guildline  two methods o f e s t i m a t i n g s a l i n i t y  n a v i g a t i o n a l methods  location,  The  the  e s t i m a t e d u s i n g t h e 1966 UNESCO t a b l e s .  d i f f e r e n c e s between t h e s e - 3  using  radar  n a v i g a t i o n was  a n d Omega  fixes  were  considered  were  taken  on  t o be  much  CAF d a t a w e r e f o r m a t t e d a n d a r c h i v e d f o r f u r t h e r p r o c e s s i n g a l o n g  with  b e t t e r t h a n + 5 km.  The  t h e USN a n d NODC d a t a . (Thomson e t a l . ,  The  U n i t e d S t a t e s Navy  Data  The  i n this  USN d a t a u s e d  multiship Wilson  1979;  from  SXBT s u r v e y s ,  a n d Dugan  investigate  a r c h i v e d data  were  various aspects  obtained  from  (Emery,  personnal  i n the North  acquired.  prepared  collected  i n three  separate  Data  s i x trans-oceanic  1981).  from  and North  were  Atlantic  by  p r e v i o u s l y used  to  variability  1983).  b y t h e USN, w e r e p r o c u r e d .  (Emery  A l s o , two d a t a The f i r s t  s e t i s from front,  The s e c o n d  of five  s e t i s from  and f o u r  -  surveys  These two d a t a  one  a  series  Laboratory  survey  i n the North  on  the  Pacific  s e t s o f AXBT s u r v e y s  et^ a l . ,  sets  i n the region of the subtropical  communication)  northeast of Hawaii  data  eddy  t h e U n i t e d S t a t e s Naval. Research  south of Hawaii.  was  Pacific  These  of t h e mesoscale  northeast of Hawaii (Miyaki,  were  files.  1 9 8 0 ; H a r r i s o n et^ a l . ,  AXBT s u r v e y s c o n d u c t e d  Miyaki  r e p o r t o f t h e CAF d a t a  investigation  conducted  (1978),  Emery et_ a l . ,  surveys  data  1984b).  programs and o b t a i n e d  by  A detailed  from eight  collected surveys  i n Washington, subtropical  D.C. front  Equatorial Current  have n o t been p u b l i s h e d ,  n o r have t h e y been u s e d t o s t u d y t h e eddy v a r i a b i l i t y o f t h e s e r e g i o n s .  10 Model  8400  Salinity  salinometer.  Scale,  salinometer  1978  (Pond  salinities and  were  Pickard,  manufacturer's  reported  equivalent salinity.  The s a l i n i t i e s  of the f i r s t  were o r i g i n a l l y  10~ , 3  over  corrections  the  were  e s t i m a t e d from,  The  Radar  observed  made.  used.  range  Thus,  adjacent  of  SSSs  salinity  used  (32  i n this  employed v a r i e d  to obtain  the best  on p o i n t s o f l a n d ,  When p o s s i b l e , ships.  of  during  Overall,  satellite  the absolute  x  10  - 3  Although the  i s less 36  x  than  .003  10~ ),  the  have  been  3  investigation S c a l e , 1978.  on t h e v e s s e l and t h e  absolute  and  n a v i g a t i o n , Loran-C  multiship surveys,  Autosal  i n the Northeast  tables.  to  depending  possible  Practical  _+. 003  two c r u i s e s ,  or corrected to, the Practical S a l i n i t y  i n order  fixes  accuracy  the  Guildline  two methods o f e s t i m a t i n g s a l i n i t y  n a v i g a t i o n a l methods  location,  using  The  e s t i m a t e d u s i n g t h e 1966 UNESCO  d i f f e r e n c e s between these x  estimated  1983).  a  Pacific,  has  The  radar  n a v i g a t i o n was  relative f i x . a n d Omega  fixes  were  considered  were  taken  on  t o be much  b e t t e r t h a n + 5 km.  The  CAF d a t a w e r e f o r m a t t e d a n d a r c h i v e d f o r f u r t h e r p r o c e s s i n g a l o n g w i t h  t h e USN a n d NODC d a t a . (Thomson e t a l . ,  The  detailed  data  r e p o r t o f t h e CAF d a t a  was  prepared  collected  i n three  separate  Data  s i x trans-oceanic  1984b).  U n i t e d S t a t e s Navy D a t a  The  USN  programs  Wilson  a n d Dugan  obtained D.C.  a r c h i v e d data  were  various aspects  from  1981).  the United  (Emery, p e r s o n n a l  northeast of Hawaii south of Hawaii.  i n the North  acquired.  Pacific  These  of t h e mesoscale  data  eddy  from  and North  Atlantic  (Emery  A l s o , two d a t a The f i r s t  s e t i s from front,  The second  of f i v e  States  N a t i o n a l Research  communication)  and four  surveys  - one s u r v e y i n the North  eta l . ,  sets  i n the region of the subtropical s e t i s from  by  were p r e v i o u s l y u s e d t o  variability  1983).  b y t h e USN, w e r e p r o c u r e d .  northeast of Hawaii (Miyaki,  were  files.  1 9 8 0 ; H a r r i s o n et_ a l . ,  AXBT s u r v e y s c o n d u c t e d  Miyaki  investigation  conducted  (1978),  E m e r y et^ a l . ,  surveys  i n this  SXBT s u r v e y s ,  investigate 1979;  data used  and obtained from  multiship  by  A  a series Laboratory  eight  collected surveys  i n Washington,  on t h e s u b t r o p i c a l Pacific  from  front  E q u a t o r i a l Current  T h e s e t w o d a t a s e t s o f AXBT s u r v e y s h a v e n o t b e e n p u b l i s h e d ,  n o r h a v e t h e y b e e n u s e d t o s t u d y t h e eddy v a r i a b i l i t y o f t h e s e r e g i o n s .  11 The  N a t i o n a l Oceanographic  The  NODC XBT ( 1 9 8 4 )  synoptic sections. and  Data Center  geographic  Initially  than  cruises.  500 m, w e r e  The f o l l o w i n g  file  the f i l e  c o n s e c u t i v e XBT number.  deeper  Data  A l l cruises  removed criteria  with  f o rfurther were used  more  than  quasi-  d e s i g n a t i o n number 25 X B T s ,  examination.  to identify  for  This  i n water  yielded  53 s i n g l e - s h i p  486  cruises  t o t h e CAF a n d USN d a t a :  c r u i s e p a t h s must be r e a s o n a b l y s t r a i g h t t r a n s e c t s a c r o s s o c e a n i c r e g i o n s of  b.  1 9 8 4 ) was s e a r c h e d  was s o r t e d b y c r u i s e  w i t h a q u a s i - s y n o p t i c q u a l i t y comparable  a.  (NODC,  interest;  t h e XBT s p a c i n g  must  be  less  than  200 km  p r o v i d e t h e same h i g h - w a v e n u m b e r r e s o l u t i o n provides  a  more  efficient  ratio  o f number  (Although  this  does n o t  a s t h e CAF a n d USN d a t a , i t o f samples  to  independent  observations);  c  t h e t i m e b e t w e e n XBT c a s t s must b e l e s s t h a n 6 h o u r s ; a n d  d.  t h e c r u i s e t r a c k s must be a t l e a s t  B.  1000 km i n l e n g t h .  DATA PROCESSING The  data  s e t was p r o c e s s e d  the subsequent  descriptive  to obtain several  and s t a t i s t i c a l  oceanographic  analyses.  variables f o r  This processing included  a v i s u a l e x a m i n a t i o n o f t h e d i g i t i z e d T-Z d a t a , t h e i n f e r e n c e o f s a l i n i t y T-S  a n d S-Z c u r v e s a n d t h e c a l c u l a t i o n o f s e v e r a l o c e a n o g r a p h i c  XBT  Traces  S p a t i a l s e r i e s o f XBTs w e r e p r o d u c e d to  check  for faulty  an  example,  Vancouver increments  I s l a n d i nMarch o f depth  spatial 1980.  f o r each  c o n v e r t e d t o a common f o r m a t .  series  errors.  o f t h e HMCS P r o v i d e r ,  Temperature was l i n e a r l y  trace  variables.  f o r each c r u i s e and v i s u a l l y i n s p e c t e d  o r s u s p e c t XBTs a n d d i g i t i z a t i o n  i s t h e SXBT  from  and t h e data  from  Figure I I - 2 , as from  Hawaii t o  i n t e r p o l a t e d t o 10 m  t h e three sources  were  13 Salinity  Inference  S a l i n i t y was geopotential and  Pickard  inferring SSS  i n f e r r e d f o r e a c h XBT  anomalies. and  Emery  salinity  f r o m t h e CAF  Mean T-S  and  (1982) w e r e  fields  by  to estimate density  this  used  and  d a t a and the i n f e r r e d  Hydrocasts  Atlantic,  north of  made i n w a t e r  curves to  from  infer  m e t h o d was  Emery a n d Dewar c o m p u t e d mean T-S Pacific  S-Z  f i e l d s and  Emery  and  salinity.  e x a m i n e d by  Dewar  The  proposed  curves,  by  comparing  except  i n the  and  10°S,  the  bucket  S-Z  c u r v e s f o r a l l 5°  squares  i n the  u s i n g NODC's h y d r o g r a p h i c 500  investigators,  regions north of  50°N, 45°W i n t h e A t l a n t i c . root-mean-square salinity S-Z  (RMS)  m  were n o t  between  salinity 40°N  I n t h e s e two  error,  used,  salinity  i n t h e s e two  Southeast  Pacific,  obtained  from  T h e i r use  curves.  regions.  the  Pickard  curves from P i c k a r d  i n the  (1978)  so  these  the  Mean T-S  Pacific  and  and  Emery  Emery  i s c o n s i d e r e d t o be  S-Z  I I - 3 p r e s e n t s a map  of  r e g i o n s t h e a b o v e T-S  dynamic  S a l i n i t y was  the  curve  of  the  5°  and  f o r use  using  the  less with  South  south of  Pacific, Atlantic  10°S.  The  the were  mean  T-S  s a l i n i t y n o r t h o f 10°S.  Figure  and  Atlantic  showing  curves were used t o i n f e r  profile 5°  The  XBT  T-S  average  o r S-Z  were  created  of  the  curves  were  the center of  each  The  false use  salinity of  a  of and  weighted  problem.  on t h e a c c u r a c y o f e m p l o y i n g mean c u r v e s f o r i n f e r r i n g and t h e b u c k e t SSS  which  s o l e l y on t h e b a s i s  created  fronts.  in  salinity.  d i s t a n c e from  the  oceanic  specifically  u s i n g a weighted  squares.  of the  containing  regions of  collected)  infer  salinity  of the f o u r c l o s e s t squares s o l v e d t h i s  samples were  the  t h a n u s i n g a mean  better  average  p l o t s o f t h e i n f e r r e d SSS  inferred  substantially  f e a t u r e s i n the  As a check  was  the  the  precise.  density  water  height  found t h a t i n f e r r i n g s a l i n i t y  square  of  therefore not  the i n v e r s e of the square I t was  northwest  and  i n f e r r e d f o r e a c h T-Z  s q u a r e t o t h e XBT.  T-S  (1982) a r e h e u r i s t i c  appropriate curves of the four closest by  and  curves were, t h e r e f o r e , used t o  Sub-Antarctic  the P a c i f i c  a n d S-Z  using the  c u r v e s f o r t h e Southwest  (1982),  curves  Following the  inferred Pacific  file.  a r e a s , Emery and Dewar f o u n d t h a t  and i s c o n s i s t e n t w i t h t h e method u s e d t o i n f e r  weighted  was  and t h e dynamic h e i g h t u s i n g t h e measured s a l i n i t y ,  c u r v e s t h a n w i t h t h e T-S  of  SSS.  shallower than  these  (1982)  accuracy  r e p r e s e n t t h e o c e a n i c w a t e r s beyond t h e c o n t i n e n t a l s h e l f - b r e a k . method  calculate  f o r e a c h o f t h e CAF (Figure  II-4).  salinity,  cruises  These  plots  (where show  F i g u r e I I - 3 Map o f t h e P a c i f i c and A t l a n t i c Oceans showing t h e T-S and S-Z c u r v e s used t o i n f e r s a l i n i t y . I n t h e r e g i o n s denoted ED, t h e mean curves from Emery and Dewar (1982) f o r each 5° square were used. The t e m p e r a t u r e - s a l i n i t y and t h e s a l i n i t y - d e p t h c u r v e s were used i n t h e areas l a b e l l e d TS and SZ, r e s p e c t i v e l y . South o f 10*S, the t e m p e r a t u r e - s a l i n i t y c u r v e s o b t a i n e d from P i c k a r d and Ki&ery (1982) were: West South P a c i f i c C e n t r a l (WSPC), E a s t South P a c i f i c C e n t r a l (ESPC), P a c i f i c S u b - A n t a r c t i c (PSA) and South A t l a n t i c C e n t r a l (SAC).  15  A . HMCS PROVIDER. 2-13 FEBRUARY 1980.  01  TTCO w  BUCKET SAMPLE - SOLID INFERREO SSS - DASHED 26 N —H-  30 N H— —h 1  RANGE : ONE TICK =  38N -f—'  34N -+J—  8  42 N  h  300 KM  B.HMCS PROVIDER. 26 MARCH - 2 APRIL 1980  cn TT  8  W  BUCKET SAMPLE - SOLIO INFERREO SSS - DASHEO  f-  27 N  -+- — H -  31N —4-  H  L  RANGE : ONE TICK =  -i  35 N —h  -i  1  39 N —h  43N  1  47 N  —H-  300 KM  GHMCS PROVIDER. 1-7 MAY 1981  cn  r r cn  T  .  BUCKET SAMPLE - SOLID INFERRED SSS - DASHED 25N.  i——i—-J-H  29N  . 33 N  1—1—y— H—i  RANGE : ONE TICK =  1-  J 37 N  41N  H—'  H  45N  300 KM  Figure I I - 4 Plots of the inferred SSS and the backet SSS f o r each of the CAF single-ship sections, where water samples were collected. For each cruise the two SSSs are plotted as a function of along-track range. The small t i c k s on the central axis are the SXBT p o s i t i o n s where SSS has been i n f e r r e d .  16  Q HMCS SASKATCHEWAN. 17-24 NOVEMBER 1981. co cn cn rr <n<n  cn fcncn  BUCKET SAMPLE - SOL10 INFERRED SSS - 0ASHED 25 N  H—  1  29N  H—'  r-  RANGE : ONE TICK  r-  cn 33 N  H  37N  f-  H  41 N '—I-  300 KM  E.HMCS TERRA NOVA. 11-12 MAY 1982,  cn  •q-tn  TT  BUCKET SAMPLE - SOLID INFERRED SSS - DASHED  H  29 N  '—(-  RANGE : ONE TICK =  E  300 KM  HMCS QITAPPELLE. 2-7 NOVEMBER 1982.  tn rr  BUCKET SAMPLE - SOLID INFERRED SSS - DASHED 36 S  H—  H-  32 S  —H-  28 S -+•+-  RANGE : ONE TICK =  CM  n 24S —H—  20 S  —H-  300 KM  Figure II-4  Continued.  16S  H— —H J  45 N  —H—  17  QHMCS QU'APPELLE. 9-18 NOVEMBER 1982. 03  CO  . 14S  I  BUCKET SAMPLE - SOLID INFERRED SSS - DASHED 12S  H  10S 1  8 S  —I—  1  6 S  H  RANGE : ONE TICK =  4 S  P  2 S  H  0  H  2N 1  4 N 6 N 8 N  —I—  1  H  300 KM  Figure II-4  Continued.  H  ION  12N  '—I—'  14N  H  16N  18N  H——H—  I,  HMCS PRESERVER. 1-7 OCTOBER 1982.  BUCKET SAMPLE - SOLID INFERRED SSS - DASHED  A/ i—i  60 V  1  1  1  1  54 W  n  r  RANGE i ONE TICK =  " I T  42 V  1  1  1  36 V  48 V 300 KM.  t  1  1  30 W  1  1  ...i  1  .  12 V  18 V  1  i  \-r-  6  24 V  J.HMCS PRQTECTEUR. 22-29 JUNE 1983.  00  h  1  rH  1—i  1  1  61 W 55 V 49 V 43 W RANGE : ONE TICK = 300 KM  1  1—I 37 V  h  31 V  1  1  25 V  Figure II-4 Continued.  1  1  19 V  1  ,  13 W  1  1— 1 tf  19 very  reasonable  exceptions sections II-1  were  the  northeastern x  10~ .  11-4-  g)  has  3  general  an  this  Oscillation sections  RMS  d i f f e r e n c e of  currents  1.07  are  region  h-j)  inferring  show a v e r y  a  10~ .  have  this  in  the  salinity To  arise  front  from  region  the  1983).  the than  (Figure  SSS  exhibits  ( P i c k a r d and  El  Emery,  the north  The  Nino  three  d i f f e r e n c e s due regions  of  the east of these  water  in  the  and  North  increased precipitation  The  the  -  North to  Atlantic  difficulties  western  boundary  differences i n the  masses  curves of  t o T-Z  very  in  Southern  regions, the bucket  a p p l y i n g mean T-S  separating  Table  higher  SSSs, a c r o s s  1982-83  agreement.  Atlantic  sections  inferred  bucket  the  RMS  The  i n c r e a s i n g toward  to  high  three  (Figure II-4 g).  The  low  due  the  Notable  equatorial Pacific  3  of  during  reasonable  current regions  across  x  SSS.  d i f f e r e n c e s no  central  anomalously  (Emery a n d Dewar, 1 9 8 2 ) .  boundary  the  ( R a s m u s s o n et_ a l . ,  II-4  in  cruise.  w i t h a minimum a t a b o u t 10°N  (ENSO) e v e n t  i n f e r r e d SSS  taken  across  The  inferred  regions  a l l h a v e RMS  characteristics  equatorial  with  each  Pacific  section  (Figures  associated  current  and  equatorial Pacific  Equatorial Countercurrent,  central  measured  for  The  subtropical regions.  Pacific  the  difference  m e r i d i o n a l SSS  the  boundary  southwestern  F i g u r e 4.9)  south  western  RMS  and  0.20  1982:  the  between  ( F i g u r e s I I - 4 h - j ) and  lists  the  agreement  and  western profiles  different  T-S  characteristics.  The  anomalously  protrude curves  much  for  deeper  should  column.  the  values  in  mixed-layer  reasonable  In the western  the  salinity  boundary  saline  underestimated, variability.  the  estimates  and  slope  curves  is  much  regions  is  waters.  anomaly  60  for  most  m,  to to  so of  the  Dewar  more  f o r the purposes of t h i s  water data (1982)  rings  and  the  variability  overestimating  appropriate  T-S  rather than  will the  t h e method o f i n f e r r i n g s a l i n i t y  considered  the  the  eddy  cold-core  not  where t h e  o f Emery a n d  Thus,  due  preferable  For the above reasons,  u s i n g a mean s a l i n i t y  about  current regions, particularly  geopotential  which  i n these  of  c o n t r i b u t i o n from o f f s h o r e oceanic waters  continental shelf from  curves  the  equatorial section w i l l  depth  t h i s i n v e s t i g a t i o n w e r e o b t a i n e d , t h e T-S  determined  T-S  salinity  than  provide  a r e d o m i n a t e d by less  low  be eddy  f r o m mean  useful  than  investigation.  Oceanographic V a r i a b l e s  Further profiles  processing  were  of  required for  the each  measured XBT  temperature  i n preparation  and for  inferred the  salinity  descriptive  and  20  T a b l e II-1  RMS d i f f e r e n c e s between backet SSS and I n f e r r e d SSS f o r t h e CAF t r a n s — o c e a n i c s e c t i o n s shown I n F i g u r e II—A.  Ship  Date  RMS D i f f e r e n c e ( x 1 0 ~ )  Ocean  3  a. HMCS P r o v i d e r  F e b 80  Northeast  Pacific  0.17  b. HMCS P r o v i d e r  A p r 80  Northeast  Pacific  0.18  c. HMCS P r o v i d e r  May 81  Northeast  Pacific  0.15  d. HMCS S a s k a t c h e w a n  N o v 81  Northeast  Pacific  0.20  e. HMCS T e r r a N o v a  May 82  Northeast  Pacific  0.13  f . HMCS Q u ' A p p e l l e  N o v 82  Southwest  Pacific  0.15  g. HMCS Q u ' A p p e l l e  N o v 82  Equatorial  h . HMCS  O c t 81  North  Atlantic  1.22  1. HMCS P r e s e r v e r  O c t 82  North  Atlantic  0.93  j.  J u n 83  North  Atlantic  0.54  Saguenay  HMCS P r o t e c t e u r  Pacific  1.07  21 statistical  analyses.  will  be  used  the  geopotential  variability  The  As w i l l  t o examine  be d i s c u s s e d i n C h a p t e r s I I I a n d I V , t e m p e r a t u r e  the mesoscale  anomaly  will  i n the upper l a y e r  be  variability used  (400 m)  of the  m i d - t h e r m o c l i n e t e m p e r a t u r e was 50 m  200 m a n d 350 t o 400 m).  applicability  d e s c r i b i n g the mesoscale IV. m)  The was  examine  segments o f  variability  as  the  of  S t a t e o f Sea Water, and s a l i n i t y  1980  S i g m a - t was  and eddy  averages of  column  the  ( i . e . 150  to  of these temperature v a r i a b l e s f o r  the  (i.e.  specific  r e q u i r e d the determination of the sigma-t p r o f i l e and i n f e r r e d s a l i n i t y .  baroclinic  as v e r t i c a l  of the ocean w i l l  integral  the  the water  g e o p o t e n t i a l a n o m a l y f r o m 0 t o 4000 k P a calculated  mid-thermocline  ocean.  calculated  m e a s u r e d t e m p e r a t u r e o v e r two The  to  i n the  be  discussed i n Chapter  0 t o 400 volume  db o r 0 t o anomaly.  400 This  from the measured temperature  obtained from the I n t e r n a t i o n a l Equation of  ( M i l l e r o and P o i s s o n ,  at atmospheric pressure.  1981) w i t h t h e g i v e n t e m p e r a t u r e  22 III.  The  purpose  DESCRIPTIVE ANALYSES  of the d e s c r i p t i v e analyses  i s to qualitatively  geographic v a r i a b i l i t y  o f t h e observed mesoscale s t r u c t u r e .  with  and amplitudes  different  typical  sections  variability  A.  scales  a n d maps o f e a c h  o f the thermal  o f mesoscale  region  discuss the  Geographic  structure a r e defined and  a r e used  t o examine  t h e geographic  s t r u c t u r e i n t h e q u a s i - s y n o p t i c XBT d a t a s e t .  GEOGRAPHIC REGIONS  Geographic regions with d i f f e r e n t h o r i z o n t a l s c a l e s and amplitudes variability the  were d e f i n e d u s i n g t h e q u a s i - s y n o p t i c  a i d o f previous  1983a;  Cheney  variability  from  dynamic  height  from  A l lthree  variability interior  near  archived  yielded  a l . 's r e s u l t s ,  t h e western  using  were c o n s i d e r e d  standard  the  observed  that  contour high-  deviations o f : and i n f e r r e d  altimetry  of high  boundary used  a n d l o w eddy  currents. t o define  variability.  purpose  the  approximate  due t o t h e g l o b a l  shows t h e g e o g r a p h i c v a r i a b i l i t y  i n  Cheney e t  These  Figure III-1,  from  mesoscale  and low v a r i a b i l i t y  a l t i m e t r y , were  for this  t h e geographic  results coverage  adapted  o f t h e eddy f i e l d  from with  d e v i a t i o n o f t h e SEASAT a l t i m e t r y .  g e o g r a p h i c r e g i o n s w e r e d e f i n e d u s i n g t h e SEASAT m e s o s c a l e  distribution  and  regions  e v e n d i s t r i b u t i o n o f t h e SEASAT a l t i m e t r y d a t a .  Six  to  currents  and i n t h e eastern  most a p p r o p r i a t e  Cheney e t a l . (1983), the  with  1975; Emery,  temperature  and s e a surface  results,  boundary  o f high  (Wyrtki,  t h e standard  records,  XBT r e c o r d s ,  t h e SEASAT  between r e g i o n s  with  hydrographic  similar  sets  i n v e s t i g a t o r s examined  structure  archived  o f t h e ocean b a s i n s  boundaries  These  o f eddy  s e c t i o n s o f each c r u i s e , w i t h  c l i m a t o l o g i c a l data  o f t h e mesoscale  height  SEASAT.  work u s i n g  e t a l . , 1983).  dynamic  and  regions  structure  i n the quasi-synoptic  o f t h e data.  o f Fu (1983), i nFigure  The'se r e g i o n s  as areas  of high  regions.  low-energy l e v e l s , a r e :  These  s e t and t h e geographic  were c l a s s i f i e d , o r l o w eddy  I I I - 1 , was u s e d a s a g u i d e  and low-energy  data  variability,  i n a manner  variability.  T h e 6 cm  t o d e l i n e a t e t h e boundary  geographic  regions,  classified  similar  between by h i g h -  Figure III-1  G l o b a l mesoscale v a r i a b i l i t y from c o l l i n e a r SEASAT a l t i m e t e r ground t r a c k s . The standard d e v i a t i o n of the a l t i m e t r y i s contoured i n c e n t i m e t e r s . The b o l d 6 cm contour separates r e g i o n s of r e l a t i v e l y h i g h and low eddy a c t i v i t y .  24 High-energy  Regions  Low-energy  Regions  NWA - N o r t h w e s t  Atlantic  NEA  Northeast  NWP - N o r t h w e s t  Pacific  SA  South  NEP  Northeast  SP  South  Two  composite  regions  were  defined  t o represent  r e g i o n s a n d t h e combined low-energy r e g i o n s . and  NWP r e g i o n s  ( i . e . t h e high-energy  NEA, S A , NEP a n d S P r e g i o n s  The  geographic  demarcation  quasi-synoptic  XBT d a t a ,  surveys,  binned  passed  were  through  both  of  geographic  Pacific  t h e combined  high-energy  regions).  The LOW r e g i o n  comprises t h e  the quasi-synoptic regions  a r e shown  XBT  data  i n Figure  and t h e III-2.  The  from t h e s i n g l e - s h i p s e c t i o n s and t h e multiship/AXBT  into high-  the appropriate and low-energy  s i n g l e - s h i p s e c t i o n s were d i s c a r d e d 1000 km i n l e n g t h .  sections  Pacific  T h e HIGH r e g i o n c o m p r i s e s t h e NWA  geographic regions,  s e c t i o n e x h i b i t e d a marked change i n t h e m e s o s c a l e  than  Atlantic  ( i . e . t h elow-energy r e g i o n s ) .  distribution  of the s i x  Atlantic  There  i f they  regions.  If a  i t was d i v i d e d expression.  cruise  where t h e  The r e s u l t i n g  h a d l e s s t h a n 25 XBTs o r w e r e l e s s  are a total  o f 95 t r a n s - o c e a n i c  single-ship  ( h e r e a f t e r known a s s e c t i o n s ) a n d 29 m u l t i s h i p / A X B T s u r v e y s  (hereafter  known a s s u r v e y s ) .  B.  GEOGRAPHIC VARIABILITY OF THE THERMAL STRUCTURE  The  purpose  of this  section i s t o describe  t h e b a r o c l i n i c eddy f i e l d data  set.  Typical  as expressed  temperature  by  important each  researchers  sections  and t o demonstrate  s y n o p t i c XBT d a t a  that  aspects  the global  geographic revealed  sets.  fields  sets  geographic  region are i n previous  I t i s  o f t h e mesoscale  t h e eddy  c l i m a t o l o g i c a l data  t o examine  each  eddy v a r i a b i l i t y  s e tare consistent with previous  different  investigators,  from  c l i m a t o l o g i c a l data  t o examine t h e q u a l i t a t i v e  region  Three  using  variability of  i n t h e t e m p e r a t u r e s t r u c t u r e o f t h e XBT  examined a n d compared t o t h e geographic works  t h e geographic  observed  considered  variability i n i n the quasi-  observations.  have  been  variability  used,  by  other  o f t h e mesoscale  F i g u r e III-2  The s i x geographic r e g i o n s as d e f i n e d f o r t h i s i n v e s t i g a t i o n a r e shown w i t h the XBT data s e t . The r e g i o n s d e s i g n a t e d as h i g h eddy energy areas a r e s t i p p l e d .  26 eddy  field.  The  historical Figure  ship  III-3.  field  g l o b a l map drift  Figure  o b t a i n e d by  altimetry. grid  file  The  the  (adapted  eddy  kinetic  from  I I I - 1 presents  Wyrtki  the  the  XBT  file  North  (1983a) i n F i g u r e  These t h r e e d i f f e r e n t g l o b a l eddy f i e l d  f o r the  current  previously discussed,  As  a l t i m e t r y d e v i a t i o n map  of  12 a n d  are  9 cm  found  standard  are found  i n the  NEA,  d e v i a t i o n of  August of  1978), the  sampled.  Fu  drift  in  with the  low  and  600  cm /s drift  values  altimetry  by  energy  Wyrtki  cm /s 2  NWA  due  over  i n the  variable  Atlantic,  has  variability  of  cm  western  eastern  contour  of  boundary  the  SEASAT  of  In Figure I I I - 1 , high  3  cm  i n the  of  the t r a n s f e r  Low  values of 4  NEP  and  cm  SP.  The  eddy p o t e n t i a l energy  (EPE)  24  SA,  values  days o f d a t a were used ( i n 24  days were  f u n c t i o n of t h i s  inadequately  24-day f i l t e r  f r o m 50  to  150  and  days  (EKE)  map  (Figure I I I - 3 ) , represents  The  1000 SA  EKE  cm /s 2  and  SP.  2  maximum  the  The  altimetry  and  of  the  1000  and  5 cm  maximum v a l u e s about  values  NWP.  ship  Minimum  drift  determined  from  barotropic signal.  of Figure I I I - 1 ,  has in  the  as  was  data  can of  be over  values  were  not  seasonal  signal  of  the  Atlantic  i n the  Oceans.  cm /s  SEASAT a l t i m e t r y  2  which  are  implies a ratio  equatorial regions  III-3  and  defined using 2000 of  cm /s 2  about  corrected f o r  of  compared  to  the  Figure III-3  to  the  about has  maximum v a l u e s  one-quarter  This  explains  F i g u r e I I I - 1 shows d e v i a t i o n s o f  regions.  equal  currents  f o r the  western  one-half  the of  SEASAT of  the  equatorial values i n the  NWA.  eddy k i n e t i c  boundary  2  300  i n the e q u a t o r i a l regions  e q u a t o r i a l regions, which are  i n the high-energy 2  winds  ship  . Highl-  t o t h e w i n d a c t i n g o n t h e v e s s e l s , t h u s o v e r e s t i m a t i n g t h e EKE.  both the P a c i f i c  the  SEASAT  near the  and  respectively.  d i s t i n c t d i f f e r e n c e between F i g u r e I I I - 1 and  in  6  represents the  et^ a l . ( 1 9 7 6 ) ,  contour.  2  and  occur  2  eddy  been u s e d as a guide f o r d e l i n e a t i n g  Since only a t o t a l  (1983) d e t e r m i n e d  overestimate  of  geographic  energies at periods longer than  eddy k i n e t i c  data  the  North  interior  the  NWP,  low-energy r e g i o n s , s i m i l a r t o those  2  and  in  suppressed.  The  the  the  (Figure I I I - 2 ) .  i n t h e NWA  the  b a s e d on a  t h a t the b u l k of the mesoscale energy a t p e r i o d s  severely  and  i n the  ( F i g u r e I I I - 1 ) has  of the b a r o t r o p i c s i g n a l .  found  activity  low-energy regions  of  a t 260  t h a t show r e g i o n s o f h i g h e d d y a c t i v i t y eddy  shown  d e v i a t i o n of  m,  the  is  standard  Pacific  s t u d i e s o f f e r views of  low  t h e h i g h - and  variability  from  III-4.  boundary c u r r e n t s and regions.  computed  et_ a l . , 1976)  the  standard d e v i a t i o n of temperature  a n a l y s i s of  energy  geographic  C h e n e y e_t a l . ( 1 9 8 3 ) u s i n g  b e e n a d a p t e d f r o m Emery  the  of  current  The  energies regions.  27  Figure  III-4  S t a n d a r d d e v i a t i o n o f temperature a t 260 m based on a g r i d a n a l y s i s o f the NODC XBT f i l e n o r t h o f 10°S.  variable  28 The  ship d r i f t data provide  the  equatorial regions,  relatively  higher  equatorial  regions  current order  of  days  variability  wind  and  data  that data.  the western III-3),  of  be n o t e d ,  w i t h t h e SEASAT a l t i m e t r y ( F i g u r e  The North  standard  1983a).  (Figure  approximated  by  The  the  maximum s t a n d a r d  the  scale.  data  SEASAT  altimetry  o f each  o f 24  data  days.  the surface  m i s s an i m p o r t a n t  EPE  on t h e seasonal  currents  record  of  the  regions  and  SEASAT  associated  the ship  drift  regions  f o r the North  data  delineated  Pacific  mid-thermocline  and  temperature  mesoscale a c t i v i t y  (Emery,  t o t h e EPE o f t h e b a r o c l i n i c  areas  of Figure  III-4.  0.5°C.  i n Figure The  III-2  NWA  (Cheney  can  a n d NWP  be  have  s e t f o r examining  This  i s  t h e eddy  different  of the data  with  on a  the  global  due t o t h e s h o r t n o t be b i a s e d  record,  by  however, i t w i l l  t h e SEASAT a l t i m e t r y , a n d t h e t e m p e r a t u r e  representations  o f t h e g l o b a l eddy  t h e EKEs w i t h t h e s h i p  and t h e temperature  will  those  variability.  e_t a l . , 1983) r e p r e s e n t s  signal.  variability  than  due t o t h e w i n d s .  t h e eddy v a r i a b i l i t y  The t e m p e r a t u r e  data,  greater than  variability  map  smaller  consistent  e t a l . (1976) a r e o v e r e s t i m a t e d underestimate  deviation  are r e l a t i v e l y  but r e l a t i v e l y  III-4).  part of the barotropic  of the b a r o c l i n i c  The t e m p e r a t u r e  which  (Figure I I I - 3 ) ,  e t a l . (1976) e s t i m a t e d  variability,  of these  with  low-energy  winds nor the length  deviations are three  altimetry  the  corresponds  l e s s than  I n summary, t h e s h i p d r i f t  Wyrtki  and  (Figure  The EKEs o f W y r t k i  record  significant  the high-energy  represents  contour  data  SEASAT a l t i m e t r y w i l l  either  than  i n the equatorial regions  of the ship d r i f t  limitations  The  1.0°C  the equatorial  d e v i a t i o n s o f o v e r 3.0 a n d 4.0°C, r e s p e c t i v e l y , w h i l e t h e NEA  shows h i g h v a l u e s  of  high-  NEP h a v e minimum v a l u e s  those  delineated  w h i c h c a n be r e l a t e d t o t h e b a r o c l i n i c  a t 260 m.  i n the  III-1).  The t e m p e r a t u r e v a r i a b i l i t y  signal  and  III-4)  of  the high-energy  d e v i a t i o n o f t e m p e r a t u r e a t 260 m  Atlantic  variability  The  i n . t h e 24-day  as  smaller  (1976)  The  an " a p p a r e n t " eddy s i g n a l i n t o t h e s h i p  that  currents,  greater f o r  ( i . e . periods  p o s i t i o n and magnitude  apparent  are s p a t i a l l y  et_ a l .  variability  the winds.  n o t be  boundary  Wyrtki  and t h e h i g h - f r e q u e n c y  induce  I t should  by  the seasonal  1981) w i l l  will  two t o f o u r times  c o m p a r i s o n o f t h e SEASAT E K E s .  reported  signal  of the meridional  drift  (Figure  to  systems,  weeks)  (Wyrtki e t a l . ,  with  energies  a r e due  winds  altimetry  than the r e l a t i v e  eddy  and t r a d e  eddy k i n e t i c e n e r g i e s  deviations  t h e EPE (Emery,  The l i m i t a t i o n s  drift of  data.  variability. The SEASAT  the barotropic  1983a) c o r r e s p o n d  of each  have  been  eddy  to the  discussed.  29 The  temperature  comparison these  d e v i a t i o n maps  with  the results  maps p r o v i d e  examine t y p i c a l for  each  o f Emery  of this  no c o v e r a g e  geographic  region  investigation, with  south  quasi-synoptic  ( 1 9 8 3 a ) a r e t h e most  o f 10°S.  appropriate f o r  the exception  The f o l l o w i n g d i s c u s s i o n  s e c t i o n s a n d maps o f t h e t e m p e r a t u r e and  compare  that  them  with  results  of  will  structure the  above  analyses.  Northwest  Atlantic  The N o r t h w e s t A t l a n t i c r e g i o n , d e f i n e d i n F i g u r e I I I - 2 , i s a r e g i o n o f h i g h eddy a c t i v i t y . Gulf  Stream  The i n t e n s i t y o f t h e e d d y f i e l d  (Figure I I I - 5 ) .  i n c r e a s e s a s one a p p r o a c h e s t h e  The mean c i r c u l a t i o n o f t h e r e g i o n i s d o m i n a t e d b y  the G u l f Stream System ( F o f o n o f f , 1981), c o n s i s t i n g o f t h e F l o r i d a C u r r e n t , t h e Gulf  Stream  and t h e North  Atlantic  Drift.  C h a r a c t e r i s t i c mesoscale  features  i n c l u d e G u l f S t r e a m m e a n d e r s a n d t h e r e s u l t i n g warm- a n d c o l d - c o r e r i n g s i n t h e continental cold-core 1983).  slope  rings Five  approximately warm-core  and Sargasso  co-exist to  eight  single  cold-core  form  year  rings  200 km a n d r a i s e d i s o t h e r m s  slope  The  form  on t h e n o r t h  largest rings,  warm r i n g s f o r m p e r y e a r  1977).  (Richardson,  in a  t o 300  t h e HMCS P r e s e r v e r  exhibit SXBT  the salient  locations.  at  51°W.  isotherm of  Gulf  are three  Stream,  smaller  diameters  bounded  form  The  by t h e  (Saunders,  to the east Typically,  than that  of  of five  of the cold  t h r e e warm-core r i n g s e x i s t a t  a  warm-core  eddies  d e f l e c t i o n s o f t h e 15°C i s o t h e r m  with  1982 ( F i g u r e  Figure  ring,  a  III-6a  cold-core  S e a c a n be c l e a r l y  III-6)  shows t h e ring  o f 350 km w i t h  a depression  ring  o f t h e 10°C  o f 450 km w i t h a n e l e v a t i o n  B e t w e e n 47°W widths  and  seen i n F i g u r e  a warm r i n g a t 57°W a n d a c o l d  The c o l d r i n g h a s a w i d t h 300 m.  The SXBT d a t a c o l l e c t e d  i n October  o f t h e NWA.  i n the Sargasso  o f about  smaller  (Richardson,  on t h e s o u t h  i n diameter  Atlantic  features  T h e warm r i n g h a s a w i d t h o f a b o u t 200 m.  region  f o r t h e NWA.  T h e G u l f S t r e a m a t 55°W s e p a r a t e s  t h e 14°C i s o t h e r m  there  km  Stream  Approximately  the North  mesoscale  s e v e r a l s m a l l e r c o l d eddies III-6b.  triangular  ten  1983).  across  The  with  (100 km) f o r m t o t h e w e s t .  T w e n t y - t h r e e s e c t i o n s were o b t a i n e d by  time  i n t h e i r c e n t e r s o f up t o 600 m.  and t h e G u l f  200  per  w i t h average diameters  ( L a i and Richardson,  a s i n g l e time  Approximately  Sea a t a  Georges Bank, however s m a l l e r r i n g s  rings  Sea, r e s p e c t i v e l y .  i n the Sargasso  anticyclonic rings  continental 1971).  waters  o f 250  a n d 32°W  (Figure  t o 300 km.  a r e 200 m a n d 175 m f o r t h e e d d i e s  The  III-6b) upward  a t 45°W a n d  140E  60N  170E  16QU  130U  100U  70U  40U  2°C  BON  30N  30N  30S  Ul  o  flOE 0 K KE AS NFC CC NBC  — -  140E  170E  160U  130U  100U-  70U  40U  10U  North E q u a t o r i a l C o u n t e r c u r r e n t  LC  EOC  Equatorial  NAD  Kuroshio E x t e n s i o n  SEC  South E q u a t o r i a l C u r r e n t  GS  A l a s k a n Stream  EAC  East Australian Current  FC  North P a c i f i c Current  PC  Peru C u r r e n t  BC  C a l i f o r n i a Current  AACC  Oyashio  NECC  Kuroahio  -  -  Undercurrent  A n t a r c t i c Circumpolar  Current  BEC  North E q u a t o r i a l Current Figure III-5  S u r f a c e c u r r e n t s o f t h e P a c i f i c and A t l a n t i c Oceans.  -—  60S 20E 1  Labrador C u r r e n t North A t l a n t i c D r i f t G u l f Stream F l o r i d a Current B r a z i l Current Benguela C u r r e n t  31 ONE 6 Q F  SQUADRON.  70U  1-7  OCTOBER  60U  1982.  SOU —  40U  30U  10U  20U  J  SON  1 50N  50N  *  r'""*—  — r r ? *a*i»»atgflB*'-*"  _ 40N  301  40N  A.  1  60U  5QU  HMCS P R E S E R V E R .  r  /  •  1-7  40U  OCTOBER  30U  30N  10U  20U  1982.  .'\,-'  ,  1  ,> / r V  SST - SOLID LINE SSS - DRSHEO  60 V 54 W RRNGE i ONE TICK =  Figure III-6  43 V 300 KM  42 V  36 V  30 W  24 V  18 V  12 V  6  W  SXBT section (PE-071082) collected by the HMCS Preserver, i n October 1982 across the North A t l a n t i c . a. SXBT locations. b. Temperature (*C) section.  32 41°W,  respectively.  isotherm. December  The  A further  eddy  a t 34"W  sample s e c t i o n ,  1976 ( F i g u r e I I I - 7 )  has a  275 m  o b t a i n e d from  (east of the Gulf  deflection  o f t h e 14°C  t h e USN m u l t i s h i p  Stream  ring  survey i n  concentrations) at  33°N, shows t h r e e c o l d e d d i e s a t 52°W, 38°W a n d 32°W.  These eddies have  of  deflections  4 5 0 , 400 a n d 350 km,  respectively,  with v e r t i c a l  widths  o f t h e 17°C  i s o t h e r m o f 200 m.  Six  surveys  multiship vertical eddies  USN  were surveys  were  Individual  examined  identified  maps  these  mesoscale  west  of these It will  surveys,  suffice  with  will  e_t a l .  Four  (1980)  of  mean  diameters  whole,  are the  closed  150 km.  These  of  here  exhibit  of  Seventeen  were G u l f Stream  n o t be e x a m i n e d  as a  these  f o r the f r a c t i o n  i n light  t o say t h a t t h e i n d i v i d u a l  and the surveys  rings. of  this  sections obtained the  characteristic  s t r u c t u r e o f t h e NWA.  two m u l t i s h i p  s u r v e y s c o l l e c t e d by t h e C A F , s o u t h e a s t o f N e w f o u n d l a n d , Both  the  meeting  Labrador  Current  survey  (Figure III-8a),  survey  width  identified.  surveys  show t h e s t r o n g s u b s u r f a c e t h e r m a l f r o n t o f  the North  Atlantic  Drift.  I n the October  t h e f r o n t has a northeast-southwest  o f 110 km,  i t i s not surprising  that  no  alignment.  1981  With  closed eddies  a  c a n be  The f r o n t r e t a i n s i t s g e n e r a l n o r t h e a s t - s o u t h w e s t a l i g n m e n t i n t h e  1983 s u r v e y  (Figure III-8b),  e x c u r s i o n o f a b o u t 150 km. warm a n d c o l d w a t e r survey  Emery  o f 30°W  surveys  are i n F i g u r e I I I - 8 .  June  by  region.  n o t e d t h a t about one-half o f t h e e d d i e s  d e t a i l e d work.  The  f o r t h e NWA  isotherm deflections associated with closed eddies.  investigators  from  obtained  with the addition  o f an eastward  cold  water  There a r e a l s o a l t e r n a t i n g n e a r - m e r i d i o n a l bands o f  t o the east of the front.  Again, the limited width of the  (200 km) d o e s n o t p e r m i t t h e h o r i z o n t a l  structure  of these  features to  be r e s o l v e d a n y f u r t h e r .  Northwest  The which western  Pacific  Northwest includes  Pacific  (Figure III-2)  the Kuroshio,  the Kuroshio  portion the North P a c i f i c  Current.  m e a n d e r a n d s h e d warm- a n d c o l d - c o r e r i n g s investigations  of h i s t o r i c a l  i s a  data  region  Extension, Both  of high  eddy  activity  t h e Oyashio  and t h e  t h e K u r o s h i o and t h e Oyashio  similar  t o t h e G u l f Stream.  i n the region (Richardson,  t h e c o e x i s t a n c e o f 13 c o l d r i n g s a n d two warm r i n g s  Recent  1983) d o c u m e n t e d  i n t h e summer o f 1 9 3 9 , a n d  suggested t h a t t h e c o l d r i n g s form a t t h r e e o r f o u r s p e c i f i c s i t e s .  A synoptic  34  50  8-1  1  48 L_  1  46 I  I  44 L_  LONGITUDE WEST I  42 I  I  40  38  '  I  36 l  l  34 I  32 I  cc o LU D  -  -3  SO 48 F I V E SON. 2 5 - 2 7 JUN 8 3 , TEMP: 15Q-2QQ t l .  Figure III-8  1  I  40  I  I  38  T  I  36  I  I  34  I  32  Maps o f temperature (°C) v e r t i c a l l y - a v e r a g e d from 150 t o 200 m i n t h e NWA, from m u l t i s h i p s u r v e y s c o l l e c t e d by t h e CAF. a . Survey PE-071081, O c t o b e r 1981. b . Survey FR-270683, June 1983.  35 s t u d y r e p o r t e d by C h e n e y of  the rings  rings  from  (1977) i d e n t i f i e d  had a diameter  the Kuroshio  o f 250 km.  and t h e Oyashio  t h r e e warm a n d t w o c o l d Kitano  (1975) examined  and found  an average  rings.  One  154 w a r m - c o r e  diameter  o f 140  km.  The  XBT  conducted  data  by t h e USN  t h e NODC.  Oyashio  north  rings.  shows t w o s a m p l e  S e c t i o n 54-000575  o f t h e mean K u r o s h i o  warm  widths  eddy  axis  (presumably  (Figure  from  t h e mean K u r o s h i o a x i s  a t 31.5°N.  176°E, w i t h  deflections  widths  of  surveys from  sections i n the region  I I I - 9 a ) was  taken  1978).  a t 165°E, 172°E a n d 178°E ( p r e s u m a b l y  a t 170°E  multiship  of the concentrations of Kuroshio  ( W i l s o n a n d Dugan,  o f 1 8 0 , 2 5 0 , 180 a n d 250 km,  and  two  temperature  Three  from  the Kuroshio).  respectively,  11°C i s o t h e r m o f 170, 3 5 0 , 200 a n d 300 m.  172°E  comprises  1978) a n d t w o s e c t i o n s a c q u i r e d  o f t h e USN s u r v e y s ) , e a s t w a r d  can be i d e n t i f i e d one  f o r t h e NWP  ( W i l s o n a n d Dugan,  Figure III-9  (one f r o m e a c h and  s e t obtained  cold  eddies  the Oyashio), and  These  with  a t 37.5°N,  features  displacements  have  of the  S e c t i o n 4 0 - 0 0 1 1 7 5 was t a k e n s o u t h o f  Three c o l d 1 8 0 , 200  o f t h e 14°C i s o t h e r m f o r t h e s e  e d d i e s a r e d i s c e r n a b l e a t 163°E, and  280  km,  respectively.  The  f e a t u r e s a r e 2 2 0 , 170 a n d 140  m,  respectively.  Emery vertical  e t a l . (1980) isotherm  individual  deflections  maps o f t h e s e  c l o s e d e d d i e s were  Northeast  The western The  boundary  North  with  surveys closed  f o r the fraction eddies.  n o t be examined h e r e .  Drift  Again,  A total  activity  G e n e r a l l y , t h e mean  of  1982) n o r t h o f 45°N a n d a t 35°N  t u r n n o r t h and south,  In the f i r s t  area,  of the five  40°N 30°W t o 50°N 20°W.  i s weak. i n two  ( n o r t h and south  of the  respectively.  perturbations of the southern isotherm displacements  o f 100 t o 150 km w i t h  large  f e a t u r e s c a n be  edge  northwest  The m e a n d e r i n g s o f t h e p o l a r f r o n t  on t h e o r d e r  t o the  t h e west  f o u r d i s t i n c t a r e a s where mesoscale  i n large  relative  circulation  crosses t h e m i d - A t l a n t i c r i d g e from  (1983) i d e n t i f i e s  radii  i s a r e g i o n o f l o w eddy  current regions.  front are manifested  typical  associated  surveys w i l l  Atlantic  Atlantic  Azores) which  found.  t w o USN  identified.  (Saunders,  Gould  these  Atlantic  Northeast  branches  examined  of the polar  of a line  (Gould,  from  1983) h a v e  g e o p o t e n t i a l anomaly  SST 20  10 DEPTH 400  300  400  300  (METERS) 200  100  I H H H I  VO  V 01  co cn  DEPTH  200 (METERS) 20 SST  10  CD  SST 20  10 DEPTH 400  300  (METERS) 200  100  cn co CO  CO  o  ft n  r~  P  300 DEPTH  200 (METERS)  100 10  9C  20 SST  37 fluctuations. confined  Howe a n d T a i t  t o t h e upper  (1967) e x a m i n e d a c o l d  500 m.  This  d i r e c t i o n and measured a p p r o x i m a t e l y  f e a t u r e was  eddy  near  elongated  200 km b y 100 km.  Intense  lenses  a b o u t 50 km. no  of Mediterranean  water  These e d d i e s a r e found  thermohaline  have  a t depths  s i g n a t u r e a b o v e 500 m.  Gould  30°N t o 40°N  The  defined,  but  Gould  Mediterranean  outflow.  Azores, appears  The  XBT  surveys.  suggests A  s e t obtained  Figure III-6b  illustrate  fourth  i n October  the reduced  mesoscale  the  four  structure isotherm the  areas  h a s numerous deflections  Azores.  survey  observed  East  conducted  above.  o f 20°W,  northwest  32°W  influence  o f 16  100  and to  characteristic  of the Azores  i s rather poorly  from  of  t h e UK  the  to the  s e c t i o n s and f o u r  east  of t h e mesoscale  the structure  30°W w i t h a d i a m e t e r o f 100 km.  line  o f t h e NEA,  Between  100 m,  s e p a r a t i n g from a  1981, r e s p e c t i v e l y .  p e r t u r b a t i o n s between  of about  cyclonic  are the trans-oceanic sections f o r  activity  Figure III-6b also provides a realization  of a  the  consists  1982 a n d O c t o b e r  mesoscale  of  activity.  f o r t h e NEA  a n d F i g u r e 111-10  reported a  variability  reflect  east  diameters  a r e a i s i n t h e z o n a l band o f  eddy  i t may  area,  t o have very l i t t l e  data  t h e CAF c r u i s e s  that  of the Azores.  reported with  I t was o b s e r v e d  The t h i r d  a n d 20°W.  southwest  area i s  b e t w e e n 700 a n d 1200 m a n d h a v e  f r o n t a l f e a t u r e i n t h e summer o f 1 9 8 1 . 12°W  north-south  The s e c o n d  (1983) a l s o  eddy a t 33°N 32°W w i t h a d i a m e t e r o f 100 km.  between  just  been  in a  I t was s p e c u l a t e d t h a t  t h i s was a p i n c h e d o f f meander o f t h e N o r t h A t l a n t i c D r i f t . above and t o t h e e a s t of. t h e m i d - A t l a n t i c r i d g e ,  53°N a n d 19°W,  Both s e c t i o n s o f about  s t r u c t u r e i n two o f  20°W, 200  the  km  temperature  i n width,  of the area  i s relatively  30°W.  with  northwest  quiescent.  of  T h e CAF  ( F i g u r e 1 1 1 - 1 1 ) shows a warm e d d y a t  From t h e t e m p e r a t u r e  section i n Figure  t h e e d d y c a n b e s e e n t o be c o n f i n e d t o t h e u p p e r 500 m o f t h e w a t e r  III-6,  column and  h a v e a maximum i s o t h e r m (14°C) d e f l e c t i o n o f a b o u t 40 m.  T h r e e o f t h e N o r t h A t l a n t i c USN s u r v e y s included  i n an  examination  o f t h e NEA.  extend Survey  A z o r e s , w h i l e 9 3 - 0 0 0 5 7 7 a n d 21-001077 a r e s o u t h Emery  et^ a l .  (1980)  found  no  closed  eddies,  d e f l e c t i o n s s i m i l a r t o those of Figure I I I - 6 b taken from these  surveys.  sufficiently 64-000776  i s north  of the Azores. although  c a n be f o u n d  eastward  t o be of the  West o f 35°W  vertical  isotherm  i n a l l the sections  38 HMCS SAQUENAY. 2 - 8 OCTOBER 1981, 1  *  i i i i i i i i i i in i II n u n  58  V  RRNGE  52 :  V  46  ONE T I C K  =  V  40  3 0 0 KM  V  34  W  SST  - SOLID  SSS  - DASHED  LINE  i n mi n i  28  V  22  V  1  I II III III 111 1111,1  16  V  10  V  Figure III-10 Temperature (°C) section (SY-051081) c o l l e c t e d by the HMCS Saguenay (CAF) across the North A t l a n t i c i n October 1981.  33  LONGITUDE WEST  31  29  I  _J  27  I  I  _!  ,  w-  25 I  23  I  L_  -5  91 4  *  o  • • • •-.•14.  4  1  13  4  •  *  14  Q  ZD  cn-  33  1  31  I  I  29  ~  \  27  r  •cn  25  23  ONE SON. 3-4 OCT 82. TEMP: 150-200 M.  Figure 111-11  Map of vertically-averaged temperature (°C) from 150 t o 200 m i n the NBA obtained by the CAF, October 1982 (MK-041082).  39 South  Atlantic  The  South  mesoscale energy  Atlantic  eddy  activity.  (Figure III-3)  III-1). Brazil  region, defined i n Figure III-2, I t i s a l o w i n t h e maps  and t h e s t a n d a r d  deviation  The r e g i o n i s b o u n d e d b y t h e S o u t h Current,  the Antarctic  There have been v i r t u a l l y  Circumpolar  has r e l a t i v e l y  little  of both  t h e eddy  kinetic  o f SEASAT  altimetry  (Figure  Atlantic  Current  Equatorial  Current, the  and t h e Benguela  Current.  no o b s e r v a t i o n a l s t u d i e s o f t h e e d d y v a r i a b i l i t y  of  the region.  The  d a t a s e t a c q u i r e d f o r t h e SA c o n s i s t s  ( F i g u r e 111-12). 200  a t 24° S.  NODC  The s t a t i o n s p a c i n g s a r e a b o u t 100 km, s o e d d i e s s m a l l e r t h a n  km i n w i d t h  1983  o f two z o n a l s e c t i o n s f r o m  cannot  be r e s o l v e d .  S e v e r a l mesoscale  S e c t i o n 4 0 - 1 9 0 2 8 3 was  taken  features are discernable:  i n February  a warm  eddy  at  27°W, a c o l d eddy a t 20°W a n d a n e d d y a t 5°W, w i t h a c o l d c o r e a b o v e 200 m a n d a  warm  core  below  200 m.  The f e a t u r e s h a v e w i d t h s  respectively, with vertical m.  km,  d e f l e c t i o n s o f t h e 15°C i s o t h e r m o f 2 5 , 25 a n d 50  S e c t i o n 04-310383, t a k e n  widths  o f 4 0 0 , 400 a n d 200  a r e 300 a n d 500 km,  a t 12°S, h a s c o l d e d d i e s a t 34°W a n d 2°E.  respectively,  with deflections  o f t h e 12°  Their  isotherm  o f 40 a n d 75 m.  Northeast  The  Pacific  Northeast  region  Pacific  r e g i o n has been  of the subtropical  Alaskan  Stream  Bernstein  (1983)  and  and subpolar  i n the  provided  south  a  by  review  defined  gyres,  the t r o p i c s . shown  This  o f t h e eddy  Royer  altimetry  (1978), i n a m e r i d i o n a l hydrographic  5 dyn-cm w i t h w i d t h s  of about  more n u m e r o u s w i t h t y p i c a l km.  the  eddies  w i t h average  Between  o f t h e NEP  a s one p r o c e e d e d higher  section,  eddy  front  34°N  5°N  a n d 22°N t h e  i s o t h e r m p e r t u r b a t i o n s of about  appeared 40 m  were  eddies,.were o f 150 t o  of the subtropical  Eddies  and  the eddies t o  (1974) a n a l y s e d a d a t a  a t 25°N.  activity  between  found  and  toward  Their t y p i c a l amplitudes  n o r t h and south  B e r n s t e i n and White  south of the s u b t r o p i c a l  data  40 km.  by t h e  Countercurrent.  a m p l i t u d e s o f 10 t o 15 dyn-cm a n d w i d t h s  Roden ( 1 9 8 0 ) f o u n d  n o r t h o f H a w a i i a t 30°N. Hawaii  variability  (Figure III-1)  be f e w i n number a n d weak b e t w e e n 54°N a n d 34°N.  200  Equatorial  activity  activity  i n the north  i s c o n s i s t e n t w i t h t h e z o n a l b a n d of  i n t h e d e v i a t i o n s o f SEASAT  25°N.  bounded  the North  d e s c r i b e d a g e n e r a l i n c r e a s e i n t h e mesoscale  a s t h e l o w eddy  front,  s e t near  regularly i n  and diameters  of  40  Figure III-12  Temperature (•C) s e c t i o n s from t h e NODC i n t h e SA. a. S e c t i o n 40-190283, F e b r u a r y 1983. b. S e c t i o n 04-310383, March 1983.  41 200  km-  1982)  The H a w a i i identified  to Tahiti two  Shuttle  types  of  Experiment  eddies  drifting  Equatorial Current.  The f i r s t t y p e a p p e a r e d  on  s e c t i o n s a n d was  nine  These  o f t h e 26  cold  eddies  were  formed  about  between  60  m.  14°N  sections  and  between  w i d t h from  extensively  t o the west  second  19°N. 150°W  type  There and  158°W,  the  North  20°N, s o u t h o f O a h u ,  s t u d i e d by  of the island  Patzert  of Hawaii  (1969). and h a d  d i s p l a c e m e n t s o f t h e 14°C i s o t h e r m  appeared  were  with  i n the North  cold  eddies  Equatorial  present  50% o f t h e t i m e .  Current  i n the meridional  These  eddies  ranged  in  150 t o 350 km w i t h p e r t u r b a t i o n s i n t h e 14°C i s o t h e r m o f 40 t o 65 m  i n amplitude.  Wyrtki found  amplitudes. strong  The  westward  a t 158°W n e a r  w i d t h s o n t h e o r d e r o f 200 km w i t h v e r t i c a l of  ( W y r t k i e t a l . 1981; W y r t k i ,  Immediately  seasonally  no o b v i o u s  south,  varying  r e l a t i o n s h i p between eddy d i a m e t e r s a n d  i s the North  eastward  Equatorial  current.  Countercurrent,  Legeckis  (1977)  a  discovered  m e a n d e r s o c c u r r i n g when t h e c u r r e n t f l o w i s s t r o n g e s t , i n S e p t e m b e r t o J a n u a r y , w i t h z o n a l wavelengths  The 32 the  d a t a o b t a i n e d f o r t h e NEP c o n s i s t o f 37 s e c t i o n s ( s i x f r o m t h e CAF a n d  f r o m t h e NODC), a n d 16 s u r v e y s . CAF  (from Hawaii  the mesoscale at  o f 1000 km a n d n o r t h - s o u t h a m p l i t u d e s o f 100 km.  35°N.  limit  t o Vancouver  structure  on e i t h e r  Climatologically,  of the North  greater  than  Pacific  side  and s a l i n i t i e s  cold  eddies  three  widths  a r e 2 0 0 , 350 a n d 150 km,  greater  c a n be  illustrates  of the North front  C e n t r a l Water,  18°C  11°C i s o t h e r m o f 30 m.  Island) that  the subtropical  front,  the  F i g u r e 111-13 i s a t y p i c a l s e c t i o n t a k e n b y  which  Pacific  Front  i s d e f i n e d as t h e n o r t h e r n  34.8 x  a t 22°N,  respectively,  Subtropical  has w i n t e r t i m e  than  identified  the difference i n  10~3. 25°N  temperatures South  of the  a n d 34°N.  with vertical  Their  displacements  of  N o r t h o f 35°N, t h e t h e r m a l s t r u c t u r e i s r e l a t i v e l y  quiescent.  The  SXBT  exhibits current  section  collected  t h e temperature system  thermocline Equatorial  a t 165°W.  and  reflects  Current  by t h e CAF  pattern  i n November  characteristic  The  14°C i s o t h e r m  the  geostrophic  (NEC) n o r t h  of  9°N,  of  1982  (Figure  the P a c i f i c  i s i n t h e lower  slope  Equatorial  (NECC) b e t w e e n 4° a n d 9°N, a n d t h e S o u t h E q u a t o r i a l C u r r e n t  equatorial  portion  associated with  the North  111-14)  of the  the  North  Countercurrent  (SEC) s o u t h o f 4°N.  I m b e d d e d i n t h e SEC, t h e E q u a t o r i a l U n d e r c u r r e n t  (EUC) i s m a r k e d b y a s p r e a d i n g  of  2°N.  t h e isotherms  at  C o u n t e r c u r r e n t (SECC),  175  m  between  also  i m b e d d e d i n t h e SEC, i s a r e l a t i v e l y weak  f l o w i n g c u r r e n t b e t w e e n 11°S a n d 8°S.  2°S  and  The  South  Equatorial eastward  A c o l d e d d y c a n b e i d e n t i f i e d i n t h e NEC  42 HMCS Q U ' A P P E L L E .  RRNGE  Figure III-13  : ONE T I C K  =  2 5 NOVEMBER  -  2 DECEMBER 1 9 8 2 .  3 0 0 KM  Temperature (°C) s e c t i o n (QE-251182) c o l l e c t e d by t h e HMCS Qu'Appelle (CAF) i n t h e NEP, from Hawaii t o Vancouver I s l a n d i n November 1982.  HMCS Q U ' A P P E L L E .  RANGE  Figure III-14  i  ONE T I C K  =  9 - 1 8 NOVEMBER 1 9 8 2 .  3 0 0 KM  Temperature (°C) s e c t i o n c o l l e c t e d by t h e HMCS Qu'Appelle (CAF) from Samoa t o Hawaii i n the c e n t r a l equatorial Pacific, November, 1982. Only t h e p o r t i o n o f t h i s s e c t i o n n o r t h o f 4*N has been r e t a i n e d (QE-151182) f o r t h e XBT data s e t summarized i n T a b l e A-4.  43 in  Figure III-14 with characteristics  Wyrtki  (1982).  14°C i s o t h e r m .  t h e 14°C  Presumably, amplitude  The  similar  t o eddy  I t h a s a w i d t h o f 350 km a n d a 25 m v e r t i c a l I n the Hawaii t o T a h i t i Shuttle Experiment,  s i m u l t a n e o u s l y i n t e r s e c t e d eddy "A". of  very  i s o t h e r m were the section  deflection of the  two s e c t i o n s  almost  27 m a n d 50 m  i n Figure  at  150°W  and  III-14 c u t through  153°W,  respectively.  the side  of a  larger  eddy.  XBT s u r v e y s  subsurface  across  d i s c u s s e d by  I t s w i d t h was 350 km a n d t h e d e f l e c t i o n s  i n t h e NEP a r e i n t h e v i c i n i t y  of the subtropical  n o r t h o f H a w a i i a n d i n t h e NEC a n d NECC s o u t h o f H a w a i i . the  "A"  temperature  the front  between  maps  of the four  February  1980  e x c e p t i o n o f t h e March  1980 s u r v e y , no c l o s e d  the  the  narrow  width  of  surveys.  In  Figure III-15  CAF m u l t i s h i p  and  May  1982.  eddies  March  front  surveys With  shows  conducted  the notable  c o u l d be d e f i n e d due t o  1980  (Figure  III-15b),  an  a n t i c y l o n i c eddy i s c l e a r l y d e f i n e d by t h e 17°C i s o t h e r m a t 28.5°N 153°W, s o u t h of the front. eddy  The a l o n g - t r a c k a n d c r o s s - t r a c k t e m p e r a t u r e  a r e shown i n F i g u r e 111-16.  i s o t h e r m o f about  I t has a v e r t i c a l  60 m a n d a d i a m e t e r  deflection  o f 130 km w h i c h  l o c a l i n t e r n a l R o s s b y d e f o r m a t i o n r a d i u s (Emery e t a l . ,  A  time  series  o f s i x AXBT  surveys  s u b t r o p i c a l front north of Hawaii. an  active  frontal  meander forms.  regime.  amplitude o f about  100 km.  collected  The t e m p e r a t u r e  Between  The n o r t h w a r d  was  18 December  s e c t i o n s through t h e o f t h e 17°C  i s consistent with the 1984) o f 45.5 km.  by  t h e USN  across the  maps i n F i g u r e I I . I - 1 7 show  1979 t o 25 J a n u a r y  d i s p l a c e m e n t o f t h e t o n g u e o f warm w a t e r  On 7 F e b r u a r y  1980, t h i s  1980, a has an  f e a t u r e i s r e p l a c e d by a  " t r o u g h " o f c o l d w a t e r o f t h e same a m p l i t u d e .  S o u t h o f H a w a i i a s e r i e s o f f o u r USN AXBT s u r v e y s shows a n o t h e r a c t i v e e d d y field  i n the North Equatorial Current  ( F i g u r e 111-18).  On 30 J a n u a r y  1981, a  c y c l o n i c eddy i s c l e a r l y d e f i n e d a t 15°N 156°W w i t h a d i a m e t e r o f a b o u t 200 km. Two w e e k s l a t e r 10  cm/s  ( F i g u r e I I I - 1 8 b ) t h e f e a t u r e h a s moved w e s t w a r d a t a s p e e d o f  t o t h e edge  of the survey  diameter)  has appeared  III-18c)  i s on average  signature  o f the annual  at  15°N  about  area.  155°W.  3°C warmer  Another  cyclonic  The  13  March  than  a  month  weakening o f , and t h e southward  1981  eddy  (150 km  survey  (Figure  eariier.  This  i s a  displacement o f , t h e  t r o p i c a l t r o u g h t h a t s e p a r a t e s t h e NEC a n d NECC, s o u t h o f t h e s u r v e y a r e a . s u r v e y o f 16 A p r i l month  earlier.  The  1981 ( F i g u r e I I I - 1 8 d ) i s a g a i n , w a r m e r t h a n t h e s u r v e y o f a  A cold  eddy  c a n be  seen  at  14°N  155°W  with  a  diameter  of  LONGITUDE WEST  TUO SON, 27-28 MRR 80, TEflP: 150-200 fl. Figure  III-15  CAF m u l t i s h i p surveys o f v e r t i c a l l y - a v e r a g e d temperature (°C) from 150 t o 200 m taken i n t h e v i c i n i t y o f t h e N o r t h P a c i f i c S u b t r o p i c a l F r o n t between February 1980 and Hay 1982. a. Survey PR-110280, February 1980. b. Survey GU-270380, March 1980.  157  LONGITUDE WEST 155  153  149  151  LONGITUDE WEST  156  154  152  150  o • cn •  •  •  . 14-  CD -  •  • on  •  oo X  • (M  16  •  o  •  * •  • cn  •CM  •  cn • CM  a  Q ZD  *  •j ^  14 . ' y 14 w £^7*16 15 y ) / . /  • CM -  •18 •  •  cn  •  y— i—i t— cr  CM •  • CM  (M •  in  17. 157  17  CM-  156  c . 155  153  151  CM CM  T  149  Continued. c. d.  T  154  i  r  152 152  in • (M  150  TUO SON, 11-12 HAY 82. TEMP: 150-200 M.  TWO SON, 1-2 MAY 81. TEMP: 150-200 M. F i g u r e 111-15  D.  fr  Survey PR-010581, May 1981. Survey TA—110582, May 1982.  RANGE  : ONE TICK =  F i g u r e 111-16  50  KM  D e t a i l e d temperature (°C) s e c t i o n s o f t h e a n t i c y c l o n i c eddy found i n t h e March 1980 CAF m u l t i s h i p survey (GD-270380) i n t h e HEP (Figure III-15b). a. A l o n g - t r a c k s e c t i o n (southwest t o n o r t h e a s t ) . b. C r o s s - t r a c k s e c t i o n (northwest t o s o u t h e a s t ) .  F i g u r e III-17  USN AXBT surveys o f v e r t i c a l l y - a v e r a g e d temperature C O from 150 t o 200 m taken i n t h e v i c i n i t y o f t h e N o r t h Pacific S u b t r o p i c a l F r o n t between December 1979 and F e b r u a r y 1980. a. S e c t i o n BB-181279, 18 December 1979. b. S e c t i o n CC-211279, 21 December 1979.  LRTITUDE NORTH m  J  0 1  30 I  L  32  H M M I  M> a n  • • o co A o ft H0 D  ft  to a o ft H- ft 0 • P  ?? o  to  o  o  00  03  o  o  LATITUDE NORTH T]  VC 00  o  30  Ln  03  O •  6fr  32  A.  F i g u r e 111-18  B.  USN AXBT surveys o f v e r t i c a l l y - a v e r a g e d temperature (°C) from 150 t o 200 m taken i n t h e N o r t h P a c i f i c E q u a t o r i a l C u r r e n t south o f Hawaii, between January 1981 and A p r i l 1981. a. S e c t i o n BB-300181, 30 January 1981. b. S e c t i o n CC-110281, 11 February 1981.  F i g u r e III-1.8  Continued. c. S e c t i o n DD-120381, 12 March 1981. d. S e c t i o n EE-150481, 15 A p r i l 1981.  52 approximately 14°N  is a  annual the  150  km.  The  signature  c y c l e of  the  of  i n t e n s i f i e d meridional temperature gradient north  an  NEC  increased  when t h e  c o l d eddy d u r i n g t h i s  westward  flow  flow,  during  a  i s generally abating.  warming t r e n d  may  account  period The  f o r the  of  the  presence  anomalous  of  of  thermal  gradients.  The  CAF  conducted a  164°W i n November  multiship  1982  survey  across  ( F i g u r e 111-19).  The  flow  t e m p e r a t u r e g r a d i e n t o f t h e NECC d o m i n a t e s t h e eddy  of Hawaii,  but  a d d i t i o n a l AXBT s u r v e y southward observed  south  the  i n January  1981  of  the  25°N 155°W.  at  of  120  r a d i u s o f 53 km  South  of  displacement  zonal width  i s zonal  survey.  km,  18°C  This  the  9°N  meridional  T h e r e i s no d i s c e r n i b l e  subtropical front, (Figure  has  with  a  a  USN  l a r g e and  cold  17°C  size  local  c o l l e c t e d an distinct  core  of  240  internal  can km  be  and  a  deformation  (Emery e t a l . , 1 9 8 4 ) .  South P a c i f i c  region, defined  Current,  the A n t a r c t i c Circumpolar  •paucity of data g l o b a l ocean  28°S a n d  i n this  the  two  Region.  identified.  The  III-1)  show  (Figure  both  station  Patzert  in  data  and  mesoscale O n l y one  maps o f W y r t k i low  eddy  the  data  obtained  f o r the  with  i t s two  spacing  east  111-21 shows a h i g h  Samoa  i n November  Countercurrent  (Tabata,  1975)  The is  Zealand  (1976) r e p o r t e d  the  sections  region  nine  r e s o l u t i o n SXBT c r u i s e by  1982.  New  e t a l . ( F i g u r e I I I - 3 ) and  c o n s i s t of  thermal apparent  signature at  The  extreme  (Stommel e t a l . ,  of  24°S  and  eddy  South E q u a t o r i a l  mesoscale feature, w i t h  in  low  trans-Pacific  r e s o l v i n g XBT  levels  SP  the  of  l e a s t - s u r v e y e d p a r t of  expedition  Bernstein  area  Peru Current.  a c t i v i t y with p r o x i m i t y t o the A n t a r c t i c Circumpolar  XBT  i s an  b o u n d e d by  and  "Scorpio"  existing  eddies.  observed  III-2,  Zealand,  Current,  The  43°S, h o w e v e r , t h e  c e n t r a l South P a c i f i c was  o f New  1983).  added t o  r e s o l v e mesoscale variability  east  i n Figure  r e g i o n makes i t p e r h a p s t h e  (Bennett,  substantially  Figure  A  meridional  which i s c o n s i s t e n t w i t h the  t o t h e n o r t h and  The  the  111-20).  isotherm  feature  activity  to  and  at  Pacific  The  km,  NECC/NEC b o u n d a r y  variability.  North  at  the  the 1973)  transects could  on  the  not eddy  taken  in  the  a width  of  200  Cheney e t a l .  increasing  eddy  Current.  s e c t i o n s and the of  CAF the  (Figure  one  survey.  f r o m New  Zealand  South  Subtropical  III-21a).  This  53  LONGITUDE WEST  .167  n  165  i  167  ^  163  I  165  i  i  163  FOUR SON, 1 4 - 1 5 NOV 8 2 , TEMP:  Figure  III-19  161  i  r  v  "  161 1 0 0 - 1 5 0 M.  CAF SXBT survey (QB-141182) o f v e r t i c a l l y - a v e r a g e d temperature (°C) from 100 t o 150 m taken a c r o s s t h e N o r t h P a c i f i c E q u a t o r i a l C o u n t e r c u r r e n t , November 1982.  158  158  F i g u r e 111-20  LONGITUDE WEST 156  154  156  154  USH AXBT survey (AA-16081) o f v e r t i c a l l y - a v e r a g e d temperature (•C) from 150 t o 200 m taken n o r t h o f Hawaii, 16 J a n u a r y 1981.  177 HMCS QU'APPELLE. 2-7 NOVEMBER 1982. in (MT i n _ tn  CM •  ERST  WEST  180  179  .-<19r . "^-18^  to CT en « •  176  178 r  rf<n  3~  • •  .tn tn •  SST - SOLID LINE SSS - DASHED  •  .18  to  • • *  *  / •  •  •  • «  CM •  ZD O CO  LU Q  CM •'  ZD  . " T o •• •  17  CE  . • /  •' 17 '  o cn -  3/ CD  CM  cnRANGE : ONE TICK =  300 KM  Figure 111-21  177  179  180  T  178  176  FOUR SON, 3-4 NOV 82. TEMP: 150-200 M.  CAF SXBT survey from New Zealand t o Samoa, November 1982. a. Temperature section C O , QE-021182. b. Map of vertically-averaged temperature (°C) from 150 to 200 m, QE-031182.  56 subsurface  thermal  front  present  i n a l l five  Zealand  to F i j i .  appears  t o be  a  permanent  SXBT s e c t i o n s r e p o r t e d by Denham The  amplitude  and h o r i z o n t a l  feature e_t aJU  scale  s t r u c t u r e e x h i b i t marked i n c r e a s e s s o u t h o f t h e f r o n t .  of  that  was  also  (1981) f r o m  the thermal  New eddy  F i g u r e I I I - 2 1 a shows a  warm eddy a t 27.5°S w i t h a w i d t h o f a b o u t 400 km a n d a 150 m d e f l e c t i o n o f t h e 16°C  isotherm.  (Figure  The  III-21b)  was  m u l t i s h i p survey t o o narrow  24-230483 ( F i g u r e 1 1 1 - 2 2 ) , t a k e n o b t a i n e d f r o m NODC. seen:  a warm e d d y  e d d y a t 85°W.  collected  (180 km)  to  by close  t h e CAF  on  the feature.  cruise Section  i n t h e n o r t h e a s t c o r n e r o f t h e SP r e g i o n , was  I t i s relatively a t 106°W, a c o l d  quiescent, although eddy  three eddies  c a n be  a t 93°W a n d a warm s u b - t h e r m o c l i n e  T h e s e f e a t u r e s h a v e w i d t h s o f 3 0 0 , 250 a n d 400 km,  with displacements  this  o f t h e 11°C i s o t h e r m o f 2 5 , 30 a n d 60 m.  respectively,  57  F i g u r e 111-22  Temperature (°C) s e c t i o n (24-230483) o b t a i n e d t h e e a s t e r n SP.  from t h e NODC  58 IV.  The the  purpose  of  this  quasi-synoptic  Statistical  STATISTICAL ANALYSES  chapter  mesoscale  analyses  were  i s to  quantify  structure  used  to  in  the  the  compress  geographic  upper  the  s t a t e m e n t s about what " u s u a l l y " happens i n t h e  how  regions  the  differ  geopotential  from  anomaly  each  other.  were  used  The  m  numerous  concise the  400  variability of  ocean.  observations  into  geographic regions,  mid-thermocline  to  the  of  represent  and  temperature  the  and  mesoscale  eddy  variability.  A  sufficient  statistics  which  uncertainties. light  of  the  increase  sample each  and  scales the  the  in  survey  were  in  regions  to  obtain the  o f weeks t o  be  therefore  This  using  required  eddy f i e l d  to  with  section  by  statistics  an  geographic  survey  these  local  of  the  the  that  radius).  error  bars,  statistics  the  processes The  assumptions.  data  First, the  as  basis  of  same g e o g r a p h i c r e g i o n  or  variances  on  in  temperature  realization.  were d e f i n e d  large  were  "averaged".  ( t r e n d s ) were removed f r o m each s e c t i o n  perturbation variables  Third, the  decrease  independant  mesoscale  the  relatively  s t a t i o n a r y , random  Only c r u i s e s i n the similar  small, i n  Rossby d e f o r m a t i o n  assumption  regions  small  ( i . e . mean e q u a l  to  g e o p o t e n t i a l anomaly, w i t h  s e c t i o n s and  surveys  i n t e r n a l Rossby r a d i u s , and  zero),  separated  of  near-normal  used were  computing  the  central  moments  of  separated i n time  by  will  i n t h e NEP  geographic  intermittency be  used.  region w i l l  of  The be  the  region. frequency  seasonal  examined.  The  variability  the  t h e wavenumber s p e c t r a o f t h e m i d - t h e r m o c l i n e  k u r t o s i s and  and  the  substantiate  g e o p o t e n t i a l anomaly f o r e a c h  skewness,  was  the  estimates  were e r g o d i c ,  survey  ways  pooled  reasonably  a q u a n t i t a t i v e r e p r e s e n t a t i o n of the mesoscale  obtained  d i s t r i b u t i o n s and the  and  sample  relatively  c r u i s e and  freedom,  obtain  years.  In t h i s chapter, will  per  with  considered  internal  t e m p e r a t u r e and  a t l e a s t the  statistics  the  obtained  distributions.  available to  of  section or  i n three  be  m u s t be  l a r g e - s c a l e c u r r e n t systems  s p a c e by  periods  of  region.  the mid-thermocline frequency  survey  o f t h e eddy f i e l d .  geographic  Second, the  population  order  i n Chapter I I I , the  the variance  or  degrees  t h a t e a c h XBT  discussed  (on t h e  baroclinic  were p r o c e s s e d  the  must  mesoscale p e r t u r b a t i o n s  statistics  and  observations  E a c h s e c t i o n and  geographic  field  of  estimate  few  decorrelation To  number  frequency  temperature  standard  deviation,  distributions  variability  of  the  and  of  each  mesoscale  I s o t r o p i c , m e r i d i o n a l and  zonal  59 autocorrelation isotropy.  be  employed  to  spectra  will  be  discuss  be used t o i d e n t i f y  wavenumber ranges, and the dominant  k i n e t i c energy e s t i m a t e s  A.  will  Wavenumber s p e c t r a w i l l  distinctive Velocity  functions  computed  using  the  the  of  s p e c t r a l bandwidths  length  scales  geostrophic  and the g e o s t r o p h i c v e l o c i t y  assumption  of  of  variability.  relation  to  obtain  s c a l e s f o r each r e g i o n .  SPATIAL SERIES  S p a t i a l s e r i e s and maps of the m i d - t h e r m o c l i n e temperature and g e o p o t e n t i a l anomaly, used t o r e p r e s e n t s t a t i s t i c a l analyses. each  XBT  and  the  circulation.  the u p p e r - l a y e r v a r i a b i l i t y ,  T h i s i n v o l v e d the c a l c u l a t i o n  removal  The  of  the  resulting  low-wavenumber  perturbation  r e l a t i v e l y high-wavenumber mesoscale eddy  vertically-averaged  vertically-averaged anomaly  temperature  between the  temperature  was  temperature  variables  surface  averaged  and  over  mid-thermocline temperatures. the water column i n d u c e d by the  (i.e.  50 m)  of  the  50  m  150  and  temperature  mid-thermocline  No  one  eddy  field  i n the XBT  m,  and  200 the  or  intervals  depth can be on  a  of  the  m,  the  geopotential  0-400 m).  to  The  represent  the  between  adequately used t o examine  global  1983a).  o f the geographic r e g i o n s  (Stommel  1982;  scale  Thomson e t a l . 1984b), t o 200 m and 350  f o r each r e g i o n .  350  and  400  whereas,  the  temperature  and SP.  The  data s e t was  be  (Emery,  Emery and Dewar,  variability,  were used i n the SA, NEP  and  400  depth  r e v e a l e d t h e most a p p r o p r i a t e depth i n t e r v a l the  signatures  i n the s e c t i o n s and s u r v e y s :  the s t a n d a r d d e v i a t i o n s of the temperatures a t 150  and NEA,  "large-scale"  t o reduce the high-wavenumber n o i s e t h a t might  thermocline  Defant, 1981;  are  ( i . e . 0-400 db  Examinations of the mean thermal s t r u c t u r e e t a l . 1960;  the  The temperatures were averaged over a p o r t i o n o f  instrument e r r o r .  variability  350  4000 kPa two  of  fields.  between  between  f o r the  of s e v e r a l q u a n t i t i e s f o r  signal  Three q u a n t i t i e s were c a l c u l a t e d f o r each XBT the  were r e q u i r e d  signature  m  were  used  and  t o 400  I n the NWA, to  between  represent 150  and  m NWP  the  200  m  of t h e u p p e r - l a y e r b a r o c l i n i c  characterized  by  the g e o p o t e n t i a l  anomaly  (0-4000kPa).  The p e r t u r b a t i o n v a r i a b l e s g e o p o t e n t i a l anomaly running  mean.  A  (D) were o b t a i n e d f o r each  running  low-wavenumber s i g n a l  of the mid-thermocline temperature  mean  of  this  of the l a r g e - s c a l e  size  (T) and  s e c t i o n by removing a 1000 was  chosen  mean c i r c u l a t i o n  to  take  systems  out  and  the km the  retain  60 the  full  amplitude  observed  in  the  mesoscale  dominant w a v e l e n g t h s  averaging with  of  interval  of  a  favour  of  the  running  km  running  the  (except  t h e USN  the  m u l t i s h i p surveys  USN  trends. to  the  were c o n f i n e d t o the  interior  c r o s s major f r o n t a l systems  of  The  Pacific,  Detrending  so  an  sections  a t some l e n g t h , b u t  rejected  500,  750,  1000,  geographic  considered small  and  1250  Figure and  IV-1  The shows  NEP.  removing  more a p p r o p r i a t e  the  zonal  adequate,  of  the  linear  since  subpolar  km  regions.  dimensions  removal of  Stream or  (1974)  the  s u b t r o p i c a l or  (e.g. G u l f  White  w e r e d e t e r m i n e d by  considered  the  North  f o r s e c t i o n s i n t h e NWP  relatively  still  and  most a p p r o p r i a t e .  T h i s was  multiship surveys). was  the  required.  considered  series obtained  mean due  in  series in different  considered  zonal l i n e a r  large running  B.  was  km  p e r t u r b a t i o n v a r i a b l e s f o r each survey  m e r i d i o n a l and the  400  Bernstein  R u n n i n g means o f  spatial  examples of the s p a t i a l  The  mean.  mean was  to  s c a l e was  l e a s t - s q u a r e s - f i tpolynomials  1000  the than  surveys trend  these  g y r e s and  of  surveys did  not  Kuroshio).  CENTRAL MOMENTS  The  mesoscale  examined  with  functions: were  the  for  for  standard  deviation,  amplitude  of the  been  survey  by t h e  T  and  their and  The  D  may  sample  survey,  region.  S,  be  will  used  by  of  and  kurtosis. and  the  1979;  (S )  sample  relation:  T  convenient  standard  mesoscale  obtained  results  of  standard  e_t  from Emery  These  pooled  to  variability  of the eddy  standard field.  measure  of  were  of  the  deviation, The  the  sample average  large-scale flow  the  (Wyrtki,  a l . , 1980; this  statistics  discussed.  quantify  field  density  statistics  d e v i a t i o n of the  eddy  Emery  use  mesoscale  oceanographers  Taft, T  The  a  be q u a n t i t a t i v e l y  probability  geographic  made a b o u t t h e  provide  fluctuations.  The  and  d e s c r i b i n g the  compared t o t h e  III-4).  of  by  t h e b a r o c l i n i c e d d y f i e l d w i l l be  d e v i a t i o n s of  directly  (Figure  geographic  variability  Ebbesmeyer  standard  section  kurtosis for  commonly  geographic 1976;  moments  comments m u s t f i r s t and  represented  d e v i a t i o n , skewness  each  and  skewness  has  central  standard  each  temperature f i e l d  A few  variability  the  calculated  obtained  and  600  greater  were a p p l i e d t o t y p i c a l  be  of  features.  intensity 1975;  Emery,  quasi-synoptic  and  Dantzler,  1983a).  The  data  may  set  (1983a) u s i n g c l i m a t o l o g i c a l d a t a  d e v i a t i o n was  obtained  f o r each  section  61  Figure IV-1  Examples of the s p a t i a l series of the mid-thermocline temperature perturbations (T) and the geopotential anomaly perturbations (D) f o r trans-oceanic sections i n the NWP and NEP.  62  ( ( ^  xj)/(n-l))  (4.1)  1 / 2  w h e r e x ^ i s T o r D a n d n i s t h e number o f o b s e r v a t i o n s .  Skewness symmetry.  is a  measure  of  departure  estimate  n  to the left  mesoscale  eddy  and consequently  field  consists  greater  observations is  i s positive.  a  number  level)  d i s t r i b u t i o n h a s a number o f  eddies  in a  relatively  i f the absolute  i n t h e i n t e r m e d i a t e r a n g e b e t w e e n t h e mean a n d e x t r e m e v a l u e s .  I t  measure  of  the  disproportionality  by t h e s t a n d a r d  and C a r r u t h e r s ,  i s termed  i f K  distribution.  near  deviation.  A useful  1953):  i n t h e i n t e r m e d i a t e ranges and a t h e mean;  "platykurtic",  i s zero  with  i f K a  i s negative  large  proportion  the of  s m a l l number o f o b s e r v a t i o n s  the distribution  The a c c e p t a n c e r e g i o n s  t h a t K=0, a t t h e 0.05 l e v e l  the  (4.3)  i n t h e i n t e r m e d i a t e ranges and a r e l a t i v e l y and  of  d i s t r i b u t i o n i s termed " l e p t o k u r t i c " and i t w i l l  l a r g e number o f o b s e r v a t i o n s  t h e mean;  where  -3  s m a l l number o f o b s e r v a t i o n s  distribution  1953),  of W i s  of  a  Carruthers,  value  number  have a r e l a t i v e l y  Gaussian  more  observations.  I f K i s p o s i t i v e t h e frequency  near  indicates that  i s  i s  and  K = ( ( ^ xj)/(n-l))  values  This  fall off  n^  f o r m o f k u r t o s i s i s g i v e n by ( B r o o k s  frequency  the frequencies  o f warm  nonzero  t h e f o u r t h c e n t r a l moment n o r m a l i z e d  relatively  2 )  skewness o f T o r D would suggest t h a t t h e  1.96(6/n^)(Brooks  t h e number o f i n d e p e n d e n t  Kurtosis  of  .  The s k e w n e s s o f t h e p o p u l a t i o n i s c o n s i d e r e d t o b e  (95% confidence  than  so t h a t  the frequency  A positive  q u i e s c e n t , c o l d background. significantly  o f t h e mean,  , t h e skewness  extreme p o s i t i v e v a l u e s .  ( 4  ".  7  t o the l e f t  values are negative  from  by t h e s t a n d a r d d e v i a t i o n .  xj)/(n-l)  . t h e mode l i e s  distribution  o f skewness i s :  W = (Z  sharply  the frequency  I t i s t h e t h i r d c e n t r a l moment n o r m a l i z e d  A convenient  If  of  i s "isokurtic",  f o r testing the n u l l  as i s a hypothesis  o f s i g n i f i c a n c e , a r e g i v e n by B r o o k s and C a r r u t h e r s  63 (1953).  The  l e s s than  In  k u r t o s i s of  100  the  independent  classical  flatness  factor  intermittency. Q,  as  the  the  state,  Q(K+3)=3 was f i e l d may  the  turbulence  record  zero  during  standard  relative  density  number o f  from zero, the  (Hinze, a  The  1975),  measure  from a sample  K  i s known  for  an  normally  of  the  state,  i n t e r m i t t e n c y of  near the  the  u s i n g the  mean.  intermittency factor,  Q,  kurtosis  Where K  may  be  degree  of  On  the  during  the  relation  the  mesoscale  above  relation.  eddy  average amplitude  is  a  symmetry  measure  is significantly  obtained.  factor,  the  skewness i s a measure of t h e and  the  occurs.  distributed  d e v i a t i o n i s a measure of t h e  distribution;  as  intermittency  nonturbulent  e s t i m a t i n g K and  v a r i a b l e ; the  values  is  the  1975).  t h u s be q u a n t i f i e d by  sampling  estimated  length over which turbulence  concerned  (Hinze,  the f l u c t u a t i o n s of the  be  i n v e s t i g a t o r s have d e f i n e d  is  suggested  not  considered  variable  and  I n summary, t h e  the  of be  Turbulence  that  turbulent  may  of  should  observations.  studies  and  fraction  assumption  a population  Q  i s the  of  of of the  different  fraction  of  the  sample where m e s o s c a l e p e r t u r b a t i o n s o c c u r .  Thus, f o r g i v e n s t a t i s t i c s , i t  may  be  mesoscale  that  said that  these  the  average  perturbations  amplitude  occur  p e r t u r b a t i o n s are predominantly  C e n t r a l Moments o f t h e  The  sample  sections.  numbers  determined from the s c a l e s may having  be  not,  of  the  course,  sections  obtained  observations.  the  perturbations region  o r warm (W>0)  of of  T  and  D  were  independent  observations (ACF)  cross  zero  obtain the  nj_.  The  the  region.  first-zero  scales  that  of  (n^)  of  each per  were  Table  IV-1  c r o s s i n g s of used  to  of  S, the  the  section  each v a r i a b l e . s i n c e t h e ACF  be  of a  d i v i d e d i n t o the  independent  observations.  presents  point  length  ACF  of  of may  each  t h e ACFs o f a l l  decorrelation  scales  each v a r i a b l e i n each r e g i o n .  These  determine  the  the  were  field  observations The  95  Spatial  at the quarter-wavelength  number o f  a c t u a l number  for  d e t e r m i n e d f o r e a c h g e o g r a p h i c r e g i o n by a v e r a g i n g in  and  is  eddies.  calculated  T h i s d e c o r r e l a t i o n s c a l e may  exceed  from the  decorrelation  of  i n f e r r e d f r o m z e r o - c r o s s i n g s o f t h e ACF,  series to  v a r i a b l e was  100%  c o l d (W<0)  a dominant wavelength s h o u l d  spatial  x  autocorrelation function  (MODE G r o u p , 1 9 7 8 ) . the  Q  the  Sections  statistics  The  in  of  numbers  of  independent  64  T a b l e IV—1  D e c o r r e l a t i o n s c a l e s o b t a i n e d from t h e f i r s t - z e r o c r o s s i n g s o f the averaged autocorrelation functions f o r the sections i n each geographic r e g i o n .  Region  Decorrelation Scales T  D  NWA  59  63  NWP  72  76  NEA  54  52  SA  95  102  NEP  78  83  SP  81  77  HIGH  66  66  LOW  76  76  (km)  65 In  order  t o examine t h e g e o g r a p h i c  variability  s t a t i s t i c s were c a l c u l a t e d f o r each r e g i o n . standard  d e v i a t i o n s (Sp) i s o b t a i n e d  S  The p o o l e d  from the r e l a t i o n  j i s t h e number  pooled  estimates  determine  1974),  of  individual  sample  (4.4)  standard  ^^v  i ) s  i i ( K  + 3 ) ) / ( E  K-  j ) / s  t h e f o l l o w i n g d i s c u s s i o n on t h e g e o g r a p h i c  population  (Walpole,  o f t h e sample  deviations,  S^.  The  o f s k e w n e s s (Wp) a n d k u r t o s i s (Kp) a r e ,  K = P  statistics,  estimate  "pooled"  = d t n . - D S ^ / d n -j)  2  where  In  of the v a r i a b l e s ,  the s i g n i f i c a n c e of the pooled statistic  whether  detailed already.  of  each  or not W  region,  and K  o  4 )  <->  3  4  variability  estimates,  i s important.  with The  of the population  The 95% c o n f i d e n c e  -  6  of the mesoscale respect  t o the  methods  a r e nonzero  used have  to been  i n t e r v a l f o r the variance of a population  (a ) i s : 2  ((n j)/x  2 0 2 5  r  2  ) S  2  < a  2  < ((n j)/ r  2 x  9 7 5  )) S  2  ( 4  -  7 )  2  where x Q 2 5 a n a - X 9 7 5 the values of a chi-square d i s t r i b u t i o n with n^-j d e g r e e s o f f r e e d o m , l e a v i n g a r e a s o f .0 25 a n d .975, r e s p e c t i v e l y t o t h e r i g h t . a  r  e  2  For  (n^-j)>30,  a normal  distribution  may b e c o m p u t e d by t h e f o r m u l a s  (Selby,  0.5 (1.96 +  i s quite  accurate,  and thus x  values  1965):  (2(n..-j)-l) ) 1/2  2  (4.8) C  2 9 7 5  = 0.5 (-1.96 + ( 2 ( , - j ) - l ) n j  1 / 2  )  2  66 i.  Mid-thermocline Temperature  The  sample  statistics  d e v i a t i o n s o f t h e NWA i n t h e low-energy  of  a n d NWP  Statistics  T  are l i s t e d  i n Table  are not s i g n i f i c a n t l y  regions are a l l equal within  1.35 t o 1.46°C f r o m  value  o f 0.54°C w i t h  1184 i n d e p e n d e n t  a  95% confidence  The  different.  standard  The S  T  values  t h e 95% c o n f i d e n c e l i m i t s .  HIGH r e g i o n h a s a s t a n d a r d d e v i a t i o n o f 1.40°C of  IV-2.  w i t h a 95% c o n f i d e n c e  observations. interval  T h e LOW  The  interval  region has a  o f 0.52 t o 0.56°C  from  2223  consistent  with  independent o b s e r v a t i o n s .  The the  geographic  variability  climatological  boundaries  results  between  and t h e v a l u e s o f S  of  Emery  t h e high-energy  (1983a)  regions  are very  T  shown  i n Figure  III-4.  and t h e low-energy  The  regions are  a p p r o x i m a t e l y d e l i n e a t e d b y t h e 1.0°C c o n t o u r o f t h e s t a n d a r d d e v i a t i o n o f t h e 260 m t e m p e r a t u r e .  The h i g h - a n d l o w - e n e r g y  r e g i o n s c a n a l s o be a p p r o x i m a t e l y  d e l i n e a t e d b y t h e 1.0°C c o n t o u r i n a s i m i l a r temperature  a t 460 m  values  greater  values  less  than  than  (Emery, 1.0°C;  1.0°C.  map o f t h e s t a n d a r d d e v i a t i o n o f  1983a).  The NWA,  NWP  a n d HIGH r e g i o n s h a v e  S  T  t h e NEA,  SA, NEP,  SP  a n d LOW  S  T  The  amplitudes  of  t h e mesoscale  regions  have  variability  r e f l e c t e d i n the standard deviations of t h e mid-thermocline temperatures quasi-synoptic data and t h e c l i m a t o l o g i c a l data a r e very  The  HIGH a n d LOW  These s t a t i s t i c s  r e g i o n s have Q  suggest  as  ofthe  consistent.  v a l u e s o f 0.45 a n d 0.49, r e s p e c t i v e l y .  T  that p e r t u r b a t i o n s of T greater than  1.40°C o c c u r i n  a b o u t 4 5 % o f t h e HIGH r e g i o n , w h i l e p e r t u r b a t i o n s o f 0.54°C o c c u r i n a b o u t 4 9 % of  t h e LOW  region.  perturbations region  T h e s k e w n e s s o f t h e HIGH r e g i o n (W <0) s u g g e s t s T  are predominantly  (W >0) s u g g e s t s  deviation  T  that  they  distribution  ( S e l b y , 1965),  temperature  2.5  times t h a t o f t h e low-energy  G e o p o t e n t i a l Anomaly  of the standard  of this  ratio,  obtained using the F  Thus t h e a v e r a g e  amplitude o f  p e r t u r b a t i o n s i n t h e high-energy  regions i s  regions.  (0-4000 k P a ) S t a t i s t i c s  statistics  perturbations are listed  The r a t i o  o f t h e HIGH r e g i o n t o t h e LOW  a r e 2.16 a n d 3.09.  mid-thermocline  sample  temperature  The 9 5 % c o n f i d e n c e l i m i t s  the  The  e d d i e s , w h e r e a s , t h e s k e w n e s s o f t h e LOW  a r e warm e d d i e s .  of the mid-thermocline  r e g i o n i s 2.59.  ii.  cold  that the  of  the  i n Table IV-3.  geopotential  anomaly  The NWA a n d t h e NWP h a v e  (0-4000  kPa)  significantly  Table IV-2  Region  n  i  Sample standard deviation, skewness, kurtosis and intermittency of the mid-thermocline temperature (T) f o r the geogxaphic regions from the sections. w and K values that are s i g n i f i c a n t l y nonzero are underlined. Q i s shown only when K i s s i g n i f i c a n t l y nonzero.  S  T  CO  95% C o n f i d e n c e Limits  w  T  Rj,  Q  T  CO  NWA.  901  1.43  1.37 - 1.50  -0.66  3.96  0.43  NWP  283  1.30  1.20 - 1.40  0.13  1.63  0.63  NEA  503  0.51  0.48-0.54  0.04  3.89  0.44  88  0.48  0.42 - 0.54  0.14  -0.22  1354  0.57  0.55 - 0.59  0.17  3.55  0.46  278  0.56  0.51 - 0.60  0.12  1.69  0.74  HIGH  1184  1.40  1.35 - 1.46  -0.51  3.60  0.45  LOW  2223  0.54  0.52 - 0.56  0.11  3.16  0.49  SA NEP SP  CM  T a b l e IV-3  Region  n^  Sample s t a n d a r d d e v i a t i o n , skewness, k u r t o s i s and i n t e r m i t t e n c y o f the g e o p o t e n t i a l anomaly (D) f o r t h e geographic r e g i o n s from t h e sections. W and K v a l u e s t h a t a r e s i g n i f i c a n t l y nonzero a r e u n d e r l i n e d . Q i s shown o n l y when K i s s i g n i f i c a n t l y nonzero.  S  95% C o n f i d e n c e  D  (m /s ) 2  2  Limits  W  D  2  854  0.69  0.66  -  0.72  0.12  NWP  271  0.58  0.54  -  0.63  NEA  517  0.21  0.19  -  85  0.20  0.18  1330  0.26  279  HIGH LOW  NEP SP  D  Q  D  2  NWA  SA  K  (m /s )  3.63  0 .45  -0.05  1 .44  0.68  0.22  0.25  1.73  0 .63  -  0.23  -0.01  0.88  0.25  -  0.27  0.21  -  3 .44  0 .47  0.32  0.30  -  0.35  0.63  4.50  0.40  1125  0.67  0.64  - 0.69  0.10  3.44  0  >  4  7  2211  0.26  0.25  - 0.27  0 . 3 3  4.10  0  i  4  2  ^  69 different  S  values.  Q  The  that are significantly  lower  significantly  different  deviation  0.67  m /s 2  of  from  2  2  is  o f 0.26  from  2  m /s  m /s 2  each  with  2  a  a l l have  The  HIGH  95% confidence  a  standard  interval  95% confidence  from  deviations  The  HIGH  of  interval  whereas,  has a  region  The skewness  zero,  positive.  region  T h e LOW  observations.  different  i s significantly  other.  observations.  with  2  2211 i n d e p e n d e n t  not significantly  region  from  2  regions  than t h e high-energy r e g i o n s and a r e g e n e r a l l y n o t  1125 i n d e p e n d e n t  deviation m /s  low-energy  0.64  t o 0.69  has a  standard  of  0.25  to  o f t h e HIGH  t h e skewness  and  standard  t h e LOW  0.27  region  o f t h e LOW  regions  have  i n t e r m i t t e n c i e s o f 0.47 a n d 0.42, r e s p e c t i v e l y .  These than  statistics  0.67  m /s 2  perturbations region  and  2  may  greater that  predominantly  suggest be  i n about  0.26 m / s 2  LOW  warm e d d i e s .  geopotential  found  than  the  that  region  has  r e g i o n t o t h e LOW r e g i o n i s 2.58 w i t h  kPa)  i n t h e high-energy  47%  i n about  i s about  that  that  are  o f t h e HIGH  o f 2.15 a n d 3.08.  anomaly p e r t u r b a t i o n s  2.5 t i m e s  that  4 2 % o f t h e LOW  deviations limits  greater  region,  perturbations  of the standard 95% confidence  perturbations  t h e HIGH  mesoscale  of the geopotential  regions  of  may b e f o u n d  2  The r a t i o  Thus, t h e average amplitude  anomaly  (0-4000  o f t h e low-energy  regions.  C e n t r a l Moments o f t h e S u r v e y s  The  c e n t r a l moments o f t h e m i d - t h e r m o c l i n e  anomaly were c a l c u l a t e d  f o r e a c h o f t h e 29 s u r v e y s .  statistic  were  subregions  were a l s o examined:  the  North  determined  Pacific  f o r the geographic the North  Equatorial  Current  d i s c u s s e d a n d compared w i t h t h o s e independent  observations,  decorrelation scale  temperature and t h e g e o p o t e n t i a l  (Table  Pacific  regions.  estimates  These  of the trans-oceanic  from t h e f i r s t - z e r o  Mid-thermocline  The standard  Temperature  o f t h e NWA  be  t h e square  of the  crossings of t h e averaged survey.  Statistics  sample s t a t i s t i c s o f T from t h e surveys deviations  will  T h e number o f  ACFs o f t h e s e c t i o n s ) o f t h e a p p r o p r i a t e r e g i o n i n t o t h e a r e a o f e a c h  i.  two  (NPSF), and  statistics  sections.  by d i v i d i n g  o f each  I n t h e NEP,  Subtropical Front  (NPEC).  n ^ , was d e t e r m i n e d IV-1,  Pooled  a n d NWP  a r e shown i n T a b l e  are significantly  IV-4.  different.  The  The S  T  Table IV-4 Sample standard deviation, skewness, kurtosis and intermittency of the mid-thermocline temperature (T) f o r the geographic regions, the NPSF and the NPEC from the surveys. W and K values that are s i g n i f i c a n t l y nonzero are underlined. Q i s shown only when K i s s i g n i f i c a n t l y nonzero.  Region  No. o f  n^^  Surveys  S  T  95% C o n f i d e n c e  CO  L i m i t s (°C)  w  T  Krp  Q  1.89  0.61  T  NWA  6  494  1.71  1.61  - 1.81  NWP  2  230  1 .42  1.30  - 1 .54  0.47  1 .06  NEA  4  466  0.66  0.62  - 0.70  0.63  1.41  0.68  NEP  16  236  1.11  1.02  - 1 .20  0.37  0 .86  0.78  NPSF  10  129  0.91  0.81  - 1.02  0.24  0.44  NPEC  4  68  1 .39  1.19  - 1 .60  0.36  0.20  1  16  0.46  0.34  - 0.71  0.04  -0.48  SP  -0  .59  •  0.74  _  71 of  t h e NEP i s s i g n i f i c a n t l y  NPEC  has a S  Compared surveys  in  i s almost NWP,  regions well  the  Q  NEP.  These  higher  (except  t w i c e as l a r g e .  statistics Q  are  than  i n each  The s i g n s o f W  region,  obtained  a n d NEP.  from  with  larger  The  the sections,  f o r t h e NEP,  consistent  from  T  the S  those  than  of  values  by  G e o p o t e n t i a l Anomaly  that of the  of Q  a r e shown i n T a b l e values  and  T  compare  a  the  factor  of  1.7.  sections.  the corresponding  The  statistics  of  (0-4000 k P a ) S t a t i s t i c s  t h e SP h a v e  larger are NWA,  IV-5.  I n the high-energy  that are equal within  confidence  values  limits.  than  equal  t o those  t h e 95% confidence  that  D  The NPEC  the value  t h e NWP  of S  t h e NWP,  t h e 95%  d e v i a t i o n which  The s t a n d a r d  The NEA  with  those  from  0.10 o f t h e c o r r e s p o n d i n g higher  Q  D  from  Q  from  D  the surveys  c o m p a r e d t o t h e NEP Q  The  the  surveys  limits  i n the  significantly  higher  S  D  The s k e w n e s s i s s i g n i f i c a n t i n a n d t h e NEA v a l u e s , o n l y , a r e intermittences are a l l within  the sections,  than  d e v i a t i o n s from  have  T h e NWP  the sections.  i s significantly  t h e 95% c o n f i d e n c e  a n d t h e NEP  t h e NEA, t h e NPSF a n d t h e NPEC.  consistent  have  are, generally, equivalent within  the sections within  a n d t h e SP.  a n d t h e NWP  t h e NEP  has a s t a n d a r d  limits.  the surveys  T h e NEA,  o f t h e NPSF.  from  r e g i o n s , t h e NWA  v a l u e s from t h e surveys than from t h e s e c t i o n s .  a  nonzero  the exception of  The s a m p l e s t a t i s t i c s o f t h e g e o p o t e n t i a l a n o m a l y o b t a i n e d f r o m  D  of the  sections.  ii.  S  T  the sections f o r  with  i s larger  The  t h a t o f t h e NPSF.  i n the SP), p a r t i c u l a r l y  f o r t h e NWA  a r e somewhat  T  larger  regions.  The skewness o f T i s s i g n i f i c a n t l y  t h e NEA a n d t h e NEP.  w i t h those  intermittencies  t h e o t h e r two l o w - e n e r g y  the sections  of the surveys,  T  than  i s significantly  of  a r e t h e same  reasonably  the  values  T  are significantly  t h e NWA,  these  o f 1.39°C w h i c h  T  t o the S  NEP w h i c h  larger  the sections.  except  f o r t h e NWA  The NPSF h a s a Q  which  has  of  0.61  D  o f 0.37.  D  Summary o f t h e C e n t r a l Moments  The  geographic  baroclinic central  eddy  moments  variability  field of  have  been  the sections  summarized as f o l l o w s :  of  the  discussed and  mesoscale with  surveys.  temperature  the pooled The  primary  field  estimates results  and  of the can  be  Table IV-5 Sample standard deviation, skewness, kurtosis and intermittency of the geopotential anomaly (D) f o r the geographic regions, the NPSF and the NPEC from the surveys. W and K values that are s i g n i f i c a n t l y nonzero are underlined. Q i s shown only when K i s s i g n i f i c a n t l y nonzero.  Region  No. o f  n.^  Surveys  S  95% C o n f i d e n c e  D  (m /s ) 2  2  Limits  W  D  K  D  Q  Q  (m /s ) 2  2  NWA  6  432  0.71  0.67 -  0.76  0.21  1 .76  0 .63  NWP  2  207  0.63  0.59 -  0.71  0.52  1 .04  0 .74  NEA  4  502  0 .32  0.30 -  0.34  0.99  2.42  0.55  NEP  16  206  0.46  0.42  -  0.50  -0.06  5.11  0 .37  NPSF  10  112  0 .32  0.28 -  0.35  0.53  1 .91  0.61  NPEC  4  60  0.53  0.45  -  0.61  -1 .09  6.75  1  17  0.46  0.34  -  0.70  0 .26  -0 .70  SP  -  73 a.  The b a r o c l i n i c m e s o s c a l e eddy f i e l d be  quantitatively  regions-  The  average with  HIGH  amplitudes  average  region o f 0.67  amplitudes  geopotential 'region  compared u s i n g  anomaly  than  that  m /s ,  the baroclinic  eddies.  The s k e w n e s s The  m /s . 2  The  2  a r e 2.58  field  o f t h e HIGH  intermittencies  are  greater  o f t h e LOW  predominantly,  same  and  over about 45% o f each  skewness o f t h e t e m p e r a t u r e  that  discussed  above.  that  the b a r o c l i n i c  The n e g a t i v e  eddy  field  standard  deviations  most p a r t , g r e a t e r the  NEP, t h i s  activity  running  region  t h e surveys  statistics  subregions I n t h e NWA,  a n d NPEC,  characteristic  of  corresponding  deviations  eddies,  as  are, f o r the  of the sections.  In  of relatively  high  eddy  NWP  this  i s a  a n d NEA,  w i t h a l i n e a r t r e n d , r a t h e r t h a n a 1000 km  as subregions t h e low-energy  statistics  o f t h e NEP, regions.  o f t h e NEP  of the mid-thermocline  greater  positive. negative  suggests  regions.  have  The  mesoscale  standard  t e m p e r a t u r e and g e o p o t e n t i a l anomaly i n t h e two s u b r e g i o n s  are  cold  with  mean.  T h e NPSF  the  of  The  i s consistent  i n t h e HIGH r e g i o n  i n t h e low-energy  of sampling  ( i . e . t h e NPSF a n d N P E C ) .  r e s u l t of detrending  The r a t i o  and i n t e r m i t t e n c i e s o f t h e s u r v e y s  i s a result  regions  o f t h e two r e g i o n s .  i n t h e LOW  than the corresponding  the  r e g i o n i s 2.59, w h i c h  c o n s i s t s of predominantly  o p p o s e d t o t h e f i e l d o f warm e d d i e s  The  t o t h e LOW  skewness  that  T h e HIGH a n d LOW  t h e same a s t h a t f o r t h e g e o p o t e n t i a l a n o m a l y  positive  different  c a n a l s o be e x a m i n e d  o f 1.40 a n d 0.54°C, r e s p e c t i v e l y .  d e v i a t i o n o f t h e HIGH r e g i o n  region  region.  have s t a n d a r d standard  HIGH  o f warm  indicate  temperature  deviations  statistics.  of the  i n the  i s not s i g n i f i c a n t l y  the  with  perturbations  amplitudes  skewness  consists,  region  has  average  The p o s i t i v e  eddy  region  times  LOW  perturbations  w i t h the mid-thermocline  is  d.  anomaly  a n d t h e LOW  2  o f t h e HIGH a n d  The g e o g r a p h i c v a r i a b i l i t y o f t h e m e s o s c a l e e d d y f i e l d  the  c.  moments  geopotential  2  region.  mesoscale p e r t u r b a t i o n s occur  b.  has  o f 0.26  i n t h e LOW  zero.  the central  perturbations  suggests  from  i n t h e h i g h - and low-energy regions can  W. D  i s consistent  This  with  f o u n d i n t h e AXBT s u r v e y s  discussed  are greater  and b a r o c l i n i c  The  of than  standard  eddy  fields  T h e s k e w n e s s o f D i n t h e NPSF i s  t h e NEP  i s consistent with  deviations  the sections.  temperature  i n t h e NPEC t h a n t h e N P S F . This  from  statistics  statistics.  the f i e l d  of cold  i n Chapter I I I .  The NPEC h a s a eddies  that  was  74  C.  SEASONAL VARIABILITY OF THE The  seasonal  variability  examined i n t h i s s e c t i o n . in  the f o u r q u a r t e r s of  particular, over  60%  generally, obvious whole,  the has  sections a  good  The  effect  The  NEP  is a  i s the  (Table  h a v e no  in  last  the  of  investigate due  the  When t h e even  seasonal  the  NEP  potential  data  The  four  f o r the  the  The  deviation,  v a r i a t i o n s f o r b o t h T and  data  have  on  the  most  even  variability  seasonal  t h e f i r s t two year.  The  of  skewness D.  of  The  NEP  first  the  data  set,  region, the  the  i s not of  of the pooled year the  will  clear.  sections  statistical be  regional  used  statistics  year.  summarized  intermittency  i n Table  factor  have  IV-7.  seasonal  s m a l l e s t i n t h e l a s t two q u a r t e r s o f of  each  r e g i o n a l l y - p o o l e d skewness  the  to  s t a n d a r d d e v i a t i o n s o f T and D a r e l a r g e s t i n  q u a r t e r l y - p o o l e d skewness  q u a r t e r s and  a  year.  variable  with  one The  i s consistent with exception.  W  the  i n t e r m i t t e n c i e s of T  smallest i n t e r m i t t e n c i e s i n the  second  and  the the  in  D  D e x h i b i t s i m i l a r seasonal v a r i a t i o n s w i t h the l a r g e s t i n t e r m i t t e n c i e s i n third  In and  (with  throughout results  the  are  f o u r t h quarter i s negative r a t h e r than p o s i t i v e .  and  be  quarter  year  distribution  b i a s i n g of  the  and  q u a r t e r s of t h e y e a r and  corresponding  will  r e g i o n s are c o n s i d e r e d as  of  quarters  quarterly-pooled statistics  standard  NEP  low-energy  throughout  distribution  biases w i l l  the  Each  t o the uneven d i s t r i b u t i o n of the s e c t i o n s over the  The  the  s e c t i o n s i n the  low-energy  region with  for  of  shows some s e a s o n a l b i a s e s .  quarter.  of  over the f o u r quarters of the year. estimates  IV-6),  regions  SA) .  geographic  statistics  d i s t r i b u t i o n o f t h e q u a s i - s y n o p t i c XBT  reasonably  t h a t these  mesoscale  distribution  exception of the there  the  year  the high-energy  of  of  The  the  STATISTICS  and  first  fourth  quarters.  In  summary,  skewness and  i t has  been  intermittency exhibit  the mesoscale s t a t i s t i c s  obtained  s e a s o n a l l y b i a s e d f o r t h e NWA, except  seen  t h e NEP  a n d LOW)  due  NWP,  that  in  the  a seasonal from the  NEP  the  standard  variability.  This suggests  q u a s i - s y n o p t i c XBT  HIGH, NEA,  SA  and  SP  deviation,  data  that  s e t may  ( i . e . a l l the  be  regions  t o the uneven d i s t r i b u t i o n of the s e c t i o n s over  the  year.  These r e g i o n s w i l l the s t a t i s t i c s variability  have s e a s o n a l l y - b i a s e d s t a t i s t i c s  have s e a s o n a l  signals.  o f t h e m e s o s c a l e eddy  field  To  the  has  author's  o n l y , of course, knowledge, the  been r e p o r t e d o n l y  in a  where  seasonal subregion  75 T a b l e IV-6  Summary o f t h e number o f s e c t i o n s by geographic o f the y e a r .  Geographic  r e g i o n and q u a r t e r  Quarter o f t h e Year  1  2  3  4  NWA  o  4  4  15  23  NWP  rj  4  0_  4  8  Total  0  8  4  19  31  NEA  1  4  4  7  16  SA  2  0  0  0  2  NEP  8  5  10  14  37  SP  3  1  0  5  9  14  10  14  26  64  Region  Tota:  HIGH  LOW  Total  T a b l e IV-7  Summary o f t h e s t a t i s t i c s o f T and D from t h e s e c t i o n s f o r t h e NEP by q u a r t e r o f t h e yearW and K v a l u e s t h a t a r e s i g n i f i c a n t l y nonzero a r e u n d e r l i n e d . Q i s shown o n l y when K i s s i g n i f i c a n t l y nonzero. The T s t a n d a r d d e v i a t i o n s have u n i t s o f ° C . The D s t a n d a r d d e v i a t i o n s have u n i t s o f ( m / s ) . 2  Variable  Quarter  No. o f S  T  D  e  c  t  i  o  n  nL  s  95% C o n f i d e n c e  W  K  Limits  s  1 2 3 4  8 5 10 14  294 205 407 448  0.68 0.65 0.42 0.58  0.63 0.59 0.39 0.54  -  0.73 0.71 0.44 0.61  0.09 0.59 0 .45 -0.12  1.17 4.43 2.04 4.05  0.72 0.40 0.60 0 .43  1 2 3 4  8 5 10 14  285 202 402 441  0.29 0.32 0.22 0.25  0.26 0 .29 0.20 0 .23  -  0.31 0.35 0.23 0.26  0.34 0.42 0.45 -0 .30  2.40 3.90 1.29 3.20  0.56 0.44 0.70 0.48  77 of  t h e NEA.  eddy k i n e t i c north  Dickson energy  e t a l . (1982) f o u n d a s i g n i f i c a n t estimates  o f the Azores  a t a number o f s i t e s  (35°N t o 60°N).  (NEADS) c o l l e c t e d t w o - y e a r - l o n g m.  The a m p l i t u d e  The N o r t h  current  of the signal  d o m i n a t e d by t h e w i n t e r maxima.  records  was  This  large  paucity  examination of  o f t h e data  of theissue.  however  i n t h e Northeast  East  Atlantic  of the  Atlantic,  Dynamics  Study  a t d e p t h s b e t w e e n 200 a n d 4000 enough  that  t h e records  were  o r roughness.  available w i l l  not permit  a more  comprehensive  T h i s a n a l y s i s may b e u s e d t o h i g h l i g h t t h e p o t e n t i a l  the biasing of the results  field,  signal  e f f e c t was s e e n f r o m 200 t o 4000 m a t a l l  the s i t e s w i t h s i g n i f i c a n t bottom slopes  The  seasonal  the biasing  due t o s e a s o n a l  cannot  s i g n a l s o f t h e mesoscale  be q u a n t i t a t i v e l y o r even  eddy  qualitatively  determined.  D.  HORIZONTAL ANISOTROPY  An  anisotropy  autocorrelation  factor,  functions  A of  has  s  been  evaluated  t h e surveys  using  the  t o parameterize  averaged  the horizontal  a n i s o t r o p y o f t h e m e s o s c a l e eddy f i e l d s .  The a n i s t r o p y f a c t o r i s o b t a i n e d  the  and  relation,  zonal  A  = L /L ,  s  M  decorrelation  averaged  where  Z  scales  meridional  obtained  and zonal  anisotropy f a c t o r i s important, been w i d e l y  used  i nthis  are n o t i s o t r o p i c , A  The  averaged  s  L  from  t o evaluate  are  the  w i l l provide  zero-crossings  20 km w i d e b i n s .  t o t h e rhumbline  Where t h e m e s o s c a l e  eddy  and zonal  autocorrelation  i n each geographic r e g i o n .  fields  functions  The A C F s o f  F o r the  distance  i s o t r o p i c ACF,  between  them.  t h e XBT p a i r s w e r e The m e r i d i o n a l  separation,  Due  respectively, within o r zonal  a r e somewhat  appropriate  The  anisotropy.  meridional  ACFs  of the  respectively.  A C F s w h e r e c a l c u l a t e d by b i n n i n g t h e XBT p a i r s b y t h e i r  meridional  and  t h eassumption o f i s o t r o p y that has  a measure o f t h a t  meridional  meridional  w e r e c a l c u l a t e d by b i n n i n g t h e p e r t u r b a t i o n v a r i a b l e s o f e a c h p a i r  o f XBTs i n t o according  z  the f i r s t  studies.  (ACFs) were c a l c u l a t e d from the surveys each survey  L  autocorrelation functions,  and other  isotropic,  M  from  extent  noisy.  individual  ACFs  20  km  wide  swaths.  o f some o f t h e s u r v e y s , The a v e r a g e d within  ACFs were  t h e geographic  regions.  p l o t s o f t h e A C F s f o r t h e NWP a n d t h e NEP a r e shown i n F i g u r e  and zonal and zonal  t o the limited  the meridional obtained  binned  and zonal  by averaging t h e As an example, IV-2.  78  NWP  NEP  F i g u r e IV-2  Sample p l o t s o f t h e averaged i s o t r o p i c , m e r i d i o n a l and z o n a l a u t o c o r r e l a t i o n f u n c t i o n s f o r t h e NWP and NEP. The p l o t s on t h e l e f t a r e t h e i s o t r o p i c ACFs w i t h 95% c o n f i d e n c e l i m i t s (dashed lines). The p l o t s on t h e r i g h t a r e t h e i s o t r o p i c ACFs (solid l i n e ) , m e r i d i o n a l ACFs (long-dashed l i n e ) and t h e z o n a l ACFs (short-dashed l i n e ) .  79  The of  the  The to  isotropic decorrelation regionally-averaged  geographic the  95%  IV-8),  exhibit  scales  from  twice  as  the  the  same  as  determined from ACFs.  The  confidence  the  first-zero  decorrelation  confidence  l e v e l where the  confidence  limits  without  a  single  significantly  The  are  limits  of  factor  L  scales  There  the  quite  K.  mesoscale  uniquely  region  95%  95%  km  Table  does not  are  about was  mean f o r  the  IV-8  may  be  limits  of  the  at  cross  It i s sufficient decorrelation  Table  signal  determined  limit  in  scales  running  in  defined  decorrelation  confidence  and  zonal  i n Table  in  error  the  bars  each  to  the  95%  zero.  The  say  scales  that,  are  examined  The  same  manner  (not  shown).  other,  thus,  therefore in  decorrelation  IV-9.  i n d i c a t i o n from  a n i s o t r o p i c and  fields  be  meridional  significant  eddy  the  isotropic  d i f f e r e n t from no  the  large-scale  1000  of  be  underlined as  scales  shown.  determined  the  the  can  IV-8.  not  other.  the  be  with  is  not  geographic  m e s o s c a l e eddy f i e l d s a r e for  are  the  a  confidence  the  and  may  z  significantly  one.  and  d i f f e r e n t from each  and  decorrelation nowhere  wide  s u m m a r i z e d by 1^  cannot  u p p e r 95%  exception,  anisotropy  scales  from  are  of  are  crossings  i n Table  that  decorrelation  because  crossings  scale  scales,  variability  s u r v e y s and  limits  first-zero  summarized  that  These  sections  f i t f o r the  95%  scales  IV-1).  the  are  decorrelation  geographic  the  from  surveys  ( i . e . the  (Table of  obtained  the  these  general  those  detrended with a l i n e a r The  of  limits  sections  large  sections.  ACFs o f  variability  confidence  scales  this  A  as  confidence  the L^j  is  s  these  the  95%  length  isotropic  and  not  L  are  z  different  results  assumption of  that  the  isotropy,  i n v e s t i g a t i o n , appears  to  be  reasonable.  WAVENUMBER SPECTRA The  purpose of t h i s  wavenumber  spectra  of  anomaly p e r t u r b a t i o n s . methods  used  distribution  to of  s e c t i o n i s t o examine t h e the This  estimate variance  eddy k i n e t i c e n e r g y , and  mid-thermocline  the  of  10~3  to  the  SEASAT a l t i m e t r y a n a l y s i s o f  cycles/km  wavenumber s p e c t r a (i.e. Fu  1000  total  space,  the b a r o c l i n i c l e n g t h  examination of 2  spectra,  i n wavenumber  This  10~  temperature  and  the  section i s divided i n t o subsections the  the  geographic v a r i a b i l i t y  the and  spectral dominant  of  the  geopotential discussing  the  variance,  the  wavelengths,  the  velocity scales.  will  be  restricted  to  100  km  wavelengths)  (1983).  The  mesoscale  to the  range  similar  s i g n a l s are  to  either  80  T a b l e IV-8  Isotropic decorrelation scales obtained from the first-zero c r o s s i n g s o f the r e g i o n a l l y - a v e r a g e d a u t o c o r r e l a t i o n functions of the surveys- The d e c o r r e l a t i o n s c a l e s t h a t can be defined to the 95% c o n f i d e n c e l e v e l a r e u n d e r l i n e d -  Region  Decorrelation Scales T  D  NWA  147  145  NWP  135  150  NEA  146  130  NEP  191  200  NPSF  150  143  NPEC  122  104  115  >180  SP  (km)  81  Table IV-9  The anisotropy factor, Ag = L / L , i s the r a t i o of the meridional decorrelation length scale ( 1 ^ ) from the averaged meridional autocorrelation function of the the surveys to the zonal decorrelation length scale ( L ) from the averaged zonal autocorrelation function. The units of L J J and L are kilometers. M  Z  Z  Z  Region A  s  T L  M  L  z  A  s  D L  M  L  z  NWA  0.34  85  250  0.55  123  224  NWP  1-10  152  138  1.08  153  142  NEA  —  >160  149  —  >160  140  0.73  210  289  2.76  387  140  NPSF  0.75  119  159  0.86  111  129  NPEC  —  89  >320  —  85  >320  1-01  117  116  —  110  >180  NEP  SP  82 sufficiently  small  unimportant intervals from  at  of  100  the  As w i l l  to  the  also and  10 3  facilitates  the  E s t i m a t i o n of the  The  SA  of  The  and  the  spectra  SP)  small  amounts  considerably  greater  range.  comparison of  The  use  of  the  of  this  the  s p e c t r a between the  the  variance  be  sampling  wavenumbers t h a t  are  than  10  variance  - 2  than  compared  wavenumber geographic  range regions  (1983).  variability  of  variance-conserving  will  be  identified  spectra  of  each  using  in  wavenumber  spectral plots,  variance-conserving  of  the  geographic  individual  region  trans-oceanic  were  space  and  will  the  spectral  obtained  sections.  The  the  UBC  Computing C e n t r e  requires  no  sections  were  cycles/km  and  x  padding  10 4  computed  into  averaged,  with  2.5 a  library  t r u n c a t i n g of  binned  and  -  or  software  x  wavenumber  to 10  the  obtain  Daniell  data.  bins  regional  cycles/km-  - 2  (Moore,  be  dominant  plots  with  averaging  the  (boxcar)  raw  This  raw  of  of  3.9  the  x  estimates  spectral five  subroutine  estimates  spectral  over  estimates  subroutine a v a i l a b l e  widths  Smoothed  window  spectral  1981).  The  with  by  raw  o f e a c h s e c t i o n were c a l c u l a t e d u s i n g a F o u r i e r t r a n s f o r m  1.95  vary  to  bars.  The  in  average  regions  Nyquist  filter  g e o p h y s i c a l s i g n a l s a t wavenumbers h i g h e r  cycles/km  examined u s i n g normalized  error  high-pass  Spectra  geographic  wavelengths  geographic  the  relatively  w i t h t h e r e s u l t s of Fu  the  cycles/km.  -  the  of  seen, the  - 2  10 3  by  c r e a t e s a wide range  contain 10  than  exception  be  to  -  less  attenuated  series i n  This the  cycles/km*  - 2  spatial  (with  cycles/km.  sufficiently  wavenumbers  t o 35 km.  generally  10  or  10~3  between  estimates  adjoining  were  spectral  estimates.  Variance-conserving  p l o t s of the  smoothed s p e c t r a l e s t i m a t e s  by  s p e c t r a w h e r e p r o d u c e d by m u l t i p l y i n g t h e  t h e i r corresponding  r e s u l t s o n a l o g a r i t h m i c wavenumber s c a l e . of  this  (If area  plot  these under  10  - 2  variance  to  the  variance  p l o t s were p r o d u c e d  conserving to  i s equal  the  curve  p l o t s of  cycles/km within  would the  by this  be  on  wavenumber  u n d e r any  the  wavenumber b a n d  w i t h i n t h a t wavenumber b a n d t i m e s  to  were the  area  n a t u r a l l o g a r i t h m i c wavenumber  equal  spectra  dividing  a  The  wavenumbers a n d p l o t t i n g  the  variance.)  produced  for  wavenumber  variance-conserving range.  The  area  scale,  Normalized  the  spectra  under  the  2.3.  variancerange  by  the  the  curve  10"-* total of  a  83 normalized  variance-conserving  plot  between  10"3  a n a t u r a l l o g a r i t h m i c wavenumber s c a l e i s e q u a l plotted  on  a  logarithmic  interpretation.  Examples  shown i n F i g u r e variability  wavenumber  IV-3.  of  the  These  the  distribution  wavelengths of  1000  and  Two  different  sets  conserving spectrum. and  eighty  percent  with  the  d e v i a t i o n of  spectral  estimates.  was  c  relation  C  using  > 0  spectral  due  t o the instrument  Spectral  was  were  wavelength, regions.  The  IV-10.  exhibit  the  estimates region,  of the  respectively. (m/s) . 4  s p e c t r a have  been  ten  to  discuss  each  facilitate spectra  the  are  geographic  v a r i a b l e between  the  n  > 30,  s  n o i s e and  and  of  variance-  Ninety-five percent using  the  standard  is  s  n  the  sample  i s the  s  number  1*960,  the  value  of  .025  the  right.  For  Student-t  confidence  to the  estimate  area  the  error  S  =  each  i n t e r v a l s were c a l c u l a t e d  where  C.025  l e a v i n g an  IV-4.  determined  confidence  ?  for  to  distribution  the n  with  account  computational  geophysical  for  the  s  same  uncertainty  p r o c e d u r e and  the  <  g  n -1  i n t e r v a l s were c a l c u l a t e d w i t h the bars,  of  of  uncertainty  signal.  Variance  obtained  Table  of  to  produced  were  95%  s  from  due  spectral variance  regions  s  These  estimates  used  were  smoothed s p e c t r a l  80%  v  the  The  5  obtained The  The  2 S /(n ) /2  > 0  For  degrees of freedom.  bars  1  normal d i s t r i b u t i o n  30» ' . 0 2 5  be  variance  intervals  estimate.  the  base  on  variance-conserving  e x a m p l e i s shown i n F i g u r e  relation + C  standard  standard  error  confidence  e r r o r of each s p e c t r a l  the  the  The  cycles/km  - 2  km.  of  An  of  will  10  t o one.  to  normalized  spectra  of  100  scale  and  The  by  o f T and  i n t e g r a t i n g the  i n t e g r a t e d up so  their  variance The  Nyquist  estimates  with  95%  confidence  of  LOW  r e g i o n c o m p a r e d t o t h e LOW  in  geographic  deviations of  of  variances  T  and  region each  this  of  the  D  are  these  variable i s  region.  at  limits  as  the  spatial  about  are  2  are  significantly  and  100  km,  SA  and  SP  the  200  km  to  the  other  summarized  band,  in  naturally,  regionally-pooled  series.  1.018°C  variances  and  The  comparable  wavenumber  variability  1000  spectra.  wavenumbers  directly  standard  variance  their  not  spectral  the  variance-conserving  are  variances In  between wavelengths of  variances  same p a t t e r n s the  to  D,  In  the  0.237  0.169°C higher  2  in  HIGH  (m/s) , 4  and the  0.040 HIGH  84  WAVELENGTH - KM 10 io io  10  4  3  2  [O  IO'  4  3 5 IO"  3  3 5 IO"  2  3 5 IO"  K - CYCLES/KM •  F i g u r e XV-3  WAVELENGTH - KM . 10 10 IO  1  1  3  4  IO-  4  3 5 10-  3  2  1  3 5 IO"  2  3 5 IO'  1  K - CYCLES/KM  Examples o f the n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a . These two spectra represent the variance of the geopotential anomaly p e r t u r b a t i o n s , D, as a f u n c t i o n o f wavenumber f o r t h e HIGH and LOW regions. The v a r i a n c e - c o n s e r v i n g s p e c t r a were n o r m a l i z e d by t h e total variance between wavenumbers of 10"^ and 10 cycles/km. These s p e c t r a a r e u s e d t o compare t h e s p e c t r a l shapes between g e o g r a p h i c r e g i o n s . - 2  85 W A V E L E N G T H •  10  4  10  3  luii M i  10-  i  in11111  IO  4  in11111  i  10'  3 5 10-* • 3 5 10"  3  -  i  W A V E L E N G T H  IO  10  4  IO-  4  C Y C L E S / K M  W A V E L E N G T H  colO  KM  2  3 5 10K  -  IO  -  KM  10  3  3 5 IO"  c£l0  IO-  3 5 IO"  3  K  -  3 5 IO"  2  3 5 10"'  C Y C L E S / K M  IO-  4  KM  1 | I | llllj  3 5 IO"  3  K  -  10*  3  [ T| 4  -  3 5 10"  C Y C L E S / K M  10  4  10'  2  W A V E L E N G T H  N  10'  2  -  KM  2  3 5 IO"  3  K  -  10  3  10'  1 | I 11 III  3 5 IO"  2  3 5 10"'  C Y C L E S / K M  F i g u r e I V - 4 Examples o f t h e v a r i a n c e - c o n s e r v i n g s p e c t r a w i t h confidence limits. T h i s f i g u r e presents the spectra o f the geopotential anomaly p e r t u r b a t i o n s f o r t h e HIGH and LOW r e g i o n s w i t h two d i f f e r e n t sets o f e r r o r bars. The s p e c t r a on t h e l e f t s i d e have 95% c o n f i d e n c e i n t e r v a l s o b t a i n e d w i t h t h e standard e r r o r o f t h e s p e c t r a l e s t i m a t e s o f t h e s e c t i o n s . The s p e c t r a on t h e r i g h t s i d e have 80% c o n f i d e n c e i n t e r v a l s o b t a i n e d i n t h e same manner. These s p e c t r a a r e used t o i d e n t i f y d i s t i n c t peak wavenumbers and t h e c o n f i d e n c e w i t h which they a r e d e f i n e d .  86  T a b l e IV-10  V a r i a n c e o f T and D w i t h 95% c o n f i d e n c e l i m i t s o b t a i n e d by i n t e g r a t i n g t h e s p e c t r a between wavelengths o f 1000 and 100 km. The SA and SP v a r i a n c e s have a s t e r i s k s s i n c e t h e s e r e g i o n s have average N y q u i s t wavenumbers l e s s than 10 c y c l e s AmThe v a r i a n c e s o f these r e g i o n s were o b t a i n e d by i n t e g r a t i n g the spectra from 10~3 cycles/km t o t h e N y q u i s t wavenumber ( a t a p p r o x i m a t e l y a 200 km wavelength). - 2  T Region  Variance  D  95% C o n f i d e n c e  (»C )  Limits  NWA  1.014  NWP  (°C )  Variance  95% C o n f i d e n c e  (m /s )  Limits  0.665 - 1.426  0.239  0.142 - 0.336  1.015  0.580 - 1.378  0.219  0.131 - 0.307  NEA  0.107  0.041 - 0.173  0.017  0.010 - 0.027  SA  0.096*  0.077 - 0.121  0.016*  0.011 - 0.023  NEP  0.194  0.149 - 0.246  0.045  0.036 - 0.056  SP  0.131*  0.092 - 0.170  0.035*  0.017 - 0.049  HIGH  1.018  0.732 - 1.304  0.237  0.168-0.321  LOW  0.169  0.139 - 0.211  0.040  0.031 - 0.049  2  2  4  4  (m /s ) 4  4  87 I n t e r p r e t a t i o n of the Spectra  The  geographic  wavelengths  variability  of  o f t h e wavenumber  variance-conserving  plots  t h e wavenumber  spectra  of  each  spectra  will  be  discussed  variable  as  depicted  and  with on  the  dominant  the normalized  maps  showing  the  geographic regions that the spectra represent (e.g. Figure IV-5).  This product  has  the  been  shapes.  designed  to  The d o m i n a n t  facilitate wavelengths  by g e o g r a p h i c r e g i o n i n t a b l e s wavelengths, variance  the  wavenumber  bands.  determined  from  bands  were  troughs  10  The  10~  dominant  2  the  by  that  wavelengths  and  the half-power  a d j a c e n t bands.  The  with  points  are  spectral summarized  the  percentage  i s accounted confidence  of  of  f o r by  The  spectral  of the  intervals  bars.  the  t h e peak  were  wavelength  peaks  the variance,  or the  that  each  1000 a n d 100 km,  was  spectra.  S p e c t r a o f the M i d - t h e r m o c l i n e Temperature  The dominant  wavelengths  are tabulated  o f T a r e shown i n F i g u r e I V - 5 .  i n Table  IV-11.  The  h a s t w o d o m i n a n t w a v e l e n g t h s a n d t h e s p e c t r u m o f t h e NWP  wavelengths low-energy are  and  v a r i a n c e between  The n o r m a l i z e d v a r i a n c e - c o n s e r v i n g s p e c t r a  NWA  variable  error  percentage  determined from n o r m a l i z e d v a r i a n c e - c o n s e r v i n g  of  This product l i s t s  cyclesAm)  w a v e l e n g t h band c o n t r i b u t e s t o t h e t o t a l  i.  o f each  bandwidths  variance-conservingspectra  defined  between  levels,  and  - 3  of v a r i a t i o n  comparisons  (e.g. Table IV-11).  confidence  (between  the geographic  which  are d i s t i n c t  to at  least  t h e 80%  r e g i o n s h a v e one d o m i n a n t w a v e l e n g t h e a c h  distinct  to at least  t h e 80% c o n f i d e n c e l e v e l .  spectrum  has t h r e e  of the dominant  confidence level.  The  ( e x c e p t f o r t h e NEP)  which  T h e NEP  has two  dominant  a t 340 km,  distinct  w a v e l e n g t h s , b o t h d i s t i n c t t o t h e 95% c o n f i d e n c e l e v e l .  T h e T s p e c t r u m o f t h e HIGH r e g i o n h a s p e a k w a v e l e n g t h s to  t h e 95% c o n f i d e n c e l e v e l s ,  levels. to  T h e LOW  r e g i o n has peak w a v e l e n g t h s  confidence  levels.  The  distinct  t o t h e 80% c o n f i d e n c e  o f 320 a n d 170 km,  difference  distinct of the  v a r i a n c e between t h e s e two s p e c t r a i s c h a r a c t e r i s t i c o f t h e d i f f e r e n c e s  between  s p e c t r a l shapes o f t h e h i g h - and low-energy  wavelengths  a r e comparable,  t h e HIGH  region  i n the  both  distribution  the  t h e 95%  a n d a t 195 km,  regions.  has a  A l t h o u g h t h e dominant  smaller  percentage  of i t s  v a r i a n c e i n t h e l a r g e r wavelength band and t w i c e t h e p e r c e n t a g e o f i t s v a r i a n c e in  t h e s h o r t e r w a v e l e n g t h b a n d t h a n t h e LOW  region.  00  CO  F i g u r e IV-5  Normalized v a r i a n c e - c o n s e r v i n g spectra of the mid-thermocline temperatures on a map showing t h e r e g i o n s t h a t the s p e c t r a represent. The s t i p p l e d areas are t h e high-energy r e g i o n s . The spectra are p l o t t e d between wavenumbers of 10 and 10 cycles/km. - 3  - 2  89  T a b l e IV-11  Region  Peak wavelengths o f t h e temperature s p e c t r a . The peaks a r e d i s t i n c t t o the c o n f i d e n c e l i m i t s shown. The wavelength band i n d i c a t e s t h e range between t h e h a l f - p o w e r p o i n t s . The p e r c e n t variance i s the c o n t r i b u t i o n t o t h e t o t a l v a r i a n c e between wavelengths o f 1000 and 100 km. The t o t a l v a r i a n c e s o f t h e SA and SP were determined between 1000 and 200 km.  Peak Wavelength (km)  Confidence Level  285  95%  560 - 220  53  165  80%  220 - 120  35  340  95%  590 - 245  58  180  80%  245 - 160  18  145  80%  160 - 120  13  NEA •  220  95%  320 - 130  63  SA  395  80%  600 - 300  73  250  ~  300 - 210  18  320  95%  600 - 200  70  170  95%  200 - 110  13  SP  395  80%  600 - 220  81  HIGH  340  95%  600 - 220  53  195  80%  220 - 130  30  320  95%  700 - 195  70  170  95%  195 - 120  15  NWA  NWP  NEP  LOW  Wavelength B a n d (km)  Percent of Variance  90 ii.  S p e c t r a o f t h e G e o p o t e n t i a l Anomaly  The The  dominant  wavelengths  wavelengths.  are tabulated  i s not d i s t i n c t  has t h r e e peak wavelengths, a l l d i s t i n c t  level.  T h e NEA  has t h r e e dominant  wavelengths  wavelengths  SA a n d NEP  s p e c t r a l shapes  are d i s t i n c t  i n t h e HIGH r e g i o n o c c u r a t 300 km, d i s t i n c t  the  95% c o n f i d e n c e l e v e l ,  distinct  iii.  level.  The  spectral  t o t h e 95% c o n f i d e n c e l e v e l , t o t h e 80% c o n f i d e n c e  r e g i o n has peak wavelengths a n d a t 170 km.  respective  The  a t 300 km,  latter  spectral  level.  distinct peak  to  i s not  t o t h e 80% c o n f i d e n c e l e v e l .  geographic v a r i a b i l i t y  wavelengths summarized  of t h e mesoscale  o f b o t h t h e wavenumber s p e c t r a a n d t h e d o m i n a n t temperature  and b a r o c l i n i c  The dominant  wavelengths  with  of v a r i a b i l i t y  fields  c a n be  confidence levels  a t which they are d i s t i n c t  IV-12).  are  no s i g n i f i c a n t  the  h i g h - e n e r g y r e g i o n s and t h e low-energy  high-energy  The dominant  o f t h e T and D v a r i a b l e s have been  and  of  eddy  as f o l l o w s :  identified  b.  The l o n g e r  Summary o f t h e Wavenumber S p e c t r a  The  a.  spectra.  155 km p e a k i s n o t d i s t i n c t  i n t h e LOW  wavelength.  regions a r e , of course, s i m i l a r t o  peaks  D spectrum  level.  a t t h e 80% c o n f i d e n c e l e v e l .  o f t h e HIGH a n d LOW  The  two  t o t h e 95% c o n f i d e n c e  t o t h e 95% c o n f i d e n c e  of the mid-thermocline temperature  The  has  The SA a n d t h e NEP h a v e t w o  those  a n d a t 155 km.  NWA  t o a t l e a s t t h e 80% c o n f i d e n c e  e a c h a n d t h e SP h a s one d o m i n a n t  o f t h e NEA,  The  t o t h e 80% c o n f i d e n c e  wavelengths.  other wavelengths a r e not d i s t i n c t  The  IV-12.  The l o n g e s t w a v e l e n g t h i s d i s t i n c t  and the s h o r t e r wavelength  dominant  o f D a r e shown i n F i g u r e I V - 6 .  i n Table  The NWP  The  kPa)  normalized variance-conserving spectra  dominant  level  (0-4000  scale  wavelengths  a r e b e t w e e n 400 a n d 100 km.  s e p a r a t i o n s between t h e dominant regions.  r e g i o n s a r e , however, s i g n i f i c a n t l y  t h e low-energy  (Tables IV-11 There  length scales of  The v a r i a n c e s o f t h e  higher than  the variances  region f o r a given variable.  I n a l l r e g i o n s , t h e l o n g e r w a v e l e n g t h bands c o n t a i n t h e g r e a t e s t p e r c e n t a g e of  the mesoscale  generally  eddy  comparable  variances. between  the  Although high-  t h e dominant and  low-energy  wavelengths regions,  are the  Figure IV-6  Normalized variance-conserving spectra of the geopotential anomaly on a map showing the regions that the spectra represent. The stippled areas are the high-energy regions. The spectra are plotted between wavenumbers of 10"^ and 10~ cycles/km. 2  92 Table I V - 1 2  Region  NWA  NWP  NEA  SA  NEP  Peak wavelengths o f the g e o p o t e n t i a l anomaly spectra. The peaks are d i s t i n c t t o t h e c o n f i d e n c e l i m i t s shown. The bandwidths a r e between the half-power p o i n t s o f the peaks. The p e r c e n t v a r i a n c e i s the c o n t r i b u t i o n t o t h e t o t a l v a r i a n c e between wavelengths o f 1 0 0 0 and 1 0 0 km. The t o t a l v a r i a n c e s o f the SA and SP were determined between 1 0 0 0 and 2 0 0 km.  Peak Wavelength (km)  Confidence Level  Wavelength Band (km)  Percent of Variance  285  95%  600 - 220  55  155  —  220 - 120  35  395  95%  600 - 240  55  195  80%  240 - 155  20  145  95%  155 - 130  205  95%  340 - 190  33  160  —  190 - 130  23  115  —  130 - 100  10  510  95%  680 - 320  63  245  —  320 - 220  15  320  95%  620 - 190  71  170  —  190 - 120  16  500 - 220  73  10  SP  300  HIGH  300  95%  620 - 220  60  155  ~  220 - 120  30  300  95%  690 - 190  73  170  —  190 - 120  15  LOW  —  •'  93 high-energy  regions,  percentages  of  their  the percentages  c  The  NEA  is  anomalous  than  of  Energy  Geostrophic  those  t h e NEA  kinetic  velocity energy  s p e c t r a have  in  the  g e o p o t e n t i a l anomaly  to  and  smaller  about  twice  bands.  dominant  wavelengths  are  geographic  regions.  The  some s e t  of  characteristic  used  to  range  estimate  10~3  to  10~  the  geostrophic  cycles/km  2  t o t h e wavenumber b a n d s o f  The  normalized  and  each peak i n  variance-conserving spectra  t h e g e o s t r o p h i c v e l o c i t y were o b t a i n e d from t h e g e o p o t e n t i a l anomaly s p e c t r a  with the geostrophic r e l a t i o n . those  of  the  calculated  these  D  spectra.  for  integrating  the  these  EKE  The  The  wavenumber  estimates  were  only  orthogonal  that  of  the  components  assumption  components  of  to  approximately  the  rigorous isotropic  that  the  confidence the  mass  by  limits  respective  to was  cycles/km  on  curves  t h e upper bound of  the  same.  eddy k i n e t i c  energy  EKE.  The  The  velocity  energy  (1983).  the  will,  isotropic  provide  one  of  an  f o r comparison  the  in  of  the be  simplistic,  each  two  and  of  with  estimates  EKE  Under  geographic function orthogonal  energy  estimate the  the  must  isotropic  similar  kinetic  two  They  autocovariance  thus, eddy  a  spectra  eddy k i n e t i c e n e r g y .  spectra  i s admittedly  i t will  to  two-dimensional  random p r o c e s s e s ,  This  due  perturbation variables  two-dimensional  but  geostrophic velocity  perturbation velocities.  perturbation velocities  argument,  (1976) and Fu  of the  kinetic  of  the  invariant.  the  contributions  95%  unit  - 2  l i m i t s and  times the one-dimensional  ergodic, stationary,  rotationally  per  10  integrating  the integration  portion  b e e n e s t i m a t e d a s two  are  to The  confidence  t h e r e f o r e be t e r m e d t h e o n e - d i m e n s i o n a l  region  10~3  by  95%  energy  very closely  limits.  horizontal  present  kinetic  band  determined  EKEs o b t a i n e d f r o m  provide  eddy  variance-conserving spectra.  t h e 95% c o n f i d e n c e  The  wavenumber b a n d s c o r r e s p o n d  total  d e f i n e d by t h e l o w e r b o u n d o f t h e  al.  due  been  wavenumber  spectra.  is  other  have  Estimates  the  the  The  the  i s perhaps  attributable  has  regions  longer wavelengths  region. of  t h e p o r t i o n s o f t h i s EKE  of  low-energy  mechanisms i n t h e r e g i o n .  Eddy K i n e t i c  eddy  the  v a r i a n c e s i n the  an  shorter  anomalous n a t u r e forcing  to  of v a r i a n c e s i n the s h o r t e r wavelength  region  noticeably  compared  by  and  their  will no  be  means  two-dimensional of  W y r t k i et^  94 The 100  two-dimensional  km  are  summarized  high-energy t h e NWP.  regions  cm /s  t h e NEA, to  are  SA,  and  NEP  and  not  different  two-dimensional 222  to  306  cm /s .  confidence times  the  of  and  100  2  respectively,  2  about The  and  SP  energies  eddy  cannot  were  from of  to  eddy  each 250  other.  cm /s 2  region 40  has  a  cm /s . 2  kinetic  energy  of  the  energy  of  compared smaller  a r e , however, region  cm /s 2  region  LOW  24  a  confidence 36  has  region  has  a  limits  of  with  95%  2  about  in  seven  wavelengths  km.  T w o - d i m e n s i o n a l i s o t r o p i c eddy k i n e t i c e n e r g i e s w e r e e s t i m a t e d by F u using  SEASAT  high-energy  altimetry regions  data.  and  e s t i m a t e d EKE  of  significantly  different  The  signals  EKEs  with  periods  m of the ocean.  The  s i g n a l because the  on  these  order  to  of  100  for  2  results  by  less  Fu  are  than  a f a c t o r o f 5.  this  investigation  m,  cm /s  of  Fu.  In  the  o f t h e XBT  The  m i s s an  EKEs  data  not  set i s  region, a factor  the  depth  estimated  in  the  used  from  the  s i n c e they  can  be  do  The  underestimated  W y r t k i e t a l . a r e o v e r e s t i m a t e d due  in this  investigation.  quasi-synoptic  XBT  not  frequency  f i l t e r any  eddy k i n e t i c  (as  the  fact  discussed  t o the wind d r i f t  data  energies  less than those  e x p l a i n e d by  400  a t which the b a r o t r o p i c  not  EKEs  this  p a r t of the b a r o t r o p i c  signal) i s generally considered  m  of  barotropic  baroclinic 400  Fu's  s i g n a l s i n the upper  important  ( i . e . the  The  LOW  with  the  regions.  d a t a s e t by  associated  (1983)  for  2  the  the  This  290  low-energy  a s s o c i a t e d w i t h the b a r o c l i n i c  w a v e l e n g t h band.  are  of  2  q u a s i - s y n o p t i c XBT  days.  and e s t i m a t e d i n t h i s i n v e s t i g a t i o n a r e by  EKEs  the  those  24  l e v e l o f no m o t i o n  1000  km  the  l a t t e r EKEs w i l l  underestimates,  1000  2  greater than those  very w e l l w i t h those of Fu, the  reported  cm /s  from  i s c o m p e n s a t e d by  the  50  estimated  i n v e s t i g a t i o n are those  signal  He  t h e HIGH r e g i o n u s i n g t h e  r e s u l t s are s i g n i f i c a n t l y 1.25.  and  40 a n d  over  HIGH  of  HIGH  20,  t h e SP  95%  value  The  2  and  NWA  directly  estimated  the  low-energy  kinetic  be  The  with  2  18,  and  of  the  In the  EKEs of  the  EKEs  in  different.  twice  SA  kinetic  LOW  32  geostrophic  b e t w e e n 1000  has  EKE  The  2  limits  cm /s ,  eddy k i n e t i c e n e r g i e s o f t h e SA  isotropic 2  two-dimensional  significantly  difference.  The  The  SP h a v e t w o - d i m e n s i o n a l  since their  signficantly  236  not  NEP  wavenumber r a n g e .  f o r t h e w a v e l e n g t h b a n d s b e t w e e n 1000  IV-13.  and  are  The  a significant  t h e NEA  Table  258  NEP  respectively.  2  estimates  in  These e s t i m a t e s  r e g i o n s , t h e NEA, 2  EKE  set  to  be  Despite compare  band o u t  of  r e p o r t e d by  Fu  o f W y r t k i e t a l . (1976) t h a t the  above),  EKEs o f F u and  of the s h i p s .  the  EKEs  and of  95  T a b l e IV-13  Two-dimensional i s o t r o p i c eddy k i n e c t i c energy e s t i m a t e s geographic r e g i o n s . The SA and SP were i n t e g r a t e d up N y q u i s t wavenumber ( i . e . about 200 km).  Region  T w o - d i m e n s i o n a l I s o t r o p i c Eddy K i n e t i c Energy ( c m / s ) 2  2  95% Confidence Limits (cm /s ) 2  NWA  258  201 - 3 1 5  NWP  236  209 - 330  NEA  18  14-21  SA  20  15-31  NEP  40  33-45  SP  24  2 1 - 3 0  HIGH LOW  of the t o the  250  222 - 306  36  32-40  2  96 The  contribution  of  spectra t o the t o t a l Table  IV-14.  In  each  dominant  two-dimensional i s o t r o p i c  the  high-energy  regions,  wavenumber s p a c e a r e v e r y c o m p a r a b l e , NWP  i n the  bands.  band  of  In the  the  eddy k i n e t i c  With  the  energies has  NEP  km, km,  EKEs  respectively.  the cm /s 2  the  EKE  The  of  the  EKEs  in  w i t h t h e e x c e p t i o n t h a t t h e energy of t h e between  NEA,  the  at  2  of  NEA  two  the has  other about  EKE  of  regions  greater  wavenumber  the  half  the  compared.  eddy  200  kinetic  km.  regions  eddy  SA  be  have  than  low-energy  The  at  kinetic  NEA  wavelengths  energy  of  the  larger  than  200  shorter  than  km.  of  65  LOW  region  has  14  cm /s .  of  the  cm /s 2  2  and  at  2  wavelengths  I n wavelengths  2  LOW  t h e HIGH a n d LOW  energies i n the shorter  total  distinct  wavenumber b a n d s may  wavelengths  EKE  HIGH  the  low-energy  an  Both  has  although  individual  l e s s t h a n 200  HIGH r e g i o n  the  distributions  i s shown i n  of  km.  the  the  energy  anomaly-  compared t o t h e o t h e r r e g i o n s , t h e g e o g r a p h i c v a r i a b i l i t y  of  200  geopotential  eddy k i n e t i c  i s divided  regions,  the  SP  20  at wavelengths  whereas  km  of  and  about  than  130  energies within  one-quarter  The  to  exception of of  greater  240  low-energy  c a n n o t be d i r e c t l y  bandwidth  region  are  185  r e g i o n s h a v e more o f  and their  200  17  cm /s ,  eddy  kinetic  2  2  wavelengths.  B a r o c l i n i c L e n g t h and V e l o c i t y S c a l e s  The fields  dominant  The  results w i l l  The  may  be  of  the b a r o c l i n i c  The  D  ( T a b l e IV-12)  square-root spectra  the  baroclinic  portion these The  at  of  dominant  of  the  the  d i v i d e d by 2 TT.  values  signal  of  the  i n the upper  barotropic scales  true velocity  EKEs r e p o r t e d b y  eddy  be d i s c u s s e d  eddy  and  the  V.  field  geopotential  i n t h e upper anomaly  level  ( i . e . the  D  l e n g t h s c a l e s were t a k e n as t h e peak w a v e l e n g t h s o f t h e The  signal  velocity  400 has  m  The of  most  be  W y r t k i et_ a l .  the water  the  a p p r o x i m a t e d by (1976)  are  velocity  certainly  are underestimates of  s c a l e s may  scales  were t a k e n as  variance-conserving geostrophic  corresponding wavelengths.  the  velocity  mesoscale  b e s t r e p r e s e n t e d by  spectra).  mesoscale  s c a l e s w e r e o b t a i n e d f r o m t h e wavenumber  be u s e d i n t h e d y n a m i c a l a n a l y s e s o f C h a p t e r  variability  spectra  of the b a r o c l i n i c  geographic v a r i a b i l i t y of these scales w i l l  the ocean  the  scales of v a r i a b i l i t y  and t h e c o r r e s p o n d i n g v e l o c i t y  spectra.  of  length  a  scales column.  been  true  considering  factor  of  five  velocity  correspond t o An  missed,  velocity  the  important therefore,  perturbations.  the f a c t  that  the  greater  than  the  97  T a b l e IV-14  Region  NWA  C o n t r i b u t i o n o f each bandwidth o f t h e g e o p o t e n t i a l anomaly s p e c t r a t o t h e two—dimensional i s o t r o p i c eddy k i n e t i c energy.  Peak W a v e l e n g t h (km)  Confidence Level  Wavelength Band (km)  P e r c e n t o f Eddy K i n e t i c Energy  Eddy K i n e t i c E n e r g y (cm /s ) 2  2  285  95%  600 - 220  20  52  155  —  220 -  120  55  142  395  95%  600 - 240  29  68  195  80%  240  -  155  31  73  145  95%  155 -  130  34  80  205  95%  340  - 190  29  5  160  --  190 -  130  40  7  115  —  130 - 100  23  4  510  95%  680 - 320  47  9  245  --  320 - 220  47  9  320  95%  620 -  190  45  18  170  —  190 -  120  48  19  SP  300  —  500  - 220  91  22  HIGH  300  95%  620 - 220  26  65  155  —  220 -  120  74  185  300  95%  690 -  190  40  14  170  —  190 -  120  48  17  NWP  NEA  SA  NEP  LOW  98 EKEs e s t i m a t e d high,  i n this  therefore,  observed  an  chapter.  upper  b a r o c l i n i c length  The e s t i m a t e s  bound  of Wyrtki  to the true  scales  may  velocity  be e s t i m a t e d  b a r o c l i n i c v e l o c i t y s c a l e , U, b y ( 5 ) V 2 t o o b t a i n  The These  dominant length  similar Table  length  scales  t o that  IV-1.  and v e l o c i t y  exhibit  a  geographic  of the decorrelation  The  decorrelation  (i.e.  the length  scales  of Table  IV-15.  Comparable  expected  regions.  from  examination  The d e c o r r e l a t i o n  however,  as a  variance  i n the shorter  multiplying the  i n Table  IV-15.  i s , of  course  which  the geopotential  said  to reflect  anomaly  the size  of the  o f T a b l e I V - 1 may b e  I V - 1 5 a f t e r m u l t i p l y i n g them scale).  i n  by  The D d e c o r r e l a t i o n  0.64  scales  s m a l l e r t h a n t h e l a r g e s t dominant s c a l e s o f T a b l e  decorrelation scales an  of the  U*.  The d e c o r r e l a t i o n s c a l e s  d e c o r r e l a t i o n s c a l e x (4/2TT) = l e n g t h  a r e t h e same s i z e o r s l i g h t l y  be  were  by s i m p l y  variability of  considered  perturbations  a r e summarized  scales  scales  l a r g e s t dominant p e r t u r b a t i o n s . compared w i t h  scales  et a l . are  scale  of  t h e HIGH a n d LOW  t h e dominant  length  o f t h e HIGH r e g i o n  r e s u l t o f t h e HIGH length  between  scales  region (Table  having  a  IV-12).  would  of  t h e two  i s significantly  larger,  larger  scales  regions  percentage  ofi t s  99 T a b l e IV-15  Length s c a l e s (L) and v e l o c i t y s c a l e s (U) o f t h e baroclinic mesoscale eddy v a r i a b i l i t y * The l e n g t h s c a l e s were o b t a i n e d from t h e peak wavelengths o f D s p e c t r a (L= A / 2 TT ). The b o l d l e n g t h s c a l e s a r e d i s t i n c t t o t h e 95% c o n f i d e n c e l i m i t s o f t h e D s p e c t r a , and t h e u n d e r l i n e d l e n g t h s c a l e i s d i s t i n c t t o t h e 80% c o n f i d e n c e limits. The o t h e r l e n g t h s c a l e s a r e n o t d i s t i n c t t o t h e 80% confidence l i m i t s . The v e l o c i t y s c a l e s (U) were o b t a i n e d from t h e geostrophic v e l o c i t y spectra. The upper bound o f t h e t r u e velocity p e r t u r b a t i o n s (D*) were o b t a i n e d by m u l t i p l y i n g D by (5)V , s i n c e Wyrtki e t a l . *s (1976) EKEs a r e a f a c t o r o f f i v e g r e a t e r t h a n t h e EKEs r e p o r t e d i n t h i s c h a p t e r , and a r e c o n s i d e r e d an o v e r e s t i m a t e o f t h e t r u e EKEs. 2  Region  L (km)  U (cm/s)  U* (cm/s)  NWA  45 25  10.2 18.1  22.8 40.5  NWP  63 31 23  8.9 14.5 18.6  19.9 32.4 41.6  NEA  33 26 25  3.8 4.6 4.8  8.5 10.2 10.7  SA  81 39  4.0 5.6  8.9 12.5  NEP  51 27  4.6 5.5  10.3 12.3  SP  48  6.3  14.1  HIGH  48 25  9.6 17.5  21.5 39.1  LOW  48 27  4.5 5.5  10.1 12.3  100  V.  The  purpose o f t h i s  DYNAMICAL INFERENCES  chapter  i s t o examine t h e g e o g r a p h i c  mesoscale dynamics u s i n g t h e preceding a  type  time  of dynamical  s c a l e s , which  quasigeostrophic Group,  balance  with  includes  turbulence.  somewhat  o f theGulf  weaker  inhomogeneity  o f t h e eddy  data  Rhines  t o make  properties really  "it  seems  withstand  dynamics  t o be  kinetic (1977)  more  the paucity  results  will  for  energy  Rossby  waves a n d  ( R i c h m a n e t a^L., 1977; MODE  be  of  linear.  with  This  that  hypothesized  t h e demonstrated  and dominant  suggested  be  useful  there  spatial  h o r i z o n t a l length and i s never  statistical  of data,  t o invent rather  quasigeostrophic  likely  estimates  crude  than  o f Chapter discussed.  dynamics  of  dynamical  make  t o be  mesoscale  tests  a monolithic  will  be  inferred  I V , and t h e geographic The  nondimensional  which  drive to  with  the  variability  of the  quasigeostrophic  scaling  u s i n g t h e dominant h o r i z o n t a l l e n g t h and v e l o c i t y  The p r o p e r t i e s o f f r e e l i n e a r b a r o c l i n i c Rossby waves w i l l be e x a m i n e d  each  geographic  region  a n d t h e wavenumber  s e v e r a l models o f n o n l i n e a r geophysical  A.  nonlinear  v e l o c i t y and  frequency-wavenumber spectrum o f t h e e d d i e s " .  p a r a m e t e r s w i l l be e v a l u a t e d scales.  length,  s a t i s f a c t o r y and t h a t ,  relevant  statistical  may  i s consistent  the stability  determine t h ef u l l  The  Quasigeostrophy i s  d y n a m i c s do n o t a p p e a r t o be a p p l i c a b l e i n  t o the east  o f t h e dynamics  enough  waves,  of the  Stream, b u t have l e d i n v e s t i g a t o r s t o suggest t h a t t h e  motions  scales.  Rossby  linear  inhomogeneity  velocity  characteristic  The r e s u l t s o f MODE-I  1978) h a v e shown t h a t  the v i c i n i t y  statistical results.  certain  linear  variability  spectra  will  be compared  with  turbulence.  Quasigeostrophic Scaling Parameters The  quasigeostrophic  systematic explicit potential  scaling choice  equations  arguments.  t o describe  vorticity  equation  for stratified  The s c a l i n g a particular  analysis class  fora stratified  depth, i nnondimensional form, i s (LeBlond  fluids  may b e d e r i v e d  i s a  consequence  of motions.  fluid  a n d Mysak,  on a  The  B-plane  1978),  of  using o f an  nonlinear constant  101  where  (5.1)  the  sphericity  . 2  h  , 2 3y  3x  These  In  fluid,it  B = (NH) /(f L) 2  Q  parameter  scale,  at a  given latitude,  L  given  i s the horizontal latitude,  6  over  the  inertial  stratification. direction The  number  The  i s inhibited  can also  quasigeostrophic  hydrostatic equations f o r  length  parameters  = -6. L/f 0  scale,  f  Burger  number  increases,  gradient  be w r i t t e n  =  i s  Coriolis  of f  at a  Q  depth and r ^  number i s t h e r a t i o o f  i s  motion  and t h e motions  U  i s the  Q  frequency, H i s t h e water The R o s s b y  a r e : Ro  where  0 #  When Ro<<1, t h e C o r i o l i s  stratification  of gravity  Burger  forces.  forces.  As  this  i s the meridional  Q  N i s the Brunt-Vaisala  to the Coriolis  6*  and  2  t h e i n t e r n a l Rossby d e f o r m a t i o n r a d i u s .  the i n e r t i a l  obtain  quasigeostrophic scaling  = (ri/L)  2  0  velocity  to  i s r e q u i r e d t h a t Ro<<1, B = 0 ( 1 ) a n d g*<<1.  three nondimensional  U/(f L),  order  e q u a t i o n from the s c a l e d i n v i s c i d  a rotating stratified  is  '  parameter.  potential vorticity  the  3yJ 3x  t h e s t r e a m f u n c t i o n , Ro i s t h e R o s s b y number, B i s t h e B u r g e r number a n d B *  is is  3x 3yJ  3t  DC  a  forces  measure  parallel  become  as . t h e square  dominate of  to the  nearly  the local  horizontal.  of the ratio  of the  i n t e r n a l deformation r a d i u s and the h o r i z o n t a l l e n g t h s c a l e .  The c o n d i t i o n B =  0(1)  the order  implies  (Pedlosky,  that  t h e motions  1979).  under  consideration  The s p h e r i c i t y p a r a m e t e r  a r e on  i s a measure o f t h e change o f t h e  C o r i o l i s parameter over t h e meridional Scale o f t h e motion 1981).  The c o n d i t i o n  examination velocity  from  Chapter  as e v a l u a t e d w i t h IV, w i l l  reveal  quasigeostrophic equations t o the observed mesoscale  Equation  (Charney and F l i e r l ,  6*<<1 i s a r e q u i r e m e n t f o r t h e u s e o f t h e B - p l a n e .  o f these parameters,  scales  of r ^  (5.1) i s a  conservation  statement  the horizontal the  An  length and  applicability  of the  variability.  f o r the quasigeostrophic  approximation t o the p o t e n t i a l v o r t i c i t y which i s a l i n e a r combination of three terms.  The f i r s t  two terms and  a r e due t o t h e r e l a t i v e  relative  vorticity  the  second  i s the  vorticity  due t o t h e s l o p i n g i s o p y c n a l s i n t h e w a t e r  motion.  contribution column.  The f i r s t to  the  i s the  potential  102 The of  Burger  the f i r s t  scale  number, B =  term  the  vorticity  (Pedlosky,  1979).  sloping  make  i s a measure  2  t o t h e second  f o r which  relative  (r^/L) ,  term.  The  isopycnals  equal  Rossby  to  than r ^ , there  importance  deformation radius  (vortex-tube  contributions  When L i s l e s s  of the r e l a t i v e  stretching)  the  and  potential  i s a negligible  i s the the  vorticity  contribution  t o t h e p o t e n t i a l v o r t i c i t y by t h e v o r t e x - t u b e s t r e t c h i n g .  The  third  term  i n (5.1) i s t h e ambient  wave s t e e p n e s s p a r a m e t e r , M = R o / B * , the  first  term  (the i n e r t i a l  term)  to  Q u a s i g e o s t r o p h i c motions  specifically,  they  be  vorticity.  i s a measure o f t h e r e l a t i v e  dispersion).  may  potential  governed  the  may by  third  be  importance o f phase  wavelike or turbulent.  More  Rossby  wave  (LRW)  n o n l i n e a r R o s s b y wave (NRW) t h e o r y o r q u a s i g e o s t r o p h i c t u r b u l e n c e The  critical  parameter  steepness parameter.  f o r distinguishing  Wavelike  (linear)  ( n o n l i n e a r ) r e g i m e s o c c u r w h e r e M>1.  LRW  steepening).  dispersion that  theory  b a l a n c e s t h e wave  the strong  inertial  NRW  effects  regimes  i s valid  where  M  steepening e f f e c t s .  nonlinear  interactions  a r e much  stronger  involved  than  (QGT) t h e o r y .  o c c u r w h e r e M<1  i s greater  that i s ,  than the i n e r t i a l =  i n QGT  0 ( 1 ) , and  phase  (1977) occur  wave  and t u r b u l e n t  w h e r e M<1,  Rhines  t h e wave  theory,  i s t h e Rossby  theory i s v a l i d  t h e wave p h a s e d i s p e r s i o n o f t h e 6 - e f f e c t (wave  these  regimes  Rossby  ( t h e wave  linear  term  The  effects  the  phase  demonstrated  only  when t h e  dispersion,  that i s ,  M>>1.  Charney it  varies  Rossby  and F l i e r 1 (1981) from  wave  one  oceanic  steepness  suggested that region  parameter  i n t h e oceans  to another. has  been  M = 0(1), but that  In this  evaluated  investigation, and  the  the  geographic  v a r i a b i l i t y o f t h e c h a r a c t e r o f t h e q u a s i g e o s t r o p h i c m o t i o n s w i l l be d i s c u s s e d . K a n g a n d M a g a a r d ( 1 9 8 0 ) h a v e shown t h a t t h e l i n e a r i z e d wave e q u a t i o n s c a n s t i l l be  used  where  therefore,  M  cannot  =  0(1) f o r s i n g l e be d i s t i n g u i s h e d  The f o l l o w i n g r e g i m e s c a n b e  The  plane with  waves.  t h e Rossby  The wave  LRW  a n d NRW  steepness  regimes, parameter.  identified:  (1)  w h e r e M < 0 ( 1 0 ) , LRW a n d NRW  t h e o r i e s a r e a p p l i c a b l e , and  (2)  w h e r e M > 0 ( 1 0 0 ) , QGT t h e o r y i s a p p l i c a b l e .  i n t e r m e d i a t e r e g i o n , where M = 0 ( 1 0 ) ,  i s a turbulent  regime  that  h a v e t h e s t r o n g n o n l i n e a r i n t e r a c t i o n s r e q u i r e d f o r QGT, b u t does h a v e t e r m s l a r g e e n o u g h t o p r e c l u d e LRW a n d NRW  theories.  does n o t inertial  103  The Table  e v a l u a t i o n of  V-1.  The  each  parameter  was  (i.e.  angular  latitude, The  and  hemisphere  region  g  rate  were  and  calculated  f  r o t a t i o n of  deformation  radii, the  the  a two-layer  r j _ were  fluid,  by  the  6371  for  the  (LeBlond  sections.  and  km  obtained  £2  =  0  i s the  7.29  x  the  et 5°  al.  quasi-synoptic Mysak,  Coriolis rad/s  average  median  in  10  the  earth).  the  northern  (1984).  square  the  - 5  of  regions  in  latitude  The  ( i . e . radius  Emery  and  from  average median  the  appropriate  from  relation  The  earth)  r^_,  were  where  r e s u l t s of  determined  the  0 ,  the  where R =  from  scales  from  2 £2 s i n  =  Q  r ^ were c a l c u l a t e d w i t h  SP,  velocity  cos 0/R,  obtained  s c a l i n g parameters i s summarized  i n Table IV-15.  was  of  20,  =  0  Rossby  averages of and  summarized  c a l c u l a t e d as  internal  SA  as  geographic  the  quasigeostrophic  h o r i z o n t a l length  wavenumber s p e c t r a of  the  Spatial  values.  In  sections,  the  assuming  1978)  2  r  = g(P "P ) —2 f P (H  ±  2  Q  where P2  and  are the  The  Pi  the  values  of  Ro,  B  and  theory.  Coriolis  forces over the  The  Burger  number  is  observed  baroclinic  internal  Rossby  to  The  3.8.  greater  than  parameter 10  - 3  to  dominant  is 4.0  r^  and  everywhere x  scales  10~ . 2  of  H ) 2  V-1  of  the  everywhere  are  values the  LOW  length  much  less  The  are  order  on  of  the  B  in  region scale than  changes  variability  required  the  the  is still of  one  Table  is  one.  small,  value  and  2  of V-1  dominance  the vary  value  the  Coriolis  and  thus  the  8.3  the  If  the  from  length  one.  that  average  the  regional  3.0  x  10  scale that  The varies  - 1  is  sphericity from  parameter 3-plane  x  of  much l e s s t h a n  smaller.  Its  with  of  indicating  b o t h h a v e one  in  H  f o r quasigeostrophy.  order  that  layer,  consistent  exceed a  indicating  i s u s e d , Ro  on  upper  g i s gravity.  are  one,  forces  scales  The  one  Table  s c a l e , U*,  HIGH r e g i o n a n d  +  density  l e s s than  everywhere  radii.  (5.2)  L  and  in  inertial  length  2  R o s s b y number d o e s n o t  much  upper bound of the v e l o c i t y  1  l o w e r l a y e r and  $*  The  I t i s everywhere  2  2  thickness  same q u a n t i t i e s i n t h e  quasigeostrophic 10~ .  are  HH  1  4.5  over is  x the  a  valid  approximation.  The  values  of  d o m i n a n t l e n g t h and was  calculated using  the  Rossby  velocity the  wave  scales  baroclinic  steepness (Table  parameter  IV-15)  velocity  are  s c a l e , U,  calculated  listed and  from  i n T a b l e V-2.  i s considered  to  the M be  Table V-1  Summary of the Rossby number (Ro), the Burger number (B) and the sphericity parameter ( B*) f o r ene geographic regions. The input parameters consist of the length scale (I#=» X/2 ir) , the v e l o c i t y scale (0), the average median l a t i t u d e , the C o r i o l i s parameter ( f ) , the meridional gradient of f ( 8) and the i n t e r n a l Rossby radius ( r ^ ) . Q  Region  NWA  NWP  U  L (m)  4.54x10*  1.02x10  _1  2.47x10  4  1.81x10  -1  4  8.9x10  6.29x10  SA  37.3"  33.3°  -2  8.84x10  8.00X10"  1.91x10  R -U/(f L)  -11  2.49x10*  2.5x10-2  3.0x10"  8.3x10-2  1.0  -11  1.7x10-2  3 .4x10  3.67x10*  0  0  1.45X-10" .  2.31x10*  1.86x10"  1.0x10  3.26x10*  3.8x10"  2.55x10*  4.6x10  2.47x10*  4.8x10-  8.12x10*  4.0x10-2  4  1  1  41.6°  2  9.68x10"  5  1.71x10"  11  2.40x10*  -2  2  17.8*  4.38x10"  5.6x10-2  5.09x10*  4.6x10-2  2.71x10*  5.5x10-  SP  4.77x10*  6.3x10"2  27.7°  6.78X10"  HIGH  4.77x10*  9.6x10-2  36.3°  8 . 6 3 X 1 0  2.47x10*  1.75x10"  4.77x10*  4.5x10"2  2.71x10*  5.5x10-2  LOW  5  1.82x10  33. T  8.08x10  5  -5  2.18x10  1.90x10  -11  -11  4.90x10*  -  5  2.03X10"  1.84x10"  11  11  8.21x10  -5  1.89x10  -11  6-8 L/f 0  1  _1  0  9.3x10  -3  5.1x10  -3  1.5x10-2  1 .4  7.4x10  -3  2.5  5.5x10  -3  5.7x10  -3  4.5x10  -3  1.2x10-2  5 . 4 X 1 0  1.9x10-2  8.9x10  2 .0x10-2  9 . 4 X 1 0  1.1x10-2  3.6x10  3 .3x10-2  1.6  -  -  1  -1  1  _1  4.4x10"  o  3  lb  4.0x10-2 1.9x10-  2  1.1  1.2x10-2  2.5x10-2  3.8  6.4x10  3.31x10*  1 .9x10-2  4.8x10-1  1.4x10-2  3.08x10*  2 .3x10-2  4.2x10  8.2x10-2  1 .6  1.1x10-2  6.9x10  2 .5x10-2  2.1  1  34.3°  -1  2  1.1x10-2  5.27x10*  2  5  B-Uj/L)  i (m)  r  (rad/(ms)  -5  3.90x10*  NEP  Bo  (rad/s)  5.8x10-2  3.10x10  NEA  Average Median Latitude  (m/s)  0  0  3.97x10*  -1  -3  1.0x10-2 5.3x10"  -1  3  1.1x10-2 6.2x10  -3  105  Table V—2  Summary of the Rossby wave steepness parameter and the i n f e r r e d dynamics from i t s value, f o r each geographic region. M and M* were determined from U and O*, respectively. The true Rossby wave steepness parameter of the observed length scales w i l l be between M and M*. The inferred dynamics include: l i n e a r Rossby wave (LRW) theory, nonlinear Rossby wave (NRW) theory and quasigeostrophic turbulence (QGT) theory.  Region  X  M  M*  Inferred Dynamics  (km) NWA  285 155  2.7 16.3  6.1 36.4  LRW/NRW QGT  NWP  395 195 145  1.1 7.8 18.2  2.5 17.4 40.7  LRW/NRW  205 160 115  2.1 4.2 4.5  4.7 9.4 10.0  LRW/NRW  SA  510 245  0.3 1.7  0.7 3.8  LRW/NRW LRW/NRW  NEP  320 170  0.9 3.9  2.0 8.7  LRW/NRW  SP  300  1.4  3.1  LRW/NRW  HIGH  300 155  2.3 15.5  5.1 34.7  LRW/NRW QGT  LOW  300 170  1.0 4.0  2.2 8.9  LRW/NRW  NEA  QGT  -  -  -  106 underestimated. velocity  M*  i s calculated using  s c a l e , U*, a n d i s c o n s i d e r e d  the estimated  upper  t o be o v e r e s t i m a t e d .  wave s t e e p n e s s p a r a m e t e r f o r t h e o b s e r v e d w a v e l e n g t h s w i l l The  dynamics  i n f e r r e d from  wavelength.  I n both  wavelengths theories.  (>200  the high-  I n t h e high-energy  are  consistent with  the  195 km w a v e l e n g t h  The  governing  t h e longer  and nonlinear  dynamics i n t e r m e d i a t e  regions,  the scales  turbulence  i n t h e NWP, w h i c h  with  parameter,  The x - a x i s  100, a s s u m i n g  i s the length  i s the velocity  a  latitude  i s o p l e t h s have a s l o p e  scale scale  with  scales  indicates  The  o f two.  wavelengths  with  dynamics  i n kilometers  (L) and v e l o c i t y on a l o g a r i t h m i c  i n cm/s o n a l o g a r i t h m i c  o f 0 . 1 , 1.0, 10 a n d  Due t o t h e r e l a t i o n ,  The m a g n i t u d e  = M 3 L ,  U  these  2  0  o f M, o b v i o u s l y ,  to thetopleft  scale.  increases  corner,  as a  perpendicular  Each p a i r o f l e n g t h a n d v e l o c i t y s c a l e s h a s been p l o t t e d and  t h e appropriate that  geographic  are distinct  a length  c i r c l e s represent level.  o f 35°.  s c a l e from t h e bottom r i g h t  the isopleths.  length  have  M, f r o m T a b l e V-2  i n F i g u r e V-1 a s f u n c t i o n s o f t h e l e n g t h  and t h e y-axis  labelled  regions,  the exception o f  consistent  I s o p l e t h s o f t h e s t e e p n e s s p a r a m e t e r a r e shown f o r v a l u e s  to  wave  b e t w e e n LRW/NRW a n d QGT  theory,  m a g n i t u d e s o f t h e R o s s b y wave s t e e p n e s s  logarithmic  dominant  Rossby  of the shorter  has scales  f o r each  b e t w e e n LRW/NRW a n d QGT t h e o r i e s .  scales.  scale  regions,  linear  Rossby  b e b e t w e e n M a n d M*.  (-<200 km) i n t h e l o w - e n e r g y  quasigeostrophic  have been i l l u s t r a t e d (U)  with  ofthe  The t r u e  o f M a n d M* a r e t a b u l a t e d  and low-energy  wavelengths  scales consistent with  intermediate  values  km) a r e c o n s i s t e n t  The s h o r t e r  theories.  these  limit  scale  region.  The s o l i d  t o t h e 95% confidence  distinct  t o t h e 80% confidence  circles  level, level  indicate  the asterisk a n d t h e empty  l e n g t h s c a l e s t h a t c o u l d n o t be d e f i n e d t o t h e 80% c o n f i d e n c e  L i n e s h a v e b e e n d r a w n t o j o i n t h e l e n g t h s c a l e s w i t h i n t h e same r e g i o n .  upper  limit  of the velocity  s c a l e s , U*, h a s n o t b e e n  plotted, t o avoid  confusion.  This  graph p r o v i d e s  properties  discussed  velocity scales. up  o n t h e graphs  each  geographic  energy.  a n i l l u m i n a t i n g p i c t u r e o f many o f t h e m e s o s c a l e  earlier.  The E K E s ,  of course,  f o r higher  Thus, t h e p o i n t s w i t h t h e l a r g e s t k i n e t i c e n e r g i e s I ti sclearly region  that  seen from t h e n e g a t i v e  the shortest  scales  slope  contain  are higher  of thelines of  t h e most  kinetic  A n i n f e r e n c e may b e made a b o u t t h e d i s t r i b u t i o n o f t h e v a r i a n c e o f t h e  g e o p o t e n t i a l anomaly i n each geographic r e g i o n lines.  are greater  eddy  The v e l o c i t y  from the slope  s c a l e s were d e t e r m i n e d f r o m  of the regional  the geostrophic  r e l a t i o n and  107 X  Q_  <  UJ z  I  0  o _i  in  < 00  I 0-  CL (Jj Z  4 - L  T" T  I00  P; (KM)  100  7"  / /  M=I00/  /  /  /  /  / /  /  /  /  /  /  /  NWP  00  o  L (KM) Figure V-1  The dominant: length (L) and velocity (0) scales plotted i n relation to the isopleths of the Rossby wave steepness parameter (M). M<1 suggests a wavelike (linear) regime and M>1 suggests a more turbulent (nonlinear) regime. The solid circles Indicate dominant length scales that are distinct to the 95% confidence level, the asterisk indicates a length scale distinct to the 80% confidence level and the empty circles indicate scales not distinct to the 80% confidence level. The scales within each region are connected by lines. The line with a slope of -1 i s the slope of the regional line that would be expected i f the variance of D within a region was constant for a l l wavenumbers.  108 thus to  are  be  proportional  constant  for  to  each  (f L) ^S .  The  -  0  D  region.  For  a  Coriolis  constant  parameter  variance,  is  assumed  (SQ ),  at a l l  2  w a v e l e n g t h s w i t h i n a r e g i o n , t h e r e g i o n a l l i n e p l o t t e d i n F i g u r e V-1 a  -1  slope.  less  A l l of  t h a n one,  conserving regional  reflecting  lines  of  than  the  the  are smaller  high-energy  length of  exception  to this  with a slope  can  the  B.  This  that  dominant  are  more  length  clearly  c o m p a r i s o n , however,  on  in  seen,  that  slopes  illustrates  the  each  fact  region.  has  in  with  D  greater that  the  Thus,  variances  magnitude  low-energy which  The  i n each high-energy  low-energy  region  the  has  high-energy  That i s , they  m u s t be made b e t w e e n  for  at  than  the  the  region. a  D The  regional  1)  long wavelengths  2)  long wavelengths i n the high-energy  3)  short wavelengths  4)  short wavelengths i n the high-energy  regions  line  be  more of  length scales.  generally l i s t e d  i n the low-energy  are  have l a r g e r v a l u e s  corresponding  o f i n c r e a s i n g n o n l i n e a r i t y , t h e s c a l e s may  (<280 km)  variance-  regions.  regions.  (>280 km)  magnitudes  the D  negative  comparable  scales  with  have  s c a l e s i n each r e g i o n .  high-energy region  g e n e r a l i z a t i o n i s t h e NEA  be  slopes  of the D s p e c t r a l peaks  s i m i l a r t o the high-energy  also  have  than the d i f f e r e n c e s i n each  n o n l i n e a r than the low-energy  order  negative  the s p e c t r a l peaks  regions.  the magnitudes  scales  variances  This  have  regions  wavenumber b a n d w i d t h s , e a c h  dominant  It  lines  the f a c t that  low-energy  d i f f e r e n c e s between  similar  regional  p l o t s are smaller f o r the shorter length  magnitudes  region  the  would  M. In  as:  regions,  regions,  i n the low-energy regions  and  regions.  L i n e a r Rossby Waves  It  i s o f i n t e r e s t t o examine  the properties  of the free  Rossby  waves w i t h w a v e l e n g t h s as  discerned  t h e wavenumber s p e c t r a .  manner  similar  to  velocities  and  geographic  region  properties  will  investigators.  that  of  phase  velocities  were be  Roden  (1977), of  determined.  discussed  and  from the  corresponding  the  dominant  The  geographic  compared  to  linear  frequencies,  length  scales  variability  the  baroclinic  results  in of of  In  a  group each these other  109 The is  dispersion relation  (LeBlond  and M y s a k ,  a) =  the  horizontal  meridional  gradient  e a s t w a r d and  -  fcyc/(k  k and  l  the  +  2  gx  e a s t w a r d and  is  k  Coriolis  2  2  z o n a l and =  H  (k  2  -2 i  l  at  a  2  group v e l o c i t y  2  i  2 20Qkl/(k2 +r+r  =  m e r i d i o n a l wavenumbers s u c h +  2  parameter  2  o  C p x  waves  (5.3)  )  _ 2 i  )  p /  given  =  -e kl/((k +l )(k +l +r." ))  2  the  latitude.  The  are,  2  ( 5  -0 k /((k +l )(k +l +r ' )) 2  is  Q  2  =  2  3  and  2  n o r t h w a r d components of t h e p h a s e v e l o c i t y  •  Rossby  2  = B (k -l -r " )/(k +l +r  gy  baroclinic  r/* )  1 are the  wavenumber of  C  The  +  2  n o r t h w a r d components o f the  c  first-mode  1978),  where u i s t h e f r e q u e n c y , that  for free linear  2  2  '  4 )  are,  2  o  i  (5-5) C  For  a  given  frequency  The were  frequencies, for  the  o  the  first  baroclinic  the  dominant  For  each  mode  wavelengths  wavelength,  z o n a l waves  relations.  internal  2  will  of  the  the  have  an  upper  By  (k =  convention,  = o)  -2TI/X,  l  to  obtain  k<0  deformation  radius  geographic  cut-off  ( r ^ ) were  of  frequencies regions  the  at  meridional  o b l i q u e waves  were  co>0.  were examined i n each g e o g r a p h i c  Rossby  cut-off  properties  1 = 2TT/X, w h e r e X i s t h e w a v e l e n g t h ) , t h e  meridional widths the  2  g r o u p v e l o c i t i e s , p h a s e v e l o c i t i e s and  latitudes.  2 T/ X) a n d  above  2  Q  determined  =  2  8 r^/2.  C  w a v e s ( k = 0, H  latitude  o f OJ =  different  k  py  2  (-k  =  calculated with Zonal  region. obtained  bands  Zonal from  1, the  with  5°  averages  of  Emery  et_ a l .  (1984).  I n v e s t i g a t i o n s i n t o the e x i s t e n c e o f l i n e a r Rossby waves, t h e i r characteristics Northeast White, 1981;  and  Pacific  1977; White,  Ocean  K a n g and 1982;  generation  mechanisms  ( B e r n s t e i n and  Magaard,  P r i c e and  1980;  have  White,  P r i c e and  M a g a a r d , 1983;  been  1974;  predominantly  Emery a n d  Magaard,  M y s a k , 1983;  propagation  1980;  in  the  Magaard,  1976;  W h i t e and  Saur,  White,  1985;  Cummins  110 et.  a l . , 1986).  Hawaii,  that  Kang  the  frequencies.  region These  waves of  waves  t h e most  and  RMS  Mysak  of vorticity  of these  mechanism.  waves  have  except  Rossby  velocities  waves  300  km  of . 2  set.  at  on t h e  (1980),  7  The t h e o r y  phase. phase  cm/s.  This  mechanisms were  and l o c a l i z e d  west o f Vancouver I s l a n d , c o u l d p r o v i d e waves.  i n the  wavelengths, to  of  annual  o f random  Generation  the intense  speeds on t h e o r d e r  eastern t h e main  p r e d i c t e d wavelengths  o f 300  o f 1 cm/s i n t h e NEP due t o t h i s  Cummins e t a l . ( 1 9 8 6 ) e x a m i n e d t h e g e n e r a t i o n  i n the North  north  concentrated  and Magaard  velocities,  (1983) s u g g e s t e d t h a t  km, a n d p h a s e a n d g r o u p  Rossby  phase  Kang  annual  particle  boundary c u r r e n t f l u c t u a t i o n s ,  generation  wave.  i n a region  energy  investigators  was b a s e d o n a 40-month XBT d a t a  only proposed.  source  demonstrated,  negligible  130°W-160°E, o b s e r v e d  cm/s  investigation  have  Rossby  had northwestward 2  (1980)  part,  of the annual  30°-40°N,  speeds  Rossby  For  characteristics  and Magaard  P a c i f i c by t h e w i n d  s t r e s s over  o f annual  t h e Whole  region.  T h i s model p r e d i c t s s i m i l a r w a v e l e n g t h s and d i r e c t i o n a l p r o p e r t i e s as Kang a n d M a g a a r d (1980) a n d M y s a k  The are  wavelengths observed  320 a n d 170 km  respectively. the  (1983),  with  a n d RMS c u r r e n t s p e e d s o f 3 t o 6 cm/s.  i n the quasi-synoptic  velocity  a b o v e w a v e l e n g t h s a r e shown i n T a b l e V - 3 .  and Magaard (1980), (1986).  scales  data  the theory  s e t , i n t h e NEP,  o f 4.6  The p r o p e r t i e s o f t h e d i s p e r s i v e b a r o c l i n i c  4.6 cm/s v e l o c i t y s c a l e i s i n v e r y  a n d 5.5  Rossby  those  n o t comparable t o those  nondispersive  models.  obtained  with  o f Kang  ( 1 9 8 3 ) a n d t h e m o d e l o f Cummins e t a l .  p r e d i c t e d i n t h e above models.  Their  waves  good agreement w i t h t h e o b s e r v a t i o n s  of-Mysak  cm/s,  T h e 320 km w a v e l e n g t h w i t h i t s  T h e 170 km w a v e l e n g t h , h o w e v e r , h a s a s h o r t e r w a v e l e n g t h  phase v e l o c i t i e s than are  perturbation  XBT  by W h i t e  and s m a l l e r  These  wavelengths  and h i s c o - i n v e s t i g a t o r s  p r e d i c t e d wavelengths  were  generally  using  about  1000  km.  T h e r e a r e no o b s e r v a t i o n s NEP,  o r m o d e l s o f LRWs, o f t h e q u a l i t y  t h a t may be c o m p a r e d w i t h  other  geographic  regions.  baroclinic  Rossby  waves  regions.  It will  be  observed  scales  of  Table obtained  assumed  motion  the  V-4 from  that  length  and v e l o c i t y  summarizes 5.3  t h e LRW  i f a l lof  near-annual period i s required. negligible  the observed  three  to  theory  of  linear  s i x geographic  i s consistent  criteria  energy a t o t h e r than t h e annual p e r i o d s .  a n n u a l p e r i o d t o be dominant i n t h e o t h e r  f o r the  i nthe  scales i nthe  the properties  5.5  Kang and Magaard  o f those  a r e met.  with First,  (1980) f o u n d t h a t t h e r e I t i s reasonable  geographic  regions  the a was  t o expect  on t h e b a s i s  111  BAROCLINIC ROSSBY WAVES - NEP  Wavelength = 320 km  Be  X  10  6  7.5  12.5  17. 5  L39. 2 1.58  86. 6 .97  Meridional • X 10* c, x iai2 dirrectlon  0 5.19 270  0 4.31 270  Latitude 32.5 37.5  22.5  27.5  66. 9 . 73  53 .56  44.4 .45  36. 2 . 35  Wave3,,  k=0 0 2.27 270  .4 .5 2.02 315 2.02 223  .7 .3 3. 58 270 .95 90  0 3.58 270  42.5  47.S  52. 5  31.2 .28  25. 2 .21  20 .15  17. 1 .12  _  0 1.68 270  0 1.29 270  0 .86 270  0 .54 270  0 .37 270  _  .32 .6 1.61 315 1.62 233  .23 .9 1.19 315 1. 25 243  .13 1.1 .91 315 . 1 249  .12 1.7 .61 315 .71 256  .07 2.7 .38 315 .47 261  .05 3.9 .26 315 .33 264  .56 .4 2.85 270 .11 90  .45 .4 2. 27 270 . 31 270  .33 .6 1. 68 270 .55 270  .25 .3 1.29 270 .58 270  .17 1.2 .86 270 .52 270  .11 1.9 .54 270 .39 270  .07 2.8 .37 270 .29 270  Latitude 27.5 32.5 37.5  42.5  47.5  52.5  44.4 .45  31.2 .28  25.2 .21  20 .15  17.1 .12  0. .91 270  0 .76 270  0 .57 270  0 .4 270  0 .29 270  -  .24 .8 . 64 315 .67 209  .2 1 .54 315 .54 217  .15 1.3 .41 315 .41 229  .1 1.9 .28 315 .29 241  .08 2.6 .21 315 .22 248  -  .34 .6 .91 270 .26 90  .28 .7 .76 270 .11 90  .21 .9 .57 270 .04 270  .15 1.3 .4 270 .12 270  .11 1.9 .29 270 .12 270  0 2.85 270  57.5  -  Oblique Waves, k = l • x 10 T C_ x direction C_ x 10 direction s  2  .6 .72 .3 .3 3.67 3.04 315 . 315 4.62 3. 39 188 199  .5 .4 2.53 315 2. 62 210  Zonal Waves, u x 10 T Cp X 10* direction C_ x 10 direction s  2  1.02 .2 5. 19 270 3.96 90  .85 .2 4. 31 270 2.09 90  s  _  _  1=0  Wavelength = 170 km  r. Me x 10  _  7.5  12.5  17.5  22.5  139.2 1.58  86.6 .97  66.9 .73  53 .56  36. 2 .35  -  57.5  Meridional Waves, k=0 a x 10 C_ x 10* direction s  0 1-6 270  0 1.49 270  0 1.37 270  0 1.23 270  0 1.08 270  Oblique Waves, k=l • X 10* T Cp X 10* direction C_ x 10 direction 1  .42 .5 1.13 315 1.54 182  .39 .5 1.05 315 1.36 186  .36 .6 .97 315 1.2 189  .32 .6 .86 315 1.01 19S  .28 .7 . 76 315 .84 200  .45 .4 1.23 270 .72 90  .4 .5 1.08 270 .5 •90  Zonal Waves, 1=0  a x 10 T Cp X 10* direction X 10* direction s  Table V - 3  .59 .3 1.6 270 1.48 90  .55 .4 1.49 270 1.23 90  .51 .4 1.37 270 .99 90  F r e q u e n c i e s (u, 1/s), p e r i o d s (T, y r ) , phase v e l o c i t i e s (Cp, m/s), and group v e l o c i t i e s (Cg, m/s) o f t h e f r e e b a r o c l i n i c Rossby waves o f t h e observed q u a s i - s y n o p t i c l e n g t h s c a l e s a t t h e a p p r o p r i a t e l a t i t u d e s i n t h e NEP. The d i r e c t i o n s a r e i n degrees c l o c k w i s e f r o m north. The I n t e r n a l Rossby r a d i u s ( r ^ , km) and t h e upper c u t - o f f frequency ( u , 1/s) o f t h e f i r s t - m o d e b a r o c l i n i c Rossby wave i s a l s o given f o r each l a t i t u d e . c  112 T a b l e V-4  Summary o f t h e p r o p e r t i e s o f t h e l i n e a r f i r s t - m o d e b a r o c l i n i c Rossby waves. X i s t h e wavelength. U i s the b a r o c l i n i c v e l o c i t y s c a l e o b t a i n e d from t h e d a t a s e t . U* i s t h e e s t i m a t e d upper l i m i t o f t h e t r u e v e l o c i t y p e r t u r b a t i o n s o b t a i n e d u s i n g W y r t k i e t a l . ' s (1976) EKEs. Cp i s t h e phase speed. The o n l y dynamics which may be i n f e r r e d from t h e s e p r o p e r t i e s i s t h e l i n e a r Rossby wave (LRW) theory.  Region  X (km)  Period (yr)  C (cm/s) p  U/C  p  U*/C  p  Inferred Dynamics  NWA  285 155  0.5 0.5 -  6.4 4.0  0.14 - 1.97 0.12 - 0.93  9.7 34.5  21.7 77.1  NWP  395 195 145  0.5 0.5 0.5 -  1.8 1.3 1.3  0.70 - 2.77 0.48 - 1.34 0.36 - 0.86  5.1 15.9 30.5  11.4 35.6 68.2  NEA  205 160 115  0.5 - 13.0 0.5 - 10.5 0.7 - 8.1  0.05 - 1.28 0.05 - 0.93 0.04 - 0.56  5.7 9.4 16.0  12.7 21.0 35.8  SA  510 245  0.3 0.3 -  1.0 0.7  1.64 - 5.68 1.06 - 2.48  1.1 3.2  2.5 7.2  LRW LRW  NEP  320 170  0.2-3.9 0.3 - 2.6  0.26-5.19 0.21 - 1.60  1.7 6.1  3.8 13.6  LRW  SP  300  0.3 -  0.34 - 3.28  3.5  7.9  2.8  113  of t h e i r r e s u l t s .  Also, t h e proposed generation  m e c h a n i s m s o f t h e LRW f i e l d i n  t h e NEP, f o r t h e most p a r t , h a v e a n n u a l p e r i o d s .  S i m i l a r mechanisms a r e l i k e l y  to  be v o r t i c i t y  sources  f o r t h e LRW f i e l d  a resonance a t t h e annual p e r i o d . of  t h e LRWs  be  investigations  on t h e o r d e r in  the  i n the other  Second,  This  Third,  i t i s  will  be  consistent  required  that  the inertial  dispersion.  Kang  effects  will  and Magaard  be  more  (1980),  important  as p r e v i o u s l y  t h a t t h e p a r t i c l e v e l o c i t i e s may be o n t h e o r d e r plane  waves  and t h e n o n l i n e a r  U*/Cp, may be u s e d a s a n a l o g s r e q u i r e d t h a t e i t h e r o f these  terms  will  than  Where t h i s  t h e wave  discussed,  phase  demonstrated  Thus, t h e terms,  single  U/Cp a n d  t o t h e R o s s b y wave s t e e p n e s s p a r a m e t e r . terms be on t h e o r d e r . o f  the  velocity  o f t h e phase speed f o r  cancel.  speed  with  the  p e r t u r b a t i o n s , U a n d U*, n o t be much g r e a t e r t h a n t h e p h a s e s p e e d s . occurs,  create  i t i s r e q u i r e d t h a t t h e phase  o f one.  NEP.  r e g i o n s , and thus  I t i s  o n e f o r LRW t h e o r y  t o be  valid. o  An  examination  •  o f t h e LRW p r o p e r t i e s , i n T a b l e V - 4 , shows t h a t t h e o b s e r v e d  l e n g t h s c a l e s have, f o r t h e most p a r t , n e a r - a n n u a l p e r i o d s the  order  the order and  o f one.  Only  a few w a v e l e n g t h s ,  of, o r less than,  velocity  criteria)  scales  one.  The r e g i o n s  consistent  with  a r e t h e SA a n d t h e NEP.  observed l e n g t h and v e l o c i t y  LRW  scales only  low-energy  C.  Nonlinear Geophysical Turbulence  spectral  U/Cp  theory  (according  theory  o r U*/Cp o n  to  length  the  above  i s consistent with the  f o r wavelengths longer  t h a n 200 km i n  regions.  A number o f m o d e l s o f n o n l i n e a r t u r b u l e n c e  spectra  have  w h i c h c a n be s a i d t o h a v e  T h a t i s , LRW  the  determine  however,  and phase speeds on  the theoretical  i n an shape  inertial  decay  coefficients  wavenumber  o f t h e form  range.  e x i s t t h a t use d i m e n s i o n a l i t y t o o f the temperature That  k~P i n t h e wavenumber  and v e l o c i t y  i s , the theory ranges  between  predicts the  a  sources  and  s i n k s o f e n e r g y , w h e r e k i s t h e wavenumber a n d p i s t h e p o w e r - l a w e x p o n e n t .  The  consistency  with  o f t h e t e m p e r a t u r e s p e c t r a , o f t h e q u a s i - s y n o p t i c XBT d a t a  the existing  models  of nonlinear  turbulence  s l o p e s o f t h e s p e c t r a between t h e l o n g e s t wavenumbers.  Since the D and geostrophic  temperature s p e c t r a , they w i l l provide  will  be e x a m i n e d  set,  using the  dominant wavelengths and t h e N y q u i s t velocity  s p e c t r a a r e dependent on t h e  n o new i n f o r m a t i o n f o r t h i s  analysis.  114 Ozmidov  (1965)  spectrum of  depicted  motions  bands,  5/3  model  are  separated  by  wavenumbers. 40-•'•and  Cromwell"  km  influx  inertial  of  a  peak  in  energy  influx  from  large  and  a s s u m e d t o be  Several  In  the  The  km  to  energy  data  results near  200  km  in  (1966) t h e o r y  the  may  turbulence  to  be  directly  to  been  a  verified  be  appropriate.  is  for  developed,  i t may  to be  The  three-dimensional  of  p o s t u l a t e d two  while  (1967) a n d of  enstrophy and  in  of  an  model,  both  enstrophy  the  range,  spectra  first  the  (and  that  The  is  The  range,  while  i n the  have power-laws  ocean)  have  predicts a  of  the  turbulence  vertical one  s c a l e , due  f o r the  vorticity)  By  exponents  cascade and  one,  range  the  conservation  velocity  turbulence. to  lower  transferred  second  range,  arguments, of  the  5/3  the  in  the  velocity  and  Charney  b a r o c l i n i c nature a  to  rotation i s  respectively.  of  is  respectively.  is  similarity  the  two-dimensional  turbulence,  model t h a t a c c o u n t s f o r t h e with  somewhat Phillips'  i s transferred uniformly  power-law  three  theory  Kolmogorov-type  (1971) p r o p o s e d  zero.  enstrophy  any  r o l e and  t r a n s f e r s of energy, i n the are  mesoscale  At  s c a l e s where t h e e a r t h ' s  ( i . e . mean-squared  are  Kolmogorov-type  processes.  wavenumbers,  Charney  none  b u o y a n c y wavenumber w h e r e  quasigeostophic  spectra  developed a three-dimensional atmosphere  At  although  important  theory  lower  g i v e n wavenumber a n d  temperature  energy-cascade  the  for  i n e r t i a l subranges f o r the two-dimensional  u n i f o r m l y t o h i g h e r wavenumbers.  temperature  between  Ozmidov's  observed  scales.  than a c r i t i c a l At  the  power-law e x p o n e n t s a r e t h r e e and  models  Energy i s i n j e c t e d a t a  velocity  high  Temperature  expected  small-scale  Phillips'  three-dimensional.  a dominant f a c t o r , Kraichnan  and  to  isotropic 5/3  this  "Townsend  with  subranges.  applicable  c e r t a i n range  a t wavenumbers h i g h e r  wavenumbers,  low  sixteen  of  in  wavenumber  representative  exponents  have been  context,  temperature spectra, r e s p e c t i v e l y .  Kraichnan  the  likely  s t r a t i f i c a t i o n m u s t e x e r c i s e an  the s t r a t i f i c a t i o n .  and  from  consistent  inertial  ocean  ocean t u r b u l e n c e  a n i s o t r o p i c when c o m p a r i n g t h e h o r i z o n t a l s c a l e s t o t h e  and  localized  three-dimensional  power-law  wavenumber  i n the  energy  from  were  full  b a s i c f e a t u r e s of  over  cascading  MBT  the  1 cm)  The  spectrum of  This  spectra  geophysical  only  l a r g e r s c a l e s , the  turbulence  of  the  spectrum  models of  realistic  has  turbulence  using  predicts  applicable only  turbulence  over  a passive tracer.  variability. be  external  eddies.  velocity  other  sufficiently  will  the  Kolmogorov,  temperature  of  1964-66.  with  by  10,000  (1967) examined t h e  model,  developed  of  subranges  wavelengths  cruises  distribution  " K o l m o g o r o v S p e c t r u m Law".  the  Wyrtki  1000  energy  ( i . e . wavelengths  accordance w i t h the idealized  the  of  pseudo-potential  115 vorticity. and  This  is a  combination  p o t e n t i a l temperature.  higher  than  the  temperature  This  excitation  spectra.  of  the  conservation  theory  wavenumber  Temperature  predicts  for  is  both  a  a  k  the  passive  of  potential vorticity law  - 3  at  wavenumbers  horizontal velocity  tracer  in  both  of  and these  theories.  Examples of  the  IV  are  HIGH a n d  LOW  p o w e r - l a w e x p o n e n t s w h e r e d e t e r m i n e d i n t h e wavenumber r a n g e  from  shown i n F i g u r e regions. the  The  peaks  of  spectra with this the  log-log representations  V-2,  the  with  dominant wavelengths  obtained  least-squares (Zar,  1974).  c a n n o t be  may  linear The  t h e u p p e r and  The  95%  lower  still  The  generally  to  the  at  scales  of  true  The  confidence  intervals  confidence  the  of  high-  and  low-energy regions  b e t w e e n two  and  three.  The  the  were  slopes  peak  spectral  temperatures  are  exponents of  the  SA  and  used  useless.  For  significantly  The  t h e most p a r t , the d i f f e r e n t between  power-law  contrast  than  associated  exponents  the  with  individual the  ( i . e . a b o u t 3.0)  of  the  HIGH  geographic eddy  has  95%  confidence  2.29  300  to  91  limits  km.  significantly  The  of  must  be  the  SP  (due  to the  considered  in are  regions low  next  each v a r i a b l e are  to not  2.65  characteristic  regions  regions. field  in  w i t h 95% 300  a characteristic and  LOW  The the  54  a  temperature HIGH  confidence  to  provide  km.  power-law  exponent  variance  region  has  a  l i m i t s o f 2.85  to  In the  LOW  power-law exponent of  ( i . e . a b o u t 2.5)  greater  region, 2.47  with  between wavelengths  of  of  region  is  spectrum  is  the  LOW  l e s s t h a n t h a t o f t h e HIGH r e g i o n .  These r e s u l t s proportional  and  between wavelengths of  temperature variance  summarized  regions.  baroclinic  the  and  power-law exponents of  c h a r a c t e r i s t i c p o w e r - l a w e x p o n e n t o f 3.01 3.17  estimates  have power-law exponents t h a t  regression  a  s p e c t r a l estimates.  Nyquist  the  with  were c a l c u l a t e d u s i n g  a s a r e s u l t o f t h e s h o r t wavenumber r a n g e in  however,  determined  have l a r g e e r r o r bars wavenumbers)  For  wavenumber,  subrange,  smoothed  of the  the  wavenumbers.  inertial  average  the  than  slopes  l i m i t s of the  exponents  i n Chapter  shown f o r  smaller a  use.  of  95%  spectra  regional Nyquist  considered  be  the  spectra  regression  s p e c t r a l power-law  T a b l e V-5.  temperature  log-log spectra  wavenumber r a n g e slopes  the  of  to  three-dimensional  show t h a t , the  -3.0  i n the  power.  geophysical  HIGH r e g i o n , This  turbulence  is  the  consistent  model.  This  temperature with  Charney's  implies that  the  (1971) energy  116  WAVELENGTH  IO 4  103  Inn  i i i  I  l  IO" 4  F i g u r e V-2  i  Inn  | i 111ii|  i t i i  I  102  - KM  Inn  | i 11  i i i  I  10' i  I  3  2  3  lllll I I I  | I 111ll|  3 5 IO" 3 5 IO" 3 5 IO" K CYCLES/KM  W A V E L E N G T H - KM 10 IO  10"  -1 1  I  10-  4  I  Inn  | I | IIW|  10'  2  i i i  i  I  11  | I  Inn  i i i  i  I  11  | I  3 5 10- 3 5 10- 3 5 K CYCLES/KM 3  2  Sample p l o t s o f t h e l o g - l o g s p e c t r a l r e p r e s e n t a t i o n s . s p e c t r a d e p i c t t h e mid-thermocline temperature v a r i a b i l i t y HIGH and LOW r e g i o n s .  I  IO' 1  These i n the  117  T a b l e V-5  Summary o f the s p e c t r a l power-law exponents o f t h e m i d - t h e r m o c l i n e temperature. The s l o p e s o f the l o g — l o g s p e c t r a (-p) were o b t a i n e d over t h e wavelength bands as shown. The r e l a t i o n E(k) =» k P d e s c r i b e s the s l o p e s o f the s p e c t r a I n t h e a p p l i c a b l e wavenumber range where E i s the temperature spectrum, k i s the wavenumber and p i s the power-law exponent. -  Region  p  95% Confidence Interval  Wavelength B a n d (km)  NWA  2.85  2.62 - 3.08  285 - 70  NWP  3.07  2.84 - 3.30  395 - 54  NEA  2.61  2.16 - 3.06  205 - 91  SA  2.70  1.10 - 4.33  510 - 210  NEP  2.40  2.19 - 2.61  320 - 88  SP  2.37  -2.50 - 7.24  HIGH  3.01  2.85 - 3.17  300 - 54  LOW  2.47  2.29 - 2.65  300 - 91  300 - 220  118 of  the  mesoscale  wavelengths  of  perturbations  about  p r o p a g a t e s away as to  higher  300  The  physical  km,  input  cascades  into to  over  a wavelength  enthusiasm  interpretation  with  must  which  be  one  tracer,  and  a  consistent with  This  geophysical  turbulence.  exponent  of  three,  regional  Rossby  permit  A  i s not The  similar  wave  steepness  quasigeostrophic  distinct  that  model of q u a s i g e o s t r o p h i c  current and  eastern  provide  evidence  2.0  i n the  and  for a  D.  energy  and  their  Charney's  model  not  the  case  the  the  NEA  high-energy V-2)  models of has  is  not  nonlinear  a  regions,  has  power-law  however,  large  the  enough  to  the  consistency  of  Charney's  regions  low-energy  There  consistent  i n the  power-law Neither  with  low-energy  they  the  reported The the  of  boundary  ocean  existing  of  slopes  western  no  regions.  characteristic  do  spectral  ( i . e . the  are  nonlinear  three-dimensional  ( i . e . the  regions  the  interior  models  of  power-law  s p e c t r a do  not  three-dimensional  suggest t h a t Kraichnan's  model  of  the  LRW  quasigeostrophic turbulence i s appropriate.  Summary o f t h e I n f e r r e d D y n a m i c s  The theory  dynamics and  results  the  are  identical  (Table  confidence  i n the  the  inferred  model t h a t  the  those The  Rossby  regions, evidence  latter,  inferred  of  LRW  while f o r the  also,  i s consistent with  wave  theory  the  the  spectral  the  wave  Rossby  of  o f QGT  the theory  specific slopes  wave  analysis  to wavelengths  analysis  validity  parameter,  summarized i n Table  from  Rossby  identified the  steepness  models a r e  linear  applicability  provided additional The  to  V-2).  low-energy  regions.  from  geophysical turbulence  parameter  in  that  cascades no  results  i s c o n s i s t e n t w i t h the  are  3.0  -5/3  of  regions).  that  Kolmogorov-type turbulence. two-dimensional  with  i s clearly  of  of  (Table  high-energy  current  turbulence  exponents between  any  been i d e n t i f i e d .  turbulence  not  boundary  geophysical  the  variability  spectra i n the  r e g i o n s ) , but  km  and  turbulence.  geographic  temperature  this  region  parameter  g e o p h y s i c a l t u r b u l e n c e models has  the  of  wavenumbers  54  fact  at  r e g i o n , the temperature spectrum  low-energy  to  to  regions  however,  these  the  I n t h e LOW  -2.5.  300  accepts by  lower  Enstrophy,  of  f o r oceanic mesoscale motions. of  high-energy  slightly  band  tempered  assumes t h a t t e m p e r a t u r e i s a p a s s i v e  slope  the  l i n e a r / n o n l i n e a r Rossby waves.  wavenumbers  transfer.  is  of  The  steepness  provided  less  than  more 200  km  spectral  power-laws  i n the  high-energy  geophysical the  V-6.  turbulence  temperature  in  the  119 Table  V-6  Summary o f t h e i n f e r r e d dynamics o f t h e dominant wavelengths ( A ) . The inferred dynamics are: linear Rossby wave (LRW) t h e o r y , n o n l i n e a r R o s s b y wave (NRW) t h e o r y a n d g u a s i g e o s t r o p i c turbulence (QGT) theory. The b o l d wavelengths are distinct t o t h e 95% confidence l e v e l , t h eu n d e r l i n e d wavelength i s d i s t i n c t t o t h e 80% confidence l e v e l and t h e other wavelengths a r e n o t d i s t i n c t t o t h e 80% c o n f i d e n c e l e v e l .  Region  X  Inferred  (km)  Dynamics  NWA  285 155  LRW/NRW QGT  NWP  395  LRW/NRW  195 145  QGT  205  LRW/NRW  160 115  -  SA  510 245  LRW/NRW LRW/NRW  NEP  320 170  LRW/NRW  SP  300  LRW/NRW  HIGH  300 155  LRW/NRW QGT  LOW  300 170  LRW/NRW  NEA  120 high-energy  regions  turbulence  The  wavelengths  the  95% confidence  are  i n bold  theories. NWP,  examine  l e v e l and t h e i r  script.  three-dimensional  i s consistent  respective inferred  than  quasigeostrophic  to this  with  that are d i s t i n c t t o  dynamics, results.  i n T a b l e V-6, These  200 km a n d a r e c o n s i s t e n t w i t h  QGT  o f 300 km t h a t  T h e HIGH e n e r g y  the shorter  eddy f i e l d  These a r e t h e most s i g n i f i c a n t  are a l l greater  wavelengths  a n d NRWs.  (1971)  of the baroclinic  The o n e e x c e p t i o n  which  dominant  Charney's  model.  dominant  wavelengths  -  strong nonlinear interactions  a n d NRW  s t a t e m e n t i s t h e 145 km w a v e l e n g t h theory.  T h e HIGH  are consistent with  a n d LOW  significant  wavelengths  r e q u i r e d f o r QGT.  i n order  i n the  regions  t h e dynamics  r e g i o n i s , o f c o u r s e , more n o n l i n e a r ,  and l e s s e r  LRW  dominant  have  o f LRWs  b u t one m u s t to find the  121 VI.  The  geographic  dynamics (XBT)  has been  data  Forces,  set.  variability examined  Over  trans-oceanic  geopotential  of  with  a quasi-synoptic  sections  and  anomaly  dynamical  29  curves  qualitatively  horizontal length  with  scales  the a i d of previous  (NWP).  regions  The l o w - e n e r g y  and work  regions  Two  regions  composite  regions,  temperature  were and  also  t h e LOW  sections  compared t o o b s e r v a t i o n s  amplitudes using  similar  confidently  t o those accepted  regions under  Several mesoscale  from  as being  statistical  eddy  (NWA)  are the Northeast  The  region  comprised  each  HIGH  geographic  data  sets.  Atlantic  Six areas.  (NEA), t h e  Pacific (SP).  region  the  were  and t h e Northwest  (NEP) a n d t h e S o u t h  defined.  with  variability  as h i g h - o r low-energy  comprised  low-energy  region  were  from other  the  regions.  examined sources.  and This  s e t t o e x h i b i t mesoscale p r o p e r t i e s  i n the literature, representative  analyses  i n t h e upper  and the g e o p o t e n t i a l  mesoscale  the  low-rwavenumber s i g n a l  variability.  from t h e surveys  and  the  variability  c l i m a t o l o g i c a l data  of the mesoscale v a r i a b i l i t y  reported  the  The  infer  and thus  the data  s e t was  o f t h e eddy  variability  to  the  i n the  examination.  structure  temperature  to  Geographic regions  of  Atlantic  Pacific  i n v e s t i g a t i o n found the quasi-synoptic very  used  Mean  f o r use i n the s t a t i s t i c a l  structure.  are the Northwest  (SA), the Northeast  high-energy  were  surveys.  discussed the geographic  temperature  South A t l a n t i c  Typical  f r o m t h e C a n a d i a n Armed  analyses.  high-energy  Pacific  inferred  bathythermograph  multiship/AXBT  g e o g r a p h i c r e g i o n s were d e l i n e a t e d and c l a s s i f i e d The  and t h e  expendable  from the temperature p r o f i l e s  d e s c r i p t i v e analyses  different  and  salinity-depth  the observed quasi-synoptic  defined  statistics  10,000 XBT p r o f i l e s w e r e o b t a i n e d  temperature-salinity  The  o f the mesoscale  t h e U n i t e d S t a t e s Navy a n d t h e N a t i o n a l O c e a n o g r a p h i c D a t a C e n t e r i n 95  single-ship  and  CONCLUSIONS  were  used  400 m anomaly  Perturbation  o f t h e ocean.  v a r i a b l e s were  w i t h z o n a l and m e r i d i o n a l l i n e a r  of the standard  i n t e r m i t t e n c i e s o f the temperature  The  quasi-synoptic mid-thermocline  (0-4000 k P a ) were u s e d  from t h e s e c t i o n s w i t h  geographic v a r i a b i l i t y  quantify  a  obtained  to  represent  by  1000 km r u n n i n g  removing mean, a n d  trends.  d e v i a t i o n s , skewness, k u r t o s i s  and t h e g e o p o t e n t i a l  anaomaly  f o rthe  122 sections the  and t h e surveys  surveys  are  perturbations average The  were d i s c u s s e d .  comparable.  with  average  amplitudes  The  HIGH  amplitudes  o f 0.26  region  o f 0.67  m /s . 2  The s t a t i s t i c s  The  2  has  m /s , 2  ratio  of the s e c t i o n s and geopotential  a n d t h e LOW  2  o f these  anomaly  region  amplitudes  i s 2.58.  p o s i t i v e s k e w n e s s o f t h e LOW r e g i o n s u g g e s t s t h a t t h e b a r o c l i n i c eddy  c o n s i s t s of predominantly  warm e d d i e s .  significantly  d i f f e r e n t " from  indicate  the mesoscale  that  regions.  The  standard  r e g i o n a n d 0.54°C i n t h e LOW the  LOW  region  The  negative  baroclinic  eddy f i e l d  North  region.  i n t h e LOW  regions  are higher  sampling  subregions  than  the f i e l d  i s 1.40°C  o f warm  eddies  above.  suggests t h a t the  of c o l d eddies,  (NPSF) a n d t h e N o r t h The s t a n d a r d  the corresponding  statistics  mid-thermocline  temperature  as opposed t o t h e  is  not consistent with  Pacific Equatorial  d e v i a t i o n s of these  two  o f t h e NEP,  since  the  a r e a s o f t h e NEP.  The  and  The p o s i t i v e skewness o f t h e b a r o c l i n i c  discussed  i n t h e HIGH  suggested  i n t h e HIGH r e g i o n  o f t h e NEP.  c o n s i s t e n t w i t h t h e NEP s t a t i s t i c s .  eddies  45% of t h e two  region.  is  cold  about  a r e i n r e l a t i v e l y h i g h eddy a c t i v i t y  the largest  perturbations.  over  and  The p o s i t i v e s k e w n e s s o f t e m p e r a t u r e i n  P a c i f i c Subtropical Front  (NPEC) a r e s u b r e g i o n s  has  occur  c o n s i s t s predominantly  Current  NPEC  i n t e r m i t t e n c i e s a r e t h e same  of the temperature  skewness o f t h e temperature  f i e l d o f warm e d d i e s  The  The  perturbations  i s consistent with  field  The s k e w n e s s o f t h e HIGH r e g i o n i s n o t  zero.  deviation  has  geopotential eddy f i e l d  The NPEC h a s a n e g a t i v e  t h e NEP, h o w e v e r ,  anomaly  i n t h e NPSF  skewness.  i t i s consistent with  i n the descriptive analysis of the four  This  the f i e l d  surveys  of  of the  area.  The  seasonal  mesoscale  variability  eddy  deviations,  field  were  skewness,  subsets  There  be a s e a s o n a l  that  discussed  sampled  over  seasonal this  data  set.  meridional  and  Significant  seasonal  i n t h e mesoscale  ( i . e . a l l b u t t h e NEP  determined  zonal  some  the isotropy detailwere  eddy  the  a n d LOW  variability  relation,  decorrelation  the surveys. A  s  =  scales,  The  of  the  standard  calculated  fields that  for  apparent. similar  to  are unevenly  regions)  may  have  i s beyond t h e a b i l i t y o f  o f h o r i z o n t a l i s o t r o p y was  from  The  s i g n a l s were  ( 1 9 8 3 ) i n t h e NEA, a n d t h e r e g i o n s  The a s s u m p t i o n  by  i n  and  intermittencies  Quantifying the seasonal  factor  determined  and  variability  t h e seasons  biases.  anisotropy was  of sections.  by G o u l d  region  investigated  kurtosis  quarterly may  o f t h e NEP  evaluated  an  factor,  A ,  z  are  the  r e s p e c t i v e l y , obtained  from  the  L /L . M  Z  anisotropy  with  L  M  and  L  s  123 meridionally The  and  regional  With  no  zonally  anisotropy  evidence  reasonable  to  f o r the  Wavenumber wavenumber  averaged factors  the  not  the  significantly  assumption  of  s p a t i a l s c a l e s of motion b e i n g  spectra  of  are  contrary,  were  space''' b e t w e e n  wavelengths  autocorrelation functions  the  used  to  examine  wavelengths  mid-thermocline  1000  dominant l e n g t h s c a l e s of t h e h i g h - and  with  the  respective  The  LOW  and  the  variance,  of  region  wavenumber  has  two-dimensional  mass  f o r the  The  HIGH r e g i o n h a s  LOW  region  those  isotropic  of  HIGH a n d  Wyrtki  understanding  (1976)  that:  the  by  a  signal;  underestimates, signal data  due  since  t o the  (Wyrtki  et  that  they  and  peak wavelengths of  300  and  170  The  250  100  a l . , 1976)  are  km  30%  In  have a  the a  the  300  and  of  the  containing  (EKEs) were  eddy k i n e t i c  and  36  km.  five.  will  of  miss  24-day s a m p l i n g  and  regions  energies  73  greater  estimated  energies  per  cm /s , r e s p e c t i v e l y . 2  2  These EKEs a r e  This  ( 0 - 4 0 0 m)  since they  will  separation  wavelengths.  are  f a c t o r of  EKEs  anomaly  t h e b a r o c l i n i c eddy k i n e t i c e n e r g y o f  baroclinic  the  scale  60  in  dominant  low-energy r e g i o n s .  ( 1 9 8 3 ) w i t h SEASAT a l t i m e t r y d a t a , b u t  data s e t are underestimates, barotropic  regions  The  significant  wavenumber b a n d .  LOW  variance  geopotential  low-energy  longer  i n w a v e l e n g t h s b e t w e e n 1000  et_ a l .  The  one.  considered  of  km.  containing  eddy k i n e t i c  about seven times  r e p o r t e d by F u  bands  respectively.  f o r e a c h g e o g r a p h i c r e g i o n and unit  i s no  s p e c t r a l peaks a t  p o r t i o n of t h e i r t o t a l variance i n the  The  100 and  g e o p o t e n t i a l anomaly s p e c t r u m has  variance. 15%  There  from  i s o t r o p y was  to  temperature  km.  surveys.  different  distribution  between the  km,  400  the  between  155  and  the  examined.  spectra are  HIGH r e g i o n , t h e  100  of  of  are  similar  l e s s than  the  quasi-synoptic  XBT  miss a s i g n i f i c a n t p o r t i o n of  the  SEASAT  altimetry  significant  window; and  the  to  those  i s consistent with  EKEs o f  the  portion  t h a t the  overestimates  due  to  (Fu, of  EKEs o f the  winds  1983)  the  are  mesoscale  the  ship  a c t i n g on  drift the  vessels.  The  relevance  of  dynamical t e s t s with parameters  ( i . e . the  sphericity  parameter  v e l o c i t y s c a l e s of it  was  found  quasigeostrophic  quasigeostrophic the  dynamics  wavenumber s t a t i s t i c s .  Rossby ( (3*))  number were  (Ro),  evaluated  each geographic r e g i o n .  that  R <<1, Q  scaling.  B  the  = The  0(1)  Rossby  The  inferred  using  several  quasigeostrophic  scaling  Burger  using  For and  was  the  number dominant  a l l regions (5*<<1, wave  (B)  and  and  the  length  and  length scales,  consistent steepness  with  the  parameter,  124 M  U/( 3 t>2),  =  was  0  fields  are wavelike  velocities  calculated  and group  with  investigate  (linear) or turbulent velocities  b a r o c l i n i c R o s s b y wave t h e o r y compared  to  were  whether  (nonlinear).  calculated using  the  baroclinic  eddy  The f r e q u e n c i e s ,  phase  free  linear  and t h e o b s e r v e d w a v e l e n g t h s .  the extensive  work,  by  other  These r e s u l t s  o f t h e temperature s p e c t r a w i t h t h e e x i s t i n g models o f  turbulence  Was  with  the  were  i n v e s t i g a t o r s , i n t h e NEP.  consistency  examined  dispersive  slopes  of  the  The  geophysical  near-inertial  spectral  subranges.  The  results  of these  dynamics governing  dynamical t e s t s imply  t h e o b s e r v e d b a r o c l i n i c eddy f i e l d s .  regions, t h e wavelengths greater wave t h e o r y theories  or nonlinear  cannot  motions  i n  the  high-energy consistent (1971)  be  distinguished with  low-energy  regions, with  model  regions  the perturbations  quasigeostrophic  with  wavelengths  are  intermediate  l e s s than between  tests.  The  those  theory,  expected  of  nonlinear  than  scales.  In  l e s s than  regions  Charney's  The  have  motions  scales  linear/nonlinear  the  200 km a r e  i n particular, turbulence.  the  that  Rossby  wave  theories.  the  p r o p e r t i e s o f t h e m e s o s c a l e m o t i o n s i n t h e o c e a n w i t h a q u a s i - s y n o p t i c XBT  data  An  inhomogeneity  examined  more  wavelengths  quasigeostrophic  turbulence  has  dynamical  of  set.  investigation  simple  200 km i n t h e l o w - e n e r g y  t h e o r i e s , and q u a s i g e o s t r o p h i c  This  turbulence  of three-dimensional  two  corresponding  with  Rossby  o f these  these  with  linear  The a p p l i c a b i l i t y  are,, o f course,  regions  of the  For a l l the geographic  t h a n 200 km a r e c o n s i s t e n t w i t h  R o s s b y wave t h e o r y .  i n the high-energy  motions  a geographic v a r i a b i l i t y  of the mesoscale  comparable t o the r e s u l t s o f previous of  the quasi-synoptic  velocity  scales.  governing inferred. determine  dynamics The  data  From of  and  sets  results of this  statistics  estimates of  velocity  of  motion,  perturbations  of the quasi-synoptic scales  of  variability  i s demonstrated The wavenumber t h e dominant an  statistics length  inhomogeneity  i n the  data  that i s  lies  variability  ocean  i n the has  been  i n the a b i l i t y from  and  which  to  simple  discussed.  Recommendations F o r F u t u r e  The  scales  the mesoscale  d y n a m i c a l m o d e l s may b e  geographic  investigators.  provided  these  strength  the length  the  Work  work have emphasized t h e v a l u e  f o r r e s o l v i n g t h e l e n g t h and v e l o c i t y  of quasi-synoptic  s c a l e s i n t h e ocean.  data  The d a t a s e t  125 e m p l o y e d h e r e i s by no means t h e c o m p l e t e c o l l e c t i o n o f t h e q u a s i - s y n o p t i c d a t a t h a t may  be u s e d f o r t h e  examination  p o t e n t i a l t o examine the but  i n more d e t a i l ,  (most  notably  First,  the  characteristics  Northwest  highlights  seasonal  signal  The  possibility  variability  was  identified  horizontal  of  the  and  these  ocean w i t h the  for  synoptic  significant  in this  a n i s o t r o p y of  the  requirement of  study,  There i s a  the mesoscale i n a s i m i l a r  of  Atlantic  the  examined.  the  of  i n several regions  the  investigation  of the mesoscale v a r i a b i l i t y .  Northeast  further  seasonal  s c a l e s of  in  not  motions  be  has  sets  of  This  four  variability  signals  could  data  Pacific).  work  mesoscale  but  available  manner,  the  areas. must  mesoscale  quantified.  not  been  Two,  adequately  resolved.  I n v e s t i g a t o r s have i d e n t i f i e d i n d i v i d u a l f e a t u r e s i n most r e g i o n s  the  with  ocean  significant large the  anisotropic characteristics,  evidence  t h a t mesoscale motions a r e ,  r e g i o n s of the ocean.  low-wavenumber  ideal. sections  I t would along  r e m o v e d by spectra  signal be  of  temperature are  the At data very  Three, the of  the  repeated  measured this  (ADCP) w i t h X B T s , o r  i t would  velocities  use  In be  a  this  and  expensive.  expendable  o b t a i n i n g the r e q u i r e d data  sets.  An  flow  series  manner  the  to  the  of  be  remove  considered  quasi-synoptic  mean  flow  with  may  the  doppler  The  measured  be  and  instruments  current  (XCPs) w o u l d  be  wavenumber  quasi-synoptic velocity  acoustic  current profilers  a n i s o t r o p i c over  obtain the  mesoscale.  of  statistically  cannot  conjunction  f o r examining  no  scheme u s e d h e r e t o  valuable  in  is  average,  time  d a t e , h o w e v e r , t h e r e a r e no  sets available new  oh  l a r g e - s c a l e mean  transect.  Fourth,  there  detrending  much p r e f e r a b l e t o  averaging.  temperatures.  required  a  but  be  profiler  capable  of  126 REFERENCES  A n d e r s o n , E.R., 1979. Expendable Bathythermograph N a v a l O c e a n S y s t e m s C e n t e r , San D i e g o , p. 143.  (XBT)  Accuracy  Studies.  A n d r e w s , J . C a n d P. S c u l l y - P o w e r s , 1976. The S t r u c t u r e o f a n E a s t A u s t r a l i a n C u r r e n t A n t i c y c l o n i c Eddy. J . Phys. Oceanogr., V o l . 6 ( 9 ) , 756-765. B e n n e t t , A.F., 1983. The In Eddies i n Marine Y o r k , 219-244.  South P a c i f i c I n c l u d i n g the E a s t A u s t r a l i a n C u r r e n t . S c i e n c e , R o b i n s o n , A.R. (ed.), Springer-Verlag, New  B e r n s t e i n , R.L., 1983. Eddy S t r u c t u r e s o f t h e N o r t h P a c i f i c O c e a n . i n M a r i n e S c i e n c e , R o b i n s o n , A.R. (ed.), Springer-Verlag, 158-166.  In Eddies New York,  B e r n s t e i n , R.L. a n d W.B. W h i t e , 1974. Time a n d L e n g t h S c a l e s o f B a r o c l i n i c Eddies i n the Central North P a c i f i c . J . Phys. Oceanogr., Vol. 4(10), 613-624. B e r n s t e i n , R.L. a n d W.B. W h i t e , 1977. Zonal V a r i a b i l i t y i n the D i s t r i b u t i o n of Eddy E n e r g y i n t h e M i d - L a t i t u d e N o r t h P a c i f i c O c e a n . J . Phys. Oceanogr., V o l . 7( 1 ) , 123-126. B e r n s t e i n , R.L. a n d W.B. W h i t e , 1981. S t a t i o n a r y and T r a v e l l i n g M e s o s c a l e P e r t u r b a t i o n s i n t h e K u r o s h i o E x t e n s i o n C u r r e n t . J . Phys. Oceanogr., V o l . 11(5), 692-703. B e r n s t e i n , R.L. a n d W.B. White, 1982. M e r i d i o n a l Eddy H e a t F l u x i n K u r o s h i o E x t e n s i o n C u r r e n t . J . P h y s . Oceanogr., V o l . 1 2 ( 1 ) , 154-159. B r o o k s , L.E.P. a n d N. C a r r u t h e r s , 1953. Handbook o f S t a t i s t i c a l Meteorology. Her M a j e s t y ' s S t a t i o n a r y O f f i c e , London, p. 412. Charney, J.G., 1087-1095.  1971.  Geostrophic  Turbulence.  J.  Atmos.  Sc.,  the  Methods  in  Vol.  28,  C h a r n e y , J.G. a n d G. R. F l i e r l , 1981. Oceanic Analogues of Large S c a l e Atmospheric Motions. I n E v o l u t i o n of P h y s i c a l Oceanography, Warren, B.A. a n d C. Wunsch ( e d s . ) , MIT P r e s s , C a m b r i d g e , M a s s . , 5 0 4 - 5 4 9 . C h e n e y , R.E., 1977. Synoptic Observations of the Oceanic of Japan. J . Geophys. Res., V o l . 8 2 ( 3 4 ) , 5459-5468.  Frontal  System  East  C h e n e y , R.E., J.G. M a r s h a n d B.D. B e c k l e y , 1983. Global Mesoscale V a r i a b i l i t y from Repeat T r a c k s o f S e a s a t A l i m e t e r D a t a . J . Geophys. Res., 4343-4359. Cummins, P.F., L. A. M y s a k a n d K. H a m i l t o n , 1986. G e n e r a t i o n o f Annual Rossby Waves i n t h e N o r t h P a c i f i c by t h e W i n d S t r e s s C u r l . J . Phys. Oceanogr. ( I n p r e s s ) .  127 D a n t z l e r , H.L., 1976. Geographical V a r i a t i o n s i n I n t e n s i t y of the North A t l a n t i c and t h e N o r t h P a c i f i c O c e a n i c Eddy F i e l d s . Deep-Sea Res., V o l . 23, 783-794. D e f a n t , A., 1981. The T r o p o s p h e r e . English P u b l i s h i n g Co., New D e l h i , p . 113.  t r a n s ed.  by  W.J.  Emery,  Denham, R.N., R. W. B a n n i s t e r , K.M. G u t h r i e , D.G. B r o w n i n g and 1981. Some H y d r o l o g i c a l F e a t u r e s o f t h e S o u t h F i j i B a s i n . M a r i n e a n d F r e s h w a t e r R e s . , V o l . 15, 2 9 9 - 3 0 6 . Department of the Bathythermograph 46.  Navy, (XBT)  F.G. New  Amerind  Crook, Zealand  1978. Guide to Common Shipboard Expendable R e c o r d i n g M a l f u n c t i o n s , NSTL S t a t i o n , S t . L o u i s , p . ^  D i c k s o n , R.R., W.J. G o u l d , P. A. G u r b u t t a n d P.D. K i l l w o r t h , 1982. A Seasonal S i g n a l i n O c e a n C u r r e n t s t o A b y s s a l D e p t h s . N a t u r e , V o l . 2 9 5 , 193-198. D o u g l a s , B.C. a n d R.W. SEASAT S a t e l l i t e 931-10937.  A g r e e n , 1983. The Altimetry Data.  Sea S t a t e C o r r e c t i o n J . Geophys. Res.,  E b b e s m e y e r , C. C u r t i s a n d B.A. T a f t , 1979. V a r i a b i l i t y of Dynamic H e i g h t , and S a l i n i t y i n t h e Main P y c n o c l i n e o f A t l a n t i c , J . P h y s . Oceanogr ., V o l . 9 ( 1 1 ) , 1073-1089.  f o r GOES-3 a n d Vol. 86(10),  P o t e n t i a l Energy, the Western North  E m e r y , W.J., 1983a. On t h e G e o g r a p h i c a l V a r i a b i l i t y o f t h e U p p e r L e v e l Mean a n d Eddy F i e l d s i n the North A t l a n t i c and N o r t h P a c i f i c , J. Phys. Oceanogr., V o l . 1 3 ( 2 ) , 269-291. E m e r y , W.J., 1983b. G l o b a l Summary: R e v i e w o f Eddy Phenomena a s E x p r e s s e d i n Temperature Measurements. In Eddies i n Marine S c i e n c e , Robinson, A.R. ( e d . ) , S p r i n g e r - V e r l a g , B e r l i n , 354-375. E m e r y , W.J. a n d L. M a g a a r d , 1976. B a r o c l i n i c R o s s b y Waves a s I n f e r r e d f r o m T e m p e r a t u r e F l u c t u a t i o n s i n t h e E a s t e r n P a c i f i c , J . Mar. Res., V o l . 3 4 ( 3 ) , 365-385. E m e r y , W.J. C C . E b b e s m e y e r a n d J . P . Dugan, 1980. The F r a c t i o n o f t h e V e r t i c a l Isotherm Deflections A s s o c i a t e d w i t h Eddies: An E s t i m a t e f r o m M u l t i s h i p XBT S u r v e y s . J . Phys. Oceanogr., V o l . 1 0 ( 6 ) , 885-899. E m e r y , W.J. a n d Dewar, J . S . , 1982. Mean T e m p e r a t u r e - S a l i n i t y , S a l i n i t y - D e p t h and Temperature-Depth Curves o f t h e N o r t h A t l a n t i c and t h e N o r t h P a c i f i c . P r o g , i n Oceanography, V o l . 11, 219-305. E m e r y , W.J., W.G. Lee and L. Magaard, 1984. Geographic and Seasonal D i s t r i b u t i o n s o f D e n s i t y , B r u n t - V a i s a l a Frequency and Rossby R a d i i i n the North A t l a n t i c and N o r t h P a c i f i c . J . Phys. Oceanogr., V o l . 14(2), 294-317. F o f o n o f f , N.P., 1981. The G u l f S t r e a m S y s t e m . In O c e a n o g r a p h y , W a r n e r , B.A. a n d C. Wunsch ( e d s . ) , M a s s . , 112-139.  E v o l u t i o n of P h y s i c a l MIT P r e s s , C a m b r i d g e ,  128 F u , L . - L . , 1 9 8 3 . On t h e Wavenumber S p e c t r u m o f O c e a n i c M e s o s c a l e O b s e r v e d by S e a s a t A l t i m e t r y . J . Geophys. R e s . , 4331-4341. Gill,  A.E., 1982. p. 662.  Atmosphere-Ocean  Dynamics.  Academic  Press,  Variability  New  York,  G o u l d , W.J., 1 9 8 3 . T h e N o r t h e a s t A t l a n t i c O c e a n . I n Eddies i n Marine Science, R o b i n s o n , A.R. ( e d . ) , S p r i n g e r - V e r l a g , New Y o r k , 1 4 5 - 1 5 7 . H a r r i s o n , W.J. E m e r y , J . P . Dugan a n d B o - C h e n g L i , 1 9 8 3 . M i d - L a t i t u d e M e s o s c a l e T e m p e r a t u r e V a r i a b i l i t y i n S i x M u l t i s h i p XBT S u r v e y s . J . P h y s . O c e a n o g r . , V o l . 1 3 ( 4 ) , 648-662. H i n z e , J . , 1975. T u r b u l e n c e , 2nd E d i t i o n .  M c G r a w - H i l l , New Y o r k , p . 7 9 0 .  H o l l o d a y , C G . a n d J . J . O ' B r i e n , 1975. M e s o s c a l e V a r i a b i l i t y Temperature. J . Phys. Oceanogr., V o l . 5 ( 6 ) , 864-870. Howe, M.R. a n d R . J . T a i t , 1967. Sea R e s . , V o l . 14, 3 7 3 - 3 7 8 .  A Subsurface Cold-Core  o f Sea S u r f a c e  Cyclonic  Eddy.  H o y o s h i , Y. , 1 9 8 1 . Space-Time C r o s s S p e c t r a l A n a l y s i s U s i n g E n t r o p h y Method. J . Met. Soc. J a p a n , V o l . 5 9 ( 5 ) , 620-624. J e n k i n s , G.W. a n d D.G. W a t t s , 1968. H o l d e n - D a y , New Y o r k , p . 4 6 0 .  Spectral  Analysis  t h e Maximum  and i t s A p p l i c a t i o n s .  J o y c e , T.M. , W. Z e n k a n d J.M. T o o l e , 1 9 8 1 . A n a t o m y o f a C y c l o n i c Drake Passage. Deep-Sea R e s . , V o l . 2 8 A ( 1 1 ) , 1 2 6 5 - 1 2 8 7 . K a n a s e w i c h , E.R., 1 9 8 1 . Time S e q u e n c e A n a l y s i s A l b e r t a , Edmonton, p . 480.  Deep  i n Geophysics.  Ring i n the  University of  K a n g , Y.Q. a n d L. M a g a a r d , 1980. A n n u a l B a r o c l i n i c R o s s b y Waves i n t h e C e n t r a l North P a c i f i c . J . Phys. Oceanogr., V o l . 1 0 ( 9 ) , 1159-1167. K i t a h b , K. , 1 9 7 5 . Some P r o p e r t i e s o f t h e Warm E d d i e s G e n e r a t e d i n t h e C o n f l u e n c e Zone o f t h e K u r o s h i o a n d O y a s h i o C u r r e n t s . J . P h y s . O c e a n o g r . , V o l . 5, 2 4 5 - 2 5 2 . K o s h l y a k o v , M.N. a n d Y.M. G r a c h e v , 1 9 7 3 . M e s o s c a l e C u r r e n t s a t a H y d r o p h y s i c a l Polygon i n the Tropical A t l a n t i c . Deep-Sea Res., V o l . 2 0 , 507-521. K r a i c h n a n , R.H., 1 9 6 7 . I n e r t i a l R a n g e s i n T w o - d i m e n s i o n a l F i d s . , V o l . 1 2 ( 7 ) , 1427-1433. Lai,  Turbulence, Phy. o f  D.Y. a n d P . L . R i c h a r d s o n , 1 9 7 7 . D i s t r i b u t i o n a n d Movement o f G u l f R i n g s . J . Phys. Oceanogr., V o l . 7 ( 9 ) , 670-683.  LeBlond, P.H. a n d L.A. M y s a k , 1978. N o r t h - H o l l a n d , New Y o r k , p . 6 0 2 . L e e t m a , A., 1 9 7 7 . A S t u d y o f MODE D y n a m i c s .  Waves  i n  the  Ocean.  Stream  Elsevier  Deep-Sea Res., V o l . 24, 733-742.  129 L e g e c k i s , R., 1977. L o n g Waves i n t h e E a s t e r n E q u a t o r i a l P a c i f i c View from a G e o s t a t i o n a r y S a t e l l i t e . S c i e n c e , 1179-1181.  Ocean:  A  L u t j e h a r m s , J.R., 1 9 8 1 . S p a t i a l S c a l e s a n d I n t e n s i t i e s o f C i r c u l a t i o n i n t h e Ocean A r e a s Adjacent t o South Africa. Deep-Sea Res., V o l . 28A, 1289-1302. L u t j e h a r m s , J.R. a n d D . J . B a k e r , 1980. A S t a t i s t i c a l A n a l y s i s o f t h e M e s o s c a l e Dynamics o f t h e S o u t h e r n Ocean. D e e p - S e a R e s . , V o l . 2 7 A , 145-159. M a l a n o t t e R i z z o l i , P., 1 9 8 2 . P l a n e t a r y S o l i t a r y Waves a n d t h e i r Existing S o l u t i o n s i n t h e Context o f a U n i f i e d Approach. I n T o p i c s i n Ocean P h y s i c s , O s b o r n e , A.R., P. M a l a n o t t e P. R i z z o l i (eds.), North-Holland P u b l i s h i n g , New Y o r k , 1 2 6 - 1 4 7 . M i l l e r o , F . J . a n d A. P o i s s o n , 1 9 8 1 . I n t e r n a t i o n a l O n e - a t m o s p h e r e E q u a t i o n o f S t a t e f o r Sea-water. Deep-Sea R e s . , V o l . 28A, 625-629. M i y a k i , M., 1981. AXBT O b s e r v a t i o n s . I n F r o n t s 80: P r e l i m i n a r y Results, P a u l s o n , C A . a n d P.P. N i i l e r ( e d s . ) , S c h o o l o f O c e a n o g r a p h y , O r e g o n S t a t e U n i v e r s i t y , R e f . 8 1 - 2 , 11-19. MODE G r o u p ,  1975.  D y n a m i c s a n d t h e A n a l y s i s o f MODE-I.  MODE G r o u p , 1978. 859-910.  The Mid-Ocean Dynamics E x p e r i m e n t .  M o o r e , C., 1 9 8 1 . UBC C u r v e . Computing V a n c o u v e r , B.C., p . 1 6 4 .  Deep-Sea R e s . , V o l . 2 5 ,  Centre, University of B r i t i s h  M y s a k , L.A., 1983. G e n e r a t i o n o f A n n u a l R o s s b y Phys. Oceanogr., V o l . 1 3 ( 1 0 ) , 1908-1923. M y s a k , L.A., 1986. E l N i n o , N o r t h e a s t P a c i f i c Ocean. 464-487.  MIT P r e s s , p . 2 5 0 .  Columbia,  Waves i n t h e N o r t h P a c i f i c .  J.  Interannual V a r a b i l i t y and F i s h e r i e s i n t h e Can. J . F i s h , and A q u a t i c Res., V o l . 4 3 ( 2 ) ,  National Oceanographic Data Center, 1984. NODC Oceanographer Data C e n t e r , Monteray, p . 503.  Users  Guide,  National  N i s h i d a , H. a n d W.B. W h i t e , 1 9 8 2 . H o r i z o n t a l Eddy F l u x e s o f Momentum a n d K i n e t i c Energy i n t h e N e a r - S u r f a c e o f t h e K u r o s h i p E x t e n s i o n . J.Phys. O c e a n o g r . , V o l . 12( 1 ) , 1 6 0 - 1 7 0 . O z m i d o v , R.V., 1 9 6 5 . E n e r g y D i s t r i b u t i o n B e t w e e n O c e a n i c M o t i o n s o f D i f f e r e n t Scales. I z v . Atm. a n d Ocean P h y s c i s S e r i e s , V o l . 1 ( 4 ) , 439-448. P a r k e r , G.E., 1 9 7 1 . G u l f Vol. 18, 981-993. P a t z e r t , W.C, 1 9 6 9 . H a w a i i , p 50.  Stream  Eddies  Rings  i n t h e Sargasso  i n Hawaiian  Waters.  Sea.  Deep-Sea R e s . ,  HIG-G9-8, U n i v e r s i t y o f  P a t z e r t , W.C. a n d R.L. B e r n s t e i n , 1 9 7 6 . Eddy S t r u c t u r e i n t h e C e n t r a l P a c i f i c Ocean. J . P h y s . O c e a n o g r . , V o l . 6, 3 9 2 - 3 9 4 . P e d l o s k y , J . , 1979. 624.  G e o p h y s i c a l F l u i d Dynamics.  South  S p r i n g e r - V e r l a g , New Y o r k , p .  130 P h i l l i p s , O.M., 1966. Dynamics P r e s s , London, p. 261. P i c k a r d , G.L. Edition.  o f t h e Upper  Ocean.  a n d W.J. E m e r y , 1 9 8 2 . Descriptive Pergamon P r e s s , T o r o n t o , p . 2 4 9 .  P o n d , S. a n d G.L. P i c k a r d , 1 9 8 3 . Introductory Edition. Pergamon P r e s s , T o r o n t o , p . 329.  Cambridge  University  Physical  Oceanography, 4 t h  Dynamical  Oceanography, 2nd  Price, J.M. a n d L . M a g a a r d , 1983. - R o s s b y Wave A n a l y s i s of Subsurface Temperature F l u c t u a t i o n s along t h e Honolulu-San F r a n c i s c a n Great C i r c l e . J . Phys. Oceanogr., V o l . 1 3 ( 1 ) , 258-268. R a s m u s s o n , E.M., P.A. A r k i n , A.F. K r u e g e r , R.S. Q u i r o z a n d R.W. R e y n o l d s , 1 9 8 1 . The E q u a t o r i a l P a c i f i c Atmospheric Climate during 1982-83. Tropical O c e a n - A t m o s p h e r e N e w s l e t t e r , No. 2 1 , 2-3. R h i n e s , P.B., 1 9 7 7 . T h e D y n a m i c s o f U n s t e a d y C u r r e n t s . I n The S e a , G o l d b e r g , E.D., I . N . M c C a v e , J . J . O ' B r i e n , J . H . S t e e l e ( e d s ) . , J o h n W i l e y , New Y o r k , 189-318. R i c h m a n , J.G. , C. Wunsch, a n d N.G. H o g g , 1977. Space a n d Time S c a l e s o f Mescoscale Motion i n t h e Western North A t l a n t i c . Reviews o f Geophysics and S p a c e P h y s i c s , V o l . C 1 5 ( 4 ) , 3 8 5 - 4 1 9 . R i c h a r d s o n , P.C., 1 9 7 9 . 90-101.  Gulf  Stream Rings.  J . Phys. Oceanogr., V o l . 10(1),  R i c h a r d s o n , P.L., 1 9 8 3 . Gulf Stream Rings. I n Eddies i n Marine R o b i n s o n , A.R. ( e d . ) , S p r i n g e r - V e r l a g , New Y o r k , 19-45.  Science,  R o b i n s o n , A.R., 1 9 8 2 . D y n a m i c s o f O c e a n C u r r e n t s a n d C i r c u l a t i o n : R e s u l t s o f POLYMODE a n d R e l a t e d I n v e s t i g a t i o n s . I n T o p i c s o f Ocean P h y s i c s , O s b o r n e , A.R. a n d P. M a l a n o t t i R i z z o l i ( e d s . ) , N o r t h - H o l l a n d P u b l i s h i n g , A m s t e r d a m , 3-29. R o b i n s o n , A.R. (ed..), York, p. 609.  1983.  Eddies  i n Marine  Science.  R o d e n , G . I . 1977. On Long-Wave D i s t u r b a n c e s o f Dynamic Pacific. J . P h y s . Oceanogr., V o l . 7 ( 1 ) , 41-49.  Springer-Verlag,  Height  New  i n the North  Roden, G.I.,. 1979. The D e p t h V a r i a b i l i t y of Meridional Gradients Temperature, S a l i n i t y and Sound V e l o c i t y i n t h e Western N o r t h P a c i f i c . Phys. Oceanogr., V o l . 9 ( 4 ) , 756-767.  of J.  R o d e n , G . J . , 1980. M e s o t h e r m o h a l i n e , Sound V e l o c i t y and B a r o c l i n i c Flow S t r u c t u r e o f t h e P a c i f i c S u b t r o p i c a l F r o n t d u r i n g t h e W i n t e r o f 1980. J . P h y s . O c e a n o g r . , V o l . 9, 7 5 6 - 7 6 7 . R o y e r , T.C., 1 9 7 8 . O c e a n E d d i e s G e n e r a t e d b y Seamounts S c i e n c e , V o l . 1 9 9 , 1063-1064.  i n the North  Pacific.  S a u n d e r s , P.M., 1 9 7 1 . A n t i c y c l o n i c E d d i e s f o r m e d f r o m S h o r e w a r d M e a n d e r s o f t h e G u l f S t r e a m . Deep-Sea R e s . , V o l . 1 8 , 1 2 0 7 - 1 2 1 9 .  131 S a u n d e r s , P.M., 1 9 7 2 a . Comments o n Wavenumber F r e q u e n c y S p e c t r a o f T e m p e r a t u r e i n the Free Atmosphere. J . Atmos. S c i . , V o l . 2 9 , 1 9 7 - 1 9 9 . S a u n d e r s , P.M., 1972b. S p a c e a n d Time V a r i a b i l i t y Ocean. Deep-Sea R e s . , V o l . 19, 4 6 7 - 4 8 0 . S a u n d e r s , P.M., 1982. Circulation R e s . , V o l . 40 ( s u p p l ) .  i n the Eastern  S c h m i t z , W.J., 1981. Observations of Eddies Deep-Sea R e s . , V o l . 2 8 A ( 1 1 ) , 1 4 1 7 - 1 4 2 1 . S e l b y , S.M. ( e d . ) , 1965. Co., O h i o , p . 4 0 7 .  o f Temperature i n t h e Upper  Standard Mathematical  in  1975.  S t o m m e l , H., 202.  XBT  1960.  System Manual. The  Gulf  the  Tables.  Sippican, 1970. O c e a n E n g i n e e r i n g B u l l e t i n No. Equations. The S i p p i c a n C o r p . , M a s s . , p . 12. Sippican,  North  1,  Atlantic.  Newfoundland  The  XBT  Cambridge  University  Mar.  Basin.  C h e m i c a l Rubber  System  The S i p p i c a n C o r p . , M a s s . , p .  Stream.  J.  Press,  Linearity  207. London,  p.  S t o m m e l , H., E.D. S t r o u p , J . L . R e i d a n d B.A. Warren, 1973. Transpacific H y d r o g r a p h i c S e c t i o n s a t L a t s . 43°S a n d 28°S: The S c o r p i o E x p e d i t i o n - I Preface. Deep S e a R e s . , V o l . 2 0 , 1-8. S t r o u p , E.D., B . J . K i l a n s k y a n d K. W y r t k i , 1 9 8 1 . AXBT O b s e r v a t i o n s d u r i n g t h e Hawaii/Tahiti Shuttle Experiments. HIG-81-1, U n i v e r s i t y o f H a w a i i , p. 98. S w a t e r s , G., 1985. On S e v e r a l A s p e c t s o f Modom T h e o r y . Ph.D. Thesis, Department of Oceanography, U n i v e r s i t y o f B r i t i s h Columbia, Vancouver, B.C., p . 147. T a b a t a , S., 1975. The G e n e r a l C i r c u l a t i o n o f t h e P a c i f i c Ocean and a B r i e f A c c o u n t o f t h e O c e a n o g r a p h i c S t r u c t u r e o f t h e N o r t h P a c i f i c Ocean, P a r t I . A t m o s p h e r e , V o l . 1 3 ( 4 ) , 133-168. T e n n e k e s , H. a n d J . L . L u m l e y , 1972. Cambridge, Mass., p. 300.  A First  Course i n Turbulence.  MIT  Thomson, K.A., W.J. E m e r y a n d D.P. K r a u e l , 1 9 8 4 a . A S a m o a - H a w a i i XBT i n November 1982. T r o p i c a l Ocean-atmosphere N e w s l e t t e r , No. 14-15.  Press,  section 27,  Thomson, K.A., D.P. K r a u e l a n d W.J. E m e r y , 1984b. S y n o p t i c SXBT O b s e r v a t i o n s f r o m C a n a d i a n A r m e d F o r c e s D e s t r o y e r S q u a d r o n s , F e b r u a r y 1980 t o J u n e 1983. R e p o r t f o r t h e D e f e n c e R e s e a r c h E s t a b l i s h m e n t - P a c i f i c , p . 146. T u r n e r , J . S . , 1981. Small-Scale Mixing Processes. I n Evolution of P h y s i c a l O c e a n o g r a p h y , W a r r e n , B.A. a n d Wunsch, C. ( e d s . ) , MIT P r e s s , C a m b r i d g e , M a s s . , 236 - 2 6 3 . V a n W o e r t , M., 1982. The S u b t r o p i c a l F r o n t : S a t e l l i t e Observations FRONTS 8 0 . J . G e o p h y s . R e s . , V o l . 8 7 C ( 1 2 ) , 9 5 2 3 - 9 5 3 6 .  During  132 V o o r h i s , A.D., 1976. The I n f l u e n c e o f Deep M e s o s c a l e E d d i e s o n S e a S u r f a c e Temperature i n the North A t l a n t i c S u b t r o p i c a l Convergence. J . Phys. Oceanogr., V o l . 6 ( 1 1 ) , 953-961. W a l p o l e , R.E. 1974. Y o r k , p. 340.  Introduction to Statistics.  M a c M i l l a n P u b l i s h i n g Co.,  W h i t e , W.B. 1977. A n n u a l F o r c i n g o f B a r o c l i n i c L o n g Waves i n t h e N o r t h P a c i f i c Ocean. J . Phys. Oceanogr., V o l . 7 ( 1 ) , 50-61. W h i t e , W.B., Pacific  1982. T r a v e l l i n g Wave-like Mesoscale Perturbations Current. J . Phys. Oceanogr., V o l . 1 2 ( 3 ) , 231-245.  New  Tropical  i n the North  W h i t e , W.B., 1985. The R e s o n a n t R e s p o n s e o f I n t e r a n n u a l B a r o c l i n i c R o s s b y Waves t o W i n d F o r c i n g i n t h e E a s t e r n M i d - l a t i t u d e N o r t h P a c i f i c . J . Phys. O c e a n o g r . , V o l . 15, 4 0 3 - 4 1 5 . W h i t e , W.B. a n d A.E. W a l k e r , 1974. Time and Depth S c a l e s o f Anomalous S u b s u r f a c e T e m p e r a t u r e a t Ocean W e a t h e r S t a t i o n s P, N, a n d V i n t h e N o r t h Pacific. J . Geophys. Res., V o l . 7 9 ( 3 0 ) , 4517-4522. W h i t e , W.B. a n d L. B e r n s t e i n , 1979. D e s i g n o f an O c e a n o g r a p h i c Network i n t h e Mid-latitude North P a c i f i c . J . P h y s . O c e a n o g r . , V o l . 9, 5 9 2 - 6 0 6 . W h i t e , W.B. a n d J . F . T . S a u r , 1981. A S o u r c e o f A n n u a l B a r o c l i n i c Waves i n t h e Eastern Subtropical North P a c i f i c . J . Phys. Oceanogr. V o l . 11(11), 1452-1462. W i l s o n , W.S. Vicinity 537-540.  a n d J . P . Dugan, 1978. Mesoscale Thermal V a r i a b i l i t y i n the of the Kuroshio Extension. J . Phys. Oceanogr., V o l . 8 ( 5 ) /  Wunsch, C , 1981. Low F r e q u e n c y V a r i a b i l i t y P h y s c i a l O c e a n o g r a p h y , W a r r e n , B.A. a n d Cambridge, Mass., 341-375.  o f t h e Sea. In Evolution of C. Wunsch, ( e d s . ) , MIT Press,  W y r t k i , K. 1967. The S p e c t r u m o f Ocean T u r b u l e n c e o v e r D i s t a n c e s B e t w e e n 40 a n d 1000 K i l o m e t r e s . Deutsche Hydrographische Z e i t s c h r i f t , V o l . 2 0 ( 4 ) , 176-186. W y r t k i , K. 1975. F l u c t u a t i o n s o f t h e Dynamic P h y s . Oceanogr. , V o l . 5 ( 7 ) , 450-459. W y r k t i , K., 1982. Eddies i n the P a c i f i c Oceanogr. V o l . 1 2 ( 2 ) , 746-749.  Topography  North  W y r t k i , K. , L. M a g a a r d a n d J . H a g e r , 1976. Geophys. Res., V o l . 8 1 , 2641-2646.  Equatorial ^  Eddy  Energy  i n the P a c i f i c .  Current.  J.  J . Phys •  i n t h e Oceans.  J.  W y r t k i , K.,. E. F i r i n g , D. H a l p e r n , R. K n o x , G . J . M c N a l l y , W.C. P a t z e r t and E.D. S t r o u p , 1 9 8 1 . The H a w a i i t o T a h i t i S h u t t l e E x p e r i m e n t . Science, 211, 22-28. Zar,  J.H., 620.  1974.  Biostatistical  Analysis.  Prentice-Hall  I n c . , Toronto,  p.  

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