WPC.\  
      2 .     B       P   Z      .     Courier 10cpi #| P              wx 6X   @ 8; X@HP LaserJet III                      HPLASIII.PRS x 
   @   ,\,42X@ USUK  3'                                          3'Standard                                  6&                                          6& Standard    rJet III   _ K  +                                          #  Xw     P 7[hXP#  2      `  "   b      X  W  +Courier 10cpi CG Times (Scalable)  "  m+O6^;C]ddCCCdCCCCddddddddddCCȲY~~wCN~sk~CCCddCYdYdYCdd88d8ddddJN8ddddYYdYC dd  ddd   C dddddd ddd8 YYYYYY~Y~Y~Y~YC8C8C8C8ddddddddddYdddddsdYYYYYYYd~Y~Y~Y~YddddddddC8C8C8C8oN d~8~8~8~8~8dvddddJJJkNkNkNkN~8~8~8dddddddYYY  d~8dJkN~8dddddC     dd   C      CCWxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNd ddCYQQddddddFddddF CC hhd44ddzzddd woo     Ch      d     F"Ȑdh             d岲  dCCȐzȲxCddodȐȅdCdYdsȐ]Ȑ ȐȧzȐ       Uw                                                                                                 ŐdȐ      Y   Y                           C   C   C   C                                                               ΐz~o  zoY~NYdYC8YooYdYzsdzd d~YYzozzzzNd88YYYzYz z zz CCddddd          dd         zzzzzzzzzzzzzzzzzzzNNNNNNNdddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYzzzzzzzzzzzzzzzzzzzzC  s  ~CzdYC x ? x x x ,    wx 6X   @ 8; X@ 8 w C ; ,  [hXw     P 7XPHP LaserJet III                      HPLASIII.PRS x 
   @   ,,42X@ USUK  3'                                          3'Sta 2 {
        Z      .  K	  	    y
  #| P          HP LaserJet III                      HPLASIII.PRS x 
   @   ,\,42X@ USUK  3'                                          3'Standard                                  6&                                          6& Standard    rJet III   _ K  +                                          #  Xw     P 7[hXP# + 2     
  v     p     k   f   "  m+O6^;C]ddCCCdCCCCddddddddddCCȲY~~wCN~sk~CCCddCYdYdYCdd88d8ddddJN8ddddYYdYC dd  ddd   C dddddd ddd8 YYYYYY~Y~Y~Y~YC8C8C8C8ddddddddddYdddddsdYYYYYYYd~Y~Y~Y~YddddddddC8C8C8C8oN d~8~8~8~8~8dvddddJJJkNkNkNkN~8~8~8dddddddYYY  d~8dJkN~8dddddC     dd   C      CCWxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNd ddCYQQddddddFddddF CC hhd44ddzzddd woo     Ch      d     F"Ȑdh             d岲  dCCȐzȲxCddodȐȅdCdYdsȐ]Ȑ ȐȧzȐ       Uw                                                                                                 ŐdȐ      Y   Y                           C   C   C   C                                                               ΐz~o  zoY~NYdYC8YooYdYzsdzd d~YYzozzzzNd88YYYzYz z zz CCddddd          dd         zzzzzzzzzzzzzzzzzzzNNNNNNNdddddddddddddddddddd888888888888YYYYYYYYYYYYYYYYYYYzzzzzzzzzzzzzzzzzzzzC  s  ~CzdYC xa8Document g        Document Style  Style                                       X X`	`	  `	

a4Document g        Document Style  Style                                      .  a6Document g        Document Style  Style                                    G  X  

 2   k        n  v     t     a5Document g        Document Style  Style                                   }    X (#

a2Document g        Document Style  Style                                  < o  
   ?                    A.        

a7Document g        Document Style  Style                                   y    X  X`	`	 (#`	

Bibliogrphy          Bibliography                                             :   X 
 (#

 2      /  	     
   l       a1Right Par         Right-Aligned Paragraph Numbers                        : ` S  @                   I.  
  X (#

a2Right Par         Right-Aligned Paragraph Numbers                        	C  	   @`	                  A.    `	`	 (#`	

a3Document g        Document Style  Style                                  
B 
 b 
   ?                     1.        
a3Right Par         Right-Aligned Paragraph Numbers                        L ! 
   `	`	 @P
                  1.  `	`	   (#

 2        
        e     -  a4Right Par         Right-Aligned Paragraph Numbers                        U  j   `	`	  @                  a.    `	 (#

a5Right Par         Right-Aligned Paragraph Numbers                        
_ o    `	`	   @h                  (1)    hh# (#h

a6Right Par         Right-Aligned Paragraph Numbers                        h     `	`	   hh# @$                  (a)  hh#  ( (#

a7Right Par         Right-Aligned Paragraph Numbers                        p fJ    `	`	   hh# ( @*                  i)  (  h- (#

 2      /       +         a8Right Par         Right-Aligned Paragraph Numbers                        y W" 3!   `	`	   hh# ( - @p/                  a)  -  pp2 (#p

a1Document g        Document Style  Style                                  X q q
    
   l   ^)                       I.           ׃

Doc Init             Initialize Document Style                                  
 
               0*0*    I. A. 1. a.(1)(a) i) a)                 I. 1. A. a.(1)(a) i) a)                                     Document g                                           Tech Init             Initialize Technical Style                              .  
k    I. A. 1. a.(1)(a) i) a)                 1 .1 .1 .1 .1 .1 .1 .1                                      Technical                                             2      1          ?       a5Technical         Technical Document Style                               ) W D                   (1)  .  a6Technical         Technical Document Style                               )  D                   (a)  .  a2Technical         Technical Document Style                               < 6  
   ?                    A.        

 a3Technical         Technical Document Style                               9 W g 
   2                    1.        
  2 :"          l      .!     !  a4Technical         Technical Document Style                               8 bv {    2                     a.        
 a1Technical         Technical Document Style                               F ! < 
   ?                         I.           

 a7Technical         Technical Document Style                               ( @ D                   i)  .  a8Technical         Technical Document Style                               (  D                   a)  .   2 4    l"    o&    B+    0  Pleading              Header for numbered pleading paper                     P@  n                         $]        X    X`	hp x (#%'0*,.8135@8:<H?A                                         y    *                    d       d d                                                                         y y    *                    d       d d                                                                         y 

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	 Ӌ "  m+O6^6=U\\===\====\\\\\\\\\\==Qs~sm=Gsizbsw===\\=Q\Q\Q=\\33\3\\\\DG3\\\\QQ\Q= \\  \\\   = \\\\\\ \\\3 QQQQQz~QsQsQsQsQ=3=3=3=3\\\\\\\\\\Q\\\\\i\QQQ~Q~Q~Q~Q\sQsQsQsQ\\\\\\\\=3=3=3=3fG \s3s3s3s3s3\m\\\\zDzDzDbGbGbGbGs3s3s3\\\\\\\wQwQwQ  \s3\zDbGs3\\\\\=     \\   =      ==WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxN\ \\=QKK\\\\\\A\\\\A == __\00\\pp\\\ mff     =_      \     A"\_             \壣  \==px=\\f\z\=\Q\iwU zp       Nm                                                                                                 ń\      Q   Q                           =   =   =   =                                                               ΄psf  pfzQsGwQ\Q=3QzffQz\Qpi\p\ \sQQzpfppppG\33QQQpQp p pp ==\\\\\          \\         pppppppppppppppppppGGGGGGG\\\\\\\\\\\\\\\\\\\\333333333333QQQQQQQQQQQQQQQQQQQpppppppppppppppppppp=  i  s=p\Q= x "  m+O6^18MSS888S8888SSSSSSSSSS88Jxir{icx{8Aui{x`xoZi{xxxl888SS8JSJSJ8SS..S.SSSS>A.SSxSSJJSJ8 SS  SSS   8 SSSSSS SSS. xJxJxJxJxJorJiJiJiJiJ8.8.8.8.{SxSxSxSxS{S{S{S{SxSxJ{SxSxSxS{S`SxJxJxJrJrJrJrJ{SiJiJiJiJxSxSxSxSxSxS{S{S8.8.8.8.z]A uSi.i.i.i.i.{S{c{S{SxSxSxo>o>o>ZAZAZAZAi.i.i.{S{S{S{S{S{SxxSlJlJlJ  {Si.{So>ZAi.xSxS{SxS{S8     SS   8      88WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNxxxS SS8JDDSSSSSS;SSSS; 88 VVS++SSffSSxS c]]     8V      S     ;"xxSxWxx             S唔  S88xfxxxxxxxxxxx8SxS]SxoS8SxJS`xlxxxxxxxxxxMxxxx xxofx       Gc                                               xxxx                                                  xxxSxxxx   xx   xJ   xxxxJ   xxxxx   xxx   xxx   xxx   xxxxxxxxxxxxxx     x   xxxxxx    xxxxxxxx8   xxx8   xxx8   xxx8   xxxx   x                                                   x   xxxx   xxxxfi]  f]oJiAlJ{SxJ8.uJo]]{JoSxJxf`SfS SiJxJofx]ffffAS..JJJfJf f ff 88SSSSS          SS         fffffffffffffffffffAAAAAAASSSSSSSSSSSSSSSSSSSS............JJJJJJJJJJJJJJJJJJJffffffffffffffffffff8  `  xi{8xxfSJ8 x "  m+O6^18PSS888S8888SSSSSSSSSS88Sffoxf`xx8Jo]oxfxfS]xff]]888SS8SSJSJ.SS..J.xSSSSAA.SJoJJAJSJ8 SS  SSS   8 SSSSSS SSS. fSfSfSfSfSooJfJfJfJfJ8.8.8.8.oSxSxSxSxSxSxSxSxS]JfSxSxSxS]JxSfSfSfSfSoJoJoJoJxSfJfJfJfJxSxSxSxSxSxSxSxS8.8.8.8.SJ oJ].].].].].oSofoSoSxSxSofAfAfASASASASA].].].xSxSxSxSxSxSo]J]A]A]A  xS].oSfASA].]J]JxSxSxS8     SS   8      88WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNxxxS SS8SMMSSSSSS;SSSS; 88 SSS..SSffSSxS ZSS     8S      S     ;"xxSxSxx             S唔  S88xfxxxxxxxxxxx8SfS]SxoS8SxJS`xlxxxxxxxxxxMxxxx xxofx       Gc                                               xxxx                                                  xxxSxxxx   xx   xJ   xxxxJ   xxxxx   xxx   xxx   xxx   xxxxxxxxxxxxxx     x   xxxxxx    xxxxxxxx8   xxx8   xxx8   xxx8   xxxx   x                                                   x   xxxx   xxxfff]  f]oJfA]JxSxJ8.oJo]]oJoSxJxffSfS S]J]Joff]ffffAS..JJJfJf f ff 88SSSSS          SS         fffffffffffffffffffAAAAAAASSSSSSSSSSSSSSSSSSSS............JJJJJJJJJJJJJJJJJJJffffffffffffffffffff8  `  ffx8x]fSJ8 x 2 D      5    5    x:    K?  Courier 10cpi CG Times (Scalable) CG Times Italic (Scalable) CG Times Bold (Scalable) Courier 10cpi (Bold) CG Times Bold Italic (Scalable)  "  m+O6^6=U\\===\====\\\\\\\\\\==\zzpGXzpfzz===\\=\fQfQA\f3=f3f\ffQG=f\\\Q\\\=\\  \\\   = \\\\\\ \\f3 \\\\\QzQzQzQzQG3G3G3G3f\\\\ffff\\f\\\\pf\\\QQQQfzQzQzQzQ\\\\\\ffG3G3G3G3iX fz3z3z3zGz3fff\\ψQQQfGfGfGfGz=z=z=ffffff\zQzQzQ  fz3fQfGz=\\f\f=     \\   =      ==WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxN\ \\=\NN\\\\\\A\\\\A == ii\00\\pp\\\ sff     =i      \     A"\i             \壣  \==px=\\f\z\=\Q\i~X zp       Nm                                                                                                 ń\      \   \                           =   =   =   =                                                               ΄pzf  pfzQzGzQQQG3QzffQz\Qpp\p\ \zQQzpfppppGQ33QQQpQp p pp ==\\\\\          \\         pppppppppppppppppppGGGGGGGQQQQQQQQQQQQQQQQQQQQ333333333333QQQQQQQQQQQQQQQQQQQpppppppppppppppppppp=  p  zGp\Q= x "  m+O6^!%377bV%%%7b%%%%7777777777%%nbn1bOEKQEAOQ%+MEdQO?OI;EQOhOOG%%%77%17171%777V7777)+77O771171n% 77  777   % 777777 777 O1O1O1O1O1bIK1E1E1E1E1%%%%Q7O7O7O7O7Q7Q7Q7Q7O7O1Q7O7O7O7Q7?7O1O1O1K1K1K1K1Q7E1E1E1E1O7O7O7O7O7O7Q7Q7%%%%P=+ M7EEEEEQ7QAQ7Q7O7O7bOI)I)I);+;+;+;+EEEQ7Q7Q7Q7Q7Q7hOO7G1G1G1  Q7EQ7I);+EO7O7Q7O7Q7%     77   %      %%WnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNOOO7 77%1--77a777bb7'7777b' %% 997bnn77CCTn7n7O7 A\\==b     %9      7  h   '"nnnnOOnnn7Onn9OObbnnn             7bbnnn  b7%%nnnnnOCnbOOOOOOOOOOx%n7O7=7bnOnI7%7O17?OVGnnOOOOOOOOOOnnnnn3nOOOOnnnnnnnnnnnnn nnnnnnOOnnnnnn\ICVnOn   nn    /A                                               OOOO                       nn          n        nn         nOOO7OOnOOnnn   OO   O1   OOOO1   OOOOO   OOO   OOO   OOO   OOOOOOOOOOOOOO     O   OOOOOO    OOOOOOOO%   OOO%   OOO%   OOO%   OOOO   O                                                   O   OOOO   OOOOCE=  C=I1E+G1Q7O1%M1I=d=Q1I7O1OC?7C7 7E1O1ICO=VCCCC+7111C1C C CC %%77777          77         CCCCCCCCCCCCCCCCCCC+++++++777777777777777777771111111111111111111CCCCCCCCCCCCCCCCCCCC%  ?  OEQ%OOC71% x "  m+O6^6=X\\===\====\\\\\\\\\\==\ppzpi=Qzfzpp\fppff===\\=\\Q\Q3\\33Q3\\\\GG3\QzQQGQ\Q= \\  \\\   = \\\\\\ \\\3 p\p\p\p\p\zzQpQpQpQpQ=3=3=3=3z\\\\\\\\\fQp\\\\fQ\p\p\p\p\zQzQzQzQ\pQpQpQpQ\\\\\\\\=3=3=3=3\Q zQf3f3f3f3f3z\zpz\z\\\zpGpGpG\G\G\G\Gf3f3f3\\\\\\zfQfGfGfG  \f3z\pG\Gf3fQfQ\\\=     \\   =      ==WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxN\ \\=\UU\\\\\\A\\\\A == \\\33\\pp\\\ b\\     =\      \     A"\[             \壣  \==px=\p\f\z\=\Q\iwU zp       Nm                                                                                                 ń\      Q   Q                           =   =   =   =                                                               pppf  pfzQpGfQ\Q=3zQzffzQz\Qpp\p\ \fQfQzppfppppG\33QQQpQp p pp ==\\\\\          \\         pppppppppppppppppppGGGGGGG\\\\\\\\\\\\\\\\\\\\333333333333QQQQQQQQQQQQQQQQQQQpppppppppppppppppppp=  i  pp=fp\Q= x 2 'W  	  PD  
  #I   ^  M    TR   "  m+O6^!%577bV%%%7b%%%%7777777777%%nbn7bCCIOC?OO%1I=\IOCOC7=OC\C==%%%77%77171771O7777++71I11+171n% 77  777   % 777777 777 C7C7C7C7C7bII1C1C1C1C1%%%%I7O7O7O7O7O7O7O7O7=1C7O7O7O7=1O7C7C7C7C7I1I1I1I1O7C1C1C1C1O7O7O7O7O7O7O7O7%%%%Z71 I1=====I7ICI7I7O7O7hIC+C+C+7+7+7+7+===O7O7O7O7O7O7\I=1=+=+=+  O7=I7C+7+==1=1O7O7O7%     77   %      %%WnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNOOO7 77%73377`777bb7'7777b' %% 777bnn77CCTn7n7O7 ;TT77b     %7      7  b   '"nnnnOOnnn7Onn7OObbnnn             7bbnnn  b7%%nnnnnOCnbOOOOOOOOOOx%n7C7=7bnOnI7%7O17?OVGnnOOOOOOOOOOnnnnn3nOOOOnnnnnnnnnnnnn nnnnnnOOnnnnnn\ICVnOn   nn    /A                                               OOOO                       nn          n        nn         nOOO7OOnOOnnn   OO   O1   OOOO1   OOOOO   OOO   OOO   OOO   OOOOOOOOOOOOOO     O   OOOOOO    OOOOOOOO%   OOO%   OOO%   OOO%   OOOO   O                                                   O   OOOO   OOOCCC=  C=I1C+=1O7O1%I1I=\=I1I7O1OCC7C7 7=1=1ICC=VCCCC+7111C1C C CC %%77777          77         CCCCCCCCCCCCCCCCCCC+++++++777777777777777777771111111111111111111CCCCCCCCCCCCCCCCCCCC%  ?  CCO%O=C71% x "  m+O6^6G_\\===\====\\\\\\\\\\==\zzzzpG\zppzfpzzpp===\\=\\Q\QA\f33\3f\\\GG3fQz\QG\\\=\\  \\\   = \\\\\\ \\\3 z\z\z\z\z\zQzQzQzQzQG3G3G3G3f\\\\ffffpQz\\\\pQ\p\z\z\z\zQzQzQzQ\zQzQzQzQ\\\\\\ffG3G3G3G3b\ z\p3p3p3pAp3fff\\ňzGzGzGfGfGfGfGp3p3p3ffffffzpQpGpGpG  \p3fzGfGp3pQpQ\\f=     \\   =      ==WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxN\ \\G\QQ\\\\\\=\\\\= == bb\33\\pp\\\ iii     =b      \     ="\s             \壣  \==px=\z\f\z\=\Q\i~X zp       Nm                                                                                                 ń\      \   \                           =   =   =   =                                                               zpzf  pfzQzGpQQQG3zQzffQz\Qpp\p\ \pQpQzpzfppppGQ33QQQpQp p pp ==\\\\\          \\         pppppppppppppppppppGGGGGGGQQQQQQQQQQQQQQQQQQQQ333333333333QQQQQQQQQQQQQQQQQQQpppppppppppppppppppp=  p  zzGpp\Q= x ? x x x ,    wx 6X   @ 8; X@ 8 w C ; ,  [hXw     P 7XP 3 m = 6 ,  #{&m     P 7&Px / c 8 1 ,  c     P 7P6z - b 8 1 , " b &_  x $&7X  2 p = 6 , = h&p _    p ^7&O  A % ! ,  JA     P 7JP	6 1 k = 6 , " W"&k &_  x $&7&X
 ? x x x , V  x     ` B; X6P  @ % ! , " gJ@ &_  x $&7JXt / n = 6 , k &n *0  x M7&tQ  B % ! , k eJB *0  x M7J O  C % ! , = JC _    p ^7J "  m+O6^!+977bV%%%7b%%%%7777777777%%nbn7bIIIOICOV+7ICbOOCMI=COIbICC%%%77%77171'7=7V=777++=1I71+777n%77  777   % 777777 777 I7I7I7I7I7fMI1I1I1I1I1++++O=O7O7O7O7O=O=O=O=C1I7O7O7O7C1O7C7I7I7I7I1I1I1I1O7I1I1I1I1O7O7O7O7O7O7V=V=++++b;7 I7CCCC'CO=OQO=O=O7O7vQI+I+I+=+=+=+=+CCCO=O=O=O=O=O=bIC1C+C+C+  O7CO=I+=+CC1C1O7O7O=%     77   %      %%WnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNOOO7 77+71177b777bb7%7777b% %% ;;7bnn77CCTn7n7O7 ?\\??b     %;      7  b   %"nnnnOOnnn7OnnEOObbnnn             7bbnnn  b7%%nnnnnOCnbOOOOOOOOOOx%n7I7=7bnOnI7%7O17?OVKnnOOOOOOOOOOnnnnn5nOOOOnnnnnnnnnnnnn nnnnnnOOnnnnnn`ICVnOn   nn    /A                                               OOOO                       nn          n        nn         nOOO7OOnOOnnn   OO   O7   OOOO7   OOOOO   OOO   OOO   OOO   OOOOOOOOOOOOOO     O   OOOOOO    OOOOOOOO%   OOO%   OOO%   OOO%   OOOO   O                                                   O   OOOO   OOOICI=  C=I1I+C1V1O1+I1I=b=O1I7O1OCC7C7 7C1C1ICI=VCCCC+1111C1C C CC %%77777          77         CCCCCCCCCCCCCCCCCCC+++++++111111111111111111111111111111111111111CCCCCCCCCCCCCCCCCCCC%  C  IIV+OCC71% x 2       YW  F   `       ,\             "  m+O6^!%377b\%%%7b%%%%7777777777%%nbn7bOIOOICVV+5VIhOVCVO=IOOnOOI%%%77%7=1=1'7=%=\=7==1+%=7O771777n%77  777   % 777777 77= O7O7O7O7O7rOO1I1I1I1I1++++O=V7V7V7V7O=O=O=O=O7O7O=V7V7O7O7C=O7O7O7O1O1O1O1O=I1I1I1I1V7V7V7V7V7V7V=V=++++d?5 V=IIII+IO=OXO=O=V7V7|QO1O1O1=+=+=+=+I%I%I%O=O=O=O=O=O=nOO7I1I1I1  O=IO=O1=+I%O7O7O=V7O=%     77   %      %%WnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNOOO7 77%7//77k777bb7'7777b' %% ??7bnn77CCTn7n7O7 E\\==b     %?      7  h   '"nnnnOOnnn7Onn?OObbnnn             7bbnnn  b7%%nnnnnOCnbOOOOOOOOOOx%n7O7=7bnOnI7%7O17?OVKnnOOOOOOOOOOnnnnn5nOOOOnnnnnnnnnnnnn nnnnnnOOnnnnnn`ICVnOn   nn    /A                                               OOOO                       nn          n        nn         nOOO7OOnOOnnn   OO   O7   OOOO7   OOOOO   OOO   OOO   OOO   OOOOOOOOOOOOOO     O   OOOOOO    OOOOOOOO%   OOO%   OOO%   OOO%   OOOO   O                                                   O   OOOO   OOOOCI=  C=I1I+I1V1O1+V1I=h=O1I7V1OCC7C7 7I1O1ICO=VCCCC+1111C1C C CC %%77777          77         CCCCCCCCCCCCCCCCCCC+++++++111111111111111111111111111111111111111CCCCCCCCCCCCCCCCCCCC%  C  OIV+VOC71% x  # &m     P 7#{&P#                  z N    # c     P 7P# Marine and Coastal Image Data Module 3:`"4 Practical Lessons: 5ă  
  7   
 
    
 

a$ Practical Lessons Using Marine and Coastal Image Data


   T 8 a  5: STUDY OF COASTAL LAGOONAL FEATURES USING IRS1A LISS DATAă


   T   a8 Aim of Lessonă


This lesson introduces the dynamical features of a tropical coastal lagoon and the fundamental ways
of studying them using remote sensing techniques.  It provides a case study using an Indian coastal
lagoon.


   S 
 ta5 Specific Objectivesă

On completion of this lesson you should be able to:

1) demonstrate the versatility of the LISS on board IRS1A

2) characterize lagoonal features from their radiance patterns

3) use the vegetation index as a means of studying the emergent vegetation in lagoons

4) identify the spatiotemporal succession in tropical lagoons.


   S z ~a3 Background Informationă

   S * Source of lesson

The work on which this lesson is based was originally carried out as part of a programme of
technology development and demonstration for the coastal and marine environment in India.  The
original data analysis was performed at the Indian Institute of Remote Sensing, on a VAX 11/780
super mini computer with VIPS 32 software , the processed image data later being converted to Bilko
format files for use in this lesson.  The image data are from the LISS sensor on the Indian Remote
Sensing Satellite (IRS1A), and also from the MSS on Landsat.

  
   S " General information on IRS 1A

The Indian Remote Sensing Satellite  IRS 1A is the first of a series of operational Indian earth
resources satellites.  It was launched on March 17th 1988, into a polar sunsynchronous orbit of 904
km by the Soviet launcher VOSTOK from a cosmodrome at Baikanur in the USSR.  With an
inclination of 99.049$ and a period of 103.19 minutes, the satellite has a mean equator crossing time
of 10.25 am on a descending node and a repeat cycle of 22 days.

IRS 1A has a payload of two sensors, namely LISS 1 and LISS 2, with ground resolution of 72.5 m   Z)         p-@*@*@@  and 36.25 m respectively.  The corresponding swath widths are 148 and 74 km, with the swath of
LISS 1 being matched by two individual LISS 2 sensors.  The following wavebands apply to both
sensors:

O  
     d d x                          
 ! d d x     `           O    	  
                / Band          x,B Spectral range m  
` 	`              c1 1   @       ,E 0.45  0.52 ` 	P               c1 2          ,E 0.52  0.59 P P @              c1 3          ,E 0.62  0.68 P               c1 4   `
       ,E 0.77  0.86     
These bands are similar to those of the Landsat Thematic Mapper (TM): indeed LISS is closely
comparable with the TM.


   S  Location of the Study

Chilka lagoon (19$28- to 19$54- N and 85$35- to 85$67- E), situated on the east coast of India, is
the largest brackish water semienclosed system in India and its adjoining countries.  It has great
importance for the interaction between man and biosphere in the region, supporting the socioeconomic life of more than 100,000 people.  It is pear shaped, approximately 65 km in length and
   T  16 km wide (see figure 1).  It has a water surface area of about 850 km2 during summer and 1165
   T  km2 during the flood season.  The lagoon is connected to the Bay of Bengal by an outer channel of
approximately 25 km which is separated from the sea by a long narrow sand spit.  The mouth to the
sea is very narrow, 300 m in width and is known to shift in position.


   S  Ecology of the area

The lagoon receives the drainage of a few deltaic branches of a major Indian river in the north called
the Mahanadi and opens to the sea through a narrow channel.  The circulation is not very active as
the rivulets discharge very little and the tide of about 1.5 to 1.8 metres amplitude is not strong enough
to ride through the outer channel into the main body of the lagoon.  As a result, the lagoon is
spatially well differentiated into different zones.  The north eastern region is heavily sedimented by
the rivulets and on the north west, where the current speed is negligibly small, a lush growth of
submerged, partially submerged, semiexposed and emergent vegetation occurs.  The fertilisers that
are washed down from the agricultural fields of the hinterland have triggered the growth of vegetation
   T (! consisting mainly of Potamogeton pectinatus and Scripus articulatus.  Leaching of the vegetation
produces large amounts of yellow substance which has also been segregated into a zone in the north. 
The weeds grow almost throughout the border of the lagoon and are a major component of the
ecology and evolution of the very productive brackish water system.  To the south lie weed free,
unsedimented, and relatively deeper waters of around 2 to 3 m in depth while the depth in the rest
of the lagoon is between 0.5 and 1 m.

In general, the sedimentation and growth of vegetation are increasing with time and the lagoon in
many parts is being transformed into a swamp in its natural process of successful evolution.  An
organically rich and productive lagoon is shrinking with the vegetationcovered area increasing by   (       p-@*@*@@     T    about 7 to 8 km2 each year.  Sedimentation from the rivulets, organic sedimentation from the
vegetation and lack of proper circulation, fertilisers from the hinterland, spatially decreasing tidal
activity, anthropogenic pressures of land reclamation, luxuriant growth and breeding of brackish water
fish and decapods, and an active nutrient cycle are the major ecological factors that are operative in
the sustenance and evolution of this very interesting system.


   S  Summary of the Research Programme

The broad objective of the research work on which this lesson is based was to develop an
understanding of the synoptic processes that apparently operate in the lagoon and to devise a
methodology to characterize the features on satellite imagery, as the basis for future operational
programmes of environmental monitoring.  It was also a preliminary experiment carried out to find
out how IRS1A data may be applied to the management of such environments as this.

The work involved intensive ground sampling.  To accomplish this, 22 stations were established in
the lagoon.  The number of stations had to be large enough to represent all features in the lagoon and
the satellite imagery was consulted before station selection in order to identify the characteristics of
the different regions.  To assess the lagoonal dynamics standard ecological investigations were carried
out periodically in these stations for 3 years from 1986 to understand lagoonal dynamics.  In addition,
the radiance from ground stations was also measured using an IRS1A LISS compatible radiometer. 
From this bank of radiance data, it was possible to characterise lagoonal features by their spectral
properties.  Figure 2 shows the spectral curves corresponding to the mean signature for each class. 
Table 1 shows the radiance ranges in different spectral bands corresponding to different ecological
zones in the lagoon.  The values are appropriate to conditions on 09.01.89 and in this table the
radiance values have been converted to the corresponding raw counts from the LISS sensor.  
  
   T  	a Table 1  Radiance of major ecological features in Chilka Lagoon

m 
 ! d d x     `          
	 A d d x     y   FFd                             m ( 	  
  
  
  
 (                        Band 1          Band 2          Band 3     @   Band 4(  
  
  
  
 ` 	 	y(                 I       Min   Y       Max   Y       Min   Y       Max   Y       Min   Y       Max   Y       Min   Y       Max ` 	 	` 	 	              Submerged Vegetation           34           36           17           20           15           20           10           13 ` 	 	` 	 	Y              Gelbstoff           37           39           24           25           22           25           10           12 ` 	 	8 	 	              Inorganic Suspended
Load   Q        44   Q        48   Q        28   Q        31   Q        34   Q        37   Q        16   Q        17 8 	 	` 	 	              Emergent Vegetation   !        31   !        32   !        14   !        16   !        15   !        17   !        35   !        36 ` 	 			Q               Weedfree Zone   A#        40   A#        42   A#        22   A#        23   A#        18   A#        20   A#         7   A#         8 		 !  	 


   S % The Image data

The image data come from two overpasses of the Chilka lagoon.  The main part of the lesson is based
on analysis of bands 1 to 4 of the LISS image for 09.01.89.  This has been geometrically rectified
and resampled with a resolution of 72 x 72 metres which is almost the original resolution of the LISS   ))       p-@*@*@@     T    data.  These have the filenames CHILIRS1, CHILIRS2, CHILIRS3 and CHILIRS4.  Their size
is 380 pixels ' 256 lines.  The pixel values correspond to the raw counts produced by the sensor. 
Only pixels covering the lagoon are included.  All other pixels, corresponding to land or the sea
offshore, have been masked and are set to zero.

A further four images are taken from channels 1 to 4 of the MultiSpectral Scanner from the Landsat
   T  overpass of 24.12.84, called CHILMSS1 etc.  These have been resampled onto the same map grid
   T  as the CHILIRSx images.  Pixel values correspond to the raw counts from Landsat.

   T  Two other images are provided, CHILCL84 and CHILCL89.  These are the result of applying
   T t standard maximum likelihood classifications to the multispectral set of images CHILMSSx and
   T M	 CHILIRSx respectively.  Sixteen classes have been defined, and so each pixel has a value between
0 and 15.  The scale of these images is not exactly the same as for the other data and their size is 360
' 240.  The following table summarises the image datasets:

 
 
r  
	 A d d x     y   FFd                            
 a d d x     
   xN           r  	 
 
!              Filename          Sensor          Description  
 
` 	 	
              CHILIRS1.DAT   f       LISS, IRS1   f       Chilka Lagoon, Band 1, 09.01.89 ` 	 	` 	 	              CHILIRS2.DAT          LISS, IRS1          Chilka Lagoon, Band 2, 09.01.89 ` 	 	` 	 	f              CHILIRS3.DAT   &       LISS, IRS1   &       Chilka Lagoon, Band 3, 09.01.89 ` 	 	` 	 	              CHILIRS4.DAT          LISS, IRS1          Chilka Lagoon, Band 4, 09.01.89 ` 	 	` 	 	&              CHILMSS1.DAT          MSS, Landsat          Chilka Lagoon, Band 1, 24.12.84 ` 	 	` 	 	              CHILMSS2.DAT   F       MSS, Landsat   F       Chilka Lagoon, Band 2, 24.12.84 ` 	 	` 	 	              CHILMSS3.DAT          MSS, Landsat          Chilka Lagoon, Band 3, 24.12.84 ` 	 	` 	 	F              CHILMSS4.DAT          MSS, Landsat          Chilka Lagoon, Band 4, 24.12.84 ` 	 	` 	 	              CHILCL84.DAT   f       MSS, Landsat   f       Classification based on CHILMSS14 ` 	 			              CHILCL89.DAT          LISS, IRS1          Classification based on CHILIRS14 		
 f   

   S  Vegetation Index

The presence of emergent vegetation is an important component of lagoon ecology and the study of
vegetation forms the central theme of lagoonal research.  The spectral properties of healthy vegetation
are well established and there is a special method of data transformation called the "vegetation index"
(VI) which enables us to delineate areas of vegetation growth.

The VI is conceptually expressed as the ratio (Infra red  red) / (Infra red + red), because healthy
vegetation has a relatively high reflectance in the near infrared part of the spectrum.  Water is a
strong absorber of infrared radiation, so even very shallow water has a low reflectance in the infrared.  Hence the VI for a lagoon is very low except where there is emergent vegetation, i.e. vegetation
protruding above the water surface.
   (        p-@*@*@@  ԌWhereas the VI could be evaluated by laborious application of several functions using previous
versions of BILKO, Version 1.3 provides a function which allows evaluation of the VI in a single
operation.  The first file to be defined should be the infrared waveband, and the second should be
the red waveband.  The resulting VI image is scaled by 255, so that the range (0<trueVI<1)
becomes (0<pixelvalue<255) on the image.  If the infrared radiance is less than the red, i.e.
(infra red  red) is negative, then the result is set to 255.


   S  a7 Lesson Outline

   S p Radiance Characteristics

   T  
 1.  Load and display image CHILIRS1.  Use the Modify LUT, Linear stretch option to clarify the
features present.  If you are using a VGA display, the default palette will be the grey scale and you
   T  may prefer to load a colour palette such as TEMP1.  With reference to figure 1, determine where
   T  the exit from the lagoon to the sea occurs.   By using the cursor function, determine the pixel values
of different features and hence identify them using table1.  Make a note of the pixel values at
particular (x,y) locations corresponding to apparently different ecological zones on the image.

   T  2.  Repeat stage 1 for the other spectral bands, loading in turn CHILIRS2, CHILIRS3 and
   T  CHILIRS4.  In each case, check whether the classification based on table 1 is consistent with the
information derived from the other channels.  Note that table 1 is ambiguous for interpreting some
ranges of channel 3 and 4 counts, but by using all channels a classification can be confirmed.  Sketch
a map of the distribution of the different ecological zone types, based on the analysis of all four
channels.

   T  3.  Use the Multi image, Scattergraph function to examine the relative values in pairs of channels. 
By setting the box cursor over a small area corresponding to what is probably a single class, it is
possible to examine the clustering of pixel values, and hence confirm the validity of using Table 1
for classification purposes.  Note, for example, that there appears to be very little spectral or radiance
contrast between submerged vegetation and Gelbstoff so that special care is required to discriminate
them.

   T  4.  Stages 1 to 3 can now be repeated using the Landsat data, files CHILMSS1ĩ4.  Note that it is not
appropriate to use Table 1 to interpret these because table 1 is based on ground measurements made
at the same time as the LISS data.  Note the banded "noise" occurring in the Landsat data which is
not present in the LISS data.


   S   Vegetation Index

   T " 5.  Use the Multi image, NDVI function (which is a new function in Bilko1.3) to derive vegetation
   T x# index (VI) images from the images CHILIRS3 and CHILIRS4.  Refer to the information provided
above about the Vegetation Index function.  You will need to apply a new LUT to the resulting VI
image.  This image is entirely different from the single band images: it features one region and one
feature has been highlighted.  Can you identify what this feature is using your previously derived
knowledge of the geographical positions of the lagoonal features?  You may wish to save the VI
   T ' image with the name CHILVI89.DAT.

6.  Can you suggest why the other type of vegetation in these images does not respond to the VI   b)         p-@*@*@@  technique?  Consider the effects of the overlying water.

Because it is being applied to raw counts and over water, much of the resulting image has a value of
255 because the infra red channel is less than the red.  If you wish to examine how the vegetation
   T ` index varies over the whole image, try adding a constant value of 32 to CHILIRS4 to create a new
   T 9 image CHILIRSX (using the function Miscellaneous, add constant) before using it in the Vegetation
index.

7.  Repeat stages 5 and 6 using the Landsat data.  Note that because the MSS bands are different from
   T  LISS, the red band is MSS2.  Hence use CHILMSS4 and CHILMSS2 in evaluating the VI. 
Because of the way MSS data is scaled into raw counts, it is essential in this case to apply stage 6 by
   T K	 adding a constant of 32 to band 4 to create CHILMSSX before applying it to create the VI image
   T $
 CHILVI84.

   T  8.  Create a suitable LUT for displaying both CHILVI89 and CHILVI84.  Now compare the two
   T  images using the Multi image, Toggle function.  Observe similarities and differences between the
two images, and interpret these in terms of changes to the lagoon over the four year period between
the two images.


   S  Classified Images

   T  9.  Load and display CHILCL84.DAT.  Use the linear stretch option in Modify LUT and observe
the features apparent on this Landsat MSS image.  

10.  Of the 16 classes on this image, class 0 is the background mask and class 15 the image title. 
The remaining 14 classes can be combined to approximate to the 5 classes which have previously been
considered in this lesson, as follows:

O  
 a d d x     
   xN         
  
d d x        /	        O  	 
f              Ecological zone           Classification categories  
` 	              Submerged vegetation   `        2, 3, 4, 10, 11 ` 	P                Gelbstoff           5, 14 P P `              Inorganic suspension            6, 7 P P               Emergent vegetation   P        1  P                Weedfree zone            8, 9, 12, 13  P   
   T ! Using the Manual stretch option in Modify LUT combine the classes to give five classes. 
   T " Alternatively use Modify Palette to so that five colours represent the five classes.  

   T 2$ 11.  Study the Histogram and calculate the number of pixels in each class.  By multiplying this by
0.020736 calculate the area of each feature in square kilometres.

   T & 12.  Now repeat stages 9 to 11 for CHILCL89.DAT which is the classified image from the LISS
sensor.

By comparing the two classified images it is possible to identify the temporal changes in the area.    D)        p-@*@*@@  Note which features have increased in area and attempt to identify the trend in natural changes.



     ` y    b 	                    d       d d                                                                         y 


This lesson was written by R. Sudarshana.


   R  Any comments or suggestions relating to this lesson should be sent to:

   R X	 Dr. R. Sudarshana% - hh4 < Telex:C 
Indian Institute for Remote Sensing
4, Kalidas Road, P.B. 135
Dehra Dun 248001
INDIA

   h         p-@*@*@@  







































   T ! 
a+ Figure 1  Location Map of Chilka Lagoon
   "         p-@*@*@@  







































   T ! ?a# Figure 2 Radiance profiles of coastal lagoonal features
   "	         p-@*@*@@     T    a4 Answers for Lesson 5 


5.  The feature highlighted is emergent vegetation.

6.  The two main categories of vegetation in Chilka lagoon are submerged and emergent types.  The
emergent type is conspicuous in VI images due to its high infra red radiance.  Although the
submerged vegetation also has a high IR radiance, the layer of water covering it absorbs the radiation
and hence the signal leaving the lagoon is weak.

11.  The area in square kilometres of the five features in the MSS image of 1984 are as follows:
   T I	  `	`	 Submerged vegetation:hh4 < 381.98
   T !
  `	`	 Gelbstoff:- hh4 < C 139.01
   T 
  `	`	 Inorganic suspension:hh4 <  44.52
   T   `	`	 Emergent vegetation:hh4 <  52.25
   T   `	`	 Weedfree zone:hh4 < C 233.37

12.  The area in square kilometres of the five features in the LISS image of 1989 are as follows:
   T 1  `	`	 Submerged vegetation:hh4 < 386.88
   T 	  `	`	 Gelbstoff:- hh4 < C  71.26
   T   `	`	 Inorganic suspension:hh4 < 103.53
   T   `	`	 Emergent vegetation:hh4 <  75.67
   T   `	`	 Weedfree zone:hh4 < C 213.75

Over a period of four years, the sedimentation and weed zones have increased progressively in area,
   T  choking the lagoon.  Consequently, the weed free zone has decreased in area by around 20 km2. 
   T  Field observations during the 1989 campaign showed that out of 386.88 km2 of submerged vegetation,
   T  about 133.75 km2 has already been transformed into semistabilised swamp.

It is clear that the lagoon is transforming very rapidly the ecological features which are inherent are
dynamically active.
   )
         p-@*@*@@  # &m     P 7#{&P#        D      z N    # c     P 7P# Marine and Coastal Image Data module 3:`"Y Practical Lessons: 6ă  

a$ Practical Lessons Using Marine and Coastal Image Data


   S 8 	a( 6: TEMPORAL AND SPATIAL VARIATIONS IN SEA ICE
<a- CONCENTRATION IN THE SOUTHERN OCEAN


   S   a8 Aim of Lesson

To use a sequence of images to look at the seasonal cycle of sea ice extent and sea ice concentration
on the southern hemisphere.


   S  a9 Objectives

On completion of this lesson you should be able to:

1) display SSM/I ice concentration images mapped into the common SSM/I polar grid for the southern
hemisphere

2) identify the seasonal cycle of sea ice extent and sea ice concentration

3) detect local differences in sea ice coverage

4) display sea ice concentration images produced from SSM/I, AVHRR with different  spectral and
spatial characteristics.


   S P ~a3 Background Information


   S  The BILKO image-processing software

Some acquaintance with the BILKO imaging system will be helpful in following through this lesson,
but adequate experience may be gained by working through one of the lessons in the package.  The
present lesson is self-containing and you may use the online <HELP> facility to explain a
highlighted command (accessed by typing <H>).


   S " Sea ice research

Sea ice plays an important role in the climate system.  The distribution of sea ice and open water in
polar regions influences the atmospheric and oceanic general circulation in several ways.  Due to its
high albedo and its insulating behaviour sea ice modifies the radiation balance and the exchange of
heat and momentum between atmosphere and ocean.  In regions where sea ice is formed, the brine
rejection generates dense water, which drives the oceanic circulation through deep convection.  There
are a number of processes controlling airseaice interaction, as illustrated in figure 1, and they must
be modelled in climate investigations.  The basic problem of current sea ice research is the limited   X)        p-@*@*@@  set of observational data for model verification and parameter determination.  Since the polar seas are
hardly accessible, remote sensing methods play a dominant role in the derivation of observed sea ice
variables.

Passive microwave data have been used for sea ice studies since 1972 when the Electrically Scanning
Microwave Radiometer (ESMR) was launched on board the NIMBUS-5 satellite.  This single channel
radiometer produced the first long time series of sea ice extent and concentration for the polar
regions.  One of the most important results of this mission was the observation of the so called
Weddell Sea Polynya, a large area of significantly lower ice concentration within the Antarctic pack
ice.  With the launch of the Scanning Multichannel Microwave Radiometer (SMMR) on board
NIMBUS-7 in 1978 multifrequency observations of the sea ice are available.  These measurements
have been continued since 1987 by the new generation of SSM/I instruments.

The physical basis for the detection of sea ice using passive microwave instruments is the strong
difference in emissivity between sea ice and water, therefore it is possible to calculate the sea ice
extent as well as sea ice concentration, at least in winter.  Detection of different ice types is possible
because of the variation of emissivity with frequency, polarisation, season and atmospheric conditions. 
This makes it possible to distinguish between first year ice and multiyear ice concentration in winter
in the Arctic.  In summer, the thin melt layers on the ice eliminate the distinction between different
ice types.  In the Antarctic the problem is of less importance because of the general absence of
multiyear ice.

The advantage of passive microwave remote sensing is the independence from cloud conditions and
solar illumination.  On the other hand, the relatively low radiance at the microwave part of the
spectrum results in a low spatial resolution.  Small scale features such as small leads of open water
within the pack ice cannot be resolved.  The ice boundaries are observed with a spatial resolution
limited by the pixel size.  However, the relatively small image size (158 x 166 pixels for the southern
SSM/I grid) allows a simple handling of the total SSM/I data set for time series and for verification
of sea ice models.


   S ( The SSM/I sensor

The Special Sensor Microwave Imager (SSM/I) is a sevenchannel passive microwaveradiometer
system.  It measures atmospheric and ocean surface brightness temperatures at four frequencies under
different polarisations.  The instrument is flown on board the satellites of the Defence Meteorological
Satellite Program (DMSP) of the US Air Force.  The satellites fly in sun-synchronous orbits with a
nominal height of 848 km, an inclination of 98.8$ and a nodal period of about 102 minutes.  The
equator crossing is at 18:11 local time.

The instrument is a socalled conical scanner.  This means that the antenna beams are at an angle of
45$ to the normal to the earth's surface.  Thus, as the antenna rotates, the beams define the surface
of a cone with an incidence angle of 53.1$.  This angle can be calculated from the scan angle and the
nominal orbital altitude.

The spatial and temporal coverage and resolution vary between channels.  In the 85 GHz channel the
sensor samples every 12.5 km: at the lower four frequencies, every 25 km.  The spatial resolution
(effective field of view) decreases with increasing frequency. The basic characteristics of the
instrument is listed in table 1.
   X)         p-@*@*@@  Ԍ   T     
 ٙa) Table 1 Channel specifications of the SSM/I

T 
  
d d x        /	      
  d d x     
   XXXX              T  X 
 
X 
 
              Bu Channel   1       3. Frequency
0 /GHz   	      ZC Polarisation   	      ZU[ Field of view
U` /km X 
 
` 	 	              Gu 1   i       @- 19.35   i       I V   i       U^ 70 ' 45 ` 	 	P  	              Gu 2          @- 19.35          I H          U^ 70 ' 45 P  P  i              Gu 3   	       @- 22.24   	       I V   	       U^ 60 ' 40 P  P                Gu 4   Y	       @- 37.00   Y	       I V   Y	       U^ 38 ' 30 P  P  	              Gu 5   
       @- 37.00   
       I H   
       U^ 38 ' 30 P  P  Y	              Gu 6          @- 85.00          I V          U^ 16 ' 14 P  
              Gu 7   y
       @- 85.00   y
       I H   y
       U^ 16 ' 14     
The wide swath of the instrument (1394 km) in conjunction with the high repetition rate of more than
14 revolutions per day results in a complete daily coverage of the polar regions.  It is therefore
possible to produce time series on the polar ice conditions with a high temporal resolution.

To simplify the data handling the National Snow and Ice Data Center of the World Data Center A
for Glaciology (Snow and Ice) at Boulder, Colorado produces daily maps of the brightness
temperatures of the SSM/I channels in a standard polarstereographic projection (SSM/I grid).  For
the southern hemisphere the map covers an area of about 7900 ' 8300 km centered at the South Pole
(figure 2).  The spatial resolution of the grid varies between 12.5 km (for the 85 GHz channel) and
50 km (for the 19.35 GHz channel).  The resulting maps of sea ice concentration calculated from
combinations of channel 1, 2, 4 and 5 data using different algorithms have a spatial resolution of 50
km. The data since July 1987 are available on CD-ROM for scientific investigations.


   S ! Data used in this lesson

Twelve SSM/I sea ice concentration images of the southern hemisphere are used to demonstrate the
high seasonal variability of ice coverage around Antarctica.  The data are daily averages of the first
completely mapped day of each month in 1989.  A list of the images is given in table 2 where the
   T Y filenames commencing with SI refer to the twelve sea ice concentration images.

The data from the 19 GHz and 37 GHz vertically polarized channels were used for the calculation
of the ice concentration, which is defined as the fractional area covered by ice, expressed as a
percentage.  The algorithm used was developed by Joe Comiso of the NASA Goddard Space Flight
Center at Greenbelt, Maryland, USA.  It uses the brightness temperatures of the two channels
   T j# mentioned above.  Two tie points, Tbw and Tbi, are located on the plane defined by the two channels
   T B$ (figure 3).  Tbw specifies the combination of brightness temperatures from each channel which
   T % correspond to the open water.  Tbi specifies the brightness temperatures corresponding to 100% ice
concentration, known as the ice signature.  The concentration is calculated according to equation 1
as the quotient of the distance on the twochannel brightness temperature plane (figure 3) between any
   T ' point, Tb, and the tie point for open water Tbw on the one hand, and the distance between the two tie
   T z( points Tbw and Tbi on the other.!  #b@      d d d d d       
  d d w                                                      b   0    ?    `/  !     ^ C  = 100 {{distance(T SUB b , T SUB { bw }) }  OVER
{distance(T SUB { bi } , T SUB { bw })}} %x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       C     cdistance     cT    /b     GcT    /bw     _ distance     _ T    U+ bi     m_ T    + bw               100      c(      c,      _	c)      e_ (      _ ,      	_ )      
 %m
     ! ߹	 1     d d d d d d d d (1)           !                   1     d d d d d d d d (1)                               	
 0  R)
        p-@*@*@@ @"d	  !  0  Ԍ$  ""  ""`!! "$ The advantage of this method is that the tie point for 100% concentration varies in position and so
accounts for continuous variation of the ice signature.  The concentration values in the SSM/I images
vary from 0 to 100 per cent in intervals of 1 per cent.  Land areas are masked.


   T  Oa. Table 2 Images used in the lesson

^ 
  d d x     
   XXXX               ?d d x     I	   j              ^  X 
 
X 
 
I	              k	P
 Image
P
 (Filename)         31 Date         &A Pixel Size
&E /km         =U Image Size
D=W /pixels X 
 
` 	 	I	              P
 SI890101   
       >30 1.1.89   
       &E 50   
       =V 158 ' 166 ` 	 	P                P
 SI890201   Q       >30 1.2.89   Q       &E 50   Q       =V 158 ' 166 P  P  
              P
 SI890301          >30 1.3.89          &E 50          =V 158 ' 166 P  P  Q              P
 SI890401          >30 1.4.89          &E 50          =V 158 ' 166 P  P                P
 SI890502   A       >30 2.5.89   A       &E 50   A       =V 158 ' 166 P  P                P
 SI890603          >30 3.6.89          &E 50          =V 158 ' 166 P  P  A              P
 SI890701          >30 1.7.89          &E 50          =V 158 ' 166 P  P                P
 SI890806   1       >30 6.8.89   1       &E 50   1       =V 158 ' 166 P  P                P
 SI890901          >30 1.9.89          &E 50          =V 158 ' 166 P  P  1              P
 SI891001          30 1.10.89          &E 50          =V 158 ' 166 P  P                P
 SI891101   !       30 1.11.89   !       &E 50   !       =V 158 ' 166 P  P                P
 SI891203   q       30 3.12.89   q       &E 50   q       =V 158 ' 166 P  P  !              P
 BT890919          >30 1.9.89          &E 25          =V 316 ' 166 P  P  q              P
 BT890937          >30 1.9.89          &E 25          =V 316 ' 166 P                .	P
 LS3009          30 30.9.89          &F 1          =V 128 ' 128     

   T A! The two images with filenames commencing BT are brightness temperature images of half of the
Antarctic on 1.9.89 as measured by channel 1 (19.35 GHz vertical polarized) and channel 4
(37.00GHz vertical polarized).  The brightness temperatures are in the range 150 K to 270 K.  The
   T # final image, with filename commencing LS, is of the reflectance values measured using the visible
channel of the Advanced Very High Resolution Radiometer (AVHRR) on one of the NOAA polar
orbiting meteorological satellites.  The resolution of this sensor is 1.1 km at nadir.  The pixels have
not been resampled for this image which therefore contains geometric distortion.  The pixel values
correspond to pseudoalbedo calculated by standard NOAA procedures.  The value range 0  255
covers the albedo range 0  25.5%.
 0  (        p-@*@*@@ @"d	  !  0  Ԍ   S      ٙa7 Lesson Outlineă

1.  Load and display each of the twelve SSM/I images in turn starting with the January image. Use
   T  the default palette TEMP1.PAL to display the images.  You will find that all values except those
   T a from land areas are represented by colours from the lower part of the palette.  Use Histogram to
calculate the histogram for one of the images.  Select the value for the strong peak at the high end
of the histogram.  This represents the land mask.  What is the value for the mask?  Modify the look
up table in such a way that the range from 0 to 100 is displayed in an optimal way.  Colour the land
mask separately to distinguish more clearly between ocean and land.  You may find it helpful to use
   T  the look up table SSMI100.STR when displaying the images.

2.  Select the two images showing the minimum and maximum ice coverage.  Which are the months
of extreme ice conditions?

   T  Select Multi image and subtract the two images to get an impression of the seasonal variability in ice
coverage around the Antarctic.  The maximum ice coverage for the southern ocean is about
   T 
 20Mkm2.  It decreases to about 2-4Mkm2 in late summer.  This enormous variation in ice coverage
influences the energy and momentum transfer between ocean and atmosphere.

   T  Select the Toggle option in Multi Image to get an impression of this seasonal variation.

3.  Display the image of minimum ice coverage.  The ice concentration is essentially restricted to two
larger areas.  Which physical processes, do you think, are responsible for the summer distribution
of the sea ice?

   T  4.  Display one of the images showing a relatively large ice extent and use the Gradients option in
   T  the Modify Image menu to calculate the regions of high spatial variability in ice concentration. 
   T  Where are these regions located and what is the mean width of the high gradient zone?  Use Zoom
to display the selected marginal ice zone in a more detailed way.

   T X Use Transect to examine the contrast of ice concentration across the Weddell Sea or the Ross Sea
from the ice shelves in the south to the open water in the north.  Calculate typical values for the
largest gradients within the marginal ice zone.

   T  5.  For a better understanding of the ice concentration algorithm used in this lesson select Multi
   T  Image and choose Scattergraph.  Select image BT890919 for the y-axis and image BT890937 for
   T l the x-axis.  These brightness temperature images show only one half of the Antarctic.  Identify in the
scatter plot the region for the open water tie point and for the line describing the 100% ice
concentration by comparing the plot with the schematic scatter diagram in figure 3.  The relatively
wide scatter will demonstrate the problem of specifying the ice concentration to a high degree of
accuracy.  The scatter is caused by the different radiation characteristics of the different ice types
within the image as well as by the influence of snow coverage.

   T V$ 6.  If you use a VGA-card select the VGA Mode together with the VGA256.PAL or REV256.PAL
palette to display one of the ice concentration images in full 8-bit resolution. Notice that the variation
in concentration is relatively high even in regions with very high absolute values of ice concentration
(>90%).  Can you think of explanations for these variations?  The next section may give you some
ideas.

   T g) 7.  Display the LS3009 image showing a small scale area of about 128 ' 128 km.  The data are   g)         p-@*@*@@  reflectance values from the visible channel 1 of the AVHRR.  These high resolution digital data were
   T   received on board the German Research Icebreaker Polarstern during the 1989 Winter Weddell Gyre
Study Expedition.  The image shown is located in the central Weddell sea at about 66.5$S and
27.5$W covering an area equal to about 4 SSM/I ice concentration pixels.  Notice the large variation
in reflectance in the image.  Single ice floes (bright) can clearly be distinguished from a variety of
   T : small leads of open water or thin young ice (dark). Use the Smooth option of the Modify Image
menu several times and observe the decrease in spatial variation. 


Acknowledgements:  SSM/I data were provided by the National Snow and Ice Data Center,
University of Colorado, Boulder, Colorado 80309-0449 USA. The SSM/I sea ice data gridding and
CD-ROM distribution project at the National Snow and Ice Data Center is part of the NASA Earth
Observing System Data and Information System (EODIS) Snow and Ice Distributed Active Archive
Center (SI.DAAC), supported by the US National Aeronautics and Space Administration, grant
NAGW-641. 

     
 y    b                     d       d d                                                                         y 


This lesson was prepared by T.Viehoff.

   R  Comments or suggestions relating to this lesson should be sent to:

   R  Dr.T.Viehoff`	`	 % - hh4 < 
   R { AlfredWegenerInstitut fur- hh4 < Fax:C 0471 4831149
Polar und Meeresforschung
Postfach 120161
ColumbusstraBeD2850
Bremerhaven
   R  Germany



















   (         p-@*@*@@  Ԍ























   T @ Figure 1  Cartoon representing air-sea-ice interaction processes (from Lemke, 1985).
            p-@*@*@@  












































   T % ha. Figure 2  SSM/I south polar grid   %         p-@*@*@@  











































   T  % Figure 3 `	`	 Schematic scatter diagram of the 19V and 37V brightness temperatures for the sea ice
concentration algorithm"`	   %        p-@*@*@@  
   T     a4 Answers for Lesson 6ă


1.  The value for the Antarctic land mask is 168.

2.  The maximum ice extent can be observed in September.  The minimum ice extent is in February.

3.  The solar radiance causes a melting of the ice which is dependent only on the geographic latitude. 
The main physical processes responsible for the spatial distribution of the remaining sea ice are the
oceanic circulation and the wind forcing that piles up the ice at the continental barriers.  This can be
observed most clearly in the Weddell Sea where the ice is concentrated in the western part of the
basin at the Antarctic Peninsula.

4.  The maximum gradients can be found at the Marginal Ice Zone (up to several hundreds of
kilometres in width) and at the continental coast where an offshore wind temporarily creates open
water areas (called Polynyas).

6,7.  The variability in ice concentration is related to the high variability of wind forcing which
causes the opening and closing of open water leads in the ice coverage.   	        p-@*@*@@     D   R    u  z N    # c     P 7P# Marine and Coastal Image Data Module 3:`"Y Practical Lessons: 7ă  

a$ Practical Lessons Using Marine and Coastal Image Data


   T 8 
a+ 7:  GLOBAL WAVES AND WINDS FROM GEOSATă


   T   a8 Aim of Lessonă

The lesson shows how global datasets of satellitederived wave height and wind speed over the ocean
can be examined in image form and related to each other.


   T  a9 Objectivesă

On completion of this lesson you should be able to:

1) determine the significant wave height and/or the surface wind speed over the ocean at a particular
point from monthly mean global image datasets derived from the Geosat altimeter

2) analyze and interpret the spatial distribution of wave height and wind speed within and between
ocean basins

3) identify seasonal variations of the distribution of waves and wind

4) observe the correlation between wave height and wind speed

5) generate the mean image from a series of images, and the anomaly of each image about the mean.


   T + ~a3 Background Informationă

   S  Equipment

For this lesson you require a PC running the Unesco image processing toolkit, BILKO (version 1.2
or later).  Load the software by entering the directory containing the programme and typing
<UNESCO13> (or <UNESCO12> for version 1.2 of BILKO).  Users unfamiliar with this
software should first use the introductory tutorial in Section 1 of this Module.  Online contextual help
can be obtained during the running of the BILKO software by typing <H>.


   S t# The Image Data

The images for use in this lesson consist of global datasets of monthly means of Significant Wave
Height and Surface Wind Speed.  These have been obtained from the radar altimeter on the Geosat
satellite for the months of July and January between 1986 and 1988.  The images are defined in the
following table:
     (        p-@*@*@@  Ԍ^    ?d d x     I	   j            
  3d d x          )              ^   
 
 
 
                :
' Filename          K6 Data type          F Month          5P Year  
 
` 	 	                HS8607          wave height          July          1986 ` 	 	` 	 	              HS8701   @       wave height   @       January   @       1987 ` 	 	` 	 	              HS8707          wave height          July          1987 ` 	 	` 	 	@              HS8801           wave height           January           1988 ` 	 	` 	 	              HS8807   `       wave height   `       July   `       1988 ` 	 	` 	 	               WI8701   	       wind speed   	       January   	       1987 ` 	 			`              WI8707   P       wind speed   P       July   P       1987 		 	   
   T ( The pixel values in the wave height images correspond to the Significant Wave Height, Hs (explained
below), in metres, multiplied by a factor of 10.  Thus the pixel range 0 to 100 corresponds to wave
heights of 0 to 10.  The pixel values in the wind speed images correspond to the surface wind speed
   T  in m sé1 multiplied by a factor of 10.  Thus the pixel range 0 to 200 in the WI images corresponds
   T  to wind speeds in the range 0 to 20 m sé1.  For all datasets the value 255 is a mask denoting either
land or no data available in that location.

The variables are defined in cells of dimension 2$ latitude ' 2$ longitude and, as given here, the data
cover 360$ of longitude and from 70$N to 68$S.  To make the images easier to interpret, they have
been "prezoomed", i.e. a single data value has been allocated to a 2'2 block of pixels so as to
provide data on a 1$ mesh with a spatial resolution of 2$.  To convert the x and y coordinates (X,Y)
to longitude and latitude corresponding to the centre of each pixel, use the following conversions:

 `	`	 East longitude = 0.5 + X$E
 `	`	 West longitude = (359.5  X)$W
 `	`	 North latitude = (70  Y)$N
 `	`	 South latitude = (Y  70)$S


   S 2 Definition of Significant Wave Height

   T  Significant wave height, Hs, is a measure of the general sea state, an "average" value of a prevailing
wave height.  It was originally defined about fifty years ago, when only visual observations could be
obtained, as the mean height of the onethird highest waves, and was thought to give about the same
value as an experienced seaman's estimate.  With the development of instruments giving sea surface
   T D! elevation  as a time series, Hs was redefined in terms of the variance of the elevation as:

   T "  `	`	 Hs = 4 <2>

   T $ where <2> is the surface elevation variance.  The factor 4 was introduced so that the old and new
definitions have roughly the same value.

     0'       p-@*@*@@  Ԍ   S    Wave height and wind speed from the Geosat radar altimeter

Seasat, which was operational for only three months in 1978, was the first satellite with an altimeter
to cover all the oceans, from 72$S to 72$N.  An earlier satellite, GEOS3, carried an altimeter but
it could not store the data on board so could not provide global coverage.

It was not until March 1985 that another satellite carrying an altimeter was launched: the US Navy's
Geosat.  This had the same inclination as Seasat.  Its classified mission ended in September 1986 and
during October the satellite's orbit was altered, placing it into a 17 day repeat pattern.  The Geosat
exact repeat mission started on 8 November 1986 and continued until the satellite failed in January
1990.  Unfortunately, it began to malfunction early in 1989, and there was a significant decline in
   T H	 global coverage from about March 1989.  It provided estimates of Hs and nearsurface wind speed
from an area of about 10km directly under the satellite at 1 second intervals, that is at 7km intervals
along the track.

Thus Geosat has provided, for the first time, several years of nearglobal coverage of wave and wind
speed data.  This unique data set has given us the opportunity to carry out long term validation of the
altimeter data and provides a useful foundation for a global climatology and for investigations of
climate variability.

   S  Estimating Hs from the radar altimeter

The slope of the leading edge of the return pulse from the downwardlooking satellite's altimeter
   T m provides an estimate of the sea surface variance, <2>, and hence of the significant wave height Hs
   T G (4<2>).  Essentially, the higher the waves over the footprint of the radar pulse (which is about 
510km in diameter,depending on the roughness of the sea), the more spreadout the time of arrival
of the return pulse, while the height of the return pulse is kept constant by automatic gain control
(AGC).

The shape of the return pulse from a nearnadir radar is determined by specular reflection, and the
   T W physics of the process are well understood.  So the derivation of Hs is based upon sound physical
   T 1 principle, no empirical factors are involved, and estimates of Hs from satellite altimeters are widely
considered to be satisfactory.  However there is some evidence that errors can be introduced by the
data processing, and it is necessary to calibrate the altimeter.  See, for example, Hayne & Hancock
(1990).

Geosat parameter values, obtained between December 1986 and November 1987, were extracted by
Glazman and Pilorz (1990) when the satellite's footprint was close to ocean buoys of the US National
Data Buoy Center of NOAA, and when the time difference between the satellite pass and the buoy
measurements was less than one hour.  Carter, Challenor & Srokosz (in press) compare the estimates
   T ! of wave height from the buoys with those from Geosat, and conclude that Geosat gives Hs values
about 13% lower than the buoys, although the values given in this lesson have not been adjusted.

   S U$ Estimating wind speed from the altimeter

   T & Over the past twenty years numerous attempts have been made to relate the radar crosssection %0 (the
strength of the return of the nearnadir altimeter transmission, estimated from the AGC) to the wind
   T ' speed near the sea surface.  Measurements of %0 from various satellites and wind speeds from buoys
   T ( have all shown a decrease in %0 with increasing wind.  These and other physical measurements have
been used to develop a number of algorithms.  The first algorithm developed for use with satellite   e)        p-@*@*@@     T    data was derived from GEOS3 data by Brown et al (1981).  Goldhirsh & Dobson (1985) fitted a
curve to the Brown algorithm to produce the widelyused smoothedBrown algorithm, often included
with Geosat data.

   T b However none of these algorithms appears to work satisfactorily with Geosat data.  Carter et al (in
   T < press) obtain a simple fit of Geosat %0 to some NOAA buoy wind speeds by linear regression.  The
best fit requires two straight lines of different gradients, joined at the boundary between two ranges
of values.  The provisional equations for such a "twostick" fit are:

   T   u = 44.73  3.424 %0, hh4 %0 < 12.2
`<!"j (1)
   T N	  u = 5.773  0.228 %0, hh4 25.3 > %0 > 12.2

   T   where u is the estimated wind speed in msé1.

   T  Here, the value of u at %0 = 12.2 is 2.97 msé1, the root mean square deviation from the regression
   T 
 is 1.46 msé1 and the upper limit of 25.3 on %0 is included to prevent negative wind speeds.  In
   T d practice, values of %0 > 20.0 are regarded as suspect; they are possibly due to sea ice, but there is
some evidence that higher values might be obtained from glassy seas, with very light winds.  Another
recent algorithm, proposed by Witter & Chelton (1990) shows good agreement with the twostick fit
   T  except at low wind speed and may be better at wind speeds lower than about 3 msé1.


   S t Construction of global monthly averages

   T $ Data have been analyzed in the same bin size (2$'2$) as used by Challenor et al (1990) and by
   T  Carter et al (1991) for their analyses of one year of the Geosat data.  The smallest number of
transects of a 2$'2$ bin during one month is at the equator where  for the 17 day repeat mission
of Geosat  the tracks are separated by 160 km or 1.4$, and give a minimum of 4 transects a month
(upcrossings and downcrossings in 34 days).  So, at least in the tropics, some smoothing of the
dataset is probably desirable.

   T  The average value of Hs in a 2$'2$ bin was obtained by taking the median of the 1 Hz values for
   T  Hs along each transect of the bin, and then calculating the mean of these values.  The result was
increased by 13%.  The average value of wind speed was obtained by taking the median of the 1 Hz
   T  values of %0 along each transect, calculating the wind speed corresponding to this median value using
equation 1, and then calculating the mean of these wind speeds.

The median value was used for the transect average because it is more robust against outliers than
the mean, even though some quality control checks were made on the data.  There is a particular
problem with data close to the shore where the radar return can be contaminated by reflections from
   T " the land giving spurious estimates of Hs and %0.  Similarly the presence of sea ice in the footprint can
cause problems.
   \$         p-@*@*@@     T    a7 Lesson Outlineă

   T  1. Load the 1987 January wave data image (HS8701) and display it.  Modify the LUT to display the
   T  range of values (a LUT file is provided with the name WAVE.STR) and select or create a suitable
palette which clearly shows the global variability.

   T  2. Now enter the Cursor function and examine the values of the wave height at a number of places.
 What is the maximum wave height on the image?  
 Where is it found?  
 Are the waves stronger at low, mid or high latitudes?
 Are the waves stronger in the southern or northern hemisphere?

   T $
 3. Load the July image (HS8707) and repeat stage 2.  What differences do you observe between the
   T 
 January and the July wave distributions?  Use the Toggle option to flick between these two images
to help in contrasting the July and January distributions.  Are there any exceptions to the general rule
that waves are higher in the hemisphere experiencing winter?  How do the heights of waves in the
southern hemisphere compare with those in the northern hemisphere?

4. Load and display in turn the rest of the wave height datasets for other years.  Are the variations
from year to year as great as the variations between July and January?

   T  5. Load the January wind data image (WI8701) and repeat the procedures in stage 1.  A LUT file
   T  called WINDWAVE.STR is provided to match the range of wind speeds encountered.  Next repeat
the questions of stage 2, for the case of wind speed.

6. Look at the July wind data and compare it with the January data.  Describe the differences and
consider whether these are as you would have expected.  Are the strongest winds found in the
northern or in the southern hemisphere?

7. Now compare the wind and wave data for July and January 1987.  You can do this first by the
   T X toggle function.  Note that you must use the LUT designed for winds, even though some resolution
is lost in the wave images, because the numerical values for the wind images are higher than for the
wave images.  Can you see a general correlation between the monthly mean winds and the
corresponding monthly mean wave heights?  Does this help to explain the pattern of global wave
height distribution?

   T i 8. A quantitative comparison of the wind and wave distribution can be made using the scattergraph
   T B function.  Enter HS8701 and WI8701.  What is the dominant shape of the scatter plot?  What does
a straight line through the origin signify for the relationship between the wave height and the wind
speed?  Are the departures from the general relation between wave and wind due to waves being
lower or higher than predicted by the trend?  Suggest a cause for this.

To identify regions where the waves are lower than might be expected from the general relationship
   T S$ with the wind, generate the ratio between the wind and waves, i.e. Enter the Multi image, twoband
   T ,% ratio function and evaluate WI8701/HS8701.  Plot the result.  High values should correspond to
where the waves are lower than normal for the given wind speed.  Where is this the case?  Does this
confirm the cause you suggested above?

9. The many small questions which you have just answered paint a picture of the spatial and temporal
distribution of winds and waves around the world.  As a final task summarise the patterns you have   e)        p-@*@*@@  identified and suggest which of this information was already available from conventional
oceanography and which is dependent on satellite remote sensing techniques.


That concludes the basic lesson investigating the relationship between wind and waves, but you may
like to continue with the following two sections about generating the mean image from a time series.

10. A helpful way to examine the interannual variability is to calculate the difference between the
monthly mean for a particular year and the mean over many years of the data for that particular
month.  We only have three years of data here, but this is enough to demonstrate the principle:
   T p (a) Using the Image Arithmetic function in the Multi image submenu, obtain the mean of HS8607
   T I	 and HS8707, by entering the coefficients 0.5, 0.5 and 0 in the linear expression.  The resulting image
   T "
 should be saved as HSpart.  To obtain the mean including July 1988, use Image arithmetic again
   T 
 with HSpart and HS8807, this time with coefficients 0.67, 0.33 and 0.  The result should be saved
   T  as HSMEAN.  
   T  (b) Now, to examine the departure of a given year from that mean, use Image arithmetic again.  For
   T 
 example, for the July 1987 anomaly, enter the images HSMEAN and HS8707, with the coefficients
1, 1 and 128.  Display the result.  You will need to adjust the LUT because an anomaly of 0 (i.e.
the wave height for July 1987 is the same as the mean July wave height for the three year period) is
represented in the anomaly image as 128.  Negative values (July 1987 waves less than the mean)
count backwards from 128 and positive values count forward from 128.  

If you wish, you can save the anomaly image and generate anomaly images for 1986 and 1988 in the
   T o same way by repeating stage (b).  Then you will be able to compare the anomalies using the Toggle
function.  Note that this highlights the interannual variability whereas when toggling between the
original July datasets the eye does not pick out the differences so readily.

11. The annual (seasonal) variability can be highlighted by comparing a particular month with the
annual mean data.  Ideally twelve months, or at least four quarters, are required to construct a
satisfactory annual mean, and these are not available for this lesson.  Instead, construct an annual
mean based on the average of four images, January and July, 1987 and 1988, following the example
of 10(a).  Note that when incorporating the fourth set of data the coefficients should be 0.75, 0.25,
0.  Why?  Then generate the difference between this annual mean and the individual months following
the example of 10(b).


   T h a9 Referencesă

 X  Brown G S, H R Stanley & N A Roy, 1981.  The wind speed measurement capability of spaceborne
   T   radar altimetry.  IEEE J. Oceanic Eng., OE6, 5963."

 X  Carter D J T, P G Challenor & M A Srokosz, (in press).  An assessment of Geosat wave height and
   T {# wind speed measurements,  J.Geophys.Res."

 X  Carter D J T, S Foale & D J Webb, 1991.  Variation in global wave climate throughout the year,
   T & Int.J.Remote Sensing, 12, 16871697."

 X  Challenor P G, S Foale & D J Webb, 1990.  Seasonal changes in the global wave climate measured
   T ( by the Geosat altimeter, Int.J.Remote Sensing, 11, 22052213."   (        p-@*@*@@  Ԍ X  Glazman R E & S H Pilorz, 1990.  Effects of sea maturity on satellite altimeter measurements,
   T   J.Geophys.Res., 95, 28572870."

 X  Goldhirsh J & E B Dobson, 1985.  A recommended algorithm for the determination of ocean surface
   T b wind speed using a satelliteborne radar altimeter. Report SIR85U005, Johns Hopkins
University Applied Physics Laboratory."

 X  Hayne G S & D W Hancock III, 1990.  Corrections for the effect of significant wave height and
   T  attitude on Geosat radar altimeter measurements, J.Geophys.Res., 95, 28372842."

 X  Witter D L & D B Chelton, 1991.  A Geosat altimeter wind speed algorithm and a method for
   T N	 altimeter wind speed algorithm development.  J.Geophys.Res., 96, 88538860."


      y    b                     d       d d                                                                         y 


Lesson prepared by D. Carter and I.S. Robinson.

   R H Comments or suggestions relating to this lesson should be sent to:

Mr.D.Carter
Institute of Oceanographic Sciences Deacon Laboratory
Brook Road
   R  Wormley`	`	 % - hh4 < Fax:C (44) 428 
Surrey
UK
            p-@*@*@@  
   T   /a5 Answers to Lesson 7ă

2.  In January 1987, according to this Geosat data, a band of high waves occurred across the mid
latitudes of the northern hemisphere, with the highest in the North Pacific, the maximum wave height
being about 5.9 m at 176177$E, 5051$N.

3.  In July 1987, the high waveheights occur at midlatitudes in the Southern Ocean, the maximum
wave height being 5.6 m at several points in the S.Atlantic and S.Pacific, at a latitude of about 50$S. 
Comparison between winter and summer shows that in the northern summer the waves are very low
whereas in the southern summer there remains a band around 50$S where waves approach 4 m.  Note
also the moderate wave heights at the equator in the Pacific Ocean in January, and the Indian Ocean
/ Arabian Sea in July.

4.  Although the patterns of wave height distribution are not identical, they are very similar for all
three July images, and the two January images are also very like each other.  It is evident that the
seasonal changes are consistent from year to year, and much larger than any yeartoyear variation
for a given month.  It would be interesting to test whether this is the case for April or October data,
when delay or advance of the seasonal changes might cause larger yeartoyear variation.

Note that sections 10 and 11 in this lesson deal with how to create images representing the mean and
anomalies about the mean from a time series of images.

5.  In the January 1987 data the strongest winds are found in the North Pacific and Atlantic Oceans,
   T A around latitudes 5060$N, with a magnitude over 14 m sé1.  Winds of up to 12 m sé1 are also found
   T  over the Southern Ocean at around 55$S, and up to 10 m sé1 in the tropical Pacific.

6.  The July 1987 data shows a belt of high winds only in the Southern Ocean.  The magnitude is
comparable with that in the North Atlantic and North Pacific in January.  There are also some zones
of weaker equatorial winds in the Indian and Atlantic Oceans.  Note that the pixels with value 255
   T Q in the Pacific and Atlantic correspond to a lack of data  not to 25 m sé1 winds.

7.  The wind and wave patterns for July correlate well with each other as do the wind and wave
images for January.  It is evident that the wind distribution tends to control the wave height
distribution.

   T a 8.  Note that when using the scattergraph function the cursor box defines the area from which pixels
are to be plotted.  Initially include the whole image.  There is a linear trend relating the wind and
wave height, although there is considerable scatter.  In general it appears that for a given wind speed
the wave heights are spread from zero or a low value to a distinct maximum cutoff which varies
linearly with the wind.  This suggests that the waves do not always reach their equilibrium value with
the wind.

Waves are lower than expected for a given wind around Indonesia and the Philippines in a belt from
Australia to China, and to a lesser extent in the Gulf of Mexico and the Arabian Sea.  A likely cause
for this is that the fetch is limited by islands and coasts, so that the waves do not reach their fully
developed height.

9.  It is worth pausing to consider that the data you have been handling in this lesson would have
   T Z) been impossible to derive without the use of satellite remote sensing.  Conventional in situ   Z)        p-@*@*@@  observations are limited to a few locations and regular shipping lanes.  Satellites have given us the
first confident knowledge about wind and wave heights in remote and inhospitable sea areas such as
the Southern Ocean where shipping avoids the highest seas.  Only remote sensing from polarorbiting
satellites provides the detailed spatial distribution which permits comparisons to be made between the
   T ` patterns of wind and waves.
   :         p-@*@*@@   z  R   k    u  z N    # c     P 7P# Marine and Coastal Image Data Module 3:z                p-@*@*@@     k   m    u  z N    # c     P 7P# Marine and Coastal Image Data Module 3:`"Y Practical Lessons: 8ă  

a$ Practical Lessons Using Marine and Coastal Image Data


   T 8 !a# 8:  OCEAN EDDY DYNAMICS GENERATED BY A NUMERICAL MODELă


   S   a8 Aim of Lesson

To demonstrate a numerical model of deep ocean eddies using BILKO for display and analysis.


   T 
 a9 Objectives

   T  The lesson includes both basic concepts in ocean dynamics and more advanced topics.  You should
obtain the accompanying references to clarify and develop wider your understanding of the presented
material.  At the end of the lesson you should have learned to:  

1) interpret fields of streamfunction and vorticity

2) estimate vorticity from the velocity gradients

3) relate stream function, vorticity and geostrophic flow

4) estimate the characteristic horizontal scale of deep ocean eddies and their direction of propagation

5) describe the decay of horizontal velocity with depth and occasional reversal of flow at depth

6) interpret (5) in terms of barotropic and baroclinic pressure gradients.


   T  ~a3 Background Information

   S  The Bilko image processing software

Some familiarity with the use of Bilko version 1.3 to display images is assumed.  To load the image
display software, enter the directory in which the programme is stored and type <UNESCO13>. 
The online HELP is contextual, and can be obtained at any point by typing <H>.  Further
information can be found in the Introductory Tutorial.

  
   S s# Description of model images

The images used in this lesson are output from a computerbased ocean model which simulates
synoptic scale ocean eddies in the deep ocean.  The model solves numerically the finite difference
representation of the equations of fluid motion in quasigeostrophic form.  This assumes that there
is an approximate balance between the Coriolis (earth rotation) force and the pressure gradients
created by the nonuniform density distribution in the ocean.  In the model we assume a block of
ocean with a horizontal length of 500km by 500km and a constant depth of 5000m.  Its boundaries   [)        p-@*@*@@  are periodic in both directions and therefore eddies move unhindered through the boundaries and
reappear at the opposite side.  Eddies are supposed to have been introduced into the model at the time
origin and have been left to evolve and propagate within the model.  The images represent conditions
sampled at either 500 or 1000 time steps from the initial time and correspond to 11.3 and 22.6 days
respectively.

The images show data fields of either the streamfunction or the relative vorticity defined on a
horizontal grid of 256 by 256 pixels.  They are evaluated at one of 7 equally spaced levels in the
vertical as defined in the following table:

r 
  3d d x          )            
 d d x     p                              r   
 
 
 
p              Level number   	       

, 1   	       q8 2   	       /]A 3   	       I 4   	       R 5   	       i[ 6   	       =c 7  
 
		p              Depth / m          0 (surface)          714          1428          2142          2857          3571          4286 		 	   
The following images are supplied:

r 
 d d x     p                            
 !	d d x                       r  	 
 
	              Filename          Type of data          Level          Timesteps  
 
` 	 	              PSI5001          streamfunction          1          500 ` 	 	` 	 	              PSI5002   H       streamfunction   H       2   H       500 ` 	 	` 	 	              PSI5003          streamfunction          3          500 ` 	 	` 	 	H              PSI5004          streamfunction          4          500 ` 	 	` 	 	              PSI5005   h       streamfunction   h       5   h       500 ` 	 	` 	 	              PSI5006          streamfunction          6          500 ` 	 	` 	 	h              PSI5007   (       streamfunction   (       7   (       500 ` 	 	` 	 	              PSI10001          streamfunction          1          1000 ` 	 	` 	 	(              PSI10002          streamfunction          2          1000 ` 	 	` 	 	              PSI10004   H       streamfunction   H       4   H       1000 ` 	 	` 	 	              VOR5001          rel. vorticity          1          500 ` 	 	` 	 	H              VOR5002           rel.vorticity           2           500 ` 	 	` 	 	              VOR5003   h!       rel.vorticity   h!       3   h!       500 ` 	 	` 	 	               VOR5004   "       rel.vorticity   "       4   "       500 ` 	 	` 	 	h!              VOR5007   ($       rel.vorticity   ($       7   ($       500 ` 	 	` 	 	"              VOR10001   %       rel.vorticity   %       1   %       1000 ` 	 	` 	 	($              VOR10002   &       rel.vorticity   &       2   &       1000 ` 	 			%              VOR10004   x(       rel.vorticity   x(       4   x(       1000 		 &   
# &m     P 7#{&P#    P)         p-@*@*@@  The value of each pixel between 0 and 255, for the stream function, corresponds to a range from
   T    4312 m2sé1 to +4312 m2sé1.  Hence to derive a streamfunction value from a given pixel value P the
following conversion formula is applied.

   T b Za1 1 = 33.69 (P  128) m2sé1 

   T  The relative vorticity pixel values (0 to 255) correspond to a range from 9.0'10é6Ġsé1 to
   T  +9.0'10 6Ġs 1. The following conversion formula is applied to convert from pixel values to vorticity
   T  in units sé1.

   T t =a1 
 = 7.03'10é8 (P  128) sé1ă

   T &
 The distance coordinates x,y of a given pixel M,N relative to the top left corner of the image can be
evaluated in metres using the following expression:

	 1     d d d d d d d d (1)           !                  1     d d d d d d d d  (1)                               	A  #b      d d d d d       }  d d "{                                                    !   b          {     $ [x,y] = { 500000 OVER 256 } [M,N] m&m     P7&P&m     P7&P&m     P7&P        [        ,      " ]      4500000      y@ 256      * [       ,       ]     R  x       y     g M     - N      m      _       { $  """"`!A "$ 
   S  Definition of stream function and relative vorticity

   T  The stream function,1, is related to the components of horizontal velocity (U,V) by:
)a  #b_      d d d d d         d d "{                                                    !   b               S  STACK {U= {PARTIAL 
 psi }over {PARTIAL y}#
V={ PARTIAL psi } over { PARTIAL x}} &m     P7&P&m     P7&P&m     P7&P      U     y     ]  V     ? x                   ,      ,              ]3,      w? ,          J       1      31 )$  ""r""!a "$ Thus the direction of the velocity is along contour lines of 1.  If there is an exact balance at every
point between the pressure gradient and the Coriolis force due to earth rotation, then the flow is
described as being geostrophic and the streamfunction 1 is equal to the horizontal pressure field.

The vertical component of vorticity, 
, is a measure of the spin of the fluid about a vertical axis.  It
is related to the horizontal components of velocity by:
   T    #b#      d d d d d       x  d d "{                                                    !   b          {     D zeta = { PARTIAL V} OVER { PARTIAL X}{ PARTIAL U} OVER{
PARTIAL Y}
&m     P7&P&m     P7&P&m     P7&P      $  
              4,      @ ,             4,      @ ,           p      p4V     p@ X     4U     @ Y{ $  """"`! "$ By elimination of U and V from the above two equations an expression for the vorticity in terms of
the stream function is obtained:
V  #b(      d d d d d       Z  d d "{                                                    !   b                 zeta = GRAD SUP 2 psi .&m     P7&P&m     P7&P&m     P7&P       @ 
      @ 1      y @        @ +z z    U 2      @ .  V$  """""! "$ This equation is used later in the lesson.

   T & Remember that the streamfunction defines just one part of a general flow; it is the rotational
(circulating) component of flow.  

   T f) The finite difference equations for the U and V components of flow are: `  f)!         p-@*@*@@A "  A ! "t  a ! #"&   ! ("+   ! `  Ԍ   T    S  #b@      d d d d d         d d "{                                                    "   b               w stack{U =  {(psi SUB {i+m}  psi SUB {i})} OVER {m* DELTA }#

V =    {(psi sub {j+n}  psi SUB {j})} over {n* DELTA }}&m     P7&P&m     P7&P&m     P7&P      Uz z   `
iz z   
mz z   
i     J'm     k  Vz z   -%jz z   %nz z   %j     ? n             z z    
      #G      '        z z    O%      _      z? A          X       G(      8G)      k_(      _)      G1      G1      <'      _1      C_1      ?  S$  ""  ""! "$ where i and m are indices of the pixels in the x direction and j and n are the corresponding indices
in the y direction.   is the length of a pixel in metres.

   T r The finitedifference equation for the vorticity at the point i,j is:
  #b      d d d d d       _
&  d d "{                                                    "   b               ~ zeta = {( psi SUB{ i+n,j}+ psi SUB {in,j}+ psi SUB{ i, j+n} +
psi SUB{ i, jn }4 psi SUB{ i, j})} OVER{ ({n DELTA})  SUP 2
}&m     P7&P&m     P7&P&m     P7&P        
      M~1      )~1      ~1      ~1      	~1      p@         z z    D      ~z z    D      ~z z    D      s~z z    D      O~            ~(z z    zD,z z    VD,z z    D,z z    D,      ~4z z    	D,      
~)      @ (      @ )z z    9 2z z   Diz z   =Dnz z   Djz z   Diz z   Dnz z   uDjz z   Diz z   Djz z   6Dnz z   fDiz z   Djz z   Dnz z   	Diz z   	Dj     @ n $  ""L	""`! "$ 

   S \ Background in Oceanography

This lesson is an introduction to the horizontal flows simulated by a dynamical ocean model and in
particular to some basic concepts used in the description of that flow.

The currents in the deep ocean beyond the continental shelves are characterized by a wealth of scales
of variability ranging from the large gyres which extend across entire ocean basins, through synoptic
eddies of 50 to 200km in horizontal extent to finer features such as ocean fronts which have scales
of less than 10km.  Of all these structures in the deep ocean, the synoptic eddy is the most energetic
   T  scale of motion.  The eddies have typical horizontal currents of order of a few cmé1 in midocean but
have stronger flows near intense western boundary currents such as the Gulf Stream.  They have a
lifetime ranging from a few weeks to one or two years, and are important for the horizontal transport
and mixing of heat, salt and nutrients in the ocean.

These eddies have the following characteristics:

 X 1) the flow is predominantly in geostrophic balance and therefore can be estimated from the
horizontal pressure field."

 X 2) the eddies continuously develop and decay as a result of hydrodynamic instabilities and 
dissipation processes within or at the boundaries of the ocean."

The basic pressure field may be caused by variations in sea level (the external or barotropic pressure
gradient) or by density variations within the ocean (the internal or baroclinic pressure gradient).  The
eddies are essentially quasigeostrophic: the basic balance is geostrophic but there are small
perturbations in current and pressure which are not.  The current perturbations are ageostrophic flows
across lines of constant pressure which result in the movement of the pressure pattern and
consequently cause eddies to intensify or decay.

   T & Baroclinic and barotropic flows 

The barotropic or external pressure gradient mentioned above is a horizontal pressure gradient which
does not vary with depth.  At any instant the barotropic pressure gradient in the surface layer equals @  ])"        p-@*@*@@! @"Z   " "   " @  the barotropic pressure gradient at the bottom of the ocean.  Since the flow is geostrophic the
barotropic flow is similar at all depths.

In contrast, the internal or baroclinic pressure gradient is dependent on variations in ocean density
and hence changes with depth.  The associated baroclinic geostrophic flow also changes with depth
but the depthaveraged baroclinic flow must be zero.  For example, in the simplest case of two layers
with different densities, a baroclinic flow in the upper layer will be compensated by an opposite flow
in the lower one.


   T p a7 Lesson Outlineă

   T !
 1. Load the image of the stream function for the surface layer of the ocean, PSI5001.  Display it and
select a suitable palette.  If you have a VGA display, you may prefer a colour palette to the greyscale
default.  Remembering that the velocity flows along lines of constant 1, in a direction such that 1
increases to the right, interpret the image in terms of the flow patterns.
 X How many eddies can you identify?"
 X Are they clockwise or counterclockwise?"
 X Are they exactly circular in form?"

   T  2. Use the transect function to display the stream function on the west to east section defined by
   T  y=57 and note the approximate positions of the turning points for the streamfunction.  Use the cursor
function to obtain the exact coordinates and values of the streamfunction: note them.  Use the finite   T l difference equation given above to obtain the northward V component of the velocity across the
section.

Repeat this exercise for different sections and examine the range of velocities in these ocean eddies.

   T  3. Deduce the U and V velocity components for the eddy centred at x=62 and y=57.  To do this,
choose 4 streamfunction values at a distance of 20 pixels to the east, south, west and north of the
centre point.  Note the direction of circulation.  Choose the adjacent eddy at x=83 and y=92  and
repeat.

4. Deduce the approximate vorticity at your selected grid points from the finitedifference equation
   T  for the streamfunction field given above.  Now load image VOR5001 and use the cursor function to
obtain the true values of the vorticity field.  How good is the agreement?

   T A 5. Use the Multi image, Toggle function to compare the streamfunction field PSI5001 with the
   T   vorticity field VOR5001.  What qualitative differences do you observe between the two fields?  Use
   T   the cursor function to identify the position and values of the maxima and a minima in the
streamfunction and note them.  Repeat this procedure with the corresponding vorticity field.  

What is the relation between vorticity and streamfunction?  To clarify this relationship derive the
vorticity from the above equation for a hypothetical streamfunction field given by:
H #bl+      d d d d d         d d "{                                                    #   b               3 psi = a sin ({n pi x} over L) sin({n pi y} over L )&m     P7&P&m     P7&P&m     P7&P      $  1      4!      4!              a     4n     ~4x     @ L     T4n     *4y     @ L      s sin      I (       )       sin       (       ):      :     A  H$  "",%""`!"$ 
 0  d)#         p-@*@*@@ l+"s.  # 0  Ԍ   T    where a is a typical amplitude, L is the width of the block of ocean (i.e. 500km ) and n is the number
   T   of eddies in the section.  Choose n from your transect displayed earlier.

   T  6. Load another streamfunction field at a greater depth.  Try first PSI5002 and then progress to the
   T e lowest layer.  Use cursor to identify the amplitude of the eddies and their horizontal scale.  For each
image it is useful to note the coordinates and maximum amplitude of a particular eddy and then to
follow the eddy in each layer.  Try the eddy at x=132, y=157.  Note the change of the intensity of
streamfunction with depth and the occasional reversal of the deepest flow.  

   T  By use of the toggle function compare level 1 with level 7. In addition to the decrease in amplitude
of the eddy with depth, you should note a horizontal displacement of the eddy.  Can you suggest a
reason for this behaviour?  Try the above on the corresponding vorticity fields and note a similar
behaviour.

7. Next look at the time evolution of the eddy field, by comparing either the streamfunction or
   T  vorticity image at the same level but at two different times.  For example, load PSI5001 and
   T 
 PSI10001 and, by using the toggle function and image arithmetic functions, distinguish changes in
the field.  What is the prevalent direction of the drift?  Estimate the speed of drift of the eddies at
   T 9 x=85, y=163 and x=107, y=200 in PSI5001.  Look at the time change for the streamfunction and
vorticity fields at different depths and estimate the speed of drift. Why do the eddies have this
prevalent drift?  By referring to the books listed in the bibliography at the end of the lesson you can
deduce theoretically the speed of drift.


   T J a9 References 

A.E.Gill (1982)" AtmosphereOcean Dynamics ", Academic Press.

P.H.LeBlond and L.A.Mysak (1989) "Waves in the Ocean" Chapter 44 416427, Elsevier.

N.C.Wells (1986) "The Atmosphere and Ocean: A Physical Introduction", Chapter 7, 191216,
Taylor and Francis, London. 

      y    b #"                    d       d d                                                        $                 y 

This lesson was prepared by N.C.Wells.
The model data was supplied by Dr A Megann.

   R S Comments or suggestions relating to this lesson should be sent to:

Dr.N.C.Wells
   R ! Department of Oceanography- hh4 < C Fax:ppK 44703593059
   R " University of Southampton- hh4 < C Telex:ppK 47661 SOTON G
   R # Southampton,  SO9 5NH,  UK   #$         p-@*@*@@  
   S   a4 Answers for Lesson 8ă

2. For transect y=57, the maximum streamfunction is 180 at x=27 and the minimum is 11 at x=61. 
The difference in streamfunction is 169 over a distance 34 pixels.  Use of the conversion formulae
   T 8 gives the S.I. equivalent of 5694 m2sé1, and 66406 m respectively.  The use of the difference formula
   T  equation yields a velocity of 0.0857msé1 (i.e. a southward flow).

   T  The northward component of flow, V, is given by:
   T  ! #b
      d d d d d         d d "{                                                    %   b          -     '   V = 0.01725{ DELTA P} OVER {DELTA M }&m     P7&P&m     P7&P&m     P7&P       V     4P     @ M                0      V .       017255     _       4      r@ - ߪ$  """"`!!"$ where P is the difference in pixel value of the streamfunction for pixels spaced M pixels apart
along the same row.

Use of the above formula gives the following meridional flows for the transect y = 57.

m 
 !	d d x                     
 Ad d x     4%   @	I{{u{                       m " 			X 
 
&"              x coordinates defining the
section         128         2963         64131         132167         168200         201249 X 
 
		4                 T  Northward velocity / msé1          0.0805          ܩ0.0857          0.0350          ܩ0.0365          0.0761          ܩ0.0129 		    
3. The eastward component of flow, U, is given by:
A #b      d d d d d         d d "{                                                    %   b          :     # U= 0.01725{DELTA P} OVER {DELTA N}&m     P7&P&m     P7&P&m     P7&P       U     4P     @ N                     | 0       .       01725            4      @ : ߷$  """"`!A"$ For the eddy centred at x=62 and y=57 and taking differences in streamfunction for 4 positions 20
   T  pixels to the east, south, west and north respectively the following velocities, in msé1, should be
   T  obtained.
   . , = ,   
   T   X east point (U,V)@$ = (0, +0.064)"
   T f  X south point (U,V)@$ = (+0.080, 0)"
   T @  X west point (U,V)@$ = (0, 0.086)"
   T   X north point (U,V)@$ = (0.084, 0)"

The flow around the eddy therefore circulates in a counterclockwise direction (cyclonic in
N.Hemisphere).
  
For the eddy centred at x=83 and y=92, calculating the components of velocity as above gives:

   T $  east point (U,V)@$ = (0, 0.055)
   T $  south point (U,V)@$ = (0.092, 0)
   T %  west point (U,V)@$ = (0, 0.040)
   T &  north point (U,V)@$ = (0.079, 0)

The eddy has a clockwise circulation (anticyclonic in the N.Hemisphere)
 @  )%        p-@*@*@@! 
"  !% "  A% @  Ԍ   T    The maximum velocity  of 0.150 msé1 occurs between x=109, y=200 and x=69 and y=223. This
is the highest that I have found, but you may find higher values! 

4. The vorticity may be estimated from the stream function field, centred at x=62 and y=57, and
using 4 positions 20 pixels to the east, south, west, and north respectively in the finitedifference
   T 8 equation for vorticity.  This gives a value of +8.06'10é6 sé1: the vorticity for the same point from
   T  VORT5001 is 6.82'10é6 sé1.
   T  For the adjacent eddy at x=83 and y=92 the approximate vorticity is 6.84'10é6 sé1 while the direct
   T  model value is  5.90'10é6 sé1.
  = , ( ,   
You should note the change in sign between the streamfunction and vorticity, and the streaky structure
of the vorticity compared with the streamfunction.

6.  Coordinates of centre of eddy and associated streamfunction for each level.
    
 
 Ad d x     4%   @	I{{u{                     
	 ad d x     &   GGGGGMM                              " 		  
 
"              Depth level   )          )       1   )       2   )       3   )       4   )       5   )       6   )       7"   
 
`  	 	"              coordinates of          x          132          132          132          132          131          123          113" `  	 	`   	 	)"               eddy centre          y          127          127          127          127          127          127          127" `   	 			"              streamfunction   y          y       227   y       221   y       209   y       190   y       170   y       153   y       150 		   	  
The westward displacement of the eddy in the lowest layers is consistent with the change of the
horizontal baroclinic pressure gradient with depth.

The decay of the streamfunction with depth is related to the superposition of the barotropic and
baroclinic pressure gradients.  In the upper layers of the model the two components of the pressure
gradient tend to reinforce one another, while in the lowest layers they tend to cancel each other.  In
the ocean, the external pressure gradient caused by the slope of sea level tends to be compensated by
the internal pressure gradient caused by density variations.  In particular the boundary between the
warm upper layer and the cold abyssal layer, i.e. the thermocline, tends to oppose the sea surface
pressure gradient, thus the geostrophic flow tends to be stronger in the upper layer (see reference).
  
7.  The westward displacement of an eddy is shown in the two examples below. 

r 
	 ad d x     &   GGGGGMM                           
  d d x     I&   xI           r  	 
 
              Time (timesteps)          500          1000  
 
` 	 	I              Streamfunction   )!       220   )!       232 ` 	 	` 	 	              x coordinate   "       85   "       66 ` 	 			)!              y coordinate   $       163   $       161 		 "   
The westward displacement of 19 pixels or 37100 metres in 500 time steps or 11.3 days, implies a
   T % westward velocity of 0.038msé1.
     &&       p-@*@*@@  ԌT 
  d d x     I&   xI         
 *d d x       '   x           T  		 
 
"              Time (timesteps)          500          1000  
 
` 	 	                Streamfunction          22          0 ` 	 	` 	 	              x coordinate   @       107   @       89 ` 	 			              y coordinate          200          195 		 @   
   T  Thus the westward velocity of the second eddy is 0.036msé1.

This corresponds to the speed of a Rossby wave which always have a westward phase velocity. The
Rossby wave speed is given by:
   T 
 a #bH      d d d d d         d d "{                                                    '   b          +     ( c =  {beta L SUP 2} over {4 pi SUP 2}

&m     P7&P&m     P7&P&m     P7&P       c     RL      m          P     X      kR      @ !z z    a2      {@ 4z z    Q 2+ ߨ$  ""
""`!a"$ where = 5.81'10é11 mé1sé1 and L is the typical diameter of an eddy.
Note that this value of  as used in the model is larger than a typical value in the oceans.
For the above eddy L is 66 pixels or 129000 m which, when substituted into the above equation,
   T  gives a westward velocity of  0.024 msé1, in reasonable agreement with the estimate above.
 0  '        p-@*@*@@ H"  a' 0   z     .   m  z N    # c     P 7P# Marine and Coastal Image Data Module 3:z  