WPC 
      2      B       N   Z           Roman 10cpi  "| x            x \	    @  X@Epson LX-400                         EPLX400.PRS  x 
   @         XC ^X@ USUK  3'                                          3'Standard                                  6&                                          6& Standard    X-400         +U                                           2      7     9  	    I   Z   K  +U "| x        +HP LaserJet III                      HPLASIII.PRS x 6X    @  ,\,C ^X@ 2 /       v     p   T  k      USUK  3'                                          3'Standard                                  6&                                          6& Standard        HPLASIII.PRS x 6X    +                                          a8Document g        Document Style  Style                                       X X`	`	  `	

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

 2 [  k   a       v   q  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 
       	   '  
        q	  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 [
     O
  
               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      
     f     2     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.           ׃

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

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

 a7Technical         Technical Document Style                               ( @ D                   i)  .  a8Technical         Technical Document Style                               (  D                   a)  .  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 

HH 1

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H 28	 + 	 Ӌ 2 J!  /     X     N   )    w  Doc Init             Initialise Document Style                                	  
 
               p-p-p-    I. A. 1. a.(1)(a) i) a)                 I. 1. A. a.(1)(a) i) a)                                     Document g                                            ? x x x ,    wx 6X   @8; X@ ? x x x ,   x     ` B; X ? x x x , #  Ax 6N h 
; XHC V " G ( $ , : hG     P 7hPCourier 10cpi Courier 10cpi (Bold) Courier 10cpi (Italic) CG Times (Scalable)  "  m+O6^$(8<<k](((<k((((<<<<<<<<<<((xkx5kWLRYLGWY(/TLmYWEWP@LYWqWWN(((<<(5<5<5(<<!!<!]<<<<,/!<<W<<55<5x( <<  <<<(((( <<<<<< <<<! W5W5W5W5W5kPR5L5L5L5L5(!(!(!(!Y<W<W<W<W<Y<Y<Y<Y<W<W5Y<W<W<W<Y<E<W5W5W5R5R5R5R5Y<L5L5L5L5W<W<W<W<W<W<Y<Y<(!(!(!(!XC/ T<L!L!L!L!L!Y<YGY<Y<W<W<kWP,P,P,@/@/@/@/L!L!L!Y<Y<Y<Y<Y<Y<qWW<N5N5N5  Y<L!Y<P,@/L!W<W<Y<W<Y<(     <<   (      ((WxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxNWWW< <<(511<<i<<<kk<*<<<<k* (( >><kxx<<II[x<x<W< GddCCk     (>      <  q   *"xxxxWWxxx<Wxx>WWkkxxx             <kkxxx  k<((xxxxxWIxkWWWWWWWWWWx(x<W<C<kxWxP<(<W5<EW]NxxWWWWWWWWWWxxxxx8xWWWWxxxxxxxxxxxxx xxxxxxWWxxxxxxdPI]xWx   xx    3G                                               WWWW                       xx          x        xx         xWWW<WWxWWxxx   WW   W5   WWWW5   WWWWW   WWW   WWW   WWW   WWWWWWWWWWWWWW     W   WWWWWW    WWWWWWWW(   WWW(   WWW(   WWW(   WWWW   W                                                   W   WWWW   WWWWILC  ICP5L/N5Y<W5(!T5PCmCY5P<W5WIE<I< <L5W5PIWC]IIII/<!!555I5I I II ((<<<<<          <<         IIIIIIIIIIIIIIIIIII///////<<<<<<<<<<<<<<<<<<<<!!!!!!!!!!!!5555555555555555555IIIIIIIIIIIIIIIIIIII(  E  WLY(WWI<5( x 2         |!                                   o1    ?9   4              U UUUUUUUUUUUU $ 
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  "P$+"P$+"P$+"P$
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  !P$1!P$1!P$1!P$
  1!P$ P$ P$ P$
   P$7 P$7 P$7 P$
  7 P$7 #7 #7 #
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  7 7 
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  7 
7 7 7 
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  &%&%&%&%
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  '%'J%'J%'J%
  'J%'J%'J%'J%
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  )P$)P$)P$)P$
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  )$y*$y*$y*$
  y*$*$*$*$
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  s+J%+J%+J%+J%
  +J%m,J%m,J%m,J%
  m,J%m,%m,%m,%
  m,%m,D&m,D&m,D&
  m,D&m,&m,&m,&
  m,&+&+&+&
  +&+?'+?'+?'
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  	(D&	(&	(&	(&
  	(&'&'&'&
  '&'?''?''?'
  '?''?''?''?'
  '?'&?'&?'&?'
  &?'&?'&?'&?'
  &?'&&&&&&
  &&&D&    ?                    Figure 1                                           Figure 1      A                    
    
 
  3   
  5.4. Current from data on tracer and CURRMOD  

 The result of modelling of wind driven current field depends
essentially on defined flows through open boundaries. A user does
not know precisely these flows and there exists a need for a
method by which these flows can be determined with a larger
precision. Of course, this can be done if certain type of data
is available. Data on conservative tracer can be used for such
purpose. The "conservative tracer" means a tracer for which halflife of extinction is much larger than the resident time of
tracer in the considered basin. How data on tracer should be
recorded in a user's file is explained in Section 3.3. Thus we
assume that the basis for defining flows through the open
boundary is

                  1                                                1                                   !  ph                      d d j                                                       p        
   (1) data on a conservative tracer,
   (2) the tracer is drifted through the basin,
   (3) the tracer has no sources in the basin. $  ""  ! $ 
 !  
 !  
 !  
 !  
 !  
  h""    Let us describe, first, the method for determining flows
through the open boundaries by using data on tracer. The basin
for the demonstration is the same as in all previous
descriptions, recorded in the user's file MANUAL.BAY. The basin
and data on tracer are illustrated in Figure 5.9. A schematic
                  Figure 1                                           Figure 1                            y !   
                     ?9  d d     SLIKA.WPG                                            
          y  $  ""P""  ! $ 
 !  
 !   y A  `	                    	T  n Z     CCC.TIF                                              `	         y  ,  """"(
! A :",  !  
 !  
 !  
   ? `"   ""`"""   Figure 5.9. Positions of data on tracer and corresponding
a  interpolated field.

                  Figure 1      A                                    Figure 1                           illustration of two possible flows through the basin and one eddy
around the second island of Figure 3.7. are given in Figure 5.2.
From three flows we can construct any other flowpattern, so that
two flows and eddy of Figure 5.2. can be taken as independent
patterns by which all the other typical patterns can be obtained.
We start with the winddriven current. From data on wind we can
construct a wind driven current where flows through open
boundaries are defined by user in some way. We admit that these
flows can be erroneous and we want to adjust them. Let us denote P  *        p-++1 h  !   o&  !  :"$  A  P     C    the winddriven current field by vo(x). Now we suppose that the
real current, reproducing the measured distribution of tracer,
is represented by
   C \ !  #b      d d d d d       	   d d w                                                       b   h `
e (5.7) i      bold v( bold x) ~=~ lambda sub 0{ bold v} sub 0( bold x) ~+~
lambda sub 1{ bold v} sub 1( bold x)~+~lambda sub 2{bold v}
sub 2( bold x) ~+~ lambda sub 3 {bold v } sub 3 ( bold x),x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      _ v     _ x     _ v     %_ x     _ v     H	_ x     +_ v     k
_ x     N_ v     _ x       _ (      z_ )     + 0     ]+ 0      _ (      _ )     + 1     + 1      _ (      	_ )     + 2     + 2      _ (      
_ )     + 3     + 3      _ (      _ )      ~_ ,      J_       m_       
_       _       _       =_       `_       _ i $  ""\""X!! "$ where vk(x) are obtained winddriven current and three respective
   C  patterns of Figure 5.1., while k, k = 0,1,2,3, are scaling
factors to be determined from data on tracer. In accordance with
the assumptions on transport of tracer, i.e. the assumptions (1)
(3), the stationary distribution of considered tracer is
governed by the equation
   ? l	 ]A  #b      d d d p p       
   d d w                                                       b    `J
 (5.8)      > D Delta c ( bold x) ~+~ bold v( bold x) Grad c( bold x) ~=~ 0x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       8       8       8 +      3	8       8 D     8 c     8 c      8       8 (      8 )      8 (      8 )      s8 (      c8 )      
8 0     8 x     8 v     8 x     8 x ]$  ""l	""X!A "$ with the current v(x) from (5.7). In all the modelling problems
till now, direct as well as inverse ones, the current field was
known. It is assumed in the present modelling problem that the
concentration field is known while the current field must be
determined from data. In the present numerical problem the
current field is known up to 4 degrees of freedom. The
   ? t concentration field c(x) must be interpolated from data on tracer
   C < and then the four parameters k are determined by solving the
problem (5.6). This task can be accomplished by using the third
option of CURRMOD. Thus we have to calculate, step by step, four
current patterns on the right hand side of (5.7). All these
calculations are automatic and a user has to follow patiently
instructions and answer the questions.

   ?   Starting phase. If there is no a current field before a user
starts CURRMOD, option 3, the user is informed immediately that
the first current pattern must be constructed by the options 1
or 2. Therefore, the starting phase in the present case consists
of the construction of winddriven current field for the
considered basin, i.e. we have to repeat the processing which is
described in Section 5.2. We assume that all the flows through
open boundaries are zero.

   C   The first current pattern. Each current pattern vk(x), k =
1,2,3, of (5.7) is a residual current field, so that all three
should be composed by repeating the option 2. Of course, this
construction is automatic so that the user has to follow messages
and answer questions, most of which are already described in the
previous sections.
 After the winddriven current is constructed and the user
starts CURRMOD, option 3, there appear the following two
messages, one after the other.

                1             !                                        1                                  A  b(D*                         d d    BUCO1.LST                                             (        
An estimation of the mean current field can be obtained from 
    the transport model by using the best fit of a linear    
 combination of at most four typical current patterns which  
             have to be defined by the user.                 
$  ""%""xA "$ and the user accepts the processing. Then P  +         p-++1 ",	  !  "-  A  D*"k/  A  P  Ԍa  b                          d d    BUCO1.LST                                                     
The current field which has been constructed already can be  
used as the first pattern field in this estimation procedure.
$  ""  ""a "$ and the user saves the field. The user is informed that the
current pattern is accepted and saved.

   ? @  The next pattern. The user is asked wether to precede with
the construction. It is supposed here that the process of
construction continues. Let us remind ourselves that there exist
two rivers with mouths into the basin which are not included in
the construction of winddriven current field. These rivers will
be included in the present current pattern. The river flows
   C 
 cannot be changed so that the current pattern v1(x) of (5.7) is
   C  fixed in the sense that 1 = 1. Of course, the rivers can be
included only in one pattern and the user will be informed in due
time that the present current pattern includes rivers while the
   C  following patterns, in our case v2(x) and v3(x), will be
constructed without river flows. Since the present current
pattern includes the river flows it has the same structure as the
residual current field of the previous section. Therefore we
assume that the flows through the upper and left hand side open
   C  boundaries are 500 m3/s and 950 m3/s, respectively, with the
corresponding directions. After the solver finishes and current
field is illustrated the user can get rid of measured velocities
at the three stations inside basin. Hence we assume that the user
has omitted all three stations. This phase of processing finishes
with the message "The present current field can be saved as the
next pattern" and the user accepts the constructed current
pattern.

   ?   Another pattern. In the present current pattern the rivers
are omitted. Therefore, the user is informed. 

  b                          d d    BUCO.LST                                                      
 There can be fixed flows in your basin. They can be included
   ONLY in one of current patterns. Therefore, if they are   
 included in the previous patterns, they will be OMITTED in  
                   the present one.                          
$  ""h"" "$ The next message is:

  bHX&                          d d    BUCO.LST                                              H        
  The user's file: MANUAL.BAY is replaced by another one in  
   which the F-codes (rivers and/or channels) are omitted.   
$  ""!"" "$ informing the user that rivers will not appear in the following
construction. However, at the end of processing the old file,
i.e. MANUAL.BAY, will be again replaced and available. Therefore,
the next message in the box underlines this message once more. P  '        p-++1 "o  a   "$    X&")    P                        1                                                 1                                    x                     d d o  MANUAL4.PRJ                                                           
                                           
                     WARNING!              
           The  fixed  fluxes are omitted  
           from the following processing.  
           Thus, the net flux through the  
           open boundaries  MUST be zero.  
                                           
        $  ""  "" "$ The user proceeds with the construction as previously. At the
open boundary the flows must be defined to follow the schematic
directions of the middle part of Figure 5.2.. It is assumed that
all the stations are ignored in the final construction of pattern
field. The user is asked again wether to accept the constructed
current pattern and we assume that the pattern is accepted. The
user is informed that the pattern is saved for the final
   ? H
 construction of v(x), and the processing continues.

                  Figure 1      A                                    Figure 1                            a  x     w              ?,  d d   SLIKA.WPG                                               oΌ    ?    Figure 5.10. The fixed current field a), winddriven component
XX b) and two auxiliary pattern fields c) and d). $  """"pa "$ 
   ? '  Last current pattern. The following message, question and
possible answers are necessary intermediate activities in order
to construct the next pattern.                  1                                 ""          x x x x 1                                  @  (        p-++! "    "*  a  @    b        x x x x        @  d d P  BUCO.LST                                                         The next current pattern can be construct by any of the
                 following options:
(a) omitting or/and changing data on measured velocities;
(b) changing boundary conditions of velocities at the open
XX boundaries;
(c) defining the centre of an eddy in the basin.
(d) Nothing of it.
    Choose one of the options, (a,b c or d):$  ""  "" "$ 
Obviously, the user must start the construction of the new
current pattern from the beginning so that (b) is the right
choice. 

After choosing (b) the construction continues in a well known
fashion. The user has to define flows through open boundaries to
simulate the flow of Figure 5.2., the right part. After the
current field is constructed and illustrated, the user must omit
three current stations as in the previous cases.

   ?   Reconstructed current field. When the construction of the
eddy is finished and accepted there follows an illustration of
all four patterns as in Figure 5.10. The user is informed that
   ?  the concentration field c(x) of (5.8) must be interpolated from
data on tracer and the user must follow instructions and answer
questions in order to accomplish the interpolation. Let us
mention that the procedure is the same as during the construction
of topography of bottom from the data on depth. After inspecting
the interpolated field the user is informed that 4 current
patterns are taken in process of minimization problem (5.6). An
auxiliary result is the extinction rate of tracerconcentration
field and the user is informed about the halflife of extinction.
   ?   The last step is an illustration of the interpolated field v(x)
of (5.7) and the precessing finishes.
