WPC 
      2      B       N   Z           Roman 10cpi "| p              x \	    @  X@Epson LX-400                         EPLX400.PRS  x 
   @         XC ^X@ USUK  3'                                          3'Standard                                  6&                                          6& Standard    X-400         +U                                           2      7     9   Z   I  	      +U"| p          HP LaserJet III                      HPLASIII.PRS x 
   @   ,\,C ^X@+ 2    N        %  v   ,  p     Courier 10cpi Courier 10cpi (Bold) CG Times (Scalable) Courier 10cpi (Italic)  USUK  3'                                          3'Standard                                  6&                                          6& Standard        HPLASIII.PRS x 
    +                                          a8Document g        Document Style  Style                                       X X`	`	  `	

a4Document g        Document Style  Style                                      .   2 5  k   D  k          v     a6Document g        Document Style  Style                                    G  X  

a5Document g        Document Style  Style                                   }    X (#

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

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

 2 	  t   g       	   u  
   	  Bibliogrphy          Bibliography                                             :   X 
 (#

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.        
 2      	     
  
   R       a3Right Par         Right-Aligned Paragraph Numbers                        L ! 
   `	`	 @P
                  1.  `	`	   (#

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#  ( (#

 2      
     
            a7Right Par         Right-Aligned Paragraph Numbers                        p fJ    `	`	   hh# ( @*                  i)  (  h- (#

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                                             2           9          n  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      G               5  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       /     X    e   w  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

HH 2

HH 3

HH 4

HH 5

HH 6

HH 7

HH 8

HH 9

H 10

H 11

H 12

H 13

H 14

H 15

H 16

H 17

H 18

H 19

H 20

H 21

H 22

H 23

H 24

H 25

H 26

H 27

H 28	 + 	 Ӌ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 V " G ( $ , # hG     P 7hP ? x x x , 7  Ax 6N h 
; XHHeading 2            Underlined Heading Flush Left                           1 4 
 2 "                F   ^   Heading 1            Centered Heading cal Style                              
 4G    Y    * Ã

Bullet List          Indented Bullet List                                   * M 0     Y     X   X`	`	  (#`	
 "  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         #                                   h  ;
  l  g    U   ?)   4              U UUUUUUUUUUUU  
  ,,,
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)EEE
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  <;
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
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4
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N *     9 0ef<I #  2    @kC Ll`@#      S-point
     C     P        0B S-point  	$   4         000@@@PPP```ppp Bh} , A          
                                                 	   
        	                                  	                  
    	     
   	    	       $             	L  5  % 
 '  	
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     	               	    
                    
   
           	    	                
  7 &         ""      
                                   	  
                 	  
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            
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ODDO,           
ODDO, 
                 	ODDO,(    ODDO,\DDDO%\DDD%\DDND%\DDND%\ DDND% 
  -DNDO!   -DND!    	             -DD!            -DND!            -DND!           -DND!              -DND!4  %"DND!\!DND!\!DD!\!DD!\ DD!  %DD!  )DNDO!       	    DND%        DND%
          DND%       DND% 
           DND%,   DND%\DNDO%\DND)\ DDNDND)\DNDDD)  .DNDDDO)  .DNDO	DD
DDO0             !DNDO	DD
DDO0   	        DNDO	DD
DDO0        DNDO	DD
DDO0     #DNDO	DD
DDO0          DNDO	DD
DNDO0\DNDO	DND
DDO0\DNDO
DNDDD1\DNDO
DNDDDOC\ DNDO
DDDOC\DNDO
DDDOC\DNDO
DODDD\DNDO/DDOG\ DNDO(DDOG\DND(DDOG\DND(DDOG DND(DDOGh DNDODDOGhDNDDDOGhDDDNDOGhDNDDNDOGh DNDDNDDhDNDDNDOChDNDDDOChDNDDDOCh DNDD@hDNDDO?hDDNDO?hDDO?h DDO<hDD<hDD<hDD<h DDDhDDO
DOhDDO
DOhDDO
DDOh DDDhDDDOhDDNDOhDDOh DDOhDDhDDhDDh DNDh DDDDhDNDh DDh DDhDDOhDDOhDDOh DDOhDDhDDhDDh DDNDhDDDh DDO
DDh DDO
DDNDhDDO
DNDDhDDODNDDhDDODNDDDh DDODDDDhDDODNDDNDhDDODNDODNDhDDODNDO$DNDh DDDNDO$DhDDODNDO$DhDDODNDO$DOhDDODNDO0h DDODNDO0hDDODNDO0hDDDNDO0hDDODNDO0h DDODND-hDDODNDO,hDDDNDO,hDD4DNDO,h DD4DNDOhDD4DNDhDDO4DNDhDDO7DNDh DDO7DNDOhDDO7DNDhDD8DNDhDDO?DNDh DDO;DNDhDDO;DNDhDD<DDhDD?DNDh DD?DNDhDD?DNDhDDO?DNDhDDVDND DDVDNDH DNDVDNDHDDVDDHDDOVDDOHDDOdDDOH DDOdDDO       
DDOdDDO   DDOdDDO    	   DOdDNDO  	 
  
DOdDDO
     
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 DDO    DDO(  DDOH DOH 􀉲DHH  h DDhA 
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U    e     P        	)4#    h  G #     2 ,$K/F(h#  2    @kC Ll@#     x
U    e     P        ,%xG #     2 -
$/&m#  >2    @kC Ll7@#     B
     =     P        0.$B  	)      h  G #     2 ,K/#h#  2    @kC Ll@#     S
U    e     P        ,!S  	,    h  G #     2 /2oh#  2    @kC Ll@#     x
U    e     P        0xG #     2 162m#  >2    @kC Ll7@#     E
     =     P        g1E    ?    
  8   
 
    
  6. TRANSPORT AND CONCENTRATION FIELD

   ?   6.1. Modelling transport in the coastal zone. A general
discussion regarding a utilization of stationary transport models
versus non-stationary transport ones is carried out in the first
   ?  chapter. The package ANCOPOL is designed to be an expert system
for an interpretation of data on transport. The demand on the
number of data inflicted the utilization of stationary transport
models. The block diagram of transport model of Chapter 1. can
be formulated now in terms of mathematical objects such as
differential operators and concentration fields. The stationary
transport model is defined by 
$!  #b      d d d p p          d d w                                                       b    `, (6.1)      d D`` Delta ``c( bold x) ~+~ bold v ( bold x) `` grad `` c(
bold x) ~+~ k`` c( bold x) ~=~q( bold x),x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       8       +8       8 +      	8       
8       8 D     8 c     8 c     
8 k     W8 c     _8 q      .8       k8 (      [8 )      s8 (      c8 )      #8 (      	8 )      8 (      8 )      8 (      8 )      ?8 ,     8 x     8 v     8 x     8 x     G8 x     O8 x $$  ""`	""X!! "$ where four terms of this equation are precisely the mathematical
models of transport mechanisms of the first block diagram of
Chapter 1., i.e. mixing, advection, degradation (sedimentation)
and input. The symbols have the following meanings:

   C    - D = eddy dispersion coefficient [m2/s],
   ? l  - c(x) = concentration at x  D,
   ? 4  - v(x) = two-dimensional advection velocity [m/s],
 - k = sedimentation coefficient related with the resistance
 `	`	 time T of (1.1),
   ?   - q(x) = input distribution,
 -  = Laplacean,
 - + = gradient.

The model (6.1) has a unique solution if appropriate boundary
   ? t conditions on the function c(x) are prescribed. The boundary
conditions are not of the same type along the whole boundary. For
instance, no flux of substance through a part of coastal boundary
is ensured by the zero gradient of the concentration normally to
the coast. No flux of substance along a part of the open boundary
is defined by the zero net flux induced by the sum of mixing and
advection, etc. The boundary B of basin is divided into the
   C  coastal boundary Bc and open boundary Bo. Let Bc1 be a part of the
   C  coastal boundary. The possible boundary conditions along Bc1 are
   C  2A  #b4#      d d d d d       D  d d w                                                       b    `(	 (6.2)       left .  {~} from {~} to {~} c( bold x) ~right  line sub {~B
sub {cl}} ~=~ c sub b ( bold x), ~~~~~~~~~ left . {partial c }
over {partial n}~ right line sub {~B sub {cl}} ~=~0,x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@             7U      
$     j  c     Bd d   Jd cl      c    g b     JXc     J{ n    G Bd d   % cl        (       )       (       )       ,       0       ,     Z x     / x             
X,      
{ ,      
  2$  """"!A "$ where cb(x) is a positive function along Bc1 defined by user and
   C 8# ,c/,n = 0 is called "no gradient" or "zero gradient" along Bc1.
   C $ Similarly, along a part Bo1 of the open boundary we can have 
   C $ a  #b)      d d d d d       i  d d w                                                       b       5     ~~~~c ~ line sub {~ B  sub {ol}} ~=~ c sub l, ~~~~~~~left .
{~} from {~} to {~} {partial c} over {partial n} ~ right line
sub {~B sub {ol}} ~=~0, ~~~~~~left . left ( `` D ` {partial
c} over {partial n} ~+~ v sub n `c `` right ) ~ right line sub
{~B sub {ol}} ~=~0, ~~~~ (6.3)x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@     r c     Bd d    ol      c    9 l     \	Xc     \	{ n    
G Bd d   
% ol     c D     Xc     { n     I v     n     , c    G Bd d   % ol      B 	             X,      { ,                    ,X,      ,{ ,      y               ,       0      	
 ,       0      & ,       (      v 6       .      f 3       )      I
U      $      fU       U g      U n     $5 ߲$  ""$""!a "$ where c1 is a number. The value c1 can be equal or larger than the
natural or background concentration in basin. The first condition
of (6.3) is called "fixed concentration" condition. Remaining two
conditions are called "no gradient (zero gradient)" and "no flux" P  +        p-++1 "!  !  4#"&  A  )",  a  P     C    along Bo1.
 If all the model parameters are defined the primary
processing of ANCOPOL consists of solving the problem (6.1) -
(6.3). However, values of some parameters can be determined from
the available data. This is possible in case that the user file
contains the data on measured concentration inside the basin,
i.e. the data which are recorded as S-codes (see Section 3.3).
The best fit of solutions is carried out by adjusting the
extinction coefficient k and input rates at point sources.
Assuming that such data are available, the primary processing
consists of the following estimation:
 - solving (6.1) - (6.3) with three different values of k and
choosing the value for which solution fits the data in the best
possible way,
   C 
  - point sources q(x) at locations xj, k = 1,2,...,K, can be
divided into 5 groups (see Chapter 3) and input rates 
  #b8      d d d d d       B  d d w                                                       b             N Q sub k ~=~ H int from { func {around}~ {bold x} sub k} q(
bold x) `` d bold xx 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      #Q      k     #Hd d   % k     3#q     ?#d      7#       L     G around      #(      #)    G x     ##x     #x $  """"! "$ are chosen in order to have the best fit of solution to data. In
agreement with accepted terminology of modelling the transport
the described processing belongs to the class of inverse
modelling problems.
 The transport model (6.1)  (6.3) is the basic object which
is implemented into ANCOPOL. Its merit is the minimum requirement
of data on concentration. One cannot expect particularly useful
results from a processing with minimum amount of data. More
powerful analysis of the transport follows from additional
utilities. However, they can be executed in case of presence of
certain specific type of data on concentration. Two utilities of
this kind are the decomposition of diffuse input and exploitation
of concentration from bottom sediment. These two utilities are
described in the remaining part of this section.

   ? (  Decomposition of diffuse input. The problem can be described
as follows. The stationary transport problem is solved with the
   ?  parameters: eddy diffusivity D, advection v(x), extinction
   ?  coefficient k, input q(x) and certain boundary conditions. These
parameters are fixed from the beginning of modelling or they are
determined from an inverse modelling problem. In an analysis of
results we come often to the following sub-problem: there must
be determined the contribution from a particular source or a sub-
set of sources to the obtained concentration field. Mentioned
   C 0# subsets of sources can be defined either by a part q1(x) of the
   ? # input distribution q(x) or indirectly by a prescribed boundary
   C $ value c1(x) along a part Bc1 of the coastal boundary Bc.
 Let us define the problem precisely. The coastal boundary
   C X& Bc is divided into parts Bcl, l = 1,2,...,K, and the remaining
   C $' part Bcr. The fixed boundary conditions of (6.2) are valid along
   C ' each Bcl, while the zero gradient condition of (6.2) holds at Bcr.
Hence, the transport problem is defined by 0  (        p-++ 8"r    0     C      #ba      d d d d d         d d w                                                       b    `Q (6.4) B     D`` Delta ``c( bold x) ~+~ bold v ( bold x) `` grad `` c(
bold x) ~+~ k`` c( bold x) ~=~sum from {j``=``1} to J q sub j(
bold x),#~#
c( bold x) ~ line sub {~B sub {cl}} ~=~ c sub l,  ~~~~~~~~~
left . partial over {partial n} c( bold x) ~ right line sub {~
B sub {cr}} ~ =~0.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       U      +U      U+      	U      
U            	      J       
W,      
z ,      W       UD     Uc     Uc     
Uk     WUc    )J    _j     Uq    =!j     h c    * Bd d   z cl      c     l     z n      c    7F Bd d   $ cr      .U      kU(      [U)      sU(      cU)      #U(      	U)      U(      U)     91      U(      }U)      U,       (       )       ,       (      
 )      ' 0       .     Ux     Uv     Ux     Ux     GUx     Ux     X x      x      I      
T      
#B $  ""  ""@! "$ There must be supplied a boundary condition along Bo which is not
   C  important for the present discussion. Each part Bcl is a source
   C  of substance as well as each qj(x). We envisage two groups of
problems:
 - we would like to know the mass rate of substance released
from the each component of the defined decomposition of the input
   C 
 distribution, i.e. q(x) = qj(x).
 - we would like to have a decomposition 
  #b@      d d d d d       #  d d w                                                       b    `
 (6.5) {     g c( bold x) ~=~ sum from {l``=``1} to K c sub l ( bold x) ~+~
sum from {j``=``1} to J c sub j ( bold x),x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       c    K    + l     { c     l    EJ    + j     9	 c    	 j        (      z )     + 1      H (      8 )     + 1      
 (      
 )      n ,      x      x     ~
 x      J      +             E+       A I       I{ $  """"! "$ so that the first K components can be identified as the
   C @ concentration fields induced by the sources along Bcl, while the
remaining J components should be identified as concentration
   C  fields which are induced by qj(x), respectively.
 This decomposition can be used to identify the main
contributors to the existing concentration field as well as mass
balance for the each component of source.
 It is not difficult to solve a problem belonging to the
first group. If the partial input distribution is defined by
   C  qj(x), the mass rate is Qj = H(qj(x)dx, where H is the depth of
   C T basin. If the input is defined by fixed concentration along Bcl
   C   of Bc the procedure is somewhat more involved. The problem must
be solved by using the transport model. Hence, it represents a
sub-problem practically of the same complexity as the problem
(6.4).
 We can solve each sub-problem straightforwardly by omitting
all undesired objects. For each sub-problem another complete
procedure must be carried out, such as defining the objects of
basin and solving the corresponding stationary transport problem.
In order to reduce the number of such repeated tasks, each
demanding for an extra editing and computing time, there can be
applied a method for solving all the sub-problems at once.
However, to use this method we must be certain that such tasks
are possible. The principal question is a correctness of
formulation of such sub- problems. If we omit all the undesired
sources of input and solve a sub-problem, are we sure that the
obtained concentration field represents the field we have
desired?
   C l&  For instance, if the value of c1 of (6.3) is equal to the
natural or background concentration then the subproblems can be
   C  ( formulated correctly. If c1 has any larger value subproblems
cannot be formulated correctly. In such case we do not know how
   C ) to prescribe the boundary conditions at Bo1 to each concentration
   C `* component cl(x) so that (6.5) holds along Bo1. In particular, @  `*        p-++! "t
    @"    @  there must hold:
   C    (1) Through each part Bok of the open boundary flow can have
only one sign,
   C \  (2) In the case of an outflow at Bok the boundary condition
can be zero gradient or fixed concentration equal to the natural
concentration,
 (3) In the case of an inflow the condition can be zero
gradient, zero flux or fixed concentration equal to the natural
concentration.
 There is a plausible interpretation of these rules. A fixed
concentration equal to the natural or background concentration
along a part of open boundary can be a right choice if sources
are far from this part of the open boundary. Similarly, the zero
gradient condition means that sources are far from the considered
part of open boundary so that the concentration field is almost
constant around it.
 Decomposition of diffuse input is available by ANCOPOL.
Details of the corresponding processing are described in the next
section.

   ?   Including data on concentration in sedimentation. Data on
concentration in sediment can be a very precise indicator of
pollution sources in the considered basin. Therefore, it is
desirable to use these data set in order to estimate the
transport parameters more reliably. Of course, we must use them
together with data on concentration in the water column. The
first step towards this goal is to describe a possibility of
including this data set into the transport model.
 Data on concentration in sediment can be interpreted in
terms of an accumulation process. To present ideas as briefly as
possible we use very simplified sedimentation model. We start
with the two-dimensional non-stationary transport model of
Chapter 1 and assume that sources start to release substance t
= 0 and their input rates are time independent after t = 0.
Hence, the concentration is zero until t = 0 and tends to a
constant, stationary concentration as t tends to infinity. The
   ? ( sedimentation rate at the location x is kc(x). In the time
   C  interval 0 < t < t1 the amount of substance deposited into
sediment is
(  #bW4#      d d d d d       /  d d w                                                       b             K S sub s ~=~ k``H`` int from { 0~~} to {~~ t sub 1} ~c( bold x)
`` d bold x.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      S      s     k     H    t     c     d      7       Ld d    1     m+ 0       (      )      .     x     ,x ($  """"! "$ Due to the fact that the concentration field in the water column
tends to a stationary concentration we can claim that the
concentration in sediment is proportional to the stationary
   ? $ concentration c(x) of the transport model. This simple model of
sedimentation can be now improved by allowing random input rates,
random fluctuation of velocity field, contribution from tides
etc. The basic idea remains unchanged and consequently we arrive
to the same conclusion: Concentration in the water column and
sediment are proportional. The scaling factor must be calculated
from the data on concentration in both media, sediment and water
column. This procedure is available in ANCOPOL whenever the user
supplies both types of data, i.e. the data on concentration in 0  +        p-++ 4#"&    0  sediment and in water column.

   ?   6.2. ANCOPOL and one-layer transport models.
 The following three main tasks can be performed by using
ANCOPOL: 
 - An estimation of the extinction constant and input rates
and the construction of concentration field,
 - Decomposition of diffuse input,
 - Calculation of mass balance.

Ail three are carried out during the primary processing. However,
the latter two tasks can be repeated an arbitrary number of times
during retrying.

   ? 
  Beginning of Primary processing. The processing of the first
task takes most of the computing time. We have to be aware that
the processing must be repeated several times until we get an
acceptable estimate of extinction constant k. In this section
this task is described in details. The data on concentration to
be processed are illustrated in Figure 6.1.
                  1                                  ""              1                                                  Figure 1                                           Figure 1                             !  xP    w              ?)  d d     SLIKA.WPG                                                @p    ?    Figure 6.1. Data on concentration for the prediction of the
9	
 concentration field.  $  """"! "$  When we start ANCOPOL the first screen is a mask as in the
previous two cases except that "ANCOPOL" is written instead of
"MAPBASIN" or "CURRMOD". By pressing <ENTER> we change the
screen. There are three messages and a question. 0  '        p-++ P")  !  0   !  b8                      d d @  BUCO.LST                                              8       1) Concentration field for the existing currents.
 2) Concentration field with zero currents.
 0) Exit.
 $  ""  ""! "$ 
The user can choose two options in order to continue the
processing and can exit ANCOPOL. The processing by the second
option is simpler because it is presumed that the current field
is zero. We shall assume that the user has already constructed
currents by processing CURRMOD and continues to make an analysis
of concentration field and corresponding mass balance by choosing
the option 1. Therefore, the user must choose the first option.
 In the case that there is no file with the current field the
user is informed about this circumstance by the following message

 A  b                     d d T  RECENICE.AUX                                                  There is no file with a current field. Therefore, the
processing proceeded with the zero velocity in the
Y	
 considered region.
 $  ""H
""A "$   ""              1             A                    ""              1                                                    Figure 1      !                                    Figure 1                           
  A  xp    w              	$  n Z     AAA.TIF                                                 mN 
   ?   ]
	 Figure 6.2. Defining the boundary conditions.  $  """"A "$   ""              1             A                    ""              1                                  We know that a concentration field can be changed by omitting
stations, changing values at stations and scaling the field as
a whole. Being aware of this it is necessary to remind the user
about current field in the present processing so that the first P  *        p-++1 "  !  "  A  p",  A  P  illustration is the current filed. As usually the user can scan
optionally the values of current field. After finishing an
inspection of current there must be defined boundary conditions
of concentration field corresponding to the illustrated current
field. There appears a display with the numerical mesh of basin
as in Figure 6.2. and the message "Press any key..." at the lower
right corner of the illustration. After pressing a key, the
following message appears at the upper right corner of display
  ""              1             A                                  1                                  
 a  h-                     d d K                                                       h      To define boundary conditions
along open boundary, one of the
following options must be
chosen for each open boundary. $  ""--  a -$ 
 a - 
 a - 
 a - 
 a - 
 a - 
 a - 
  --""   
After pressing <ENTER> this box is replaces by another one (see
the picture on the next page), a part of open boundary is marked
by twinkling, encompassing box and also a sound signal is heard
trying to catch the user's eye to this part of open boundary. The
user must define the boundary condition at this part of open
 y a                      <^ `d d    BBB.TIF                                                       y  $  ""0::  a :"$ boundary by choosing one of four
 a :" offered possibilities. We can
 a :" choose: the zero gradient
 a :" briefly denoted as "Gradient =
 a :" 0", the fixed concentration
 a :" equal to the natural
 a :" concentration denoted as "Natura
  ::""   concentration", the zero net flux of substance through the open
boundary denoted by "Transport = 0", and finally any fixed value
of concentration along the boundary. Any of these is chosen by
moving the cursor over the corresponding four boxes "G", "N", "T"
or "D". Let us assume that the user's choice is "Transport = 0"
by moving the cursor to the small box denoted by "T" and pressing
<ENTER>. The same procedure must be repeated for the other parts
of open boundary. Sometimes only two possibilities are offered
instead of four ones just described. For instance, if the current
is flowing out of the basin we can have either zero gradient or
the natural concentration along such part of the open boundary.
We assume that the boundary value of concentration field along
the third part of open boundary is defined to be 3 ppb. When the
last part of open boundary is finished the processing continues
with the message:                1             a                    ""              1                                  

   b8'                      d d @  BUCO.LST                                              8        

 ATTENTION !
In case that you have defined conditions on the open
boundary incorrectly, you can ABORT the processing.
 $  ""(#"" "$ 
giving the user an opportunity to define the boundary conditions
anew in the case of an erroneous defining of any of them. The
next message is about the accepted depth. We know that there are
two rivers with mouth in the basin. There are not data of P  *        p-++1 -  a  :"W  a  '",    P  concentration field at these locations in the file MANUAL.BAY
although these location must be included among Bk- points.
Therefore, the user is informed that the concentration field must
be defined at these additional points. Generally, at each mouth
the concentration field must be specified. The message is  ""              1                                 ""          x x x x 1                                  

F  b8`	        x x x x           d d j  BUCO.LST                                              8                    ADDITIONAL DATA ON CONCENTRATION
There exist water inflows for which the concentrations
are not defined. You are asked to define the concentrations
at such locations in the following procedure.F$  """" "$ 
and after pressing <ENTER> there appears an illustration of the
basin with current filed and a twinkling mark at that grid knot
which represents the river mouth (see Figure 6.3). When the
illustration is finished there appears a box with the message
"Press ENTER to continue". The user must press <ENTER> and this
box is replaced by another one:
   8
        x x x x           d d j  BUCO.LST                                             8        Define concentration at the location
which is marked in the illustration.
Only  positive  values are accepted.
Enter in ppb: $  ""

   
$ 
  
   
  
 
  
 
  
 
  
 
  

""   
The user must insert the value of concentration at the river
mouth. From the chart in Figure 6.1, the value must be 19.5 ppb.
After entering this value and pressing <ENTER> the user must  ""          x x x x 1                                 ""              1                                                    Figure 1      a                                    Figure 1                             H
 y   RX                    ;  } d     AAA.TIF                                                       y  $  ""   "$ 
  " 
  " 
  " 
  " 
  " 
  " 
   ?     " 		 Figure 6.3.ă
  " The concentrations at
  " river mouths must be
  " defined by entering
  " values during the
  " processing.
  " 
  " 
  " H
  " 
  " 
  " 
  %""   repeat the same procedure for the other river mouth. When the
definition of concentrations at river mouths is finished the user
is asked wether to redefine these concentration in case of
mistyping.

   ? h)  Input from atmosphere. The user's file MANUAL.BAY contains
data on input from atmosphere. An input distribution must be
interpolated from data and the user is informed about this task P  *        p-++1 `	"
    
    X"/*    P  by the message:  ""              1                                 ""          x x x x 1                                  

   b@        x x x x        X  d d j  BUCO.LST                                          	            An interpolation of the input-distribution from data must be 
                 carried out, first.  
 $  """"  "$ 
This interpolation is performed in the same way as for bottom
topography. The user is informed about locations of measuring
stations and then the process of interpolation is carried out as
described previously. There are messages about the minimal and
maximal values of input field, as well as the net input into the
basin. Then the user is asked:  ""          x x x x 1                                 ""          x x x x 1                                  

  b        x x x x          d d j  BUCO.LST                                          	            The input field can be scaled in order to fit the solution of
transport model to the data in the best possible way. $  ""
"" "$ 
so that the user can fix this input distribution by avoiding the
option and can allow a scaling by choosing the option. The
resulting input can be illustrated. The user is informed about
the illustration and an illustration can be obtained as usually.

   ?   6.3. Finishing the Primary processing. All the objects
necessary for the definition of concentration field are defined
and illustrated. The construction of concentration field is the
next task of processing. The stiffness matrix is formed and the
solving starts. The user is informed about the process of
solving:

The field: 1 is being calculated.
The continuous input has been read out.   

                                                                                                  C"                                                                                     ҇

 number of knots:
 entries of stiffness matrix:

 SOLVING THE SYSTEM:

 forward reduction: @   	         p-++! @"	   	 "o  	 @  0 occupied

0  1219
0 91425 @  	        p-++! @"	   	 "o  	 @    @ occupied

  @   4500
  @ 600000 b  	        p-++  	 	   	        ++! @"	   	 "o  	 b  ԯ
and an indicator shows the amount of computation to be done
for both, forward and backward reduction. This is repeated until
the third concentration field is finished. In this way the
concentration field is constructed for three extinction constants
according to the description in Section 6.1. For each constructed
field the quadratic error is calculated and that concentration
field is chosen which has the smallest error. In the case that
this field correspond to the initial value of extinction constant
(the value in the user's file) the processing proceeds with the
message:

 The prediction for the extinction constant is:  8 days
 @  *	        p-++! @"	   	 "o  	 @  ԌIn the case that the choice is the field with the smaller or
larger value of extinction constant there appears an additional
message informing the user about necessary actions to be
undertaken in order to improve the result. The corresponding
messages can be of the following two types:

Reconstructed fields are insensitive to the variation
of half-life of extinction in the interval (E/2,2E).

The user is advised to repeat the processing with extinction
constant  5.33.

In the case of former message there is no need to repeat the
processing. In the case of latter message the user should insert
the new value of extinction constant into the user file
MANUAL.BAY and repeat the processing after the present session
is over. To avoid a repetition of processing we intend to accept
the predicted value of extinction constant and continue the
processing. From Figure 6.1. we see that there exist four point
inputs. For one of them the input value is fixed and equal 1000
kg/d. The other three values must be predicted from the
surrounding measured concentrations. The user is informed that
these inputs are scaled with the scaling factor 227. Their
precise values will be given at the end of processing. The first
message is about the fit of concentration field to data:

 Measured and calculated concentrations:

 C"                                                                                    E

ppPP00"                                                                             ҇S-station 

  1
  2
    
         p-++  coordinates

  3 23
  5 15   8
        p-++  measured

12.00
11.00   8
        p-++  calculated

12.01
15.76   8
        p-++  differences

 .01
4.76 J  8
        p-++,   
 
 
 
     
        ++J  ԯe.t.c. for the remaining 17 stations. Unfortunately some of data
on concentration on coastal part of boundary are not defined
correctly, so that the concentration field at these Bk-points is
smaller than the field at surrounding points. This disadvantage
is caused in most cases because data are not representative for
the considered stationary transport problem. Data can originate
from various seasons e.t.c. The user must be informed about this
discrepancy of data:

There is a Bi-point at which the concentration field has a
smaller value than the values in its neighbourhood. This can
cause a large error in the mass balance.  Therefore,  you are
advised to change such  point into an S-point and run  the
present  option once more

   ? %  `	`	      FROM THE BEGINNING.pp5  

 `	`	       Such points are:

 E

ppPP00"                                                                            D``"0"                                                                             ҇No. 

1
   *
        p-++  grid coord.

20 11   0*
        p-++  concent.

.160E+02   0*
        p-++  max. concent.

.196E+02 D  0*
        p-++&+**
 
 
    (
        ++D  ԰e.t.c. for the remaining locations. From the list of such Bkpoints it follows that B3 and B4 points in MANUAL.BAY make
trouble. They could be removed in oredr to get rid of this
difficulty. The user is also informed
that the net input from two rivers is 800 kg/d.
 An illustration of the predicted concentration field is
displayed in a familiar way. Therefore, we skip this part of
description. After an inspection of field is finished the user
is informed that results can be documented by using RETRYING:

! b        x x x x          d d j  BUCO.LST                                                      For documentation there can be created (ASCI) HPGL-files of
the
  a) grid for the calculation of concentration field,
  b) reconstructed concentration field.
To create them, you have to run ANCOPOL once more with 
the same option i.e. (2) or (3), and with RETRYING.$  """"@!"$ 
Let us mention that the results of this processing are based on
the data in sediment. Therefore, each input rate has a rather
abstract meaning which is associated with the accumulation
process in sediment. Due to this fact the mass balance is not
carried out for the case an accumulation process.
      In the user's file MANUAL.BAY the data on concentration are
available for both, bottom sediment and the water column. In
accordance with description in Section 6.1. of a utilization of
both types of data the present phase of primary processing
finishes with the estimates of parameters of the accumulation
process from the data on concentration in sediment. Therefore,
the user is informed

 A b        x x x x          d d j  BUCO.LST                                                      You can scale the concentration field in sediment into an
estimate of the concentration field in the water column. $  "" "" A"$ 
and, after accepting this option the user is informed about the
result of scaling. The scaling factor is 0.36. The result of
processing are no more related to the data in sediment but to the
data in the water column. After exiting the code the user has to
run ANCOPOL once more, the option RETRYING. The results of
processing will be related to the concentration field in the
water column.

   ? (#  Secondary processing. This phase of processing starts in the
known way by displaying the mask. After this the user gets an
illustration of the concentration field in water column. One of
the following messages is:
 @  H&        p-++! "  ! "   A @  Ԍ;a b8        x x x x           d d j  BUCO.LST                                              8        The decomposition of the concentration field is a
time-consuming process. The user is advised, therefore,  to
execute this option after the half-life of considered 
substance had been optimized.;$  ""  ""a"$ 
Let us postpone this option until the next section because we
have to describe this important option in more details. Now the
mass balance can be carried out. If the user chooses the option
there follows the following sequence of massages:

   ? `	 The area of the region is* .56E+02 km^2.

For part:  1 of the open boundary,
   ?  the output is equal (plus = out):0 pp5    .94E-03 kg/day.

For part:  2 of the open boundary,
   ?  the output is equal (plus = out):0 pp5    .13E+04 kg/day.

For part:  3 of the open boundary,
   ? h the output is equal (plus = out):0 pp5    .64E+02 kg/day.

For part:  4 of the open boundary,
   ?  the output is equal (plus = out):0 pp5    .31E+00 kg/day.

   ? P Transform. or sedimentation rate:0 pp5    .77E+03 kg/day.

 `	`	 press ENTER to continue

  ""          x x x x 1             a                   ""              1                                                    Figure 1                                          Figure 1                            The mass balance can be calculated also for each rectangular
part of basin. This is the last part of the present secondary
processing. The user is asked wether to proceed with this
possibility by the message

@ b                      d d @  BUCO.LST                                                                     CHECKING MASS BALANCE LOCALLY              
       
The quality of approximate (numerical) solution can be
checked by calculating the mass balance in various
sub-regions of the basin.
@$  ""X""@"$ 
The processing finishes if the user skips the option. Otherwise,
the user can check mass balance for various parts of basin. This
part of processing starts with an illustration of basin with
outlined boundary and filled interior (see Figure 6.4). The
cursor (small cross) is positioned in the middle part of basin
and there appears the message on the top of illustration "Define
the lower left corner by moving the cursor and press ENTER"
informing the user that this part of processing must be carried
out. In the same time there appear a box in the lower right
corner of illustration with the grid coordinates of cursor as in
the picture on the left. The user must imagine a rectangle
covering a part of basin, must move @  *        p-++! "  a  "%   @  Ԍ   ""              1                                                1                                  w  (                  @  d d   BUCO.LST                                          
   (      

	square coordinates:	
	lower left : 31 15 	
	upper right: 52 27 	


w$  ""  gg""  g$     `	     ?              	   d     BBB.TIF                                           
   `	  wL 
   ?   Figure 6.4.  Checking mass
H balance locally.  ,  gg""  gg::  g :", 
 g :" 
 g :" 
 g :" 
 g :" 
 g :" 
 g :" 
$  gg::x::   :"$ 
  :" the cursor to the lower left
  :" corner of this imagined
  :" rectangle and press <ENTER>. Let
  :" us assume that its grid
  :" coordinates are 31 and 15.
  :" Immediately after defining the
  :" lower left corner the previous
  :" message is replaced by another
  :" one: "Do the same with the upper
  ::H
""   right corner". Let these coordinates be 52 and 27. Hence, the
coordinates are the same as in the picture on the left hand side.
If the mouse is available the cursor is moved by mouse. If a
mouse is not available to move the cursor the user can use any
of keys with arrow or <PgUp>, <PgDn>, <Home> and <End>. If the
user tries to define a too large rectangle there appears the
message "The square cannot be enlarged. Press any key to
continue.", so that the user has to diminish the rectangle after
this message. After the rectangle is defined the user reads
information about inputs and follows instructions. If the
rectangle is defined as mentioned there appear six boxes with
information about Bkpoints, Qkpoints, Fkpoints, input from
atmosphere, sedimentation rate and net mass balance for the
defined rectangle. After checking mass balance locally at several
locations of basin the users finishes this part of processing and
exits ANCOPOL.
                  1                                ""              1                                   There is a file INFORM.AUX created during the processing so
that the use can edit this file, or save it to another directory,
for a later use during the composition of report. Such file is
created anew during any RETRYING (secondary processing). In the
present case this file has the same content after each RETRYING.
However, in some cases the content of this file is changed as
described in one of next titles.

   ?    6.4. Continuous input of substance through coastal boundary.
In order to describe some other possibilities of processing with
   ? ! ANCOPOL we intend to process the same set of data with the same
definition of numerical mesh, but without currents. In addition,
we wish to demonstrate the possibility of defining the continuous
flux of substance through the boundary. Therefore, the user is
asked to edit DOC\MANUAL.BAY to move to the last line of file and
omit x in front of xBC, of the last line. The new form of the
last line of this file must be

BC,

in accordance with description of data in Chapter 3., Section
3.4.
 Let us start ANCOPOL, the option (2) with nonretrying. In @  *
         p-++! g	  
 :"N   
 @  this case all information from the previous processing is erased.
Hence, the processing starts from the beginning and a part of
previous steps must be repeated, again. It is important for the
present discussion that all the boundary conditions at open
boundary are zero gradient conditions. Hence, the user must
choose the option "G" in defining these conditions. After the
user finishes an inspection of input distribution from
atmosphere, before the grid is displayed there appear the
following message
  ""              1                                ""              1             A                   
( b8                      d d #r  BUCO.LST                                             x8        Data on continuous input are not included yet. The other
data, relevant for the concentration field are illustrated,
first, in the following display.                         
($  """""$ 
Then the grid is illustrated. This grid contains two objects less
than in the previous case, and they are the Bkpoints at two
river mouths. River flows are not used in the present case and,
therefore, there is no need to define concentrations at these
locations. After pressing <ENTER>, the user is informed that the
continuous input must be defined along the coastal part of
boundary. Let us point out that it cannot be defined along a part
of open boundary. The next screen is a brief rehearsal of the
procedure to be used in defining the continuous input. The
continuous input extends along a connected part of coastal
   C  boundary beginning at some point xB  Bc and ending at a point xE
   C   Bc. Only one piece of such input can be defined. There are
three functions for this purpose, B(eginning), S(ampling) and
E(nding). When the user presses <ENTER> there appears an
illustration of basin as in Figure 6.5. The user must move the
   C  cursor to the point xB, press <B> and move along Bc until reaching
   C  the first sampling point xS (see Figure 6.6), where the
concentration must be defined. At this point the user presses
<S>. Immediately there appears a small window in the middle
location of right margin asking the user to enter the value of
concentration. The users enters the value presses <ENTER> and
   C  proceeds with the sampling until the point xE. At this point the
user presses <E> and the screen disappears. The continuous input
is defined. The result can be seen on the next screen where the  0  T        p-++ "   0  Ԍ H
ř     p                   	$  s Y     AAA.TIF                                              p  ?#rJ 

   ?  Figure 6.5. Starting to define
a continuous input.  $  ""  ""   $     
O     ?              ?.  d d     AAA.WPG                                              
  wp^    ?    Figure 6.6. The beginning and
endpoint of continuous
 input.    ,  ""    ",   " H
  " 
  ""   illustrated numerical mesh contains all previous objects and
additionally Bkpoints which are defined by the described
procedure. These additional points of input are treated
equivalently with the other Bkpoints so that the remaining part
of processing is the same as in the previous case. When the
concentration field is constructed and illustrated the user is
asked about performing a new procedure which must be described
in more details.

   ?   6.5. ANCOPOL and diffuse input. Basic notion and methods for
a decomposition of the diffuse input are given in Section 6.1.
   ?  In ANCOPOL this procedure is implemented in the following way.
The input is defined by means of input from atmosphere, by input
through the open boundary, by Qkpoints, and Bkpoints. If there
is no Bkpoints the net input can be easily obtained by summing
all the inputs into the basin. The same is true if only one Bkpoint is defined. In this case the input can be obtained by the
simple rule. First we calculate the input from this Bkpoint by
using the equation: input from Bkpoint = output from the basin
  input into the basin. This input must be added to the other
input terms in order to get the net input into the basin.
However, in the case of more Bkpoints this simple rule cannot
be applied. Therefore, the user must divide Bkpoints into groups
belonging to the same source. There can be 9 groups at most. All
Bkpoints belonging to the first group are denoted by B1, those
belonging to the second group by B2, e.t.c. The decomposition of
input means a representation of input by a sum of component
inputs where each component corresponds to one of defined groups.
Hence, there must be 2 groups of Bkpoints at least to carry out
the decomposition of diffuse input. In accordance with the
description in Section 6.1 the decomposition can be preformed
only if the boundary conditions are zero gradient, zero flux or
fixed concentration equal to the natural concentration. This is
the reason that the decomposition could not be carried out in the
previous processing. One of boundary conditions did not match
this rule (3 ppb along the third part of open boundary). In the
present case the boundary conditions are zero gradient and a
decomposition is enabled. It starts with the message:  ""              1                                ""          x x x x 1                                 @  *        p-++! &    "    @  ԌL b8        x x x x           d d   BUCO.LST                                              8          The decomposition of the concentration field is a time 
consuming process. The user is advised, therefore,  to execute 
this option after the half-life of considered  substance had

	 been optimized.L$  ""  """$ 
We assume that the user chooses the option. The next message is

The number of groups of Bi-points is equal 5.

The user is informed again about Bkpoints for which the
concentration is less than at surrounding gridknots. It is
stressed that this may cause an error in the mass balance. The
decomposition is carried out by solving certain systems as
described in Section 6.1. Therefore, the user has to wait until
the solver finishes. The next message is

The number of point sources is 4 and their total input is 1000
kg/day.

Let us remind that the scaling factor for three point inputs is
zero. The following question about mass balance is familiar from
the previous description:

  b8        x x x x          d d   BUCO.LST                                                      1	 Do you wish to calculate the mass balance? $  """"X"$ 
It is assumed that the users proceeds with the calculation of
mass balance. There appears a number of messages regarding values
of output and input through various parts of the open boundary
as described previously. However there is one new notion. The
user is informed that the relative error of decomposition is
around 16%, a quite large value. There is a suggestion that this
large value can come from a large gradient of concentration field
at open boundary. We know that it cannot be the reason because
all the boundary conditions are zero gradient conditions. The
actual reason is already mentioned two times. There are 11 Bkpoints for which the concentration field is less than at
neighbouring grid knots. In principle, the user should edit file
MANUAL.BAY, correct values at these Bkpoints and process data
from the beginning. We intentionally disregard this suggestion
and proceed with the processing. The user can check the mass
balance locally.
 The last function of processing is an illustration of
   ? # component concentration fields. The concentration field c(x) on
D is decomposed as
   C %  #b0*      d d d d d       
#  d d w                                                       b    `+ (6.6)      L c( bold x) ~=~ c sub 0( bold x) ~+~ sum from {j ~=~1} to M c
sub j( bold x),x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       c      c    M    r+ j     
 c     j        (      z )      0       (       )     + 1       (      	 )      B
 ,      x     Z x     R	 x      J             +        I ߚ$  ""%""!"$ where co(x) is caused jointly by input from atmosphere, Fkpoints
   C 4* and Qkpoints, while each ck(x) is defined exclusively by the
corresponding group of Bkpoints. Sometimes it is important to P   +        p-++1 "   8"   0*"~-   P  illustrate each component and save a document about it, such as
a HPGPfile. Therefore the user is informed and asked

P! b(        x x x x          d d   BUCO.LST                                              (        There follows an illustration of that component-field which
is induced by any/all of the sources:
      a) input at F-points,
      b) the total input/output through the open boundaries,
      c) input at Qi-points.P$  ""X""x!"$ 
and immediately after this message the user is informed that the
component 0 of the total field is illustrated. Hence the
   C (
 component co(x) of (6.6) is illustrated by isolines, in colours
and corresponding documents can be saved. Otherwise, this part
is skipped. The next question is

aA b8        x x x x           d d   BUCO.LST                                              8             The last step of processing consists of a sequence of
  illustrations each representing one component-field. This
process ends after your first negative reply to the question:
          "Do you wish to illustrate these fields?"a$  ""L
""A"$ 
Again, if the answer is affirmative there appears an illustration
   C  of the concentration field c1(x) as in the previous case. In the
case of negative answer the processing exits to DOS. Each
   C   component field ck(x) can be illustrated and documented. Some of
   C  component fields ck(x) can be trivial, ck(x) = cB, where cB is the
background or natural concentration. Such components are skipped.

   ? H  Other possibilities. The file COMPLEX.BAY which is created
during the installation of packages does not contain data which
are generated with a caution, i.e. in a realistic manner. Rather,
data are arbitrary so that a lot of erroneous tries and dead
alleys are met during a processing of data from this file. At
each such incorrect or meaningless step of processing the user
is informed about errors, advised what to do, and the processing
aborts. Therefore, at such interruption the user must edit
COMPLEX.BAY remove erroneous records and continue the processing
by using retrying. After finishing a processing of data in 
COMPLEX.BAY starting with any of two saved initial configuration
   ?   a user can get a better insight about abilities of ANCOPOL.
 For a detailed analysis of pollution obtained results can
be additionally processed by methods which are not included in 
   ? 8# ANCOPOL. Such are the calculation of blooming, input from one
layer into another, resuspension from sediment into the water
column e.t.c. If the structure of generated files in a session
is known such additional processing can be carried out by user.
A basic description of several files is given in Chapter 8. Also
   ?  ' available extensions of ANCOPOL containing such functions can be
obtained from the author.  @  '        p-++! "/  ! "3  A @     ?     7. APOSTERIORI ANALYSIS BY COMPARING DATA AND MODELLING
   ?   a) RESULTSă

   ? X  7.1. Statistical description in terms of the nonlinear
   ?   regression analysis. 
 So far the results obtained by modelling the transport are
based on deterministic models such as current models and
transport model. The underlying assuming is that the data
represent the transport process in the considered basin. Now,
this assumption must be verified aposteriori by comparing the
model solution and data and by checking the existence of possible
nonconsistences.
 We are familiar with linear regression analysis as a method
   C (
 to smooth data. Suppose we have N measurements {xk,ck}, k =
   C 
 1,2,...,N, of the concentration c at sampling points xk along a
line. Very often we try to smooth the data by fitting a
   C  polynomial Pn(x) = ao + a1x +  + anxn of some order n to this
data set. This polynomial is called the regression curve and
usual presentation of results consists of a joint illustration
of the data and the regression curve. There are problems for
which the polynomial coefficients have nontrivial physical
interpretation like in the case of bending a bar. This follows
from the simple fact that the solution of an ideal bar subjected
to forces is a polynomial of the forth order. In such cases the
   C  polynomial Pn(x) is not merely a device to present the data. It
is the fundamental object of an interpretation of the data. In
case of a concentration field resulting from the transport in a
basin, polynomial coefficients are rather useless for an
interpretation of data. Instead of a polynomial one has to use
solutions of transport models. Precisely this approach is carried
   ?  out in modelling the transport which is implemented into ANCOPOL.
Instead of polynomial coefficients we have transport parameters
such as input rates, extinction coefficients, advection etc. The
fitting problem is nonlinear so that the relevant regression
analysis is called nonlinear regression analysis. The last step
of processing is the preparation of results for a statistical
   C 0 analysis of deviations ck  c(xk) of measured concentrations ck
   ?  from the model predicted concentration field c(x) at sampling
   C  stations xk. This simple plan is available by the code POSTANIS.
The basic two statistics to be used are the mean concentration
field and standard deviation. The mean concentration field is
predicted by modelling the transport (using ANCOPOL). Then the
standard deviation is estimated from a statistical model and by
using the linear least square method (LLSE).
 Let us use the following notation

   C $   cm = the sediment sample concentration at xm, m =
1,2,...,N,
   ? %   c(x) = the average or mean concentration field at x,
   ? d&   %(x) = the standard deviation at x.
   C ,'   cest(x) = concentration field estimated from the data cm.

 Since the concentration field depends on location in the
   ? ) basin, the two statistics are functions of position x. To get rid
of this dependence the measured values are reduced to the same
mean value and standard deviation by using the following   +        p-++  statistical model
   C   C! #bsx      d d d d d       <  d d w                                                       b,            ] { sigma ( bold x)} over { c( bold x)} ~=~ func
{const},~~~~~~~~ func { for ~~ all} ~~ bold x.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@     ?        \ %       (      )       8 (      8 )       const       ,      	 for      0 all      
 .     Sx     O8 x     H
 x     _ 8 c        C$  "" "" !!"$ Instead of sample concentrations cm we use the nondimensional
concentrations
   C | A #b,
      d d d d d          d d w                                                       b,         V     5 xi sub m ~=~ { c sub m } over { c ( {bold x} sub m)}.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      !        m     cc    |/m     D_ c    + m      9 E     '      _ (      _ )       .     4_ xV $  ""|""!A"$ The variables m are realizations (measurements) of the random
   ? 0
 field (x) with the mean value or expectation E[(x)] = 1. Its
variance can be estimated in the standard manner,
   C  a #bp      d d d d d       P#  d d w                                                       b,   `A
 (7.1) :      func{ Var}`` [`` xi ``] ~ SIMEQ ~ 1 over {N} ~ sum from
{i``=``1} to N ~ left ( {`} from {`} to {`} xi sub i~~1``
right ) sup 2.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      !  Var       [       ]      <1     + 1      	 1     
z2      
 .      Y               s     *+        
            I      vx g      F
x n     _ N    *N    + i    * i: $  """"!a"$ Let us point out that the random variables m = (xm) are
dependent so that the proposed statistics defined by (7.1) must
be theoretically justified.
 After estimating the nondimensional concentration field
   C  (x) from all the data m we can write down the field
 #bH      d d d d d          d d w                                                       b    `	 (7.2) w     5 c sub {est} ( bold x) ~=~ c( bold x ) `` xi ( bold x)x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      _ c     + est     
_ c      z_ (      j_ )      _ (      r_ )      _ (      v_ )     _ x     _ x     _ x      :_       _ w $  """"X!"$ Then the following two derived fields are calculated and
illustrated
o #b0      d d d d d         d d w                                                       b    `w (7.3)      } d ( bold x) ~=~ c sub {est} ( bold x) ~~ c ( bold x),
~~~~~~~~ r ( bold x) ~=~ {c sub {est} ( bold x) } over { c (
bold x)}.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@     !  d     ) c     est     ! c     9 r     |<c    est     8 c        (       )       (       )       (       )      	 ,       (      
 )      <(      <)      l8 (      \8 )      i .      x     	 x      x     )
 x     \<x     8 x      Y       Q       q C     _  o$  """" !"$ They are called the deviation from the mean concentration field
and ratio of estimated and mean concentration fields,
respectively.

   C   The interpolation method. The method to estimate cest(x) which
is used here is a slightly generalized Linear Least Square
   C T Estimation (LLSE). By the standard LLSE the field cest(x) at a
   ?    grid-knot x is estimated by using a linear estimator of data. Let
   C   there be M sampling stations at x1, x2,..., xM, and corresponding
   C ! data c1, c2,..., cM. Then the estimated field is given by the
expression
   C H# p #b'      d d d d d       #  d d w                                                           `O (7.4)       c sub {est} ( bold x) ~=~ sum from {k``=```} to M ~ w sub m (
bold x) ~ c sub m , ~~~~~~~~~ sum from {k``=``1} to M ~ w sub
m ( bold x) ~=~ 1.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       c      est    VM    
+ k      w     m      c     m    M    k+ k     $ w     m      z (      j )      N (      > )       ,     E
+ 1       (       )       1       .      x      x     i x      :      w+      +               I       I p$  ""H#""!"$ The weights wm(x) are obtained from a system of linear algebraic
equations, which characterize the method. However, some estimates
   C ( wm(x) can be negative and, consequently, the estimated values
   C ) cest(x) at some knots x can be also negative. To avoid such
disadvantages, one has to add the additional constraints:   \*        p-++a x"N  ! ,
"P
  A p"  a H"h   0"-   '"F+     a #b      d d d d d       
   d d w                                                           `
 (7.5)      5 w sub m ( bold x) ~ >=~ 0, ~~~~~~~~~ m ~=~ 1,2,...,M.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@      _ w     + m     w_ m     _ M       _ (      _ )      o_ 0      _ ,      	_ 1      	_ ,      
_ 2      
_ ,      
_ .      o_ .      _ .      __ ,      O
_ .     W_ x      _       G_  a$  ""  ""X!"$ The system (7.4), (7.5) is a generalization of the standard LLSE.
 The described method is implemented into the code POSTANIS
   ?  as follows. For each knot x the number of data, M, to be used is
   ?  not larger than 20. They are chosen by encircling the knot x by
a circle so that 20 data at most is encompassed. Then these data
are used in the course of solving the problem (7.4), (7.5).
   C   The estimated field cest(x) has values not larger than the
   C  maximum and not smaller than the minimum measured value m. If
the number of data is zero in the maximum allowed circle the
estimation cannot be performed and such grid-knots are excluded
from the presentation. Therefore, the estimated concentration
fields can be realized on a smaller region than the original
region.
   C   The reliability of the estimated field cest(x) can be also
   ? T
 calculated and illustrated. Let us define the variance v(x) =
   C  Var[cest(x)  c(x)]. It is estimated by LLSE as described in this
section. Now we use the Tschebishev formula
 #b`      d d d d d       :  d d w                                                       b    `L (7.6) E      func {bold P} ``left \{ ``  line {~} from {~} to {~} c sub
{est} ( bold x) ```` c ( bold x ) ``  line ~> ~ sigma ( bold
x)`` right \} ~<~ 1~~ {v( bold x)} over { sigma ( bold x )
sup 2}.x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@     !  P       m       m  0     M       0 	              	      _
       c    P est     x c     1v      @ (      0 )       (       )      , >      {	 (      k
 )       <       1      
1(      1)      8 (      8 )     Qz 2       .      x     h x     	 x     1x     a8 x       %      j8 %E $  """" !"$ The right hand side of this inequality is a function depending
on points of the basin and accepting the values in the interval
[0,1]. We can illustrate this function by isolines and get the
following probability interpretation of the estimated field
   C  cest(x):
  The estimated values are exact at the sampling stations.
   C    Otherwise, the value of estimated field, cest(x), differs from
   ? P the mean concentration field, c(x), by the value less than the
   ?  one standard deviation, %(x), and the probability of the event
:! #b      d d d d d       
   d d w                                                       b             H line`` c sub {est}( bold x) ~~ c ( bold x) ``line ~<=~  sigma
( bold x)x 6X   @8; X@x 6X   @8; X@x 6X   @8; X@       _ 	      _       _ 	      :_       _ c    + est     _ c      _ (      _ )      _ (      _ )      _ (      y	_ )     n_ x     v_ x     	_ x      
_ % :$  """"X!!"$ is illustrated in POSTANIS by using isolines.

   ?   7.2. POSTANIS and aposteriori analysis of modelling results.  ""          x x x x 1             A                   ""          x x x x 1             A                   
 When the user finishes the processing by ANCOPOL the
comparison of modelling results and data can be carried out and
consequently check wether the data are representative for the
postulated transport model. The user has to start POSTANIS. The
first screen is a known mask like in previous codes. The first
new information for the user is the screen with the message

 a b(        x x x x          d d   BUCO.LST                                                           The first step of processing is an estimate of the
 concentration field from data. This process takes some time. $  ""$"" a"$ 
In the next screen the user has to answer to `  '         p-++A "   `"\   "   ! ("+  a `   b        x x x x        X  d d   BUCO.LST                                                    An evaluation of the quality of estimated concentration field
can be obtained by a probabilistic interpretation of this
	 field.$  ""  """$ 
and we assume that the user accepts the suggestion. The
processing continues with the information that a probabilistic
interpretation will be available and the process of estimation
is carried out for each gridknot according to (7.4), (7.5). The
actual number of used data is written on the screen for each
gridknot by the message of the form

 grid coordinates    numb. of data
   ? 
  6 17`	`	    hh% 12

This part of processing finishes with the illustration of the
   C H
 estimated field cest(x) of Expression (7.2). Now the user is
informed that the difference between the estimated concentration
field and the mean field of (7.3) is illustrated. The
illustration is given in the standard way. After finishing it the
user is asked

  b        x x x x          d d   BUCO.LST                                                       You can get an illustration of this field once more with
 another set of isolines. Choose the option and execute it. $  """" "$ 
and the same field can be illustrated by another definition of
isolines. The possible number of repetitions is not limited. A
similar procedure is carried out with the nondimensional field
   ? < r(x) of (7.3). Again, this field can be illustrated repeatedly
with variously defined isolines.
 The last step of processing consists of an illustration of
a probabilistic interpretation of the obtained results by using
the Expression (7.6). The user is informed

" b!        x x x x        X  d d   BUCO.LST                                                        The field of probability values can be illustrated by using
the probability isolines. You are advised to define the values
                equal to 0.25, 0.5 and 0.75."$  """""$ 
The processing of POSTANIS finishes with the desired illustration
of probability isolines. P  d"        p-++1 "3   "{   !"%   P     ?     8. TEMPORARY FILES CREATED DURING PROCESSING

   ?   8.1. Temporary and permanent files. All three packages,
CURRMOD, ANCOPOL and POSTANIS consists of a sequence of modules
which can be executed successfully if the data are prepared
correctly in relevant "input files". A successful execution
results in creating one or more "output files". Most of these
input and output files are auxiliary files (having the extension
AUX). They are erased at the beginning of each primary
processing.

   ?   Fixed parameters of the processing. There are 13 or 14 files
with the extension *.DAT:
 INDCOL.DAT: The first two integers of the first row are the
colour indices of the textcolour and backcolour in the text mode.
The remaining three indices define the graphical mode colours for
filling the basin, for filling the Bpoints in the basin and the
colour of arrows indicating the current direction. Two integers
in the second row are the colour indices of the textcolour and
backcolour of HELP messages.
 MESSAGE.DAT: This file contains the messages which appear
on the screen during the processing.
 DOSHLP01.DAT  DOSHLP11.DAT: These files have the same
function as the file MESSAGE.DAT.
 NOBEEP.DAT: If this file exists there are no sound signals
(beeps) during the processing.
 The first 13 files are generated during the installation.
The last one can be created or erased at the beginning of
processing by any of the codes.
 The parameter values of the file INDCOL.DAT can be changed
eventually by editing this file or in the following way:
  the user has to erase all *.AUX files,
  pkunzip *.AUX files from acpl0301.zip,
  pkunzip BOJE.EXE file from acpl0301.zip,
  run BOJE.EXE and make desired changes.

   ?    Auxiliary files. Various biochemical processes can be
studied starting from the predicted concentration fields and/or
mass balance. However, in order to use the results of processing
the user should know the structure of auxiliary files and the
format of data recorded in these files. The most important ones
are described in the remaining part of this section.
 Before we begin with description of the files it is useful
to remind the user that two coordinate systems and two units are
permanently utilized in the course of processing. The user
coordinate system is utilized to define the geometry of the
considered basin and all the relevant objects. The corresponding
units are called the user's units. They are always scaled to
kilometres. The grid coordinate system is defined by the frame
cutting a rectangle from the user's map. The origin of the grid
coordinates is the lowerleft corner of the frame. Its
coordinates are x = 1, y = 1. The units of the grid coordinate
system are called the grid units.
 DOMAIN.AUX: In the first row the user's file is specified.
In addition, if the processing is a repetition of some earlier
successfully finished processing the integer 1 is contained in   *        p-++  the 40th column of the first row. The second row consists of two
integers M, N and three reals, cs, sn and scl. The first two
integers are the proposed numbers of knots in the x and ydirection of the frame. They are usually diminished during the
grid optimization. The numbers cs and sn are the cosine and sine
of the rotation angle of the frame compared to the user's
coordinate system, and scl is the scaling factor, associated with
the code U in the user's file. The third line contains the
coordinates of that point in the frame from where the filling
starts.
 IZVOR.AUX: The first line contains the three integers and
three reals, M1, M2, N, Xm, XM, Ym. Here, M1 and M2 are the
numbers of knots in the x and ydirection of the grid coordinate
system, N is an integer, Xm, Ym are the user coordinates of the
lowerleft corner of the frame, and Xm is the xcoordinate of the
lowerright corner, measured in the user units. Thus, a grid step
has 1 grid unit (non dimensional) and (XMXm)/(M11) user units
(kilometres). The integers M1, M2 are in principle smaller than
the integers M, N of DOMAIN.AUX due to the grid optimization. In
the second row there are 11 integers which are not important for
the present discussion. All the remaining rows represent the
mosaic of the frame. There are M2 such rows. The mosaic consists
of numbers 0 (outside of the basin), 1 (inside the basin) and 3
(open boundaries). The first row of mosaic (3th row of the file)
describes the gridknots from the lowerleft corner to the upper
leftcorner i.e. the left boundary of frame. The last row of
mosaic defines the right boundary of frame.
 Here is an example of the described file:

  45  30   1   0.132900E+01   0.621000E+01   0.650300E+01
   1  45  30
000000000000000000000000000000
000003333333333333333300000000
000001111111111111111100000000
000001111111111111111111000000
000001111111111111111111000000
000001111111111111111111000000
000001111111111111111111000000
000001111111111111111111100000
000000111111110111111111100000
000000111111100011111111100000
000000111111110001111111110000
000000111111110001111111110000
000000111111110001111111111000
000111011111111111111111111000
000111111111111111111111111000
000111111111111111111111110000
011111111111111111111111110000
011111111111111111111111110000
011111111111111111111111100000
001111111111111111111110000000
001111111111111111111110000000
001111111111111111111100000000
031111111111111111111111110000
031111111111111111111111110000
031111111111111111111111110000   *         p-++  Ԍ031111111111111111111111110000
031111111111111111111111110000
031111111111111111111111110000
031111111111111111111111111000
031111111111111111001111111000
031111111111111111000111111000
031111111111111111000111111000
031111111111111111000011111130
031111111111111111000011111130
031111111111111111000011111130
031111111111111111000000111130
031111111111111110000000000000
001111111111111110000000000000
001111111111111111000000000000
000001111111111111100000000000
000001111111111111100000000000
000001111111111111110000000000
000011111111111111110000000000
000033333013333113330000000000
000000000000000000000000000000

 SLOJ.AUX: The real number contained in this file is the
average depth.
 GRANICA.AUX: The natural boundary is digitalized and
presented by pieces of straight lines. The grid coordinates of
the beginning and end of each straight piece is recorded, one
after the other. All the coordinates are given in the grid unites
(of the grid coordinate system).
 ADJUST.AUX: The first line contains two integers and three
reals, M1, M2 and r1, r2 and r3. Here, M1 and M2 have the same
meaning as in IZVOR.AUX. The real numbers r1 and r2 are the
minimal and maximal value of frame in the x direction. The real
number r3 is the minimal value of frame in the y direction. The
second line contains 12 integers, Io,I1,...,I11. The first one
defines the number of Gpoints, the following 9 integers define
the number of Ckpoints, the 11th integer is abundant, and the
12th integer defines the number of Fpoints. The remaining M1
rows represent the mosaic of the numerical mesh of current
modelling. The mosaic consists of numbers 0 (outside of the
basin), 1 (inside the basin), 2 (on the coastal boundary) and 3
(open boundaries). There follows Io rows containing the data on
velocities for the general measuring stations, i.e. Gpoints;
then Ik rows containing the data on velocities for Ckpoints, k
= 1,2,...,9. Apparently, the number of these rows is equal to Io
+ I1 +...+I9. At the end there are I11 rows associated with the
Fpoints. The file ADJUST.AUX corresponding to the previous
example of IZVOR.AUX has the following form:

  45  30  0.13290E+01  0.62100E+01  0.65030E+01
   0   1   0   0   0   0   0   0   0   0   1   0
000000000000000000000000000000
000003333333333333333300000000
000002111111111111111200000000
000002111111111111111222000000
000002111111111111111112000000
000002111111111111111112000000   *         p-++  Ԍ000002111111111111111112000000
000002211111122211111112200000
000000211111220221111111200000
000000211111200022111111200000
000000211111220002111111220000
000000211111120002111111120000
000000221111120002111111120000
000000021111122222111111120000
000222221111111111111111120000
000211111111111111111111120000
002211111111111111111111120000
002111111111111111111111220000
002111111111111111111122200000
002111111111111111111120000000
002111111111111111111220000000
002111111111111111111200000000
032111111111111111111222220000
031111111111111111111111120000
031111111111111111111111120000
031111111111111111111111120000
031111111111111111111111120000
031111111111111111111111120000
031111111111111112222111122000
031111111111111112002211112000
031111111111111112000211112000
031111111111111112000221112000
031111111111111112000021112000
031111111111111112000021112000
031111111111111112000022222000
031111111111111122000000000000
032111111111111120000000000000
002111111111111120000000000000
002222111111111122000000000000
000002111111111112200000000000
000002111111111111200000000000
000002111111111111200000000000
000002222221111111200000000000
000000000023333222200000000000
000000000000000000000000000000
  15  22 -0.15273E+01  0.40896E+00
  44  18  0.00000E+00   1

 OPBOUN.AUX: Each row has 6 integers Bx, By, Dx, Dy, I and
No, then 2 reals r1, r2, and finally 2 integers in the 9th and
10th columns. The interpretation of the first 6 integers is as
follows: Bx, By are the grid coordinates of one of the end points
of the considered open boundary, Dx, Dy define the direction of
the boundary, I is the indicator of forward or backward
direction, and No is the number of intervals contained in the
considered part of open boundary. The integer in the eighth
column can have the value 1 or 1. The former value defines an
outflow and the latter one an inflow through this boundary. The
integer in the ninth column can have the value 1, 2 or 3. This
value defines the uniform, halfsine and full sine profile of the
normal component of velocity at the considered part of open
boundary (see Figure 5.1). The integer in the last column can   *        p-++  have the value 0 or 1. In the former case the value of flow is
defined in the 7th column, while in the latter case the value
of normal velocitycomponent is defined.
 It should be stressed that some of the data on the open
boundaries could be ignored. The accepted open boundaries are
defined in REST.AUX. The following file OPBOUN.AUX corresponds
to the previous file IZVOR.AUX:

  23   2   1   0   1  14  5.000E+02  -1   2   0
  33  29   1   0   1   3  0.000E+00  -1   1   0
   2   6   0   1   1  16  5.000E+02   1   2   0
  44   5   0   1   1   4  0.000E+00  -1   1   0
  44  12   0   1   1   3  0.000E+00  -1   1   0
  44  18   0   1   1   2  0.000E+00  -1   0   0

 REST.AUX: Each row has 6 integers, 2 reals and one integer
in the last column. The first 6 integers have the same
interpretation as in OPBOUN.AUX. The last integer defines the
type of velocity profile as in the case of OPBOUN.AUX.
 The following file REST.AUX is associated to the previous
file OPBOUN.AUX:

  23   2   1   0   1  14  -0.4734E+02  -0.1000E+01   2
   2   6   0   1   1  16   0.4694E+02   0.1000E+01   2
  44  12   0   1   1   3   0.0000E+00  -0.1000E+01   1

 DRAGA.AUX: The components of velocities corresponding to the
knots in ADJUST.AUX are recorded in this file. The velocities are
recorded in the following way. To the first row of mosaic in
ADJUST.AUX there correspond M2 vxcomponents of the velocity and
M2 vycomponents. These components are written in the format
10E8.2. The same procedure is repeated for each row of the file
ADJUST.AUX. Thus, the file DRAGA.AUX corresponding to the above
examples has altogether 6 times M1 rows. The first 12 rows
contain the information on velocities associated to the first and
second rows of the file ADJUST.AUX. We could not present here all
10 velocities in each row because of the limited page width.
Therefore, we had to cut the right margin of the file DRAGA.AUX
and give here only 7 velocities of each row instead of 10
velocities:

0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00-.30E+00
-.41E+01-.47E+01-.51E+01-.52E+01-.51E+01-.47E+01-.41E+01
-.30E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00
0.00E+000.00E+00-.48E-060.24E-06-.95E-06-.48E-060.95E-06
0.00E+000.00E+000.00E+000.00E+000.00E+000.00E+000.00E+00

It is clear that the first 6 rows of this file contain only zero
values. These values define velocities at the knots of the first   *        p-++  row of ADJUST.AUX and we see that these knots are outside of the
considered basin.

 ZATON.AUX: The first line contains two integers and a real,
M1, M2 and st. Again, M1 and M2 have the same meaning as in
IZVOR.AUX. The real number st has the value equal to the value
of grid step in the user units, i.e. st = (XMXm)/(M11) km. Now
we have the mosaic of the region defining the numerical mesh for
the calculation of the concentration field. After the mosaic
there follows a line with values of eddy diffusion constant,
extinction constant, the background concentration and some other
parameters. The following line contains 5 integers, N1,
N2,...,N5. The first one counts Bkpoints, the second one Qkpoints, and the third one Spoints. The corresponding
coordinates, concentrationvalues and input rates are given in
the continuing N1, N2, and N3 rows, respectively. The first two
numbers in each of these rows are coordinates. The third number
is the value of concentration or input rate (in certain internal
units). In case of the first two groups (N1 + N2) the fourth
number is the value of k in the codes Bk and Qk, respectively.
The following example of ZATON.AUX is associated with the file
IZVOR.AUX which is illustrated in this section:

  45  30 0.1109E+00
000000000000000000000000000000
000002222222222222222200000000
000002111111111111111200000000
000002111111111111111222000000
000002111111111111111112000000
000002111111111111111112000000
000002111111111111111112000000
000002211111122211111112200000
000000211111220221111111200000
000000211111200022111111200000
000000411111420002111111220000
000000211111120002111111120000
000000221111120002111111122000
000222021111122222111111112000
000212221111111111111111122000
000211111111111111111111120000
022211111111111111111111120000
021111111111111111111111220000
022111111111111111111122200000
002111111111111111111120000000
002111111111111111111220000000
002111111111111111111200000000
044111111111111111111222220000
041111111111111111111111120000
021111111111111111111111120000
021111111111111111111111120000
021111111111111111111111120000
021111111111111111111111120000
021111111111111112222111122000
021111111111111112002211112000
021111111111111112000211112000
021111111111111112000221112000   *         p-++  Ԍ021111111111111112000021112220
021111111111111112000021111120
021111111111111112000022211120
021111111111111122000000222220
022111111111111120000000000000
002111111111111120000000000000
002222111111111144000000000000
000002111111111114200000000000
000002111111111111200000000000
000002111111111111220000000000
000002112241111111120000000000
000002222044222222220000000000
000000000000000000000000000000
   0.272497E+05   0.802254E-07   0.300000E+01   0.102020E+02
  11   2  24   0   0
  11  13 0.2200E+02   1 0.0000E+00 0.0000E+00
  11   7 0.9000E+01   1 0.0000E+00 0.0000E+00
  23   2 0.5300E+02   2 0.0000E+00 0.0000E+00
  44  11 0.2300E+02   3 0.0000E+00 0.0000E+00
  39  18 0.7500E+01   4 0.0000E+00 0.0000E+00
  23   3 0.5300E+02   2 0.0000E+00 0.0000E+00
  24   2 0.5300E+02   2 0.0000E+00 0.0000E+00
  39  17 0.7500E+01   4 0.0000E+00 0.0000E+00
  40  18 0.7500E+01   4 0.0000E+00 0.0000E+00
  43  11 0.2300E+02   3 0.0000E+00 0.0000E+00
  44  12 0.2300E+02   3 0.0000E+00 0.0000E+00
   3  17 0.8327E+02   0 0.0000E+00 0.0000E+00
  34   3 0.4163E+00   1 0.0000E+00 0.0000E+00
  33   2 0.3370E+02   0
  35   5 0.3899E+02   0
  37   8 0.3620E+02   0
  38  11 0.2630E+02   0
  39  14 0.2000E+02   0
  28   6 0.3490E+02   0
  29   9 0.3400E+02   0
  30  12 0.3440E+02   0
  31  16 0.3610E+02   0
  20   8 0.2330E+02   0
  21  12 0.2180E+02   0
  22  15 0.1950E+02   0
  23  19 0.3400E+02   0
  29  24 0.2380E+02   0
  13  11 0.1320E+02   0
  14  14 0.1320E+02   0
  15  17 0.5970E+02   0
  16  21 0.2860E+02   0
   2   9 0.2140E+02   0
   5  13 0.1690E+02   0
   6  16 0.2220E+02   0
   6  19 0.2480E+02   0
   8  23 0.5030E+02   0
   2  17 0.7560E+02   0

 OPBOVAL.AUX: This file is completely analogous to the file
OPBOUN.AUX which is already described. For each part of the open
boundary there is a row in the considered file. Each row consists   *        p-++  of 6 integers, a real, and an additional integer. The first 6
integers have the same meaning as in the file OPBOUN.AUX.

 REZUL.AUX: The calculated concentration values at gridknots
are written in this file. This file has the structure similar to
the file DRAGA.AUX in which velocities at gridknots are
recorded. In the example which is used here the 13 beginning rows
of REZUL.AUX have the following form:

  0.1050E+02  0.1796E+03  0.1604E-06   0
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01
0.839200E+020.839200E+020.849500E+020.871200E+020.905600E+02
0.954000E+020.101770E+030.109800E+030.119900E+030.132700E+03
0.150500E+030.179600E+030.155600E+030.143200E+030.136300E+03
0.133000E+030.133000E+030.300000E+010.300000E+010.300000E+01
0.300000E+010.300000E+010.300000E+010.300000E+010.300000E+01

In the first row we have the minimal and maximal value of
calculated concentration field, and value of some other two
parameters. In the remaining rows we have concentration values
at gridknots. The values along the gridknots of the first row
of mosaic in ZATON.AUX are given in the rows 2.7. We see that
the values are equal to the background concentration. The values
along the second row of mosaic are given in the following 6 rows
e.t.c.

   ?    8.2. Illustrations.
 The user can get pictures on the screen and grab them after
the processing is finished without starting CURRMOD  or ANCOPOL,
the option retrying (secondary processing). This possibility is
described here.
   ?   Current field. There must be present the following three
files: DOMAIN.aux, IZVOR.aux and DRAGA.aux. They are always
present after a successful processing of CURRMOD. Now, the user
has to perform the following (DOS) operations: 
DEL CRTEZ.AUX
FLOW5
SLIKA1
During the processing the user has to choose relevant options.
Also, the HPGPfiles for plotting of the figures can be obtained.
After the mentioned three operations are performed, the user has
to run the modules
GRIDPL
FLOWPL
CRS 1
and follow the instructions which are described in Section 5.2.

   ? h)  Concentration field. There must be present the following
three files: DOMAIN.aux, IZVOR.aux and REZUL.aux. They are always
present after a successful processing of ANCOPOL. Now, the user   *        p-++  has to perform the following (DOS) operations:
DEL CRTEZ.AUX
DEL DOPUN2.AUX
DEL TOCKE.AUX
NUTRIP
SLIKA2
NUTRIB
SLIKSPRE
SLIKA3
SLIKSPRE -D
NUTRI1 4
CRS 1
and follow the instructions. The TIFFfile of the grabbed picture
is obtained by the procedure which is described at the end of
Section 5.2. In order to get the HPGP plotter files of the
corresponding pictures the user has to execute, additionally, the
following operations: 
DEL MOSAIC.AUX
DEL POLUPO.AUX
GRIDPL
NUTRPL
FORMPL
CRS 1
The result are the files of grid and concentration fields.            p-++     ?     BIBLIOGRAPHY:

   ?  [1] A. Okubo, Diffusion and Ecological Problems. Mathematical
 Models. Springer, New York 1982

   ?  [2] K.F. Bowden, J.Fluid Mec., 21, (1965) p. 8395

   ? x [3] H. Ridderinkhoh and J.T.F. Zimmerman, Science, 258, (1982)
p. 11071111
   ?  [4] R.E. Wilson and A. Okubo, J. Marine Res., 36, (1987)
 p. 427447
   ?  [5] J.T.F. Zimmerman, Nature, 290, (1981) p. 549555

   ? (
 [6] T. Legovia, N. Limia and V. Valkovia, Estuarine and Coastal
   ? 
  and Shelf Science, 30, (1990) p. 619.

   ?  [7] E. Coffou, N. Limia: A minimization problem in residual
   ? H
 current modelling. Applied Math. Modelling 9, 325-330 (1985)
