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3.  Thin  ice  growth  in  the  area  of  Szczecin  Lagoon
Knowledge  of  the  ice  development  and  expected  ice  thickness  in  a  particular  water  area  is  of
high  practical  value  to  shipping  and  offshore  engineering.  In  general,  the  thickness  of  the  ice
(h)  is  a  function  of  a  whole  series  of  factors:

h  =  f  (tp,  X,  S%o,  T,  t w ,

v,  H’,  H s ,  L,  Q,  Q’,  Q m ,  Q l ,  p,  x),

where

cp  and  X
S%c,  t w ,  v
H’
H s
L
Q
Q'
Qm
p
X
T

-  latitude  and  longitude  of  the  water  area,
-  water  salinity,  water  temperature  and  flow  velocity,
-  depth  of  water,
-  snow  depth,
-  distance  from  the  shore,
-  sun  radiation,
-  heat  storage  of  the  water,
-  heat  flux  to  atmosphere,
-  density  of  ice  and  snow,
-  thermal  conductivity  of  ice  and  snow,
-  air  temperature.

Theoretically,  ice  thickness  can  be  derived  from  an  equation  describing  the  heat  flux  through
the  ice.  With  respect  to  the  thickness  of  sea  ice,  the  first  equation  of  this  type  was  set  up  by
Stefan  in  1891

h 2  =  2%  /  Ql  p  *  E ( ,  E t  =  J  6dt,  where
/0

0  is  the  temperature  difference  between  the  top  surface  of  an  ice  cover  and  the  water  below
the  ice  cover,  Q L  is  the  latent  heat  released  by  freezing  an  additional  ice  layer,  and  the  integral
E,  is  called  the  freezing  exposure  and  usually  quoted  in  degree-days  [Pounder,  1965].  The
solution  was  later  completed  and  developed  by  Subow  [1945],  Doronin  [1963,  1975],  Hibler
[1974]  and  others.
To  calculate  the  ice  thickness  for  a  particular  water  area  under  specific  conditions,  numerous
physical  characteristics  must  be  known  which  are  practically  not  available.  By  simplification
and  use  of  mean  values  for  relevant  characteristics,  the  theoretical  equations  attain  the  form  of
empirical  deduced  formulas  for  the  description  of  ice  growth,  for  example:
h 2  +  50  *h  =  8  *Ks  [Subow,  1945],
h  =  -25  ±  ((25  +  h 0 ) 2  +  8*K s ) m  [Subow,  1945],
h  =  -7.7*H S  +  ((7.7*H S  +  h 0 ) 2  +  12  *K s ) m  [Doronin,  1969,1975].
Systematic  observations  of  ice  growth  have  made  it  possible  to  establish  a  relationship
between  ice  thickness  (h)  and  the  sum  of  coldness  (Ks).  This  dependence  is  well  described  by
the  curve  which  is  most  often  given  by  a  parabola:
h  =  a*(Ks)”,
where  a  and  n  are  the  characteristic  coefficients  of  the  special  water  area.