olar ra- 
(1) 
(zenith 
surface 
n the 
lent beam, 
3 of the 
led sea, 
reflected 
astion. 
oilitv 
n the 
liance 
lection 
ting 
iding us 
5. Hence, 
(2) 
(3) 
zenith 
-the 
this 
ation 
jo -solid 
'ident 
tion 
incident 
“band sky 
(4) 
»f the 
azimuth 
it's better 
n- lux; onto 
.able. As 
(5) 
jave- sure 
  
IE 
cám mtm n sls 
aee BE nn RD CSE land RENE SO OQ ORE ABRE Dots t omia IAE A EL ORBE AO Lu AE ER EEE 
  
Here 20nme -angle between the directions of obser- 
vation and the sun, 9€ no and ie - Correspondingly the 
azimuth and zenith angle of the normal of sea surface element in 
case of the incident direct solar radiation. Both Xh. and n 
are calculated as the azimuth and zenith angle of the bisectrix 
of the angle between the directions of ( Sm dn )'and' («39 ). 
In case of'the"direct radiation , "e. and ve are calcula- 
ted for the ‘bisectrix. of the anale between ( 96 mas ) and 
( Xe ; 9e y. m 
The first term of the formula (6) describes the reflec- 
ted sky radiance, the second the sun glitter. 
Evidently the data on B. as a function of ao and -3 
for various Sun's" "locations is needed: Practically, in most cases, 
we have the experimental results of total solar and Sky irradiance, 
but not the angular distribution of Bes (ot, 3) . Por the first 
approximation we took the sky radiance as subjected to the follo- 
wing assumptions: l)the maximum value of Bs corresponds to the 
direction of the visible Sun's disc: 2) the Sky radiance decreases 
continuously with the direction (e¢, 9 ) moving away from the 
sun's direction. Under these restrictions the angular distribution 
of 945: CC 9^ can be described mathematically by an ellipsoid 
assuming the longer axis of symmetry directed straight to the 
Sun's disc. For our model such a function Bot, Ru )was determined 
for absolutely clear (for various sun's heights) and completely 
cloudy sky. It must be pointed out that one way to improve our 
mathematical model is to obtain more perfect description of 
Bs (9) : 
The values-of-reflectivity RED Kos) both for the 
Cases of pure water and a thin oil "film on the .sea sur- 
face are computed by the formulae presented by Arst, Kard (1981) 
while using the optical constants of water and oil taken from the 
investigations of Irvine, Pollack (1968) and Zolotariev et al. 
E97. ; 
For determining the function =P (en. SA ),the results 
of the investigation by Cuinn et al. (1979) are very convenient: 
on the basis of the data of Cox and Munk (1954) they have presen- 
ted the formulae for calculations of P Coi Sa) as well as the 
necessary expressions for computational parameters (both for pure 
water and oil slick). The expressions are developed in the form 
that depends only on the velocity and direction of the wind. 
Those characteristics are easily available. We have used these 
formulae for computing the values of Pest. rad ) "and 
l n 
pO Nis o ; 
The given model is realized as a program for a computer. 
The initial "data is: 1) wavelength of. incident radiation; 
2)solar zenith angle and azimuth; 3) zenith angle of observation 
(the azimuth of observation is considered to be zero); 4)thick- 
ness of oil film; 5) optical constants of water and oil; 6) wind 
velocity and direction; 7) downwelling total and direct solar 
irradiance measured on the sea surface. (It is possible to refine 
the results, having some measured values of sky brightness as 
initial data that help to determine the function Bs iw OS for the 
case under consideration). The results of the program's single run 
are the values of the upwelling reflected radiance,separately for 
the reflected sky radiation and sun glitter (both for the calm 
and ruffled ‘sea with" "and "without "oil fiim covering). 
The model may become of practical use for the ana- 
lysis of measuring results of upward radiation above the sea. 
One of the possible applications can be the estimation of re- 
lative contribution of the sun glitter to the results of the 
227