51
1 INTRODUCTION
One of the important duties in port activities and
shipping is the prevention of oil release from port
installations and ships and the spread of oil spills that
often have dangerous consequences for port and sea
water areas (Bogalecka & Kołowrocki 2018,
Dąbrowska & Kołowrocki 2019A, NOAA). Thus, as
the first step, there is a need for methods of oil spill
domain movement modelling based on determination
of the oil spill central point drift curve determination
and the oil spill domain probable placement at any
moment after the accident that could be the tools for
increasing the shipping safety and effective port and
sea environment protection. Even if, the real trajectory
of the oil spill central point and the oil spill domain
movement are different from those determined by the
proposed methods, they can be useful in the port and
sea environment protection.
The oil spill central point drift trend, the oil spill
domain shape and its random position distribution
fixed for different hydro-meteorological conditions
allow us to construct the model of determination of
the area in which, with the in advance fixed
probability, the oil spill domain is placed (Dąbrowska
& Kołowrocki 2019A). This way, the area determined
for oil spill allow us to mark the domain where the
actions of mitigating the oil release consequences
should be performed. This approach is proposed to
make oil releases at the sea prevention and mitigation
actions more effective.
The general model of the oil spill domain
determination based on the probabilistic approach
may be practically applied in the oil spill
consequences mitigation actions at the sea after its
unknown parameters’ statistical identification.
Statistical experiments should be performed
according to the methods of the model unknown
parameters estimation. Thus, the methods of
evaluation of unknown parameters of the oil spill
central point drift curve and the joint density function
should be proposed. Moreover, the procedures of
their practical evaluations should be done as well
(Dąbrowska & Kołowrocki 2019A).
Probabilistic Approach to Determination of Oil Spill
Domains at Port and Sea Water Areas
E. Dąbrowska
& K. Kołowrocki
Gdynia Maritime University, Gdynia, Poland
ABSTRACT: A new method of oil spill domains’ determination, based on a probabilistic approach, is
recommended. A semi-Markov model of the process of changing hydro-
meteorological conditions is
constructed. To describe the oil spill domain central point position a two-dimensional stochastic process is
used. Parametric equations of oil spill domain central point drift trend curve for different kinds of hydro-
meteorological conditions are determined. The general model of oil spill domain determination for various
hydro-meteorological conditions is proposed. Moreover, approximate expected stochastic prediction of the oil
spill domain movement in constant and changing hydro-meteorological conditions is proposed.
http://www.transnav.eu
the
International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 14
Number 1
March 2020
DOI:
10.12716/1001.14.01.05
52
2 MODELLING PROCESS OF CHANGING
HYDRO-METEOROLOGICAL CONDITIONS AT
OIL SPILL AREA
We denote by A(t) the process of changing hydro-
meteorological conditions at the sea water areas
where the oil spill happened and distinguish m its
states from the set A = {1,2,...,m} in which it may stay
at the moment t, t ∈ <0,T>, where T > 0.
Further, we assume a semi-Markov model of the
process A(t) and denote by
θ
ij its conditional sojourn
time in the state i while its next transition will be done
to the state j, where i, j = 1,2,...,m, i ≠ j (Dąbrowska &
Kołowrocki 2019A). Under these assumptions, the
process of changing hydro-meteorological conditions
A(t) is completely described by the following
parameters (Dąbrowska & Kołowrocki 2019A):
− the vector of probabilities of its initial states at the
moment t = 0
[p(0)] = [p
1(0), p2(0),..., pm(0)]; (1)
− the matrix of probabilities of its transitions
between the particular states
[p
ij
] =
mm
mm
m
m
p
p
p
p
p
p
pp
p
21
222
21
1
12
11
, (2)
where p
ii = 0 for i = 1,2,...,m;
− the matrix of distribution functions of its
conditional sojourn times θij at the particular states
[W
ij
(t)] =
, (3)
where W
ii
(t) = 0 for i = 1,2,...,m;
− the expected values (mean values) of its
conditional sojourn times θij at the particular states
M
ij
= E[
θ
ij
]=
∫
∞
0
tdW
ij
(t), i, j = 1,2,...,m, i ≠ j. (4)
Having the above parameters of the process
of changing hydro-meteorological conditions A(t),
t ∈ <0,T>, T > 0, this process following characteristics
can be determined (Dąbrowska & Kołowrocki 2019A):
− the distribution functions of the unconditional
sojourn time θi of the process of changing hydro-
meteorological conditions at the particular states i,
i = 1,2,...,m,
W
i(t) =
∑
=
m
j 1
p
ij
W
ij
(t), i = 1,2,...,m; (6)
− the mean values of the unconditional sojourn time
θi of the process of changing hydro-meteorological
conditions at the particular states i, i = 1,2,...,m,
M
i = E[
θ
i] =
∑
=
m
j
1
p
ij
E[
θ
ij], i = 1,2,...,m. (7)
3 MODELLING TREND OF OIL SPILL CENTRAL
POINT DRIFT
First, for each fixed state k, k ∈ {1,2,…,m}, of the
process A(t) and time t ∈ <0,T>, where T is time we
are going to model the behaviour of the oil spill
domain
),(tD
k
we define the central point of this oil
spill domain as a point
)),(),(( tytx
kk
t ∈ <0,T>,
k ∈ {1,2,…,m}, on the plane Oxy that is the centre
of the smallest circle, with the radius
),(tr
k
t ∈ <0,T>, k ∈ {1,2,…,m}, covering this domain (Figure
1). Thus, for the fixed oil spill domain
),(tD
k
we
have
12
() ()
() ,
2
kk
k
xt xt
xt
+
=
,
2
)()(
)
(
21
tyty
ty
kk
k
+
=
t ∈ <0,T>, k ∈ {1,2,…,m}, (8)
where the
))
(),((
11
1
tyt
xP
kk
and
))(
),((
222
t
ytx
P
kk
are the most distant points of the oil
spill domain
),(tD
k
t ∈ <0,T>, k ∈ {1,2,…,m}, and
the radius
),(tr
k
called the radius of the oil spill
domain
),(
tD
k
is given by
,)]()
([)]()([
2
1
)(
2
21
2
21
tyt
ytxtxtr
k
kk
kk
−+−=
t ∈ <0,T>, k ∈ {1,2,…,m}. (9)
P
1
(x
1
(t), y
1
(t))
y
x
t
k k
P
2
(x
2
(t), y
2
(t))
k k
C(x
k
(t), y
k
(
t))
D
k
(t)
r
k
(t)
0
0
t
Figure 1. Interpretation of central point of oil spill
definition.
53
Further, for each fixed state k, k = 1,2,…,m, of the
process A(t) and time t, t ∈ <0,T>, we define a two-
dimensional stochastic process
)),(),(( tYtX
kk
t ∈ <0,T>,
such that
)
,
(
kk
Y
X
: <0,T> → R
2
,
where
),(tX
k
)(tY
k
respectively are an abscissa and
an ordinate of the plane Oxy point, in which the oil
spill central point is placed at the moment t while the
process A(t), t ∈ <0,T>, is at the state k. We set
deterministically the central point of oil spill domain
in the area in which an accident has happened and an
oil release was placed in the water as the origin O(0,0)
of the co-ordinate system Oxy. The value of a
parameter t at the moment of accident we assume
equal to 0. It means that the process
)),(),(( tYtX
kk
is
a random two-dimensional co-ordinate (a random
position) of the oil spill central point after the time t
from the accident moment and that at the accident
moment t = 0 the oil spill central point is at the point
O(0,0), i.e.
).0,0())0(),0(( =
kk
YX
After some time, the central point of the oil spill
starts its drift along a curve called a drift curve. In
further analysis, we assume that processes
)),(),(( tYtX
kk
t ∈ <0,T>, k ∈ {1,2,…,m},
are two-dimensional normal processes
)),(),(),(),(),(( ttttmtmN
k
Y
k
X
k
XY
k
Y
k
X
σσρ
with varying in time expected values
)],([)(
tXEtm
kk
X
=
)],
([)
( tYE
tm
kk
Y
=
standard deviations
),(t
k
X
σ
)(t
k
Y
σ
, t ∈ <0,T>, k ∈ {1,2,…,m},
and correlation coefficients
),(t
k
XY
ρ
i.e. with the joint density functions
),( yx
k
t
ϕ
=
2
))((1)(
)(2
1
ttt
k
XY
k
Y
k
X
ρσπσ
−
2
2
2
))((
))((
[
)))((1(2
1
exp{
t
tmx
t
k
X
k
X
k
XY
σρ
−
−
−
)()(
))())(((
)(2
tt
tmytmx
t
k
Y
k
X
k
Y
k
X
k
XY
σσ
ρ
−−
−
+
]
))((
))((
2
2
t
tmy
k
Y
k
Y
σ
−
},
,),(
2
Ryx ∈
t ∈ <0,T>, k ∈ {1,2,…,m}. (10)
where
),(tX
k
)
(
tY
k
respectively are an abscissa and
an ordinate of the plane Oxy point, in which the oil
spill central point is placed at the moment t while the
process A(t), t ∈ <0,T>, is at the state k. We set
deterministically the central point of oil spill domain
in the area in which an accident has happened and an
oil release was placed in the water as the origin O(0,0)
of the co-ordinate system Oxy. The value of a
parameter t at the moment of accident we assume
equal to 0. It means that the process
)),
(),(( tYtX
kk
is
a random two-dimensional co-ordinate (a random
position) of the oil spill central point after the time t
from the accident moment and that at the accident
moment t = 0 the oil spill central point is at the point
O(0,0), i.e.
).0,
0())
0(),
0(( =
kk
YX
Thus, the points
))(),(( tmtm
k
Y
k
X
, t ∈ <0,T>, k ∈ {1,2,…,m},
create a curve K
k
called an oil spill central point drift
trend (Figure 2) which may be described in the
parametric form
:
k
K
>∈<=
=
.,0
),(
)(
Ttty
y
txx
kk
kk
(11)
y
x
t
(m
X
(t), m
Y
(t))
k k
t
0
0
Figure 2. Oil spill central point drift trend.
4 MODELLING OIL SPILL DOMAIN
4.1 Probabilistic approach
We are interested in finding the search domain D
k
(t), t
∈ <0,T>, k ∈ {1,2,…,m}, such that the central point of
54
oil spill domain is placed in it with a fixed probability
p. More exactly, we are looking for c such that
,
),
(
))())(),(((
)(
pdxdy
y
xtDtYtXP
t
k
D
k
t
kkk
=
∫∫
=∈
ϕ
t ∈ <0,T>, k ∈ {1,2,…,m}, (12)
where
)
(
t
D
k
2
2
2
))
(
(
))
((
[
))(
(
1
1
:
)
,{(
t
t
m
x
t
y
x
k
X
k
X
k
XY
σ
ρ
−
−
=
–
)(
)
(
))())(
(
(
)
(2
t
t
tm
y
tm
x
t
k
Y
k
X
k
Y
k
X
k
XY
σσ
ρ
−
−
+
]
))((
))((
2
2
t
tmy
k
Y
k
Y
σ
−
}
2
c
≤
, t ∈ <0,T>,
k ∈ {1,2,…,m}, (13)
x
y
z
D
k
(t)
Figure 3. Domain D
k
(t) of integration bounded by an ellipse.
is the domain bounded by an ellipse being the
projection on the plane 0xy (Figure 4) of the curve
rising as the result of intersection (Figure 3) of the
density function surface
},),(),,(:),,{(
2
1
Ryxyxzzyx
k
t
k
∈==
ϕπ
(14)
and the plane
:),
,{(
2
zyx
k
=
π
],
2
1
exp[
))((
1)()(2
1
2
2
c
ttt
z
k
XY
k
Y
k
X
−
−
=
ρσπσ
(x,y) ∈ R
2
}, t ∈ <0,T>, k ∈ {1,2,…,m}. (15)
Since
))())(),((( tDtYtXP
kkk
∈
=
],
2
1
exp[1
2
c−−
t ∈
<0,T>,
k ∈ {1,2,…,m}, (16)
then for a fixed probability p, the equality
)))(),(((
kkk
DtYtXPp ∈=
,
t ∈ <0,T>, k ∈ {1,2,…,m}, (17)
holds if
).1ln(2
2
pc −−=
(18)
Thus, the domain in which at the moment t the
central point of oil spill is placed with the fixed
probability p is given by
)(tD
k
2
2
2
))((
))((
[
))((1
1
:),{(
t
tmx
t
yx
k
X
k
X
k
XY
σρ
−
−
=
–
)()(
))())(((
)(2
tt
tmytmx
t
k
Y
k
X
k
Y
k
X
k
XY
σσ
ρ
−−
+
]
))((
))
(
(
2
2
t
tm
y
k
Y
k
Y
σ
−
≤ – 2ln(1 – p)}, t ∈ <0,T>, k ∈ {1,2,…,m}. (19)
Considering the above and the assumed in Section
3 definition of the central point of oil spill, for each
fixed state k, k ∈ {1,2,…,m}, of the process A(t) and
time t ∈ <0,T>, we define the oil spill domain
)
(t
D
k
2
2
2
))(
(
))
((
[
))((1
1
:),
{(
t
t
mx
t
y
x
k
X
k
X
k
XY
σρ
−
−
=
–
)()(
))
())(((
)(2
tt
tmytmx
t
k
Y
k
X
k
Y
k
X
k
XY
σσ
ρ
−−
+
]
))((
))((
2
2
t
tmy
k
Y
k
Y
σ
−
≤ – 2ln(1 – p)},
t ∈ <0,T>, k ∈ {1,2,…,m}, (20)
where
),()()( trtt
kk
X
k
X
+=
σσ
),
()(
)( tr
tt
kk
Y
k
Y
+
=
σσ
t ∈ <0,T>, k ∈ {1,2,…,m}, (21)
and
),(tr
k
t ∈ <0,T>, k ∈ {1,2,…,m}, (22)
is the radius of the oil spill domain
),(tD
k
t ∈ <0,T>, k ∈ {1,2,…,m}.
55
y
x
D
k
(t)
α
(t)
y – m
Y
(t) = ρ
XY
(t) (x – m
X
(t))
k k k
σ
Y
(t)
σ
X
(t)
k
k
m
Y
(t) +
cρ
XY
(t)
σ
Y
(t)
k
k k
(m
X
(t), m
Y
(t))
k k
m
X
(t) – cσ
X
(t)
k k
m
X
(t) + cσ
X
(t)
k k
m
Y
(t) – cρ
XY
(t)
σ
Y
(t)
k
k k
Figure 4. Domain D
k
(t) covering oil spill central point with probability p.
y
x
D
k
(t)
α
(t)
y – m
Y
(t) = ρ
XY
(t) (x – m
X
(t))
k k k
σ
Y
(t)
σ
X
(t)
k
k
m
Y
(t) + cρ
XY
(t)
σ
Y
(t)
k k k
(m
X
(t), m
Y
(t))
k k
m
X
(t) – cσ
X
(t)
k k
m
X
(t) + cσ
X
(t)
k k
m
Y
(t) – cρ
XY
(t)
σ
Y
(t)
k k k
D
k
(t)
m
X
(t) + cσ
X
(t)
k
k
m
X
(t) – cσ
X
(t)
k
k
k k k
m
Y
(t) + cρ
XY
(t)
σ
Y
(t)
m
Y
(t) –
cρ
XY
(t)
σ
Y
(t)
k k k
Figure 5. Oil spill domain
).(tD
k
The graph of the oil spill domain
)(t
D
k
is given
in Figure 5.
To find the oil spill domain
)(tD
k
determined
by (20)-(22) and presented in Figure 5, the statistical
methods of its general model unknown parameters
estimation are proposed in (Dąbrowska & Kołowrocki
2019A). These methods are presented in the form of
algorithms giving successive steps which should be
done to evaluate these unknown model parameters
on the base of statistical data coming from
experiments performed at the sea.
4.2 Oil spill domain for fixed hydro-meteorological
conditions
We suppose that the process A(t) for all t ∈ <0,T>, is at
the fixed state k, k ∈ {1,2,…,m}. Assuming a time step
∆t and a number of steps s, s ≥ 1, such that
(s – 1)∆t < M
k ≤ s∆t,
,Tts ≤
∆
(23)
where
M
k = E[θk], k ∈ {1,2,…,m}, (24)
are the expected value of the process A(t), t ∈ <0,T>,
sojourn times θ
k, k = 1,2...,m, at the state k determined
in Section 2, after multiple applying sequentially the
procedure from Section 4.1, for
,,,2,1 tsttt ∆∆∆=
(25)
we receive the following sequence of oil spill domains
(Figure 6)
).(.,..),2(),( tsDtDtD
kkk
∆∆∆
(26)
Hence, the oil spill domain
,
k
D
k ∈ {1,2,…,m}, is
described by the sum of determined domains of the
sequence (26)
),(...)2()1()(
1
tsDtDtDtiDD
kkk
s
i
kk
∆∪∪∆∪∆=∆=
=
,,...,2,1 mk =
(27)
56
and illustrated in Figure 6.
y
x
t
(m
X
(0), m
Y
(0))
k k
0
2∆t
s∆t
D
k
(2∆t)
D
k
(s∆t)
...
Figure 6. Oil spill domain for fixed hydro-meteorological
conditions.
Remark 1. The oil spill domain
k
D
defined by (27)
and illustrated in Figure 6 is determined for constant
radius
,)(
kk
rtr =
t ∈ <0,T>, k ∈ {1,2,…,m}. If the
radius is not constant, we define the sequence of
domains (Dąbrowska & Kołowrocki 2019A)
...
)
2(
)1
()()(
1
∪∆∪∆=∆=∆
=
tDtDtaDtb
kk
b
a
kk
D
),
( tbD
k
∆∪
,
,...,2,
1 sb
=
k ∈ {1,2,…,m},
where
),
(:)( t
aDtaD
kk
∆=∆
,,...,2,1 ba =
,
,...,2
,1
s
b =
,
,...,2,
1 mk =
defined by (20) with the following substitutions:
),(:)( tamtm
k
X
k
X
∆=
y
x
t
(m
X
(0), m
Y
(0))
k k
0
1∆t 2∆t
s∆t
D
k
(1∆t)
Figure 7. Oil spill domain at the time 1∆t.
y
x
t
(m
X
(0), m
Y
(0))
k k
0
s∆t
D
k
(1∆t)
D
k
(2∆t)
1∆t
2∆t
Figure 8. Oil spill domain at the time 2∆t.
y
x
t
(m
X
(0), m
Y
(0))
k k
0
s∆t
D
k
(2∆t)
D
k
(3∆t)
3∆t
D
k
(1∆t)
1∆t
2
∆t
Figure 9. Oil spill domain at the time 3∆t.
y
x
t
(m
X
(0), m
Y
(0))
k k
0
s∆t
D
k
(2∆t)
D
k
(s∆t)
D
k
(1∆t)
D
k
((s – 1)∆t)
1∆t 2∆t
...
Figure 10. Oil spill domain at the time s∆t.
),(:)
( tamtm
k
Y
k
Y
∆=
),()()(:)( tbrtbtbt
kk
X
k
X
k
X
∆+∆=∆=
σσσ
),()()(:)( t
brtbtbt
kk
Y
k
Y
k
Y
∆+∆=∆=
σσσ
,,...,2,1 ba =
,,...,2,1 s
b =
k ∈ {1,2,…,m}.
This oil spill domain movement is illustrated in
Figures 7-10.
4.3 Oil spill domain in varying hydro-meteorological
conditions
We assume that the process of changing hydro-
meteorological conditions in succession takes the
states k
1, k2, ..., kn+1, ki ∈ {1,2,...,m}, i = 1,2,...,n+1. For a
57
fixed step of time ∆t, after multiple applying
sequentially the procedure from Section 4.1:
− for
,
,,
2
,1
1
t
st
t
t ∆
∆∆
=
(28)
at the process A(t) state k
1;
− for
,,,)2(,)1(
211
tststst ∆∆+∆+=
(29)
at the process A(t) state k
2;
− for
,,,
)2
(,)1(
11
tststst
nnn
∆∆
+
∆+=
−−
(30)
at the process A(t) state k
n;
we receive the following sequence of oil spill domains
(Figure 11):
),(
.,..),2(),1(
1
1
11
t
sDtDtD
k
kk
∆
∆∆
(30)
),(.,..),)2((),)1((
2
2
1
2
1
2
tsDtsDtsD
kkk
∆∆+∆+
(31)
),(
.,.
.),)2
((),)
1((
11
ts
Dts
Dts
D
n
n
k
n
n
k
n
n
k
∆∆+
∆+
−−
(32)
where s
i, i = 1,2,...,n, are such that
(s
i-1)∆t <
∑
=
i
j 1
Mk
j
k
j
+1 ≤ si∆t, i = 1,2,...,n,
,
Tts
n
≤∆
(33)
and
M
k
j
k
j
+1 = E[θk
j
k
j
+1], j = 1,2...,n, (34)
are the expected value of the process A(t), t ∈ <0,T>,
conditional sojourn times θ
k
j
k
j+1
, j = 1,2...,n at the states
k
j, upon the next state is kj+1, j = 1,2...,n, ki ∈ {1,2,...,m},
i = 1,2...,n, determined in Section 2.
Hence, the oil spill domain
,
,...,
2
,
1 n
kkk
D
k1, k2, ..., kn
∈ {1,2,...,m}, is described by the sum of determined
domains of the sequences (30)-(32), given by
n
i
i
s
i
s
j
i
i
k
n
kkk
tjsDD
1
1
1
1
,...,
2
,
1
))((
=
−
−
=
−
∆+=
)](...)
2()1([
1
111
tsDtDt
D
kkk
∆∪∪∆∪∆=
(
) (
)
)](
...)2()
1([
2
2
1
2
1
2
ts
Dts
DtsD
kk
k
∆∪∪∆+
∪∆+∪
( ) ( )
)](...)2()1([
11
tsDtsDtsD
n
n
k
n
n
k
n
n
k
∆∪∪∆+∪∆+∪
−−
for k1, k2, ..., kn ∈ {1,2,...,m},
,0
0
=s
(35)
Remark 2. The oil spill domain
n
kkk
D
,...,
2
,
1
defined by
(35) and illustrated in Figure 11 is determined for
constant radiuses
,)(
i
k
i
k
rtr =
t ∈ <0,T>,
k
i ∈ {1,2,...,m}, i = 1,2,...,n. If the radiuses are not
constant, we define the sequence of domains for each
sate k
i, ki ∈ {1,2,...,m}, i = 1,2,...,n, in a way similar to
that described in Remark 1 in Section 4.2, i.e. we
define the sequence of domains
n
i
i
b
i
a
ii
i
k
i
n
kkk
tasDtb
1 1
1
,...,
2
,
1
)()(
= =
−
∆+=∆D
( ) ( )
)](...21[
1
11
1
tsDtDtD
kk
k
∆∪∪∆∪∆=
( ) ( )
)](...)2()1([
2
2
1
2
1
2
tsDtsDtsD
kkk
∆∪∪∆+∪∆+∪
( ) ( )
)](...)2()1([
11
tsDtsDtsD
n
n
k
n
n
k
n
n
k
∆∪∪∆+∪∆+∪
−−
for
,
,...,2
,
1
1
−
−
=
ii
i
s
s
b
ki ∈ {1,2,...,m}, i = 1,2,...,n,
where
),(:)(
11
tasDtasD
ii
k
ii
i
k
∆+=∆+
−−
,,...,2,1
ii
ba =
,,...,2,1
1−
−=
iii
ssb
ki ∈ {1,2,...,m},
i = 1,2,...,n,
defined by (20) with the following substitutions:
),(:)(
1
tasmtm
ii
i
k
X
k
X
∆+=
−
),(:)(
1
tasmtm
ii
i
k
Y
k
Y
∆+=
−
)(:)(
1
tbst
ii
i
k
X
k
X
∆+=
−
σσ
),()(
1
1
1
tbsrtbs
jj
i
j
j
k
ii
i
k
X
∆+
∑
+∆+=
−
=
−
σ
)(:)(
1
tbst
ii
i
k
Y
k
Y
∆+=
−
σσ
),()(
1
1
1
tbsrtbs
jj
i
j
j
k
ii
i
k
Y
∆+
∑
+∆+=
−
=
−
σ
,,...,2,1
ii
ba =
,,...,
2
,1
1
−
−
=
iii
s
sb
ki ∈ {1,2,...,m},
i = 1,2,...,n.
y
x
t
(m
X
(0), m
Y
(0))
k k
2∆t
s
n
∆t
D
k
1
(2∆t)
D
k
(s
n
∆t)
1∆
t
s
1
∆t (
s
1
+ 1)
∆t
0
D
k
1
(1∆t)
D
k
1
(s
1
∆t)
D
k
2
((s
1
+ 1)∆t)
Figure 11. Oil spill domain for changing hydro-
meteorological conditions.
The oil spill domain movement in this case can be
illustrated in a similar way (a bit more complicated)
to that given in Figures 7-10.
58
5 CONCLUSIONS
The improvement of the methods of the oil spill
domains determination is the main real possibility of
the identifying the pollution size and the reduction of
time of its consequences elimination. Therefore, it
seems to be necessary to start with the new and
effective methods of the oil spill domains at port and
sea waters determination in constant and changing
hydro-meteorological conditions. The most important
criterion of new methods should be the time of the oil
spill consequences minimising. One of the essential
factors that could ensure these criteria fulfilment is
the accuracy of methods of the oil spill domain
determination. Those methods should be the basic
parts of the general problem of different kinds of
pollution identification, their consequences reduction
and elimination at the port and sea water areas to
elaborate a complete information system assisting
people and objects in the protection against the
hazardous contamination of the environment. One of
the new efficient methods of more precise
determination of the oil spill domains determination
could be a probabilistic approach to this problem
presented in this paper and preliminarily in
(Dąbrowska & Kołowrocki 2019A).
The oil spill domains determined for different
hydro-meteorological conditions can be also done for
other kind of spills, dangerous for the environment.
The proposed probabilistic approach to oil spill
domains determination would surely improve the
efficiency of people activities in the environment
protection. A weak point of the method is the time
and cost of the experiments necessary to perform at
the port and sea water areas in order to identify
statistically particular components of the proposed
models (Dąbrowska & Kołowrocki 2019A). Especially
experiments needed to evaluate drift trends and
parameters of the central point of oil spill position
distributions can consume much time and be costly as
they have to be done for different kind of spills and
different hydro-meteorological conditions in various
areas. A strong and positive point of the method is the
fact that the experiments for the fixed port and sea
water areas and fixed hydro-meteorological
conditions have to be done only once and the
identified models may be used for all environment
protection actions at these regions and also
transferred for other regions with similar hydro-
meteorological conditions.
The proposed stochastic approach can be
supplemented by the Monte Carlo simulation
approach (Dąbrowska 2019) to the spill oil domain
movement investigation proposed in (Dąbrowska &
Kołowrocki 2019A, 2019B). These two approaches are
the authors’ primary original approaches to the oil
spill domain determination which are intended to be
significantly developed with the close considering the
contents of publications cited in references below.
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