International Journal
and Safety of Sea Transportation
Volume 2
Number 2
June 2008
167
Probabilistic Model of Underkeel Clearance in
Decision Making Process of Port Captain
L. Gucma & M. Schoeneich
Maritime University of Szczecin, Szczecin, Poland
ABSTRACT: The paper presents practical implementation process of developed probabilistic model of ships
underkeel clearance. The model was implemented in “on-line” version and could be used for decision making
process of harbour captain in everyday practice. The paper presents the results of validation of the model and
the practical guidelines of use in decision making process.
1 INSTRUCTION
Underkeel clearance is most important factor which
determines the possibility of ships hull touching the
bottom. Maintaining safe clearance is the basic
navigator’s responsibility among his other usual
duties. Till now method of constant clearances has
been used to determine the minimal safe underkeel
clearance. This method calculates safe underkeel
clearance as a sum of several components. Many
factors are taken into account within this method
which have constant values for a particular area.
In many cases this solution might be too general.
The paper presents model of underkeel clearance
with probabilistic method. Uncertainties taken into
account within the model are: depth, draught and
water level together with their determination
uncertainties. The paper presents the hints for
practical use of the model. Model presents predicted
underkeel clearance distribution. The method allows
to determine the probability of ships hull hitting the
bottom, which might be helpful to assess whether
maximal vessel can or cannot enter to the port.
2 PROBABILISTIC MODEL OF UNDERKEEL
CLEARANCE DETERMINATION
The model determinate predicted underkeel clearance
for chosen ship and probability of ships hull contact
with the bottom. It uses probabilistic method, which
shows underkeel clearance distribution.
On the grounds of vessel type and length program
gives underkeel clearance for chosen ship, which
might be helpful to assess whether maximal vessel
can or cannot enter to the port.
Depth measurement uncertainty, uncertainty of
draught determination in port, error of squat
determination, bottom irregularity, tides and waves
influence are deciding factors for underkeel clearance
of ships. Program is modelling above mentioned
errors using distributions and their parameters
(Monte Carlo simulation is used) [Gucma L. 2004a].
Program is iterating to a predefined n
max
. While
n n
max
calculations are made for randomly selected
parameters. If n > n
max
results are analysed and
underkeel clearance distribution is printed.
The following parameters are randomly selected
from their distributions:
depth – hi ,
168
sounding error –
i
BS
δ
,
mudding component clearance –
i
Z
δ
,
draught determination error –
i
T
δ
,
ship's heel error –
i
P
δ
.
Length between perpendiculars L, ship service
speed V
serv
, ship’s block coefficient C
b
are
determined on the basis of vessel type and length
overall. If given length is outside then alert message
will be given. Each iteration consist of 5 main
analytical modules.
2.1 Random draught module
User-entered draught is corrected for draught
determination error value and ship's heel error.
Iterated draught (T
i
) is calculated as follows:
ii
i TP
TT
δδ
=++
where: T Ships draught [m],
i
T
δ
draught
determination error,
i
P
δ
– ships heel error.
2.2 Water level module
Water level PW
i
is automatically fed from Maritime
Office in Szczecin. For Gdańsk Harbour water level
value must be entered manually.
2.3 Depth module
Random depth h
i
and current water level in port are
used to calculate up-to-date depth.
2.4 Squat module
Squat in each iteration is calculated in three stages.
First module calculates squat with methods used to
obtain moving vessel squat (Huusk, Milword 2,
Turner, Hooft, Barrass 1, Barrass 2) [PIANC 1997;
PIANC 2002]. Next standard errors of each methods
are allowed. Squat model selection and their
standard errors were verified by GPS-RTK
experimental research [AM 2004a; Gucma L.,
Schoeneich M. 2006]. As a result of the experiment
uncertainty of each model was assessed and each
squat method assigned weight factor w
i
= σ
i
/Σσ
i
.
Method's weights and Bootsrap method are then
used to calculate ship's squat.
2.5 Underkeel clearance module
Underkeel clearance Z
i
is determined by using
draught, depth, water level and squat results which
were calculated before. Underkeel clearance is
defined as:
( )( )
ii i
i i Z BS i i N WP F
Z h TO
δδ δδ δ
= + + ++ + +
where: h
i
– up-to-date depth in each iteration,
i
Z
δ
mudding component clearance,
– sounding
error,
i
T
iterated draught,
i
O
iterated squat,
N
δ
i
WP
δ
– high of tide error,
F
δ
wave clearance.
The result of method of constant clearances is
presented to compare it with the proposed
probabilistic method. This method calculates safe
underkeel clearance as a sum of several components.
Any probabilistic characteristics of underkeel
clearance can be taken account. The value of this
clearance is calculated in accord with “The
guidelines for Designing of Maritime Engineering
Stuctures”.
3 COMPUTER IMPLEMENTATION OF MODEL
The model was implemented using Python compiler
and it is available “on-line” on Maritime Traffic
Engineering Institute web site. Figure 1 presents
form for entering parameters. It is possible to enter
the basic ship and water region data. The remaining
necessary data are taken from XML file located from
the server.
Fig. 1. User defined data form for probabilistic model of
underkeel clearance (UKC)
Model underkeel clearance is evaluate after
running the application. The results are presented as
a histogram. Also the numerical value of mean squat
and conventional calculated underkeel clearance are
presented (Figure 2).
169
4 EXAMPLE RESULTS
Example entering to the harbours of Świnoujście,
Szczecin, Police and Gdańsk were simulated.
Maximum draught for these harbours decided of
vessels’ parameters selection. In the Table 1 harbour
and input data are presented. Simulation results are
presented on figures 2, 3.
Table 1. Ship parameters used in simulation
Harbour
Ships
parameters
Świno-
ujście
Szczecin Police Gdańsk
Vessel type
Bulk
Carrier
General
Cargo
Chemica
l Tanker
Bulk
Carrier
L[m]
240
160
170
280
T[m]
12,8
9,15
9,15
15
B[m]
36,5
24,2
23,7
43,3
V[kt]
6
8
8
7
The most important result is the probability that
clearance is less than zero. This is the probability of
accident due to insufficient water depth. Table 2
presents result of simulations as probability, values
of mean squat, conventional calculated underkeel
clearance, 5% and 95% percentiles of under keel
clearance (UKC).
Table 2. Simulation results
Harbour
Simulation results
Świno-
ujście
Szcze-
cin
Police Gdańsk
P(UKC<0)
0,02
0,033
0,04
0,006
Mean squat
0,23 m
0,32 m
0,32 m
0,30 m
Constant UKC
component method
3,11 m
2,56 m
2,57 m
3,12 m
5% UKC percentile
0,15 m
1,2 m
0,04 m
0,35 m
95% UKC percentile
1,98 m
3,19 m
3,36 m
1,71 m
Results show small values of probability that
clearance is less than zero. It is obvious that not all
the cases when UKC<0 is ended with serious accident.
Fig. 2. Underkeel clearance simulation results at the maximum
vessel’s draught in Świnoujście Port (Górników Wharf)
The distribution have positive asymmetry. Mean
underkeel clearance of maximal ships is equal to
UKC
M
= 0,9 m. 95% values are less than 1,98 m
when value conventional calculated underkeel
clearance is equal to 3,11 m.
Fig. 3. Underkeel clearance simulation results at the maximum
vessel’s draught in North Port Gdańsk
In this case the disribution is nearly symmetrical.
Mean underkeel clearance of maximal ships is in
range <0,5; 1,3>. 95% values are less than 1,71 m
when value conventional calculated underkeel
clearance is equal to 3,12m.
5 SHIP ENTRANCE DECISION MODEL
Simplified decision model is presented as decision
tree in Fig. 2 [Gucma 2004b]. The actions are
denoted as A, possible state of nature as P and
outcomes as U. The P can be understood as state of
nature (multidimensional random variable) that
could lead in result to ship accident. The main
objective of decision can be considered as
minimisation of accident costs and ship delays for
entrance to the harbour due to unfavourable
conditions. The limitation of this function can be
minimal acceptable (tolerable) risk level. The
expected costs of certain actions (or more accurate
distribution of costs) can be calculated with
knowledge of possible consequences of accident and
costs of ship delays. The consequences of given
decision actions expressed in monetary value can be
considered as highly non-deterministic variables
which complicates the decision model. For example
the cost of single ship accident consist of:
salvage action,
ship repair,
ship cargo damages,
ship delay,
closing port due to accident (lose the potential
gains), etc.
170
The decision tree can be used also for
determination of acceptable level of accident
probability if there are no regulations or
recommendations relating to it. If we assume that
accident cost is deterministic and simplified decision
model is applied (Fig. 4) then with assumption that
the maximum expected value criterion is used in
decision process, the probability p
a
*
can be set as a
limit value of probability where there is no
difference for the decision maker between given
action a
1
and a
2
. This value can be expressed as
follows:
1
1
24
31
*
+
=
uu
uu
p
a
where: u
1
...u
4
consequences of different decisions
expressed in monetary values.
Fig. 4. Simplified decision tree of ship entrance to the port
5.1 Costs of ships accident and delay
Usually during the investigation of ship grounding
accident on restricted waters it is not necessary to
take into consideration the possibility of human
fatalities nor injures. The cost of accident Ca could
be divided into following costs:
CpcCosCraCrCa +++=
where: Cr cost of ships repair, Cra cost of rescue
action, Cos cost of potential oil spill, Cpc cost of
port closure.
The mean cost of grounding accident in these
researches was calculated for typical ship (bulk
carrier of 260m). The mean estimated cost of serious
ship accident is assumed as C
1
= 2.500.000 zl
(around 700.000 Euro) [MUS 2000]. The oil spill
cost is not considered. Following assumption has
been taken in calculations:
number of tugs taking part in rescue action:
3 tugs,
mean time of rescue action.: 1 day,
trip to nearest shipyard: 0.5 day,
discharging of ship: 4 days,
repair on the dry dock: 2 days,
totel of oil spilled: 0 tons.
Mean cost of loses due to unjustified ships delay
according to standard charter rate can be estimated
as 90.000 zl/day. It is assumed that after one day the
conditions will change scientifically and the decision
process will start from the beginning.
5.2 The decision making process
The maximization of mean expected value criterion
is used to support the decision of port captain.
Decision tree leads to only 4 solutions. Each
decision could be described in monetary values. The
expected results (losses) of given decisions are as
follows:
u1 = 0 zl;
u2 = - 2.500.000 zl;
u3 = - 90.000 zl;
u4 = 0 zl.
Taking into consideration the results of grounding
probability calculations of example ship entering to
Swinoujscie Port (Fig.2) the probability of ship
under keel clearance is less then zero equals p2=0.02
which is assumed as accident probability. No
accident probability in this case is estimated as
p1=1-p2=0.98. We can evaluate the mean expected
value of given decisions a1 and a2 as:
a1 = 0 zl+(-0.02*2.500.000 zl)= -50.000 zl;
a2 = -(-0.98*90.000 zl)+0zl= - 88.200 zl;
With use of mean expected value it can be
justified to prefer action a1 (to let the ship to enter
the port) because total mean expected loses are
smaller in compare to unjustified delay due to
decision a2.
6 CONCLUSIONS
The paper presents probabilistic method of ships
dynamic underkeel evaluation. Previously developed
Monte Carlo model was implemented as online
program. The program allows to calculate the
probability of grounding accident with consideration
of several uncertainties.
Simplified decision model based on mean
expected value was presented and applied in case
study of ships enter to Świnoujscie. Results were
discussed.
171
The model after validation is intended to be used
in every day decision making practice of port
captains and VTS operators.
REFERENCES
PIANC. 1997. Approach Channels. A Guide for Design. Final
Report of the Joint PIANC-IAPH Working group II-30 in
cooperation with IMPA and IALA. June 1997.
PIANC 2002. Dynamic Squat and Under-Keel Clearance of
Ships in confined Channels, , 30
th