International Journal

on Marine Navigation

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,

i

BS

δ

– sounding

error,

i

T

– iterated draught,

i

O

– iterated squat,

N

δ

–

navigational clearance,

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

International Navigation

Congress, Sydney, September 2002, S10B P152.

MUS 2000. Efficiency evaluation of Swinouscie – Zalew

Szczeciniski (0,0 – 18,8 km) waterway modernization.

Unpublished results of researches, Maritime University of

Szczecin 2000.

Gucma L., 2004a, Metoda probabilistyczna Monte Carlo okreś-

lania zapasu wody pod stępką, Proc. of the XIV

International Conference: The Role of Navigation in

Support of Human Activity on the Sea, Gdynia 2004.

Gucma L., 2004b. Risk Based Decision Model for Maximal

Ship Entry to the Ports. PSAM7-ESREL04, C. Spitzer et. al

(eds.), Springer-Verlag, Berlin.