219
1 INTRODUCTION
Thedangerousseaandriverwaterlevelincreasedoes
not only destroy the human lives, but also generate
the severe flooding in coastal areas. The rapidly
changes in the direction and velocity of wind and
associatedwith them sea level changes could be the
severe threat for navigation,
especially on the
fairwaysofsmallfisheryharborslocatedintheriver
mouth. There is the area of activity of two external
forcings:stormsurges and flood wave.Apossibility
ofpredictingwaterlevelchanges in a portincreases
safetyofnavigation–especiallyonthefairways–and
makes
port operation more efficient. It is extremely
important for fishing ports, located in river mouths,
where water level fluctuation is affected by two
factors: sea level changes (forced by atmospheric
pressurefield)andtheriverlevelchanges–forcedby
a flood wave. The advanced sea land water level
forecasting is
based on mathematical modeling. For
the Polish coast of the Baltic Sea, there have been
developed by the State forecast service 2 up to 4
models(dependonthelocalization).Howeveronly1
model is used for the Wisla River; it is to forecast
waterlevelsfromZawichosttoTczew
localities.The
models to forecast water levels in the Gul f can be
extrapolated to the mouth section during the storm
surge(itmeanstopredicttrendsofchanges).Onthe
other hand, the water level forecast’s extrapolation
based on the forecast for Tczew and upper part of
Wisla River, essential on
passing of the flood wave,
wouldnotbringpositiveresults.
The implementation of ANN into the routine
forecast service was done as the first in the
Netherlandstoforecastthecurrentsinthefairwayof
theIjchannel(WustandNoort,1994), however none
of numerical models used there could satisfy
the
implementation conditions. Another ANN
hydrologicalforecastingmodel,wasconstructedalso
in the Netherlands for the forecast for Ijsselmeer
(Boogaard et al. 1998). Also in Germany were done
the attempt and investigation of abilty of ANN
methodology for level prediction (Röske, 1997). In
Poland, the ANN method was tested for level
prediction in Odra estuary and western coast
Application of Artificial Neural Network into the
Water Level Modeling and Forecast
M.Sztobryn
InstituteofMeteorologyandWaterManagement,MaritimeBranch,Gdynia,Poland
ABSTRACT:Thedangerousseaandriverwaterlevel increasedoesnotonlydestroythehumanlives,butalso
generatetheseverefloodingincoastalareas.Therapidlychanges inthedirectionandvelocityofwind and
associatedwiththemsealevel
changescouldbetheseverethreatfornavigation,especiallyonthefairwaysof
smallfisheryharborslocated intherivermouth.Thereistheareaofactivityoftwoexternal forcing: storm
surgesandfloodwave.TheaimoftheworkwasthedescriptionofanapplicationofArtificialNeural
Network
(ANN)methodologyintothewaterlevelforecastinthecasestudyfieldinSwibnoharborlocatedislocatedat
938.7kmoftheWislaRiverandatadistanceofabout3kmupthemouth(GulfofGdansk‐BalticSea).
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 7
Number 2
June 2013
DOI:10.12716/1001.07.02.09
220
(SztobrynM.,1999).Theresultsoftheseworks were
verypromising.
The aim of the work was the investigation of an
application of Artificial Neural Network (ANN)
methodologyintothewaterlevelforecast(forcingby
river)inthecasestudyfieldinSwibnoharborlocated
about3kmabove
theentranceofWisla Riverintothe
GulfofGdansk(BalticSea).
2 LOCALISATIONANDDATA
The fishing harbor inŚwibno (Fig. 1) is located at
938.7kmoftheWislaRiverandatadistanceofabout
3 km up the mouth. The harbour is situated on the
westernbank
oftheriveranditsstructurecomprises
twoconcretequays(160x90mbasin).
Figure1.HarbourinSwibno(http://monimoni.flog.pl/wpis/
1557132/swibno‐‐port‐rybacki)
Depthsintheharbour rangebetween2and3m.
The harbour is used by Rybacka Spółdzielnia
Rybołówstwa Morskiego „Wyzwolenie” [fishing
cooperative society]. Besides, there are also located
BrzegowaStacjaRatowniczaŚWIBNO(coastalrescue
station)andhydrologicalstation(withtelelimnigraph
andwater‐gauge)oftheInstituteofMeteorologyand
WaterManagement–StateResearchInstitute(IMGW‐
PIB).Acharacteristicfeatureoftheharbourentrance
is rapidly changing depth at the fairway and
approachingarea.Itresultsfromtheharbourlocating
within a zone of cross sea and river penetrations
influence, causing sanding up of the water area (for
exampleduring
thefloodwave).
The observation and measurement data used for
the analysis have been produced on the stations of
IMGW‐PIB from April 2007 to December 2010. A
frequency of data recording at the station was 10
minutes;anyhow,thedataobservedeveryhourwere
taken for further analyses (31082 water
levels). The
statistics of characteristics of the analyzed
hydrological data is presented in the Table 1. (an
elevationofthewatergaugeinŚwibnoisequalto–
5.08mabovesealevelacc.toKronstadt).
Table1 The statistics of characteristics of the analyzed
hydrologicaldata
_______________________________________________
WaterlevelinŚwibno
_______________________________________________
numberofobservation31082
mean530
median524
min462
max710
lowerpercentile511
upperpercentile541
_______________________________________________
The maximal observed water level, during the
investigatedperiod,was710cm(wheretheabsolute
maximumisequalto767cmfromwholeobservation
period) and the minimal was 462 cm (absolute
minimum is equal to 420 cm). An average sea level
value was computed to be equal to
530 and it is
higherthanthemedianby6cm.Standarddeviation
was29,81cm.Percentileswerecalculatedasequalto
562and500cmrespectively.
The analysis of empiric frequency distribution
(Fig.2) of water levels occurrence inŚwibno shows
that,morethan72%ofthewholepopulationiswithin
arangeof500–550cm,itmeanswithinthemeansea
water levels zone (500 cm is assumed as equal to
mean sea level along the Southern Baltic coast).
Within the low water level zone in the time under
researchthere was observed notmanyresultsabove
10%
of population, whereas within the high levels
zone16%(including 13.7%within550÷600cmrange
and2.3%above600cm).
Figure2. Frequency distributionof water levels in Swibno
duringtheinvestigatedperiod (KrzysztofikK.,KańskaA.,
2011)
Itreveals thatacceptingforthemodelcalculations
the data, which are characteristic for water levels
withinarangeof500‐550cmwouldcausecalibration
ofthemodel(assumingparameters)tobesetonlyto
thisrange.Takingitintoconsiderationitwasdecided
to make further analyzing only on
the data which
representthehighestrisk,itmeansforthehighwater
zone and flood wave passing one ( over 555 cm).
Storm surges cause not so intense sanding up as
passingthefloodwave.Finallythestudiescomprised
over 2700 of cases, representing the observed in
Świbnohigh
waterlevelszone(i.e.above555cm)and
for imminence threatening from the river. The
imminence was represented by the input data ( the
221
levels observed/forecasted at the stations located
upwards (Gdansk Głowa, Tczew, Chełmno and
Toruń).Aninfluenceofsea was modelled usingthe
sea levels recorded in Gdańsk Port Północny. The
model calibration and verification was carried out
takingintoconsideration24hoursleadtime.
3 ARTIFICIAL
NEURONNETWORKMETHOD
Theartificialneuronnetwork(ANN)werecreatedas
an attempt to a human brain activity
performance/quality. The detailed description of the
methods was included in papers worked out by
Tadeusiewicz (1995/6), Sztobryn (1999, 2001, 2003),
Sztobryn and Krzysztofik (2001), and on website of
STATISTICAprogram(2010).
Thebaseforoperationandsoftwareisthemodel
of a singular neuron called from the neuron model
authors’namestheMcCullochPittsmodel.
AstructureoftheANNiscomposedofinputdata
(so‐called input layer), the hidden layers and the
outputlayer.Theinputlayercontainsparameters
(i.e.
input vector) which, in the opinion of investigator,
influenceon themodelledphenomenon.It has tobe
emphasized that there are no limits in selection of
parameters (on contrary to models of mathematical
physics). Generally a list of such parameters is very
long; moreover, they are often connected with
each
otherandinternallycorrelated.Reductionoftheinput
parameters, called also reduction of the input data
space dimension, is one of the elementary but also
oneofthemostdifficulttasksincalibrationofANN
model. Modelling the hidden layer/layers through
selection of suitable number of hidden neurons is a
next step in calibration of the model. A number of
output neurons is determined by the phenomenon
character,intheanalysedcaseitwaswaterlevelwith
24hoursleadtime.
Building of ANN model was done by the
followingstages:
reduction of the input data dimension ( find the
finalandoptimalinputdatavector),
neuronnetworkstructure(i.e.decisionhowmany
hidden layers with how many neurons are
includedintothemodel),
function of activation of neuron layers ( i.e. the
function of transformation of input vector to the
outputinsidetheindividualneuron),
learning method ( way of comparison and
correctionoferror,equaltothedifferencebetween
modelledva lueandobserved–forcalibrationthe
network,
The final work was the analysis of the results in
respect of quality and implementation to
operational/routineworkofforecastservice.
Over100parameters,affecting
waterlevelchanges
in Swibno cross‐section were selected. They
representedonehydrology (levels,theirchangesand
water table drops) of the Lower Wisla (from the
Torun profile) and the Gulf of Gdansk ( Hel and
Gdañsk) as well as the meteorological conditions:
currentandforecastedfortheGulfofGdansk.

Reduction of the dimension was carried out
applying 3 methods: correlation, genetic algorithm
andbythemodelsensitivitytesting(itmeanstesting
themodel abilitytogivethegoodsimulation/forecast
for input data containing and without tested
parameters).
Under the literature revive and comparison of
learning methods of ANN (there
is the way of
calculation and reduction of errors between the
known i.e. observed and modelled output data
values)thebackpropagationmethodswaschosenas
well as mulitpreceptron structure ANN ( it means
thatinvestigatedstructurewasconsistsfrom3layers).
The next problem was the division of whole data
population into 3 series : learning and tested (for
modelcalibration)andvalidationseries(independent
datausedformodelverification).70‐15‐15 %division
wasapplieditmeansthat70%ofthepopulationwas
the learning series, 15% each for the testing and
validating ones. To compare the
quality of
performanceandreliabilityofforecast,thestatistical
indicators were applied, calculated for each of the
threetimeseriesseparately:rootmean squareerror
(RMS)andcorrelationcoefficientR(standardPearson
correlationcoefficientwithp=0.92confidence
interval).
4 RESULTSOFMODELLING
There were tested 500 network in respect of
imminence from river; in case of the best 5
representations the results are presented in Table 2.
There are included the characteristics of 5 best
network(withchangeablenumberofhiddenneurons
andoneoutputneuron)representingthewaterlevel
inSwibnowith24hoursleadtimeanddissectionof
by70‐15‐15.
The first column in Table 2 specifies the grid
structure.Thus MLPstands formulti‐layer
preceptron(MultilayerPreceptron)–one‐layerinthis
case,itmeanswithonelayerhidden.Symbols5‐34‐1
showanumberofneurons.
Table2.Characteristicsof5bestcalibratednetworks
__________________________________________________________________________________________________
network corelationcorrelation correlation MREfor MREfor MREfor number activationactivation
(forlearning (fortested (forvalidation learning tested validationofused functionfor function
series)series)series)=model series series series=modellearninghiddenlayer/ foroutput
verificationverificationperiods neurons layer
__________________________________________________________________________________________________
1234 567 89 10
__________________________________________________________________________________________________
MLP5‐34‐1 0,990,990,994,81 5,71 5,97 910Tanh Logistic
MLP5‐35‐1 0,990,990,995,03 5,78 6,52 816Tanh Logistic
MLP5‐31‐1 0,990,990,995,52 6,22 6,53 950Tanh Logistic
MLP5‐35‐1 0,990,990,995,23 6,49 6,90 934Tanh
 Logistic
MLP5‐26‐1 0,990,990,995,63 6,58 6,91 819Tanh Logistic
__________________________________________________________________________________________________
222
Thus MLP 5‐34‐1 defines a one‐layer preceptron
with5inputneurons(inputvector),onehiddenlayer
containing 34 neurons and one output neuron. The
values of coefficient of correlation between the real
observed levels and the levels modelled ( as output
layer/neuron)byANNarepresentedin
thenextthree
columns (2, 3 and 4). The columns are to represent
series: learning, testing and validating. The learning
and testing series are used for calibration of the
model. The validating one is to represent the
independent data (not used in the calibration
process), so the model verification. The
achieved
correlationcoefficientvalueof0.99provesverygood
performance/quality of the model and usability of
ANNmethodologyinmodelling/forecastingofwater
level. The significant performance/quality parameter
isadifferencebetweenthelearningandtestingseries
errors. It displays capacity of the model to
generalization of the gained knowledge (too large
difference shows the neural network over‐learning).
Incaseofthenetworkunderresearchthedifferences
betweentheerrorsoflearninganfjdf455dtestingare
less than 1cm, it means the ANN – from the
methodologystandpoint‐keepsoperatingproperly.
Columns5,6and7 aretocharacterizeavalues
of
RME error (root mean error) obtained for each of 5
networkandeachof3series.AccordingtotheANN
methodology,theRMEvaluesshouldbethelowestin
case of the learning series, the highest for the
validationseries(independentdata).Incaseofallthe
network the values
are close each other and
practically they are equal to the measurement
accuracy.ThevaluesofRMEerrorobtainedwereless
than7 cm – what is considered to be the very good
result.
Thenext,8thcolumnistoinformafterhowmany
epochs the algorithm achieves convergence. The
epochisanameforthecalibrationprocesswhenthe
ANNistocalculateoutput,basingonallthedataof
thelearningandtestedseries.Theerrorreceivedfrom
comparing of the real output value with the value
modelled applying ANN is a basis for correction of
weights denominated to
each of neurons in the
function of activation, to reduce the error in the
following calculation epoch. A number of epochs
oscillated between 816 and 950, what confirms a
convergenceoftheappliedalgorithm.
Information put in column 9 (hyperbolical
tangent)andcolumn10(logisticfunction)represents
theactivationfunction
ofhiddenandoutputlayer.
Figure3. Validation error as the function of number of
hidden neurons in network for activation functions tanh (
hiddenlayer)andlogisticinoutputlayer(Sztobryn,Mielke
2012)
Thedependenceofvalidationerrorfromnumber
ofhiddenneuronsinnetworkforactivationfunctions
tanhandlogwasshownontheFig,3.Theminimum
ofthisfunctionislocatedfor34hiddenneurons.
Figure4. Comparison of observed and modelled values
(Sztobryn,Mielke2012)
Thecomparisonofmodelledandobservedvalues
arepresented onthefigure4.Thevertica laxisstands
bythewaterlevelwhenthehorizontal:bythecases
invalidationseries(i.ethehoursofobservations).In
general the slope and shape of the lines thick
(observed water level) and
thin line (modelled) are
similar.The highest valuesof error are recorded for
the2extremeevent: stormsurgeinOctober2009and
floodwavein2010(theabsolutevalueofwaterlevel
abovetheŚwibnowereexceeded).Thecomparisonof
thevaluesgeneratedbyANNandother
operational
modelsshowthat,thattheseerrorsweregeneratedby
themeteorologicalfactorsasguestandfrontpassing,
which aren’t modelled by meteorological models. It
means,thatANNisn’tthecauseoftheseerrors.
5 CONCLUSION
Good agreement with observed and modeled water
level, especially the results gained in correlation
investigation,
allows to find : the presented
methodologycouldbeuseformodelingandforecast
ofthewaterlevel.
ACKNOWLEDGEMENTS
Theworkwasdone in theframeofinternalIMGW‐
PIB project ( task DS‐P1.5.1 “Opracowanie i
wdrożenie metodyki sieci neuronowych do
prognozowaniazmianpoziomówwodywujściowym
odcinku Wisły”)coordinated by prof. M.Ostojski.
The author wish to thank Directors prof. M.Ostojski
and prof. M.Maciejewski (Institute of Meteorology
and Water Management – National Research
Institute) for valuable suggestions. The special
acknowledgements are directed to co‐workers from
BPH Gdynia for participation in very useful
discussionandalsofor
theirsupport.
223
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