729
1 INTRODUCTION
Thepreparationofthestudiesonforecastingthedrift
of survivors in the Szczecin Lagoon waters was the
inspiration for this topic. The long‐term goal of the
authorsistodevelop driftmodelsofvariousobjects
for employing them in the search‐and‐rescue
operations and for
including them as an additional
sourceoflocationdata.Suchalgorithmsarecurrently
beingdevelopedandtheyfitintotheareaofmodern
navigation[2,14,23,24].
Small boats with limited drafts are main
participantsofsailingintheSzczecinLagoonwaters,
due tothe specificity ofthatreservoir. The Szczecin
Lagoon
characterizeslowdepths.Theaccidentswith
theparticipationofsuchvesselshappenmostoftenon
theSzczecinLagoonwaters.
For example, on 08.05.2017 at noon, three sailors
went on a cruise of the Szczecin Lagoon. On
09.05.2017atafternoon,therescueservicesfoundthe
capsizedyachtoftheBEZtypeand
thebodyofoneof
thosesailors.Theremainingtwomenwerenotfound.
The Rescue Station in Dziwnów and a rescue ship
from Trzebież attended in the rescue operations.
Additionally, the Border Guard also helped on the
water and in the air. In turn, the WOPR and police
searched
an area from the land side [18]. At night,
19.06.2015, the man fell overboard from the S/y
HAARLEMyacht.Despiteanintensivesearchaction,
thesurvivorwasnotfound.Theyachtwastowedon
the island of Wolin. Six search‐and‐rescue units
attended in the rescue operation. Additionally, the
fire
brigadeandpolicesearchedanareafromtheland
side[18].
Comparative Analysis of the Data on the Surface
Currents and Wind Parameters Generated by Numerical
Models on the Szczecin Lagoon Area
M.Kijewska,K.Pleskacz,&L.Kasyk
M
aritimeUniversityofSzczecin,Szczecin,Poland
ABSTRACT:Thisstudyfocuses onthe investigationofavailablesurfacecurrents andwind parametersfor
employingtheminordertopredictthesurvivormovementintheSzczecinLagoonwaters.Forthispurpose,the
surfacecurrentsandwindparametersweregeneratedbyselectednumericalmodelsand
thewindparameters
werealsomeasuredwiththetelemetrydevices.Inthispaper,thePM3DhydrodynamicmodelandtheNEMS,
ECMWF, GFS weather forecast models have been investigated. The measurements of the wind parameters,
recordedattheBramaTorowaIandTrzebieżstations,werealsoanalyzed.Aspartofthe
research,anexpert
methodwas used to evaluate the surface currents parameters. In turn,the method based on comparing the
forecastedwindparameterswiththemeasuredwindparameterswasappliedinordertoassessuncertaintiesof
theseparameters.Thecomparativeanalysesofthedataonthesurfacecurrentsandwindparameters
havebeen
done and probabilistic models for uncertainties of these forecasted parameters have been formulated.
Additionally, relations between the surface currents speeds and the wind speeds, in the case when their
directionswereconsistent,havebeenalsodiscovered.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 4
December 2018
DOI:10.12716/1001.12.04.12
730
ThemostimportanttaskoftheSARservicesisto
look for the people who have fallen overboard or
drifting in the water after overturning the boats. In
the literature [3‐7,9,10,13,17,20,21,25,27], the search‐
and‐rescue areas, in waters used for the navigation,
are determined by employing the Monte Carlo
methods,Bayesianmethods,regressionmodelsforan
object’sdriftvelocity,theFokker‐Planckequationsor
certain graph models. To determine such areas, it is
necessary to obtain data about surface currents and
wind. That data are often generated by numerical
models.Theaccesstosuchdatamightbeobtainedby,
e.g., theGeographic Information System such as the
Maritime Network‐Centric Geographic Information
System Gulf of Gdansk [16]. Sometimes, some
relationsbetweenthewindandwind‐drivencurrents
are established [20]. Based on the wind parameters,
theleewayparametersalongwiththeiruncertainties
aredetermined,e.g.,bythelinearregressionor
onthe
basis of constructed probability distributions. The
potentialtotaldriftofasurvivoristhevectorsumof
the current and leeway. The position vector of a
survivoratagiventimetiscalculatedastheintegral
of the survivor’s velocity vector from the initial
momenttothe
timetincreasedbythevelocityvector
fromtheinitialmoment.
AccordingtoIAMSAR(InternationalAeronautical
and Maritime Search and Rescue Manual) [8], an
estimation of the surface current and wind
parameters can be derived from direct observations,
diagrams,charts, wind roses, reliablehydrodynamic
models and weather forecast models. The direct
observations may be obtained from the in situ
measurements,fromvesselspassingthroughanarea;
aircrafts flying over an area, installed appropriately
buoys,platformsorsatellitemeasurements.However,
suchdataarenotalwaysavailable.Bydiagramsand
charts,thelong‐termaverageseasonalparametersof
the currents and wind could
be determined.
However,thesesourcesareemployedintheareasfar
away from shores. Nevertheless, an estimation of
these parameters provided by these sources should
not be used in coastal areas, and especially in the
offshore areas less than 25 nautical miles distance
from the shore and less than 300 feet
(100 meters)
water depth. Reliable hydrodynamic models with
high resolution and weather forecasts models are
other sources of such. The authors consider these
sourcesofdata.
The first aim of this paper is to verificate the
available data on the surface currents and wind
parameters on the Szczecin Lagoon area
for the
summer season in 2017. The forecasted surface
currentsparameters have beenexamined with using
an expert method. In turn, the real and forecasted
wind parameters have been compared. Some
statisticalcharacteristics of the uncertainties of those
parameters havebeen presented. Furthermore, some
probabilisticmodelsfortheobtaineduncertaintiesof
the considered parameters have been determined.
Additionally, linear relations between the surface
currentsandwindspeedswereestablished.
The remainder of this paper is organized as
follows.InSection2,researchareaanditshydrology
conditions are described. In Section 3, the materials
and methods are presented. Section 4 contains
a
comparative analysis of numerical data on surface
currents and wind parameters collected for the
SzczecinLagoonduring thesummer season in2017.
InSection5,adiscussionoferrorsinforcingfieldsis
conducted.Section6concludes.
2 RESEARCHAREAANDITSHYDROLOGY
CONDITIONS
2.1 Researcharea
The Szczecin Lagoon
(Polish: Zalew Szczeciński)
coverswaters atthemouth ofthe Odra River. From
thenorthernsideofthislagoon,theislandsofWolin
and Uznam separate it from the Baltic Sea. In the
middle part of this lagoon, it is subdivided into the
LargeLagoon(Polish:WielkiZalew),with
thesurface
areaof
2
488 km lyingwithinPoland,andtheSmall
Lagoon(German:KleinesHaff),coveringtheareaof
2
424 km ,whichbelongsalmostentirelytoGermany.
The Szczecin Lagoon lies on the longitude: approx.
'
13 53 E
'
14 36 E
and the latitude: approx.
'
53 42 N
'
53 52 N
.Itisabout 28 km long and
over
52 km wide [1]. The southern limit of the
Szczecin Lagoon is designated by the Jasienica
channel outlet (on the west bank)and the mouth of
theKrępaRiver(intheeast).
ThePomeranianBay(Polish:ZatokaPomorska)is
connected with the Szczecin Lagoon via the straits:
Dziwna,Świna and Peennestrom.Ś
wina is the most
important for the Szczecin Lagoon hydrological
system. These straits are not the Odra River arms,
becausetheircurrentisnotarivercurrent,butitisthe
result of the constant sea and the Szczecin Lagoon
waterlevelling.
TheaveragedepthoftheSzczecinLagoonisabout
3,8 m . The largest natural depth of the Szczecin
Lagoon is
8,5 m . However, it is not a region
deprivedofshoalsandshallows.Nearly
25% ofthe
areais
02
‐meterdeep,andthehighaverageisdue
tothefactthatthereisthe
10,5 ‐meterdeepchannel
across the Szczecin Lagoon from Szczecin to Baltic
waters [1]. This channel is called the Szczecin‐
Świnoujście fairway. The Szczecin‐Świnoujście
fairway is the dredged channel in the Szczecin
Lagoonarea.
2.2 Descriptionofthehydrologicalconditionsonthe
SzczecinLagoon
TheSzczecinLagoonis
perceivedasasmallandfairly
safeareaforsailingandmotorboatsport.Thedanger
is the shape of its coastline and bottom, which in a
combination with varying hydrodynamic conditions
led already too many woes. Particularly dangerous
are squalls, which are strong and unexpected. In
addition to the wind
dynamic action, generated
waves affect also boats. The wave height is directly
relatedtothedepthofalagoonarea.
Windwavesaretheimmediatethreats.Thewave
dimensionsaredeterminedbythewind.Theduration
of the wind forcing practically does not affect the
developmentofthewave.Thefull
wavedevelopment
can take place within a period of no more than one
hour. After the wind stopping, the wave quickly
731
disappears. The currents directions in the Szczecin
Lagoon generally lay along the dredged channel.
However, there may also be the currents which are
perpendiculartoit.Thecurrentsduringtheinflowof
Balticwaterscanreach
24 knonthestraits:Świna
andDziwna.
Thechangeofthewaterlevelmaycausecurrents.
Itis importantto note that large, sudden, butshort‐
termfluctuationsinthewaterlevelcausestorms.The
stormy winds from the northern sector cause the
water level increasing of
0,7 1,0 m
, while the
southern winds – the decreasing of
0,6 m . The
winds, with the speed of more than
10 /ms
, cause
the water‐level variation. The north or south
variations rarely exceed
0,1 m , and in the west or
east direction –
0, 2 m
. However, the stormy
southwest winds cause the water‐level difference of
0,6 m .
Thesurfacecurrentsandalsowindareimportant
forestablishingtheparametersofthesurvivor’sdrift
inthe water. In order to develop and determine the
potentialsearcharea,thedirectionofthewaterflow
should be taken into account in addition to the
direction and force of the wind
parameters. The
fluctuationsinthewaterleveldependmainlyonthe
windparameters.ForthewindfromNWtoNE,the
water level can rise by about
1 m per day. In turn,
forthewindfromthesouthernsector,itdecreasesby
0,6 m in the relation to the average level. The
exemplary fluctuations of the water level on the
indicator at the Trzebież hydrological station are
presentedin Figure 1. With such shallow water and
mostlyswampyandlowbanks,suchamplitudeofthe
water level radically changes the shape of the
shoreline
insomeareas.
Figure1. Change in the water level on the Trzebież
indicator–from25.06to03.07.2017.
3 MATERIALSANDMETHODS
Foranalysispurposes,theauthorschosethemonths:
July and August in 2017, since experiments will be
donebythisseasoninthefeature.Theanalysiscovers
only this season due to the unavailability of any
forecasted wind parameters generated by the
consideredweatherforecastmodels:ECMWF,
NEMS,
GFS fromtheprevious summer seasons. In order to
discuss the surface currents parameters on the
Szczecin Lagoon, the authors generated the surface
currents charts by the SatBałtyk system [19]. The
parametersofthesurfacecurrentswerederivedfrom
the PM3D hydrodynamic model [15]. The PM3D
hydrodynamic model
works at the Institute of
OceanographyattheUniversityofGdańskinPoland
[11]. The PM3D model covers the Szczecin Lagoon
with 1/6NM resolution (approximately 300 m). It is
worth adding that thishigh resolution of the PM3D
modelfortheSzczecinLagoonareaaffectsthemuch
better description
of this area’s bathymetry and
coastline [12]. It may be seen that the widths of the
narrow straits connecting the Szczecin Lagoon with
the Pomeranian Bay (Świna, Dziwna, Peennestrom)
areclosetotheirrealsize[12].TheSatBałtyksystem
data, e.g., the surface currents parameters, are
updated four
times a day: 0000UTC, 0600UTC,
1200UTC,1800UTC.
Itisworthaddingthatthevalidationofthesurface
currents parameters with using the in situ
measurements was not possible. By this reason, the
generated surface currents fields were discussed by
the expert method. The expert method utilizes the
knowledge of experiencedprofessionals
in
evaluating the goodness of the generated surface
currents fields. The authors presented the generated
chartsofthesefieldstotheexperts–thegroupofport
pilots – which know the hydro meteorological
conditions of the Szczecin Lagoon. Additionally, the
authors created the list of the questions which
facilitated
the evaluation of these charts. These
expertsassessedthereceivedchartsandrespondedto
the submitted questions. These questions concerned
thehydrologicalandmeteorologicalconditionsonthe
Szczecin Lagoon area, e.g., whether the information
contained on the generated charts coincides with
many years of experience of the practitioners – the
pilots;
what are the directions and speeds of the
surface currents on the Szczecin Lagoon; what do
their directions and speeds depend on; how the
shapingoftheshorelineandlandaffectsthedirection
and speed of the wind at various points of the
SzczecinLagoon;duetothevariabilityof
parameters,
i.e.,theshapeofthebottomprofileandshoreline,the
impact of the Odra River; in which areas of the
Szczecin Lagoon the currents are the most variable
andunpredictable,etc. Itisworthnotingthat,upto
this date, there exists no research work that has
attempted to validate
the surface currents fields
presentedintheSatBałtyksystem.
In the world, currently in certain water areas,
measurements ofthe sea currents are carried out
using the High Frequency Surface Wave Radars
(HFSWR).However,suchradarsarenotavailablein
the Polish zone of responsibility. Indeed, the typical
range
of the surface velocity measurements is
30 100 km
from the coast and inthe case of high
spatial resolution depending on the radar working
frequency– a fewkilometres. Due tothesizeof the
Szczecin Lagoon, it is currently too expensive
solution.
The authors further have established the linear
relations between the surface currents and wind
parameters
at two points of the Szczecin Lagoon:
Brama Torowa I (longitude:
'
014 20
E; latitude:
'
53 49
N) and at the point in the area nearby the
Trzebież (longitude:
'
014 28
E; latitude:
'
53 41
N).The Szczecin Lagoonis aflowable reservoirand
the water flow at these two points reflects to a
significantextentthewatermovementinthislagoon.
Inturn,theprobabilisticapproachwasusedinorder
732
todescribeuncertaintiesfortheparametersachieved
withtheobtainedformulas.
In turn, for a comparative analysis of the wind
parameters, the authors firstly generated charts
depictingthewindyconditionsforJulyandAugustin
2017. These charts were generated on the website
https://www.windy.comForthisresearch,thedataon
the wind parameterswere collected from the Brama
Torowa I and Trzebież meteo stations. These data
were recorded by the Maritime Office in Szczecin
(UMS) and the Institute of Meteorology and Water
ManagementinWarsaw(IMGW).Theforecastsofthe
wind parameters were obtained from the NEMS,
ECMWForGFS
models.Thedatafromthesemodels
are generally available in [26]. The NEMS (NOAA
Environmental Modelling System) model has the
resolution of approximately
4 km and its data are
updated every
12 hours: 0830UTC, 2030UTC. The
ECMWF (European Center for Medium‐Range
Weather Forecasts) model, with the resolution of
approximately
9 km , is updated every
12
hours:
0715UTC, 1915UTC. The GFS (Global Forecast
System) model has the resolution of approximately
13 km and it is updated every 6 hours: 0615UTC,
1215UTC,1815UTCand0015UTC.TheNEMSmodel
is a local European model. The ECMWF and GFS
modelsareglobalweathermodels.
Inthispartofthepaper,theauthorscomparedthe
measuredandforecastedwindparameters. Moreover,
the authors described statistically the differences
betweentheseparameters.Inturn,
theprobabilistic
models for the absolute values of the differences
between the measured and forecasted wind
parametersareachieved.
4 COMPARATIVEANALYSISOFTHE
NUMERICALDATAONTHESURFACE
CURRENTSANDWINDPARAMETERS
COLLECTEDFORTHESZCZECINLAGOON
WATERSDURINGTHESUMMERSEASON
4.1 Thesurfacecurrentsparameters
In general, the
experts did not have any significant
objections to the water circulation presented on the
generated charts of the Szczecin Lagoon. They
observed that, substantially the charts appropriately
reflect the wind‐driven currents. For example, the
experts, analyzing the surface currents chart for
08.07.2017at12:00UTC,establishedthattheimpactof
the wind field has been reflected in the surface
currents field, that is, the surface currents field was
directlydependenton changes inthe air flowat the
air‐water interface. Moreover, they noted that the
generated surface currents field was quite uniform.
Thatis,thisfieldwasclosetothe
stationaryfield.The
differencesinthecurrentsdirectionsandspeedswere
not significant in the central part of the Szczecin
Lagoon. By these reasons, the experts recommended
thatdownscalingcouldbeconsideredinthefeature.
The hydrodynamic model, generating the surface
currents, could be adapted in order to describe
conditions
intheSzczecinLagoonalmosttwoorders
of magnitude smaller. Furthermore, this approach
couldunveilsub‐gridwatermovements,providinga
more complicated description of the water transport
process on the Szczecin Lagoon. The experts also
observed that the surface currents circulation was
strictlyconnectedwiththeshoreline’sshape,butthe
waterexchangebetweentheSzczecinLagoonandthe
PomeranianBaywaspreserved.
However, in the area of complicated shoreline
configuration and significant shallows, there are
clearly noticeable differences between the display of
the charts and the experts’experience. Indeed, there
are areas on the Szczecin Lagoon where the PM3D
model
forecasts the surface currents directions
opposite to those estimated by the experts. In such
areas,thesurfacecurrentdirection,forecastedbythe
PM3Dmodel,isnotjustifiedbythebathymetryofthe
lagoon.Duringthebackflow(thatis,thewaterinflow
from the Baltic Sea to the Szczecin Lagoon),
particularlystrong
surfacecurrentsoccurinthearea
ofthemouthofthePiastowskiChaneltotheSzczecin
Lagoon. The similar phenomenon, wherein the
currentdirectionisopposite,occursespeciallyinthe
southernandsoutheasternwindsatthemouthofthe
Oderriver.Thecomplicatedshaping oftheshoreline
(especially,inthe
easternpartoftheSzczecinLagoon)
causes a turbulent water flow and changes in the
surfacecurrentsdirections.
In addition, the experts noticed that the surface
currents directions depend on: the depth of the
Szczecin Lagoon (e.g., the area of the Szczecin‐
Świnoujście fairway), the shape of the bottom
(e.g.,
shallows),the shape of the shoreline, the Odra river
inflow to the Szczecin Lagoon or thebackflow from
theBalticSeatotheSzczecinLagoon.
Asthenextstep,sincethesurfacecurrentsonthe
Szczecin Lagoon – in the experts’ opinions – were
reflectedwithgoodagreement,theauthors
usedthem
inordertoestablishsomerelationsbetweenthemand
windparameters.Thisisasecondapproachinorder
to generate the surface currents on the Szczecin
Lagoon.Withthisapproach,therewillbenoproblem
withthecomputationalcomplexityandtherewillbe
noneedtowritingfurther
algorithmsallowingforthe
assimilation of data on the surface currents
parameters sent from another server after being
generatedbythePM3Dmodel.Thisapproachcanbe
used when conducting pilot studies. Moreover, the
parametersofthesurfacecurrentsgeneratedinsuch
way may be used when the access to such
data is
limited or when the assimilation of such data
generatedfromthePM3Dmodelisrequired.
The authors observed that the surface currents
directions, generated with the PM3D model by the
SatBałtyksystem, andthe measuredwind directions
intheareanearbytheTrzebieżmeteostationshowed
a
satisfactory agreement. Such agreement also was
observed at the Brama Torowa I. The authors
determined that the differences between these
parameters are insignificant when the wind
conditionsarestable ornot verychangeable.Due to
this observation, some linear relations between the
surface currents and wind speeds, when their
directions
were consistent, have been established.
Moreover,probabilisticmodelsoftheuncertaintiesin
thesurfacecurrentsspeedsfoundedwithusingthose
relationshipshavebeenachieved.
Theformulawasobtained withusingthe surface
currents parameters generated by the SatBałtyk
733
system and the measured wind parameters. These
datawerereceivedwithtwomonths:JulyandAugust
2017 from two measuring stations: Brama Torowa I
andTrzebież.Theobtainedformulafortheareaatthe
BramaTorowaIstationisasfollows:
3,82% ,
cw
VV (1)
where:
w
V –10‐mwindspeed[m/s],
c
V –surfacecurrentsspeed[m/s].
The standard deviation between the surface
currentsspeeds
c
V obtainedbyformula(1)andthe
surface currents speeds measured in the SatBałtyk
system at the Brama Torowa I station equals
0,06 /ms.
In turn, the formula for the Szczecin Lagoon
watersattheTrzebieżstationisasfollows:
2,24% .
cw
VV (2)
The standard deviation between the surface
currentsspeeds
c
V obtainedbyformula(2)andthe
surface currents speeds measured in the SatBałtyk
system at the Trzebież station’s waters equals
0,03 /ms.
Thesmallercoefficientinformula(2)thanthatin
formula(1)resultsfromthedifferenceinthedistance
to the coastline between the Brama Torowa I and
Trzebieżstationsandalsofromthesmallerdepthof
theSzczecinLagoonintheTrzebieżarea.
Moreover, at the Brama Torowa I station
the
differences between the surface currents speeds,
calculated by formula (1), and the surface currents
speeds, collected with using the SatBałtyk system,
have been described by the t‐Student distribution
withthefollowingparameters:thelocationparameter
0,017
,thescaleparameter 0,06
,andthe
degreeoffreedom
240v
(Fig.2):
241
2
287
2
1
4,3427 10
240 277,778 0,017
fx
x
(3)
Figure2. The histogram for the differences between the
surface currents speeds calculated by formula (1) and the
surface currents speeds collected at the Brama Torowa I
station.Theprobabilitydensityfunction(PDF),fittedtothe
exposure data, is depicted the blue colour. The t‐Student
distributionhavebeenemployed.
In Table 1, the statistical tests’ results are
presented. The compliance tests provide the
conclusion that there is no reason to reject the
hypothesis that the t‐Student distribution describes
the differences between the surface currents speeds,
calculated by formula (1), and the surface currents
speeds, collected with using the SatBa
łtyk system,
since P‐Value is greater than
0,05 (significance
level)inthree presented tests:theAnderson‐Darling
test, the Cramèr‐von Mises test and thePearson
2
χ
test.
Table1. The results of the statistical tests regarding the
goodness‐of‐fit of the t‐Student distribution to the
differencesbetweenthesurfacecurrentsspeeds,calculated
by formula (1), and the surface currents speeds, collected
withusingtheSatBałtyksystem.
_______________________________________________
“test”“P‐Value”
_______________________________________________
“Anderson‐Darling” 0,22
“Cramèr‐vonMises” 0,24
“Pearson”
2
χ 0,06
_______________________________________________
Inturn,intheareanearbytheTrzebieżstationthe
differences between the surface currents speeds,
calculated by formula (2), and the surface currents
speeds, collected with using the SatBałtyk system,
have been described by the t‐Student distribution
withthefollowingparameters:thelocationparameter
0,005
, the scale parameter 0,032
, and
thedegreeoffreedom
150v (Fig.3):
151
2
165
2
1
2, 4543 10
150 976,5625 0,005
fx
x
(4)
Figure3. The histogram for the differences between the
surface currents speeds calculated by formula (2) and the
surface currents speeds collected in the area nearby the
Trzebież station. The probability density function (PDF),
fittedtotheexposuredata,isdepictedthebluecolour.The
t‐Studentdistributionhavebeenemployed.
In Table 2, the statistical tests’ results are
presented.Thereisnoreasontorejectthehypothesis
that the t‐Student distribution describes the
differences between the surface currents speeds,
calculated by formula (2), and the surface currents
speeds, collected with using the SatBałtyk system,
since P‐Value is greater
than 0,05 (significance
level)inthree presented tests:theAnderson‐Darling
test, the Cramèr‐von Mises test and thePearson
2
χ
test.
734
Table2. The results of the statistical tests regarding the
goodness‐of‐fit of the t‐Student distribution to the
differencesbetweenthesurfacecurrentsspeeds,calculated
by formula (2), and the surface currents speeds, collected
withusingtheSatBałtyksystem.
_______________________________________________
“test”“P‐Value”
_______________________________________________
“Anderson‐Darling” 0,41
“Cramèr‐vonMises” 0,39
“Pearson”
2
χ 0,07
_______________________________________________
It is worth adding that sometimes at the chosen
measuringstationsignificantly‐differentdirectionsof
surfacecurrentsandwindweremeasuredinthesame
timefromtwoabovementionedmonths(alittlemore
at the Trzebież station than at the Brama Torowa I
stationdueto,amongothers,thedifferentaccuracy
of
themeasurement).
ForJulyandAugustin2017,thewesterndirection
of the surface currents was prevailing in the area
nearby the Trzebież station (Tab. 3). The eastern
direction of these currents occurred less frequently.
Otherdirectionshavebeensporadicallyreported.
Table3.Frequencyofthesurfacecurrentsdirectionsforthe
Szczecin Lagoon waters at the Trzebież station – July and
Augustin2017
_______________________________________________
Directions Percent(%)
_______________________________________________
W47
E24
SE9
SW7
NW5
S4
NE2
N2
_______________________________________________
Forthesameseason,thewesterndirectionsofthe
surface currents were also prevailing for the Brama
TorowaIstation(Table4),buttheseonesarenottoo
significant(
26% ) likethose for the area nearby the
Trzebieżstation(
47%)
.
Furthermore, many directions of the surface
currents were coming from south‐west and east
(
34%) attheBramaTorowaIstation.Nevertheless,
attheBramaTorowaIstationthesoutherndirections
were coming less frequently and other directions
constitutedafewpercentofalldirections.
Table4.Frequencyofthesurfacecurrentsdirectionsforthe
SzczecinLagoonwatersattheBramaTorowaIstation–July
andAugustin2017.
_______________________________________________
Directions Percent(%)
_______________________________________________
W26
SW17
E17
S11
SE9
NE8
NW7
N5
_______________________________________________
Thedistributionspresentedbyformulas(3)and(4)
(or in Figures 2 and 3) have been described in both
cases by the t‐Student distribution, but with the
different parameters. This results from: the
neighbourhoodoftheŚwinastrait,theoutflowofthe
waterfromtheŚwinaduringabackflow,the
different
distance to the Szczecin‐Świnoujście fairway, the
shape of the bottom in these locations (shoals,
shallows),variousshapingoftheshoreline,adifferent
number of the available data. Thus, in these two
regions there is a different characteristic of the
SzczecinLagoon.
4.2 Thewindparameters
The wind
parameters for the Szczecin Lagoon,
read from the charts generated by the NEMS,
ECMWF,GFS models, indicated different agreement
with those measured. In stable weather conditions,
thegoodagreementwasoftenmaintained.However,
some differences between the forecasted and
measured parameters were also observed. For
example, for 12.07.2017 at 16:00UTC at
the Trzebież
measuring station, one was measured the real wind
direction
175
andthereal 10 ‐minutewindspeed:
theaveragespeed‐
1, 8 /ms,themaximumspeed‐
2,7 /ms
.Inturn, byanalyzing thewind chartsfor
12.07.2017 at 16:00UTC generated by the SatBałtyk
system and on the website https://www.windy.com
for the NEMS, ECMWF, GFS models, one could be
seen that these models have generated the slightly
differentvectorfields.ForTrzebież,theNEMSmodel
forecasts the
wind blowing from the direction 100
and at the speed
2,7 /ms. The ECMWF model
givesthe direction:
220
and thespeed: 3, 6 /ms.
Inturn, theGFSmodelproducesthedirection:
210
and the speed:
2,7 /ms
. One can observe that in
thiscasetheforecastedwinddirectionbytheNEMS
modelhasthesmallestaccuracy,butthisisduetothe
long time since the forecast was calculated. In this
case, the average absolute value of the difference
betweenthemea s uredandforecastedwinddirection
equals
approximately 40
and the wind speed is
closertothemaximalmeasuredspeed
2,7 /ms.
Due to the size of the differences between the
measured and forecasted wind parameters and
knowingthatthemeasuredwindparameters are15‐
min or 10‐min average values, one was decided in
order to establish the absolute values of the
differences between the measured and forecasted
wind parameters. In
Table 5, various statistics
parameters describing the absolute values of the
differencesbetweenthewinddirectionsmeasuredat
theTrzebieżstation andthe directions forecastedby
the NEMS, ECMWF and GFS models at this station
have been established. One can see thatthe average
absolute value of difference between the
mentioned
directions equals
36
, the median of such absolute
valueofdifferencesis
22
,thefirstquartileisequal
to
10
andthirdquartile– 42
.Thismeansthatthe
most of these absolute values of differences are less
than
43
.Theseabsolutevaluesofdifferenceshardly
ever achieve the maximum value
179
. The root‐
mean‐square‐error(RMSE)fortheabsolutevaluesof
thesedifferencesequals
54
.
735
Table5.Thestatistics(m/s)describingtheabsolutevaluesof
differences between the wind directions measured at the
TrzebieżstationandthedirectionsforecastedbytheNEMS,
ECMWF,GFSmodels.
_______________________________________________
ParameterValue(degree)
_______________________________________________
minimum0
maximum179
average36
median22
quartile110
quartile343
RMSE54
_______________________________________________
InTable6,thestatisticsparametersdescribingthe
absolutevaluesof the differences between the wind
speeds measured at the Trzebież station and the
speeds forecasted by the NEMS, ECMWF, GFS
models are presented. One can see that the average
andmedianofsuchabsolutevaluesofthedifferences
arenot
toomuchdifferentfromeachother.Moreover,
75%oftheseabsolutevaluesofthedifferencesareless
than
2,8 /ms. The root‐mean‐square‐error (RMSE)
for the absolute values of these differences equals
2, 4 /ms.
Table6.Thestatistics(m/s)describingtheabsolutevaluesof
the differences between the wind speeds measured at the
Trzebież station and the speeds forecasted by the NEMS,
ECMWF,GFSmodels.
_______________________________________________
ParameterValue(m/s)
_______________________________________________
minimum0
maximum7,5
average2
median1,7
quartile10,9
quartile32,8
RMSE2,4
_______________________________________________
Theabsolutevaluesofthedifferencesbetweenthe
measured wind directions and the directions
calculated by thechosen weather forecast models at
the Trzebież station have been described by the
exponentialdistributionwithparameter
0,0277
(Fig.4):
0,0277 exp 0,0277
f
xx
for 0x (5)
Figure4. The histogram for the absolute values of the
differencesbetweenthemeasuredwinddirectionsandthe
directions, calculated by the chosen weather forecast
models, at the Trzebież station. The probability density
function(PDF),fittedtotheexposuredata,isdepictedthe
blue colour. The exponential distribution have been
employed.
In Table 7, the statistical tests’ results are
presented.Onemightconcludethatthereisnoreason
to reject the hypothesis that the exponential
distribution describes the absolute values of the
differences between the measured wind directions
and the directions calculated by thechosen weather
forecastmodelsattheTrzebieżstation,
sinceP‐Value
is greater than
0,05 (significance level) in the
Cramèr‐vonMisestest.
Table7. The results of the statistical test regarding the
goodness‐of‐fit of the exponential distribution to the
absolute values of the differences between the measured
winddirectionsandthedirectionscalculatedbythechosen
weatherforecastmodelsattheTrzebieżstation.
_______________________________________________
“test”“P‐Value”
_______________________________________________
“Cramèr‐vonMises” 0,33
_______________________________________________
In turn, the absolute values of the differences
between the measured wind speeds and the speeds
calculated by thechosen weather forecast models at
the Trzebież station have been described by the
extreme value distribution with the location
parameter
1, 3
andthescaleparameter 1,1
(Fig.5):
0,909 exp exp 0,909 1,3 0,909 1,3
f
xxx
(6)
In Table 8, the statistical tests’ results are
presented.One can gatherthatthereis no reason to
reject the hypothesis that the extreme value
distribution describes the absolute values of the
differences between the measured wind speeds and
the speeds collected by the chosen weather forecast
models at
the Trzebież station, since P‐Value is
greater than
0,05 (significance level) in three
presented tests: the Anderson‐Darling test, the
Cramèr‐vonMisestestandthePearson
2
χ test.
Table8. The results of the statistical tests regarding the
goodness‐of‐fit of the extreme value distribution to the
absolute values of the differences between the measured
wind speeds and the speeds calculated by the chosen
weatherforecastmodelsattheTrzebieżstation.
_______________________________________________
“test”“P‐Value”
_______________________________________________
“Anderson‐Darling” 0,46
“Cramèr‐vonMises” 0,61
“Pearson”
2
χ
0,19
_______________________________________________
Figure5. The histogram for the absolute values of the
differences between the measured wind speeds and the
speedscalculatedbythechosenweatherforecastmodelsat
theTrzebieżstation.Theprobabilitydensityfunction(PDF),
fittedtotheexposuredata,isdepictedthebluecolour.The
extremevaluedistributionhasbeen
employed.
736
In our case, on the Szczecin Lagoon in July and
August in 2017 the average wind direction is
202
and its standard deviation equals
36
. In turn, the
average wind speed is equal to
2,3 /ms and its
standarddeviationis
2 /ms.BasedonTables5and
6,onecanassumethattheaveragefluctuationforthe
wind direction equals
36
and its standard
deviationis
54
.Inturn,theaveragefluctuationfor
thewindspeedisequalto
2 /ms anditsstandard
deviationis
2, 4 /ms.
5 DISCUSSIONOFERRORSINFORCINGFIELDS
The errors in the force fields are caused by many
factors. The initial conditions and boundary
conditionsintroducedintothemodelsareoneofsuch
factors. These data being these conditions are
burdened with the measurement uncertainties and
theuncertaintyofthemodel
forecasts,fromwhichthe
data are assimilated. In addition, an interpolation
shouldbe performed in order to establish the initial
valueofthe parameterintroducedinto themodel in
many meshes of the discretizationgrid. The bilinear
interpolation is most often performed. The
interpolation’s calculations also introduce some
errors.
The
selected numerical models have certain
resolutions. On one hand, maintaining a high
temporal and spatial resolution is desirable. On the
other hand, the calculations have to be made in a
huge number of meshes of the discretization grid.
This is associated with a significant increase in
computational complexity: time and/or spatial.
Moreover, the spatial resolutions, at which the
numerical models are applied, affect the solution of
theequationsdescribingthemodelledphenomena.In
many cases this also leads to being incapable to do
such calculations. In spite of the huge modern
computational memories and computing powers,
theyturnouttobe
insufficientfortherequirementsof
thenumerical models. The calculations are made on
supercomputers doing them in petaflops, but this is
notenoughtogetperfectforecasts.
A mathematical description of the phenomena
occurring in the atmosphere is an another factor
influencingtheoccurrenceoftheerrorsintheforcing
fields.
It results from the assumptions and the
simplifications defined at the stage of designing the
numerical model’s concept. While the phenomena
occurring on a global scale are quite well reflected,
the local phenomena are often less well described.
They are often treated as so‐called the sub‐grid
processes. To
a certain extent, these phenomena are
taken intoaccount when downscaling (nested)grids
are created. In addition, the differential equations
describingthechangesinthestateoftheatmosphere,
when solving them in a numerical manner, are
replaced by the difference equations. The obtained
solutions are an approximate solutions. This is
also
due to the occurrence of the rounding errors and
calculation errors. From the point of view of
modelling the survivor’s drift route in the Szczecin
Lagoon waters, it seems reasonable to model the
uncertainty in the surface currents and wind
parameters in order to minimize errors in the
obtained
forecasts of these parameters. Indeed, the
probabilistic models of the absolute values of the
differences between the real and modelled wind
parametershavebeenpresented.
An another direction of an improvement in the
qualityofforecastsofthesurfacecurrentsandwind
parameters is taking into account the real
measurementsof
suchparametersmadebyallocating
the measuring buoys and meteo stations in the
SzczecinLagoonwaters’area.Asaresult,thenumber
oftherealmeasurementsenteredintothe numerical
modelsastheinitialdatawillbeincreased.Providing
additionalmeasurementdatawouldcertainlyreduce
theerrorsintheforecasted
parameters.
It seems advisable to carry out: the in situ
measurements of the surface currents and wind
parameters in order to validate the predicted
parametersintheopenwatersoftheSzczecinLagoon,
apossibleimprovementoftheforecastsgeneratedby
selected numerical models in the Szczecin Lagoon
areaorthe
selectionofappropriatemethodsandtools
to more accurately model the uncertainty of these
parameters. The in situ measurements could also
indicate possible locations on the Szczecin Lagoon,
where automatic meas uring stations could be
allocated in order to increase the amount of the
available data constituting the initial conditions for
theselectednumericalmodels.
6 CONCLUSIONS
The forcing fields always contain errors. Processes,
that take place in the atmosphere and the
hydrosphere, are different temporal and spatial
scales. Furthermore, they are characterized by great
complexityandvariability.Amodelforaforcingfield
may welldescribe large‐scale movements, but it
can
significantly underestimate or overestimate or even
ignore small‐scale movements. However, small‐scale
processes may, be relevant and, depending on the
issue,theirinclusionshouldbeconsideredinorderto
predict as accurately as possible, for example, the
surfacecurrentsandwindparameters.
Analyzingthesurfacecurrentschartsgenerated
by
the PM3D model in the SatBałtyk system, one can
observe that the impact of the wind field has been
reflected in the surface currents field. Moreover,
surface currents circulation was strictly connected
with the shoreline’s shape. The water exchange
between the Szczecin Lagoon and Pomeranian Bay
has been provided
with good agreement. In the
feature,itisworthdoingrealexperimentsinorderto
determinepossibledifferencesbetweentheforecasted
and real surface currents parameters. Furthermore,
theimpactofthesedifferencesonthesurvivor’sdrift
will be also established. In turn, some fluctuations’
models for the surface currents speed,
when their
directions are consistent, have been established. In
this case, the t‐Student distribution has been
employed.
The wind fields, generated by weather forecast
models such as the NEMS, ECMWF, GFS models,
often differ slightly over the same time period. But
sometimesthefluctuationsinthewinddirectionsand
737
speedsaresignificant.Inthispaper,themodelsofthe
windparametersfluctuationshavebeenpresented.In
order to describe the absolute values of the
differences between the forecasted wind directions
anddirectionscollectedattheTrzebieżstationinthe
SatBałtyk system, the exponential distribution has
been employed. In
turn, in order to establish the
absolute values of the differences between the
forecasted wind speeds and the speeds recorded at
the Trzebież station in the SatBałtyk system, the
extremevaluedistributionhasbeenused.
The fluctuations’ models in the forcing fields
(wind and surface currents) on the Szczecin
Lagoon
have been presented in order to employ the Monte
Carlo techniques. These techniques will generate an
ensemblewhichyieldsanestimatelocalizationofthe
survivorevaluatingoveratimeperiod.
ACKNOWLEDGEMENTS
TheauthorswouldliketothanktheMarineOfficein
SzczecinandtheInstituteofMeteorologyandWater
Management
forsharingthedataonwindparameters
and water level for the chosen meteorological
stations.
This research outcome has been achieved under
thegrantNo4/S/INM/15finansedfromasubsidyof
the Ministry of Science and Higher Education for
statutoryactivities.
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