Sea Topography of the Ionian and Adriatic Seas Using Repeated GNSS Measurements

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Article Sea Topography of the Ionian and Adriatic Seas Using Repeated GNSS Measurements

Sotiris Lycourghiotis 1,2

1 Department of Civil Engineering, University of Peloponnese, 1 M. Alexandrou Str., Koukouli, 26334 Patras, Greece; [email protected] 2 School of Science and Technology, Hellenic Open University, Tsamadou 13-15, 26222 Patras, Greece

Abstract: The mean sea surface topography of the Ionian and Adriatic Seas has been determined. This was based on six-months of Global Navigation Satellite System (GNSS) measurements which were performed on the Ionian Queen (a ship). The measurements were analyzed following a double-path methodology based on differential GNSS (D-GNSS) and precise point positioning (PPP) analysis. Numerical ﬁltering techniques, multi-parametric accuracy analysis and a new technique for removing the meteorological tide factors were also used. Results were compared with the EGM96 geoid model. The calculated differences ranged between 0 and 48 cm. The error of the results was estimated to fall within 3.31 cm. The 3D image of the marine topography in the region shows a nearly constant slope of 4 cm/km in the N–S direction. Thus, the effectiveness of the approach “repeated GNSS measurements on the same route of a ship” developed in the context of “GNSS methods on ﬂoating means” has been demonstrated. The application of this approach using systematic multi-track recordings on conventional liner ships is very promising, as it may open possibilities for widespread use of the methodology across the world.

Keywords: kinematic GPS; ellipsoid; geoid; GNSS; Global Navigation Satellite System; coastal mapping Citation: Lycourghiotis, S. Sea Topography of the Ionian and Adriatic Seas Using Repeated GNSS Measurements. Water 2021, 13, 812. 1. Introduction https://doi.org/10.3390/w13060812 For many years the precise determination of the geoid has been one of the basic problems of physical geodesy. The geoid is the equipotential surface that describes the Academic Editor: Simone Marini irregular shape of the Earth and is used as the zero reference for elevation measurements. This would coincide with the Mean Sea Level (MSL), provided that dynamic factors (wind, Received: 22 January 2021 atmospheric pressure, tide, sea currents, etc.) were to be excluded—that is, if oceans and Accepted: 12 March 2021 Published: 16 March 2021 atmosphere were to be considered in equilibrium. If we extended the MSL below the continents by means of hypothetical canals, we could obtain the whole image of the geoid

Publisher’s Note: MDPI stays neutral surface. The precise knowledge of the geoid is very important in several applications, e.g., with regard to jurisdictional claims in in investigating petroleum deposits. It is worth noting that the altitudes on the geoid are published maps and institutional affil- estimated with respect to the ellipsoid Earth. The methods for determining the geoid can iations. be classified into indirect and direct ones. Traditionally, the geoid has been determined indirectly either by gravitational or by astro-geodetic measurements in combination with various mathematical transformations (such as the Stokes equations). However, these calculations involve a great amount of uncertainty that can be up to several meters. Copyright: © 2021 by the author. Licensee MDPI, Basel, Switzerland. The more recent direct methods for geoid determination include marine surface This article is an open access article measurements by altimetry satellites [1] and airplane laser scanners [2], and “GNSS on distributed under the terms and floating means” measurements [3]. The first two methods face double uncertainty, since conditions of the Creative Commons the calculation of the Global Navigation Satellite System (GNSS) position is required in Attribution (CC BY) license (https:// addition to the distance estimation of the altimetry satellite or plane from the sea surface. creativecommons.org/licenses/by/ Furthermore, they face significant problems in coastal areas and closed seas due to land 4.0/). obstacles. To address these problems, a new method based on direct GNSS measurement

Water 2021, 13, 812. https://doi.org/10.3390/w13060812 https://www.mdpi.com/journal/water Water 2021, 13, x FOR PEER REVIEW 2 of 23

Water 2021, 13, 812 2 of 22 Furthermore, they face significant problems in coastal areas and closed seas due to land obstacles. To address these problems, a new method based on direct GNSS measurement on the surface of the sea has been developed. During the decade 2003–2013, a number of on the surface of the sea has been developed. During the decade 2003–2013, a number of research groups have proposed “on-ship” GNSS measurements for the determination of research groups have proposed “on-ship” GNSS measurements for the determination of sea surface topography, contributing to the development of this method [4–14]. sea surface topography, contributing to the development of this method [4–14]. The installation of one or more GPS/GNSS receivers on a navigable medium was The installation of one or more GPS/GNSS receivers on a navigable medium was based on earlier research efforts involving GPS/GNSS placement on a buoy [15–17]. These based on earlier research efforts involving GPS/GNSS placement on a buoy [15–17]. These buoysbuoys used GPS/GNSS GPS/GNSS to to measure measure the the dynamic dynamic characteristics characteristics of the of waves the waves and the and aver- the averageage sea sealevel level of a of particular a particular point. point. Thus, Thus, th thee topography topography of of a a mari marinene area could notnot bebe assessed.assessed. TheThe GPS/GNSSGPS/GNSS buoy methodology waswas developeddeveloped mainlymainly forfor thethe constructionconstruction ofof earlyearly tsunamitsunami warningwarning systemssystems [[18,19].18,19]. TheThe goalgoal of of this this work work was was the the determination determination of of the the mean mean surface surface topography topography (MST) (MST) of theof the Ionian Ionian and and Adriatic Adriatic Seas. Seas. This This was was attempted attempted by developing by developing an alternative an alternative methodol- meth- ogyodology in the in context the context of the “GNSSof the “GNSS on floating on fl means”oating techniques.means” techniques. The methodology The methodology followed infollowed the present in the work present is highly work promising is highly forprom variousising for reasons. various Firstly, reasons. the exactFirstly, knowledge the exact ofknowledge the shape of of the the shape sea surface of the maysea surface provide ma quitey provide useful quite information useful information concerning concern- climate change.ing climate It is wellchange. known It is thatwell in known most cases that thein most investigation cases the concerning investigation the effectconcerning of global the warmingeffect of global on the warming sea level ison limited the sea tolevel certain is limited places to of certain the coast, places where of the tide coast, gauges where are installedtide gauges [20]. are However, installed this [20]. approach However, does this not approach allow investigating does not theallow important investigating effects the of globalimportant warming effects on of the global shape warming of the sea on surface. the shap Thosee of the effects, sea surface. to the extent Those of effects, the author’s to the knowledge,extent of the remain author’s for knowledge, the moment remain largely for unknown. the moment This largely issue could unknown. be investigated This issue throughcould be studies investigated like the through present studies one, repeated like the atpresent regular one, intervals. repeated Secondly, at regular an intervals. obvious advantageSecondly, ofan theobvious present advantage method withof the respect present to themethod methods with based respect on to altimeter the methods satellites based is thaton altimeter the hundreds satellites of thousands is that the of hundreds passenger of andthousands cargo ships of passenger traveling and worldwide cargo ships provide trav- aeling continuous worldwide grid provide of potential a continuous measurements. grid of Itpotential is actually measurements. simpler to place It is aactually GNSS onsim- a shippler thanto place to launch a GNSS an on altimeter a ship than satellite. to launch Moreover, an altimeter the satellites satellite. measure Moreover, the the sea satellites surface atmeasure specific the points, sea surface only along at specific their orbit points, (Figure only1 ),along whereas their theorbit method (Figure “GNSS 1), whereas on ship” the allowsmethod one “GNSS to identify on ship” possible allows small one to changes identify or possible anomalies small anywhere changes on or theanomalies sea surface any- andwhere to focuson the at sea specific surface points and to not focus covered at specif by satellites.ic points Furthermore,not covered by the satellites. methods Further- based onmore, satellites the methods fail to provide based on good satellites accuracy fail to in provide coastal areasgood [accuracy21]. In these in coastal areas, areas however, [21]. theIn these determination areas, however, of the the average determination marine topography of the average and marine the geoid topography is of great and scientific the ge- interestoid is of [22 great]. The scientific detection interest of significant [22]. The changes detection in specific of significant parts of changes the marine in specific topography parts couldof the revealmarine interesting topography geological could reveal structures interest ofing the geological marinesubsoil structures related of the to marine fissures sub- or oilsoil and related gas fieldsto fissures [23]. or This oil perspectiveand gas fields is very[23]. important,This perspective especially is very for important, the study area,espe- becausecially for it the presents study veryarea, highbecause seismicity it presents but alsovery stronghigh seismicity indications but for also the strong existence indica- of hydrocarbontions for the existence deposits [of24 ].hydrocarbon deposits [24].

Figure 1. Trajectories of the TOPEX/POSEIDON, Jason-1, Jason-2, Envisat and ERS-2 satellites in the Figure 1. Trajectories of the TOPEX/POSEIDON, Jason-1, Jason-2, Envisat and ERS-2 satellites in easternthe eastern Mediterranean Mediterranean region. region. The darkThe dark area area describes describes our studyour study area. area.

Water 2021, 13, 812 3 of 22

The region under consideration extends from the Gulf of Patras to the northern Ionian Sea and the southern Adriatic Sea up to the port of Brindisi. It covers 250 km north–south and 150 to 200 km east–west. A schematic representation of the region studied is illustrated in Figure1 (red region) together with the trajectories of the TOPEX/POSEIDON, Jason-1, Jason-2, Envisat and ERS-2 satellites in the eastern Mediterranean region. The mean sea level in the region studied, approached satisfactorily by the estimates of the geoid, has changed considerably, creating differences in height of several meters, in some cases larger than 10 m. For example, the EGM96 model estimates a sea level in the area near to the port of Brindisi as 14.2 m higher than that estimated in the sea area near the port of Patras, with respect to the ellipsoid reference [25]. The study of surface sea surveying in the above area following the new approach is of interest for several reasons. Specifically, the few tide recording stations do not allow developing a clear picture concerning the eventual changes in sea level due to medium-term meteorological factors or to even more permanent fluctuations due to climate change. Thus, in many cases we cannot know whether the sinking or rising shores observed in the area are due to geological causes, meteorological fluctuations or both. Additionally, the trajectories of the TOPEX/POSEIDON, Jason-1, Jason-2, Envisat and ERS-2 altimetry satellite missions intersect over the area studied (Figure1, red). However, the estimates of altitude satellites are subject to significant uncertainties ranging from five to ten centimeters in the assessment of marine topography near coastal areas or areas with extensive coastline [26]. Although the idea of placing a GNSS receiver on a passenger ship for recording a single track has been suggested [8], the technique presents significant weaknesses as far as the uncertainties are concerned [3]. Developing an approach of repeated measurements on the same route offers the potential of significantly reducing uncertainties and improving the methodology. Thus, the main approach of the present contribution is to carry out multiple measurements (passes) for the same maritime route over several months in order to include all possible conditions. Adopting this approach is expected to lead to higher accuracy estimations for marine topography, especially when compared with older methodologies. In the present work we have used the “Patra – Igoumenitsa – Brindisi” line for developing our methodology, using measurements from the “Ionian Queen” passenger ship over a period of 6 months. Using our method, we studied the change of the sea level altitude along the ship’s route, to determine the sea surface topography and compare our estimates to those of the geoid EGM96 model. Two alternative methods were used to resolve our data, differential GNSS (D-GNSS) and precise point positioning (PPP). The main difference between these methods is that the first one requires a fixed GNSS reference station at a short distance from the moving receiver, in order to remove the atmospheric noise from the data [27]. This fixed station must be on land. The greater the distance from land, the poorer the accuracy. Thus, despite the fact that the D-GNSS method potentially provides data with much higher accuracy than any other method [28], its use away from the shore is quite problematic. On the contrary, the PPP method does not require a fixed station and is ideal for marine topography. However, its accuracy still remains lower than D-GNSS, though it is constantly improving [29]. In the present work, a combination of both methods was adopted, to constitute a model approach for studying marine topography.

2. Experimental Measurements 2.1. GNSS Records on the Boat The ship utilized was the “Ionian Queen of Endeavor Lines.” The GNSS receiver (GB-1000 from Topcon with PG-A1 antenna) was placed in a suitable position on the ship’s deck for decreasing the multi-reﬂection effect. Figure2 shows the locations of the receiver antenna (A) and the receiver (B)—which was located inside a watertight suitcase used for its protection. The records concern the period from 30 January to 20 July 2010 and involved 142 passes. These were recorded at a sampling rate of 1 Hz and a circumferential angle of 15 degrees, which protected the GNSS receiver from any side obstacles. Water 2021, 13, x FOR PEER REVIEW 4 of 23

Water 2021, 13, 812 its protection. The records concern the period from 30 January to 20 July 2010 and4 of in- 22 volved 142 passes. These were recorded at a sampling rate of 1 Hz and a circumferential angle of 15 degrees, which protected the GNSS receiver from any side obstacles.

FigureFigure 2.2. TheThe “Ionian“Ionian Queen” passenger ship used for the Ionian Ionian and and Adriatic Adriatic Sea Sea measurements, measurements, andand thethe basicbasic GlobalGlobal Navigation Navigation Satellite Satellite System System (GNSS) (GNSS) equipment. equipment. The The antenna antenna of of the the receiver receiver was placedwas placed at point at point A with A with a tribrach a tribrach in order in order to ensure to ensure leveling. leveling. The receiver The receiver was placed was placed at point at point B in a specialB in a special waterproof waterproof case for case its protection.for its protection.

InformationInformation concerning concerning the the 142 142 routes routes is iscompiled compiled in Table in Table S1. Each S1. Each route route (code (code num- numberber ID) concerns ID) concerns a separate a separate voyage voyage of the of ship the shipfrom from Patras Patras to Brindisi to Brindisi or vice or viceversa. versa. The Thedata data were were analyzed analyzed using using two twomethods methods (D-GNSS (D-GNSS [30] [and30] andPPP PPP [31]). [31 In]). some In some cases, cases, un- uncertaintiescertainties in inthe the frame frame of of D-GNSS D-GNSS and and some some error error reports reports when when solving with PPPPPP couldcould notnot bebe resolved. Thus, Thus, some some of of these these routes routes we werere not not finally ﬁnally utilized utilized for for the the assessment assessment of ofmarine marine topography. topography. As As shown shown in in Table Table S1, S1, data data from from 127 127 and and 121 routes were utilized,utilized, respectively,respectively, inin thethe contextcontext D-GNSS D-GNSS and and PPP. PPP.

2.2.2.2. ShipShip DepthDepth AltimeterAltimeter DataData AΑ systematicsystematic recordingrecording ofof thethe ship’sship’s elevationelevation waswas performedperformed atat twotwo pointspoints ofof thethe shipship (bow(bow (B)(B) andand sternstern (A))(A)) alongalong withwith thethe collectioncollection ofof thethe GNSSGNSS records.records. TheseThese pointspoints areare illustratedillustrated inin FigureFigure3 3.. TheThe altitudesaltitudes werewere recorded recorded by by the the ship’s ship’s crew crew at at each each of of the the portport stationsstations ofof thethe routeroute (Patras–Igoumenitsa–Brindisi).(Patras–Igoumenitsa–Brindisi). DueDue toto thethe ship’sship’s loadingloading andand unloading,unloading, thethe draughtsdraughts werewere takentaken byby thethe crewcrew justjust priorprior toto departuredeparture andand afterafter thethe shipship hadhad beenbeen fullyfully loaded.loaded. DevicesDevices calculatingcalculating thethe draughtdraught atat pointspoints AA andand BB werewere permanentpermanent ship equipment and operated—according to their speciﬁcations—with a precision of 1 cm. ship equipment and operated—according to their specifications—with a precision of 1 cm. The received draught data were used for determining accurately the distance of the receiver The received draught data were used for determining accurately the distance of the re- Water 2021, 13, x FOR PEER REVIEWfrom the surface of the sea. Table S2 illustrates indicative data concerning the5 of ship’s 23 ceiver from the surface of the sea. Table S2 illustrates indicative data concerning the ship’s draughts (hA and hB) at points A and B. draughts (hΑ and hΒ) at points A and B.

FigureFigure 3. Schematic 3. Schematic representation representation of the of shipthe ship “Ionian “Ionian Queen.” Queen.” The pointsThe points of calculation of calculation concerning concerning the elevation the elevation (draught) of the(draught) ship up of on the its ship loading up on are its illustrated. loading are The illustrated. projection The of pr theojection position of the of the position receiver of the on thereceiver AB segment on the AB divides segment it into divides it into two subsections, ΧΑ and ΧΒ. two subsections, XA and XB. 2.3. Data from Permanent GNSS Stations Data from permanent GNSS stations in Greece and Italy were also collected, in addition to those collected by the GNSS on the boat. The locations of the recording stations are shown in Figure 4.

Figure 4. Map of the study area showing the ship’s principal route as well as the GNSS ground stations used during the processing. The route was not exactly the same each time, because the ship followed a slightly different path on each voyage. The points a–s marked here along the “principal route” refer to some of the figures. The stations RLSO, VLSM, PONT, SPAN and KASI belong to the National Observatory of Athens (NOANET GNSS NETWORK), and the station LECC to the Italian Positional Service (ItalPoS).

These stations were tested due to their proximity to segments of the ship’s seaway, in order to be used as reference stations when resolving with the D-GNSS method. The networks utilized provide free data compatible with the resolution methods we have chosen. Moreover, the stations were recording during the marine experiments and provided data with a sampling period of 15 and/or 30 sec.

Water 2021, 13, x FOR PEER REVIEW 5 of 23

Figure 3. Schematic representation of the ship “Ionian Queen.” The points of calculation concerning the elevation Water 2021, 13, 812 5 of 22 (draught) of the ship up on its loading are illustrated. The projection of the position of the receiver on the AB segment divides it into two subsections, ΧΑ and ΧΒ.

2.3.2.3. Data Data from from Permanent Permanent GNSS GNSS Stations Stations DataData from from permanent permanent GNSS GNSS stations stations in in Greece Greece and and Italy Italy were were also also collected, collected, in in addi- addi- tiontion to to those those collected collected by by the the GNSS GNSS on on the the bo boat.at. The The locations locations of of the the recording recording stations stations are are shownshown in in Figure Figure 4.4.

FigureFigure 4. 4. MapMap of ofthe the study study area area showing showing the theship’s ship’s principal principal route route as well as well as the as GNSS the GNSS ground ground stationsstations used used during during the the processing. processing. The The route route was was not not exactly exactly the the same same each each time, time, because because the the ship shipfollowed followed a slightly a slightly different different path path on eachon each voyage. voyage. The The points points a–s a–s marked marked here here along along the “principalthe “principalroute” refer route” to some refer of to the some ﬁgures. of the The figures. stations The RLSO, stations VLSM, RLSO, PONT, VLSM, SPAN PONT, and SPAN KASI belongand KASI to the belongNational to the Observatory National Observatory of Athens (NOANET of Athens GNSS (NOANET NETWORK), GNSS NETWORK), and the station and LECC the station to the Italian LECCPositional to the Service Italian (ItalPoS).Positional Service (ItalPoS).

TheseThese stations stations were were tested tested due due to to their their pr proximityoximity to to segments segments of of the the ship’s ship’s seaway, seaway, inin order order to to be be used used as as reference reference stations stations when when resolving resolving with with the the D-GNSS D-GNSS method. method. The The networksnetworks utilized utilized provide provide free free data data compatible compatible with with the resolution the resolution methods methods we have we cho- have sen.chosen. Moreover, Moreover, the stations the stations were were recording recording during during the the marine marine experiments experiments and and provided provided datadata with with a asampling sampling period period of of 15 15 and/or and/or 30 30 sec. s.

3. Methodology 3.1. General Procedure for Calculating the Mean Sea Level (MSL)

The calculation of the sea altitudes is inevitably quite complex because it is based on multiple crossings for marine topography. The ultimate goal of the analysis of the time series which were received from the GNSS solutions was the determination of the mean sea level (MSL). In this section the methodology for calculating the MSL using GNSS receiver’s altitude measured at each moment is presented and analyzed. For each separate route, the measured geometric altitude H (i,t) of the receiver on the ship at time t and position i is deﬁned by the equation:

H(i, t) = Ψ(i) − hGNSS(i, t) ± hwave(i, t) ± htide(i, t) ± u(i, t), (1)

where Water 2021, 13, x FOR PEER REVIEW 6 of 23

3. Methodology 3.1. General Procedure for Calculating the Mean Sea Level (MSL) The calculation of the sea altitudes is inevitably quite complex because it is based on multiple crossings for marine topography. The ultimate goal of the analysis of the time series which were received from the GNSS solutions was the determination of the mean sea level (MSL). In this section the methodology for calculating the MSL using GNSS receiver’s altitude measured at each moment is presented and analyzed. For each separate route, the measured geometric altitude H (i,t) of the receiver on the Water 2021, 13, 812 ship at time t and position i is defined by the equation: 6 of 22

𝐻(𝑖,) 𝑡 =𝛹(𝑖) −ℎ(𝑖,) 𝑡 ±ℎ(𝑖,) 𝑡 ±ℎ(𝑖,𝑡) ±𝑢(𝑖,) 𝑡 , (1) where hGNSS(i, t): The height of the receiver relative to the sea surface. ℎ(𝑖,) 𝑡 : The height of the receiver relative to the sea surface. htide(i, t): The effect of astronomical and meteorological tide. ℎ(𝑖, 𝑡): The effect of astronomical and meteorological tide.

hℎtide(i(,𝑖,t) ) 𝑡==ℎhastro(i,(t𝑖,) +) 𝑡 +ℎhmeteo(i,(𝑖,t) 𝑡) (2)(2) ℎ (𝑖, 𝑡): The effect of waves. hwave(i, t): The effect of waves. 𝑢(𝑖,u(i, t):: 𝑡) The total error of the measurement (random(random and systematic) of the geometric altitude of the receiver,receiver,𝐻H((𝑖,i, t) 𝑡 .. 𝛹(𝑖)Ψ(i): The requested (unknown) geometric altitudealtitude ofof thethe MSLMSL atat positionposition i.i. The above parameters refer to a position ii at time tt.. Figure 55 showsshows a schematic representation of of the the main main parameters parameters of of Equation Equation (1). (1). It shouldIt should be be noted noted again again that that the the parameter parameter H(t,i)H(t,i) isis deduced deduced from from the the GNSS GNSS recordings, whereas the parameterparameter hhGNSSGNSS isis calculated calculated by by means means of of geometric characteristics of thethe ships taking into account the draught of the ship. Moreover, the estimations of the effects of astronomical and meteorological factors of the tide were based on GNSS measurements in ports and static solutions in orderorder to determine thethe geometricgeometric altitudealtitude HH ((i,ti,t)) inin ports.ports.

Figure 5. Parameters of Equation (1). The red line depicts the mean seal level (MSL), and the light blue line illustratesillustrates thethe seasea levellevel atat aa givengiven timetime withoutwithout thethe wavewave effect.effect.

The determination ofof allall parametersparameters of of Equation Equation (1) (1) and and the the estimation estimation of of their their uncer- un- certaintiestainties allows allows approaching approaching the the desired desired altitude altitudeΨ(i )Ψ together(i) together with with its precision. its precision. This This can canbe done be done for eachfor each route route separately. separately. The The contribution contribution of theof the present present approach, approach, however, however, is isthat that it usesit uses multiple multiple paths paths and and thus thus it it can can determine determine altitudes altitudesΨ Ψ((ii)) moremore accuratelyaccurately thanthan methods usingusing singlesingle paths.paths. To To calculate calculate a reliablea reliable altitude altitude at eachat each point pointΨ(i )Ψ for(i) for each each of the of theaforementioned aforementioned parameters parameters of Equation of Equation (1), we (1), should we should into account into account the uncertainties the uncertainties which whichcan affect can the affect ﬁnal the results. final results. For the calculationFor the calculation of these of parameters, these para ameters, step-by-step a step-by-step analysis wasanalysis followed, was followed, which is which described is described in the next in sections.the next sections. Starting withStarting the with parameter the parameterhGNSS, it was calculated by means of the geometric characteristics of the ships and corrected by taking into account the draught of the ship (Section 3.2). Continuing, the impact of astronomical tide, the meteorological factor of the tide and the estimation of the effect of waves (Section 3.3)

are presented. Finally, we are presenting our methodology relevant to the solution of the GNSS raw data for determining the H(i,t) values, following the differential GNSS (D-GNSS; Section 3.4) and precise point positioning (PPP; Section 3.5) methods. Before the next subsections, it is important to note that the multiple-paths approach developed in this work had to address the following methodological problem: The ship, on each separate route, although driven by an automatic satellite navigation system (using GNSS), does not always follow an identical route. It deviates in the horizontal plane. Figure6 illustrates an indicative area, near to the port of Brindisi, with nine different crossings. It is seen that the different routes, although somewhat parallel, may vary by Water 2021, 13, x FOR PEER REVIEW 7 of 23

hGNSS, it was calculated by means of the geometric characteristics of the ships and corrected by taking into account the draught of the ship (Section 3.2). Continuing, the impact of astronomical tide, the meteorological factor of the tide and the estimation of the effect of waves (Section 3.3) are presented. Finally, we are presenting our methodology relevant to the solution of the GNSS raw data for determining the H(i,t) values, following the differential GNSS (D-GNSS; Section 3.4) and precise point positioning (PPP; Section 3.5) methods. Before the next subsections, it is important to note that the multiple-paths approach developed in this work had to address the following methodological problem: The ship, on each separate route, although driven by an automatic satellite navigation system (using Water 2021, 13, 812 GNSS), does not always follow an identical route. It deviates in the horizontal plane.7 Fig- of 22 ure 6 illustrates an indicative area, near to the port of Brindisi, with nine different crossings. It is seen that the different routes, although somewhat parallel, may vary by tens of meters.tens of meters.The deviation The deviation may be mayeven begreater. even greater.An example An example is illustrated is illustrated in Figure in S1. Figure It con- S1. cernsIt concerns eight different eight different routes routes(11/2–19/2, (11/2–19/2, route IDs route 13–21, IDs Table 13–21, S1). Table In view S1). of In the view above of thefor determiningabove for determining the altitude the H altitude(i,t), we cannotH (i,t), weuse cannota point useon an a point individual on an route individual (e.g., route 1,(e.g., Figure route 6), 1, but Figure instead6), but must instead use a must “mean use poin a “meant” on point”the straight on the section straight that section intersects that almostintersects vertically almost all vertically the different all the paths different at corresponding paths at corresponding points. These points. “mean These points” “mean con- stitutepoints” the constitute “principal the path” “principal illustrated path” in illustratedFigure 4. It in is Figureimportant4. It to is note important that the to differ- note encesthat the in differencesthe values of in H the (i,t values) determined of H (i ,att) determinedthese corresponding at these correspondingpoints are actually points negli- are gible,actually and negligible, this allows and us this to draw allows conclusions us to draw conclusionsfor a broader for zone a broader around zone the around“principal the “principalroute.” route.”

FigureFigure 6. 6. DifferentDifferent routes routes near near to to the the port port of of Brindisi Brindisi which which are are indicated indicated by by different different colors. colors. The The routesroutes were taken placeplace inin thethe periodperiod 3–11/2/2010 3–11/2/2010 corresponding corresponding toto IDID numbersnumbers 5–135–13 (Table (Table S1). S1). The Thedots dotsi, i + i, 1, i +i +1, 2,i +i +2, 3,i +i 3,+ 4,i + etc., 4, etc., represent represent indicative indicative measurements measurements on routeon route 1. 1.

3.2.3.2. Correction Correction of of the the Altitude Altitude of of th thee Receiver Relative to the Sea Level (h GNSS) )to to Take Take into into Account the Cargo Changes after each Each Loading Loading and and Unloading Unloading of of the the Ship Ship AsAs already already mentioned, mentioned, the the GNSS GNSS receiver receiver was was stationary stationary on the on ship the (Figure ship (Figure 3). How-3). ever,However, its altitude its altitude in relation in relation to the to sea the level sea level(light (lightblue in blue Figure in Figure 5) was5) waschanged changed at each at porteach due port to due cargo to cargo changes changes after aftereach eachloading loading and unloading. and unloading. This Thisrequired required a suitable a suitable cor- correction for each route. rection for each route. The recordings of the draughts at positions A and B (Table S2) were adjusted by means The recordings of the draughts at positions A and B (Table S2) were adjusted by of a simple linear interpolation at the projection point of the GNSS receiver (see Figure3) means of a simple linear interpolation at the projection point of the GNSS receiver (see according to the equation: Figure 3) according to the equation: (hb − ha) hGNSS = Z0 − Hs = Z0 − xa + ha (3) (xa + xb)

where hGNSS is the requested height of the receiver relative to the sea surface; Z0 is the known height of the receiver relative to the ship’s bottom level horizontal keel; h , h is the a β measured ship draughts at control points A and B (see Figure3); xa and xβ are horizontal distances from the A and B points of the depth-meters in relation to the projection point of the GNSS receiver on the AB section of the horizontal keel; Hs is the draught altitude at the intersection point corresponding to the projection point of the GNSS receiver on the AB section of the horizontal keel. Figure7 illustrates the geometric calculation of the antenna height relative to the plane of the sea surface. Water 2021, 13, x FOR PEER REVIEW 8 of 23

(ℎ −ℎ) ℎ =𝑍 −𝐻 =𝑍 −𝑥 +ℎ (3) (𝑥 +𝑥)

where ℎ is the requested height of the receiver relative to the sea surface; 𝑍 is the known height of the receiver relative to the ship’s bottom level horizontal keel; ℎ,ℎ is the measured ship draughts at control points A and B (see Figure 3); 𝑥 and 𝑥 are horizontal distances from the A and B points of the depth-meters in relation to the projection point of the GNSS receiver on the AB section of the horizontal keel; 𝐻 is the draught altitude at the intersection point corresponding to the projection point of the GNSS receiver on the AB section of the horizontal keel. Water 2021, 13, 812 Figure 7 illustrates the geometric calculation of the antenna height relative to8 the of 22 plane of the sea surface.

FigureFigure 7. 7. GeometricGeometric calculation calculation of ofthe the antenna antenna height height wi withth respect respect to the to the plane plane of the ofthe sea seasurface. surface. TheThe calculation calculation is isbased based on on the the dr draughtaught at atpoints points A and A and B, which B, which must must be measured be measured at each at each port port beforebefore the the ship ship leaves leaves and and after after the the final ﬁnal loading loading (moving (moving loads, loads, tanks). tanks). The The data data ofof the the draught draught at at pointspoints A A and and B B were were calculated calculated by by an an electron electronicic sensor sensor and and recorded recorded in in the the ship’s ship’s book. book.

BasedBased on on the the accuracy accuracy of of the the A A and and B B dr draughtaught measurements, measurements, as as provided provided by by the the ship’sship’s instrument instrument specifications, specifications, the the error error of ofthe the determined determined parameter parameter hGNSShGNSS has hasbeen been estimated.estimated. The The calculations calculations are are presented presented in inAppendix Appendix AA and and resulted resulted to to an an error error equal equal to to 0.765890.76589 cm. cm. 3.3. Calculation of Impact of Astronomical Tide and Meteorological Factor of the Tide, h : Static ℎtide 3.3.Calculation Calculation of Altitude of Impact in of Ports Astronomical Tide and Meteorological Factor of the Tide, : Static Calculation of Altitude in Ports. The determination of the impacts of the astronomical and meteorological factors of the The determination of the impacts of the astronomical and meteorological factors of tide, htide, on the requested parameter, Ψ(i), allows removing their influence. To determine thesuch tide, an ℎ impact,, on wethe usedrequested to a staticparameter, solution Ψ(i in), allows the ports. removing The ship their remained influence. each To de- day terminein the ports such ofan Patrasimpact, or we Brindisi used to for a static a period solution of 4 in h andthe ports. this allowed The ship solving remained statically each daythe in altitudes the ports in of all Patras cases. or The Brindisi time periodfor a period chosen of for4 h resolutionand this allowed (2.5 h) solving was less statically than 4 h thein altitudes order to correspondin all cases. The to the time time period that chosen the ship for was resolution completely (2.5 h) empty was less and than not 4 in h thein orderprocess to correspond of loading orto the unloading. time that Taking the ship into was account completely the magnitude empty and ofnot the in tidethe process and the ofrate loading of its or change unloading. in the areaTaking [32 into] we account considered the thatmagnitude at this periodof the tide the seaand level the rate remained of its changeconstant, in the and area thus [32] a static we considered solution could that provideat this period a reliable the estimatesea level ofremained the altitude constant, of the andsea thus level a in static ports. solution The static could solution provide of altitudea reliable in estimate ports was of performed the altitude following of the sea the level PPP inmethodology. ports. The static Figure solution8 illustrates of altitude the resultsin ports of was the staticperformed resolutions following in both the PPP ports. meth- The odology.mean values Figure and 8 theillustrates standard the deviation results of values the static are alsoresolutions illustrated. in both Representative ports. The resultsmean are also illustrated in Table S3. Since our measurements cover almost one full semester, and they take into account all possible weather conditions, which justifies the variations observed, we considered that the average sea level altitude (mean values in Figure8) is an estimate of the MSL in the ports (see Figure5). Thus, we have obtained two points of “control and correction” in the two ports that are the “extremes” of each route. The obtained MSL values and the individual values resulted from the static resolutions at both ports, and were used in order to correct the altitude estimation curves for each route (linear correction). Essentially, the effect of the tide, h (i,t), was eliminated without using data from the tide gauges, given that they were not in operation. After this correction, our differential resolutions did not show any significant differences at a given point (i) for different routes. Water 2021, 13, x FOR PEER REVIEW 9 of 23

Water 2021, 13, 812 values and the standard deviation values are also illustrated. Representative results 9are of 22 also illustrated in Table S3.

FigureFigure 8. 8.GraphicGraphic representations representations of the of theelevation elevation values values in the in theports ports of Patras of Patras and andBrindisi. Brindisi. The The averageaverage altitudes altitudes in inthe the two two ports ports (mean (mean values) values) an andd the the standard standard deviation deviation values values are are illustrated. illustrated.

SinceRecently, our measurements in 2017, we had cover the almost opportunity one fu toll semester, confirm the and aforementioned they take into account mean sea alllevel possible at the weather port of Patra.conditions, In effect, which navy justifies services the provided variations us theobserved, opportunity we considered to calculate thatthe the coordinates average sea of level the benchmark altitude (mean GNSS. values The elevationin Figure 8) of is the an benchmark estimate of was the linkedMSL in to thethe ports sea-level (see Figure recorder—which 5). Thus, we duringhave obtained our experiments two points was, of “control unfortunately, and correction” out of order. in theHowever, two ports the that recent are measurements the “extremes” have of confirmedeach route. our The calculation obtained forMSL the values average and value the of individualsea topography values atresulted the port from of Patras. the static This resolutions demonstrates at both the accuracyports, and of were the above used in described order methodology for obtaining the mean sea level using the GNSS of the ship. to correct the altitude estimation curves for each route (linear correction). Essentially, the To confirm twice the static GNSS results above, our estimates of the sea level altitude effect of the tide, h (i,t), was eliminated without using data from the tide gauges, given in the ports were compared with the estimates of the DTU10 global ocean tide model. that they were not in operation. After this correction, our differential resolutions did not Tide model estimates are usually preferred but have the disadvantage of being indirect show any significant differences at a given point (i) for different routes. estimations of the sea level altitude. The DTU10 model’s differences from the estimations Recently, in 2017, we had the opportunity to confirm the aforementioned mean sea of our GNSS measurements were very small (<16 cm), except for three cases where the level at the port of Patra. In effect, navy services provided us the opportunity to calculate difference was greater, and those routes were removed. These differences can be considered the coordinates of the benchmark GNSS. The elevation of the benchmark was linked to negligible, if we consider that the estimated accuracy of the model is about 20–25 cm [33]. the sea-level recorder—which during our experiments was, unfortunately, out of order. Since the calculations of the impacts of the astronomical and meteorological compo- However, the recent measurements have confirmed our calculation for the average value nents of tide were not done using modern time-series via tidal collectors, but using the of sea topography at the port of Patras. This demonstrates the accuracy of the above de- limit values measured at ports, the uncertainty of this factor cannot be accurately estimated. scribedHowever, methodology the basic componentfor obtaining of the astronomicalmean sea level tide using (M2) the expected GNSS of in the the ship. area does not exceedTo confirm a maximum twice rangethe static of 5–7 GNSS cm results [34]. Therefore, above, our it seemsestimates plausible of the sea to assume level altitude that the inastronomical the ports were tide compared is eliminated with the to such estimates an extent of the so DTU10 that its global effect isocean not actually tide model. detectable. Tide modelIf, for estimates example, are despite usually the pref aforementionederred but have the linear disadvantage correction, of in being some indirect segments estima- of the tionspath, of e.g.,the sea in thelevel middle altitude. section, The DTU10 the astronomical model’s differences tide adds from or removes the estimations 1–2 cm from of our our GNSSestimation, measurements it is very were difficult very tosmall be detected. (<16 cm), Thisexcept is becausefor three the cases uncertainty where the estimated difference of each separate route covers this range. In other words, the astronomical component cannot contribute beyond this range.

Water 2021, 13, 812 10 of 22

In our previous works we examined in detail the relationship between meteorological and astronomical tides in some parts of the Mediterranean [35]. The ratio of meteorological to astronomical tides in these areas is very high (up to 40). This makes the effect of the astronomical factor practically insigniﬁcant [36]. At the same time, the most important meteorological factor in terms of its effect on the average sea level is completely random [37]. In contrast, the meteorological component of tide is related too much wider ranges than those of the astronomical component; in extreme conditions up to 50 cm [32]. However, the change of its amplitude per time unit is much smoother. Thus, the aforementioned linear correction is sufﬁcient to confront the meteorological component of the tide. Obviously, the presence of noise cannot be excluded. However, the use of data of a 6-month period, during which almost all weather conditions occur, randomizes any uncertainty. Finally, a few sentences concerning the effect of waves (hwave): Reinking et al. [8], faced with a problem similar to that of the present work, analyzed the dynamics of a ship with a similar size to the “Ionian Queen.” Although their work concerned a marine area with worse wave conditions (the Atlantic Ocean), the authors concluded that the dynamic movement of the ship is not actually affected by the vertical component of the gravitational ripple. Thus, the negligible displacement of a ship of the magnitude of “Ionian Queen” almost eliminates the effect of small-scale waves. Moreover, taking into account that our data cover a period of almost six months and more than 140 passes, as well as the high frequency of sampling on each route (1 Hz), it seems plausible to assume that the effect of the gravitational wave is zero, as it is randomized.

3.4. Solution of the GNSS Raw Data for Determining the H(i, t) Values Following the D-GNSS Method The data obtained from the GNSS recordings were classified into separate routes illustrated in Table S1. Each route corresponds to a passage of the ship in the line Patra– Igoumenitsa–Brindisi or Brindisi–Igoumenitsa–Patra. These 142 routes were solved by all six reference stations (Figure4). However, fifteen routes were not used because they could not be resolved by the base stations, as they showed unresolved uncertainties. Moreover, seven additional routes cannot be solved by the LECC station. Thus, 120 of the 142 routes Water 2021, 13, x FOR PEER REVIEW were finally utilized. For improving the accuracy of the results, a static solution11 ofof the23 six reference stations and a correction of their coordinates were completed prior to carrying out the kinematic solution. Figure9 depicts the horizontal coordinates of the ship’s principal route as solved by the PONT-based D-GNSS method (see also Figure4).

Figure 9. Horizontal coordinates of the ship’s principal path as solved by the PONT-based D-GNSS Figuremethod. 9. Horizontal The logs coordinates refer to the of route the ship’s from Patras princi topal Brindisi path as with solved a stop by the at Igoumenitsaat PONT-based D- 30/31-1-2010 GNSS(Route method. ID 1).The Coordinates logs refer to are the in route UTM from meters Patr (UTMas to Brindisi zone 34N). with a stop at Igoumenitsaat 30/31-1-2010 (Route ID 1). Coordinates are in UTM meters (UTM zone 34N).

The solutions were calculated using Leica Geo Office software (LGO). In order to confront the signal distortion due to the atmospheric delay and take into account the large length of the maritime route, a suitable ionospheric model was automatically adopted by the software. This was based on the updates of the orbital satellite corrections. A full ambiguity-fixed solution was chosen. Since the recordings of our data exceeded 45 min, the calculation of the ionospheric model was chosen from the LGO software. This option has the advantage that the calculations of the model are consistent with the particular conditions prevailing in the region. The software’s ability to calculate the troposphere model was also utilized. This option calculates variations of troposphere delay between the moving and the reference receivers. Different solutions were tested with respect to the degree of resolution of their uncertainties, and those segments in which the uncertainties had not been resolved were rejected. The distances between the six reference stations range from a few to several hundred kilometers from the ship’s crossing points. According to the literature, the distances of the recording points from the reference stations in the D-GNSS method should not be greater than 50 km, though calculations have shown that a distance of 60 km does not lead to additional uncertainty greater than 2 cm [38]. At higher distances, the noise may become quite large. This is exemplified in Figure S2. It concerns an area in Patra Bay where the data have been resolved by different stations. It is obvious that the noise level increases with the distance of the station from the region mentioned. However, it does not exceed 5 cm. The aforementioned effect of distance is more clearly illustrated in the examples shown in Figure 10.

Water 2021, 13, 812 11 of 22

The solutions were calculated using Leica Geo Office software (LGO). In order to confront the signal distortion due to the atmospheric delay and take into account the large length of the maritime route, a suitable ionospheric model was automatically adopted by the software. This was based on the updates of the orbital satellite corrections. A full ambiguity-fixed solution was chosen. Since the recordings of our data exceeded 45 min, the calculation of the ionospheric model was chosen from the LGO software. This option has the advantage that the calculations of the model are consistent with the particular conditions prevailing in the region. The software’s ability to calculate the troposphere model was also utilized. This option calculates variations of troposphere delay between the moving and the reference receivers. Different solutions were tested with respect to the degree of resolution of their uncertainties, and those segments in which the uncertainties had not been resolved were rejected. The distances between the six reference stations range from a few to several hundred kilometers from the ship’s crossing points. According to the literature, the distances of the recording points from the reference stations in the D-GNSS method should not be greater than 50 km, though calculations have shown that a distance of 60 km does not lead to additional uncertainty greater than 2 cm [38]. At higher distances, the noise may become quite large. This is exemplified in Figure S2. It concerns an area in Patra Bay where the data have been resolved by different stations. It is obvious that the noise level increases with Water 2021, 13, x FOR PEER REVIEW 12 of 23 the distance of the station from the region mentioned. However, it does not exceed 5 cm. The aforementioned effect of distance is more clearly illustrated in the examples shown in Figure 10.

Figure 10.Figure Typical 10. examplesTypical examplesof initial D-GNSS of initial solutions D-GNSS by: solutions VLSM (ID by: route VLSM 18), RLSO (ID route (ID route 18), RLSO24), SPAN (ID (ID route route 24), 110) and LECCSPAN (Stack (ID ID route route 110) 2).The and points LECC a–s (Stack are the ID route route points 2). The illustrated points in a–s Figure are the 4. Thus, route they points visualize illustrated the parts in of the routeFigure presented4. Thus, each they time. visualize Indicative the lengths parts of inside the route the parts presented of the route each time.presented Indicative each time lengths are illustrated. inside the The values illustrated on the y-axis have not been corrected for the height of the receiver relative to the sea surface, hGNSS. parts of the route presented each time are illustrated. The values illustrated on the y-axis have not been corrected for the heightIt is evident of the that receiver the noise relative level to theis generally sea surface, increasedhGNSS. with the distance of the base station from the part of the ship’s journey in focus. In this study, we have generally It is evident that the noise level is generally increased with the distance of the base adopted the critical distance of 50 km in order to ensure high reliability. However, this station from the partdistance of the is rather ship’s specific, journey as in focus.resolving In thiscan study,be done we successfully have generally over somewhat adopted larger the critical distancedistances. of 50 An km overview in order of to the ensure parts high of the reliability. route situated However, inside the this distance distance of isthe 50 km rather speciﬁc, asfrom resolving a given canbase be station done is successfully illustrated in overFigure somewhat 11. It is seen larger that distances.the area south An of Igou- menitsa and a large area between Corfu and Brindisi are located at distances greater than 50 km from base stations. In view of the above, we are accepting the individual solutions of a given base station, for a given part of the route on the basis of their proximity. For example, the individual solutions from the LECC station were used for the part of the route inside the upper–left circle of Figure 11. From the parts of the route being outside the radius of 50 km, we have used the closest neighboring base station from a given point of the route.

Water 2021, 13, 812 12 of 22

overview of the parts of the route situated inside the distance of the 50 km from a given base station is illustrated in Figure 11. It is seen that the area south of Igoumenitsa and a large area between Corfu and Brindisi are located at distances greater than 50 km from base stations. In view of the above, we are accepting the individual solutions of a given base station, for a given part of the route on the basis of their proximity. For example, the individual solutions from the LECC station were used for the part of the route inside the Water 2021, 13, x FOR PEER REVIEW 13 of 23 upper–left circle of Figure 11. From the parts of the route being outside the radius of 50 km, we have used the closest neighboring base station from a given point of the route.

Figure 11. 11. AnAn overview overview of the of parts the partsof the route of the situated route situatedinside of the inside distance ofthe of the distance 50 km from of the a 50 km from a given base base station. station. The The base base station station PONT PONT (Figure (Figure 4) is not4 )presented is not presented here for clarity here forreasons clarity be- reasons because cause the corresponding circle is strongly overlapped with the circles of base stations VLSM and theSPAN. corresponding circle is strongly overlapped with the circles of base stations VLSM and SPAN.

AnAn example example of the of thesolution solution following following this approach this approach is illustrated is illustrated in Figure 12. in Figure 12. It concerns the final configuration of a “combinatorial” solution using the segments that we consider as most appropriate for the path ID 71, taken as an example. It should be stressed that the synthesis of the solutions was not automated. It was done by examining the suitability of the individual solutions from each station with respect to the noise level. In this example (path ID 71), the solutions of the VLSM and SPAN stations were not used because in the parts c–e their signals had more noise than PONT. A comparison of the results illustrated in Figure 12 with those illustrated in Figures 10 and S3 clearly shows that the above described approach leads to significant decrease of the noise level. To decrease the noise level further, we proceeded to a noise correction with the Savitzky–Golay filter. The filter is based on the repeated adjustment of a polynomial utilizing the least squares method [39]. Figure 13 (top) illustrates the part of the Patra– Igoumenitsa route resolved by the RLSO station and the estimate of the moving average (red line). By subtracting the original signal from the estimates of the moving average, Figure 13 (bottom) was obtained. The left-hand side of the figure (white) represents part of the route near the settlement station, justifying the quite small standard deviation. In contrast, the differences on the right-hand side of the figure (gray), representing part of the route at a significant distance from the settlement station, are characterized by larger

standard deviation. This was to be expected, taking into account the considerations of the Figure 12. Example of a “combinatorial” solution using the D-GNSS method for path ID 71. The previousRLSO, PONT, paragraph. KASI and LECC stations have been used. The RLSO, PONT, KASI and LECC stations were used, respectively, for the parts of the route, Patras to c, c to g, g to m and m to Brindisi.

Water 2021, 13, x FOR PEER REVIEW 13 of 23

Figure 11. An overview of the parts of the route situated inside of the distance of the 50 km from a given base station. The base station PONT (Figure 4) is not presented here for clarity reasons because the corresponding circle is strongly overlapped with the circles of base stations VLSM and SPAN. WaterWater2021 2021, ,13 13,, 812 x FOR PEER REVIEW 14 of 2313 of 22

An example of the solution following this approach is illustrated in Figure 12.

The values illustrated on the y-axis have not been corrected for the height of the receiver relative to the sea surface, hGNSS.

It concerns the final configuration of a “combinatorial” solution using the segments that we consider as most appropriate for the path ID 71, taken as an example. It should be stressed that the synthesis of the solutions was not automated. It was done by examining the suitability of the individual solutions from each station with respect to the noise level. In this example (path ID 71), the solutions of the VLSM and SPAN stations were not used because in the parts c–e their signals had more noise than PONT. A comparison of the results illustrated in Figure 12 with those illustrated in Figures 10 and S3 clearly shows that the above described approach leads to significant decrease of the noise level. To decrease the noise level further, we proceeded to a noise correction with the Sa- vitzky–Golay filter. The filter is based on the repeated adjustment of a polynomial utilizing the least squares method [39]. Figure 13 (top) illustrates the part of the Patra–Igou- menitsa route resolved by the RLSO station and the estimate of the moving average (red line). By subtracting the original signal from the estimates of the moving average, Figure 13 (bottom) was obtained. The left-hand side of the figure (white) represents part of the FigurerouteFigure 12.near 12. Example theExample settlement of a “combinatorial” of a “combinatorial” station, solutionjustifying usin solution theg the quite D-GNSS using small themethod standard D-GNSS for path methoddeviation. ID 71. The for In path contrast, ID 71. The RLSO,theRLSO, differences PONT, PONT, KASI KASI on and the andLECC right-hand LECC stations stations have side been have of used. the been figureThe used. RLSO, (gray), The PONT, RLSO, representing KASI PONT, and LECC KASI part sta- andof the LECC route stations tions were used, respectively, for the parts of the route, Patras to c, c to g, g to m and m to Brindisi. atwere a significant used, respectively, distance forfrom the the parts settlement of the route, station, Patras are to characterized c, c to g, g to mby and larger m to standard Brindisi. The deviation.values illustrated This was on to the be y-axis expected, have nottaking been in correctedto account for the the considerations height of the receiver of the previous relative to the paragraph. sea surface, hGNSS.

FigureFigure 13. 13. (top(top): ):An An example example of ofsolving solving the the sea seaaltitude altitude of the of route the route (Patras–Igoumenitsa) (Patras–Igoumenitsa) (points (points a a toto k; k; see see Figure Figure 4)4 )which which was was resolved resolved by by the the RLSO RLSO station station using using the D-GNSS the D-GNSS method method (ID route (ID route3). 3). ThisThis displays displays different different noise noise levels levels in inrelation relation to the to thedistance distance of the of measuring the measuring station. station. The red The line red line representsrepresents the the adjusted adjusted moving moving av averageerage curve. curve. Indicative Indicative length length is illustrated. is illustrated. The The values values illus- illustrated trated on the y-axis have not been corrected for the height of the receiver relative to the sea sur- on the y-axis have not been corrected for the height of the receiver relative to the sea surface, hGNSS. (Bottom): Differences (residues) from the moving average curve. The standard deviation in the ﬁrst segment is much smaller than that in the second segment, which represents part of the route at a great distance from the base station. Indicative length is illustrated.

Water 2021, 13, x FOR PEER REVIEW 15 of 23

face, hGNSS. (Bottom): Differences (residues) from the moving average curve. The standard deviation in the first segment is much smaller than that in the second segment, which represents part of the route at a great distance from the base station. Indicative length is illustrated.

Water 2021, 13, 812 14 of 22 The technique of the Savitzky–Golay moving average filter does not only correct the noise of GNSS measurements, but also the wave dynamic effect. As already mentioned, the wave action on a big ship is practically negligible because it is eliminated by the dy- The technique of the Savitzky–Golay moving average filter does not only correct the namic behavior of the ship’s construction; only waves higher than 4 m and longer than 10 noise of GNSS measurements, but also the wave dynamic effect. As already mentioned, the m can exert a significant effect [8]. However, even in this case the action of the filter per- wave action on a big ship is practically negligible because it is eliminated by the dynamic manently eliminates this dynamic phenomenon. behavior of the ship’s construction; only waves higher than 4 m and longer than 10 m can exert a significant effect [8]. However, even in this case the action of the filter permanently 3.5. Solution of the GNSS Raw Data for Determining the H(i,t) Values Following the PPP eliminates this dynamic phenomenon. Method 3.5. SolutionAs an alternative of the GNSS to Raw the DataD-GNSS for Determining method, all the route H(i,t) data Values were Following also resolved the PPP by Methodthe PPP method.As an The alternative PPP method to the does D-GNSS not need method, referenc all routee stations, data wereand thus also resolvedit is at an by advantage the PPP method.regarding The the PPP sections method of the does route not that need are reference at long stations,distances and (<50 thus km) it from is at anthese advantage stations. regardingAs the track the logs sections were oflarge the in route volume that and are atcould long not distances be resolved (<50 with km) fromthe current these stations.features Asof the trackeditor, logs they were were large split in into volume shorter and records. could not In bethis resolved way the with routes the currentwere divided features in ofhalf the and editor, doubled they in were their split number. into shorter In Figure records. 14 shows In this a solution way the with routes the were PPP dividedmethodol- in halfogy. and It concerns doubled the in their two number.sections in In which Figure a14 given shows route a solution has been with divided. the PPP methodology. It concerns the two sections in which a given route has been divided.

FigureFigure 14.14.Solving Solving withwith thethe PPPPPP methodmethod onon aa horizontalhorizontal andand aa verticalvertical plane.plane. ((AA,,BB)) ResolvedResolved horizontalhorizontal coordinates,coordinates,track track ID.ID. ((AA)) TheThe routeroute betweenbetween PatrasPatras andand IgoumenitsaIgoumenitsa (30(30 January).January). ((BB)) TheThe restrest ofof thethe routeroute upup toto thethe portport ofof BrindisiBrindisi (31(31 January).January). ((CC,D,D)) TheThe vertical vertical components components of of the the sections sections ( A(A,B,B),), respectively. respectively.

The steps followed in the previously described D-GNSS analysis were also followed here except for base stations, as this is not necessary in the PPP method. These are illustrated in Figure 15. The ﬁgure concerns the “Patra–Igoumenitsa“ route with code ID1, taken as an example. Three other examples concerning the routes with codes ID3, ID11 and ID141 are illustrated in the Figures S3–S5. WaterWater 20212021,, 1313,, 812x FOR PEER REVIEW 1715 of of 2223

Figure 15.15. IllustrationIllustration of of the the Patra–Igoumenitsa Patra–Igoumenitsa route route with with ID1 ID1 (see (see Table Table S1). (S1).A) The (A) rawThe data raw of data the GNSSof the altitudeGNSS altitude during theduring route the as route they as emerged they emer fromged the from PPP the solution. PPP solution. (B) The (B) raw The data,raw data, the curve the curve of mean of mean values values (red (red curve) curve) obtained obtained by applyingby applying the the Savitzky–Golay Savitzky–Golay moving moving average average ﬁlter filter and and the twothe curvestwo curves (light (light blue) blue) indicating indicating the limiting the limiting values values imposed im- byposed the bandby the ﬁlter. band (C filter.) hGNSS (Creceiver) hGNSS receiver elevation elevation correction correction at port check at port points check described points described in Section in3.2 Section.(D) Linear 3.2. ( correctionD) Linear basedcorrection on deviations based on ofdeviations measured ofport measured levels fromport levels the medium from the marine medium level marine (linear level tidal (linear correction tidal described correction in described Section 3.3 in). (ForSection more 3.3). examples (For more see examples also: Figure see S3–S5).also: Figure S3, Figure S4 and Figure S5)

3.6. OutlineIn all cases, of the the Analysis curve Procedure in part A of each of the aforementioned figures describes the raw data.In Three this section, of the four the examplesanalysis procedure concern the that middle has been of winterfollowed (end to ofrender January, it more ID1, com- ID3 prehensibleand ID11) with is briefly adverse visualized. weather conditions, The basic st whileeps of the the fourth methodology (ID141) concerns are illustrated mid-summer in Fig- withure 16 very in the smooth form of weather a flowchart. conditions The raw (see GNSS Table data S1). are The those examples obtained were from chosen ship’s to renderroutes visible(kinematic the largeraw data) difference and those in the obtained range of noisefrom the we encounterground stations. when theThe weather first step changes. involved It staticis evident solutions that the in rangethe base of noisestations, is much whereas greater the insecond the passes step withwas a code kinematic numbers solution ID1, ID3 of alland routes ID11 illustratedfrom all base in Figurestations 15 following, Figures S3 the and D-GNSS S4 than method. that in theThen route two ID141 different illustrated calcu- lationsin Figure were S5. done in parallel. One concerned the application of the D-GNSS method, and the second,Part B ofthe each application of the aforementioned of the PPP method. figures Concerning presents the the curve D-GNSS with application, the original it data; was firstthe curve examined of mean whether values the (red D-GNSS curve) obtained (LGO) soft by applyingware resolved the Savitzky–Golay the uncertainties method relevant [38]; toand a given the two route. light-blue If that had curves, not happened, which indicate the results a band were filter discarded. selected to For have the aroutes total widthwhere theof 1 uncertainties m beyond which were eachresolved, value a wascombinatorial deducted. solution It can be was seen chosen that the (Section band 3.4, filter Figure does 10).not removeAfter this any selection, value, as the the procedure range of all involved values is numerical smaller than filtering the bandwidth, (Section 3.4, in theFigure last 13),example followed (Figure by S5B)the removal referring of to static good heights weather of conditions. the receiver (Section 3.2, Equation (3), FigureIn 7) part and C, then of each the of linear the aforementioned tidal correction figures, described the inhGNSS Sectionreceiver 3.3. elevation correction at port check points described in Section 3.2 is illustrated. The height of the receiver on the vessel measured at the ports was removed from the data in order to generate the height of the sea topography. Finally, in part D of the aforementioned figures, the linear correction concerning the influence of astronomical and meteorological components of tide, htide, which is based on calculations of altitude in ports described in Section 3.3, is illustrated. With this correction, as explained earlier, the effect of the tide was removed.

Water 2021, 13, 812 16 of 22

3.6. Outline of the Analysis Procedure In this section, the analysis procedure that has been followed to render it more com- prehensible is briefly visualized. The basic steps of the methodology are illustrated in Figure 16 in the form of a flowchart. The raw GNSS data are those obtained from ship’s routes (kinematic raw data) and those obtained from the ground stations. The first step involved static solutions in the base stations, whereas the second step was a kinematic solution of all routes from all base stations following the D-GNSS method. Then two different calculations were done in parallel. One concerned the application of the D-GNSS method, and the second, the application of the PPP method. Concerning the D-GNSS application, it was first examined whether the D-GNSS (LGO) software resolved the uncertainties relevant to a given route. If that had not happened, the results were discarded. For the routes where the uncertainties were resolved, a combinatorial solution was chosen (Section 3.4, Figure 10). After this selection, the procedure involved numerical filtering Water 2021, 13, x FOR PEER REVIEW 18 of 23 (Section 3.4, Figure 13), followed by the removal of static heights of the receiver (Section 3.2, Equation (3), Figure7) and then the linear tidal correction described in Section 3.3.

Figure 16. Illustration of the basic methodology developed in the present work. Figure 16. Illustration of the basic methodology developed in the present work. A parallel process was followed with the PPP method. The only exception was that the procedureA parallel did process not involve was followed the aforementioned with the PPP combinatorialmethod. The only solution, exception but awas simple that solutionthe procedure from thedid beginning. not involve Once the aforementioned all the paths were combinatorial resolved, the solution, ones that but had a simple been solution from the beginning. Once all the paths were resolved, the ones that had been solved were selected. Then the procedure involved noise removal by numerical filtering, the removal of static heights of the receiver (Section 3.2, Equation (3), Figure 7) and then the linear tidal correction described in Section 3.3 (see also Figures 15 and S4–S6). Having achieved the estimates of the Ψ(i) values from both methods, we proceeded to a final assessment of the marine topography by calculating the dynamic means both between the individual routes–resolutions and between the different methods. This allowed constructing the map of the mean marine topography for the area studied.

4. Estimation of the Mean Sea Level in the Area Studied On the basis of what were described above, the final assessment of the mean marine topography in the studied area was achieved (Figure 17).

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solved were selected. Then the procedure involved noise removal by numerical ﬁltering, the removal of static heights of the receiver (Section 3.2, Equation (3), Figure7) and then the linear tidal correction described in Section 3.3 (see also Figures 15 and S4–S6). Having achieved the estimates of the Ψ(i) values from both methods, we proceeded to a ﬁnal assessment of the marine topography by calculating the dynamic means both between the individual routes–resolutions and between the different methods. This allowed constructing the map of the mean marine topography for the area studied.

4. Estimation of the Mean Sea Level in the Area Studied Water 2021, 13, x FOR PEER REVIEW 19 of 23 On the basis of what were described above, the ﬁnal assessment of the mean marine topography in the studied area was achieved (Figure 17).

Figure 17. SeaFigure surface 17. topographySea surface intopography the area studied. in the area The studied. heights wereThe heights calculated were while calculated taking while as reference taking theas ellipsoid WGS 84. Thereference numbers the illustrated ellipsoid concern WGS 84. the The corresponding numbers illustrated segments. concern the corresponding segments.

This assessmentThis was assessment obtained waswhile obtained taking into while account taking jointly into account the final jointly calculations the ﬁnal calculations performed usingperformed the D-GNSS using and the D-GNSSPPP methods. and PPP It is methods.worth noting It is worththat for noting each Ψ that(i) (line for each Ψ(i) (line segment vertically intersecting all the different paths; see Figure6), the average of all segment vertically intersecting all the different paths; see Figure 6), the average of all es- estimates from all the crossings for both methods was calculated. When creating the map timates from all the crossings for both methods was calculated. When creating the map illustrated in Figure 17, as an application area on the horizontal plane, we considered a illustrated in Figure 17, as an application area on the horizontal plane, we considered a zone that encompasses all the ship’s routes and covers an area of tens of meters up to a zone that encompasses all the ship’s routes and covers an area of tens of meters up to a few kilometers on either side of the principal route. It is evident that we can distinguish very significant altitude differences of up to 16 m. Moreover, the marine topography in the region shows a nearly constant slope of 4 cm/km in the N–S direction. A final estimation of the accuracy of the contour map (parameter u(i,t) in Equation (1)) was obtained while taking into account the following: (a) the accuracy of calculating the height of the HGNSS receiver based on the draught measurements (Section 3.2), (b) the mean range of the standard deviation of the differences of the kinematic data from the mean value, as it was derived by the moving average filter (e.g., Figures 13, 15B, S4B, S5B and S6B) and (c) the standard deviation of static estimations at ports (Figure 8). Factors α and β were thought to contribute linearly to the final estimate of uncertainty. Concerning factor c, the linear correction described in the Section 3.3 eliminates completely the factors of the meteorological component. However, it would be rather exaggerated to consider

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few kilometers on either side of the principal route. It is evident that we can distinguish very significant altitude differences of up to 16 m. Moreover, the marine topography in the region shows a nearly constant slope of 4 cm/km in the N–S direction. A final estimation of the accuracy of the contour map (parameter u(i,t) in Equation (1)) was obtained while taking into account the following: (a) the accuracy of calculating the height of the hGNSS receiver based on the draught measurements (Section 3.2), (b) the mean Water 2021, 13, x FOR PEER REVIEW 20 of 23 range of the standard deviation of the differences of the kinematic data from the mean value, as it was derived by the moving average filter (e.g., Figures 13, 15B, S4B, S5B and S6B) and (c) the standard deviation of static estimations at ports (Figure8). Factors α and β were completethought toelimination contribute of linearly this parameter, to the final as we estimate cannot of assess uncertainty. the tidal Concerning effect upon factor travel, c, exceptthe linear in the correction ports. Thus, described adopting in thea more Section rigorous 3.3 eliminates approach, completely we assumed the an factors uncertainty of the ofmeteorological 2 cm as a representative component. value However, of the it tide would in this be rather area. exaggeratedBy taking into to consideraccount the complete influ- enceelimination of factors of thisa, b parameter,and c and asusing we cannotthe well-known assess the error tidal effecttransmission upon travel, law, exceptan accuracy in the ports. Thus, adopting a more rigorous approach, we assumed an uncertainty of 2 cm as a of 3.31 cm was obtained for the MSL in the area studied (σhMSL = 3.31 cm). representativeFinally, the value results of theof the tide proposed in this area. methodology By taking intoare compared account the to influencethose of the of factorsgeoid modela, b and EGM96 c and (Figure using the 18). well-known Taking into erroraccount transmission the accuracy law, of the an accuracyEGM96′s ofown 3.31 estimates cm was obtained for the MSL in the area studied (σ = 3.31 cm). and other estimates of the mean sea level, hMSLthe differences are relatively small (up to 50 Finally, the results of the proposed methodology are compared to those of the geoid cm). The most significant difference is between points I and O, north of Corfu, where our model EGM96 (Figure 18). Taking into account the accuracy of the EGM960s own estimates estimate appears to be significantly lower than the estimates of EGM96, up to a maximum and other estimates of the mean sea level, the differences are relatively small (up to 50 cm). of 48 cm. The most significant difference is between points I and O, north of Corfu, where our estimate appears to be significantly lower than the estimates of EGM96, up to a maximum of 48 cm.

FigureFigure 18. 18. ComparisonComparison of of the the final ﬁnal results results (principal (principal route) route) of of this this work work with with the the geoid geoid model model EGM96. EGM96. We We observe observe general general agreementagreement of of our our results with those of the geoid and small variations (<50 cm cm).). The The heights heights were were calculated calculated based based on on the the referencereference ellipsoid WGS 84.

2. The precision of the factor HGNSS based on the measurements, is actually much higher (σ: 0.76 cm). Nevertheless, due to factors that could not be accurately determined (e.g., due to the lack of tide data in the area), we adopted a much more conservative approach, increasing the σ value to 3.1 cm. Nonetheless, the precision determined by the measurements is the highest ever published. This indicates the great potential for

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5. Concluding Remarks 1. The precision was estimated as 3.31 cm, taking into account all the uncertainty factors under quite rigorous assumptions. Higher precision would be achieved by further use of the proposed methodology. 2. The precision of the factor hGNSS based on the measurements, is actually much higher (σ: 0.76 cm). Nevertheless, due to factors that could not be accurately determined (e.g., due to the lack of tide data in the area), we adopted a much more conservative approach, increasing the σ value to 3.1 cm. Nonetheless, the precision determined by the measurements is the highest ever published. This indicates the great potential for improvement of the method “repeated GNSS measurements on the same route of a ship”, in the near future. 3. The significant differences between the estimates of the present work (SST estimate) and the geoid model (EGM96) in the d, e and m regions may be related to strong tectonic changes of the marine subsoil. In fact, in both areas strong tectonic activity has been inferred [39,40]. Moreover, recent studies have provided evidence for serious deposits in the area [41]. However, further investigation is required to corroborate this evidence. 4. The application of this approach using systematic multi-track recordings on conventional liner ships is very promising, as it may open up possibilities for widespread use of the methodology across the world. 5. The focus of floating GNSS on specific areas in conjunction with satellite data can provide complex, localized, high-precision solutions. The “GNSS method on floating means” can cover the areas not covered by the scanning of altitude satellites and thus may provide an important service in the exploration of marine topography.

Supplementary Materials: The following are available online at https://www.mdpi.com/2073-444 1/13/6/812/s1, Table S1: Information for the 142 maritime routes of the ship. For each route, the date, the ports of departure and destination (path), as well as from how many base stations it has been solved using the D-GNSS method (base) and whether it has been solved by the PPP method, Table S2: Indicative data from the ship’s draughts at the points of the calculation (A and B) for the period from 30 January to 6 February 2010 and the correction of the Hs of the geometric altitude according to Figure7, Table S3: Extract from the total table with the calculated values at the ports of Patras and Brindisi, Figure S1: Map depicting the multiple paths of our records. We focus on two areas A and B, where we observe different spreading of the routes. In area A, where we have open sea and the ship is not required to maneuver, we have differences in the order of even 7km, while in the relatively closed area B, the distances are much smaller (1.700m). The 8 paths (11/2-19/2) shown in the figure are consecutive and are reported in codes ID 13-21 (see Table SM1), Figure S2: Resolves part of the route from different base stations. The section mentioned here concerns the commencement of the route at the Patraikos Gulf near the port of Patra (Point (a) in Figure4). The base stations used and their distances from point (a) are illustrated (see also Figure4). An indicative length inside the part of the route presented is illustrated, Figure S3: Illustration of the Patras-Igoumenitsa route with code ID3 (see Table SM1). (A) It concerns the raw data of the GNSS altitude during the route as they emerged from the PPP solution. (B) It concerns the raw data, the curve of mean values (red curve) obtained by applying the Savitzky-Golay moving average filter and the two curves (light blue) indicating the limiting values imposed by the band filter. (C) hGNSS receiver elevation correction at port check points described in Section 3.2. (D) Linear correction based on deviations of measured port levels from the medium marine level (linear tidal correction described in Section 3.3), Figure S4: Illustration of the Patras-Igoumenitsa route with code ID11 (see Table SM1). (A) It concerns the raw data of the GNSS altitude during the route as they emerged from the PPP solution. (B) It concerns the raw data, the curve of mean values (red curve) obtained by applying the Savitzky-Golay moving average filter and the two curves (light blue) indicating the limiting values imposed by the band filter. (C) hGNSS receiver elevation correction at port check points described in Section 3.2. (D) Linear correction based on deviations of measured port levels from the medium marine level (linear tidal correction described in Section 3.3), Figure S5: Illustration of the Patras-Igoumenitsa route with code ID141 (see Table SM1). (A) It concerns the raw data of the GNSS altitude during the route as they emerged from the PPP solution. (B) It concerns the raw data, the curve of mean values (red Water 2021, 13, 812 20 of 22

curve) obtained by applying the Savitzky-Golay moving average filter and the two curves (light blue) indicating the limiting values imposed by the band filter. (C) hGNSS receiver elevation correction at port check points described in Section 3.2. (D) Linear correction based on deviations of measured port levels from the medium marine level (linear tidal correction described in Section 3.3). Funding: This research received no external funding Acknowledgments: This research took place during the time I was a student in the Laboratory of Geodesy and Geodetic Applications of Patra’s University, under the supervision of Stathis Stiros. Conflicts of Interest: The authors declare no conflict of interest

Appendix A

Calculation of the accuracy of determination of the parameter hGNSS in relation to its correction for taking into account the draught changes. " # (hb − ha) hGNSS = Z0 − Hs = Z0 − xa + ha (xa + xb)

hGNSS = f (Zo, xa, xb, ha, hb)

If Zo, xa, xb = C (ﬁxed), then based on the error transmission law, Equation (3) becomes

∂ f 2 ∂ f 2 ∂ f 2 ∂ f 2 ∂ f 2 σ2 = σ 2 + σ 2 + σ 2 + σ 2 + σ 2 hGNSS ha hb Z0 xa xb ∂ha ∂hb ∂Z0 ∂xa ∂xb

xa = 76.422mxb = 31.507m ∂ f x = a − 1 = −0.291925466 ∂ha xa + xb ∂ f −x = a = −0.708074534 ∂hb xa + xb ∂ f ∂ f ∂ f = = = 0 ∂Z0 ∂xa ∂xb Since the accuracy of sonar measurements is 1 cm (according to the instrument speciﬁ- cations) we have: = = σha σhβ 1cm = σhGNSS 0.76589cm.

References 1. Pascual, A.; Pujol, M.I.; Larnicol, G.; Le Traon, P.Y.; Rio, M.H. Mesoscale mapping capabilities of multisatellite altimeter missions: First results with real data in the Mediterranean Sea. J. Mar. Syst. 2007, 65, 190–211. [CrossRef] 2. Cocard, M.; Geiger, A.; Kahle, H.G.; Veis, G. Airborne laser altimetry in the Ionian Sea, Greece. Glob. Planet. Chang. 2002, 34, 87–96. [CrossRef] 3. Lycourghiotis, S.; Stiros, S. Sea Surface Topography in the Gulf of Patras and the southern Ionia sea using GPS. In Proceedings of the 12th Internasional Congress of the Geological Society of Greece, Patras, Greece, May 2017; Volume XLIII, pp. 1029–1034. 4. Bonnefond, P.; Exertier, P.; Laurain, O.; M’enard, Y.; Orsoni, A.; Jan, G.; Jeansou, E. Absolute Calibration of Jason-1 and TOPEX/Poseidon Altimeters in Corsica. Mar. Geod. 2003, 26, 261–284. [CrossRef] 5. Rocken, C.; Johnson, J.; Van Hove, T.; Iwabuchi, T. Atmospheric water vapor and geoid measurements in the open ocean with GPS. Geophys. Res. Lett. 2015, 32.[CrossRef] 6. Foster, H.; Carter, G.S.; Merriﬁeld, M.A. Ship-based measurements of sea surface topography. Geophys. Res. Lett. 2009, 36. [CrossRef] 7. Bouin, M.-N.; Ballu, V.; Calmant, S.; Boré, J.-M.; Folcher, E.; Ammann, J. A kinematic GNSS methodology for sea surface mapping, Vanuatu. J. Geod. 2009, 83, 1203–1217. [CrossRef] 8. Reinking, J.; Härting, A.; Bastos, L. Determination of sea surface height from moving ships with dynamic corrections. J. Geod. Sci. 2012.[CrossRef] Water 2021, 13, 812 21 of 22

9. Guo, J.; Liu, X.; Chen, Y.; Wang, J.; Li, C. Local normal height connection across sea with ship-borne gravimetry and GNSS techniques. Mar. Geophys. Res. 2014, 35, 141–148. [CrossRef] 10. Chupin, C.; Ballu, V.; Testut, L.; Tranchant, Y.T.; Calzas, M.; Poirier, E.; Bonnefond, P. Mapping Sea Surface Height Using New Concepts of Kinematic GNSS Instruments. Remote Sens. 2020, 12, 2656. [CrossRef] 11. Lycourghiotis, S. Developing a GNSS-on-boat based technique to determine the shape of the sea surface. In Proceedings of the 7th International Conference on Experiments/Process/System Modeling/Simulation/Optimization, Athens, Greece, 5–8 July 2017; Volume I, pp. 113–119, ISSN: 2241-9209, ISBN SET: 978-618-82173-2-4, ISBN Vol. I: 978-618-82173-3-1. 12. Lycourghiotis, S. Sea surface topography determination. Comparing two alternative methods at the Gulf of Corinth. In Proceedings of the 7th International Conference on Experiments/Process/System Modeling/Simulation/Optimization, Athens, Greece, 5–8 July 2017; Volume II, pp. 410–415, ISSN: 2241-9209, ISBN SET: 978-618-82173-2-4, ISBN Vol. II: 978-618-82173-4-8. 13. Lycourghiotis, S. Improvements of GNSS–on-boat methodology using a catamaran platform: Application at the gulf of Patras. In Proceedings of the 7th International Conference on Experiments/Process/System Modeling/Simulation/Optimization, Athens, Greece, 5–8 July 2017; Volume I, pp. 255–261, ISSN: 2241-9209, ISBN SET: 978-618-82173-2-4, ISBN Vol. I: 978-618-82173-3-1. 14. Bonnefond, P.; Exertier, P.; Laurain, O.; Thibaut, P.; Mercier, F. GPS-based sea level measurements to help the characterization of land contamination in coastal areas. Adv. Space Res. 2013, 51, 1383–1399. [CrossRef] 15. Kelecy, T.M.; Born, G.H.; Parke, M.E.; Rocken, C. Precise mean sea level measurements using the Global Positioning System. J. Geophys. Res. Ocean. 1994, 99, 7951–7959. [CrossRef] 16. Marshall, A.; Denys, P. Water level measurement and tidal datum transfer using high rate GPS buoys. N. Z. Surv. 2009, 299, 24. 17. Key, K.W.; Parke, M.E.; Born, G.H. Mapping the sea surface using a GPS buoy. Mar. Geod. 1998, 21, 67–79. [CrossRef] 18. Kato, T.; Terada, Y.; Kinoshita, M.; Kakimoto, H.; Isshiki, H.; Moriguchi, T.; Johnson, J. A new tsunami monitoring system using RTK-GPS. In Proceedings of the International Tsunami Symposium, Seattle, WA, USA, 7–10 August 2001; pp. 5–12. 19. Doong, D.J.; Lee, B.C.; Kao, C.C. Wave measurements using GPS velocity signals. Sensors 2011, 11, 1043–1058. [CrossRef] 20. Wöppelmann, G.; Miguez, B.M.; Bouin, M.N.; Altamimi, Z. Geocentric sea-level trend estimates from GPS analyses at relevant tide gauges world-wide. Glob. Planet. Chang. 2007, 57, 396–406. [CrossRef] 21. Deng, X.; Featherstone, W.E.; Hwang, C.W.; Berry, P.A.M. Estimation of contamination of ERS-2 and POSEIDON satellite radar altimetry close to the coasts of Australia. Mar. Geod. 2002, 25, 249–271. [CrossRef] 22. Hipkin, R. Modelling the geoid and sea-surface topography in coastal areas. Phys. Chem. Earth Part A Solid Earth Geod. 2000, 25, 9–16. [CrossRef] 23. Majumdar, T.J. Satellite Geoid/Gravity for Offshore Exploration. In Geospatial Technologies and Climate Change; Springer: Cham, Switzerland, 2014; pp. 203–218. 24. Karakitsios, V. Western Greece and Ionian Sea petroleum systems. AAPG Bull. 2013, 97, 1567–1595. [CrossRef] 25. Lemoine, F.G.; Kenyon, S.C.; Factor, J.K.; Trimmer, R.G.; Pavlis, N.K.; Chinn, D.S.; Wang, Y.M. The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. In Gravity, Geoid and Marine Geodesy; Springer: Berlin/Heidelberg, Germany, 1998. 26. Vignudelli, S.; Cipollini, P.; Roblou, L.; Lyard, F.; Gasparini, G.P.; Manzella, G.; Astraldi, M. Improved satellite altimetry in coastal systems: Case study of the Corsica Channel (Mediterranean Sea). Geophys. Res. Lett. 2005, 32, L07608. [CrossRef] 27. Jin, S.; Cardellach, E.; Xie, F. GNSS Remote Sensing; Springer: Dordrecht, The Netherlands, 2014. 28. GGrejner-Brzezinska, D.A.; Kashani, I.; Wielgosz, P. On accuracy and reliability of instantaneous network RTK as a function of network geometry, station separation, and data processing strategy. GPS Solut. 2005, 9, 212–225. [CrossRef] 29. Malinowski, M.; Kwiecień,J. A comparative study of Precise Point Positioning (PPP) accuracy using online services. Rep. Geod. Geoinformatics 2016, 102, 15–31. [CrossRef] 30. Larsson, P.; Henriksson-Larsén, K. The use of dGPS and simultaneous metabolic measurements during orienteering. Med. Sci. Sports Exerc. 2011, 33, 1919–1924. [CrossRef] 31. Zumberge, J.F.; Heflin, M.B.; Jefferson, D.C.; Watkins, M.M.; Webb, F.H. Precise point positioning for the efficient and robust analysis of GPS data from large networks. J. Geophys. Res. 1997, 102, 5005–5017. [CrossRef] 32. Tsimplis, M.N.; Proctor, R.; Flather, R.A. A two-dimensional tidal model for the Mediterranean Sea. J. Geophys. Res. Ocean. 1995, 100, 16223–16239. [CrossRef] 33. Cheng, Y.; Andersen, O.B. Improvement in global ocean tide model in shallow water regions. In Proceedings of the OSTST2010, Lisbon, Portugal, 18–20 October 2010. 34. Lozano, C.J.; Candela, J. The M (2) tide in the Mediterranean Sea: Dynamic analysis and data assimilation. Oceanologicaacta 1995, 18, 419–441. 35. Lycourghiotis, S.; Kontoni, D.-P.N. Analysing the Flood Risk in Mediterranean Coastal Areas with a New Methodology. In Proceedings of the 5th International Conference from Scientific Computing to Computational Engineering, Athens, Greece, 4–7 July 2012; Volume I, pp. 74–79, ISBN SET: 978-960-98941-9-7, ISBN Vol. I: 978-618-80115-0-2. 36. Lycourghiotis, S.A.; Stiros, S.C. Coastal Flooding Hazard in Low-Tide and High-Tide Coasts: Evidence from the North Aegean Coast. In Coastal Hazards; Springer: Dordrecht, The Netherlands, 2013; pp. 231–243. 37. Lycourghiotis, S.; Stiros, S. Meteorological tide and food risk at the Aegean basin. In Proceedings of the 4th Congress, Management and Improvement of Coastal Zones, Lesvos, Greece, 23–27 September 2008; pp. 63–73. Water 2021, 13, 812 22 of 22

38. Grejner-Brzezinska, D.A.; Wielgosz, P.; Kashani, I.; Smith, D.A.; Spencer, P.S.; Robertson, D.S.; Mader, G.L. An analysis of the effects of different network-based ionosphere stimation models on rover positioning accuracy. Positioning 2004, 1, 115–131. [CrossRef] 39. Louvari, E.; Kiratzi, A.A.; Papazachos, B.C. The Cephalonia transform fault and its extension to western Lefkada Island (Greece). Tectonophys. 1999, 308, 223–236. [CrossRef] 40. Altıner, Y.; Baˇcić,Ž.; Bašić,T.; Coticchia, A.; Medved, M.; Mulić,M.; Pavlides, S. Present-day tectonics in and around the Adria plate inferred from GPS measurements. Postcollisional tectonics and magmatism in the Mediterranean region and Asia. Spec. Pap. Geol. Soc. Am. 2006, 409, 43–55. 41. Zelilidis, A.; Maravelis, A.G.; Tserolas, P.; Konstantopoulos, P.A. An overview of the petroleum systems in the Ionian Zone, onshore NW Greece and Albania. J. Pet. Geol. 2015, 38, 331–348. [CrossRef]