Identifying the Dynamics of the Sea-Level Fluctuations in Croatia Using the RAPS Method

S S symmetry

Article Identifying the Dynamics of the Sea-Level Fluctuations in Croatia Using the RAPS Method

Danko Markovinović 1, Nikola Kranjˇcić 2,* , Bojan Ðurin 1 and Olga BjelotomićOršulić 3

1 Department of Civil Engineering, University North, Jurja Križani´ca31b, 42000 Varaždin, Croatia; [email protected] (D.M.); [email protected] (B.Ð.) 2 Faculty of Geotechnical Engineering, University of Zagreb, Hallerova aleja 7, 42000 Varaždin, Croatia 3 IGEA Ltd., Frana Supila 7/b, 42000 Varaždin, Croatia; [email protected] * Correspondence: [email protected]

Abstract: Seawater level changes are affected by natural and anthropogenic impacts. While climate changes are considered to be a cause for all significant recent variations in meteorological and hydrological parameters, there is still a need for the analysis at the smaller regional scale, especially of the seawater level changes. A regional analysis is essential for early warning of upcoming changes that could, firstly, affect islands and coastal areas and, subsequently, expand on larger areas. The determined regional changes could affect the salinity of drinking water sources, increase the presence of natural flooding, and impact land degradation. In this paper, an analysis of local seawater level fluctuations is provided for three available locations in Croatia distributed along the Adriatic Sea’s coast. The rescaled adjusted partial sums (RAPS) method was used and applied on time series of the average daily seawater levels for each location. Visual interpretation of the RAPS method

indicated the appearance of common regularities of the observed quantities, in this case, averaged daily seawater level changes. Also, it was shown that the regional shape and indentation of the coast

Citation: Markovinović,D.; Kranjˇcić, did not have a strong effect on the seawater level’s rise. Seasonal changes in the sea level are mostly N.; Ðurin, B.; BjelotomićOršulić,O. periodic and, therefore, have symmetry visible in its behavior. Fluctuations in the dynamics of sea Identifying the Dynamics of the level studied in this paper were not regular and predictable with simple linear equations, but the Sea-Level Fluctuations in Croatia symmetry was also found to be present in the irregularities identified with the RAPS method. Using the RAPS Method. Symmetry 2021, 13, 289. https://doi.org/ Keywords: sea level; climate impact; regularities; climate changes; RAPS; Adriatic Sea 10.3390/sym13020289

Academic Editor: Francisco G. Montoya 1. Introduction Received: 3 January 2021 Generally, relative sea-level changes are caused by transfers of water mass between oceans Accepted: 4 February 2021 Published: 8 February 2021 and continents due to the enlargement and deflation of immense ice layers. These changes are mainly caused by global climate changes. However, significant vertical movements in

Publisher’s Note: MDPI stays neutral the Earth’s crust appear over long periods of time that should also be taken into the account. with regard to jurisdictional claims in These movements cannot be exactly determined and their value stated, but they can be published maps and institutional afﬁl- identified and eliminated to some extent from Earth observations. This includes co-seismic iations. uplift and subsidence during hazardous earthquakes (Mw > 8), Earth’s surface displacements caused by a long-term process of glacial isostatic adjustment, and global ocean volume changes as a result of plate–tectonic movements [1]. Not only are vertical changes affected by the mentioned Earth processes, but sea-level changes also reshape coastal surroundings by their horizontal shift. The main impacts of sea-level rise are increased coastal erosion and loss of the Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. land, increased risk of flooding, and saltwater intrusion into freshwater resources [2]. This article is an open access article The abovementioned processes occur at different locations on Earth. There is no single distributed under the terms and location at which all of these processes are happening at the same time. Therefore, it is conditions of the Creative Commons impossible to record them collectively at once. However, we can record and monitor the Attribution (CC BY) license (https:// behavior of one of the processes, observing its behavior, and analyze any possible regular creativecommons.org/licenses/by/ trends that can be identiﬁed as a systematic and periodic Earth behavior resulting in a 4.0/). clearer set of original measurements.

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regular trends that can be identified as a systematic and periodic Earth behavior resulting in a clearer set of original measurements. The rate of sea-levelsea-level rise has increased. Between the years 1900 and 1990,1990, studies showshow that that the the s seaea level rose between 1.2 mm and 1.7 mm per year on average at a global levellevel as as measured by satellite altimetry [3]. [3]. By By the the year year 2000, 2000, that that rate had increased to approximately 3.2 mm per year, and the rate in 2016 was estimated to be 3.4 mm per year. approximately 3.2 mm per year, and the rate in 2016 was estimated to be 3.4 mm per year. In 2019, the sea level rose 3.3 mm. Figure1 shows the rise in sea level over the last three In 2019, the sea level rose 3.3 mm. Figure 1 shows the rise in sea level over the last three decades at a global level. As mentioned in Reference [4], during the period 1993–2018, decades at a global level. As mentioned in Reference [4], during the period 1993–2018, the the sea level varied from −1.41 + −0.47 mm per year for six locations in the Adriatic Sea sea level varied from −1.41 + −0.47 mm per year for six locations in the Adriatic Sea

FigureFigure 1. 1. RiseRise in in the the sea sea level level at at a a global global level from from 1993 1993 to to 2019 2019 [ 3[3]]. .

Numerous studies studies havehave dealt dealt with with the the estimation estimation of how of how much much and how and fast how the fast global the globalaverage average sea level sea is level rising. is Therising. main The difference main difference among the among studies the is studies the analytical is the analytical approach. approach.The first approach The first quantitatively approach quantitatively describes the describes physical the processes physical contributing processes contributing to the global tosea the rise global [2], such sea rise as thermal [2], such change as thermal influence change on influence ocean water on ocean volume, water land volume, ice melting, land iceand melting, changing and the changing depth of globalthe depth ocean of basinsglobal [ocean5], while basins the second[5], while approach the sec triesond approach to predict trtheies future to predict rise inthe sea future levels rise based in sea on level observeds based temperature on observed changes. temperature The first changes. approach The firstwas approach used in Intergovernmental was used in Intergovernmental Panel on Climate Panel Change on Climate (IPCC) Change climate (IPCC) assessments. climate assessments.Within this approach, Within this physical approach, models physical are used models to estimate are used contributions to estima fromte contributions the sea level fromcomponents, the sea level such components as thermal expansion, such as thermal and melting expansion from glaciers and melting and the from dynamics glaciers of and ice thesheets, dynamics with their of ice summation sheets, with in their the last summation stage of estimation in the last [stage6–8]. of The estimation second approach [6–8]. The is secondbased on approach a hypothesis is based that on the a sea hypothesis level rises that faster the as sea it gets level warmer rises faster [2]. This as it approach gets warmer uses [2].semiempirical This approach models uses insemiempirical order to form models statistical in order relationships to form statistical between relationships sea-level change be- tweenand global sea-level temperature change and [9–11 global] or radiative temperature forcing [9– [11]12, 13or], radiative respectively. forcing [12,13], respectively.Sea-level fluctuations, which occur over wide ranging timescales, may have periodic or aperiodicSea-level characteristics fluctuations, which visible. occur Symmetry over wide can beranging detected timescale in irregularitiess, may have in periodic rescaled oradjusted aperiodic partial character sumsistics (RAPS) visible. graphs, Symmetry since the can dynamics be detected of sea in level irregularities studied in in this rescaled paper adjustedare not predictable partial sums with (RAPS linear) graphs, trendlines. since The the mostdynamics recognizable of sea level periodic studied oscillations in this paper are the ones that occur due to the fact of seasonal changes in density or meteorological param- are not predictable with linear trendlines. The most recognizable periodic oscillations are eters [14]. Aperiodic sea-level changes cannot be assigned to an exact cause, since their the ones that occur due to the fact of seasonal changes in density or meteorological pa- behavior does not reoccur in the same shape at the same time intervals. They are the rameters [14]. Aperiodic sea-level changes cannot be assigned to an exact cause, since their result of several meteorological dynamic processes that cannot be determined separately behavior does not reoccur in the same shape at the same time intervals. They are the result and eliminated from observations. In addition, anthropogenic influences [14] were re- of several meteorological dynamic processes that cannot be determined separately and cently acknowledged and recognized as significant factors regarding sea-level changes, eliminated from observations. In addition, anthropogenic influences [14] were recently comprising greenhouse gases and increases in the temperature of Earth’s atmosphere, acknowledged and recognized as significant factors regarding sea-level changes, compris- which consequently also induce a rise in sea levels. ing greenhouse gases and increases in the temperature of Earth’s atmosphere, which con- Figure2 shows a schematic illustration of the climate and non-climate driven processes sequently also induce a rise in sea levels. that can influence global, regional (green colors), relative, and extreme sea-level events Figure 2 shows a schematic illustration of the climate and non-climate driven pro- (red colors) along coasts. Major ice processes are shown in purple, while general terms cessesare shown that incan black. influence Sea level global, equivalent regional (SLE) (green reflects colors), an increaserelative, inand the extreme global meansea-level sea

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events (red colors) along coasts. Major ice processes are shown in purple, while general terms are shown in black. Sea level equivalent (SLE) reflects an increase in the global mean sea level if the levelmentioned if the ice mentioned mass is completely ice mass is melted completely into the melted ocean into [15]. the Figure ocean 2 [gives15]. Figure2 gives insight into theinsight complexity into the and complexity impacts andof the impacts different of the causes different of rises causes in oflevels rises of in levelssea of sea water. water. Due to tDuehe processes to the processes’’ complexity complexity,, which occur which due occur to duethe rise to the and rise fall and of the fall sea, of the in sea, in Croatia, Croatia, there isthere the danger is the danger of coastal of coastal and island and island settlements settlements becoming becoming flooded ﬂooded..

Figure 2. NaturalFigure and 2.anthropogenicNatural and anthropogenicimpacts on the impactssea level on rising. the sea level rising.

The main aim ofThe this main study aim was of thisto identify study was possible to identify connections possible between connections three avail- between three available seawater ablelevel seawatermeasuring level stations, measuring i.e., between stations, their i.e., betweenaverage daily their averageseawater daily level seawater level changes. The RAPSchanges. method The RAPSwas used method for this was purpose used for, and this the purpose, effects andof the the coast effects’s relief of the coast’s relief on seawater levelon seawaterchanges were level analyzed. changes were analyzed.

2. Methodology2. Methodology The applicationThe of linear application trend determination of linear trend for determination sea-level observations for sea-level is a observationswell-es- is a well- tablished and familiarestablished approach. and familiar However, approach. linear trend However,s as a method linear trends only point as a method out pre- only point out dictable and obviouspredictable disturbances and obvious over disturbances a large set of over data a largethat setoccur of datain some that repetitive occur in some repetitive periodical aspect.periodical To detect aspect. and identify To detect possible and identifydisturbances possible outside disturbances of the scope outside of sea- of the scope of sonal changes,seasonal some scientific changes, areas some use scientific the RAPS areas method. use the It RAPS is statistical method. method It is statistical which method which can deal with acan large deal set with of data a large in order set of to data detect in order and describe to detect periodic and describe and/or periodic aperiodic and/or aperiodic behavior. This behavior.method was This chosen method due was to chosen the fact due of to its the applicability fact of its applicability in detecting in varia- detecting variational tional trends aparttrends from apart the from main the trend main in trend a time in series a time of series a monitored of a monitored occurrence; occurrence; it can it can be used be used for hydrologicalfor hydrological analysis analysis of river of riverflows flows [16] ( [as16 ]well (as wellas in as most in most hydrological hydrological re- research [16]), search [16]), precipitationprecipitation [17], [17 water], water temperatures temperatures [18], [18 meteorological], meteorological parameters parameters for forthe the purpose of purpose of the theclay clay excavation excavation [19], [19 waste], waste water water quality quality analysis analysis [20], [20 etc.], etc. We used it in thisWe paper usedit on in a this large paper time on series a large of available time series 18 ofyears available of averaged 18 years daily of averaged daily seawater levelsseawater to examine levels whether to examine it would whether highlight it would the subsets highlight of thedefault subsets (original) of default (original) time series if theytime exist seriesed. if they existed. The RAPS methodThe RAPSis a time method series isanalysis a time method series analysis based on method visual baseddetermination on visual of determination of a subseries from the original (given) series of continued data. By using the values of a subseries from the original (given) series of continued data. By using the values of an an average value and standard deviations of the observed time series, sums of the RAPS average value and standard deviations of the observed time series, sums of the RAPS val- values provide insight into the new subseries parts, where occurrences of the data grouping, ues provide insight into the new subseries parts, where occurrences of the data grouping, fluctuations, and similar appearances during the time is based on: fluctuations, and similar appearances during the time is based on: k k YY Yt − Y RAPSt k = (1) RAPSk  ∑ (1)  t=1 Sy t1 Sy

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where Yt is the value of the analyzed member (parameter) of the considered time series, Y is anwhere average Yt is value the value of the ofconsidered the analyzed time member series, (parameter)Sy is standard of the deviation considered of the time considered series, timeY is series, an averagen is a value number of the of considered members oftime the series, considered Sy is standard time series, deviation and ofk = the 1, consid- 2,..., n is a counterered time during series, summation n is a number procedure of members [16]. of the considered time series, and k = 1, 2,..., n is a Thecounter plot during of the RAPSsummation offers procedure a reasonable [16]. visualization of the readily apparent mode of the underlyingThe plot of trend, the RAPS which offers cannot a reasonable be seen in thevisualization standard timeof the series readily plots apparent [21]. The mode RAPS methodof the underlying could be applied trend, which to the cannot data time be seen series. in the standard time series plots [21]. The RAPSThe method first step could in thebe applied analysis to is the defining data time the linearseries. trend, which is a common procedure in theThe determination first step in of the the analysis rise or is fall defining of average the linear daily seawatertrend, which levels is a time common series. proce- In cases wheredure in such the adetermination determination of cannotthe rise beor realizedfall of average due to daily the lowseawater values levels of the time determination series. In coefficient,cases where the such RAPS a determination method has been cannot found be realized to be suitable. due to the Apart low from values the of main the deter- analysis ofmination the resulting coefficient, subseries, the RAPS consequently, method has a been comparison found to be of suitable. the RAPS Apart single from and the summed main valuesanalysis for of all the measuring resulting stationssubseries, was consequently, done. a comparison of the RAPS single and summed values for all measuring stations was done. 3. Case Study 3. CaseTo apply Studythe RAPS method on time series data of sea levels, the Croatian Meteoro- logicalTo and apply Hydrological the RAPS method Service on (CMHS) time series provided data of average sea level dailys, the seawater Croatian level Meteoro- data for threelogical locations and Hydrological on the Croatian Service part (CMHS) of the provided Adriatic average coast. These daily wereseawater Martinšˇcica,on level data for the islandthree oflocations Cres, and on the Prosika Croatian and part Golubinka, of the Adriatic which coast. are on These the coast. were SeawaterMartinščica levels, on the were measuredisland of Cres using, and a mareograph Prosika and onGolubinka an hourly, which basis are and on averaged the coast. to Seawater daily values. levels Figurewere 3 presentsmeasured the using locations a mareograph of observed on measurements,an hourly basis and all situated averaged along to daily the values. eastern Figure side of 3 the Adriaticpresents Sea. the location Figuress4 of–6 observed show the measurements, available time all series situated of averagedalong the eastern seawater side levels of the (H) forAdriatic the measuring Sea. Figures stations 4–6 show of Martinšˇcica,Prosika, the available time series and Golubinkaof averaged [ 22seawater]. levels (H) for the measuring stations of Martinščica, Prosika, and Golubinka [22].

FigureFigure 3. 3.Locations Locations ofof thethe measuringmeasuring stations for for sea sea water water levels levels [23]. [23 ].

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FigureFigure 4. 4.Linear Linear trendtrend ofof the averaged daily daily sea sea water water levels levels from from the the Martinščica Martinšˇcicameasuring measuring station station [24] [.24 ].

FigureFigure 5. 5.Linear Linear trend trend of of thethe averagedaveraged daily sea water water levels levels for for the the Golubinka Golubinka measuring measuring station station [24] [24. ].

Figure 6. Linear trend of the averaged daily sea water levels for the Prosika measuring station [24].

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Symmetry 2021, 13, 289 6 of 14 Figure 5. Linear trend of the averaged daily sea water levels for the Golubinka measuring station [24].

Figure 6. Linear trend of the averaged daily sea water levels for thethe ProsikaProsika measuringmeasuring stationstation [[24]24]..

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The northeastern coast of the Adriatic is the western part of the Balkan Peninsula. It is mostly a hill. Consistent with the relationship between tectonic structures, it refers to a well- defined longitudinal type. As a result of the combined effect of Holocene transverse and tectonic coastal precipitation, the sea in domes with positive structures attacked geosynclinal depressions and exposure wastes, creating numerous long and narrow bays that stretch along the abrupt coast. This is the busiest coast in the world with a large number of ports, coves, peninsulas, 1185 islands and islets, and differently shaped rocky outcrops that make-up the most interesting configurations and have small rocky and pebble beaches. It is intersected by several bays and coves, the largest of which are the Kvarner and Trieste bays, separated by an elevated Istrian peninsula. They align longitudinally near the shore, repeating the corresponding series of positive tectonic folds. The “inner” coast is well protected from the undulating movement of the island fence. It was practically not exposed to the action of the sea and retained vivid traces of initial dissection (tectonic and denudation). [22] Therefore, Martinšˇcica and Golubinka are located in semi-closed bays and are not directly exposed to the waves, which does not affect short-term sea level changes. Prosika, however, is located in a channel between the Adriatic Sea and Lake Vransko jezero and, therefore, water level changes are affected not only by the Adriatic Sea but by lake water as well. Linear regressions between average daily sea water level H (cm) and time t (days) were also calculated and are shown in Figures4–6. The obtained values of the coefficient of determination, R2 (0.0263 for Martinšˇcica,0.0363 for Golubinka, and 0.3101 for Prosika), were in favor of that. Although the value of R for Prosika (0.5569) showed salient regression, there was no justification for defining a linear trend. Especially for Martinšˇcica(R = 0.1622) and Golubinka (R = 0.1905), which point out weak regression. It was obvious that defining a linear trend, as a most common procedure for such analysis, was not justified. Characteristic statistical parameters for the measuring stations Martinšˇcica,Prosika, and Golubinka are shown in Table1[24].

Table 1. Average values, standard deviations, minimum and maximum values, and a range of the averaged daily sea water levels (cm) for the 18 year time series for the measuring stations Martinšˇcica, Prosika, and Golubinka.

Measuring Station Martinšˇcica Prosika Golubinka Average value 34 46 49 Standard deviation 12 14 12 Minimum value −10 0 4 Maximum value 89 95 97 Range 99 95 93

Values of standard deviation indicate that changes of the average daily sea water levels are similar. The correctness of this statement needs to be examined using the RAPS method.

4. Results and Discussion Based on linear trend problem explained in Section3, the RAPS method was applied to the observed time series for each measuring station. Figures7–9 present the RAPS method applied to each measuring station. The RAPS analysis was based on identifying the next “higher hill” or “lowest bottom”. Such points divide the original time series of the average daily sea water level rising on new subseries. As can be concluded from Figures7 and8, the Martinšˇcica and Golubinka measuring stations have almost the same overlapping pattern of the RAPS values. Hence, subseries of the original sea level changes series can have possibly similar causes. RAPS values for Prosika also overlap with RAPS values of the mentioned two stations but not in the same shape of the pattern. It could be seen that RAPS values for the Martinšˇcica and Golubinka stations separated at the end of the 2008, while separation of the Prosika station had a ‘’delay” of one year, at the end of 2009. Regarding geographical position and indentation along the coast (Figure3), it can be concluded that those two factors did not have an impact on the RAPS values due to the topography in the station’s vicinity. Symmetry 2021, 13, x FOR PEER REVIEW 8 of 14

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RAPS Martinščica Days RAPS Martinščica

Days

1 78 155 232 309 386 463 540 617 694 771 848 925 1002 1079 1156 1233 1310 1387 1464 1541 1618 1695 1772 1849 1926 2003 2080 2157 2234 2311 2388 2465 2542 2619 2696 2773 2850 2927 3004 3081 3158 3235 3312 3389 3466 3543 3620 3697 3774 3851 3928 4005 4082 4159 4236 4313 4390 4467 4544 4621 4698 4775 4852 4929 5006 5083 5160 5237 5314 5391 5468 5545 5622 5699 5776 5853 5930 6007 6084 6161 6238 6315 6392 6469 6546 -5050 -150-50 -150-250 -250-350 -350-450 -450-550 -550-650 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 -650 Years 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Years Figure 7. Rescaled adjusted partial sums (RAPS) values of the averaged daily sea water levels for the Martinščica measuring station. Figure 7. Rescaled adjusted partial sums (RAPS) values of the averaged daily sea water levels for the Martinšˇcicameasuring station. Figure 7. Rescaled adjusted partial sums (RAPS) values of the averaged daily sea water levels for the Martinščica measuring station. RAPS Golubinka RAPS GolubinkaDays

Days

1 79 157 235 313 391 469 547 625 703 781 859 937 1015 1093 1171 1249 1327 1405 1483 1561 1639 1717 1795 1873 1951 2029 2107 2185 2263 2341 2419 2497 2575 2653 2731 2809 2887 2965 3043 3121 3199 3277 3355 3433 3511 3589 3667 3745 3823 3901 3979 4057 4135 4213 4291 4369 4447 4525 4603 4681 4759 4837 4915 4993 5071 5149 5227 5305 5383 5461 5539 5617 5695 5773 5851 5929 6007 6085 6163 6241 6319 6397 6475 6553

79 157 235 313 391 469 547 625 703 781 859 937 1015 1093 1171 1249 1327 1405 1483 1561 1639 1717 1795 1873 1951 2029 2107 2185 2263 2341 2419 2497 2575 2653 2731 2809 2887 2965 3043 3121 3199 3277 3355 3433 3511 3589 3667 3745 3823 3901 3979 4057 4135 4213 4291 4369 4447 4525 4603 4681 4759 4837 4915 4993 5071 5149 5227 5305 5383 5461 5539 5617 5695 5773 5851 5929 6007 6085 6163 6241 6319 6397 6475 6553 -30 1

-130-30

-130-230

-230-330

-330-430

-430-530

-530-630

-630-730

-730-830 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 -830 Years 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Years Figure 8. RAPS values of the averaged daily sea water levels for the Golubinka measuring station. FigureFigure 8. RAPSRAPS values values of of the the averaged averaged daily daily sea water levels for the Golubinka measuring station.

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RAPS Prosika

Days

Figure 9. RAPS values of the averaged daily sea water levels for the Prosika measuring station. Figure 9. RAPS values of the averaged daily sea water levels for the Prosika measuring station. As can be concluded from Figures 7 and 8, the Martinščica and Golubinka measuring stations have almost the same overlapping pattern of the RAPS values. Hence, subseries of the original sea level changes series can have possibly similar causes. RAPS values for Prosika also overlap with RAPS values of the mentioned two stations but not in the same shape of the pattern. It could be seen that RAPS values for the Martinščica and Golubinka stations separated at the end of the 2008, while separation of the Prosika station had a ‘’delay’’ of one year, at the end of 2009. Regarding geographical position and indentation along the coast (Figure 3), it can be concluded that those two factors did not have an impact on the RAPS values due to the topography in the station’s vicinity.

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The Prosika measuring station has different RAPS values from Martinšˇcicaand Gol- ubinka, which can be seen from Figures7–9. The Martinšˇcicaand Golubinka measuring The Prosika measuringing stationstation hashas differentdifferent RAPSRAPS valuesvalues fromfrom MartinščicaMartinščica andand Golu-Golu- stations are open to the sea, while the Prosika measuring station is located in the channel binka, which can be seen from Figures 7–9. The Martinščica and Golubinka measuring stationsstationsand between areare openopen thetoto thethe Adriatic sea,sea, whilewhile Sea thethe andProsikaProsika Lake measuring Vransko station jezero. is located in the channel and betweenPossible thethe AdAd connectionsriaticriatic SeaSea and among Lake Vransko changes jezero. in seawater levels were tested by the analysis of thePossible mutual connection correlationsss among between changes RAPSin seawaterseawater single levellevel valuesss were testedtested (Figures byby thethe 10 analysisanalysis–12) as well as between of the mutual correlations between RAPS single values (Figures 10–12) as well as between ofRAPS the mutual summation correlations values between (Figures RAPS single 13– 15values). (Figures 10–12) as well as between RAPS summation values (Figures 13–15).).

FigureFigure 10. 10. CorrelationCorrelation among among singlesingle valuesvalues single ofof thethe values RAPSRAPSof forfor the GolubinkaGolubinka RAPS andand for Martinščica GolubinkaMartinščica.. and Martinšˇcica.

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FigureFigure 11. 11. CorrelationCorrelation among among singlesingle valuesvalues single ofof thethe values RAPSRAPSof forfor the ProsikaProsika RAPS andand for Martinščica.Martinščica. Prosika and Martinšˇcica.

FigureFigure 12. 12.CorrelationCorrelation among among single values single of the values RAPSof for the Prosika RAPS and for Golubinka. Prosika and Golubinka.

The Martinščica and Golubinka measuring stations had the biggest correlation (R = 0.9275), which means a strong significance. This is due to the observed overlapping of the subseries from Figures 5 and 6. Other observed correlations between other measuring stations also had significance. Prosika and Martinšćica, with R = 0.8186, as well as Prosika and Golubinka, with R = 0.8757, also had a close significance but smaller compared with the connections between Martinščica and Prosika. It can be seen that same conclusion regarding the connection between the Martinščica and Golubinka stations, obtained from Figure 10, was derived from Figure 13. In this case, the significance was functional (R = 0.9595). The same conclusion was established for the Prosika and Martinšćica stations (R = 0.9443) as well as between the Prosika and Golu- binka stations (R = 0.9037).

Figure 13. Correlation between summed values of the RAPS for Golubinka and Martinščica stations.

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Figure 12. Correlation among single values of the RAPS for Prosika and Golubinka.

The Martinščica and Golubinka measuring stations had the biggest correlation (R = 0.9275), which means a strong significance. This is due to the observed overlapping of the subseries from Figures 5 and 6. Other observed correlations between other measuring stations also had significance. Prosika and Martinšćica, with R = 0.8186, as well as Prosika and Golubinka, with R = 0.8757, also had a close significance but smaller compared with the connections between Martinščica and Prosika. It can be seen that same conclusion regarding the connection between the Martinščica and Golubinka stations, obtained from Figure 10, was derived from Figure 13. In this case, the significance was functional (R = 0.9595). The same conclusion was established for the Symmetry 2021, 13, 289 11 of 14 Prosika and Martinšćica stations (R = 0.9443) as well as between the Prosika and Golu- binka stations (R = 0.9037).

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FigureFigure 13. 13.Correlation Correlation between between summed summed values values of of the the RAPS RAPS for for Golubinka Golubinka and and Martinšˇcicastations. Martinščica stations.

FigureFigure 14. 14. CorrelationCorrelation between between summed summed values values of of the the RAPS RAPS for for Prosika Prosika and and Martinščica Martinšˇcicastations. stations.

Figure 15. Correlation between summed values of the RAPS for Prosika and Golubinka stations.

The results revealed that a relationship between all three measuring stations, i.e., daily seawater level changes is remarkably high. As mentioned earlier, high average daily seawater levels could result in flooding of settlements that are at lower altitudes. The main correlations between these stations will be thoroughly discussed in further research/papers, where additional parameters will be analyzed. Seawater level changes can especially

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Symmetry 2021, 13, 289 12 of 14 Figure 14. Correlation between summed values of the RAPS for Prosika and Martinščica stations.

Figure 15. Correlation between summed values of the RAPS for Prosika andand GolubinkaGolubinka stations.stations. The Martinšˇcica and Golubinka measuring stations had the biggest correlation (R = 0.9275), The results revealed that a relationship between all three measuring stations, i.e., which means a strong significance. This is due to the observed overlapping of the subseries daily seawater level changes is remarkably high. As mentioned earlier, high average daily from Figures5 and6. seawater levels could result in flooding of settlements that are at lower altitudes. The main Other observed correlations between other measuring stations also had significance. correlations between these stations will be thoroughly discussed in further research/pa- Prosika and Martinšćica,with R = 0.8186, as well as Prosika and Golubinka, with R = 0.8757, pers, where additional parameters will be analyzed. Seawater level changes can especially also had a close significance but smaller compared with the connections between Mart- inšˇcicaand Prosika. It can be seen that same conclusion regarding the connection between the Martinšˇcica and Golubinka stations, obtained from Figure 10, was derived from Figure 13. In this case, the significance was functional (R = 0.9595). The same conclusion was established for the Prosika and Martinšćicastations (R = 0.9443) as well as between the Prosika and Golubinka stations (R = 0.9037). The results revealed that a relationship between all three measuring stations, i.e., daily seawater level changes is remarkably high. As mentioned earlier, high average daily seawater levels could result in flooding of settlements that are at lower altitudes. The main correlations between these stations will be thoroughly discussed in further research/papers, where additional parameters will be analyzed. Seawater level changes can especially affect the quality of drinking water in coastal areas, which could pose a huge threat to this area.

5. Conclusions The presented research was conducted over a sea-level time series to determine the unseasonal non-linear trend of data behavior if present. The preliminary analysis of the RAPS method applied over the sea-level measurements resulted in a possible correlation detected between average daily seawater level rises at the regional scale level in Croatia, regarding the three different locations of observed measurements. Periodic overlapping was observed between all measuring stations. The analysis showed that the regional shape and indentation of the coast did not have an effect on the rise in seawater levels, although land movement could have impact on long-term seawater level changes. Furthermore, the results showed the joint presence throughout the aperiodic visible subset of the observed Symmetry 2021, 13, 289 13 of 14

sea-level time series of different kinds of Earth movements, mentioned in the Introduction, that do have an impact on sea-level rise. Since the RAPS method is a statistical and not a deterministic method, it is not possible to extract the further impact of such influences on sea-level in deterministic, millimeter values. However, the analysis showed that it can be used as a useful tool for a supplementary insight in data’s behavior and detection of possible sea-level fluctuations apart from seasonal periodic trend. Further analysis should be more complex with regards to the analysis of the impact of climate factors as well as the measurement of raising and lowering the terrain. The RAPS analyses, as well as mutual connections of RAPS values between particular stations, indicated particular periods that need to be paid attention to during subsequent analysis. This refers primarily to a mutual comparison of the time series of climate factors. The next recommendation is a comparison with values and trends of the coastal terrain. This will complete the overall picture of the problem, while the first step is the analysis presented in this paper. Despite the limitations of using a partly visual analysis comprising RAPS solu- tions, determined conclusions indicate reliability in identifying nonlinear trends obtained from such an approach.

Author Contributions: Conceptualization, D.M. and N.K.; methodology, B.Ð.; software, B.Ð. and N.K.; validation, D.M. and O.B.O.; formal analysis, B.Ð.; investigation, D.M.; resources, D.M. and N.K.; data cu- ration, B.Ð.; writing—original draft preparation, B.Ð.; writing—review and editing, N.K. and O.B.O.; visualization, N.K.; supervision, D.M. and B.Ð.; funding acquisition, D.M. and N.K. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Data available on www.dhmz.hr the official web site of Croatian Meteorological and Hydrological Service. Data is available on request. Acknowledgments: The authors want to express their acknowledgment to the Croatian Meteorologi- cal and Hydrological Service for providing the data. Conflicts of Interest: The authors declare no conflict of interest.

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