entropy

Article Complex Extreme Sea Levels Prediction Analysis: Coast Case Study

Faisal Ahmed Khan 1, Tariq Masood Ali Khan 1, Ali Najah Ahmed 2 , Haitham Abdulmohsin Afan 3,*, Mohsen Sherif 4,5 , Ahmed Sefelnasr 4 and Ahmed El-Shafie 4,6

1 Institute of Environmental Studies, University of Karachi, Karachi 75270, Pakistan; [email protected] (F.A.K.); [email protected] (T.M.A.K.) 2 Institute for Energy Infrastructure (IEI), Universiti Tenaga Nasional (UNITEN), Kajang 43000, Selangor, Malaysia; [email protected] 3 Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam 4 National Water Center, University, Al Ain P.O. Box 15551, UAE; [email protected] (M.S.); [email protected] (A.S.); elshafi[email protected] (A.E.-S.) 5 Civil and Environmental Eng. Dept., College of Engineering, United Arab Emirates University, Al Ain 15551, UAE 6 Department of Civil Engineering, University of Malaya, Kuala Lumpur 50603, Malaysia * Correspondence: [email protected]

 Received: 16 April 2020; Accepted: 11 May 2020; Published: 14 May 2020 

Abstract: In this study, the analysis of the extreme sea level was carried out by using 10 years (2007–2016) of hourly tide gauge data of Karachi port station along the Pakistan coast. Observations revealed that the magnitudes of the tides usually exceeded the storm surges at this station. The main observation for this duration and the subsequent analysis showed that in June 2007 a “Yemyin” hit the Pakistan coast. The joint probability method (JPM) and the annual maximum method (AMM) were used for statistical analysis to find out the return periods of different extreme sea levels. According to the achieved results, the AMM and JPM methods erre compatible with each other for the Karachi coast and remained well within the range of 95% confidence. For the JPM method, the highest astronomical tide (HAT) of the Karachi coast was considered as the threshold and the sea levels above it were considered extreme sea levels. The 10 annual observed sea level maxima, in the recent past, showed an increasing trend for extreme sea levels. In the study period, the increment rates of 3.6 mm/year and 2.1 mm/year were observed for mean sea level and extreme sea level, respectively, along the Karachi coast. Tidal analysis, for the Karachi tide gauge data, showed less dependency of the extreme sea levels on the non-tidal residuals. By applying the Merrifield criteria of mean annual maximum water level ratio, it was found that the Karachi coast was tidally dominated and the non-tidal residual contribution was just 10%. The examination of the highest water level event (13 June 2014) during the study period, further favored the tidal dominance as compared to the non-tidal component along the Karachi coast.

Keywords: extreme sea level prediction; complex system prediction; annual maximum method; joint probability method; Pakistan coast

1. Introduction Many studies were made for extreme sea levels from several other regions, which helped the researchers conclude that, for tidally dominated coasts, most often the cause behind frequent extreme sea level events is sea level rise (SLR) [1–4]. Mean sea level trends, determined from the tide gauge data

Entropy 2020, 22, 549; doi:10.3390/e22050549 www.mdpi.com/journal/entropy Entropy 2020, 22, 549 2 of 12 sets, were noticed as the main cause of the height increment of extreme sea levels [2,5–7]. A significant increase in the frequencies of extreme sea levels is expected with the global SLR [8,9]. The and rim countries are very much prone to SLR, storm surges, high waves and swells [10–12]. Pakistan’s coastline values its aesthetic, ecological and economic assets. Sustainable coastal management of increasing population stress and the protection of coastal assets has become challenging for the concerned authorities. In the coming future, climate change is a severely intimidating issue for coastal management [12]. Because of the changing climate and SLR, the coast is not stagnant anymore and due attention is required from coastal planners and managers. For better coastal management it is necessary to assess the impact of sea level and climate changes. If there is a mean SLR then the frequency of extreme sea levels will also increase. Even a slight change in the mean sea level can have a major increasing impact on the frequency of extreme sea level events. This will intensify the effect of tropical cyclones [1,12], having more amplified storm surges hitting the coast and experiencing higher extreme sea levels. The impact of SLR is expected to be intensified due to increased meteorological events, by shortening the return periods of extreme sea levels. Sea level analysis with reference to extreme events is very much needed because there is not much evidence available of any such studies conducted for the Karachi coast in the recent past. Extreme sea level events can be predicted and visualized by studying their association with tidal fluctuations and meteorological extreme events [13]. All the components related to the observed sea level, including mean water level, surges and tides, should be considered for the reliable estimation of future maximum water levels [14]. The co-occurrence of high tides and extreme meteorological events make a coast vulnerable to coastal flooding [15]. Coasts with abrupt increasing mean sea level trends must be investigated for extreme sea levels in upcoming years for the provision of technical bases for proper coastal management [16]. As far as coastal management is concerned, the variability of extreme sea levels is of much concern with reference to climate changes in the area. To estimate the return period and extent of maximum water levels, observed sea level data from tide-gauges provided potent bases for researchers [17]. Erosion is one of the known impacts of SLR, which furthermore is a reason for coastal slumping. The Bruun rule can estimate the extent of coastal slumping caused by SLR [5,18–20]. According to the Bruun rule, the rate of coastal slumping is 100 times the extent of SLR. This multiplied impact will have far-reaching consequences for the coastal infrastructure. In addition, the accelerated erosion of the coastline, the groundwater contamination and seawater intrusion are the direct consequences of SLR and the associated extreme events [12,21,22]. Statistical examination of the observed sea level is a common technique to predict extreme sea levels along with their return periods. Many statistical and mathematical approaches, like the annual maximum method (AMM), peak over threshold (POT) method and the joint probability method (JPM), have been used in the past. The accuracy and reliability of any used technique for predicting extreme sea levels depend on the frequency and length of available observed sea data. In the present study, we used AMM and JPM to analyze 10 years of hourly sea level data. The AMM is a useful tool to estimate the return periods by calculating the probabilities of any extreme event. It has been shown that the annual maxima exhibited an almost linear increase when plotted against the logarithm of the number of years, hence it could be a convenient estimator for the recurrence of extreme events [23]. The AMM involves the analysis of a series of annual maxima to predict extreme sea levels for the future. Since this method uses only one value per year, the length of available data is very important. This method can be used by considering the limits for prediction [24]. Pugh and Vassie presented the JPM in the year 1978. In comparison, the JPM can be considered as a reliable technique even for short-term data and can be used for long-term predictions [25]. The AMM is based on an analysis of frequency, per year, of a time series data set. The quality of data should therefore be ensured in terms of the possibility of any outlying value. The main Entropy 2020, 22, 549 3 of 12 limitation of the AMM is the continuity of the data record. Split data records are not reliable for good estimation [26]. For the AMM the estimation of the return period of any extreme event can be done for the numberEntropy 2020 of,years 22, x FOR that PEER is REVIEW five times the available number of years of data [24]. The JPM, being3 of 12 more complex, relies on the availability of hourly sea level data. Detailed examination of sea level oscillation is onlyfor possible the number with of high-frequencyyears that is five data.times the Although available the number length of of years data of can data be [24]. compromised The JPM, being to a few more complex, relies on the availability of hourly sea level data. Detailed examination of sea level years, the execution of the method needs not only the tide gauge data but also the predicted tide level oscillation is only possible with high-frequency data. Although the length of data can be data forcompromised each hour. to In a termsfew years, of the the accuracy execution of of estimation the method of needs the returnnot only periods the tide of gauge an extreme data but event, also the JPM couldthe predicted be considered tide level as data more for reliable each hour. than In the term AMMs of [27the]. accuracy of estimation of the return periods of an extreme event, the JPM could be considered as more reliable than the AMM [27]. 2. Study Area The2. Study Pakistan Area coast has semi-diurnal tides with diurnal inequality. The mean tidal range is 2.3 m for the KarachiThe Pakistan port. The coast proposed has semi-diurnal study comprised tides with thediurnal analysis inequality. for extreme The mean events tidal linkedrange is with 2.3 m strong stormfor surges the Karachi and extreme port. The high proposed tides study as impacts comprised of rising the analysis sea levels for extreme in the events Karachi linked coast. with The strong extreme sea levelstorm analysis, surges and for extreme the assessment high tides as of impacts the return of rising periods sea levels of di inff erentthe Karachi extreme coast. sea The levels, extreme is very beneficialsea level for analysis, effective for coastal the assessment management of the and return provides periods technical of different bases extreme for coastalsea levels, engineers is very [28]. beneficial for effective coastal management and provides technical bases for coastal engineers [28]. In In this extreme sea level study, the estimation of return periods was done by analyzing the hourly this extreme sea level study, the estimation of return periods was done by analyzing the hourly tide tide gauge data recorded at Karachi port along the Pakistan coast. The tide gauge was installed at gauge data recorded at Karachi port along the Pakistan coast. The tide gauge was installed at the the northnorth sideside of the the slipway slipway control control room room at Karachi at Karachi port trust port at trust 24.8° at N 24.8 and◦ 66.9°N and E. For 66.9 the◦ E. sea For level the sea level measurement, the the chart chart datum datum was was 4.39 4.39 m mbelow below a benchmark, a benchmark, which which was wasmarked marked 0.5 m 0.5 above m above groundground level. level. The bathymetry,The bathymetry, topography topography and and the the location location of theof the tide tide gauge gauge at Karachiat Karachi port port is shownis in Figureshown1. Thein Figure study 1. will The be study very will useful be very in the useful identification in the identification of the issues of the associated issues associated with extreme with sea levelextreme events and sea level the possible events and eff ectsthe poss of aible rising effects sea of level a rising on thesea lowlevel lying on the areas low lying along areas the coastalalong the belt of Pakistan,coastal such belt as of thePakistan, Indus such deltaic as the region Indus and deltaic Karachi region coast. and Karachi coast.

Figure 1. Bathymetry, topography and the location of the tide gauge at Karachi port, along the Figure 1. Bathymetry, topography and the location of the tide gauge at Karachi port, along the Pakistan coast. Pakistan coast. A range of natural hazards poses risks to the coastline of Pakistan. Extreme sea level events, by SLR A range of natural hazards poses risks to the coastline of Pakistan. Extreme sea level events, by and stormSLR and surges, storm can surges, initiate can coastal initiate flooding coastal flooding in the low in the lying low regions lying regions along the along coast. the Thecoast. shorelines The mayshorelines experience may severe experience erosion severe during erosion extreme during sea extreme level sea events. level events. Saltwater Saltwater intrusion intrusion isalso is also a very seriousa very problem serious in problem the low lyingin the Induslow lying delta. Indus This delt problema. This ofproblem seawater of seawater intrusion intrusion has been has reported been by manyreported authors by [12 many,21,22 authors,29–33 [12,]. 21,22,29–33]. In the coming future, the intensity and frequency of extreme sea levels are expected to increase due to the intensified impact of weather conditions and mean SLR. Pakistan's coastal territory is

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In the coming future, the intensity and frequency of extreme sea levels are expected to increase due to the intensified impact of weather conditions and mean SLR. Pakistan’s coastal territory is facing serious issues of coastal flooding and coastal erosion as impacts of the SLR. The observed tide gauge dataEntropy at Karachi 2020, 22 port, x FOR indicated PEER REVIEW that the sea level is rising for the coast [34]. In the Karachi4 coast, of 12 the SLR wasfacing estimated serious issues at the of ratecoastal of flooding approximately and coastal 1.1 erosion mm per as year impacts in the of the past, SLR. calculated The observed in year tide 1988. The observedgauge data change at Karachi in seaport level indicated may that be treatedthe sea leve as al is eustatic rising for rise, the ascoast the [34]. Indus In the delta Karachi is on coast, a passive continentalthe SLR margin was estimated and isostatically at the rate stableof approximatel [35]. y 1.1 mm per year in the past, calculated in year The1988. change The observed in sea levelchange is in important sea level may for coastal be treate morphologyd as a eustatic (i.e., rise, erosion as the orIndus accretion delta is problems) on a and coastalpassive inundationcontinental margin in the coastaland isostatically areas of Pakistan.stable [35]. The Pakistan coast, being tidally dominated, is facing changesThe change in the in coastlinesea level is due impo tortant the impactfor coastal of morphology high tidal activity (i.e., erosion and or extreme accretion sea problems) level events. A limitedand coastal number inundation of studies in the have coastal been areas conducted of Pakistan. for The coastal Pakistan erosion coast, inbeing Pakistan. tidally dominated, In the year is 1997, the spacefacing and changes upper in atmospherethe coastline due research to the impact commission of high (SUPARCO), tidal activity and the extreme national sea space level agencyevents. A of the limited number of studies have been conducted for coastal erosion in Pakistan. In the year 1997, the government of Pakistan, conducted a study on the coastal erosion of Pakistan. The study concluded space and upper atmosphere research commission (SUPARCO), the national space agency of the that ingovernment the Indus of delta, Pakistan, accretion conduct anded erosiona study wereon the observed coastal erosion during of thePakistan. period The from study 1978 concluded to 1994 [22]. Stormthat in the surges Indus can delta, contribute accretion and to higherosion sea were levels, observed especially during the when period accompanied from 1978 to 1994 by high [22]. tides. For studyingStorm extreme surges can sea contribute levels, meteorologicalto high sea levels, forcing especially in when terms accompanied of storm surges by high should tides. For also be consideredstudying [36 extreme]. During sea thelevels, study meteorological period, four forcing tropical in cyclonesterms of passedstorm surges along should the Pakistan also be coast (Tableconsidered1, Figure 2[36].). In During all of thesethe study four period, cyclones, four Cyclone tropical cyclones Yemyin waspassed the along deadliest the Pakistan as it killed coast 730 people(Table in Pakistan 1, Figure and 2). In prominently all of these four contributed cyclones, to Cyclone the high Yemyin tide gauge was the readings deadliest at as Karachi it killed port. 730 people in Pakistan and prominently contributed to the high tide gauge readings at Karachi port. Table 1. List of tropical cyclones during the study period (2007 to 2016). Table 1. List of tropical cyclones during the study period (2007 to 2016). Cyclone Year Dates Cyclone Year Dates CycloneCyclone Gonu Gonu 2007 2007 1 June–8 1 June–8 June June CycloneCyclone Yemyin Yemyin 2007 2007 21 June–26 21 June–26 June June CycloneCyclone Phyan Phyan 2009 2009 9 November–11 9 November–11 November November 2010 31 May–7 June Cyclone Phet 2010 31 May–7 June

FigureFigure 2. Tracks 2. Tracks of allof all four four of of the the tropical tropical cyclonescyclones during during the the study study period period (2007 (2007 to 2016). to 2016).

3. Methodology3. Methodology The tideThe gaugetide gauge data data of Karachi of Karachi were were analyzed analyzed for for extreme extreme sea sea levels. levels. ResearchResearch qualityquality hourly tide gaugetide data gauge were data obtained were obtained from the from University the University of Hawaii of Hawaii Sea Level Sea CenterLevel Ce (UHSLC)nter (UHSLC) [37]. [37]. To calculate To the returncalculate periods the return of extreme periods seaof extreme levels, asea statistical levels, a investigationstatistical investigation was done was by done using by theusing AMM the and JPM.AMM To ensure and JPM. the qualityTo ensure of thethe data,quality in of terms the data, of any in terms outlying of any value, outlying only value, “research only “research quality” data quality” data were used. were used. To calculate the return period of extreme sea level for the Karachi coast, harmonic and statistical To calculate the return period of extreme sea level for the Karachi coast, harmonic and statistical analyses of the hourly observed sea level data for the past 10 years (2007–2016) were performed. In analysesthe first of the phase hourly of the observed study, the sea hourly level tide data gaug for thee data past were 10 yearsdecomposed (2007–2016) into two were components, performed. i.e., In the the tide level and the surge (non-tidal component) for the whole time series, using an application

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first phase of the study, the hourly tide gauge data were decomposed into two components, i.e., the tide level and the surge (non-tidal component) for the whole time series, using an application WORLD TIDES [38] on MathWorks MATLAB v9.1 (Natick, MA, USA). The WORLD TIDES was used to examine the observed sea level data by using the harmonic analysis method of least squares (HAMELS). Power spectral density (PSD) calculation was a reliable analytical approach for analyzing the tide gauge data series [39]. The spectral analysis of the observed sea level data was done to calculate the PSD for the different frequencies, using the ‘pwelch’ function available in MATLAB. The 35 tidal constituents were used for tidal predictive analysis. The predicted tide data by WORLD TIDES were compared with the locally predicted tide tables generated by the Hydrography Department and were found to be reliable for use in the study. Generalized Pareto distribution (GPD) and POT are analytical approaches used by researchers for analyzing extreme sea levels. GPD is a probability distribution which explains the extreme value data in terms of scale and shape factors. The POT method works with data only above a specified data value, called the threshold. In comparison, the JPM counts on even short time series available data by considering the components of each data point and estimates the return periods of extreme sea levels with better precision. For statistical analysis, the AMM and JPM were used. From the past 10 years of data, 10 annual maxima of observed sea levels were selected for analysis in the AMM [40]. The frequency analysis of the selected annual maxima was done and the probability Pη (in percent) Equation (1) and the return periods Tη (in years) Equation (2) for each sea level (η) were calculated. Following the formulae used for calculations: 100(2r 1) Pη = − (%) (1) 2N where ‘r’ is the allocated rank of the annual maximum value and ‘N’ is the total number of values used. Then T(η) is calculated as the reciprocal of probability as

1 Tη = (2) P(η)

Return sea levels for the Karachi coast were to be determined after plotting a graph between the corresponding sea level ‘η’ and ‘lnTη’ and extending the plotline using a regression analysis. The selection of AMM for a small data set (i.e., 10 years) was considered with the limitation of the number of years for extrapolation. While using the AMM extrapolation of return periods, the result, in years, must be less than the magnitude of the product of integer five with the number of years for which the data is available [24]. Therefore, the return sea levels for the Karachi coast were to be determined for 50 years. For the JPM, the joint probability of the tide and surge time series data was analyzed and the return periods were calculated. Initially, the hourly observed sea level data (ηO(t)) were separated into tidal (ηT(t)) and surge components (ηS(t)) using the MATLAB application WORLD TIDES. Here: ηo(t) = ηT(t) + ηs(t) (3) η (t) = η (t) η (t) (4) S O − T By using the probabilities of tide PT(ηT) and surge PS(ηS), the joint probability of tide and surge PJ(η) Equation (5) is determined [25,27]: Z ∞ P (η) = PT(ηT) PS(ηS) dηS (5) J × −∞ Then, the return period T(η) for each sea level η is calculated and the return sea levels for the period of 50, 100 and 1000 years for the Karachi coast are determined. In this study, an episode of was discussed for the duration when hit the Baluchistan coast in June 2007. Entropy 2020, 22, x FOR PEER REVIEW 6 of 12 Entropy 2020, 22, 549 6 of 12

4.Entropy Results 2020 and, 22, xDiscussion FOR PEER REVIEW 6 of 12 4. ResultsInitially, and Discussionthe hourly tide gauge data was decomposed into two components i.e., the tidal levels 4. Results and Discussion and the surges. The contribution of surges to the observed sea level was calculated by subtracting the Initially,predictedInitially, the tidethe hourly hourly levels tide tidefrom gauge gauge the datatide data gauge was was decomposeddecomposed data. The spectral into two two analysis components components of the i.e., i.e., Karachi the the tidal tidal tide levels levels gauge anddata,and the thefrom surges. surges. 2007 The Theto contribution 2016,contribution showed of of surges ansurges almost to to the th invers observede observede relation sea sea level level between was was calculated calculated the spectral by by subtracting subtractingdensities theand predictedfrequencies.the predicted tide In levels tidethe levelsPSD from plot, thefrom tide many the gauge tide sharp gauge data. peaks data The were. spectralThe presentspectral analysis inanalysis low of thefrequencies of Karachithe Karachi tide(Figure tide gauge gauge3). data,In the fromanalysis,data, 2007 from tothe 2016, 2007most showedto prominent 2016, anshowed almost peaks an inversewere almost observed relation inverse betweenat relation 1.932, the1.003,between spectral 2, 1.895,the densities spectral 0.93 and anddensities 0.839cpd frequencies. and with In the PSD plot, many sharp peaks were present in low frequencies (Figure3). In the analysis, the most periodsfrequencies. of 12.42, In the 23.93, PSD 12, plot, 12.66, many 25.81 sharp and peaks26.87 h,were referring present to in the low tidal frequencies constituents (Figure M2, K3).1, InS2 ,the N2 , O1 prominentanalysis, peaksthe most were prominent observed peaks at 1.932, were 1.003, observed 2, 1.895, at 1.932, 0.93 and 1.003, 0.839cpd 2, 1.895, with 0.93 periods and 0.839cpd of 12.42, with 23.93, and Q1, respectively. The peaks present in the PSD facilitated decomposing the observed sea level 12,dataperiods 12.66, into 25.81 ofsurge 12.42, and and 23.93, 26.87 tide 12, h,components. referring12.66, 25.81 to and the 26.87 tidal h, constituents referring to M the2,K tidal1,S constituents2,N2,O1 and M Q2, 1K,1 respectively., S2, N2, O1 Theand peaks Q1, respectively. present in the The PSD peaks facilitated present in decomposing the PSD facilitated the observed decomposing sea level the dataobserved into sea surge level and tidedata components. into surge and tide components.

Figure 3. Spectral density of the tide gauge data. FigureFigure 3. 3.Spectral Spectral densitydensity of the tide gauge gauge data. data. During the study period (i.e., years 2007 to 2016) the highest water level recorded was on 13 DuringDuring the the study study period period (i.e., (i.e., years years 2007 2007 to 2016)to 2016) the the highest highest water water level level recorded recorded was was on on 13 June13 June 2014 (Figure 4). On this extreme event, the observed sea level was 3.64 m, dominantly 2014June (Figure 20144 ).(Figure On this 4). extreme On this event, extreme the observedevent, the sea observed level was sea 3.64 level m, dominantlywas 3.64 m, contributed dominantly to bycontributedcontributed a tidal component to to byby aa tidal oftidal 3.17 component m with a non-tidal ofof 3.173.17 m m residualwith with a anon-tidal non-tidal of 0.47 m. residual residual Furthermore, of of0.47 0.47 m. the m.Furthermore, whole Furthermore, time seriesthe the ofwhole thewhole annual timetime maximum seriesseries ofof the along annu withalal themaximummaximum associated alongalong tidal with with level the the and associated associated non-tidal tidal residualstidal level level showedand and non-tidal non-tidal that the Karachiresidualsresiduals coast showed showed was tidally thatthat thethe dominated. Karachi coastcoast was was tidally tidally dominated. dominated.

Figure 4. Hours from the highest water event at 11:00 PST (local time) on 13 June 2014 in the Karachi FigureFigure 4. 4.Hours Hours from from the the highest highest water water event event at at 11:00 11:00 PST PST (local (local time) time) on on 13 13 June June 2014 2014 in in the the Karachi Karachi coast during the study period (i.e., years 2007–2016). coastcoast during during the the study study period period (i.e., (i.e., years years 2007–2016). 2007–2016).

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On a global scale, the regions where the tidal contribution in the mean annual maximum water level is dominated, can be identified by calculating the ratio ‘γ’[41]: Entropy 2020, 22, x FOR PEER REVIEW 7 of 12 Entropy 2020, 22, x FOR PEER REVIEW   7 of 12 γ = h/ 2.5 σp (6) On a global scale, the regions where the tidal contribution in the mean annual maximum water On a global scale, the regions where the tidal contribution in the mean annual maximum water level is dominated, can be identified by calculating the ratio ‘γ’[41]: where hlevelis the is meandominated, annual can maximum be identified water by calculating level and theσ pratio is the ‘γ’[41]: standard deviation of the predicted tidal γ = h/(2.5 σp) (6) elevation. The γ calculated for the Karachi coastγ = h was/(2.5 1.1,σp) which was showing the tidally dominated(6) where h is the mean annual maximum water level and σp is the standard deviation of the predicted nature ofwhere the coasth is the along mean with annual a 10%maximum contribution water level of and non-tidal σp is the residuals. standard deviation of the predicted tidal elevation. The γ calculated for the Karachi coast was 1.1, which was showing the tidally Duringtidal elevation. the study The period, γ calculated all the for recorded the Karachi meteorological coast was 1.1, eventswhich was which showing were the documented tidally by dominated nature of the coast along with a 10% contribution of non-tidal residuals. dominated nature of the coast along with a 10% contribution of non-tidal residuals. the PakistanDuring Meteorological the study period, Department all the recorded (PMD) meteor wereological analyzed events for which studying were documented the storm surgeby the events. During the study period, all the recorded meteorological events which were documented by the Four tropicalPakistan cyclones, Meteorological including Departme Cyclonent (PMD) Gonu were (June analyzed 2007), for Cyclone studying Yemyinthe storm (June surge 2007), events. Cyclone Pakistan Meteorological Department (PMD) were analyzed for studying the storm surge events. Phyan (NovemberFour tropical cyclones, 2009) and including Cyclone Cyclone Phet Gonu (May (June 2010) 2007), moved Cyclone over Yemyin the (June Pakistan 2007), coast. Cyclone Cyclone Four tropical cyclones, including (June 2007), Cyclone Yemyin (June 2007), Cyclone Phyan (November 2009) and Cyclone Phet (May 2010) moved over the Pakistan coast. Cyclone “Yemyin”,Phyan being (November the most 2009) prominent and Cyclone of all Phet four, (May crossed 2010) the moved Pakistan over coast the Pakistan in the west coast. of Cyclone Karachi on 26 “Yemyin”, being the most prominent of all four, crossed the Pakistan coast in the west of Karachi on June 2007“Yemyin”, (Figure being5). The the most signature prominent of the of all storm four, surgecrossed event the Pakistan is seen coast in thein the tidal west analysis of Karachi of on Karachi June 26, 2007 (Figure 5). The signature of the storm surge event is seen in the tidal analysis of Karachi coast seaJune level 26, data2007 (Figure (Figure 5).6 ).The signature of the storm surge event is seen in the tidal analysis of Karachi coast sea level data (Figure 6). coast sea level data (Figure 6).

Figure 5. The track of Cyclone “Yemyin”, June 2007. FigureFigure 5. The5. The track track of of CycloneCyclone “Yemyin”, “Yemyin”, June June 2007. 2007.

Observed Sea Level Observed Sea Level Surge Surge 3.5 1.5 3.5 1.5

3.0 1.0 3.0 1.0

2.5 0.5 2.5 0.5

2.0 0.0 2.0 0.0 Surge (m) Surge

1.5 -0.5 (m) Surge 1.5 -0.5 Observed Sea Level (m) Observed

Observed Sea Level (m) Observed 1.0 -1.0 1.0 -1.0

0.5 -1.5 0.5 -1.5 20-Jun 21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun 20-Jun 21-Jun 22-Jun 23-Jun 24-Jun 25-Jun 26-Jun 27-Jun 28-Jun

Figure 6. The signatures of the storm surges are seen in the tidal analysis of the Karachi Data during the period 20–28 June 2007 (Cyclone Yemyin). Entropy 2020, 22, 549 8 of 12 Entropy 2020, 22, x FOR PEER REVIEW 8 of 12

ForFigure extreme 6. The signatures value analysis, of the storm the use surg ofes the are AMM seen in is the common. tidal analys Inis the of AMM,the Karachi the Data data during set of each yearthe is examined period 20–28 for June the highest2007 (Cyclone value Yemyin). of the year, which is taken as the annual maximum. The trend analysis of the maximum observed sea levels for each year, presented in Table1, showed an annual increaseFor ofextreme 2.1 mm value for extremeanalysis, sea the levels. use of All the the AMM annual is common. maxima forIn the all theAMM, years the in data the dataset of series each wereyear is plotted examined against for log10the highest of return value periods of the toyear have, which a linear is taken regression as the analysis. annual maximum. Then, theestimation The trend ofanalysis the extreme of the maxi sea levelmum for observed 50 years sea was levels done for using each the year, regression presented line. in TheTable probability 1, showed and an annual return periodsincrease areof 2.1 shown mm infor Table extreme2 and sea Figure levels.7, respectively. All the annual maxima for all the years in the data series were plotted against log10 of return periods to have a linear regression analysis. Then, the estimationTable 2.ofThe the estimated extreme valuesea level of the for probability 50 years and was the done return using periods the byregression using the annualline. The maximum probability and returnmethod periods (AMM). are shown in Table 2 and Figure 7, respectively.

Annual Maxima Probability p = 100(2r-1)/2N Return Period T = 1/p TableRank 2. r The Year estimated value of the probability and the return periods by using the annual maximum (m) (%) (year) method (AMM). 7 2007 3.493 65 1.538 Annual Maxima Probability p = 100(2r-1)/2N Return Period T = 1/p Rank r Year 2 2008 3.637(m) (%) 15 (year) 6.667 107 20092007 3.416 3.493 95 65 1.538 1.053 32 20102008 3.538 3.637 25 15 6.667 4.000 10 2009 3.416 95 1.053 8 2011 3.488 75 1.333 3 2010 3.538 25 4.000 98 20122011 3.450 3.488 85 75 1.333 1.176 69 20132012 3.494 3.450 55 85 1.176 1.818 16 20142013 3.640 3.494 55 5 1.818 20.000 1 2014 3.640 5 20.000 5 2015 3.496 45 2.222 5 2015 3.496 45 2.222 44 20162016 3.536 3.536 35 35 2.857 2.857

Figure 7. Return period by using the AMM (annual maximum method). Figure 7. Return period by using the AMM (annual maximum method). The predicted tide levels for each hour were deducted from the observed hourly sea levels and the The predicted tide levels for each hour were deducted from the observed hourly sea levels and residuals were taken as surges. As a result, from the observed sea level data, we obtained an hourly the residuals were taken as surges. As a result, from the observed sea level data, we obtained an data series of the tides and the surges. The JPM provided good statistical grounds by considering the hourly data series of the tides and the surges. The JPM provided good statistical grounds by tides–surge interaction, for estimating the return periods of extreme sea levels. Based on the JPM and considering the tides–surge interaction, for estimating the return periods of extreme sea levels. AMM approaches, the estimated return periods for the extreme sea levels for Karachi are shown in Based on the JPM and AMM approaches, the estimated return periods for the extreme sea levels for Figure6. The determination of the 95% confidence was achieved to check the consistency of both Karachi are shown in Figure 6. The determination of the 95% confidence was achieved to check the methods (Figure8). It could be observed that the consistent levels of confidence were attained using consistency of both methods (Figure 8). It could be observed that the consistent levels of confidence both the AMM and JPM approaches, which were more than the 95% confidence limits. were attained using both the AMM and JPM approaches, which were more than the 95% confidence limits.

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Figure 8. Estimated return period of extreme sea level utilizing the AMM and the JPM (joint probability method) for Karachi, Pakistan. The vertical lines show 95% confidence limits. Figure 8. Estimated return period of extreme sea level utilizing the AMM and the JPM (joint probability Figure 8. Estimated return period of extreme sea level utilizing the AMM and the JPM (joint method)The summary for Karachi, of the Pakistan. return The sea vertical level height lines show for 95%50, 100 confidence and 1000 limits. return periods by using the probability method) for Karachi, Pakistan. The vertical lines show 95% confidence limits. AMM and JPM are shown in Table 3. The summary of the return sea level height for 50, 100 and 1000 return periods by using the AMM The summary of the return sea level height for 50, 100 and 1000 return periods by using the and JPM are shownTable 3. inSummary Table3. of the return level estimation for 50, 100 and 1000 return periods. AMM and JPM are shown in Table 3. Return Level for 50 Year Return Level for 100 Year Return Level for 1000 Year Method Table 3. Summary of the return level estimation for 50, 100 and 1000 return periods. Table 3. SummaryPeriod of (m) the return level estimationPeriod for 50,(m) 100 and 1000 return periods.Period (m) AnnualMethod Return Level for 50 Year Period (m) Return Level for 100 Year Period (m) Return Level for 1000 Year Period (m) 3.74 - - AnnualMaximum Maximum Return Level 3.74 for 50 Year Return Level - for 100 Year Return Level - for 1000 Year Method JointJoint Probability Probability Period 3.73 3.73 (m) Period 3.76 3.76 (m) Period 3.92 3.92 (m) Annual 3.74 - - MaximumIn comparison, both the rate of change of extreme sea levels and the rate of change of mean sea Joint ProbabilityIn comparison, both the 3.73 rate of change of extreme sea 3.76 levels and the rate of change 3.92 of mean sea levelslevels areare showingshowing anan increasingincreasing trend.trend. ObservedObserved seasea levellevel datadata atat KarachiKarachi portport forfor thethe studystudy periodperiod i.e., 2007–2016, showed an increment rate of 3.6 mm/year for the mean sea levels and 2.1 mm/year for i.e., 2007–2016,In comparison, showed both an the increment rate of change rate of 3.6of extrem mm/yeare sea for levels the mean and the sea rate levels of andchange 2.1 mmof mean/year sea for the extreme sea levels (Figure 9). Here at Karachi port, the SLR is contributing to increasing extreme thelevels extreme are showing sea levels an increasing (Figure9). Heretrend. at Observed Karachi port, sea level the SLR data is at contributing Karachi port to for increasing the study extreme period sea levels along the Pakistan coast. The SLR may therefore increase the frequency of extreme sea seai.e., levels2007–2016, along showed the Pakistan an increment coast. The rate SLR of may3.6 mm/year therefore for increase the mean the sea frequency levels and of extreme 2.1 mm/year sea level for level events with a subsequent decrease in their return periods. eventsthe extreme with asea subsequent levels (Figure decrease 9). Here in their at Karachi return periods.port, the SLR is contributing to increasing extreme sea levels along the Pakistan coast. The SLR may therefore increase the frequency of extreme sea level events with a subsequent decrease in their return periods.

FigureFigure 9.9. Annual mean and extreme extreme sea sea levels levels for for the the Ka Karachirachi tide tide gauge gauge data data from from the the year year 2007 2007 to to 2016. 2016. Figure 9. Annual mean and extreme sea levels for the Karachi tide gauge data from the year 2007 to 2016.

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5. Conclusions The JPM and AMM provided useful statistical bases for the calculation of extreme sea levels along the Pakistan coast. These statistical techniques were used for the first time in the assessment of extreme sea levels for the Karachi tide gauge data. The present study showed the prominent contribution of the tidal components in contrast with the non-tidal components of observed sea levels, for the estimation of extreme sea levels. The extreme sea level analysis, presented in this study for the estimation of return periods, indicated the technical causes of a maximum water level. Although the results based on statistical bases should be rectified on the bases of coastal engineering, understanding meteorological events and more advance tidal observation will facilitate the outcomes of this study. The main problem during this study was the less and non-consecutive availability of tide gauge data. Furthermore, Karachi is the only station that has relatively long historical tidal data. It was suggested to install more tide gauges in the and coasts. Thus, tide gauge installation along the whole Pakistan coast at different locations would help to analyze the tidal heights. Moreover, in the stations where tide gauges are not installed, the use of the satellite altimetry sea surface height data and numerical model results may probably help in the assessment of return periods of extreme sea levels [28,41]. Along the Pakistan coast at Karachi port, the intensification of coastal slumping due to SLR is putting the natural coastal defense at risk. Tidal height will increase due to SLR, which most probably causes coastal slumping [12]. Likewise, on the west side of Karachi on different sandy coastlines, erosion has been observed [42]. The erosion is taking place due to intensive wave action, seawater flooding and intensified tidal activity. Increasing rates of mean sea levels are among the leading causes of more frequent extreme sea level events. Low lying regions of Indus are at risk due to SLR and extreme sea level events. In the next few decades, a minor SLR could cause significant suffering for the masses near the coast in this region. Coastal erosion is associated with the flooding of low lying areas and freshwater depletion in the Indus River due to seawater intrusion, which negatively affects , aquatic species and a variety of flora and fauna in the region. Therefore, if this ecological destruction is not considered, then the biological identity of the Sindh coast, including Karachi, is in danger as different aquatic species are reducing and many of them could disappear forever. The present study can be used to project future SLR based on the present and past trends and the study of physical phenomena such as seawater intrusion and coastal erosion. Moreover, the knowledge of the present trends of SLR and extreme sea levels along the Karachi coast helps to adopt protective measures by following the estimated SLR and extreme sea level events, which usually have a great impact on the coastal community and ecosystem of the area.

Author Contributions: Formal analysis, F.A.K., T.M.A.K., A.N.A., M.S. and A.E.-S.; methodology, F.A.K. and T.M.A.K.; software, F.A.K. and H.A.A.; supervision, A.E.-S.; validation, A.S.; writing—original draft, T.M.A.K. and M.S.; writing—review and editing, A.N.A., H.A.A. and A.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by University of Malaya Research Grant (UMRG) coded RP025A-18SUS University of Malaya, Malaysia. Acknowledgments: The authors wish to express their gratitude to Philip L. Woodworth, National Oceanography Centre, Liverpool, UK for his guidance and useful comments. We also thank the Karachi Port Trust for providing the sea level data of Karachi Port. The research quality data were obtained from the University of Hawaii Sea Level Center data archive. The authors would like to appreciate so much the financial support received from the University of Malaya Research Grant (UMRG) coded RP025A-18SUS University of Malaya, Malaysia. Conflicts of Interest: The authors declare no conflict of interest. Entropy 2020, 22, 549 11 of 12

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