Criteria of sea level, return periods, and design risk factor in Port Said Harbor (Egypt)

This work delivers comprehensive information on the statistical metrics of sea level in Port Said Harbor, which can be used for the mitigation plans and protection measures in its vicinity. The study used hourly sea level data extended over 10 years from January 2002 to December 2011. A comprehensive descriptive statistical analysis of sea level monthly variations was introduced. The T_Tide package was used to obtain the astronomical constituents, which are in turn used to calculate the form factor to specify the tidal cycle in the Harbor, and to obtain the main water level characteristics. The meteorological factor was calculated by subtracting the tidal elevation from the recorded sea level. The impact of the meteorological factors on the observed sea level fluctuations was more obvious in winter than in summer. The effect of the meteorological conditions on the observed possible largest sea level range was 13\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${~}^{1}\!\left/ \!{~}_{3}\right.$$\end{document} that of the tidal impact. No extreme sea level year, considered when the annual mean deviates from the regression line by more than twice the standard deviation, appeared during the decade of investigation. The return periods and the design lifetime risk were calculated. The highest probabilities of occurrence were concentrated in the levels between 70 and 80 cm, while the lowest were below 5 cm and above 110 cm. The return periods for all water levels ranged between 0.4 and 4.5 years. The coastal structures in the vicinity of the Harbor may have a short lifetime of only 50 years for its most pronounced level (75 cm). It is recommended to consider the present results upon designing mitigation plans and constructions within Port Said Harbor territory.


Introduction
Ports are designed to withstand various stresses during their lifespan and operations. It is anticipated that as the climate changes, the frequency and size of these stressors will increase. For instance, exceptionally powerful storms or sea level rise (SLR) may have a significant impact on the reliability of port services. Then, 64% of all seaports would be under water if the global mean sea levels rose, as predicted by the IPCC in 2012 (IPCC 2012). The number of ports at the risk of floods is expected to be more than treble by 2080 compared to 2030. The SLR is the key aspect of climate change that will influence ports ). This will amplify the effects of climate risks (Becker et al. 2013). In fact, it actually threatens the port industry and will undoubtedly continue to do so in the future by raising the likelihood of floods (McLeod et al. 2018). Additionally, it can seriously harm the port's equipment and infrastructure (Zviely et al. 2015). Also, the SLR may reduce vessel safety inside the port or impede loading and unloading activities, which may severely impact the port's operability and, consequently, its reputation (Hanson and Nicholls 2020;Verschuur et al. 2020). Moreover, SLR will deepen the water around and within the harbor, altering wave propagation patterns (Sierra et al. 2017). This could affect processes such as wave agitation (wind-wave oscillations within the port), siltation, scouring, and structure stability (Sierra and Casas-Prat 2014). According to the most recent IPCC report (AR6) on the Mediterranean Sea region, which was published in 2022, the Mediterranean Sea exhibits robust, accelerating SLR rates at different magnitudes at different locations (Ali et al. 2022). Therefore, it is crucial to comprehend the behavior of changes in the major sea level features, as well as to have accurate information on the highest and lowest water levels in the proximity of harbors and to use proper mitigation strategies and countermeasures, to avoid and prevent any coastal disasters or flooding (Moursy 1994;Kim et al. 2014).
Port Said Harbor, in the eastern Nile Delta region, is the second largest Egyptian harbor on the Mediterranean Sea, after Alexandria Port. The importance of the Harbor stems from being the northern entrance of the Suez Canal and hosting the Suez Canal administration's primary workshops, in addition to the expanded fishing facilities. Port Said is also an important port for Egyptian exports such as cotton and rice, as well as a fueling station for ships passing through the Suez Canal. It flourishes as a duty-free port and a tourist destination, especially during the summer. Port Said Harbor has a total surface area of 3 km 2 , of which 1.7 km 2 is water area and 1.3 km 2 is land area. According to the Maritime Transport Sector website (https:// www. mts. gov. eg/ en/ port/), the maximum capacity of the Harbor is 12,175 × 10 6 tons/ yr, of which 4.9 × 10 6 tons are general cargo, 2.54 × 10 6 tons are dry bulk cargoes, and 4.735 × 10 6 tons are containerized cargo. Also, the main channel in Port Said Harbor is of 8-km length and 13.72-m depth, while its eastern verge waterway is of 19.5-km length and 18.29-m depth. The dominant wind direction blowing over Port Said is NNW-N, with the lowest wind speed recorded in summer and the highest in winter (El-Sharkawy et al. 2016). Port Said Harbor lies within the territory of the Nile Delta, which is one of the world's recognized low elevated coastal zones (LECZ). Thus, it is considered to be highly subjected to the problems associated with variations in sea level and extremes. Regulated retreat may be required in the LECZ Mediterranean regions (37% of its coastline), particularly in delta regions such as the Nile, to mitigate coastal flood threats caused by continuing SLR (Wong et al. 2014). Among the adaptation possibilities to SLR in the Mediterranean are nature-based solutions such as beach and shore replenishment, dune restoration, or ecosystem-based adaptation and restoration in the LECZ (Aspe et al. 2016;Danovaro et al. 2018;Ali et al. 2022).
The sea level variation in the vicinity of Port Said Harbor was previously investigated. The Harbor exhibits a 36-cm lower mean sea level (MSL) than Suez, the southern tip of the Suez Canal, in March and 23 cm higher than Suez in September (Morcos 1960). The leveling along the Suez Canal revealed a variation of 24 cm between Port Said (north) and Port Tawfik (south) based on Lisitzin's observations from 1923 to 1925 (Morcos 1970). According to Eid et al. (1997), the sea level at Port Said is higher than that at Port Tawfik from July to December, with a maximum difference of 10.5 cm in September, whereas it is higher at Port Tawfik than that at Port Said for the rest of the year, with the maximum difference (31.5 cm) in March. Moursy (1998) used hourly sea level data over 1986 to determine the four principal astronomical constituents and the main water levels at Port Said Harbor. She specified its tidal cycle to be semidiurnal. Tonbol and Shaltout (2013) analyzed hourly data from February 1999 to January 2000 off Port Said and produced the criteria (amplitudes and phases) of the five important tidal constituents: O 1 , K 1 , N 2 , M 2 , and S 2 . Recently, El-Geziry and El-Wakeel (2023) used 10 years of hourly sea level records (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011) and produced 69 tidal constituents and presented the residual elevations at Port Said Harbor. They also calculated a SLR rate of 2.1 mm/yr over that decade.
Technical knowledge of periodic changes, various sea level ranges, and design lifetime risk factors is crucial for navigational purposes and for coastal engineering projects, especially in shallow sea zones such as harbors and ports. The current study may be regarded as the first to shed light on the peculiarities of the sea level at the significant Port Said Harbor on the Egyptian Mediterranean Coast. Therefore, the main aim of this research is to describe the general behavior of variations in the sea level in Port Said Harbor. The objectives of the research can be pointed out as follows: (1) to calculate the main water levels, (2) to examine the effect of meteorology on the observed sea level, (3) to calculate the return periods of diverse sea-level ranges, (4) to examine the existence of an extreme sea-level year over the decade (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011), and (5) to draw-up the design risk curve for coastal structures of the most dominant water level in the vicinity of the Harbor.

Data and methods of analysis
This study used hourly sea level data from the water level recorder, Inter Ocean Wave and Tide Gauge (WTG904), positioned at 31.2577°N; 32.3092°E ( Fig. 1) and managed by Port Said Harbor's authority. The gauge measures the water column pressure in real time and converts it to the height of the water in relation to a user-defined location. The pressure sensor output was digitized at a sampling rate of 2 Hz using a 14-bit A/D converter controlled by a 32-bit CMOS microprocessor. The gauge's measurement depth range is 0 to 35 m, and it has a resolution and precision of 0.006% and 0.15%, respectively, of the measuring range (Dawod and Mohamed 2002). The data span extended over a period of 10 years, from January 2002 to December 2011. A total of 3652 days (87,648 h) were logged, although the actual number of hours that could be really obtained for hourly recording was only 87,557, i.e., 91 h were missing. Referred to as the tidal gauge's zero level, the recorded sea level was measured. To determine the sea level features, the accessible data were subjected to a descriptive statistical analysis. The four main diurnal and semidiurnal tidal components, namely, O 1 , K 1 , M 2 , and S 2 , were obtained using the T_Tide package of Pawlowicz et al. (2002), which works in the Matlab® environment. The T_Tide is primarily based on the idea of being able to depict tidal elevations at a particular place as the sum of all harmonic components. The following equation expresses this mathematically: where η (t) denotes the vertical displacement of the sea surface as a function of time t (m), the amplitude of the n th harmonic component (m) is denoted by A n , T n is the n th harmonic component's period (s), and ϕ n is the n th harmonic component's phase (°).
The form factor to specify the tidal cycle in the Harbor was calculated according to Pugh (2004). This was calculated as the ratio of diurnal (O 1 and K 1 ) to semidiurnal (M 2 and S 2 ) amplitudes. The different ranges and corresponding types of tidal cycles are defined according to Pugh (2004), as shown in Table (1). (1) Furthermore, the different theoretical primary terms connected to the tidal phenomenon in the Harbor were estimated using the MSL value and the obtained astronomical information, according to Doodson (1957).
According to Ekman (1996), an extreme sea level year is considered when the annual mean deviates from the regression line by more than twice the standard deviation (Eq. (2)): where |ΔL| is the annual deviation and σ is the total standard deviation.
(2) |ΔL| > 2.0  Last of all, the return periods and the design risk factor in the vicinity of Port Said Harbor were calculated according to Pugh (2004), using the following equation: where Q(z) is the probability of an exceeded level (cm) and TL is the design lifetime (years).

Statistics of sea level in Port Said Harbor
The monthly descriptive statistical parameters of the sea level over the study period were calculated (Table 2). This demonstrated that the monthly mean high water level (MHWL) changed between 93.3 (January) and 109.4 cm (December), with an overall mean MHWL of 101.4 cm. However, the monthly mean low water level (MLWL) fluctuated between 12.5 (January) and 37.8 cm (November), with an overall mean of 25.2 cm. Calculations revealed that the lowest monthly mean range (MMR) was 71.6 cm in December, while the highest was 80.9 cm in January, resulting in a mean monthly sea level range of 76.2 cm over the research period. The sea level in Port Said Harbor exhibited a seasonal pattern of variation throughout the period of investigation, with the lowest monthly MSL observed in spring (47 cm) and the highest in summer (79 cm). Over the study period, Port Said Harbor had a MSL of 69.1 cm. The lowest monthly mean standard deviation, i.e., deviation from the mean, was summer (9.2 cm) and the highest in spring (17.9 cm). The most often lowest sea level value over the study period was recorded in spring (43.0 cm), and the most often highest value in autumn (81.0 cm). The monthly mean median (middle recorded sea level value in the available data set) was identical to the monthly MSL during four months: January, February, October, and December, i.e., mainly during winter season. This is statistically confirmed by getting no skew in these months except for December, which had a tiny negative skewness of − 0.2.
Annually, the MHWL and MLWL examined opposite trends of variation (Fig. 2). The former had a steady upward tendency throughout the research period, whereas the latter had a dramatic downward trend. However, the graph shows an upward trend in the mean annual range (MAR), which is the difference between the MHW and MLW levels. This revealed that despite the opposite trends between the mean annual water levels with the decreasing MLWL trend, the sea level in Port Said Harbor exhibited a general SLR over time.

Principal characteristics of astronomical tides in Port Said Harbor
The main diurnal and semidiurnal constituents were obtained using the T_Tide package, and compared with previous results in Port Said Harbor (Table 3). For a full list of the obtained 69 astronomical constituents, the reader may refer to El-Geziry and El-Wakeel (2023). The principal lunar semidiurnal constituent (M 2 ), which represents the rotation of the Earth with respect to the Moon, had the highest amplitude among the four constituents with a value of 13.4 cm. This is followed by the amplitude of the lunisolar diurnal constituent (K 1 ) of 3.16 cm. The principal solar semidiurnal constituent (S 2 ) had an amplitude of 2.2 cm, representing the rotation of the Earth with respect to the Sun. The lunar diurnal constituent (O 1 ) had the lowest astronomical amplitude of only 1.15 cm. According to Hicks et al. (2000), the K 1 with O 1 constituents express the effect of the Moon's declination, and they account for diurnal inequality and tides. The form factor was calculated to be 0.28, indicating that the tidal cycle in the Harbor is mixed mainly semidiurnal. Table 4 shows the main water level characteristics in the Harbor, compared with those previously calculated by Moursy (1998).

Sea level ranges in Port Said Harbor because of tides and meteorological factors
The largest possible variation in the recorded sea level (H w ) is the difference between the recorded highest and lowest water levels (Table 5). This precisely stems from the joint effect of astronomical and meteorological forces on the recorded sea level. To examine the effect of the meteorological forces solely on the highest observed sea level, the largest tidal range denoted hereafter as H t equals 40.0 cm (Table 4) must be removed from the records. This allowed calculating the sea level range based solely on meteorological conditions, which is denoted as H m (Table 5). This revealed that while the lowest H m values occurred from April to September, the highest occurred from October to March, which designated distinct seasonal variations (Fig. 3). This also demonstrated that the effect of the meteorological conditions on the observed sea level in winter in Port Said Harbor is greater than in summer. Furthermore, we can deduce the mathematical relationships between the three largest water level ranges, namely, H t , H m , and H w in Port Said Harbor; to conclude the proportion of the contribution of each factor on the observed largest range. Based on the given values, the largest possible sea-level range due to meteorological conditions is almost 1 3 of the largest range of tides.

Extreme year, return periods, and design risk curve
A thorough examination of the existence of an extreme year, the return period, and the design risk factor can be used to determine the safety of the Harbor's berths and coastal structures. Using the current data in conjunction with Eq. (2), it was revealed that there were no extreme years in Port Said Harbor between 2002 and 2011. Estimates of the return period of sea levels are required for the design of harbors and coastal defenses. The probability of occurrence of the different sea level intervals was determined and shown in Table 6 based on the accessible hourly sea levels in Port Said Harbor over the period of investigation. The return period of each level was calculated using these probability distributions and Eq. (3). Figure 4 depicts the corresponding design risk curve to these return periods for the most pronounced level of occurrence of 75 cm.

Discussion
This study contributes to our understanding of sea level variations in the vicinity of the famous city of Port Said. This research was based on accessible hourly sea level records over one decade period from January 2002 to December 2011. The calculated MSL over the study period was 69.1 cm. This is higher than the previously calculated of 53.0 cm (Moursy 1998). This discrepancy could be explained by the varied time periods between the two studies or by the general altered conditions affecting the sea level variability in the study area. Also, the present MSL is higher than those calculated respectively to the west and in front of the Nile Delta: Alexandria and Abu Qir (48.0 cm; El-Geziry  With nodal approximations, inference, and a wide range of user-specified settings, the T_TIDE program offers a user-friendly Matlab platform for performing classical harmonic analysis (Pawlowicz et al. 2002). The package has been widely used in many locations and regions around the world, e.g., the Qiongzhou Strait (Zhu et al. 2015) and the Bohai Sea (Wang et al. 2020) (2022). The reader can consult El-Geziry and El-Wakeel (2023) for more specific results produced by the T_Tide at Port Said. The mixed mainly semidiurnal tidal cycle in Port Said Harbor was confirmed by a calculated form factor of 0.28. M 2 , the principal lunar tidal component, is the main tidal constituent for this type of tides. According to the present analysis, it had an amplitude of 13.4 cm, which is a bit higher than those previously calculated in Port Said, as shown in Table 3. The main water level characteristics dominating Port Said Harbor are in good agreement with those previously calculated in 1986 by Moursy (1998), as shown in Table 4. Moreover, the calculated HAT and LAT in this work are in a very good agreement with those previously calculated by Tonbol and Shaltout (2013) over the year 1999/2000. The present HAT is 22.7 cm compared to 21.5 cm (Tonbol and Shaltout 2013), while the present LAT is − 19.5 cm compared to − 21.2 cm (Tonbol and Shaltout 2013). Results revealed that Port Said Harbor exhibited more sea level variations induced by meteorological conditions in winter than in summer. The effect of the meteorological conditions on the observed possible largest sea level range was 1 3 that of the tidal impact. This is in agreement with the conclusion of Tonbol and Shaltout (2013) that the observed sea level off Port Said is significantly impacted by the tidal part than the non-tidal part. In general, the sea level fluctuations in Port Said Harbor typically follow a seasonal pattern. According to Tsimplis et al. (2005), Gomis et al. (2008), and Oddo et al. (2014), the Levantine Basin experiences an identical atmospheric pressure regime of highs and lows that affects the region throughout the year. This is in line with the findings of Sharaf El Din et al. (1989), Tonbol andShaltout (2013), andEl-Wakeel (2023). According to Ekman's theory, no extreme sea level year existed at the Harbor during the study period. However, the return periods and the design risk factor were examined for the first time in the Harbor, to reasonably mitigate and secure coastal structures within its territory. Over the study period, the highest probabilities of occurrence were concentrated in the levels between 70.0 and 80.0 cm, while the lowest were above the level of 110 cm and below 15.0 cm. The return periods of the different water levels ranged between 0.4 and 4.5 years. The design risk factor curve revealed that coastal structures in the vicinity of the Harbor may have a short lifetime of only 50 years for the most pronounced level of 75 cm, after which the structures will be at the highest risk to any variations in the sea level. This coastal structure lifetime is the same as calculated for Alexandria Eastern Harbour (El-Geziry 2021). However, it is shorter than that calculated for other harbors along the Egyptian Mediterranean coast: 200 years for El-Burullus New Harbour (El-Geziry and Said 2019), 200 years in Abu-Qir Bay , and 250 years in Alexandria Western Harbor (Hendy et al. 2021). Therefore, mitigation plans must be set according to this information. This is consistent with the conclusion of El-Geziry (2020) that the area comprising Port Said Harbor is highly vulnerable to sea level variations and SLR.

Conclusion
To conclude, the sea level variations in Port Said Harbor were examined over a decade (January 2002 to December 2011), and analysis revealed that they are of seasonal behavior. The different water level characteristics in the Harbor, which may impact its navigational services, are introduced and are consistent with those previously calculated in 1986. Moreover, it is recommended to consider the present results regarding the return periods, the design risk factor, and the design lifetimes upon designing mitigation plans and constructions within the Harbor territory.
Author contribution The authors of the submitted manuscript have participated in the conception and design of the manuscript (TMG and YMW), data source (YMW), analysis and interpretation of the data (TMG), drafting the article (TMG), revising the manuscript content (TMG and YMW), and approval of the submitted manuscript version (TMG and YMW).
Funding Open access funding provided by The Science, Technology & Innovation Funding Authority (STDF) in cooperation with The Egyptian Knowledge Bank (EKB).

Data availability
The data that support the findings of this study are available upon reasonable request.

Conflict of interest
The authors declare that they have no competing interests.
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