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Issue 2 -  2001/02

 ISSN 1311-8978

Abstract

In the report are presened basic results from the performed research activities in the sphere of different by genesis variations of the extremal sea levels in the Bourgas bay, conducted from Pacific Consultants International, Japan, in relation with the building and the exploatation of object “Expansion of Port Bourgas”, by project “Port of Bourgas Expansion Project JBIC ODA LOAN No BG-P4”.

On the base of statistical and corelational analysis of data from the archive source of the Main Government for Geodesy and Cartography, Institute of oceanology, National Institute of meteorology and hydrology, as well as performed own measurements, are obtained the basic characteristics of the different by character, amplitude and period sea level variations:

·         Maximal and minimal sea levels under different return period, caused by wind influence;

·         Harmonics of daily variations under influence of the planetarium strengths;

·         Long-term variations under influence of atmospheric pressure oscilations.

Missing information in the data set at Bourgas mareograph station in the period of disastrous storm 16-22 February 1979 is restored applying corelational analysis of daily sea level series about February 1979 from the Bourgas, Ahtopol and Irakly mareograph stations.

Introduction

The variations of sea level under untidal sea conditions, such as conditions in the Western part of the Black Sea, are generally formed under influence of the wind energy upon the sea surface, oscillations of atmospheric pressure and planetary forces.

Fig. 1. Variations of sea level under influence of different factors.

In the report are presented main results from investigations and research works in the field of different in genesis, amplitudes and periods sea level variations in the Bourgas bay held by the Japanese consulting company Pacific Consultants International (PCI) for the purpose of design (project, plan), building and exploitations of “Port of Bourgas Expansion Project JBIS ODA LOAN No BG-P4” [11].

In order statistical and correlation analysis of different kind of sea level variations to be performed it was principally used archive sources over the period 1928-1987, publications and our own measurements.

Data from surveying of MGGC*, NIMH** and IOBAS*** from the mareogpaph and pegel stations were used (Fig. 2.).

Fig. 2. Location of the stations, measuring the sea level of the Bulgarian Black Sea coast.

In the report are presented the main characteristics of sea level variations for the purpose of design, building and exploitations of the object “Port of Bourgas Expansion Project” including:

·         Maximal and minimal sea levels;

·         Long-term variations;

·         Tidal variations.

MGGC* -Main Government for Geodesy and Cartography, Sofia

NIMH** -National Institute of Meteorology and Hydrology, BAS, Sofia

IOBAS*** -Institute of Oceanology, BAS, Varna

I.  Maximal and minimal sea levels.

Maximal sea levels are especially important at determining of project elevations and wave effect upon breakwater constructions as well as determining of project elevations on quay walls.

Under analysis of the published information it is ascertained that a main omission in research of the maximal sea level in the Bourgas bay was using of the sea level variation series excluding extremal high levels during catastrophic storm on 16-22 of February, 1979. The main reason was that the mareograph station in the port of Bourgas did not register this phenomenal sea level rise as a result of comparatively low elevation of the station "zero" and consecutive reduction in the registration range of the maximal levels.

In the same period, 16-22 of February 1979, in the mareograph station Irakly and Ahtopol, at a higher zero of the mareograph, it was registered an sea level increase in the order of 1.40m in comparison with the average Black Sea longyears level (Fig. 3.)

Fig. 3. Variations of the sea level at the mareofraph station Irakly over the period 16-22 of February, 1979

This extreme event is due to the continued wind influence for more than 78 hours at the speed of 20-28 m/s under a dominated NE direction (Table 1.).

The combination between mentioned extreme increase (with 200 years return period) and wind waves is the reason for catastrophic damages on installations and sea coast of Bulgarian sector of the Black Sea.

Table 1. Maximal speed of the wind (m/s) over the period 16-22 February 1979.

In order to precise the regime characteristics of the maximal levels in the Bourgas bay it was held an additional statistical and correlation analysis of the data base (1928-1980) by including in the extreme level series for the period of the catastrophic storm in February, 1979 additional information for the sea levels during period 1980-1987.

Under additional statistical and correlation analysis, it is used the data base of the GUGK mareograph stations in Varna, Bourgas, Ahtopol and Irakly, and data from NIMH pegel stations in February, 1979.

The minimal sea levels at a higher repetition (1, 5, 10 year return periods) are very important for exploitation of the object “Port of Bourgas Expansion Project” including seafaring conditions in the new approaching canal at the designed elevation - 15.20 m, load-unload processes of the fasting ships to Terminal 2A and dragging works.

Measuring points of MGGC are equipped with self-writing mareographs from Valdai type, on a scale of record 1/10.

National institute of meteorology and hydrology has been carrying out measurements of the sea level in different points with the assistance of measuring cast-iron yards (pegels) for many years (Fig. 4.).

Fig. 4. Cast-iron (pegel) for measuring sea levels

Fig. 5. Position by height of the measuring cast-iron (pegel)

Two methods are used at researching of the extreme sea level values for composition of statistic excerpt. First method consists in building the empiric distribution functions using the annual maxima series. In the second method the excerpt is composed by data that go out of the limits of any arbitrary chosen basis level.

The disadvantage of the first method leads to loss of part of the information as a result of the circumstance that the secondary maxima are not included in the excerpt although in some cases they exceed the highest levels from other years. A disadvantage of the second method is the random choice of the basis level, from which the shape of the curve of distribution depends on in a high degree. Moreover, such choice can lead to disturbance of the extremums.

The periods of repetition are equal to  

 ,                                                                                                                         (1)

respectively

 .                                                                                                                                 (2)

The optimal choice of a formula for estimating empiric possibility has major importance from the point of view of designing of hydrotechnical installations, because on one and the same maximum replies different periods of repetition, depending on the formula which was used for its estimation.

Weibull’s formula is used to estimate the period of repetition:

                                                                                                                         (3)

where:

1-P – possibility of exceeding of the observed maximum

m – the sequent number of values in the maximum series, ordered in descending order.

N – total number of values in of the maximum series.

An important condition, determining the possibility for statistic extrapolation of empirical distribution functions in the interval of the little possibilities of exceeding, turns out to be the stationarity, used in longyears observation series.

In most of the cases the series of extreme annual sea level elevations vary. Their non-stationarity is determined by the following factors:

·                     Longyears variability of the climate and heliophysics processes produced by the disturbance of the rate of the water balance individual elements appeared as cyclic variations or one direction variations with periods from some years to hundreds of years.

·                     Vertical motions on the land, which are determined by the intensive development of the tectonic processes and which are displayed, as a rule, in the kind of centuries sea level changes in one direction.

·                     Disturbance of the sea water balance as a result of the influence of the practical action of people upon the river effluent, displaying in the kind of one directional level change.

At statistical research of the extreme levels it is observed the special feature that the empiric ensure curve built for different coast points of a determined sea basin or a part of it, differ considerably one from other. Particularly large differences exist in the area of the little possibilities of exceeding.

The main goal of the statistical theory for the extreme values is calculation of the extremums with rare repetition on the base of existing observations. It is accepted that the used observation series for this purpose continues enough time. In the practice of the statistical researches of the extreme sea levels, as a rule, it is used little excerpts, which are not representative enough and, apart from this, very often they are characterized with existing trend with one direction in a chronological speed of the sea level.

The method for estimating of the extreme sea levels is based on the asymptotic theory for extremums and it includes:

·         Excluding the tendencies (trends) with one direction in the row of the extreme sea level series.

·         Give an account of the unrepresentative extreme sea level series (building of the regional distribution functions).

Aproximation and extrapolation of the regional distribution functions on the base of the assessmant of the parameters at the boundary distribution of the extremums.

·         Calculation of the extreme levels and assessment of their punctuality.

The statistic of the extreme values is based on double exponential low. It is taken out of the assumption for the independence of the observer, which meets rare in the nature. Such assumption limits the theory for the extreme values. The theory agrees with the results, such as it reflects just the asymptotic behavior of the exit distribution.

Application of double significant law is based on the following considerations. In case, that in course of the year are completed n observation of sea level at every hour, including the statistical variable , for  cases, when  exceeds arbitrarily chosen value . Then the probability, that  is greater than x, is equal to , and the probability of the contrary event, at that  will be less than x, is equal to

                                                                                                                              (4)

It is examinated the probability, when the maximal  value for a year will be less than x. As the value  supposes independent quantities, then the probability that all of them are less than , equal to the production of their probabilities, turn out to be less than . If number of the values for a year is equal to n, then

.                                                                                                                      (5)

At researching of the extremums with long return period number of the exceedings  is usually small. To find out the exact value of distribution of the exceeding, it is necessary to pass to limit at  in the formula (5).

                                                                                             (6)

or                                                                                                                              (7)

If we assume that the number of exceedings  may be presented by exponent

,                                                                                                                               (8)

It is obtained, the distribution function of the extreme values of the sea level altitude

                                                                                                                    (9)

It is necessary to note, that the assumption for exponential character of distribution correspondes to the distribution properties of the sea level heights and all series of other hydrometeorological elements to describing sea state.

The value y in formula (9) is called reduced variable, which is function of statistical variable , i.e. . After double applying of logarithmic law formula (9) gives

                                                                                                                  (10)

Substituting P with its value, expressed by period of repetition

 ,                                                                                                                          (11)

it is received

 .                                                                                                            (12)

If the expression (9) is differentiated by y, it is received formula for the distribution density

                                                                                                        (13)

or          .                                                                                                    (14)

Maximal annual height series of the level are unsteadily in most of the cases. That is why for input data for calculating of the distribution functions is used the formula

,                                                                                                                (15)

where

·                      h_max – maximal annual diversion

·                      H_max – maximal annual sea level heights

·                       - average annual sea level heights.

Utilizing the maximum annual diversions of the sea level h_max  allows, at a high degree, to be excluded the determining composer (trend) of the extreme values.

Applying of the extreme annual diversions of the level h_max  allows with enough for the practical purposes punctuality, to be done one of the main conditions of the statistical extrapolation – stationarity of longyears observation series. Except this, applying the maximum annual level diversions h_max, allows to be calculated the dimensionless values, excluding the influence of different zeros for the reports of the sea levels over the character of the distribution in the investigated points.

For a base in the investigation of the extreme levels in the Bourgas bay the actualized series of the maximum H_max and the average annual  sea levels for the mareograph station Bourgas for the period 1928-1987 are used.

The statistical analysis was done by using of the diversion h_max from the maximal annual levels H_max, according to formula (15).

Average longyears value  (-0.28m by Baltic zero) at utilization of the annual levels-maximal H_max and minimal H_min is determined by the formula (16)

=                                                                                                      (16),

where N=52 is the number of years of observation period (1928-1980). Consequently

= .

The value =98.35 does not differ from that one obtained by processing of the average annual levels, where the extreme storm situation in 1979 was not taken into account.

After statistical analysis of the annual diversions h_max  of the maximal annual levels H_max  (1928-1987) and making the correlation of H_max for 1979, in Fig. 6 are presented the regime functions of the maximal diversions h_max towards the average longyears level  (-0.28m by Baltic zero) for the Bourgas and Varna bays.

Fig. 6. Ensure function of the maximal diversions h_max for the Bourgas bay on

 the base of the row of data by including the storm in February 1979.

Regardless of existing negligible difference in the maximal levels H_max , determined in source and the actualized row for the mareograph station Varna (1928-1980), the new row, including the extreme situation in February 1979 is put under statistical analysis.

The average longyears value  (-0.28m by Baltic zero) is determined by utilization of the annual maximal H_max and minimal H_min sea levels by formula (16).

= ,

where N=53, number of the years of observations (1928 - 1980).

The value =94.98 cm does not differ considerably from , which is obtained by the processing of the average annual levels, according to the literature and archive sources.

Fig. 7. Ensure function of the maximal diversion h_max for the Varna bay.

The lineal trend of measuring of the annual levels, including average longyears values like the maximal annual diversions h_max, cm, at utilization of lineal regression, is well researched. 

Table 2. Repetition of the maximal diversions h_max for the Bourgas bay.

* In the maximal sea level series the storm from February 1979 is omitted.

** Maximal sea level series is restored by using the Irakly series.

*** Maximal sea level series is restored by using the Ahtopol series.

Table 3. Repetition of the maximal diversions h_max for the Varna bay.

 - Maximal level series is restored by using the Irakly series. 

The results from the investigations are presented in the tables 2 and 3. Regardless of fact that determining the trend authors use lineal regression, the annual variations do not have lineal character and vary on unpredictable shape. Probably, this is due to the tectonic processes, river flow in the Black sea and some technical negligence of the mareograph stations generally at filtering capability from the approach canal to the mareograph station.

 2. Long-term variations of the sea level in the Bourgas bay.

Short-time baric oscillations in the atmospheric pressure over the Black Sea basin form long-term changes in the sea level in the order of heights from 1 to 10 cm and average periods 10-180 m. The main characteristics of this kind of variations (seiche) depend on the configuration, topography of the basin and the port water area. These variations are especially important at the resonant interactions of the system “ship-quay” in the coming widening of the object “Port of Bourgas Expansion Project”.

On the base of the attained statistical elevation series and periods of the long-term variations are estimated summarized distribution function [6].

                                                                                              (16)

                                                                                     (17)

where H- variation elevation; - average variation height; T- variation period; - average variation period.

3. Tidal sea level variations in the Bourgas bay.

Because of interaction between the gravity forces in the Solar system (in particular between the Sun, the Moon and the Earth) variable tidal motions are induced in the ocean, respectively on sea surface.

In the Black Sea basin, as a semi-closed water basin, the tidal variations are not of practical interest, because they have insignificant amplitude in the integral scheme of the sea level variations [7].

Regardless of this circumstance, many researchers analyze this kind of planetary sea level variations, basically in the region of Bourgas and Varna bays.

V. Minkov [15] first noticed that the tidal sea level variations in front of the Bulgarian Black Sea coast are in the order of 5-8 cm.

The Institute of oceanology has also registered these variations, which could be found on each twenty-four hours mareograme in the Bourgas and Varna bays, with the same order of amplitudes and periods as the basic harmonic variable movements [13].

Rogev [10] investigated experimentally and theoretically the tidal movements of the sea level in Bourgas and Varna bays. Their values are presented in Table 4 and Table 5.

Table 4. Astronomical tidals (experimental data), port of Bourgas. [Rogev]

A – amplitude, cm.; K^’ – angle to the position,degree, about zonal meridian ;

K₀ – angle to the position, degree, about meridian of the point M₀ ()

Table 5. Astronomical tidals (theoretical investigations), port of Bourgas. [Rogev]

R – Theoretical amplitude, cm.,  - The theoretical angle in the position, degree

Obviously the values of the 12 hours and 24 hours astronomical tidal variations in the Bourgas and Varna bays do not exceed 6-8 cm.

Regardless of comparatively not high values of the amplitudes, they are not of practical interest for the hydro technicians, because the same values are obtained by the formula for the maximal and minimal levels (15). 

Conclusion:

·         Main statistical characteristics are systematized and reduced to the standard of data base with assistance of literature and archive sources for sea level variation in Bourgas and Varna bays from type of the surface variations (with periods from 0.5 to 7 min), long-term variations (with period from 7 min to several hours) and tidal variations (with period of a day).

This data base is recommended to use by research of the resonance phenomena of the system “vessel-quay” in harbour areas as in the region of water circulation and water exchange in the coastal zone.

·         It is received the best correlative dependence for the maximal sea levels (H_max) between the GUGK mareograph stations respectively for Bourgas and Ahtopol- 0.891, Varna and Irakly – 0.861. These correlative dependences are used to update the longyear for maximal sea level series (H_max), respectively for Bourgas and Varna.

·         It is composed updated data base for maximal sea levels (H_max) in Bourgas and Varna bays, respectively for the period 1928 – 1987 and 1928 – 1980.

In the data series for the Bourgas bay are included the values of extreme sea levels in February 1979.

·         On the basis of the currently data base H_max for period 1928 – 1987 are received the regime function of maximal diversions (h_max) of sea level in Bourgas bay. The received values for h_max are higher than published results [2, 7] in the order of 20%.

These results contribute to the rise of reliability of coming for building hydrotechnical objects in Bourgas bay, including “Port of Bourgas Expansion Project” and “Oil Harbour Expansion Project”.

·         It is established, that for Varna bay the extremal sityation in February 1979, does not exert influence on the regime function of distribution of maximal diversions (h_max) of the sea levels.

References:

1.  Belberov, Z., D. Kostichkova, Z. Cherneva. 1978. Wind wave regularities in the Varna and Bourgas bay. IO-BAS Archive.

2. Belberov, Z., V. Zakhariev, Y. Krilov, D. Kostichkova, R. Manyarova, Y. Polyakov. 1982. Catastrophic storm analysis in February 1979. Oceanology, 9.

3.  Belyashki, Т., 1982. Numerical statistic analysis of observation results in Varna and Bourgas. Bulletin, MGGK, №1.

4.  Bichkov, V. S., S. S. Strekalov, 1971. Sea irregular waves.

5.  German, V. H., 1971. Investigation and estimation of probability characteristics of extreme sea levels. Proceedings of SOI, Vol. 107, p. 149.

6.   Kostichkova, D. R., Z. I. Cherneva, 1980. Long-term variations of sea level in Varna and Bourgas bay. Оceanology, 6, р. 24-29.

7.   Kostichkova, D. R., Z. К. Belberov, 1985. Analysis of maximal sea level along the Bulgarian Black Sea Coast. Оceanology, 14, р. 3-8.

8.    Кrasteva, Е., 1972. Longyear variations of sea level in Varna and Bourgas. Sofia Univ.. Geol.-geogr. Fak., 64, №2.

9.    Кrasteva, Е., 1976. Seiche-like sea level variations in Varna and Bourgas bays. Problems of the geography, S.

10.  Rogev, Б., 1975. Variation of level in front of Bourgas and Varna. Geographical Institute, S.

11.  Kostichkova, D. R, Z. К. Belberov, Е. V. Тrifonova, D. I. Grudeva, 2001. Maximal sea level in Bourgas bay. Proceedings IO, р. 3-12.

12. Pacific Consultants International (PCI), 1999. Oceanographic Investigations. Annex A 3-1: Tide & Water-Level Observations. Port of Bourgas Expansion Project.

13.   Data base of sea levels variations, IO-BAS Archive.

14.   Master Plan of Port of Bourgas Expancion Project, 1995. Vol. 2, Part 2.2. Wind, wave, sea level.

15.   Minkov, V.М., 1971, Harbour construction, SPH Technika, Sofia.