Starting from the end of the 90s not perodic and unpredictable variations in the depth of harbor waters were observed. Long period (from 24 hours to a few days) and wide amplitude are their main features. Experience showed that this phenomenon is a risk for harbor navigation and mooring. It may be a serious obstacle to waterside port activities. The first observation of the data does not link the super-highs and the super-dry tides to the meteorological dynamic of sea-atmosphere interaction ( i . e. Storm Effect). More, the attempt to compensate for these sea depth fluctuations by means of the well-known offshore hydrobarometric inverse parameter (1 [cm] sea level variation for - 1 [hPa] atmospheric pressure variation) underestimates the amplitude of the phenomenon. In the first years of 2000, the Italian Ministry of Transport launched a national project for the definition of thee - amplitude and time of these tidal anomalous waves. The measure of harbors hydrobarometric inverse factors showed a much more intense value than the theoretical one (computed for the offshore). These amplification factors are characteristic of each harbor and can be double (in exceptional cases even more) than offshore. The delay between the arrival time s of these tidal waves (induced phenomenon) respect to the time of arrival of the atmospheric pressure variation (inducing phenomenon) depends on 1) morphology of the port basin sea floor and 2) harbor and off-shre water dynamics relationship (first approximation) . For these reasons the hydro barometric inverse parameter is not effectiveness computable but it can be determined statistically.
From 2000-2005 many Italian Port Authorities have detected anomalous fluctuations in the depth of port waters. These events created an obstacle to port navigation and, more generally, to the merchant activities of the port. A qualitative and preliminary study showed these phenomena were connected to the local variation of atmospheric pressure. The phenomena were not predictable in amplitude, time of arrival, and duration. The law linking the inducing phenomenon (variation of atmospheric pressure) to the induced phenomenon (hydrostatic balancing tide of the port basin) was not available. The purpose of the present research is the definition of the hydrostatic compensation law in port basins and therefore the ability to predict the hydrostatic port-coastal compensation tide. The forecast of these events increases the safety of coastal and port navigation, of the ports waterside activities and allows optimizing the use of piers and docks.
The port waters depth fluctuation due to the tide is the natural phenomenon having the greatest influence on port-coastal navigation and it can interfere with ships admittance capability to the docks. These limitations to port activities are more evident when the depth of the port basin is low. A port with shallow access routes is forced to work with ships with reduced displacement or with ships not fully loaded. The productivity limits of the port due to this phenomenon are evident and very studied. Under these conditions the tide action is the object of particular attention by the port management. The scientific approach to the problem of the variation of harbors waters depth is based on two aspects modifying the bathymetry of the ports: the control of the sediments deposition on the seabed and the forecast of the tide. The accumulation of sediment on the seabed can be considered a medium-long term phenomenon (apart from rare cases) and it is controlled with direct measurements of depth, generally of an acoustic type. Its contrast is based on the dredging operations of the seabed that are part of the normal life of many ports. Instead the action of the tide produces variations in sea water highness with a shorter period. The capability to forecast the tides is fundamental for optimizing the port navigation security and docks activity. The tide is constituted only in part by a periodic component of astronomical origin well modeled and therefore predictable (astro-tide). This component (α) 1) is produced to a very large extent by the gravitational effects of the dynamic Newtonian system Earth-Sun-Moon (
The values of
F t = α + β + γ ≅ F g 10 − 7 (1)
β and γ (
| Harm. | T [≈h] | v [˚/h] |
|---|---|---|
| M2 S2 N2 K2 K1 O1 P1 S1 M4 MS4 | 12 12 12 12 24 24 24 24 6 6 | 28.9841 30 28.43973 30.08214 15.04107 13.94306 14.95893 15 57.97 58.98 |
If for meteorological reasons the weight of the gaseous district (atmosphere) varies (increase or decrease in density), the local column loses its condition of geodetic equilibrium (
Before looking at the Jp factor quantization method (abs value) it is good to clarify
with a preliminary example the real value of the hydrostatic compensation tide (induced phenomenon) with respect to thveatmosphere weight local variation (inducing phenomenon). As is known in offshore the mass of water involved in the phenomenon of hydrostatic compensation is free to move in any direction of the three-dimensional space Instead along the coasts the horizontal component of the compensation motion is inhibited by the presence of the coast. The compensation defect due to the inhibition of the horizontal compensation movements is discharged on the vertical ones accentuating them (semi-binding basin effect = basin closed in one direction only). To quantify preliminarily this effect, we observe the value of Jp in the event recorded in the port of Civitavecchia from 00.00 january 01 2010 to 24.00 january 07 2010 (
possible interferences both the port navigation (ship’s draft-depth of the sea bottom) and the docks loading-unloading operations. In practice, in the present case, assuming a port water depth of 850 [cm], the standard hydro-barometric compensation forecast e a water residue of 829 [cm] while the real residue is 812 [cm] (real event). The interference of this ε is a known and documented risk from many years of port activities observation. These types of tide, having anomalous amplitudes with respect to astronomical one, are called super-high or super-dry (or super low). The risks due to these events are classified into three groups: the ordinary obstacles to the port navigation and to the loading-unloading works, the straordinary accidents (i.e. stranding), the warning in the design of the harbour coast line and sea bottom infrastructures For example, experience has shown that if the super-dry phenomenon is not expected, the heaviest maritime traffic is exposed to the risk of keel-sea bottom contact even in the most safe access routes to the docks. Often these accidents are interpreted with the presence of new accumulations of sediments on the seabed (confusing the temporary water decreasing with an apparent phenomenon of rising seabed). On the contrary, the super-highs can generate problems in the mooring lines due to the increase in the level of buoyancy of the ship and consequent over-tension of the mooring cables themselves. These effects can be amplified in extraordinary activity, for examples, for ships refloating actions or wrecks removal actions. Another aspect of particular attention is the interference of the γ-type tide component with the design of maritime coastal structures.
Low pressure γ-type tides persist for long periods (from a few hours to a few days). If, for example, during these meteorological-marine conditions the wave motion develops, the peaks of the waves will develop on a sea level higher than the standard one and therefore higher structures s will be needed to contain them. With the same degree of sea state to be contained, it will be necessary to have to a greater raising of the containment structure. On the contrary, this phenomenon requires deeper dredging to ensure safe ships transit even in the worst conditions of γ.
The problem of the measurement and prediction of hydrostatic balancing port tides was addressed from a statistical point of view. The measurement-calculation flow is based on the following steps:
Forecast computation of the amplitude:
• Measures and normalized comparison of the amplitude of the change in atmospheric pressure and the amplitude of the compensating tidal wave.
• Statistical calculation of the numerical correlation factor between signal pressure amplitude and sea level signal amplitude (dimensional factor).
• Application of the numerical compensation factor to the meteorological forecast of the amplitude of pressure variation to obtain the prediction of the sea level variation.
The time arrive computation and the forecast o the tide delay with respect to the variation in atmospheric pressure is obtained by replacing the amplitude of the signals with their arrival time.
The prediction can also be based on the measurement of the gravity acceleration variation (by means of the gravimeter). The flow of calculation remains the same. In the amplitude forecast, the gravity acceleration value replaces the atmospheric pressure value. The forecast procedure based on the gravity measure has a higher order of precision but the gravimetric measure systems is significantly more expensive.
At today the definition of the hydrostatic relationship between the variation of the atmosfere weight and the sea level in natural or artificial coastal basins cannot be effectively modeled due to the high number of physical-geographical factors involved in the phenomenon. This defect exists both the modeling of the amplitudes of γ and for the fluid response times of the basin (time of arrival of the force inducing the geodetic imbalance, delay necessary for marine dynamics for rebalancing). The non-modelability condition is due to the morphological characteristics of each port and to the dynamic relationships between port waters and the marine circulation of its offshore. We propose new statistical parameters (Jp, Jg, K) that allow to describe quantitatively the phenomenon both in amplitude and in time of arrival. The parameters Jp, Jg, K are called “Harbor Newtonian Parameters” (
The J factors (also called transfer Newtonian factors) formalize the amplitude relationship between the induced phenomenon and of the inducing one [
Jp normalizes the variation of sea level measured by the mareograph to the variation of atmospheric pressure measured by means of the barometer according to the Equation (2)
J p = Δ h [ m ] Δ p [ hPa ] (2)
The second order factor Jg normalizes the variation of sea level measured by the mareograph to the variation of acceleration of gravity measured by means of a gravimeter according to the Equation (3)
J g = Δ h [ m ] Δ g [ μ gal ] (3)
The translation of the inducing quantities expressed in [hPa] (1st order) or in [μgal] (2nd order) in the corresponding induced quantity expressed in [m] is shown in the dimensional analysis (4).
Δ h [ m ] { Δ p [ hPa ] × J p Δ h [ m ] Δ p [ hPa ] Δ g [ μ gal ] × J g Δ h [ m ] Δ g [ μ gal ] (4)
The first-order factor Jp has a negative value (inverse) while the second-order factor Jg is direct.
Jp is the most used parameter, at today when we speak generically of J factor we mean the 1st order hydrobarometric inverse factor based on the merge of the signals detected by the barometer with those detected by the mareograph [
The prediction of changes in the depth of the port basin is therefore obtained by multiplying the hydro barometric inverse factor by the measured or expected pressure (meteorological forecast). To date, on an experimental basis it is possible to produce operative forecasts of hydrostatic variations at 6, 12, 18, 24, 30 hours for the ports of which the Jp factor is known (
| Harbour | Adm | D | T [year] | N | Jμ [cm/hPa] | σ |
|---|---|---|---|---|---|---|
| GENOVA LA SPEZIA MARINA di CARRARA LIVORNO PIOMBINO CIVITAVECCHIA RAVENNA | AP MM AP AP AP AP AP | 1 1 1 1 1 1 2 | 2 6 1 3 - 2 1 | 14 44 9 23 COMPUTED 14 10 | 1.9 2.0 2.1 2.0 1.8 1.7 2.8 | 0.2 0.2 0.3 0.2 - 0.3 0.8 |
This singularity can be connected both to hydrostatic characteristics of the District 6 with respect to the Hydrostatic District 1 and to the specific morphology of the port of Ravenna (port channel).
As described above the 1st order factor Jp bases its performance on the measurement of atmospheric pressure variation. But this parameter does not act directly on the hydrostatics of the basin which, in the final analysis, is governed by the variation in the acceleration of gravity, induced by the weight variation of the gaseous district in the local column (
This is because the surface of the sea, in a first approximation, can be considered the equipotential balance surface between atmosphere and sea and therefore the fluctuation of its geometric position is the sensitive element of the measure system. A too high position of the gravimeter (>50 [m]) can produce the signal smoothing effect due to the distance from the phenomenon indicator compared to the measuring device. This measurement condition would increase the smoothing effect in a fatal way because the material interposed between the sensor and the sea surface is denser (water instead of air). In the Gulf of La Spezia a Newtonian meteomaregrafica station was built (
station, LSP_SSN_01 (La Spezia_Stazione Sperimentale Newtoniana_01) was built with the logistical-technological support of Italian Navy, the funding of EU-PRAI-FESR-Regione Liguria (NMS Technoproject) and the technical collaboration of ISPRA-Servizio Mareografico. The standard instrumental component (mareograph), owned by ISPRA, is located at a pier of the “Porto Lotti” Company of La Spezia, the Newtonian component (gravimeter) was located at Italian Navy Naval Base (2007 → 2012 CSSN e = 1.68 [m], La Spezia; 2013 → 2016 COMSUBIN, e = 8.16 [m], Dogana Settecentesca of Varignano)
The results of the qualitative analysis of sea level changes in the port basins of
they can be calculated effectively with Fourier analysis. [
Δ p = a p M 2 + b p M 2 − a p m 2 + b p m 2 (5)
Δ g = a g M 2 + b g M 2 − a g m 2 + b g m 2 (6)
Δ h = a h M 2 + b h M 2 − a h m 2 + b h m 2 (7)
where, according to the Fourier harmonic serie (8)
f ( t ) = 1 2 a 0 + ∑ n = 1 ∞ ( a n cos ω n t + b n sin ω n t ) (8)
a0 is the carrier component of the signal and a, b are the Fourier harmonic coefficients (10), (11):
a 0 = 2 T ∫ − T / 2 T / 2 f ( t ) d t (9)
a n = 2 T ∫ − T / 2 T / 2 f ( t ) cos ω n t d t , n = 0 , 1 , 2 , ⋯ (10)
b n = 2 T ∫ − T / 2 T / 2 f ( t ) sin ω n t d t , n = 1 , 2 , ⋯ (11)
and
Δp = atmospheric pressure variation.
Δg = local gravity variation.
Δh = sea bathymetry variation.
p = atmospheric pressure.
g = gravity.
h = bathymetry.
M, m = Maximum and minimum of the function.
T = period.
t = time.
The results of the elaboration of the super-dry phenomenon of
1st order
| J p | Δ h [ cm ] Δ p [ hPa ] = 49 − ( − 3 ) 1020 − 992 [ cm / hPa ] = 52 28 [ cm / hPa ] ≈ 1.9 [ cm / hPa ] (12)
2nd order
| J g | Δ h [ cm ] Δ g [ μ gal ] = 49 − ( − 0.3 ) 5139 − 4860 [ cm / μ gal ] = 52 279 [ cm / μ gal ] ≈ 0.2 [ cm / μ gal ] (13)
The Jp of the example of
The full description of the phenomenon of hydrostatic tides is obtained if, in addition to the amplitude ratio between forcing (variation of density of the atmosphere) and forced (tidal wave of compensation), the delay K of arrival arrival of the forced with respect to arrival is defined of forcing. K is of fundamental importance in the safety of port waterside activities as it indicates the useful time before the arrival of the hydrostatic tide wave. The value of this parameter can be obtained in two ways: geometric comparison (automatic) on the LP graphs of the tide signals and of the pressure-gravity signals or amplitude comparison in the frequency domain of these signals. The second one has the advantage of allowing a more accurate evaluation of the computations (14), (15).
K p = Φ h − Φ p = ⌊ tan − 1 | b h a h | ⌋ − ⌊ tan − 1 | b p a p | ⌋ (14)
K g = Φ h − Φ g = ⌊ tan − 1 | b h a h | ⌋ − ⌊ tan − 1 | b g a g | ⌋ (15)
where a, b Fourier harmonic coefficients (10), (11):
and
T = period of the harmonic considered.
Kp = delay of marine compensation to the variation in atmospheric pressure.
Kg = delay of marine compensation to the variation in local gravity.
Φp = phase (time) signal atmospheric pressure variation.
Φg = phase (time) signal local of gravity variation.
Φh = phase (time) signal of sea depth variation.
g = local gravity.
h = sea level.
With reference to
K p = Φ h − Φ p = 1 h 15 min , K g = Φ h − Φ g = 3 h 30 min { Φ h = | 36 h 50 min | day2 = | 12 h 50 min | day3 Φ p = | 35 h 35 min | day2 = | 11 h 35 min | day3 Φ g = | 33 h 20 min | day2 = | 09 h 20 min | day3 16)
As shown in (16) the analysis based on the variation of gravity produces the information (prediction of delay beetwen inducing signal - induced signal) with a greater advance ΔT with respect to the analysis based on atmospheric pressure (17)
Δ T = K g − K p = 3 h 30 m − 1 h 15 min = 2 h 15 min (17)
This advance in the availability of information (2h15min) (17) can be fundamental information in the management of port navigation and dockside activities.
The delay K = K [h, min] of the compensation wave arrival is calculated in Fourier transform. This numerical action provides a very simple and fast method of controlling K. But if we apply the FFT protocol directly to our raw data series we can have an unstable response as shown by the high standard deviation σ1 18). In fact we note that the value of the response is strongly dependent on the frequency (or wavelength) of the cut. This evidence can significantly decrease K’s operational forecasting effectiveness. The K values dispersion of each HP function analyzed is depending on the shear wavelength of the HP frequency filter (
σ = ( x 1 − μ ) 2 + ⋯ + ( x 13 − μ ) 2 l 2 → σ K ≅ 10 ; σ K C B ≅ 4 (18)
This problem is significantly reduced by the use of a numerical smoothing operator that stabilizes the FFT action. This is more valid for elaborations in short data windows (σ2) (
− ( L + M ) → L + M (19)
where
• = series to be analyzed.
M = 2L/10.
| ΛLP [min E3] | K [min] | KCB [min] |
|---|---|---|
| 1.44 1.38 1.32 1.26 1.2 1.14 1.08 1.02 0.96 0.9 0.84 0.78 0.72 | 155 159 148 162 139 141 138 145 167 140 144 151 139 | 142 139 144 143 152 139 135 142 139 142 138 146 140 |
Each nnt sample of (19) is multiplied, in the time domain, by
C B n = { 1 2 [ 1 + cos π ( n + L ) M ] − ( L + M ) < n < − L 1 − L ≤ n ≤ L 1 2 [ 1 + cos π ( n − L ) M ] L < n < L + M (20)
the numerical operator (20) does not pollute the L series subjected to analysis and avoids the well known FFT reconstruction problems of non-derivable edges (box car → causal function). In the case under discussion the 2L series consists of 1440 samples (24 [h,] sr 1 [m]) so the length of the smoothimg segments is | L + M | = 144 [ min ] and the length of the complete series is Fx of 1728 data (from −864 to +864) [
The measurement and forecasting of 1st order is based on standard maregraphyc stations. In general, a mareographyce station consists of a mareograph and of its TLC system. The mareograph is often associated with some meteorological instruments completing the monitoring of the meteo-marine environment (barometer, anemometer, hygrometer, ...). This type of station is able to provide the necessary and sufficient information to apply the 1st order measurement and forecasting procedure of tidal waves amplitude of hydrostatic origin (by means mareograph and barometer).
Mareograph and barometer measure the sea level variation and of the atmospheric pressure. The informations are transferred to the system CPU by TLC (the TLC option chosen for the network of
To obtain the prediction of ∆h (first order tide compensation), the forecasted γp is algebraically added to the astronomical component α provided by the astronomical tide tables (
After 12 hours, in the current experimental asset, the Newtonian station abandons the meteorological forecasting and moves on to direct barometric forecasting extrapolation (instrumental reading of the atmospheric pressure variation trend and its extrapolation whit T = 2[h]) 21).
48[h] f.∆p (forecasted ∆p data) → 24[h] f.∆p → 12[h] f.∆p
→10 [h] e. f.∆p(extrapolated ∆p data) ®®8 [h] e. f.∆p6 [h] e. f.∆p. (21)
Although some preliminary statistical correlation studies “long-term forecast of atmospheric pressure variation, local gravity variation forecast” (correlation time > 24[h]) have given interesting results, at today no conclusive results have been achieved. Barometry therefore remains an integral part of the hydrostatic port tidal forecasting process for the remote forecasting sector.
Instead for the proximity forecast sector the use of the gravimeter is very important because it adds precision to the determination of this forecast sector (
The role of the gravimetric forecasting system (
In the current experimental protocols, after the prediction at 6 [h], the algorithm migrates into the Newtonian area to use the local gravity variation data for the amplitude forecast and the gravimetric K (LP 135 [min]),
Below we show some examples (raw data) to quantitatively visualize the real effects of the hydrostatic tide in some Italian ports (
line). All the events of Figures 17-19 (a, b, c, d) took place with wind speed v < 3 [knots]. The records come from the standard mareographyc stations (
LEGEND (Figures 17-19): X = T [dd_mm_yy], sampling rate s = 1 [h], Y left (red line) Atmospheric Pressure [hPa], Y right (black line) sea level variation [m]
• Station1: Imperia IMP_11 (*)
• Station 2: Genova GNV_02 (*)
• Station 3: Civitavecchia CVT_06 (*)
(*) Data collection: ISPRA Servizio Mareografico-Ministero dell’Ambiente e della Tutela del Mare e del Territorio, Italia Republic. Open source.
The qualitative observation of changes in sea level in Italian ports showed the presence of exceptional phenomena of high (super-high) and low (super-dry) tide both in amplitude and duration. In the last decade these phenomena have increased in frequency up to severely interfere with the maritime activities of various ports. The statistical study of the phenomenon has made it possible to associate these anomalous tidal waves with the variations in atmospheric pressure
and therefore to frame the phenomenon in the field of the hydrostatic relationship atmosphere-sea level (ratio of weight of the atmosphere: sea level). Technological studies (MeNFor project Meteotide Newtonia Forecasting Tecnoproject) and phenomenological studies (GraMAS project Gravimetric Maritime Automatic System for Port Navigation Safety) have made it possible to quantify the amplitude of the hydrostatic component for these tide waves. The time relationship between the arrivals of the inducing phenomenon (variation of atmos
pheric pressure) and the induced hydrostatic response (inverse variation of the sea level) in various Italian ports has also been defined and therefore the forecast parameters of the hydrobarometric tides in several Italian ports have been defined. In particular, the phase difference between the barometric and gravimetric signals and the hydrostatic tide one indicates the delay of the hydrostatic tidal
wave with respect to the variation of local atmospheric pressure. This delay, like the amplitude, is characteristic of each port and it is substantially constant over time. Therefore, it can be associated with the forecasts of atmospheric pressure variation to obtain forecasts of the port sea level hydrostatic fluctuation. The standard meteo-mareographic stations can be used for the quantitative prediction of the amplitude and time of arrival parameters of these phenomena based on barometric measurements. The use of the gravimeter (Newtonian component) has substantially implemented the short-time forecasting accuracy. The integrated forecast (long period = barometric, short period = gravimetric) has allowed to measure and predict the phenomenon with sufficient precision to satisfy the needs of the port maritime traffic and to the ordinary and extraordinary quay operations. The introduction of this new technique for predicting the hydrostatic port tide parameters has an ordinary use: optimizing moorings and coastal navigation and their safety and improving the design of the sizing of coastal and seabed structures. The technique can be used also in case of maritime accident. In particular, for example, it is useful to forecast of the real sea level during the refloating actions in ship stranding accidents or to improve the tracking precision of the movement of non-water-soluble polluting substances (for example hydrocarbons). Hydrobarometric meteomareography has been successfully used in several Italian ports for experimental periods lasting between 6 and 12 months. Also its use in extraordinary cases has shown high operational effectiveness (e.g. checking the stability of the Costa Concordia ship during the wreck recovery operations (Isola del Giglio, January 2012) and the refloating operations of the stranded Sigma ship (Port of Livorno, January 2017)).
The tide and atmospheric pressure data presented are owned by the Serevizio Mareografico-ISPRA-Ministero dell’Ambiente e della Tutela del Mare e del Territorio-Repubblica Italiana. They are available on the website of this State organization.
This research action was coordinated by “Commissione Nazionale di Studio dei Flussi di Marea Meteorologica per la Sicurezza della Navigazione di Approccio Portuale, delle Opere Marittime e dell’Ambiente Marino Portuale (COM.SI.PORT)-CONSUPLP SEZ. III, Ministero delle Infrastrutture e Trasporti-Italian Republic” (Gra.M.A.S. Gravimetric Maritime Austomatic Aid to Port Navigation System research action 2007-2014). EU-PRAI-FESR Regione Liguria and Genova, La Spezia, Marina di Carrara, Livorno, Piombino, Civitavecchia, Cagliari, Bari, Ancona, Ravenna Port Authorities (old definition) have supported this research action. Special thanks to Italian Navy (CSSN and COMSUBIN-La Spezia ITA) and CMRE (North Atlantic Treaty Organization La Spezia ITA) for the logistic and technological support to the Newtonian mareographyc station.
Thank you very much to everybody.
The author declares no conflicts of interest regarding the publication of this paper.
Faggioni, O. (2020) Measurement and Forecasting of Port Tide Hydrostatic Component in North Tyrrhenian Sea (Italy). Open Journal of Marine Science, 10, 52-77. https://doi.org/10.4236/ojms.2020.102005