Description
To our knowledge, only two other similar instruments were operating at that time, all of them (including that of Marseille) built by the same firm of Dennert & Pape in Altona, near Hamburg, Germany. They were installed the same year 1880, in Cadiz, Spain, and in Helgoland, a British possession at that time (Fig. 1). Both Cadiz and Helgoland tide gauges stopped recording a long time ago, in 1924 (Marcos et al. 2011) and presumably in 1901 (Rohde 1982), respectively. Only Marseille has kept operational since its installation in 1885.
Figure 3a shows an overview sketch of the Marseille tide gauge. The gauge was firmly set above the stilling well on the upper floor (Fig. 2b). Briefly, it is a high-precision mechanical floating gauge supplemented with a mechanical integrator. The mechanical integrator (‘totalisateur’) is located on the left part of the sketch in Fig. 3a (left of the platinum ribbon) and is further detailed in Fig. 3b with frontal (bottom right) and lateral (bottom left) views. A most important part of the tide gauge is the ‘40.500 litres’ (original unit) copper float of 0.9 m in diameter and 0.2 m in width. It is connected with a pulley mechanism to the recording devices, that is, the pen carriage tracing out the sea level variations on a paper chart and the roller carriage of the ‘totalisateur’. The paper roll is set on a 48-h rotating cylinder driven by a mechanical clock, resulting in a paper speed of 12 mm/h or about 105 m per year. The graphical recording is a duplicate one. Originally, two pens with diamond points were simultaneously tracing out the sea level variations on a specific blackened glazed paper which was split into two tidal charts while rotating: one was kept on-site, whereas the other was sent to Paris for archiving. The tide gauge has a reduction ratio of 10 (ratio of the amplitude of sea level variations in the open sea to that recorded).
The design of the Marseille tide gauge was supplemented with substantial original instructions from Charles Lallemand (Lallemand and Prévot 1927). However, the most ingenious part is definitely the mechanical integrator (Reitz 1878). This mechanical integrator was designated as the ‘totalisateur’ in French, hence giving its name to the tide gauge. Figure 3a indicates how it works. As the float rises and falls with the sea level in the stilling well, its vertical movement is reduced by a factor of 10 and horizontally translated to the rack and its pen carriage. The horizontal movement further transforms into a vertical one of the carriage holding the rollers (\(r1\)) and (\(r2\)). The platinum ribbon is intended to ensure the rigorous mechanical translation of the rack movement. The rollers are made of agate (SiO3) while the integrator disk (\(Q\)) upon which they are in contact is made of glass, ensuring an exact contact so that there is no slipping or hooking on it. The integrator disk rotates with the chart cylinder driven by the same mechanical clock. Its axis is aligned to that joining the rollers (\(r1\)) and (\(r2\)).
For the sake of simplicity, Fig. 3b illustrates the principle of the mechanical integrator mechanism with only one roller (\(r\)). The diameter of the roller (\(r\)) is a given constant \((\lambda )\). Both the integrator disk (\(Q\)) and the roller (\(r\)) are equipped with loop counters. Provided there is no slipping or hooking on the integrator disk, the following relationship (E1) holds:
$$\begin{aligned} \frac{\lambda }{2}\times \delta n=z\times \delta N \end{aligned}$$
(E1)
with \((\delta n)\) the difference of the readings (\(n1\)–\(n0\)) on the roller counter of (\(r\)) between two successive epochs (t0) and (\(t1\)), (\(z\)) the sea level variations (reduced by a factor of 10) between those two epochs and \((\delta N)\) the corresponding difference (\(N1\)–\(N0\)) on the disk counter of (\(Q\)). The latter quantity \((\delta N)\) is proportional to the time difference (\(\delta t\) or \(t1\)–\(t0\)) between the two epochs, K being equal to 1/2 if expressed in days (one loop every two days):
$$\begin{aligned} \left\{ {{\begin{array}{l} {\delta N=K\times \delta t} \\ {K=1/2} \\ \end{array} }} \right. \end{aligned}$$
(E2)
From Eqs. (E1) and (E2) can be derived the integration of the sea level curve between two epochs (\(t0\)) and (\(t1\)) and subsequently its rigorous mathematical mean (Zm) by simply subtracting the corresponding readings on the loop counter (\(n1\)–\(n0\)) and dividing by the elapsed time (\(t1\)–\(t0\)) as follows:
$$\begin{aligned} \begin{array}{l} z_m \!=\!\frac{10}{t_1 \!-\!t_0 }\int \limits _{t_0 }^{t_1 } {z\cdot \delta t\,{=}\,} \frac{10\lambda }{2\cdot (t_1 \!-\!t_0 )}\int \limits _{t_0 }^{t_1 } {\frac{\delta n}{\delta N}\cdot \delta t=\frac{10\lambda }{2K\cdot (t_1 -t_0 )}\int \limits _{n_0 }^{n_1 } {\delta n} } \\ z_m =\frac{10\lambda }{2K}\cdot \frac{n_1 -n_0 }{t_1 -t_0 } \end{array} \end{aligned}$$
(E3)
The factor of 10 corresponds to the mechanical reduction factor (see above). Consequently, the ‘totalisateur’ directly yields mean sea levels between two epochs following the rigorous mathematical definition (integration of a curve), at any desired frequency determined by the time interval between the operator’s readings. Further description on the mechanical integrator can be found in old German from the original publication by Reitz (1878) or in French (Bernard 1899; Lallemand and Prévot 1927). Coulomb (2014) provides an extensive and comprehensive review of the substantial amount of material gathered so far (correspondence, account, photographs, sketches, etc.).
Data sets and datum relationship
Table 1 summarizes the various tide gauge data sets that are presently available for Marseille. A data set is defined here as a comprehensive set of sea level observations that are related to the same location and gauge.
Table 1 Overview of tide gauge data sets at Marseille
The earliest sea level observations at Marseille date back to 1849 from one of the first self-recording float tide gauges devised in France (Chazallon 1859). Figure 1 shows its location in the Harbour of La Joliette, about 3 km north of the ‘totalisateur’ tide gauge. Values every half an hour from November 1849 to May 1851 were recently rediscovered in the form of handwritten tabulations. The associated tidal charts have not been found so far. Surprisingly, the tabulated data were expressed in ‘apparent solar time’, in spite of ‘mean solar time’ being the legal time since 1816 in France. Pouvreau (2008) reports on this anachronism, which lasted between 1846 and 1860 in the recording of tide gauges under Chazallon’s supervision. Indeed, using a variable time scale such as the apparent solar time requires daily corrections to adjust from the naturally linear time scale of a mechanical clock. In the case study of Marseille, the historical documentation states that the Chazallon tide gauge recorded in mean solar time, whereas the tabulated data had been corrected to be in apparent solar time. Consequently, the following corrections have been applied to the tabulated (only the hourly values were digitized) Marseille 1849–1851 record:
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correction from apparent solar time to mean solar time at Marseille by applying the ‘equation of time’ given in Savoie (2001);
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correction from mean solar time to universal time (UT) by subtracting 21.575 min, a value corresponding to the difference in longitude between Marseille and Greenwich.
The latest data sets come from an acoustic and a radar tide gauge (sets 3 and 4 in Table 1, respectively). These gauges have provided high-frequency sea level data directly in digital form and UT system from October 1998 to April 2009 and from April 2009 to the present, respectively. The radar gauge replaced the acoustic one in April 2009, mostly because of repeated malfunctioning of the acoustic sensor since November 2000 (discussed later on in Sect. 4.4). The sea levels of the above-mentioned modern and oldest data sets (data sets 1, 3 and 4 in Table 1) are referred to a common nautical chart datum, the so-called ‘Zéro hydrographique’ (ZH). These observations were undertaken under the supervision of French hydrographers, whose golden rule since the early nineteenth century has been to refer to that datum for sea level observations (Beautemps-Beaupré 1829). The ZH is usually represented by a local set of tide gauge benchmarks, including tide staffs installed in such a way that their zero graduation marks coincide with the nautical chart datum ZH, whatever the practical realization of the ZH (Wöppelmann et al. 2006a). Considering that both the Fort Saint-Jean marble staff and the Chazallon tide gauge were contemporary and their zero set to be at the ZH, it is reasonable to speculate that levelling operations had connected them, ensuring the same datum.
The main data set comes from the ‘totalisateur’ tide gauge, which has been working continuously from February 1885 to the present, with short interruptions due to mechanical failures or maintenance. Actually, two separate records result from this tide gauge: one from the mechanical integrator (‘totalisateur’), which consists of tabulated MSL readings from the loop counters (daily), and the second from the tidal charts (continuous curve). The main record has been that of the mechanical integrator, to which most of the geodesists’ attention has been focused. Its MSL data from 1885 onward have been readily provided to the international community and public data banks such as the PSMSL. The modern tide gauges have taken over the MSL provision since 1998, despite the readings performed on the integrator continuing on a roughly weekly basis since 1988, instead of a daily basis when there was a dedicated gauge attendant. The tidal charts were barely exploited, but scrupulously archived in Marseille and Paris. Chart recording eventually stopped in August 1988 with the retirement of the last gauge attendant, the difficulty to acquire the specific nine-metre-long and 17-cm-width paper rolls, and the somehow lack of interest for sea level observations at the French mapping agency. However, under the pressure of the national committee representative of the International Union of Geodesy and Geophysics (IUGG), the tidal charts were gathered and digitized with variable efforts depending on the human resources available at the French mapping agency. The years 1909 (important works at the tide gauge), 1913 (missing tidal charts at both the Marseille and Paris archives), 1921 and 1924 (tidal curves illegible) were not digitized.
In agreement with its geodetic rationale, the internal reference of the mechanical integrator was referred to the French national levelling datum (NGF-Lallemand), once it was established using MSL data from February 1885 to December 1896 (Lallemand and Prévot 1927). The fundamental benchmark for France, which defines that datum, is a brass bolt covered with a very hard alloy of platinum and iridium. It is embedded in a granite block set in the bottom floor of the tide gauge building (Fig. 2b). Figure 4 summarizes the relative position of the NGF datums and the most significant reference levels at Marseille that we have dealt with. For the sake of completeness, the PSMSL datum (RLR in Fig. 4) and the GPS antenna reference point are indicated as well. The nautical chart datum ZH is defined at Marseille as 0.329 m below NGF-Lallemand or 1.989 m below the fundamental benchmark. It corresponds to the zero graduation mark of the Fort Saint-Jean marble tide staff. It is worth noting here for future historical studies that there is about 1 mm difference between the heights expressed in NGF-Lallemand and those expressed in NGF-IGN69 which arises from the type of heights (orthometric versus normal heights, respectively). Most precisely, the height of the fundamental benchmark is 1.660 m in NGF-Lallemand and 1.6607 m in NGF-IGN69.
Figure 4 also shows the relationship between the tide gauge (TG) index or rack index and the centre separating the two integrator rollers (Fig. 3a), which corresponds to the zero of the mechanical integrator. They are mechanically linked to be 1 metre. By calibrating the TG index, the MSL readings on the ‘totalisateur’ can be referred to the levelling datum as follows:
$$\begin{aligned} \hbox {MSL}=h-(1{,}000+\eta )-\frac{10\lambda }{2K}\times \frac{{\left( {\delta n^{\prime }+\delta n^{\prime \prime }} \right) }/2}{\delta T} \end{aligned}$$
(E4)
where (h) is known as the tide gauge constant which relates the TG index to the levelling datum, \((\eta )\) is intended to take into account any mechanical distortion of the rack or the platinum ribbon (none observed since 1909), and the last term comes from (E3) by averaging the difference of readings over the time interval \(\delta T\) from two rollers instead of one in (E3), that is, \(\delta n\)’ on roller (\(r1\)) and \(\delta n\)” on (\(r2\)). The negative sign corresponds to the roller carriage falling while the float rises and vice versa (Fig. 3a).