Geometric Stalemate and De-Evolution of Adriatic Sea Representations on Early Modern Age Nautical Charts

ABSTRACT

Cartographic representations of the Adriatic Sea basin on 11 (manuscript and printed) Early Modern Age nautical charts, made between 1538 and 1771, were subjected to a cartometric analysis in which their geometrical features were inspected. Additionally, four of them on which the graticules were plotted and were subjected to the analysis of their spherical coordinates, which was conducted in parallel. The results show that cartographers who produced printed charts in seventeenth and eighteenth centuries, never succeeded in surpassing the geometric accuracy of manuscript portolan charts from the sixteenth century, regardless of whether their charts contained graticules or not. According to the results and the historical context of contemporary technological development, it appears that in the era that preceded systematic hydrographic surveys, their authors had no other choice but to (partially) copy the inherited ‘framework’ of portolan charts as a reference model, and to implement certain localized trial and error modifications.

KEYWORDS:

• Early modern nautical charts
• chart accuracy
• Adriatic Sea

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Notes

1 Tratado sobre certas duvidas da navegação and Tratado em defensam da carta da marear com o regimento da altura, respectively.

2 Late-medieval and Early Modern attempts to reconstruct the (lost) cartographic content of Geographike Hyphegesis.

3 The entire analytical procedure conducted in this research can be performed in (open-source) QGIS software and Microsoft Excel.

4 Charts AGN_1538, HOM_1570, VOL_1593, BAR_1595, JAN_1650 and FAS_1679 have the rhumb networks drawn on them exclusively, while chart BEL_1745 contains a graticule of latitudes only (besides the rhumb network), meaning it was not suitable for complete coordinate dataset extraction.

5 The composite chart DUD_1646 (1032×791 mm) consists of three sheets: North Adriatic (708×492 mm), CentralAdriatic (755×498 mm) and SouthAdriatic (386×519 mm). The North Adriatic sheet differs from the other two in map scale, so it had to be shrunk to 78.9% (along both axes) of its original size in order to fit properly into the composite.

6 The reference modern map shapefiles were downloaded from marineregions.org webpage (Claus et al., 2017).

7 The mathematical expressions are: $\mathrm{RMSE}|\mathrm{dX}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{(X_i-{\hat{X}}_i)}^2}{2n-4}}},\mathrm{RMSE}|\mathrm{dY}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{(Y_i-{\hat{Y}}_i)}^2}{2n-4}}}$

8 The mathematical expressions are: $\mathrm{RMSE}|\mathrm{dLON}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{({\lambda }_i-{\hat{\lambda }}_i)}^2}{n-1}}},\mathrm{RMSE}|\mathrm{dLAT}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{({\phi }_i-{\hat{\phi }}_i)}^2}{n-1}}}$. The‘$(-1)$’ is in the denominator because (only) a sample of selected coordinates was considered (not the complete coordinate dataset which could possibly be extracted).

9 For the sake of simplification, and because the determination of identical points on charts and maps is never completely error-free, spherical corrections of the residuals [km] were computed as follows: $|\mathrm{dLON}|[\mathrm{km}]=|\mathrm{d\lambda }|{[}^{\circ }]\times 111.092\times \cos (\mathrm{midLAT})$ and $|\mathrm{dLAT}|[\mathrm{km}]=|\mathrm{d\phi }|{[}^{\circ }]\times 111.092$. The factor of 111.092 [km] represents ${\mathrm{\Delta }}_{\mathrm{lat}}^{1^{\circ }}$ at $\phi ={43}^{\circ }\pm {30}^{\mathrm{\prime }}$ (the approx. central latitude of the Adriatic Sea) on the WGS84 ellipsoid, obtained by using the formulae: ${\mathrm{\Delta }}_{\mathrm{lat}}^{1^{\circ }}=1111132.954-559.882\times \cos 2\phi +1.175\times \cos 4\phi$. The midLAT factor represents the mid-latitude between the reference point and its corresponding (georeferenced) identical point. After the approximate corrections from Euclidean into spherical geometry are performed, the map’s accuracy is calculated by the expression: $\mathrm{RMSE}|\mathrm{dLON}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{(\mathrm{LO}{N}_i-{\widehat{\mathrm{LON}}}_i)}^2}{2n-4}}},\mathrm{RMSE}|\mathrm{dLAT}|=\sqrt{{\displaystyle \frac{{\sum }_{i=1}^n{(\mathrm{LA}{T}_i-{\widehat{\mathrm{LAT}}}_i)}^2}{2n-4}}}$.

10 RMSE|Re_calc.| [km] is the calculated value of reference-identical residual length along the ellipsoid surface, generated by the GIS software (Figures 1–3), and which can be approximated with the expression: $\mathrm{RMSE}|\mathrm{Recalc}.|=\sqrt{{(|\mathrm{dLON}|)}^2+{(|\mathrm{dLAT}|)}^2}$. It is not the measure of map accuracy, because it should be the larger one between its two axial components (RMSE|dLON|[km] or RMSE|dLAT|[km], depending on the particular result) (Nicolai, 2014: 209–210).

11 See note 10.

12 This ‘E–W shift optimization’ of longitudes was performed in order to ‘expose’ the geometry of the extracted coordinates dataset of the Adriatic Sea exclusively (as a standalone territorial unit), that is regardless of the location of their absolute zero (which is, in the case of longitudes, always arbitrarily determined). For example, the location of the Paris prime meridian on the WGS84 ellipsoid is about 2.3° E, which suggests that both Bellin’s charts (made in 1737 and 1771) should be longitude-wise corrected by the Δλ₀ factor of +2.3°. However, if his 1737 chart were, for example, longitude-wise ‘correctly’ corrected by Δλ₀= +2.3°, its RMSE|dLON| would be 0.51° (40.89 km), compared to 0.23° (18.57 km), obtained by using its optimal longitude-optimization factor of +1.9° for the Adriatic Sea basin alone (see Table 3), because the entire dataset (which had remained intact in relative terms) were arbitrarily shifted farther westward. For the sake of standardization, the same procedure was conducted for the latitude values, by using the ‘N–S shift optimization factor’.

Additional information

Funding

This research is a part of scientific project IP-2020-02-5339 Early Modern Nautical Charts of the Adriatic Sea: Information Sources, Navigation Means and Communication Media (NACHAS) funded by the Croatian Science Foundation.

Notes on contributors

Tome Marelić

Tome Marelić is a research assistant at Department of Geography, University of Zadar, Croatia. His prime research interest is quantitative (cartometric) analysis of old maps and charts with the application of GIS and statistical software. His current research is focused on the geometric properties of Adriatic Sea basin coastline renderings on late-medieval and Early Modern navigational charts.