The 1516 World Map by Martin Waldseemuller, known as the Carta Marina, looks very much like a Portolan Chart even though it is a printed map. Many scholars have surmised that the sources for the map were in fact Portolan Charts but no one has ever attempted any calculations that might allow conclusions beyond these speculations.
The above figure (click on figures to enlarge view) is the sheet from the 1516 Carta Marina that contains Europe and most of the Mediterranean. Portolan charts contain two analytic features that are very important in distingushing them from other maps of the period. First, the axis of the Mediterranean basin is deflected or rotated by between 5 and 11 degrees. This orientation shift most likely results from an orientation to magnetic and not true North. A.C. Mitchell's paper "Chapters in the history of terrestrial magnetism" (Terrestrial Magnetism and Atmospheric Electricity, XLII (1937) 241-280) is one of the earliest to suggest this and is worth reading.
In order to test the Carta Marina for rotation of the Mediterranean basin we used an affine transformation and a Hampel estimator to control the error distribution of the chosen landmark points. The figure below shows the sheet of the Carta Marina with a distortion grid calculated using M-estimators. M-estimators (see links) are part of a large family of statistical estimation functions (known as robust) that try to reduce the effect of outliers or points of large error on the overall tranformation calculations.
Hampel gives several answers to the question of when to apply Robust estimators:
There are two observations which when combined give an answer. Often in statistics one is using a parametric model implying a very limited set of probability distributions, such as the common model of normally distributed errors, or that of exponentially distributed observations. Classical (parametric) statistics derives results under the assumption that these models were strictly true (this is especially important in our cartographic applications where are chosen landmarks are rarely evenly distributed). However, apart from some simple discrete models perhaps, such models are never exactly true. We may try to distinguish three main reasons for the derivations: (i) rounding and grouping and other "local inaccuracies''; (ii) the occurrence of "gross errors'' such as blunders in measuring, wrong decimal points, errors in copying, inadvertent measurement of a member of a different population, or just "something went wrong''; (iii) the model may have been conceived only as an approximation anyway, e.g. by virtue of the central limit theorem.
One can imagine using these estimators as an application of Tobler's first law of geography, "everything is related to everything else, but near things are more related than distant things" (see Waldo Tobler's article in Economic Geography 46 234-40).
The application of the transformation to the European sheet yields a rotation of 7.6 degrees for the Mediterranean which is consistent with a Portolan source. Below is the bare grid displayed for clarity. The other feature that most Portolan's display is a lining up of the tip of Brittany with the location of Venice, showing both places on the same east-west line. The area of Brittany should be displaced by more than 3 degrees. The 1516 map shows a lining up of these two places consistent with most Portolans. The cause of this distortion most likely comes from an error in the interpretation of the data from the Atlantic coast, the prototype being measured in Catalan miles which are shorter than the Italian miles typically used in the Mediterranean.
Although none of this conclusively proves that Waldseemuller used Portolan charts as sources for the 1516 Carta Marina it a least implies it as a possibility and suggests a place to look for possible prototypes of this region..
More on this soon.