The methodology used here builds on the method developed by \citet{nokey_2d8ed}, which was in turn derived from \citet{nokey_e93a9}, to quantify curvature and wavelength of the Amazon Channel. The minimum radius of curvature (which coincides with the location of maximum curvature) is not a representative value for calculating the centrifugal acceleration because it is sensitive to measurement errors and would give an underestimate of the radius (or an overestimate of curvature). On the other hand, using too many centerline points in this estimation results in a significant mismatch between the centerline and the fitted circles, plus an overestimation of the radius of curvature values. The radius of curvature (R) values obtained here are overall smaller than those calculated by \citet{nokey_2d8ed} as a result of the fact that \citet{nokey_2d8ed} used the entire segment between two inflection points in the calculation.
In contrast with \citet{Peakall_2011}, who have used only the peak sinuosity for each channel system, we have argued that all available measurements, not just the maximum values, should be used in such an analysis \citep{Sylvester_2013}. This choice is justified by the fact that the forces we are interested in act on all channel bends, and a pole-ward decrease in sinuosity should be obvious not just in the extreme values of the sample distributions but in other measures of the upper range of the distributions as well.
The analysis shown in \citet{Sylvester_2013} only includes new sinuosity measurements from the Danube Channel; the data for the rest of the systems come from \citet*{nokey_f708d} and \citet{nokey_2d8ed}. The sinuosities were derived in three slightly different ways: for example, \citet{nokey_2d8ed} used full wavelengths in the calculation, whereas \citet{Sylvester_2013} worked with half wavelengths. Although the results should not be significantly different, for the present study we have made an effort to compare only sinuosities derived using the same scripted—and therefore fully reproducible— methodology, described above.
Using this methodology, we have digitized and analyzed channel centerlines from nine systems (Amazon—\citealt{nokey_2d8ed}; Zaire— \citealt{Babonneau_2010}; Danube—\citealt{Popescu_2001}; Monterey— \citealt*{Fildani_2004}\citealt{Paull:2011dt}; North-Atlantic Mid- Ocean Channel [NAMOC]—\citealt{Klaucke:1997wi}; Knight Inlet— \citealt{Conway_2012}; Rhone—\citealt{TORRES_1997}; Nile—\citealt{Migeon_2010}; and Tanzania—\citealt{Bourget_2008}). The sinuosity distributions are all strongly skewed, with lots of small values (close to 1.0), and many fewer values that are larger than 2.
Both the channel centerline data and the scripts used for analysis and plotting can be downloaded at the following data repository: https://github.com/zsylvester/channel_sinuosities.

Analysis and interpretation

Sinuosity–Latitude Relationship

For the sake of completeness, we reproduce here the results of our previous analysis of the sinuosity–latitude relationship (Fig. \ref{518222}). Using sinuosity values for all channel bends, as opposed to relying on peak sinuosities, and after adding the Amazon and Danube channels to the \citet*{nokey_f708d} data set, we have shown that—at least for those channels under consideration—both sinuosity and valley slope correlate with latitude \citep{Sylvester_2013}. Thus, the impact of the Coriolis force is not the only possible explanation for the low sinuosities at high latitudes; it has been suggested before that, just like in the case of rivers, steeper valley gradients result in lower channel sinuosities \citep{Clark_1992,nokey_2d8ed}. Therefore, the pole-ward decrease in sinuosity in this data set is likely a reflection of the fact that many of the higher-latitude channels are steeper than the rest (Fig. \ref{518222}A). We have suggested that this difference in gradient is primarily a reflection of the nature of the sediment source for the turbidite system  \citep{Sylvester_2013}: submarine channels that are fed by large rivers with high sediment discharge are located on extensive submarine fans or continental slopes with lower gradients, and these are the settings in which high-sinuosity channels tend to develop. Plotting only slope values for the bends with maximum sinuosities, \citet{Peakall_2011}, have essentially ruled out the possibility that slope might play a significant role in the sinuosity–latitude relationship that they have observed. Furthermore, relying only on the extreme values of the sample distributions reduces the robustness of the analysis, and our more inclusive approach does show an overall increase of valley slope with latitude, at least for the systems that were included in this initial, and still fairly limited, data set (Fig. \ref{518222}A).