Constraints on Titan's topography through fractal analysis of shorelines

Titan's north polar hydrocarbon lakes offer a unique opportunity to indirectly characterize the statistical properties of Titan's landscape. The complexity of a shoreline can be related to the complexity of the landscape it is embedded in through fractal theory. We mapped the shorelines of 290 of the north polar titanian lakes in the Cassini synthetic aperture radar dataset. Out of these, we used a subset of 190 lake shorelines for our analysis. The fractal dimensions of the shorelines were calculated via two methods: the divider/ruler method and the box-counting method, at length scales of (1-10) km and found to average 1.27 and 1.32, respectively. The inferred power-spectral exponent of Titan's topography (β) from theoretical and empirical relations is found to be ⩽2, which is lower than the values obtained from the global topography of the Earth or Venus. Some of the shorelines exhibit multi-fractal behavior (different fractal dimensions at different scales), which we interpret to signify a transition from one set of dominant surface processes to another. We did not observe any spatial variation in the fractal dimension with latitude; however we do report significant spatial variation of the fractal dimension with longitude. A systematic difference between the dimensions of orthogonal sections of lake shorelines is also noted, which signifies possible anisotropy in Titan's topography. The topographic information thus gleaned can be used to constrain landscape evolution modeling to infer the dominant surface processes that sculpt the landscape of Titan.