Constraints on Titan’s topography through fractal analysis of shorelines

Sharma, P.; Byrne, Shane

doi:10.1016/j.icarus.2010.04.023

Cited by 23 publications

(27 citation statements)

References 34 publications

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“…This is similar to the classic 4/3 scaling Mandelbrot conjectured for the frontiers of Brownian islands (Mandelbrot, 1983) and since proven by Lawler et al (2000). This same value is also found from the perimeter-area relationship for lakes on Earth (Cael & Seekell, 2016) and Titan (Sharma & Byrne, 2010) and also is the average value for coastlines around the world (Mandelbrot, 1975). The NWI wetlands also show a small second peak around D = 1.5 not captured by the TDI (Figure S5).…”

Section: 1029/2018gl079094supporting

confidence: 86%

Wetlandscape Fractal Topography

Bertassello

Rao

Jawitz

et al. 2018

Geophysical Research Letters

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Natural wetlands are ecological, biogeochemical, and hydrological hot spots yet continue to disappear under human pressure. Their shapes and sizes control their hydroecological functions. We propose that elevation data can be used to delineate potential wetlands and that the (statistical) distributions of potential wetlands should be identical to the distributions of actual wetlands. We compare the shape and size distributions of wetlands reported in the National Wetland Inventory with those of potential wetlands identified using a topographic depression identification model. We estimated area and perimeter distributions as well as shoreline fractal dimension in six contrasting locations in the United States. Pareto distributions described the tails of these distributions, with similar slopes for both model and data. The shape of shorelines was also similar, and their fractal dimension clustered around D = 4/3, a pervasive value in nature. We also analyzed the entire wetland inventory data set for the conterminous United States (~20 million wetlands) for reference and found the statistics to be invariant across scales. Our results demonstrate that a simple topographic model can identify most reported wetlands as well as potential wetlands missing from the inventory. These findings could inform strategic surveys and the conservation of wetlandscapes.

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Section: 1029/2018gl079094supporting

confidence: 86%

Wetlandscape Fractal Topography

Bertassello

Rao

Jawitz

et al. 2018

Geophysical Research Letters

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“…One of the first and simplest applications of fractal analysis to natural geomorphic phenomena was the analysis of the British coastline by Mandelbrot [1967]. In this and many subsequent investigations [e.g., Phillips , 1986; Jiang and Plotnick , 1998; Schwimmer , 2008; Sharma and Byrne , 2008], researchers have noticed that coastlines are often found to follow an allometric relationship: where L ( s ) is the observed length of a section of coastline using a measure stick of length s , and is the fractal dimension of the coastline. We have observed an allometric relationship for the extended smooth region of Ontario's eastern shoreline using the divider method defined in [ Klinkenberg and Goodchild , 2006].…”

Section: Model Validationmentioning

confidence: 99%

Bathymetry and absorptivity of Titan's Ontario Lacus

et al. 2010

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[1] Ontario Lacus is the largest and best characterized lake in Titan's south polar region. In June and July 2009, the Cassini RADAR acquired its first Synthetic Aperture Radar (SAR) images of the area. Together with closest approach altimetry acquired in December 2008, these observations provide a unique opportunity to study the lake's nearshore bathymetry and complex refractive properties. Average radar backscatter is observed to decrease exponentially with distance from the local shoreline. This behavior is consistent with attenuation through a deepening layer of liquid and, if local topography is known, can be used to derive absorptive dielectric properties. Accordingly, we estimate nearshore topography from a radar altimetry profile that intersects the shoreline on the East and West sides of the lake. We then analyze SAR backscatter in these regions to determine the imaginary component of the liquid's complex index of refraction (). The derived value, = (6.1 −1.3 +1.7 ) × 10 −4 , corresponds to a loss tangent of tan D = (9.2 −2.0 +2.5 ) × 10 −4 and is consistent with a composition dominated by liquid hydrocarbons. This value can be used to test compositional models once the microwave optical properties of candidate materials have been measured. In areas that do not intersect altimetry profiles, relative slopes can be calculated assuming the index of refraction is constant throughout the liquid. Accordingly, we construct a coarse bathymetry map for the nearshore region by measuring bathymetric slopes for eleven additional areas around the lake. These slopes vary by a factor of ∼5 and correlate well with observed shoreline morphologies.

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“…Fractal dimension is independent of the dataset resolution since a fractal shape by definition is scale‐invariant (as long as we do not attempt to map features smaller than the resolution). As the results of our previous study [ Sharma and Byrne , 2010] indicated, both the terrestrial and Titanian lake shorelines are well described as fractal shapes.…”

Section: Statistical Parametersmentioning

confidence: 70%

“…We performed some initial processing on the backscatter data, including contrast stretching and mosaicking. Next, we manually outlined the shorelines of these example terrestrial lakes using the same methods and criteria employed to map Titan's shorelines [ Sharma and Byrne , 2010]. Before carrying out the fractal analysis, we converted these shorelines from latitude and longitude to stereographic coordinates centered on each of the lakes.…”

Section: Analysis Of Terrestrial Analogsmentioning

confidence: 99%

“…[4] Our previous study of Titan's north polar shorelines revealed them to be closely approximated by fractal shapes [Sharma and Byrne, 2010], a property also demonstrated by terrestrial shorelines [Mandelbrot, 1967;Richardson, 1961;Sapoval et al, 2004], i.e., measured lengths of these shorelines increases, as the measuring scale decreases, because smaller measuring scales are sensitive to smaller features of the shoreline. We performed a similar fractal analysis on terrestrial lake shorelines and created additional statistical descriptors of shoreline morphology in order to compare them to Titan's lakes.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of Titan's north polar lakes with terrestrial analogs

Sharma

Byrne

2011

Geophys. Res. Lett.

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.[1] The discovery of hydrocarbon lakes in the polar regions of Titan offers a unique opportunity to compare terrestrial lakes with those in an extraterrestrial setting. We selected 114 terrestrial lakes formed by different processes as analogs for comparison with the 190 Titanian lakes that we had mapped in our previous study. Using the Shuttle Radar Topography Mission (SRTM) C-band backscatter data and the SRTM Water Body Data (SWBD), we carried out an assessment of manual mapping versus existing automated mapping techniques, and found the automated techniques to produce as good representations of the lake shorelines as the manual mapping in the terrestrial dataset. We then calculated and compared terrestrial and Titanian shoreline statistical parameters including fractal dimension, shoreline development index and an elongation index. We found different lake generation mechanisms on Earth produce "statistically different" shorelines. However, we cannot identify any one mechanism or set of mechanisms to be responsible for forming the depressions enclosing the lakes on Titan, on the basis of our statistical analyses.

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Constraints on Titan’s topography through fractal analysis of shorelines

Cited by 23 publications

References 34 publications

Wetlandscape Fractal Topography

Wetlandscape Fractal Topography

Bathymetry and absorptivity of Titan's Ontario Lacus

Comparison of Titan's north polar lakes with terrestrial analogs

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