And so it would seem that in no time at all, I’m nearly at the halfway point of my time as an intern at the Neish lab! As befits such an occasion, I’ll be discussing in this post my goals for the remainder of my internship. This will be divided into 2 sections: a ‘summary’ section of broad, overarching goals, and a more comprehensive section containing detailed goals and methods for achieving such. Of the latter, most of these were suggested during discussions with Mike, while a couple are things that I came up with, and are correspondingly of a more speculative nature (both in terms of the utility in attempting them at all, and in terms of their expected results).

 

I) BROAD GOALS (month-by-month) 

End of July:

a) Continue work in 2D characterization methods for roughness parameters -such as the RMS Slope and Hurst Exponent- and applying these methods to new COTM LiDaR datasets, such as those from Highway Flow and Kings Bowl [2 weeks].

b) Classify and map the mushroom/popup features postulated by Mike, using ArcGIS [2 weeks].

c) Be adequately prepared for the field season, ie. bought all relevant supplies/clothing/etc, prepare laminated field reference maps for all sites of interest (need to formulate field plans with both Mike/Alexandra (in Kings Bowl) and Raymond (stereophotography) to determine which areas to create maps for), read “Volcanic Textures” and refresh mineralogy/petrology geology knowledge base. [ongoing].

 

End of August:

a) Conduct a systematic, comprehensive analysis of different implementations of roughness algorithms.

b) Design an Adaptive Bandpass Gaussian Filter to pre-process DEM’s before running of roughness algorithms

c) Organize all data from COTM fieldwork (ie. assisting Gavin and Mike), and transferred all such data into formats allowing for subsequent analysis.

e) Complete a report/poster summarizing the work completed over the course of the internship.

f) Have rough drafts of 1 or 2 LPSC abstracts.

 

II) DETAILED FINAL GOALS

–Roughness Algorithms: Show and compare the results achieved by choosing to apply: a) 1D profiling vs. 2D areal algorithm, b) various detrending methods (none (control) vs. subtraction of the best-fitting local plane vs. global Gaussian filtration), c) methods to alleviate anisotropic effects (ie. Taking of profiles in orthogonal directions (4-connected), as opposed to orthogonal directions plus diagonals (8-connected), d) interleaving* vs. no interleaving when calculating variograms, and e) different 2D cell sizes (analogous to different 1D profile lengths) for a sample COTM LiDaR DEM. On the basis of analyzing these methods, determine an optimal roughness algorithm (some choice of these various factors), and apply it for all COTM LiDaR DEM datasets, comparing the variability of the roughness parameters calculated at different field sites at COTM. Classify the time required to perform each of these methods, with respect to the pixel size dimensions of the DEM in question. Determine if the fractal dimension, as determined by applying a moving-window (for each pixel) box-counting method, is similar to that determined via variogram analysis.

-Roughness/Waviness Differentiation (Pre-processing via Adaptive Bandpass Gaussian Filtration): Design an adaptive bandpass Gaussian filter with central transmission frequency centred at that of a given radar wavelength, such that transmission attenuates with respect to wavelengths increasing or decreasing away from this central wavelength. The filter should be adaptive in the sense that it automatically adapting to the particular dataset used, based on only a few key parameters such as data resolution and the scale(s) of interest, and should consist of the superposition of a Gaussian high-pass filter (to filter out long-wavelength waviness/topography) and a Gaussian low-pass filter (to filter out short-wavelength roughness information of sufficiently small size that radar EM wave scattering would not be responsive to).

–Mushroom Mapping: Create shapefiles of both mushroom border polygons and centroid points, in addition to recording the longitudes/latitudes of their centroids, individual areas/perimeters and basic statistics regarding the entire mushroom population. Determine a minimum/maximum size threshold, below/above which mushrooms will not be considered. Create point density maps of the mushrooms, in addition to calculating histograms for the distance distribution of mushrooms with respect to the linear fissure. Compare the mean CPR + roughness parameters (eg. RMS height) to their surroundings, to see if they are detectable via either. Compare the RMS heights of mushrooms with their heights determined from ArcGIS (as defined by the vertical distance from their rims to their highest points).

–Fine-scale Roughness Characterization of Raymond’s Stereocamera Orthophotos: Determine optimal methods for creating disparity (and thus 3D distance) maps from orthophoto pairs, then characterize the typical 3D sizes of all rocks within these ‘mini-DEM’s’ and calculate statistics. For instance, the standard deviation of the heights within individual rocks could represent the ‘characteristic height’ of such rocks. Have discussions with Raymond pertaining to field goals for stereophotography, methodology for the standardization of orthophoto acquisition, and desired data analysis of orthophotos.

-Organization: Clean-up/comment MATLAB code, such that others may apply them without difficulty.

 

*For a 1D-profile, interleaving would be implemented if, for instance, for a 5m long profile for which step sizes (lag) of 1cm were to be investigated, instead of just analyzing the deviations between 0cm/10cm, 10cm/20cm, 20cm/30cm, …, the deviations between 1cm/11cm, 11cm/21cm, 12cm/22cm, … ; 3cm/13cm, 13cm/23cm, 23cm/33cm, … ; …… were also calculated. In this particular example, interleaving enhances tenfold the quantity of statistical roughness information – information that would not have otherwise been used. Of course, assuming the Hurst exponent of the region in question is relatively low, there is most likely a significant degree of correlation between adjacent pixels, such that our roughness estimates will not in fact be 10 times more accurate. Nonetheless, the low degree of fit amongst many of the variograms I have calculated implies that more measurements may improve their accuracy, by removing the bias in non-interleaved profiles towards points at particular positions. The largest concern the new technique would present is likely computation time, and thus I think it prudent to investigate whether the improvement in accuracy (if any) is worth increased computational expense.

 

III) OTHER COMMENTS 

I have some lingering questions regarding the big picture, though they don’t necessarily need to be addressed now, and probably won’t be until after I have completed the above tasks.

-I am curious as to what the geomorphological questions at COTM are that we intend to elucidate. For instance, Morris’ paper “Roughness of Hawaiian Volcanic Terrains” (Morris et. al. 2008) claims in its conclusion that: “We anticipate detailed analysis of high-resolution images and DEMs derived from stereo imaging of young volcanic terrains on Mars will be highly conducive to studies of the spatial and temporal relationships among lava flows.” Are we able to answer these kinds of questions at COTM? And if so, how?

-Assuming that I am able to attain 2D areal roughness maps over a variety of scales, and hence determine the (fractal) scale-dependence of roughness, what kinds of questions will we be able to answer regarding spatio-temporal relationships among lava flows at COTM? Morris et. al. appear to use the roughness for a fairly specific purpose: elucidating the emplacement history and characteristics of their Hawaiian lava flows, and distinguishing/differentiating the petrogenesis of the various flows (amongst which they make comparisons of 6 flows). Is such a flow-based comparison the relevant benefit at COTM as well, or is it more about being able to make comparisons with lunar impact melt flows, or potentially even other flow features on other planetary bodies? Or is the issue of greater relevance the determination of the size scales at which breakpoints in the variograms at specific field sites occur, offering the ability to determine the spatial scales over which different geomorphic processes are at play?