Remotely sensed dune celerity and sand flux measurements of the world’s fastest barchans (Bodélé, Chad)
1 IntroductionMeasuring dune celerity and sand flux is a crucial step towards understanding aeolian systems, which represent some
of the most dynamic geomorphic environments on our planet. Traditionally, such measurements have been carried
out by (a) geodetic field surveys and/or long term monitoring of stakes set out in the (inter)dunes (e.g., Stokes et
al., 1999; Bristow and Lancaster, 2004), (b) short term sand trap and anemometer studies (e.g., Greeley et al., 1996)
or more recently (c) the use of saltation flux impact responders (Baas, 2004). We here propose an approach for
measuring sand flux using pairs of high resolution optical satellite images. Although remote sensing has been used to
study dune migration before (e.g., Crippen and Blom, 1991; Brown and Arbogast, 1999; Yao et al.,
2007), our method is new in that it is fully automated and because dune celerity is combined with a
digital elevation model (DEM) to determine sand flux. To detect dune migration we use the software
package COSI-Corr, which stands for Co-registration of Optically Sensed Images and Correlation and
was developed for the purpose of detecting surface deformation caused by earthquakes (Leprince et
al., 2007, 2008). Because co-seismic deformation is typically on the order of centimeters to meters,
their detection requires sub-pixel accuracy and precision, which can only be achieved by carefully
projecting and resampling the two satellite images (‘before’ and ‘after’) onto a common reference frame.
COSI-Corr currently performs this operation for SPOT, ASTER and QuickBird imagery as well as
aerial photographs. ASTER is the only one of these formats that is freely available to the research
community while routinely producing DEMs and these are the main reasons why we have chosen it
over the higher resolution alternatives. We use pairs of the 15 meter resolution ASTER nadir near
infrared band (V3N) with COSI-Corr to determine dune celerity. We employ all three 15 m visible and
infrared bands (VNIR) to produce colour composites that allow us to discriminate between dunes
that have different chemical compositions. Finally we employ the DEM to calculate dune volumes.
ASTER’s nadir-looking V3N and backward-looking V3B sensors form a stereographic pair that allows the
calculation of DEMs with a spatial resolution of 30m and a vertical precision of 13m (Cuartero et al.,
2005).
We have tested our approach on barchan dunes because they are better suited to this kind of study than more
complex dunes as they completely overturn over relatively short time spans and often lack second order features that
might otherwise ‘confuse’ the image correlation algorithm. We chose the Bodélé depression of northern Chad
(Figure 1) as our test area for two reasons. First, the Bodélé is characterised by extremely strong
north-easterly winds (Washington et al., 2006) ensuring easily detectable dune migration over relatively
short time spans. Second, two types of dunes exist in the area (Figure 2), making it a particularly
interesting target for understanding the mechanics of dune migration. The Bodélé is a subbasin of
Palaeolake Megachad (Drake and Bristow, 2006) and is covered by lacustrine diatomite (Washington et
al., 2006; Warren et al., 2007). Dunes around the edges of the depression consist mostly of quartz
whereas dunes in the center also contain diatomite pellets (Warren et al., 2007). The low density of the
latter futher increases dune celerity and the false colour contrast between the blue dunes and the
white interdunes facilitates their identification (Figure 2.c,d). The combination of readily eroded lake
sediments and strong winds make the Bodélé depression the ‘dustiest place on Earth’ (Giles, 2005)
and the dune sand flux rate may well be related to the amount of dust produced (Chappell et al.,
2008).
In the following paragraphs, we will demonstrate that COSI-Corr is very successful at orthorectifying otherwise relatively imprecise ASTER imagery; illustrate that ASTER imagery orthorectified by COSI-Corr accurately shows dune migration over relatively short timescales; explain how to automatically extract displacement maps and display them as vector fields; show how the calculations break down when the time interval between two images is too long; confirm that dune celerities are highest in winter when winds are strongest; introduce an algorithm for using the displacement field to extract a base level from ASTER-generated DEMs, which can then be used to calculate dune volumes; calculate sand flux for some very large diatomite barchans in the eastern and western Bodélé; show that the dunes move faster and have higher sand flux rates than than any others that have been reported in the literature; and conclude with some proposals for future research.
2 Orthorectification, correlation, and dune migrationWe will first consider four sets of overlapping ASTER images (using band V3N) from the eastern part
of the Bodélé depression, taken in 2000, 2005, 2006 and 2007 (Figure 1). Because the footprints of
these images differ (causing parallax errors), and because of uncertainties in the satellite orbit and
optics, it is not possible to directly compare the raw images. COSI-Corr provides a series of tools to
precisely coregister and resample two images onto a common reference frame, correcting for all of the
above effects. This requires the identification of a number of tie points that have not moved during the
time interval between two images. In the Bodélé, such tie points are abundant in the form of patches
of massive diatomite crust that can be easily identified as intricately shaped white patterns (Figure
2.a,b). Using the 2000-2007 image pair as an example, it is possible to see, with the naked eye, how
small barchan dunes move significantly faster in a southwesterly direction than larger ones do (Figure
2.a-d).
After the orthorectification and resampling step, the two images are fed into the correlation engine. Using a square sliding window, COSI-Corr employs a Fourier algorithm to calculate the relative N-S and E-W displacement fields by maximising their cross-correlation (Leprince et al., 2007). We used a variable window size of 64 to 32 pixels wide with a step size of two pixels. This causes the output resolution of the displacement field to be 30m, i.e. half of the ASTER VNIR system resolution, but identical to the DEMs generated by combining the satellite’s stereographic V3N-V3B pair. This common resolution facilitates the calculation of sand flux, as discussed below. The N-S and E-W displacement maps can be visualised as a vector field or converted to a Euclidean distance map (Figure 2.d). COSI-Corr successfully detects dune displacements of as little as 5 m over a period of only one month (Figure 2.e). The precision of the correlation is ± 3 m (1 σ), as determined from the residual displacement over stable ground. The signal-to-noise ratio (as defined by Leprince et al., 2007; Equation 43) of the displacement map improves over somewhat longer time scales of 15 months (2005-2007), but then decreases again for even longer time scales of 6.5 years (2000-2007; Figure 2.f,g). The reason for this is that dune shapes and patterns change over such time scales as small dunes overtake larger ones, are shed from them or absorbed by them, thus complicating the correlation process. Two image displacement maps can be directly compared on a pixel-by-pixel basis because they are projected onto a common reference frame. This reveals that dune celerities between December 2006 and January 2007 are 2.5 times faster than between October 2005 and January 2007, consistent with the higher wind speeds of the Bodélé ‘Low Level Jet’ during winter (Warren et al., 2007).
3 Measuring sand fluxIn this section, we will study the diatomite area of the Bodélé depression, where barchans reach heights of 50m, well
above the detection limit of ASTER DEMs (Figure 3). In order to calculate dune volumes, the ‘base level’ must be
subtracted from the raw DEM. Rather than doing this by hand, we use the displacement map by selecting all
pixels with a displacement less than 0.1m and interpolating their elevations (Figure 3.b). Because the
Bodélé depression is very flat, this creates a smooth and even surface. We estimated the precision of
the dune elevation map as 9 m (RMSE) by measuring the difference between two different DEMs
that were closely spaced in time. Sand flux is defined as the volume (or mass) of dune sand passing
through a line of unit length perpendicular to the wind direction per unit time. For a sand column of
width w and height h, moving over a distance d in time t, the volume is given by h×w×d, so the
sand flux equals h×w×d/(w×t) = h×d/t. In other words, the sand flux of any given location on a
sand dune is calculated by multiplying its elevation above ‘base level’ with the celerity at the same
location.
We follow the recommendations of Ahmedou et al. (2007) and consider a number of possible definitions for the
dune sand flux. The first definition is the flux measured at the summit of a dune (Q∘), which is estimated by simply
multiplying dune height with dune celerity. Although Q∘ in itself is not a particularly interesting quantity, it is very
useful in that it is an objective point of comparison with other dune fields. We compared the dune celerity
of 75 large diatomite dunes from the eastern and western Bodélé with barchan fields in Mauritania
(Ahmedou et al., 2007), California (Long and Sharp, 1964), and Saudi Arabia (Fryberger et al., 1984)
(Figure 4.e). Not only are the Bodélé dunes much larger than these other active barchans, they are
faster too, with Q∘>200m3/m/yr. There appears to be no difference between the eastern and the
western parts of the Bodélé, although this is hard to assess because of the significant amount of scatter
in the results, which is caused by the limited precision of the DEM and by noise in the correlation
results.
A second and arguably more relevant definition of dune sand flux is the average flux of all the dunes in a certain
area (Qdune). We calculated this by selecting all the pixels above 5 meters height and averaging the
corresponding sand flux values. The results are 76 and 99 m3/m/yr for the western and eastern diatomite
dune areas, respectively. To quantify the spatial variability of these estimates, we divided the dune
areas into 10 equal parts and calculated the average dune sand flux for each of them. The resulting
Qdune-values vary from 30 to 190 m3/m/yr, with an average and median value of 101 m3/m/yr, a standard
deviation of 50m3/m/yr and an interquartile range of 55-140m3/m/yr. This substantial scatter at
least partly reflects real variations of the dune flux in different parts of the dune field. Chappell et
al. (2008), for example, measured the total sand flux of three Bodélé dunes by a conventional sand
trap and anemometer study and found a similar degree of variability both within and between the
dunes.
Finally, one can simply average the contribution of sand dunes to the sand flux of the entire area (dunes +
interdunes), yielding the bulk transport rate (Qfield; Ahmedou et al., 2007). We measured values of 24 and 29
m3/m/yr for the eastern and western Bodélé, respectively. These values are, of course, strongly dependent on which
area is chosen for the analysis. We did not attempt to quantify the variability of the bulk sand flux, as some of the
subregions would not contain enough dunes to calculate a meaningful Qfield. Comparison with a similar analysis in
Mauritania (2.5m3/m/yr; Ahmedou et al, 2007) confirms that sand flux in the Bodélé is an order of magnitude
higher than in other deserts.
Chappell et al. (2008) measured integrated horizontal saltation mass flux values of between 57 and 12,500 tons/m/yr for the dunes and interdunes of the eastern Bodélé, with averages of 1350-3800 tons/m/yr. Using a bulk density for the diatomite dunes of 0.9 g/cm3 (Chappell et al., 2008) yields averaged volume fluxes of 1500-4200 m3/m/yr. Therefore, the flux associated with dune migration is ~10% of the saltation flux, consistent with earlier experiments (Ahmedou et al., 2007).
4 Conclusions and outlookCOSI-Corr is an exciting new tool for the remote sensing of changes in Earth surface form. We have demonstrated the first application of this tool to aeolian geomorphology. We presented a case study of the Bodélé depression of northern Chad, successfully measuring dune celerity over a time interval of as little as one month. Most importantly, we have outlined and demonstrated, for the first time, a method for measuring sand flux from satellite images. We do this by combining the displacement map with a high resolution DEM calculated from the same set of satellite images. The displacement map is used to detect the interdune areas, which define the ‘base level’ that is subtracted from the topography to yield dune volumes. The advantages of this remote sensing approach to field measurements of sand flux are obvious. Remote sensing is cheaper, can be applied to larger areas and over longer time scales than field measurements, and allows us to study otherwise inaccessible places, independent of logistic or political constraints. Because of the relatively low resolution of ASTER imagery (15m), the method currently only works for the largest barchans in our study area. Applying our algorithm to the higher resolution SPOT (2.5-5m) and QuickBird (0.6-2.4m) systems will significantly improve the accuracy and precision of the method and allow us, for example, to compare the sand flux of the diatomite and quartz sand dune areas within the Bodélé area. As new satellite systems come online, the possibilities will further increase, opening tremendous opportunities for aeolian research.
AcknowledgmentsWe would like to thank Chris Knell (UCL Geography) for granting access to the Chorley Institute Linux cluster; Charlie Bristow for discussions and suggestions; Sebastien Leprince for promptly replying to COSI-Corr enquiries; the USGS for free access to the ASTER image library under the LPDAAC scheme; and two reviewers for constructive comments.
References
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