ESurfEarth Surface DynamicsESurfEarth Surf. Dynam.2196-632XCopernicus PublicationsGöttingen, Germany10.5194/esurf-6-971-2018Measuring decadal vertical land-level
changes from SRTM-C (2000) and TanDEM-X (∼2015) in the south-central AndesVertical land-level change from SRTM-C and TanDEM-XPurintonBenjaminhttps://orcid.org/0000-0001-8504-8115BookhagenBodohttps://orcid.org/0000-0003-1323-6453Institute of Earth and Environmental Science, Universität Potsdam, Potsdam, GermanyBen Purinton (purinton@uni-potsdam.de)30October20186497198720June20186July201817September201822October2018This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://esurf.copernicus.org/articles/6/971/2018/esurf-6-971-2018.htmlThe full text article is available as a PDF file from https://esurf.copernicus.org/articles/6/971/2018/esurf-6-971-2018.pdf
In the arctic and high mountains it is common to measure vertical changes of
ice sheets and glaciers via digital elevation model (DEM) differencing. This
requires the signal of change to outweigh the noise associated with the
datasets. Excluding large landslides, on the ice-free earth the land-level change
is smaller in vertical magnitude and thus requires more accurate DEMs for
differencing and identification of change. Previously, this has required
meter to submeter data at small spatial scales. Following careful
corrections, we are able to measure land-level changes in gravel-bed channels
and steep hillslopes in the south-central Andes using the SRTM-C (collected
in 2000) and the TanDEM-X (collected from 2010 to 2015) near-global 12–30 m
DEMs. Long-standing errors in the SRTM-C are corrected using the TanDEM-X as
a control surface and applying cosine-fit co-registration to remove
∼1/10 pixel (∼3 m) shifts, fast Fourier transform (FFT) and filtering to
remove SRTM-C short- and long-wavelength stripes, and blocked shifting to
remove remaining complex biases. The datasets are then differenced and
outlier pixels are identified as a potential signal for the case of gravel-bed
channels and hillslopes. We are able to identify signals of incision and
aggradation (with magnitudes down to ∼3 m in the best case) in two
>100 km river reaches, with increased geomorphic activity downstream of
knickpoints. Anthropogenic gravel excavation and piling is prominently
measured, with magnitudes exceeding ±5 m (up to >10 m for large
piles). These values correspond to conservative average rates of 0.2 to
>0.5 m yr-1 for vertical changes in gravel-bed rivers. For
hillslopes, since we require stricter cutoffs for noise, we are only able to
identify one major landslide in the study area with a deposit volume of
16±0.15×106 m3. Additional signals of change can be
garnered from TanDEM-X auxiliary layers; however, these are more difficult to
quantify. The methods presented can be extended to any region of the world
with SRTM-C and TanDEM-X coverage where vertical land-level changes are of
interest, with the caveat that remaining vertical uncertainties in primarily
the SRTM-C limit detection in steep and complex topography.
Introduction
Geodynamic and geomorphological processes operating at different timescales
result in vertical change (herein dh) on the earth's surface. In the
cryosphere, dh studies use repeat surveys or digital elevation model (DEM)
differencing on annual to sub-annual time steps
e.g.,. Changes to snow and ice occur most rapidly (aside from
landslides), but dh measurement outside of the cryosphere also provide
aggradation and incision monitoring for rivers
e.g.,, volumes of landslides and extruded
lava e.g.,, and
earthquake displacements . Large-scale monitoring of
dh on soil, rock, and unconsolidated sediment is an elusive problem
requiring signals that outweigh the noise in collection methods and resulting datasets.
Vertical accuracies for modern gridded spaceborne DEMs are on the order of
2–8 m in mountainous regions, though significantly worse on steepening
slopes e.g.,. Using DEMs from
sources like the Advanced Spaceborne Thermal Emission and Reflection
Radiometer (ASTER; ) with higher uncertainties is
acceptable for monitoring glaciers and ice sheets e.g.,,
where dh between even sub-annual time steps can be tens to hundreds of
meters over areas of many square kilometers. On the other hand, dh of soil,
rock, and unconsolidated sediment are often at the centimeter to meter scale
and far more localized over up to a few hundred to thousand square meters.
Due to these limitations, previous studies relied on intensive mapping from
aerial photos e.g.,, sparse cross sections with
large temporal spans e.g.,, or – more
recently – meter to submeter topographic data from lidar or photogrammetric
point clouds e.g., or select optical satellites with
submeter resolution like Pleiades and WorldView
e.g.,. Despite recent
advances in meter to submeter lidar, satellite, and unmanned aerial vehicle
data availability , these remain limited in spatial
and temporal coverage, and sometimes prohibitively expensive. Coarser gridded
DEMs from radar and optical spaceborne sensors remain the best and often the
only option in large or remote areas.
The publicly available Shuttle Radar Topography Mission (SRTM) DEM is an
earth snapshot from its 10-day collection aboard the Space Shuttle Endeavour in
February 2000. The mission produced an interferometric synthetic aperture
radar (InSAR) DEM from C-band (5.6 cm wavelength) radar for 80 % of earth's
landmasses from typically 2–3 ascending and descending swaths
. The SRTM-C has seen numerous succeeding releases and void
filling e.g.,. We use the most recent
floating-point-reprocessed 1 arcsec (∼30 m) NASADEM, taking only the
non-void-filled original SRTM-C tiles (herein SRTM-C;
; found in the “srtmOnly” directories under
https://e4ftl01.cr.usgs.gov/provisional/MEaSUREs/NASADEM/, last access: 26 October 2018).
The TanDEM-X 0.4 and 1 arcsec (∼12 and ∼30 m) DEM
released in 2016 – here received through scientific German Aerospace Center (DLR) proposals –
is the next generation of radar-derived
global topography following the SRTM. The TanDEM-X, covering 97 % of earth's
landmasses, was generated by semi-automated processing and stacking of
>470000 ascending and descending X-band (3.1 cm wavelength) TerraSAR-X and TanDEM-X
satellite bistatic scenes collected from December 2010 to January 2015
. As elevations are averaged
between scenes, we take the date of the TanDEM-X as January 2015, thus
providing a 15-year time step of dh between SRTM-C and TanDEM-X. Using the
latest possible date for TanDEM-X elevations means that rates of change are
conservative minimum values.
In this submission we discuss the errors associated with each of these
datasets and the corrections applied to mitigate uncertainties in their
differencing for dh detection outside of the cryosphere. This is therefore
a data quality and methods-focused study. Geomorphic change detection is
applied via correction and differencing of the TanDEM-X and SRTM-C over the
south-central Andes in northwestern Argentina (Fig. ) to identify
and measure areas of dh in gravel-bed channels specifically and then across
the landscape. Here, steep gradients in elevation (∼1–4 km),
rainfall (∼0.1–1 m yr-1), and vegetation (subtropical forests
and croplands to arid, succulent-covered slopes) cause high rates of mass
transfer ,
further influenced by climate change and anthropogenic modification
(gravel mining and weirs). To conclude, we discuss caveats driven by
remaining uncertainties prevalent in spaceborne DEMs collected over complex topography.
Spaceborne DEM errors
classify spaceborne DEM errors into speckle noise,
stripe noise, absolute bias, and tree height bias. We divide this further for
the case of SRTM-C and TanDEM-X (both radar DEMs) into (i) sensor specific
related to radar and spacecraft collection and (ii) terrain specific related
to land-surface cover and topographic complexity. We do not consider DEMs
from optical sensors such as ASTER and the
Advanced Land Observing Satellite (ALOS; ), which have
well documented errors e.g., and perform worse than radar, with vertical
accuracies >5 m (1σ) and persistent high-frequency artifacts
. Additionally, a dearth of cloud-free,
high-quality ASTER imagery covering the study area precludes the automated
DEM generation of and regression techniques of
. On the other hand, within the study area, the
SRTM-C and TanDEM-X both exhibit vertical uncertainties <3.5 m
and also have an appropriately long time
difference for vertical land-level change detection. Auxiliary rasters
including the water indication mask (WAM), height error mask (HEM),
consistency mask (COM), and coverage map (COV) delivered with TanDEM-X
allow enhanced understanding of DEM quality (see
Sect. S1 in the Supplement).
Overview of study area in NW Argentina with (a) elevation,
(b) rainfall (Tropical Rainfall Measurement Mission 12-year average;
TRMM2B31; ), and (c) vegetation (MODIS
product 13C1 enhanced vegetation index 14-year average; MODIS EVI;
), where lower, brown (higher, green) values
represent sparse (dense) vegetation. Note strong east–west gradients in all
three maps. The white watershed boundary delineates the internally drained
Altiplano–Puna Plateau. The gray line in (b) and (c)
indicates the 2000 m contour line. The yellow patches in (c) are
areas identified in the TanDEM-X water indication mask (WAM) as having low
amplitude and/or low coherence. These patches correspond to salt flat (salar)
regions on the plateau, water bodies (e.g., reservoirs in the low-elevation
areas), steep and vegetated areas (DEM error), and other zones of coherence
loss, such as the dunes identified. Inset boxes in (c) indicate
locations of dh map-view Figs. –, with the TanDEM-X tile
boundary in green. Note anthropogenic tampering of natural gravel-bed
channels (Río Grande and Río Toro) with downstream flow diversion
(weirs) and gravel mining activity near the populous cities of Salta and
Jujuy.
Random, or speckle, error caused by instrument thermal noise and localized
de-correlation is the primary sensor bias for radar .
These localized, small magnitude errors reduce with increasing looks used in
the final mosaic. Speckle presents a greater issue in SRTM-C given the
maximum three swaths at lower latitudes . Such noise is
expected to be minimal in the TanDEM-X, with average coverage in our study
area of 7 ascending and descending scenes and up to 14 in many steep
areas (Fig. S1 in the Supplement). Smoothing data prior to and after phase unwrapping (e.g.,
multi-looking, adaptive filters, or down-sampling) can further reduce
speckle. The SRTM-C raw resolution of ∼30 m is similar to the
final 1 arcsec product, though, due to interferogram smoothing to reduce
noise, the estimated true ground resolution of the final product is 45–60 m
. This may be
improved in the newly released data , but this
remains to be tested. Multi-looking of 4×5 pixels of raw radar returns
(resolution ∼3.3 m) was used in the case of TanDEM-X to
generate a final 0.4 arcsec (∼12 m) product, thus significantly
smoothing and reducing speckle .
Besides a small geolocation error expected in both DEMs from instrument
uncertainties, the SRTM-C has a number of spacecraft-specific biases,
manifested in short- and long-wavelength striping .
The short-wavelength (∼0.5–1 km, magnitudes
typically <0.5 m) stripes are related to jitter in the antenna mast caused
by the periodic firing of shuttle attitude thrusters .
Longer-wavelength errors with magnitudes >1 m are caused by individual swath
tilts and form complex undulating patterns over ∼100 km
distances . TanDEM-X satellite
biases can be found in slight tilting of individual TerraSAR-X and TanDEM-X
scenes e.g.,, though these tilts were removed
during stacking in the end product . The careful
monitoring and control maintained over flight geometry, in addition to
post-processing to remove tilts using ICESat (Ice, Cloud, and land Elevation
Satellite; ), restricts most of the TanDEM-X
uncertainty to the second category of terrain-specific error .
Land-surface cover plays a key role in modulating radar returns. TanDEM
X-band and SRTM C-band radar have different penetration depths in dense
vegetation and
snow and ice , leading to different height
returns. We note this important caveat but are able to ignore it for our
particular study question (land-level change of bare material) and area (only
partial vegetation and no permanent snow and ice). Subtropical vegetation in
our study area does allow some exploration of the effect on dh; however, we
find no clear relation (see Sect. S2). In any case, vegetation
differences are expected to be less significant than for optical data, which
returns only the canopy heights e.g.,. Both DEMs
have major inconsistencies and speckle over water bodies, wet salt flats, and
deserts caused by de-correlation, variable reflectance, and/or weak
backscatter of the radar signal . For the SRTM-C, these areas are
largely voids anyway, and for TanDEM-X the WAM raster provides information on
coherence and amplitude for each pixel to identify these untrustworthy
measurements (Fig. c).
Remaining errors in the SRTM-C and TanDEM-X are related to terrain
characteristics (see Sect. S2). This is the result of topographic
complexity below the resolution of the sensor, radar geometry considerations
(layover, foreshortening, and shadowing), and interferometric phase
unwrapping errors, all most pronounced in steep mountains. Such terrain
biases are demonstrated in the SRTM-C with elevation ,
slope and aspect , and resolution
(manifested in curvature) , and in the TanDEM-X with
only slope . Terrain
slope – also related to relief (Fig. S7) – is the primary cause of error in
any DEM, demonstrated in the division of vertical uncertainties for most DEMs
into slope bins e.g.,. Slope-dependent errors
may be reduced with finer-resolution data and increased look angles for
mosaicking, as in the case of TanDEM-X, but these uncertainties are expected
to remain as the most prevalent cause of error in any spaceborne DEM.
With this framework for understanding the potential error sources in the
SRTM-C and TanDEM-X, it is possible to correct one dataset to another in a
multistep processing chain e.g., allowing
dh identification and measurement with greater certainty.
Methods
Given the excellent agreement with differential GPS globally
and in the study area
along with the minimal errors associated with
orbital characteristics, we consider the TanDEM-X DEM as our reference
surface in order to correct the more problematic SRTM-C. During correction,
we do not apply any speckle reduction (e.g., via an adaptive filter as in
), as we are interested in raw elevation values and
not a smoothed DEM. For the SRTM-C we select the non-void-filled NASADEM data
so as not to include any auxiliary elevation measurements from, for instance,
ASTER . Importantly, both DEMs are referenced to
the WGS84 ellipsoid vertical datum, whereas previous SRTM-C releases have
been referenced to the EGM96 geoid , thus requiring a
geoid-adjustment step introducing additional uncertainties prior to comparison.
For correction and differencing we use the 0.4 arcsec TanDEM-X that we
bilinearly resampled to 1 arcsec to match the raw resolution of the SRTM-C.
notes that the delivered TanDEM-X 1 arcsec tiles,
which we also have a number of, were generated with average resampling of the
0.4 arcsec tiles by DLR and not by any increase in multi-looks or
interferogram smoothing. We tested a number of resampling schemes including
average, bilinear, cubic, and cubic spline on the original 0.4 arcsec tiles
and found better results (lower vertical uncertainty compared with
differential GPS) from the commonly used bilinear resampling, whereas the
unedited 1 arcsec tiles delivered by the DLR – generated by average
resampling – had higher vertical uncertainties.
The TanDEM-X and recently updated SRTM-C were both referenced to
high-accuracy ICESat
measurements (collected between 2003 and 2009) during final block adjustments
. While this removes the
complete independence of these datasets, the relative sparsity of these
points (170 m along track and up to 80 km across track) does not provide a
continuous adjustment surface, but rather acts to improve local elevations
and overall DEM quality with respect to remaining tilts
. Throughout the study dh refers to the
TanDEM-X–SRTM-C 15-year differences (including both real change and
vertical uncertainties).
SRTM-C correction steps
Our correction chain was applied using the previous SRTM-C output at each
stage as input in the following step. All steps were carried out on a
1∘× 1∘ tile-by-tile basis (unprojected WGS84 vertical and
horizontal datums); however, merging tiles and then processing produced
identical results. We also found comparable results using Universal
Transverse Mercator (UTM) equal area projected tiles. The correction steps
served to correct SRTM-C orbital biases and did not attempt to correct for
terrain characteristics. We assumed that actual vertical change in our study
area represented an extremely small fraction of pixels in the
∼13 million pixel dh raster for each tile. This ensures that
the corrections only rectified SRTM-C biases on stable terrain and were not
influenced by smaller areas of true vertical land-level changes. Comparison
of correction steps was done using normalized percentage difference
histograms and quantile–quantile (QQ) plots.
Co-registration
We corrected for subpixel offsets known to affect DEM comparisons
using the universal co-registration of
. This rigid translation is based on a cosine function fit
to the relationship between terrain aspect and dh normalized by terrain slope:
dhtan(α)=a⋅cos(b-ψ)+c,
where α is slope; ψ is aspect; and the variables a, b, and
c are the magnitude, direction, and mean bias, respectively. The shifts
were applied to the SRTM-C by bilinear resampling with the dx=a⋅cos(b)
and dy=a⋅sin(b) vectors used to weight the neighboring cells, and the
mean shift dz=c⋅tan(α‾) was added at the end.
We fit Eq. (1) to only slopes >5∘ and, if necessary based on
goodness-of-fit parameters, continued iteration of the fitting, shift vector
solving, and interpolation until the magnitude of the shift vector (a) was
<0.5 m or the reduction in normalized median absolute difference (NMAD;
) on stable terrain was <5 % .
Our co-registration did not correct for slope and curvature using polynomial
fitting e.g., as this introduces
empirical models and additional uncertainties. We did not observe a linear
positive or negative trend between slope and dh (Fig. S7). Curvature versus
dh demonstrates the difference in actual resolution of raw sensor data
between the SRTM-C and TanDEM-X (Fig. S10); however, correction of this
intrinsic measurement limit introduces artificial elevations and is thus
inappropriate for dh mapping between DEMs from different data sources and
time steps (see Sect. S2).
Iterative shifting and bilinear resampling of one DEM to another by decimeter
steps had the same effect on rectifying aspect biases (same shift vectors
leading to minimization of bias) as the empirical fitting of the cosine
relationship and calculation of shift vectors (see Iterative
Shifting Video in the Supplement). This indicates the robust nature of the method of
, assuming a sufficient distribution of high-slope,
multi-aspect-facing topography is available for cosine fitting. The
minimization of the sum of errors and cross-correlation methods
e.g., were unsuccessful at removing shifts in our
study region.
Destriping
For removal of long- and short-wavelength striping patterns in the SRTM-C, we
followed previous work using frequency analysis techniques to identify
striping artifacts e.g., and noise
e.g., in DEMs. We took particular
inspiration from and used fast Fourier transforms (FFTs)
to filter the dh. In a first step, we removed all pixels identified
as having low coherence in the TanDEM-X WAM. This filtered large water bodies
and other areas that may show artifact noise affecting FFT analysis.
Following this, any void pixels (including the low-coherence areas) were set
to dh=0 and an FFT was run. The power spectral density (PSD) was calculated
as the magnitude of the FFT squared and a mean 5×5 filter was passed
over it. The ratio of original and smoothed PSD was then taken to identify
regions of the spectrum with high outliers (high ratio) representing cyclic,
tile-spanning stripe bias. We used the 97.5th percentile of the ratio as
the cutoff value. The remaining top 2.5 % high- and low-frequency outliers
received an inverse FFT, which produced a map of the long- and
short-wavelength stripes. These stripes were then removed from the SRTM-C and
the process was repeated iteratively until the improvement in root mean
squared error (RMSE) was <5 %.
We refer to the above parameters as nonaggressive destriping, since we are
just “shaving off” the top of the distribution. In aggressive tests, we
experimented with lower percentile cutoff values (e.g., 95th) and lower
tolerance for RMSE convergence (e.g., <2 % improvement). While these more
aggressive destriping schemes did successfully eliminate the SRTM-C orbital
biases, we also found that the true topography was often filtered following
the more than five iterations needed to meet the RMSE convergence requirements
(Fig. S11). Therefore, we chose to use the nonaggressive cutoffs and ran
additional blocked shifting discussed in the following section.
Blocked shifting
Patchy positive and negative regions in the co-registered, destriped dh map
were solved by breaking the 1∘× 1∘ tile into square blocks
and shifting each block by the median value. These areas likely correspond to
remaining orbital biases that were not removed in our nonaggressive
destriping technique. There may be local correspondence between these patches
and atmospheric water vapor conditions at the time of SRTM-C collection in
February 2000; however, such data at the sub-kilometer scale necessary for
analysis is unavailable. Furthermore, local adjustment of the SRTM-C and
TanDEM-X to ICESat measurements could contribute to these shifts, though the
contribution is difficult to quantify.
We began by masking the low-coherence pixels (again from the WAM) since these
would disproportionately contribute to local median shifts. Using a variety
of block sizes with edge lengths ranging from 1.35 to 7.2 km, we found the
median dh and median slope in each block. We used the median slope to
normalize the median dh values, since we expect areas of higher slope to
have greater uncertainties and biases (Fig. S7) unrelated to SRTM-C orbital
biases. Furthermore, we allowed a maximum shift per block of ±1 m, thus
ensuring that this step did not cause unreasonably large shifts due to
outliers contained in a given block.
Differencing for change detection
Following orbital SRTM-C bias corrections, it is possible to merge corrected
tiles and create maps of dh to measure areas of actual change. Previous
change mapping over gravel-bed channels has relied on level-of-detection
cutoffs and probabilistic thresholding e.g.,. These studies have, however, been developed for meter
to submeter photogrammetric or lidar data. Here we use a hybrid approach of
statistical outlier detection on the entire distribution of pixels followed
by a level-of-detection cutoff for remaining pixels well within the bounds
for expected noise between the datasets. Remaining uncertainties are
primarily caused by speckle noise and terrain characteristics, with the
biggest impact from slope. The following sections provide a detailed
description of the change detection method for channels and hillslopes.
Channels
We know from field observations that large braided gravel-bed channels in the
study area (Fig. b) change rapidly with local incision and
aggradation (natural and anthropogenic in the form of gravel mining) on the
order of meters during the past decade. Outlines of the bank-to-bank active
width of the primary channel branch were digitized from open-source satellite
imagery from BingTM and GoogleEarthTM. We
buffered the resulting channels by -60 m (upper limit of gridded SRTM-C
resolution). This means we only use the wide (>120 m), non-vegetated channel
reaches from Río Toro and Río Grande where there has been recent
aggradation and incision.
Change mapping was done by separating the in-channel dh values into bins of
contributing error factors (local relief and TanDEM-X individual scene
consistency) and applying 5th and 95th percentile cutoffs to each
bin, thus only taking the top (positive equals aggradation) and bottom
(negative equals incision) 5 % of outliers. We first used the TanDEM-X WAM to remove
the untrustworthy dh pixels where coherence was lost three or more times
. Because gravel-bed channels represent a low-slope
environment with no vegetation and we are only measuring wide valleys, we
assumed that DEM errors from SRTM-C and TanDEM-X were restricted to random
speckle noise. Nonetheless, to account for steeper areas with potentially
more error from phase unwrapping, we separated dh into relief bins using
the pixels' 500 m radius relief values. We also separated dh by the
TanDEM-X consistency and height error masks (Figs. S2 and S3). Taken
together, dh pixels in high-relief, high-height error, and low-consistency
bins required greater magnitudes to avoid noise cutoffs than vice versa. A
minimum-level-of-detection approach was taken as
the RMSE of the entire dh map on low-slope (similar to channel slope)
areas. In a final step, all remaining in-channel dh values below this RMSE
cutoff were removed as likely noise. Volume changes are calculated from the
sum of the pixel area (900 m2) multiplied by vertical change, with
uncertainties taken as the level-of-detection RMSE and propagated via
Eq. (15) in .
Entire landscape
When considering dh over the entire landscape, we include far more
uncertainties related chiefly to steeper terrain. Thus, the error must be
handled differently than for strictly low-slope pixels (in-channel). First, a
corrected dh map for the entire study area was generated. Similar to
channel mapping, low-coherence pixels were removed with the WAM and dh was
separated into bins of slope, height error, and consistency to retrieve only
the top and bottom 5 % of outliers in each bin set. The level-of-detection
cutoff was taken as the RMSE across the entire landscape, which was almost
entirely stable terrain, and remaining dh values below this cutoff were eliminated.
At this stage, a great many lone and patchy dh values remained. Given this,
it was not possible to automatically identify areas of change that were only
a small number of pixels in size. Interested in large-scale changes, likely
not associated with a single pixel, we sought connected pixels showing all up
or all down vertical motion. To winnow the potential change pixels, we
applied binary opening with a 1-pixel radius circular kernel, thus removing
many unconnected outliers and small patches. Next, we took the summed dh of
each separate patch. It was assumed that the majority of patches, and thus
the majority of summed values, were remaining noise in the difference map,
whereas signal should be spatially coherent and largely positive or negative.
Therefore, by applying a standard deviation cutoff over summed patches (here
we used 1σ, though this can be easily set for testing), we removed a
vast majority of remaining pixels and only kept the largest outliers. This
limited the method to only assessing the largest coherent vertical changes in
the landscape but eliminated the possibility of misidentifying change that
was in fact noise. These remaining patches can be explored in map view and
compared with satellite or historical imagery for further confirmation and analysis.
Relationship of dh (normalized by the tangent of the slope) to aspect
(a) before and (b) after co-registration and bilinear
resampling of SRTM-C. We fit to Eq. (1) on all raw data. Note the close match
between equation fit and median values. The cosine relationship
in (a) is caused by overestimation of the SRTM-C on NE-facing
aspects (peaking at ∼60∘) and underestimation on SW-facing
aspects (peaking at ∼220∘). The resulting (dx, dy) shift
vector is directed SW.
One iteration of FFT destriping from one tile (24∘ S,
66∘ W). Both median and RMSE improve from (a) the
co-registered map to (c) the destriped map. Stripes removed by FFT
are shown in (b). Note that (c) is not the final corrected
map as the iteration was run twice more before RMSE began to converge at a 5 %
tolerance level. Voids (white space) are untrustworthy pixels removed by
TanDEM-X WAM cutoff prior to destriping.
ResultsCorrection steps
Co-registration of SRTM-C to TanDEM-X revealed X–Y shifts of
∼1/10 of a pixel (∼3.7 m). Although minor Z shifts
(∼1 m) were also determined and corrected during
co-registration, these were not unique across entire tiles, but rather
related to long-wavelength SRTM-C biases. The cosine fitting to dh
normalized by terrain slope can be seen in Fig. , whereas in
map view the change is more subtle and difficult to discern.
In Fig. , we demonstrate one iteration of destriping for a
single SRTM-C tile (24∘ S, 66∘ W). It is apparent in the
co-registered dh map that a number of long- and short-wavelength shifts are
affecting the tile. Using our FFT, statistical cutoffs, inverse transform,
and stripe removal, the resulting dh map has a much more uniform appearance
and the median and RMSE are both reduced. This process was typically repeated
2–4 times per tile, until the RMSE began to converge. While topographic
uncertainties remain in steep and high-relief regions, the overprinting
biases are reduced.
Blocked shifting on three destriped and merged tiles
(24–26∘ S, 66∘ W). Blocks are 3.6 km in height and width.
The (a) destriped median and RMSE both improve slightly in
(d) the final shifted dh map. Note that the original blocked
medians (b) show a slight pattern resembling the long-wavelength
stripe bias from SRTM-C. In (c) we have normalized the median shifts
by the median slope values, so as not to overcorrect the steeper regions
with higher uncertainties. The color scheme is changed for (b)
and (c), and the scale of (c) is half the width
of (b) since it only extends to the maximum allowable shift of
±1 m. Scales and color scheme in (a) and (d) are
identical. Voids (white space) are untrustworthy pixels removed by TanDEM-X
WAM cutoff prior to median calculation.
Since we do not use an aggressive FFT filtering scheme, a number of patchy
outliers remain. We attempted to correct these regions using blocked shifting
(Fig. ), shown in this case over three tiles covering the foreland
and Altiplano–Puna Plateau region (24–26∘ S, 66∘ W). After
testing multiple block sizes, we preferred blocks with an edge length of 3.6 km,
since these provide a small enough area to correct highly localized
inconsistencies, while also being far greater in size than the largest
vertical changes we would expect in the landscape.
Comparison of correction steps
Since stacked histograms are difficult to interpret and larger magnitude
outliers are fewer in number and thus obscured, we plotted the normalized bin
percentage difference of dh in each step of correction (Fig. ).
Co-registration mostly caused a mean shift in the distribution. Moving to
destriping, the number of pixels at high outlier values went down
significantly (>20 % drop in ±15–20 m bins) and there was some
(∼10 %) increase in bins ±5 m, whereas the number of values
close to zero dh decreased. This represents an overall redistribution of
error from the SRTM-C orbital biased patterns (Fig. ) to a more
uniform spatial pattern (Fig. ). The final blocked shifting caused
very little overall change in the distribution, which was mostly in the form
of another mean shift (this time directed the other way from
co-registration). These effects can also be seen in a QQ–plot of each
subsequent correction step (Fig. ), where co-registration caused a
mean shift and some outlier reduction, de-striping had a large effect on
narrowing the distribution at the tails, and blocked shifting again had a
minimal effect on narrowing the distribution at the most extreme outliers. In
all cases, the median value (0.5 quantile) moved closer to zero. Overall,
these plots indicate the importance of SRTM-C correction and of the
destriping step in particular prior to using TanDEM-X–SRTM-C dh maps for
change mapping.
Characteristic (a) stacked histograms and
(b) normalized percentage bin difference from three tiles merged and
processed (24–26∘ S, 66∘ W). Though it is difficult to
interpret the histograms, plotting their difference (normalized by bin count)
as percentage change between successive steps demonstrates the shifting of
the median to near zero and the reduction in outliers.
Areas of change
As discussed in the methods, we separated potential change identification and
measurement from corrected (co-registered, destriped, block shifted) dh maps
between the in-channel pixels and the entire landscape.
Channels
Binning corrected in-channel dh and cutting off any remaining outliers
within the low-slope RMSE of ∼3 m reduced the data density
significantly by cutting out any pixels within expected noise. The potential
signal pixels were then plotted atop longitudinal profiles from the Río
Toro and Río Grande (Fig. ). The point clouds of dh values
were colored with a Gaussian kernel density estimate (KDE) to demonstrate the
denser (warmer colors) versus sparser (cooler colors) zones of measurement.
The density is displayed as percentiles of the full distribution of the 2-D
KDE of dh from both channels. Turning to map view, we can observe the
location of these pixels in the channel and their relation to local
characteristics, upstream factors, and anthropogenic tampering (Fig. ).
Quantile–quantile (QQ) plots showing the difference between each
successive correction step from three tiles merged and processed
(24–26∘ S, 66∘ W). (a) Original to co-registered,
(b) co-registered to destriped, and (c) destriped to block
shifted. We note that co-registration and destriping have the greatest effect
on zero-median shifting and narrowing the outliers. The quantiles (0.01,
0.05, 0.5, 0.95, and 0.99) and their respective values are indicated on each
axis to highlight this effect.
Longitudinal profiles of (a) Río Grande and
(b) Río Toro overlain with the point cloud of the potential dh signal
(pixels outside of the range of expected noise). Error bars are RMSE from
low-slope (<5∘) terrain outside of the channel area. Each
dh point cloud is colored by probability density from a Gaussian 2-D KDE to
show the denser (warmer) versus sparser (cooler) reaches. The KDE is scaled
over all measurements from both channels and relative percentiles of the full
distribution are used to highlight denser zones, particularly in
(b) Río Toro. Note the x-axis range is 100 km greater for the
longer Río Grande, despite the same axis scaling. The color scheme for
elevation profiles on right axes matches the map-view color of each channel in
Fig. b. The knickpoint in Río Grande is caused by the large
Del Medio fan , whereas the origin in Río Toro is
tectonic, caused by the Gólgota Fault
. In both cases, the majority of
the dh signal appears downstream of the knickpoint. The map view of green
highlighted regions is shown in Fig. .
Entire landscape
To be mapped as true vertical change, an area in the greater landscape must
be significantly large and coherently positive or negative since many of the
pure noise patches are >10 pixels in size (>0.01 km2). Furthermore, the
individual pixels must show significant height changes above the overall RMSE
of ∼6 m and outlier cutoffs in each bin, which in steeper bins
may be >10 m. Examining results in map view (Fig. ) allows
assessment of the potential true signal versus noise. At this stage it is
necessary to include auxiliary data from field knowledge or remote sources
like aerial or satellite imagery (e.g., GoogleEarthTM). Our
method was able to identify one major landslide in the study area
(Fig. d); however, most other measurements are remaining large artifacts
attributable to both the SRTM-C and TanDEM-X. Low-coherence zones that may
represent change between the TerraSAR-X and TanDEM-X contributing scene collection
(Fig. b and c) are necessarily removed in the WAM cutoff prior to binning.
Map views of the in-channel dh measurements for Río
Grande (a) and Río Toro (c) highlighted in the
longitudinal profiles in Fig. . For location of each map refer to
Fig. c. More details are shown in zoomed-in images of the in-channel dh
measurements in (b) and (d). The solid outline is the
digitized bank-to-bank channel and the stippled line is the -60 m buffer
area of measurement. We note large areas of incision related to the steep and
narrow channel downstream of the Del Medio fan and knickpoint in Río
Grande (a), immediately followed by a zone of aggradation with levee
structures to direct gravels (b). For Río Toro (c) we
highlight the anthropogenic influence of gravel mining generating large piles
and also causing incision due to local excavation (d).
DiscussionNecessity of correction steps
The original SRTM-C is plagued by numerous terrain- and sensor-specific errors
and biases e.g.,. Despite reprocessing
of the original data in the new NASADEM product, many of these errors remain
. On the other hand, the newer TanDEM-X apparently
has far fewer biases related to satellite geometry, and most of the error is
restricted to terrain characteristics like slope and vegetation, though
results are still nascent e.g.,. Our correction steps do not seek
to eliminate bias related to terrain characteristics at the scale of a few
hundred meters, but rather to correct large-scale biases related to primarily
the SRTM-C at scales of several hundred meters to kilometers. Perhaps this
reduction in bias is most obvious in the map view of the subsequent dh patterns
between processing steps (Figs. a to a to Fig. d),
but we also show statistically that these steps lead to a
narrowing of the distribution and centering of the differences on zero-median
(Figs. and ). We assume that the vast majority of the
pixels (outside of the cryosphere) should be unchanged over 15 years, and
thus median shifts between the datasets at large scales are biases in need of correction.
(a) Map view of landscape-wide dh identification. For
location refer to Fig. c. Our method returns little change on the
low-erosion Altiplano–Puna. The dunes (b–c) are not
identified since they are masked out using the TanDEM-X auxiliary WAM as
low-coherence zones. This indicates their rapid displacement between
the TerraSAR-X and TanDEM-X scene collection. Our method is able to identify one
major landslide (d) in the Del Medio catchment
; however, there are many erroneous results in steep
and vegetated zones to the east, shown in (e) over the TanDEM-X
hillshade.
Co-registration indicates NE-facing aspects are overestimated by the SRTM-C
causing a negative excursion in the cosine fit, whereas SW-facing aspects are
underestimated and thus the dh compared to TanDEM-X is positive. This error
mostly affects higher slopes , which is the reason for
the normalization of dh by the tangent of the slope. The directions of bias
correspond to the look direction orthogonal to the SRTM-C descending path and
parallel to the ascending path. This indicates that the source of this bias
is the SRTM-C, as reported by previous authors ,
and not TanDEM-X. A shift – accompanied by bilinear resampling – of just
∼3.7 m (magnitude a of Eq. 1 fit) to the SW rectifies this aspect bias.
As opposed to , we do not set a user-defined ratio
for FFT destriping, but rather use statistical “shaving off” of only the
outlier stripe noise until the data converge. This conservative approach
retains the true topographic signal at the expense of remaining stripe noise.
In the case of more aggressive FFT filtering, using lower percentiles for the
ratio cutoff and more strict RMSE convergence requirements, the actual
topography began to filter out of the dh maps (Fig. S11), which, as stated,
is not the aim of our orbital bias correction steps and would lead to the
inclusion of artificial (i.e., FFT generated) dh measurements.
Remaining stripe noise is apparent in Fig. b, where the blocked
medians resemble the original long-wavelength stripe pattern, though
discontinuous. Despite the appearance in some areas of more negative values
in the western parts of tiles (higher elevation, Altiplano–Puna Plateau), we
do not find any clear relation between block medians and elevation at any
block size or in any tile (see Sect. S3). Block shifting removes
the remaining noise, but again we avoid correcting for strongly overprinting
topographic biases related to slope by normalizing the block median dh by
median slope. Overall, these steps provide a more trustworthy dh map, while
respecting the inherent biases in radar-derived
spaceborne DEMs.
Potential change mapping
For lower-slope regions (i.e., channels), the potential for change mapping is
greater than in steeper areas. This is caused by the better agreement and
lower vertical uncertainty of the two datasets in flatter, vegetation-free
areas. In both channels, the largest density of measurements is found below
the respective knickpoints. This corresponds to an order of magnitude
increase in the 2-D KDE shown by the warm-colored patches in Fig. .
In terms of the actual number of measurements (number of dh pixels) per
binned channel reach, Fig. S13 demonstrates this approximately
5- to 10-fold increase in the downstream reaches with a simple histogram.
This result partially has to do with a narrower channel and thus less
measurements available above the knickpoints (hence the numerous gaps in
measurement in the upstream reaches); however, these results also appear to
indicate that the most geomorphic work is happening downstream of the
oversteepening point. This also coincides with a transition to a wetter
environment in both cases.
The Río Toro has a particularly dense zone of measurements at the
mountain front where naturally high rates of aggradation are enhanced by
human gravel excavation and piling. On the other hand, in the Río Grande
the downstream measurements are spread over a greater channel reach and thus
appear less dense in the 2-D KDE (the measured Río Grande is
∼100 km greater in length than the Río Toro). Downstream of
the knickpoint, Río Toro is in a net aggradation state with a corrected
dh volume of 0.81±0.15×106 m3, whereas for Río Grande
the net state is incision with a volume of -0.69±0.15×106 m3.
In comparison, the pre-correction volume in each case is
-1.18±0.12×106 and 2.80±0.11×106 m3
for Río Toro and Río Grande, respectively, thus indicating a flip in
sign and reduction of magnitude following careful corrections applied prior
to differencing.
Locally, the aggrading and incising patches may be related to braided channel
avulsion and subsequent rapid incision into the unconsolidated bed material
during frequent high-discharge events brought by convective rainfall in the
summer monsoon .
In map view (Fig. ), we see that these
automated measurements can be correlated with additional sources. For Río
Grande, the steep knickpoint at the Del Medio fan
causes a major zone of incision immediately followed
by aggradation where the material is deposited. Fieldwork has indicated that
some of this incision is man-made, caused by attempted removal of aggrading
material coming from the productive (e.g., debris flows
see ) Del Medio catchment. Levee structures
(Fig. b) are a testament to this tendency towards aggradation downstream
of this extremely erosive fan. The cause of aggradation in the Río Toro
is clearly enormous gravel piles being created just at and downstream of the
mountain front. The volume of the large gravel pile indicated in
Fig. d directly at the mountain front in Río Toro is
0.78±0.06×106 m3, with this growth between SRTM-C and
TanDEM-X observed during field work over the past decade and from
GoogleEarthTM historical imagery back to 2003. This is
coupled with incision in the active channel upstream of the piles where
gravel is being removed to prevent widespread aggradation.
In terms of rates of change, our minimum measurable dh of ±3 m
corresponds to a rate of ±0.2 m yr-1, given the conservative 15-year time
difference between DEMs. This rate represents an average for the entire
measurement period and assumes constant geomorphic change, whereas the true
rates are more stochastic, following rainfall and anthropogenic activity
variation. The area of greatest point density in the longitudinal profiles in
Fig. is centered at ±5 m, corresponding to a rate of
±0.33 m yr-1, with maximum rates of incision and aggradation, occurring at
anthropogenic gravel piles and excavation sites, in excess of ±0.5 m yr-1.
Human tampering is known to cause significant excursions from natural river
dynamics , and we have shown
that signals of excavation and piling are highlighted as above-the-noise
outliers. Previous studies have demonstrated similar rates over longer
timescales (tens to hundreds of years) using more sparse measurements
e.g., and at shorter timescales (<5 years) from meter-scale
lidar data . The
identification and quantification of incision and aggradation have important
implications for infrastructure and agriculture given that 60 % of global
sediment delivery to coasts originates in high mountain regions .
Mapping dh signals across the entire landscape presents a greater challenge
given the higher uncertainties on steeper more complex topography.
Nevertheless, using the binning method, binary operations, and outlier
selection removes a large portion of the noise from the corrected data. Our
method displays very little change on the low-relief, low-slope
Altiplano–Puna besides some salt flat areas that were not removed by the
coherence masking from the TanDEM-X WAM. Remaining noise mapped as potential
change is clear at the mountain front where steep slopes and heavy vegetation
causes complication of accurate radar measurement. In many locations these
erroneous patches correspond with low-amplitude or low-coherence zones also
identified in the WAM. We were able to automatically map one landslide,
previously reported on by , in the Del Medio
sub-catchment of the Humahuaca Basin using this method. This material likely
contributes to the aggradation we see occurring downstream of the fan in the
longitudinal profile (Fig. a) and in map view (Fig. a).
The calculated detachment and deposit volumes from this massive earth
movement are -10.5±0.12×106 and
16±0.15×106 m3, respectively, with vertical land-level
changes greater than ±50 m associated with the break-off and lobe
(Fig. d). These magnitudes of change show little difference in the
pre- and post-corrected mapping, indicating (a) this is a localized region of good
agreement between SRTM-C and TanDEM-X and (b) this large landslide can be
identified in uncorrected difference maps.
The area of sand dunes, clearly visible as a low-coherence region from the
TanDEM-X WAM in Figs. c and b and c, is not mapped
as potential change since the coherence masking prior to binning eliminates
this area from consideration. Examination of dh in this region is very
noisy since the TanDEM-X contains measurements spanning 5 years, thus causing
completely different height inputs for the same pixel in many scenes. This
indicates the potential of the WAM alone for mapping change on shorter
timescales outside of very steep areas.
Caveats of the data and method
Spaceborne DEMs present significant challenges for accurate height
measurements, though, until lidar or submeter satellite data become more
widespread and cheaper , they are the only option in
many study areas. On the other hand, unmanned aerial vehicles and point
clouds generated using structure-from-motion technology could already provide
a viable alternative , but
applying these methods at the scale of entire catchments or over
tens of kilometers of river reaches is not feasible. Previously,
dh measurement from space has been primarily focused on the cryosphere
e.g., due to
limitations in data accuracy. Certainly radar data are more adequate than
optical data e.g., for the
case of unconsolidated sediment, particularly since different penetration
depths do not affect measurement , assuming
limited vegetation.
Here we have demonstrated the potential of new high-accuracy datasets such as
TanDEM-X to correct outstanding biases in the SRTM-C and potentially
contribute to land-level change mapping and measurement over previously
unattainable scales. Given remaining noise in the datasets, change mapping is
limited to large areas of coherent change (e.g., massive landslides) or
specific low-slope areas of interest such as wide gravel-bed rivers. In any
case, field data (e.g., repeat total station or GPS surveys), field knowledge
(e.g., via observations of incising reaches or roads damaged by aggrading
channels), and/or auxiliary data (e.g., GoogleEarthTM
historical imagery change mapping) are necessary for accurate assessment of
the location of true change signals versus noise. Further, the magnitude of
change must be significantly above the expected uncertainty between DEMs,
which in the case of SRTM-C and TanDEM-X is as low as ∼3 m on
flat, sparsely vegetated terrain, and increasing with slope and topographic
complexity. We posit that these correction steps may also be applied to
cryospheric studies; however, radar penetration would need to be carefully
considered first as this may exceed dh signals.
Conclusions
In this study we have presented a novel use of two near-global spaceborne
DEMs (SRTM-C and TanDEM-X) separated by ∼15 years to measure
land-level changes in the south-central Andes in northwestern Argentina.
Previous measurement of land-level changes at the scale of entire mountain
belts has been restricted to the cryosphere, where the signal of snow and ice
change outweighs the noise associated with DEMs used for differencing
(typically ASTER or single TerraSAR-X and TanDEM-X CoSSC DEMs). On the other
hand, studies outside of the cryosphere have relied on high-accuracy meter to
submeter data at much smaller scales to measure height changes in rivers and
hillslopes. Using the TanDEM-X DEM as a control surface, we corrected
long-standing SRTM-C errors related to orbital biases. We then successfully
differenced the two datasets to identify and quantify land-level changes
outside of expected noise caused by radar DEM speckle and other
terrain-dependent errors, increasing with steep and complex topography. Noise from
imperfect datasets continues to hinder signal detection in low-magnitude
geomorphic change detection; however, this study continues to push the
envelope of the potential for change mapping using the data currently
available to many scientists.
Our method is useful for the case of large gravel-bed rivers where the width
far exceeds SRTM-C 1 arcsec resolution considerations. In such flat,
vegetation-free environments it is useful to analyze the river alone and not
include additional uncertainties brought by increasing slopes and dense
vegetation. For these steeper regions, the use of greater outlier cutoffs and
the necessity for large and coherent patches of land-level change, both to
remove the majority of noise, limit the method to only very large earth
movements. In either case, only signals outside of expected noise can be
confidently identified, which in the case of gravel-bed rivers typically fall
in the realm of human tampering. From the TanDEM-X auxiliary data alone it is
also possible to identify regions that changed during TanDEM-X collection (2010–2015)
using the water indication mask; however, this does not provide quantifiable change.
Overall, the use of relatively coarse (1 arcsec) spaceborne DEMs to derive
land-level changes benefits from higher-accuracy radar-derived data, whereas
the use of optical data is limited to submeter-resolution satellites. The
application of this method to other regions around the world could indicate
previously unmapped vertical changes. In the future, both the SRTM-C and
TanDEM-X will continue to be used as snapshots of the earth's surface
separated by over a decade and thus useful for differencing against newer
datasets yet to be developed to continue measuring vertical change outside of
the cryosphere.
Python codes for co-registration, FFT destriping,
blocked shifting, and potential change mapping are available on GitHub at
https://github.com/UP-RS-ESP/TanDEM-SRTM-dh. The SRTM-C
updated NASADEM tiles can be found at https://e4ftl01.cr.usgs.gov/provisional/MEaSUREs/NASADEM/. TanDEM-X data are only available from DLR commercially
for the time being.
The supplement related to this article is available online at: https://doi.org/10.5194/esurf-6-971-2018-supplement.
BB and BP defined the project. BP carried out the analysis,
produced the figures, and wrote the manuscript. BB provided funding, guidance
in data analysis, and manuscript edits.
The authors declare that they have no conflict of interest.
Acknowledgements
The authors thank the DLR for TanDEM-X DEMs received through grants DEM_CALVAL1028
for Benjamin Purinton and DEM_GEOL1762 for Stephanie Olen. Additional funding was
sourced from DFG Funded IRTG-StRATEGy (IGK2018) and
NEXUS funded through the MWFK Brandenburg, Germany, both for Bodo Bookhagen.
We acknowledge the support of the Open Access Publishing Fund of the University of
Potsdam.
Edited by: Simon Mudd
Reviewed by: two anonymous referees
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