Introduction
Valleys with theater-shaped heads exist in the landscapes of
Earth and Mars. On Mars, examples of such valleys are Louros Valles
(Fig. a) and Nirgal Vallis .
Terrestrial examples can be found in the Atacama Desert in Chile
(Irwin et al., 2014; Fig. b), on the Canterbury Plains in New Zealand, on the
Colorado Plateau and on Hawaii
. Furthermore, much smaller
examples that are similar in shape are valleys that emerge in eroding
riverbanks (Fig. c) or those on the beach that develop
during a receding tide .
Examples of theater-headed valleys. (a) Louros Valles on
Mars (perspective view); (b) valleys on the coast of the Atacama
Desert, Chile (oblique photo, human for scale); (c) a riverbank
(oblique photo); (d) side valleys of Snake River, Idaho, USA
(orthorectified image); (e) valleys on the coast of the Atacama
Desert, where the star indicates position of viewpoint of (b) (orthorectified
image); (f) Apalachicola Bluffs near Bristol, Florida, USA
(orthorectified image). Image credits: (a) Google Earth (NASA/USGS,
ESA/DLR/FU Berlin), (b) Tjalling de Haas, (c) Wouter Marra,
(d, f) Bing Maps Imagery, (e) courtesy of GFZ Potsdam.
Such theater-headed valleys can form by the seepage of groundwater in
erodible sediment e.g.,. These valleys form due to
headward erosion that is produced by mass-wasting processes where groundwater
seeps to the surface (Fig. a). In this paper we
define seepage as the hydrological process of groundwater emerging at
the surface and groundwater sapping as the geomorphological process of
erosion by undercutting which is triggered by seepage, although not all
erosion by seepage of groundwater results in undercutting. A channel
is a body of flowing water, i.e., an active fluvial feature. A valley
is an eroding (active) or eroded (inactive) depression in the landscape,
usually linear, elongated or sinuous. Persistent fluvial erosion by a channel
results in the formation of a valley larger than the channel, but other
processes (glacial, mass wasting) can result in the formation of valleys as
well. The morphology of former channel that did not result in the formation
of a larger valley are referred to as channel remnants. Confusingly,
in Martian geomorphology, large valleys formed by catastrophic floods are
referred to as outflow channels; we conform to this definition for the
outflow channels.
Valley formation by seepage (Fig. a) is different
from valley formation by overland flow. In the former, headward progression
is the result of knickpoint retreat and fluvial incision
(Fig. b). However, overland flow can also produce
similar theater-headed valleys when incising into a substrate with an erosion
resistant top layer . This process is a likely candidate for
the formation of the theater-headed valleys next to the Snake River in Idaho
(Fig. d). The ambiguity in the mechanism of formation
of the valleys hampers the interpretation of their origin based on their
theater-shaped morphology alone. This ambiguity is particularly problematic
for the explanation of theater-shaped valley heads on Mars, where direct field
observations and material properties are lacking and a long period of
weathering obscures morphological details.
Fundamental processes at valley heads for overland flow and
groundwater seepage. (a) Valleys formed by groundwater seepage
extend in a headward direction by mass-wasting processes. (b) Valleys
by overland flow deepen by fluvial incision and extend in a headward direction
by knickpoint retreat.
The morphological properties of entire landscapes with multiple valleys may
help in the interpretation of these Martian valleys when single entities
have an ambiguous origin. An important mechanism for the landscape formation
by groundwater seepage is groundwater flow piracy: since valleys are
topographic depressions, they attract more groundwater from their
surroundings, resulting in a decrease in discharge to nearby
valleys . As a result, smaller valleys cease to develop in
favor of larger valleys. Landscape metrics may show the presence of this
feedback mechanism. Furthermore, splitting of valleys during their headward
development (headward bifurcation) produces typical angles between valley
segments . In the case of valley formation
by seepage from uniform precipitation, the theoretical angle between valley
segments becomes 72∘ . Such properties as well
as the orientation of valleys can be extracted from the
landscape and indicate the responsible hydrological system.
Our knowledge of groundwater seepage processes and their relation to
landscape evolution is limited, particularly as systems with only groundwater
processes are absent on Earth and previous studies have mostly been limited to the
same boundary conditions of groundwater from an upstream constant-head tank
(e.g., ). These experiments simulated a distant groundwater
source and showed the basic morphology of valleys formed by groundwater
seepage and also revealed the importance of groundwater flow piracy as a key
process for valley evolution. However, alternate hydrological systems exist
where other processes are significant and result in a different landscape
evolution. In contrast to a distant groundwater source, groundwater seepage
could come from nearby infiltration of precipitation. Such systems exist on
Earth (; Fig. f) and have been
studied in experiments to some extent , but require more
attention in terms of their morphological impact on landscape dynamics. We
hypothesize that a local groundwater source, e.g., as result of locally
infiltrated precipitation, results in less groundwater flow piracy compared
to groundwater that first travels some distance before seepage to the
surface, because seepage from a nearby source is less influenced by the
topographic gradient responsible for flow piracy. Since flow piracy is an
important mechanism in the formation of valleys by groundwater seepage, we
expect different and distinct morphological development for valleys formed by
seepage from a local source compared to those produced by distally fed
systems. Specifically, distant sources of groundwater produces landscapes
with many small valleys that ceased developing early, whereas in landscapes
produced by local sources of groundwater, valleys have similar lengths as
most valleys developed continuously.
In this paper, we aim to improve our understanding of groundwater seepage
processes, specifically on the resulting valley formation at a landscape
scale using morphological experiments. We specifically study the difference
in morphological development of valleys that result from a distant
groundwater source (simulated with an upstream constant-head tank) and a
local groundwater source (simulated by infiltrating precipitation).
Furthermore, we combine our experimental insight with previous studies in
order to show a complete range of landscapes formed by groundwater seepage
under different conditions. The objective is to provide a framework that
shows the arrangement of multiple valleys, i.e., the orientation and length
distribution that results from different hydrological boundary conditions.
These properties will aid in the identification of the formative processes
when the single-valley morphology is ambiguous, and will constrain the
underlying hydrological conditions. To demonstrate the application of this
framework for landscape interpretation, we use two frequently cited cases of
groundwater seepage on Mars, Nirgal Vallis and Louros Valles, and relate
their landscape metrics to the possible sources of groundwater.
Methods
Experimental design
We conducted a series of flume experiments in the Total Environmental
Simulator (TES) facility at the University of Hull to investigate the
morphological development of theater-headed valleys by groundwater seepage.
Moreover, with these experiments we simulated the difference between
groundwater seepage generated by a distant source of groundwater, using
a constant groundwater level at the upstream end of the experimental setup,
and groundwater seepage produced by infiltration of precipitation applied
over the entire experimental domain. We repeated both experiments with an
idealized initial morphology and with a heterogeneous initial morphology that
was the result of a previous experiment. In this section, we present the
setup, the initial topography and applied boundary conditions across the
experimental set.
Setup of the experiments. (a) Oblique photo from downstream
end of the flume, showing the initial sediment surface, gutter and constant-head tank in the back. The rain simulators and cameras are above the
photographed area; their approximate locations (C1–C6) are shown.
(b) Cross section showing setup with impermeable floor, constant-head tank (ch), gutter, approximate location of spray nozzles (sn) and
brickwork. (c) Plan view showing the locations of the rain
simulators (x), camera locations (C1–C6) and positions of the laser scanner
(LS1, LS2).
The initial idealized morphology consisted of a volume of sand with a median
grain size of 0.7 mm, which comprised (1) a flat area of 1.7 m
upstream and (2) a slope of 0.22 mm-1 for 3.5 m
(Fig. ), which was uniform over a width of 4 m.
We used natural, moderately angular sand to mimic natural groundwater and
surface flow processes. The grain size was such that groundwater flow was
neither too rapid nor too slow for the formation of valleys within a
reasonable period of time. The sloping section ensured seepage of groundwater
from a hydrostatic groundwater level, that is, without applying extra
pressure to the groundwater.
The sediment was placed on top of a partially sloping impermeable floor to
increase groundwater flow in the downstream half of the setup and to reduce
the amount of sediment required. This floor was flat for 2.6 m and
the slope was 0.11 mm-1 for 2.6 m. Pond liner ensured
the impermeability of the floor and walls. A rough cloth on top of the pond
liner prevented the entire block of sediment from sliding down the smooth
pond liner surface. The total sediment depth was 0.5 m in the
upstream flat part, sloping towards the downstream end. At the downstream
end, a row of 6 cm high bricks truncated the wedging slope to prevent
the sediment from sliding down. In addition, the small spaces between these
10 cm wide bricks acted as initial surface perturbations. This
ensured the initiation of channels was evenly distributed over the entire
width of the sediment surface.
The constant-head tank was designed to simulate a distant groundwater source
and was constructed opposite of the sloping wedge of sediment. It spanned the
entire width and depth of the sediment fill with a 0.6 mm mesh
fabric, braced with chicken wire and steel gratings at the water side to
retain the sediment and avoid collapse into the reservoir under the weight of
the sand. This setup enabled water from the constant-head tank to enter the
body of sediment over the entire width and depth at the upstream side of the
flat section of the sediment fill.
For the experiment with precipitation as the water source, we used an array
of spray nozzles above the setup to supply water over the sediment surface.
These nozzles were fed with a discharge such that the water spray infiltrated
in the flat area and seeped out on the sloping wedge. The discharge feed was
slightly lower than the infiltration capacity of the sediment. A rising
groundwater table induced seepage, but, in contrast to the constant-head
tank, the seepage areas were fed by nearby infiltrated groundwater. Twelve
spray nozzles with square spray patterns were used to ensure uniform spray
distribution and pressurized water was fed from a ring main to ensure equal
spray rates for all nozzles.
We carried out five experiments with the above-described boundary condition
combinations (Table ) under terrestrial
conditions. The experiment labeled distant source was carried out
with the constant-head tank throughout as the boundary condition using the
initial topography described above. The final surface morphology from the
distant source experiment was used as initial morphology of the
experiment labeled local after distant, which was run with water
input from the spray nozzles. The experiment labeled local precipitation was run with water input from the spray nozzles on the
above-described initial topography. The experiment labeled local precipitation 2 was run to generate an initial morphology with the same
conditions as local precipitation and this experiment was ceased
early. The final morphology of local precipitation 2 was the initial
morphology of distant after local, which was subject to groundwater
flow generated by the constant-head tank.
Experimental runs, their duration, discharge setting and data
acquisition intervals; video number corresponds with videos in the Supplement. Abbreviation used: d – days; h – hours; min – minutes.
Experiment
Duration
Mean Q (Lmin-1)
Cumulative Q (m3)
Time-lapse interval
SfM interval
Video
Distant source
3 d 3 h
2.4
10
5 min
1 d 3 h 2 d 2 h 2 d 22 h 3 d 3h
video 1
Local precipitation
1 h 50 min
11.9
0.95
30 s
end of exp.
video 2
Local precipitation 2
40 min
Local after distant
3 h 10 min
10.5
1.9
30 s
end of exp.
video 3
Distant after local
3 d 16 h
2
10
5 min
0 d 2 h 0 d 21 h 2 d 0 h 2 d 20 h 3 d 16 h
video 4
Experimental imagery and elevation models
We captured the morphological development of the experiments using time-lapse
photography. These images enabled us to study the experiments in detail from
different angles. Moreover, we derived valley dimensions from orthorectified
time-lapse images. The time-lapse setup consisted of six cameras (Canon
PowerShot A640), mounted around the experimental setup (see C1–C6 in
Fig. ), which were triggered synchronously at set
intervals. These intervals ranged from 30 s to 5 min, based on the rate of
morphological development during the ongoing experiment (values in
Table ).
For each experiment, time-lapse imagery from four cameras (C1, C2, C4 and C5)
was processed to construct a single orthorectified photograph
(Fig. ). Orthorectification was implemented using the
“Image Processing” and the “Camera Calibration” toolboxes in the
MATLAB software suite. Orthorectification was performed using the initial
surface elevation model, due to absence of elevation data at each time step.
This method resulted in warped imagery in areas with elevation change, i.e.,
within the valleys. However, these images were used to extract valley lengths
and widths which are calculated from the distances between non-eroded valley
walls. The outside edges of these walls form in the original surface and are
therefore correctly represented in the orthorectified photograph using this
method.
For detailed morphological analysis, we generated digital elevation models
(DEMs) and orthorectified images at the end of each experiment using a large set of
images and a structure-from-motion (SfM) algorithm . In
addition, we also acquired these data every day during the distant source and distant after local experiment at irregular intervals
(Table ). Each DEM and
associated orthorectified image was derived from 70 to 100 digital images
with about 80 % overlap. We took these images by hand, allowing us to
capture the area of interest. Twenty-four targets with known coordinates
within the experimental setup enabled referencing of the images. Camera
positions and orientations were solved using these known target coordinates
and matched features between images. To improve the quality of the result, we
removed features in wet areas to eliminate faulty matches in reflective areas
due to different lightning angles between images. Elevation models were
generated for each set of images, which were processed to a gridded elevation
model with 1 mm cell size and a 0.5 mm orthorectified images.
We used a Canon 550D DSLR camera with an 18–55 mm f/2.8
lens to take the photos, which we processed in RAW format to 16 bit TIF
images to eliminate compression artifacts. We used Agisoft PhotoScan for SfM
processing .
A laser scanner was also used to obtain DEMs at the end
of each experiment. Point-cloud elevation data of the final morphology were
scanned from two different angles in order to eliminate data shadows outside
the line of sight of the laser scanner (see Fig. ). These
point clouds were oriented and merged using fixed targets in the experimental
setup to produce a combined scan gridded onto a DEM with
a 2 mm cell size. We used a Leica ScanStation 2 laser scanner for
data acquisition, CloudCompare for point-cloud orientation and ArcGIS for
gridding of the point-cloud data.
Valley development and erosion rates
To quantify the morphological development, we measured valley widths, lengths
and depths during the experiments. Based on these data, we calculated valley
shapes, and erosion rates and compared the latter to measured sediment
output.
The length L (m) and width W (m) of each valley that formed during the
experiments were determined for each time-lapse interval from the
orthorectified time-lapse images. The valley width was taken just downstream
of the valley head where the valley walls were parallel. Valley depth D (m)
was defined as the deepest point of each valley, i.e., the largest elevation
difference between the original surface and the eroded surface. Valley depth
was measured at each SfM interval. The final valley floor slope
Sf (mm-1) was extracted from the final DEM. We
defined the valley floor as the lowest point in each valley cross section. We
estimated the erosion rates of each valley during the experiments by
combining the valley dimensions and valley shapes.
First, the eroded volume V (m3) was estimated as
V=W×L×D×SIc×0.5,
for which W and L were taken at each time-lapse interval, D (m) is the
valley depth that was interpolated between SfM measurements for each
time-lapse interval. SIc is the shape index of the
valley cross section, which is the average ratio of the actual valley
cross section to the square cross section of W×D. The factor 0.5
corrects for the longitudinal profile of the valley, which is in all cases
approximately triangular. Valley volume was transformed into an erosion rate
E (gs-1):
E=ΔVρs(1-n)×10-3ΔT,
where ΔV is the change in volume, ρs is the density of
sand (2300 kgm-3), n the porosity of the sediment (0.3) and
ΔT (s) is the time over which the change in volume occurred.
Cumulative erosion was compared to sediment output measurements collected
from bucket traps.
Martian landscape metrics
We constructed elevation profiles and extracted the orientation in degrees
from north (i.e., azimuth) of valley segments, the angles between converging
valleys and valley lengths of Louros Valles and Nirgal Vallis. Elevation
profiles were extracted from HRSC image H0380_0001 (125 m resolution
DEM) for Louros Valles; valleys of Nirgal Vallis were too small to produce
elevation profiles. Valley segments for both systems were digitized from
THEMIS daytime infrared mosaic and HRSC
imagery. We distinguished different stream orders, based
on the Hack stream-ordering number . In this system, the
first order is the main, downstream, valley; the first tributary is the
second order and so on. We choose this system since it represents the
chronology of valley formation by headward erosion.
The data set of valley segments was transformed to a network topology to
distinguish between upstream and downstream directions, using logical
operators based on the methods described in using
ArcGIS and MATLAB. In this data set, we identified converging valley segments,
valley heads and outlets based on the network topology. Building upon the
work of , the orientation relative to north of each valley
segment was extracted for each stream order identified in the data set.
Orientation distributions were normalized per stream order to clearly show
the differences between valley orientations of different stream orders. At
each node of converging valleys, we calculated the angle between the upstream
valley segments (following ). Such a converging valley is
referred to as headward bifurcation; this definition relates to the
chronological order of events in valley formation. In active rivers, the term
bifurcation is used for a fluvial channel that splits into two in the
downstream direction, which relates to the direction of water movement.
Furthermore, for each valley head in the network, we calculated the distance
to the first lower-order valley segment.
Experimental results
In the following section, we first describe the observed morphological
development during the experiments, and then we link this morphological
development to the acting processes. Time-lapse imagery and elevation models
support these observations (time-lapse movies are available in the Supplement).
Distant source
The experiment with seepage from a distant constant-head tank was
characterized by slowly developing valleys. This experiment took over 3
days to complete and was carried out with a constant discharge of
2.4 L min-1 (Table ).
The sediment saturated in the first hours of the experiment. During this
stage, a visible wetting front at the surface progressed from the upstream
constant-head tank in the downstream direction. The sediment became fully
saturated at the foot of the slope where seepage occurred after 2.5 h over
the full width of the sediment surface (Fig. a–i).
The initial seepage pattern remained roughly the same, though the seepage
area extended upslope to about 1 m from the foot of the slope.
Initially, the seepage was too low for fluvial transport to occur. As the
seepage rate increased, fluvial transport started after 4 h and the first
channels started to form at the foot of the slope within the seepage area.
Stills from time lapses of the experiments showing the main
morphological development. Full time-lapse movies are available in the
Supplement.
The initial channels at the foot of the slope featured a combination of
mass-wasting and fluvial processes. Mass wasting of saturated sediment at the
head caused headward erosion, and fluvial processes in the channel resulted
in incision and the formation of valleys
(Fig. a–iii). As the valleys developed in the
upstream direction, the seepage area retreated and seepage focused within the
valleys as shown by drying of the sediment between the valleys and
a concurrent increase in discharge within the valleys
(Fig. a–iii). Seepage was limited to a declining
number of valleys, as the valleys that reached most upstream progressively
attracted more groundwater. From the 10 valleys that started to form in the
initial stage of the experiment, only 6 remained active after a few hours
(Fig. a–iv), and only 3 remained active for
several days (Fig. a–v).
The decreasing number of actively developing valleys illustrates the process
of groundwater flow piracy as the largest valleys attract most of the
groundwater flow since these are the deepest point in the landscape. As a
result, more groundwater is directed to those largest valleys, which are
therefore more active and smaller valleys cease developing. This feedback
resulted in a final morphology with a few large and several small valleys
(Fig. ).
The remaining valleys grew and as they became deeper, the head- and
side walls gained strength by cohesion as the sediment was moist. As
a result, the headwall retreat was governed by collapse due to undercutting
at the toe, in contrast to the slumping of the entire valley head before the
development of this cohesive top layer. In this process, the toe of the head
wall was destabilized by fluvial erosion, resulting in collapse of the
headwall. The collapsed material spread over a distance of 0.1 to
0.2 m into the valleys. Fluvial transport removed this material from
the upstream end to the downstream end of the experimental setup. These
processes showed a cyclic behavior: head collapse only occurred after
a destabilization of the head due to the removal of the sediment by fluvial
transport. This cycle is essential for the continuation of the process as the
valley head would stabilize without such erosion and sediment transport. The
final morphology shows the former presence of these various processes. In the
three most developed valleys, the upstream end had a steeper slope than the
downstream sections with a break in slope separating the two
(Fig. a). This change in slope is the
result of the transition of mass-wasting processes upstream to fluvial
processes downstream.
Erosion maps/final morphology of the experiments showing valley
letters used in subsequent figures. (a) Distant source experiment,
(b) local precipitation experiment (c) distant after local experiment
and (d) local after distant experiment.
Valley profiles and slopes. (a) Profiles of valleys C, D
and E of the distant source experiment and valleys N and L of local
precipitation experiment, displayed with factor of 2 vertical exaggeration.
Elevations are arbitrary and plotted with offset for clarity. The three
distant source experiment profiles show three arrested stages of development
also seen in larger valleys: incipient valley without a steep valley head
(D), developing valley with moderate steep valley head (C) and developed
valley with steep valley head and reduced valley floor gradient (E); arrows
indicate break in slope at the valley floor. (b) Box plot of slope in
upstream and downstream part of all valleys of the distant source (n=9)
and local precipitation (n=14) experiments. The horizontal dotted line
shows the initial surface slope Si=0.22.
The collapse of unsaturated material at the valley heads resulted in steep
head walls (Fig. ). The step-wise increase in valley width
and length shows distinct peaks of collapse
(Fig. a and b) and erosion rates
(Fig. d). Steps in width and depth of the
valleys are not simultaneous, which shows that collapse of the head- and
side walls occurs at different moments. Although erosion takes place in
distinct peaks of activity, these valleys show a linear trend in valley
length and width during the most part of their development. Interestingly, the width-to-length ratio of the three main valleys is the same during the entire experiment (Fig. a).
Local precipitation
The local precipitation experiment took 1 h and 50 min with an
average discharge of 11.9 Lmin-1. This discharge is higher than
in the distal source experiment. A part of the precipitation fell
directly into the valleys since the precipitation was distributed evenly over
the experimental domain. Furthermore, the groundwater table in the
local precipitation experiment was close to the surface compared to a
relative deep groundwater table in the distal source experiment. As a
result this setup allowed for more seepage due to the higher seepage area,
explaining the higher discharge and shorter run of this experiment. In this
experiment we distinguished two stages in valley development. In roughly the
first half of the experiment, overland flow was the main source of water
feeding the channels. In the second half, groundwater fed the channels.
Valley development in the distant source (left panel) and local
precipitation (right panel) experiments. Main valleys indicated with colors;
letters in legend correspond with letters in Fig. .
(a, f) Valley width and (b, g) length derived from
orthorectified time-lapse imagery, (c, h) valley depth derived from
SfM DEMs, (d, i) estimated erosion rated from these properties and
(e, j) total cumulative erosion estimate from valley volume compared
to measured sediment output.
Development of valley width vs. length of the (a) distant
source and (b) local precipitation experiment. Colored symbols in
(a) represent the three main valleys. Values are plotted for all
time-lapse intervals (valley dimensions increase with time). The open symbols
in (a) represent valley dimensions when the measured valley section
flowed at the side wall which influenced the valley width. Dotted line
indicates trend of the three persisting valleys when the flume wall did not
influence their width.
In the first stage of the experiment, the sediment in the downstream part of
the slope saturated rapidly due to the limited sediment thickness
(Fig. b–i). On this saturated sediment, precipitation
transformed directly into runoff, resulting in channels that formed valleys
by fluvial incision. These valleys formed over the entire width of the
sediment and had valley heads with a V-shaped planform
(Fig. b–ii). During this stage, valleys developed in
a headward direction by fluvial erosion and valley heads were within the area
of saturated sediment. Seepage inherently occurred in the valleys due to the
setup of the experiment. However, the overland flow processes dominated the
seepage processes.
As the groundwater table rose during the experiment, the boundary of
saturated sediment moved upslope. This progression of the saturated area
slowed down as it progressed. In the first stage, valley development did not
keep up with this moving front. However, the valleys caught up and developed
upstream of the saturated area as the experiment progressed
(Fig. b–iii). This marks the second stage in valley
development wherein groundwater seepage rather than surface runoff fed the
valley heads. From the moment the valley heads were fed by groundwater, their
planform changed from V-shaped to theater-shaped
(Fig. b–iv and b–v). This change indicates a change
from fluvial flow to mass-wasting processes at the headwall. The headward
growth showed similar characteristics to that in the experiment with seepage from
a distant source: growth governed by failure of the headwall and fluvial
transport that removed the failed material. Similar to the distant source experiments, there was also a distinguishable difference in slope in
the upstream and downstream half of the valleys
(Fig. ), although this difference was
less pronounced.
The valleys in the local precipitation experiment were shallow
compared to the valleys in the distant source experiment. In both
cases, the valleys developed around the groundwater table, which was close to
the surface in the local precipitation experiments. The limited depth
was presumably the result of the high groundwater table; there was no zone of
unsaturated sediment resulting in valleys without steep walls
(Figs. b and a).
The valleys in the local precipitation experiment became longer and
slightly wider by lateral erosion during the experiment
(Fig. f and g). An important difference
with the distant source case was that all valleys continued to develop
and had similar sizes during the experiment
(Fig. i). This is due to the absence of
groundwater flow piracy since each valley was fed by locally infiltrated
groundwater (Fig. ). In contrast to the valleys from a
distant source, the relation between valley length and width in the
locally fed valleys is not linear and different valleys do not have the same
ratio (Fig. b).
Effect of initial morphology on seepage from a distant source
We studied the effect of an initial morphology on the valley development in
experiment distant after local by repeating the experiment on an
initial morphology. This initial morphology was the result of experiment
local precipitation 2, which consists of multiple parallel shallow
valleys created by overland flow (Fig. ).
Experiment distant after local showed the same general characteristics
and development as the distant source experiment; the main difference
is where valleys started to form. In the distant after local
experiment, initial seepage at the downstream end focused within the valleys
of the initial morphology. However, due to groundwater flow piracy, only
a limited number of these valleys fully developed. Six valleys started to
form, but only two valleys fully developed (Fig. c).
Development in the two remaining valleys was the same as described for the
distant experiment. In the early stages of valley development, the valleys
followed the path of the existing valleys in the initial morphology. When
they became larger, they still followed the path of the initial valleys,
although these were straight and the new valleys were much wider than the
initial valleys. In our view, these mature valleys seemed to develop
independently from the initial morphology.
Effect of initial morphology on local precipitation experiment
In the local after distant experiment, the final morphology of the
distant source experiment acted as the initial morphology of this run
(Fig. a). The same processes acted in this experiment,
though the initial morphology had a much larger effect on the final
morphology in this case.
In the first stage of the local after distant experiment, the existing
valleys reactivated as the sediment saturated. Due to the rising groundwater
level, the steep side- and headwalls of the previous valleys became unstable
and collapsed. This resulted in a decreasing valley depth and increasing
width. The valleys that were abandoned in the distant source
experiment due to groundwater flow piracy reactivated as they were fed by
local precipitation and subsequently infiltrated groundwater, resulting in
a smaller difference in valley size (Fig. d) compared to
the initial situation (Fig. a). Collapse of the headwall
caused headward erosion and lateral erosion caused widening of the valleys.
These are the same processes as in the local precipitation experiment
with no initial morphology, but the final morphology showed much wider
valleys. The initially present valleys were relatively deep in comparison to
the final valleys. The reduction in depth of these valleys corresponded with
this widening.
At the end of the local after distant experiment, water ponded at the
upstream flat section of the experimental setup. This ponding seemed to be
the result of the sediment becoming fully saturated towards the end of the
experiment. The headward developing valleys tapped into this shallow
reservoir, resulting in a final slightly catastrophic stage of erosion due to
the breach of this reservoir (Fig. d). This stage is not
representative of the main objectives of this paper and therefore not
further considered here.
Examples of Martian valley systems
In this section, we show the morphology of Louros Valles and Nirgal Vallis
(Figs. and ), two Martian
valley systems that were previously attributed to a groundwater seepage
origin e.g.,. These two
system serve as an example of how to apply our experimental results and have
received much attention in recent literature. Furthermore, these systems show
branching valleys, which also aids the interpretation of these systems. In
this section, we describe Louros Valles and Nirgal Vallis; their interpretation is
part of the discussion.
Louros Valles
Louros Valles is located at the north and south flanks of Valles Marineris.
These valleys have circular valley heads cutting into flat plains. The
valleys have a total relief of several kilometers and are between 10 and
100 km long (Fig. b and c). Upstream of the
valley heads, there are no visible tributaries or depressions in the
elevation data or imagery. Downstream of the valleys, in Valles Marineris,
there are no clear deposits associated with these valleys. Sediment output in
this case could be spread over a large area on the floor of Ius Chasma as
a thin veneer and not recognizable as fluvial deposits. The valleys on the
northern flank are shorter than the valleys at the south. Of the southern
valleys, there are two larger valleys in the west; all other valleys are
approximately equal in size. The valleys are closely spaced and several
valleys touch or intersect, resulting in a relatively densely dissected plain
(Fig. c and d).
Final morphology of experiment local precipitation 2, which is the
initial morphology of experiment distant after local.
Maps and profile of Louros Valles. (a) Overview map showing
location of (b) (MOLA shaded relief). (b) THEMIS daytime
infrared mosaic with color-coded MOLA DEM, showing location of (c)
and (d). (c) Valley centerlines, color-coded by
stream order on THEMIS daytime infrared mosaic. (d) Detail of the network
showing a densely dissected landscape and bifurcating valleys.
(e) Elevation profile based on HRSC data, moving average using a
10 km window (plotted with 1000 m vertical offset) and slopes of two
segments. Location of this profile is the first order valley indicated
in (c).
Maps of Nirgal Vallis. (a) Overview map showing location of
(b) (MOLA shaded relief). (b) THEMIS daytime infrared
mosaic with color-coded MOLA DEM, showing location of (c)
and (d). (c) Valley centerlines, color-coded by
stream order on THEMIS daytime infrared mosaic. (d) Detail of the network
showing a sparsely dissected landscape with many small and a few large
valleys.
Landscape metrics of Louros Valles and Nirgal Vallis.
(a–c) Valley orientation for valleys on the north (a) and
south flank (d) of Louros Valles and Nirgal Vallis (c).
(d–e) Valley length (distance to lower-order valley) distribution
for different stream orders, most main valleys (order 1) plot far outside the
shown window for (d) Louros Valles and (e) Nirgal Vallis.
(f–g) Distribution of bifurcation orientation and box plots per
stream order for (f) Louros Valles and (g) Nirgal Vallis.
As an example, we show an elevation profile of the largest valley of Louros
Valles (Fig. e). These and other elevation data show
a rough, irregular profile, likely related to post-valley formation wall
collapse or tectonism. At the downstream end of the valley, the elevation
quickly drops, which shows the onset of Valles Marineris. Based on
a 10 km moving average, we show the valley has a change in slope
about halfway to a lower slope than the upstream part
(Fig. e). However, the irregular elevation data
limit the interpretation of these observations.
All valleys show headward bifurcations. For the northern valleys, the
orientation of the first-order valleys varies from northwest to northeast, with
most valleys oriented to the north-northeast
(Fig. ). The first tributaries, or second
order valleys, have a similar spread in orientation, but most
are oriented to the west-northwest. For the southern valleys, most
first-order valleys are oriented towards the southwest, while higher-order
valleys are directed towards the south-southwest or towards the
west-southwest (Fig. b). Interestingly, a few
third- and fourth-order segments are oriented in the opposite direction
(180∘) to the first-order valleys (e.g.,
Fig. d).
The lengths of the tributaries range between 5 and 15 km (the main
valleys are longer, but most are outside the graph), with no specific trend
in the distribution of valley length (Fig. d).
Mean headward bifurcation angles of the different stream orders are between 70
and 90∘ (Fig. f).
Nirgal Vallis
Nirgal Vallis consists of a > 500 km long main valley and several
sparsely distributed side valleys of various sizes
(Fig. ). Valley depths range from several tens to
several hundreds of meters. The valley cuts into the plateau through several
north–south-oriented wrinkle ridges, which are in places the highest
points in the landscape. Several side valleys align with these wrinkle ridges
.
The orientation of the main valley is dominantly west-northwest; the
first-order tributaries have the same dominant orientation, but a large part
is deflected north- and southward (Fig. c).
This tendency of dominantly westward-oriented valleys is shown in the
landscape (Figs. d and
c). There are a few larger side valleys, but most
side valleys are very short (Figs. d and
e). This results in the sparsely dissected
landscape. The mean headward bifurcation angle between valleys is
70.7∘ with a standard deviation of 18.6
(Fig. g), similar but slightly less than the
results of for the same valley network but with less
measured junctions. Headward bifurcation angles are similar for different
stream orders.
Discussion
Valley morphology related to groundwater source
The valleys in our experiments with a distant source of groundwater have
semi-circular, theater-shaped valley heads with a sharp transition to the
upstream, uneroded surface. These are similar to those found in previous
studies on valleys formed by groundwater seepage e.g.,. Valleys in our experiment
fed from nearby infiltrated precipitation also featured semi-circular valley
heads but lacked the steep theater-shaped head wall. The valleys from both
boundary conditions developed in a headward direction by destabilization of
the valley head due to either undercutting or slumping. The eroded material
is transported along the valley by fluvial processes. These two main
processes showed a cyclic behavior as the fluvial erosion in the valley was
the trigger for collapse at the valley head. Furthermore, in both
experiments, the slope in the upstream section of the valley floor was
steeper than in the downstream valley floor
(Fig. ), which relates to the transition
from mass-wasted material released at the valley head to the fluvial
transport of material downstream.
The morphological similarity between theater-headed valleys in groundwater
sapping features (undercutting and failure by groundwater seepage erosion) at
the beach , in sandbox experiments , on
the Colorado Plateau and on Mars is often used as an
argument for a groundwater origin of the Martian valleys
e.g.,. A complication in the
study of such morphology on Mars is that different processes yield a similar
morphology. For example, waterfall erosion or groundwater
weathering can also produce theater-headed valleys. We
do not solve this controversy in this paper since the experiments here do not
explore the morphological differences between all these possible processes.
Here, we focus on morphology related to groundwater flow processes and
subsequent erosion in further detail and provide metrics of entire landscapes
to aid the interpretation of Martian landscapes.
In the following discussion, we start by considering the applicability of our
experiments. Then, we propose different end-member landscapes based on
knowledge from our experiments combined with previous experimental work,
modeling results and theoretical considerations. The main landscape
properties are the distribution of valley lengths, valley order, valley
orientation and the angle between valley segments. We close the discussion
with an interpretation of the Martian valleys described using the proposed
landscape metrics framework.
Scalability of experimental results
The experiments described in this paper are not dimensionally scaled or
direct analogues to the Martian case studies. Instead, the experiments
provide insights into the fundamental processes that result from groundwater
seepage and the resultant morphology. These experiments were devised to
contrast distinct sources of groundwater and complement previous work. The
experimental setup was designed to be simple in order to show clearly the
effect of different hydrological boundary conditions. Different initial
conditions will produce different landscapes, but again, our work is focused
on the essential underlying processes and representative morphological
features.
The experiments presented in this paper, and previous work on seepage
erosion, applies to landscapes formed by groundwater and thus landscapes that
form in porous and erodible material. The overall patterns are expected to be
similar on different scales and for different materials that meet these
conditions, but details will differ. Our analyses are therefore limited to
the large-scale patterns in the landscapes and not expected to explain
details. Below we point out the scale effects in our experiments and how we
take these into account.
An important difference between the distant source and local precipitation experiments was the steepness of the valley heads and
side walls, which were much steeper in the distant source case. In the
distant source experiment, the groundwater table was deeper, resulting
in an unsaturated (moist) top layer above the groundwater table, which has
more apparent cohesion than the saturated (wet) top layer in the local precipitation experiment. In natural systems, such contrasts in material
strength arise from differences in soil or substrate properties rather than
formative processes. The depth of the unsaturated layer relates to capillary
forces, which are scale-independent and thus relatively small for large
experimental valleys (see discussion in ).
Nevertheless, theater-head formation took place in both cases with and
without an unsaturated top layer, which indicates that this process takes
place under both conditions and is not the result of this scale effect.
Destabilization of the headwall is a necessary condition for the development
of valleys by seepage. This only takes place if sufficient sediment is
removed from the toe of the headwall, which requires channels with enough
discharge for sediment erosion and transport along the entire valley length.
In previous smaller-scale experiments, report on
experiments in a 1×3m flume with sand where the channels
clogged and valleys ceased developing due to the absence of downstream
sediment removal. Their solution to sustain upstream processes and valley
formation was to flush away sediment at the downstream end. In that same
setup, valleys from groundwater seepage did develop when lightweight plastic
sediment was used, which enabled sufficient sediment transport due to the
lower material density. In other words, sufficient downstream erosion by
fluvial processes is essential to keep the formation of valleys by seepage
going. In the experiments described in this paper, sediment was not flushed
at the downstream end, which shows that the scale effect of having
a insufficient discharge for sediment erosion and transport was overcome in
our setup.
Additional work is required to understand the morphological details of
valleys formed by groundwater seepage. In particular, we expect important
effects on valley shapes to result from layered substrates with alternations
in material erodibility. These effects can be studied experimentally, but to
model erosion rates on larger scales than can be represented in the
laboratory, numerical modeling will be more informative about the formative
timescales of such systems and may elucidate on terraces found in Martian
valley systems. Furthermore, using such models, Martian scenarios with a
thick layer of permafrost can be simulated which are unpractical to recreate
in most laboratories.
Groundwater flow piracy, valley spacing and length distribution
The morphology of the entire landscape shows important differences that are
related to subsurface groundwater flow processes. In the distant source experiment, a decreasing number of valleys remained active when
smaller valleys ceased to develop. This behavior relates to groundwater flow
piracy by the larger valleys, since these depressions attract groundwater.
Due to the travel distance and direction of the groundwater, areas downstream
of large valleys receive less or even no groundwater as shown by surfacing
drying. The resulting landscape consists of several small valleys with
a terminated groundwater supply (Fig. a) in between a few
large active valleys oriented towards the groundwater source
(Fig. a). In contrast, the local precipitation experiments did not feature groundwater flow piracy since the
groundwater source is distributed everywhere and therefore cannot be captured
by nearby valleys. The resulting landscape is densely dissected with valleys
of similar size in close proximity to each other (Figs. b
and b).
An important parameter for groundwater flow piracy is the fraction of the
groundwater flow that a valley captures. This is controlled by the ratio of
cross-stream to downstream groundwater flux , which is proportional to the groundwater gradient in
isotropic conditions. In the case of valleys formed by groundwater seepage,
the emerging valley itself leads to a topographic low that introduces
a cross-stream groundwater slope, which increases the flow towards that
valley. This morphological feedback causes flow piracy when a valley attracts
enough groundwater to cease the flow to other valleys. This feedback and
tendency for flow piracy is stronger for flat surfaces in contrast to valley
formation on a slope, since a depression in a flat surface has a larger
effect on the convergence of groundwater flow .
Landscape end members formed by groundwater seepage as result from a
distant source or local precipitation, and steep or horizontal surface. Each
panel shows a schematic diagram (upper left), an Martian case showing a
similar morphology (upper right) as an example, and the expected valley length
distribution and valley orientation (bottom). A distant source (a, c) results in valley abandonment due to upstream capture of groundwater,
whereas a local groundwater source (b, d) is less prone to flow
piracy. Horizontal surfaces (c, d) have a strong tendency to form
valley bifurcations in contrast to steep slopes (a, b). Valleys
emerging from a distant groundwater source result in an open landscape as no
valleys develop downstream of large valleys. Similar Martian landscapes
in (a) Noctis Labyrinthus (THEMIS image), (b) Gale Crater
(CTX image), (c) Nirgal Vallis (THEMIS image) and
(d) Louros Valles (THEMIS image).
Our experiments show that the valley width-to-length ratio is similar for
valleys formed by a distant source of groundwater
(Fig. a), but this is not the case for valleys fed
by a local groundwater source (Fig. a). The
similarity in the development of several distally fed valleys is indicative
of valley formation by the same source of groundwater. The size of the
valley is the dominant control on the amount of water delivered to that
valley since a larger and deeper valley yields more groundwater seepage. In
turn, the amount of erosion relates to the size of the valley, and hence the
morphological development is similar for the different valleys. The amount of
water delivered to the valleys fed by local precipitation is only partly
controlled by this mechanism. In this case, the amount of groundwater
delivered to the valley head also depends on upstream area and local
watersheds.
Initial conditions may affect the location where channels emerge and valleys
start to form, and thereby the spacing of valleys in the final landscape. In
our distant after local experiment with minor initial morphology and a
distant groundwater source, the initiation of valleys was related to
the initial perturbation of the surface, but the resulting processes and the
final landscape was similar to the experiment with no initial perturbations.
This shows that seepage is robustly driven by the subsurface flow pattern and
agrees with the observations of that valleys of
a composite origin dominantly reflect the last process. In contrast, in the
local after distant experiment, there was a significant effect of the
initial morphology as old valleys reactivated. Importantly, the valley
patterns in the distant after local experiment are similar to those in the
distant source experiment; thus, they are hardly influenced by the
initial morphology. An implication is that the location and orientation of
valleys fed from a distant source strongly relates to the responsible
hydrology and, to a lesser extent, to initial condition. Therefore, the
morphology is a reliable indicator for the source of groundwater that shaped
such landscapes.
Headward bifurcations
Our experimental valleys did not bifurcate at their valley head, which is
considered a typical property for valleys fed by groundwater seepage
e.g.,. The absence of headward bifurcations in our
experiments is the result of the steep slope in the downstream half of the
setup. showed that valleys that formed in a flat
surface result in more seepage at the flanks of the valley head, which
increased the tendency of the valleys to split when growing in a headward
direction. Our results show that seepage on a steep slope suppresses the
tendency to form such headward bifurcations, compared with similar
experiments on horizontal surfaces, which do show headward bifurcations
(Fig. a and c; e.g., ).
Besides the initial slope, showed that valleys fed from
a local source have a higher tendency to bifurcate in a headward direction.
This tendency relates to the groundwater flow that enters the valley head
from a wide range of directions and not mainly from upstream or the direction
of the groundwater source. As a result, valleys formed by seepage from a
local source on a flat topography have many headward bifurcations, which
results in a densely dissected landscape
(Fig. d). This pattern is similar to the
Apalachicola Bluffs (Florida), which have been shown to be formed by seepage
of locally infiltrated precipitation .
The flow field that results from local infiltration into a flat substrate
results in headward bifurcation angles of 72∘ .
This value has been considered as evidence for a groundwater origin of Nirgal
Vallis by , but this value is only characteristic for
seepage from uniform precipitation on a flat surface and is therefore not
universally applicable. Furthermore, structural controls from tectonics may
also dictate the angles between valleys , which is also likely
the case for Nirgal Vallis .
The combined occurrence of developing headward bifurcations and groundwater
flow piracy results in the formation of typically stubby tributaries. When
a valley bifurcates in a headward direction, there are two valley heads close
to each other, which will in result in abandonment of one of these
(Fig. c) due to the presence of groundwater flow
piracy. This behavior and the resulting morphology is indicative of valley
formation by seepage from a distant groundwater source.
Origin of Martian examples
We analyzed the landscape of Louros Valles and Nirgal Vallis, two valley systems
often attributed to groundwater seepage. Two additional examples are shown in
Fig. a and b, and these examples are described
below to serve as an illustration of how the morphology can appear but are
not analyzed further. The valleys in Noctis Labyrinthus
(Fig. a) show valleys with no headward
bifurcations and a few small valleys in between larger valleys. Although the
plateau where these valleys cut into is flat, there is a strong gradient
between valley head and outflow point, which illustrates our contention that
a steep slope suppresses the tendency for headward bifurcation to form. The
small valleys in Gale Crater (Fig. b) are
similar in size and shallow, and there is a regional slope.
Alternate hypotheses for similar valley formations are bedrock erosion by
catastrophic release of surface water or bedrock weathering
and erosion by groundwater , which would result in the
same combination of boundary conditions and morphology as seepage in
unconsolidated materials. Another hypothesis for the formation of Louros
Valles is focused erosion by meltwater in between patches protected from
erosion by the presence of an ice cover (“glacial selective linear
erosion”; ).
The evidence in favor of a groundwater origin over surface flow in both
Nirgal Vallis and Louros Valles is the absence of remnants of channels
feeding the main valleys. However, billions of years of weathering and a dust
cover could have obscured such small morphological features. The elevation
profile of one of the valleys in Louros Valles is bumpy (Fig. e), likely due to
later activity. Consequently, the interpretation of such a profile in
comparison to elevation profiles of the experiments
(Fig. ) is limited. Therefore, we use the
properties of multiple valleys and valley segments in the entire landscape
rather than single-valley morphology for our interpretation.
The orientation of valley segments of Louros Valles is diverse and has
a broad range of valley lengths, resulting in a densely dissected landscape
(Fig. ). Such a landscape is typical for a local
groundwater source (Fig. d). Furthermore, in
Louros Valles, some higher-order valley segments are oriented in the downstream
direction with respect of the main valleys (Fig. d),
which can be the result of a local source of groundwater and not groundwater
coming from greater distances. Additionally, the presence of valleys on both
sides of Valles Marineris suggests a local groundwater source and not
groundwater coming from a great distance.
A possible local source of groundwater for Louros Valles is precipitation;
melt of snow, ice or permafrost; or upwelling groundwater from
a cryosphere-confined aquifer e.g.,. The presence of
this type of aquifer in this region may also have been the source of water
for the outflow channels further northeast which are likely to have formed by
the release of pressurized groundwater from a confined aquifer. The timing of
events here is crucial since the presence of Valles Marineris, and the clear
formation of Louros Valles after the opening of Valles Marineris, suggests
that this aquifer was at that point cut off and split between the north and
south. Seepage at Louros Valles rather than the formation of an outflow
channel could represent low aquifer pressure, which fits a trend of lower
groundwater pressures at higher elevations in Ophir and Lunae Plana
. Furthermore, the subsidence of Valles Marineris
into the aquifer may have been a trigger for outflow or upwelling of
groundwater. This hypothesis could be further explored and the asymmetry
between the valleys on the north and south flank may provide additional
insight into the nature of such an aquifer.
The landscape of Nirgal Vallis is an example of valley formation by seepage
from a distant source, given the large number of small valleys typical for
groundwater flow piracy (Figs. ,
a, a and c). The groundwater
source was likely to have been west of the valley due to the orientation of
most valleys towards that direction. A possible source of groundwater flow
from the west could be recharge in the Tharsis region .
Seepage of groundwater likely took place before the formation of a global
confining cryosphere, which is considered a requirement for aquifer
pressurization for Martian outflow channels in the Hesperian
. Alternatively, a regional
discontinuity may be the reason for seepage at Nirgal Vallis. In that case,
seepage took place during an early stage in the formation of the cryosphere.
The climatic implications are the presence of precipitation in the source
region which could be aqueous or icy , but widespread
precipitation is not required and a groundwater system as the dominant
element of the hydrology shows that these valleys could form in the absence
of a long-lived hydrological cycle at the surface.
Based on our and previous experiments, this study now provides a framework
that links landscape properties to the groundwater source location. The two
Martian examples shown further illustrate this link. Although different
processes could produce similar valley morphologies, the strong
correspondence of the landscape metrics of these examples and those produced
by seepage points towards a groundwater origin. In particular the distant
groundwater source of Nirgal Vallis implies a well-developed groundwater
system. Perhaps most significantly, outflow of groundwater and resulting
valley formation of such a system could have taken place regardless of
climate conditions being optimal for the sustained presence of liquid water
on the surface.
Conclusions
We studied groundwater seepage processes and subsequent valley formation
using a series of large sandbox experiments. Our experiments focused on the
difference between valleys fed from groundwater originating from a distant
source or from infiltrated local precipitation. In both cases, valley heads
developed in a headward direction by mass-wasting processes triggered by
steepening due to fluvial sediment transport through active channels out of
the valley.
Combined with previous experimental work, we provide a framework of driving
processes and resulting landscape metrics for valleys fed by a distant source
and local precipitation, and for a steep and flat topography. Their main
characteristics are as follows. (1) Due to groundwater flow piracy, seepage
erosion from a distant groundwater source results in a sparsely dissected
landscape with a few large and many small valleys. Valleys fed from a local
source of groundwater, e.g., precipitation, are not characterized by flow
piracy and have a range sizes, resulting in a densely dissected landscape.
(2) Valley formation in horizontal surfaces promotes the development of
headward bifurcations in contrast to steep surfaces where this tendency is
suppressed. For valleys fed by a distant source of groundwater, the combined
occurrence of bifurcating valleys and flow piracy results in valley systems
with stubby tributaries. Valleys fed by locally infiltrated groundwater on
horizontal surfaces grow in a wide range of directions due to the development
of many headward bifurcations which remain morphologically active.
As an example, we applied these characteristics to two Martian systems.
Firstly, Louros Valles shows a densely dissected landscape with a broad range
of valley orientations and valley lengths. This landscape is typical for
a local groundwater source. Such a local source could relate to an aquifer that
fed the outflow channels, but is more likely related to local precipitation
or melt of ice or snow. Secondly, Nirgal Vallis illustrates
a sparsely dissected landscape with many small, and only a few large, valleys with a
single dominant orientation. This indicates a distant groundwater source in
the west, which is likely produced from recharge at Tharsis. Further study of
similar landscape properties as a result of overland flow is required to
advance the ambiguous interpretation of these valleys.