JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, E00H14, doi:10.1029/2011JE004000, 2012
Origin of lunar sinuous rilles: Modeling effects of gravity,
surface slope, and lava composition on erosion rates during
the formation of Rima Prinz
Debra M. Hurwitz,1 James W. Head,1 Lionel Wilson,2 and Harald Hiesinger3
Received 11 October 2011; revised 21 December 2011; accepted 11 January 2012; published 13 March 2012.
[1] Lunar sinuous rilles have long been interpreted as features that formed as the result
of surficial lava flow, though the precise mechanism responsible for channel formation
(constructed versus eroded origins) is still debated. In assessing the origin of Rima Prinz,
a channel interpreted to have formed by erosion, two erosion regimes, mechanical and
thermal, are considered. Measurements of channel dimensions are used as inputs to
analytical models to constrain the origin of Rima Prinz, including lava compositions,
mechanical and thermal erosion rates, eruption durations, and lava volumes required to form
the feature. Key results indicate that Rima Prinz and other large sinuous rilles could have
formed as the result of thermal erosion under the weak gravity and low slope conditions
characteristic of these lunar features. Further analysis indicates that lava composition has
significant effects on channel formation. Model results of four considered lava compositions
show that komatiite-like lava will erode a similarly composed substrate most efficiently
whereas a high-Ti basalt will erode a similarly composed substrate least efficiently; ocean
island basalt and low-Ti basalt erode similarly composed substrates at intermediate rates.
Results indicate that Rima Prinz may have formed over 0.4–2.2 Earth years, depositing
50–250 km3 of lava over a plausible deposit area of 2450 km2. Resulting deposit thicknesses
suggest that the lava that incised Rima Prinz was most likely similar in composition to a
terrestrial komatiite, ocean island basalt, or lunar low-Ti basalt. Further constraints on
sinuous rille formation will serve as a window into the nature of volcanic activity of the
Moon’s past.
Citation: Hurwitz, D. M., J. W. Head, L. Wilson, and H. Hiesinger (2012), Origin of lunar sinuous rilles: Modeling effects
of gravity, surface slope, and lava composition on erosion rates during the formation of Rima Prinz, J. Geophys. Res., 117,
E00H14, doi:10.1029/2011JE004000.
1. Introduction
[2] Sinuous rilles observed on the Moon are widely
accepted to represent the remains of channels formed by
lava that erupted in effusive, high volume volcanic events.
The exact mode of channel formation is still debated, as
researchers attempt to distinguish between channels that
formed due to construction of bounding levees [Spudis et al.,
1988; Komatsu and Baker, 1992; Gregg and Greeley, 1993],
due to mechanical erosion of the substrate [Siewert and
Ferlito, 2008], due to thermal erosion of the substrate
[Hulme, 1973, 1982; Head and Wilson, 1981; Wilson and
Head, 1981; Williams et al., 1998, 2000; Kerr, 2009], and
due to thermomechanical erosion of the substrate [Williams
1
Department of Geological Sciences, Brown University, Providence,
Rhode Island, USA.
2
Lancaster Environment Centre, Lancaster University, Lancaster, UK.
3
Institut für Planetologie, Westfälische Wilhelms-Universität Münster,
Munster, Germany.
Copyright 2012 by the American Geophysical Union.
0148-0227/12/2011JE004000
et al., 1998, 2001; Fagents and Greeley, 2001]. Some sinuous rilles are contiguous with distinctive source depressions,
the geometry of which suggests that the lava flow forming
the rille overflowed from a lava pond fed by pyroclasts falling from an optically dense fire fountain [Head and Wilson,
1980; Wilson and Head, 1980; L. Wilson and J. W. Head,
Lunar sinuous rilles and their associated source depressions:
The role of thermal erosion and implications for eruption
conditions, submitted to Journal of Volcanology and
Geothermal Research, 2011], with thermal erosion at the
base of the pond as well as at the base of the flow leading to
the observed morphology. In each of the proposed formation mechanisms, the composition of lava that flowed
through the channel can affect the volume of lava and the
amount of time required to form the observed feature. The
current study simulates the formation of Rima Prinz, a lunar
sinuous rille interpreted to have an eroded origin, by modeling erosion rates and expected erosion depths for four
distinct lava compositions. Comparisons between expected
and observed channel depths can provide constraints for the
composition of the lava that formed the observed channel.
These interpretations in turn can provide insight into the
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Figure 1. Lava channels interpreted to form from various
mechanisms observed on the Moon. (a) A channel observed
in the southern Imbrium basin that is interpreted to have
formed as the result of construction. The channel is relatively
shallow, and marginal levees are observed along the length of
the channel (white arrow). In addition, a local source is not
evident, indicating that this channel formed concurrently
with the surrounding lava flows. (b) Rima Prinz, a channel
observed east of the Aristarchus Plateau that is interpreted
to have formed as the result of erosion from lava flowing
through a surface channel. This channel is relatively deep,
with laterally continuous, nearly parallel walls that lack marginal levees. Rima Prinz originates in a source depression
that can be seen in Figures 3 and 4. (c) A channel observed
west of the Marius Hills that is interpreted to have formed as
the result of erosion from lava that flowed through a subsurface lava tube. The walls are not laterally parallel nor
continuous (white arrow), suggesting the currently observed
feature formed due to collapse of a structurally stable roof.
conditions that were present during the volcanically active
era in lunar history.
2. Background
[3] Sinuous rilles have commonly been identified as constructed or eroded features, and substantial analysis has been
conducted previously in an attempt to distinguish between
these two origins. Constructed channels are typically considered to form as the result of marginal cooling of a broad
lava flow. As the flow cools and solidifies inward from the
margins, levees form and bound the fastest moving, still
molten part of the lava flow, forming a channel [i.e., Hulme,
1974]. Constructed channels, such as those found in southern
Imbrium basin lava flows (Figure 1a), tend to be shallow
features, forming within the initial sheet lava flow rather than
incising into the substrate.
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[4] A constructed mode of origin has also been suggested
for the formation of larger sinuous rilles identified on the
Moon as well as other terrestrial bodies [i.e., Spudis et al.,
1988; Komatsu and Baker, 1992; Gregg and Greeley,
1993]. However, many of these larger sinuous rilles, such
as Rima Prinz located east of the Aristarchus Plateau
(Figure 1b), are significantly deeper features that appear to
lack levees and incise into the substrate, suggesting that the
development of these features is likely to have involved
erosion [Hulme, 1973, 1982; Carr, 1974; Hulme and Fielder,
1977; Coombs and Hawke, 1988; Coombs et al., 1990;
Pinkerton et al., 1990]. In many cases, these eroded channels,
with laterally continuous, nearly parallel walls, are expected
to represent open channels that developed a thin surface crust
[i.e., Williams et al., 1998, 2000]. In some cases, channels
might construct a structurally stable crust that remains intact
once the lava recedes, or channels might form completely
submerged within the substrate, forming a lava tube [i.e.,
Greeley, 1971]. Collapse of a lava tube roof may result in
the formation of a skylight that can be observed remotely
[Haruyama et al., 2009; Huang et al., 2011; Boyd et al.,
2011], such as that visible in a lava tube observed west of
the Marius Hills (Figure 1c). Aligned skylights might indicate the track of a subsurface lava tube. These skylights
observed in association with lava tubes represent distinct
features from the laterally continuous, nearly parallel walls
observed in association with the open channels of eroded
origin considered in this study.
[5] Two classes of erosion are commonly considered in the
origin of eroded channels: mechanical erosion and thermal
erosion. Mechanical erosion occurs when a flowing fluid
removes particles that lay loosely on the ground and involves
particles suspended in the flowing fluid colliding with the
substrate, shearing substrate particles and incising into the
substrate [i.e., Sklar and Dietrich, 1998]. While some work
has been done investigating this erosion regime in the origin
of lava channels [i.e., Sklar and Dietrich, 1998], this previous
approach assumes that the vertical load of the lava is
responsible for the erosion of the substrate rather than shear
stress. However, the low viscosity expected of lunar lavas
would allow for relatively high lava flow velocities, facilitating erosion by shear. The second type of erosion considered is thermal erosion, a process that involves a flowing
fluid whose temperature exceeds the melting temperature of
the substrate. As the hot fluid comes into contact with the
substrate, the substrate is melted and assimilated into the
flowing fluid, resulting in incision into the substrate. Analytical models must be used to supplement observations of
channel dimensions and morphology in order to distinguish
between these two erosion regimes.
[6] The goal of the current study is to discern the detailed
origin of Rima Prinz, a lunar sinuous rille west of the Aristarchus Plateau that is interpreted to have an eroded origin.
Remote observations of channel dimensions and morphology
described in section 3 are used in conjunction with analytical
models discussed in section 4 to calculate the erosion rates
and eruption durations required in each erosion regime to
form the observed channel. Effects of gravity, slope, and lava
composition are explored in sections 5 and 6 to determine
whether Rima Prinz formed as the result of mechanical or
thermal erosion. Model results for each of four lava
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Figure 2. Context image of the Aristarchus Plateau – Harbinger Mountain region with LOLA topography
data (120 m pixel1 resolution) overlying the LROC WAC global mosaic (100 m pixel1 resolution).
Rima Prinz (white box) has a source depression that is located on the northern ejecta deposits of Prinz
crater, and Rima Prinz extends north into Oceanus Procellarum.
compositions considered are explored in order to constrain
reasonable lava compositions that may have been responsible
for the formation of the observed sinuous rille. This approach
uses sinuous rilles as a window into the lunar interior to
provide constraints for the conditions that were present during the volcanically active period of lunar history.
3. Geologic Setting
[7] The Aristarchus Plateau (Figure 2) has been identified
as an uplifted block of lunar crust that shows compositional
evidence for highlands material (excavated by the Aristarchus
impact) that is superposed by Imbrium ejecta material and
a regional surface veneer of dark mantle deposits [McEwen
et al., 1994; Hawke et al., 1995; Chevrel et al., 2009] and
is surrounded to the north and east by mare basalts of
intermediate TiO2 content [Whitford-Stark and Head, 1980;
Giguere et al., 2000; Hiesinger et al., 2003]. Nearly 20 volcanic vents are preserved on the plateau in the form of typically circular depressions that act as the source for sinuous
rilles that extend from the plateau into the surrounding mare
basalt deposits [i.e., Schubert et al., 1970; Whitford-Stark and
Head, 1977]. Many additional sinuous rilles are observed
in the area surrounding the plateau, making the Aristarchus
Plateau – Harbinger Mountain region one of the more
densely concentrated volcanic centers that was likely to have
been active during the Imbrian period of lunar history [i.e.,
Zisk et al., 1977].
[8] Rima Prinz (Figure 3) is the westernmost sinuous rille
in a cluster of sinuous rilles near the Harbinger Mountains
located on a smaller plateau east of the Aristarchus Plateau.
The source depression of Rima Prinz lies on the northern
extent of ejecta associated with Prinz crater. The sinuous rille
is characterized by two channels, one larger valley and a
smaller, nested sinuous rille that is interpreted to have formed
in a second, independent eruption after an initial eruption
formed the larger valley [i.e., Strain and El-Baz, 1977;
Wilson and Head, submitted manuscript, 2011]. Both channels were heavily influenced by slope during their formation,
with an upper segment forming on Prinz ejecta (Figure 3b), a
middle segment forming in the mare abutting the northern
extent of Prinz ejecta (Figure 3c), and a lower segment
forming in the mare (Figure 3d), directed down-grade to the
north and terminating in Oceanus Procellarum (Figure 3e).
[9] Rima Prinz originates in a circular depression that is
interpreted to be the site of the eruption that fed the associated
lava channel [Head and Wilson, 1981; Wilson and Head,
1981]. A perspective view of Lunar Reconnaissance Orbiter
Narrow Angle Camera (LROC NAC) images M104805368LE
and M104805368RE (0.5 m pixel1) overlaid on Lunar
Orbiter Laser Altimeter (LOLA) data (120 m pixel1)
shows that the source depression for Rima Prinz has a steep,
well-consolidated rim (Figure 4a). The southern depression
wall (image left) is steep down to the depression floor while
the northern depression wall slopes more gradually to the
interpreted eruption location. This morphology is similar to
that observed in the source crater of Mauna Ulu, Hawaii
(Figure 4b), a feature that also has a steep, rocky rim and
one wall that slopes more gradually toward the eruption
location. Both source depressions are expected to have
formed during a fire fountain eruption due to erosion of the
surface beneath a lava lake [i.e., Head and Wilson, 1981;
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Figure 3. Images and observations of Rima Prinz. (a) Full view of Rima Prinz using the LROC WAC
global mosaic (100 m pixel1 resolution) with the source depression located on the northern ejecta deposits
of Prinz crater in the bottom center of the image (see Figure 4). The channel has been divided into three
segments, with (b) the upper segment extending from the source depression to the northern edge of the
ejecta deposits, (c) the middle segment following the northern boundary of the ejecta deposits, and (d) the
lower segment extending north before (e) terminating in Oceanus Procellarum. Detailed observations of
each channel segment are discussed in section 3 of the text.
Wilson and Head, 1981]. Remnant deposits of this lava lake
might still be visible in a long wavelength, hummocky texture on the floor of the source depression of Rima Prinz
(Figure 5a), a texture that is similar to that of deposits
observed in the remnant lava lake in Kilauea Iki, Hawaii
(Figure 5b). These observations of similar morphologies
between terrestrial fire fountain eruption features and lunar
sinuous rille source depressions support the theory that lunar
source depressions also formed as the result of fire fountain
eruptions [i.e., Wilson and Head, 1981; Head and Wilson,
1981].
[10] The three channel segments of Rima Prinz connect
the source depression on the ejecta of Prinz crater to the
mare plains of Oceanus Procellarum to the north. Each
channel segment is analyzed independently to assess channel
dimensions and morphology. Dimensions of interest include
1) channel length, which is measured by averaging the
lengths of the two bounding channel rims for each channel
segment; 2) channel width, which is measured by averaging
rim-to-rim distances along the length of each channel segment; 3) channel depth, which is measured by averaging the
differences between channel rim elevation and channel floor
elevation as documented by LOLA track data; 4) channel
sinuosity, which is measured by averaging distances between
meander extremes (i.e., meander wavelength) for each channel segment; and 5) regional slope, which is determined by
measuring the average regional slope along the channel rim
using LOLA gridded data. Sinuosity is measured in order to
provide an estimate of the width of the lava within the currently observed valley, as the valley was unlikely to have
been filled with lava [Pelletier, 2008]. Uncertainties in these
measurements are generally reported as the standard deviation of measurements made along the length of each channel
segment, with the exception of the uncertainty in channel
length, which is reported as the variation between the rim
length measurements and the length measurement of the
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Figure 4. Perspective view of the source depression of Rima Prinz, with LROC NAC images
M104805368LE and M104805368RE (0.5 m pixel1) overlying LOLA topography data (120 m pixel1).
(a) The source depression is characterized by a consolidated rim of highly reflective layers, a relatively
steep southern (left) wall, and a relatively gradually sloped northern (right) wall. This morphology is similar
to that of the source depression of Mauna Ulu, Hawaii, shown in Figure 4b. (b) The source depression for
Mauna Ulu formed as the result of a lava lake fed by a series of fire fountain eruptions, and a similar process
is thought to have occurred on the Moon to form the source depression of Rima Prinz.
interpreted channel thalweg. Measurements are summarized
in Table 1.
[11] The upper segment of Rima Prinz (Figure 3b) is
11 km +/ 3.0 km in length, 1.8 km +/ 0.7 km in width,
230 m +/ 20 m in depth, and has a sinuosity wavelength of
1.7 km +/ 0.7 km. This channel segment formed downgradient at a slope of 0.7 +/ 0.6 ; the uncertainty is higher
because the channel cut through relatively hummocky terrain
consistent with ejecta deposits. The channel is characterized
by steep, nearly parallel walls that lack obvious marginal
levees, and the walls appear to be well-preserved, lacking
evidence of substantial subsequent slumping. The nested
rille remains clearly visible throughout the channel segment and typically mirrors the sinuosity of the larger outer
channel.
[12] The middle segment of Rima Prinz (Figure 3c) is
19 km +/ 8.0 km in length, 1.0 km +/ 0.4 km in width,
210 m +/ 40 m in depth, and has a sinuosity wavelength of
2.4 km +/ 2.0 km. This channel segment formed downgradient at a slope 0.5 +/ 0.1 , forming along the bottom of
the northern extent of Prinz crater ejecta. While the northern
wall of the middle channel segment remains steep and
apparently well-preserved, the southern wall has been subjected to substantial slumping, possibly due to the collapse of
Prinz ejecta material during a subsequent impact such as one
responsible for the formation of Aristarchus crater to the
southwest. This deformation of the southern wall has resulted
in the concealment of the nested rille in many places along
this channel segment and led to the higher uncertainty values
in the reported length and depth measurements.
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Figure 5. (a) The floor of the source depression of Rima Prinz, shown with LROC NAC image
M104805368RE (0.5 m pixel1), and (b) the floor of Kilauea Iki, Hawaii. The deepest part of the Rima
Prinz source depression lies close to the southern steep wall, a wall that is characterized by boulder tracks
that formed as boulders rolled down the wall from the consolidated layers near the depression rim
(Figure 5a). The depression floor is characterized by a long wavelength, hummocky texture that is similar
to the texture observed in the remnant lava lake on the floor of Kilauea Iki (Figure 5b). These observations suggest that deposits associated with a remnant lava lake may still reside in the floor of the source
depression of Rima Prinz.
[13] The lower segment of Rima Prinz (Figure 3d) is
57 km +/ 3.0 km in length, 1.0 km +/ 0.3 km in width,
145 m +/ 30 m in depth, and has a sinuosity wavelength of
2.0 km +/ 1.0 km. This channel segment formed downgradient at a slope of 0.4 +/ 0.1 and extends northward
into Oceanus Procellarum. The lower segment of Rima Prinz
is characterized by the steep, parallel, and laterally continuous walls that are observed in the upper channel segment.
This portion of the channel also lacks obvious levees, consistent with a channel that formed as the result of erosion
processes. The nested rille is visible for much of the length of
the lower channel segment, and whereas the sinuosity of the
nested channel mirrors the outer channel along most of the
length of the channel segment, in some places the nested
channel is significantly more sinuous. This may be a result
of the duration of flow in the nested channel, with a longer
duration flow forming more stable, larger meanders, or it
may be the result of the low slope characteristic of this portion of the channel segment.
[14] Rima Prinz terminates (Figure 3e) in Oceanus Procellarum at the 1700 m contour, the same elevation
at which its neighboring sinuous rille to the east, Rima
“Beethoven,” terminates. Rima Prinz appears to increase in
sinuosity (i.e., decrease in sinuosity wavelength) as it nears
its terminus, and the walls remain nearly parallel and laterally
continuous, though the channel depth has decreased substantially. Deposits are not observed beyond the currently
observed channel terminus, indicating either that these
deposits are too thin to be observed due to the low viscosity
of the lava, or that they have been covered by subsequent
mare volcanic flows. Because Rima “Beethoven” to the east
terminates at the same elevation as Rima Prinz, embayment
by subsequent mare volcanism is the more likely scenario,
and careful inspection of the terminus of Rima Prinz indicates that mare lava may have flowed up-gradient through the
channel, partially flooding the observed channel terminus for
approximately 3–5 km (Figure 3e). It should be noted that the
embaying lava flows may have covered the distal part of
Rima Prinz, leading the length measurement for the lower
channel segment to represent a minimum value of the actual
length of this channel segment.
4. Theory of Lava Channel Formation by Erosion
[15] The morphology of Rima Prinz, specifically the lateral
continuity of the channel walls and the lack of levees
observed along the channel margins, supports the theory that
Rima Prinz formed as the result of erosion into the substrate.
The observations reported in section 3 represent the currently
observed product of this erosion and can thus be used in
Table 1. Observations and Measurements of Rima Prinz
Channel
Segment
Length
(km)
Uncertainty
Width
(km)
Standard
Deviation
Depth
(m)
Standard
Deviation
Sinuosity
(km)
Standard
Deviation
Slope
( )
Standard
Deviation
Upper
Middle
Lower
11
19
57
3 km
8 km
3 km
1.8
1.0
1.0
0.7 km
0.4 km
0.3 km
230
210
145
20 m
40 m
30 m
1.7
2.4
2.0
0.7 km
2 km
1 km
0.7
0.5
0.4
0.6
2
1
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HURWITZ ET AL.: ORIGIN OF RIMA PRINZ
conjunction with analytical models to distinguish between
two possible erosion regimes. The analytical models considered in this study include one mechanical erosion model
[Sklar and Dietrich, 1998] and two thermal erosion models
[Hulme, 1973; Williams et al., 1998, 2000]. As stated earlier,
mechanical erosion occurs as the result of collisions between
particles in the flowing fluid and the substrate, and the rate of
change in channel depth dchan as the result of mechanical
erosion is given by
dðdchan Þ
¼ KrgQw sina;
dt
mech
provided by the lava flow and the energy required to melt the
substrate, and is generally defined by
hT T Tmg
dðdchan Þ
¼
;
dt
Emg
therm
ð2Þ
where T and T mg represent the temperature of the lava and
the melting temperature of the substrate, respectively, hT is
the heat transfer coefficient, and Emg is the energy required to
melt the substrate and is given by
Emg ¼ rg cg Tmg Tg þ fmg Lg ;
ð1Þ
where Qw is the average lava flux per unit width through the
channel in m2 s–1 (Qw = dlava vlava, as calculated in
equations (6) and (7)), r is the lava density (see Table 2 for
parameter values), g is the acceleration due to gravity on the
Moon, a is the ground slope, and K is a factor with units of
Pa1 that represents the erodibility of the substrate [Sklar and
Dietrich, 1998; Hurwitz et al., 2010].
[16] The model simulating mechanical erosion is most
significantly affected by the erodibility factor K, as explained
in more detail by Hurwitz et al. [2010]. Higher values of the
factor K (107) represent a less consolidated substrate, like
the lunar regolith, that is more susceptible to mechanical
erosion at the lower slopes observed in relation to the lunar
sinuous rilles. Lower values of the factor K (109) represent a more consolidated substrate, like lunar basalt, that
is more susceptible to thermal erosion at lower slopes.
An unconsolidated surface with an erodibility of 107
results in a modeled mechanical erosion rate that is 5 times
higher than the mechanical erosion rate modeled for a consolidated substrate with an erodibility of 109. Slope also
represents a significant parameter in the model of mechanical
erosion, and analysis of how slope affects erosion rates is
explored in more detail in section 4.
[17] As discussed in a similar study of the origin of
a Martian lava channel, equation (1) can be thought of
conceptually as modeling the erosion rate as a function
of substrate erodibility and unit stream power, W, where
W = r g Q sin a [Sklar and Dietrich, 1998; Hurwitz et al.,
2010]. A different, more fundamental way to think about
equation (1) is to separate it into different energy components: the flux term Q is a function of lava velocity and thus
kinetic energy, and the term r g sin a represents the potential
energy stored in the flowing fluid. Equation (1) therefore
indicates that mechanical erosion depends on how efficiently
the kinetic and potential energies stored in the flowing fluid
are transferred to the substrate. Substrate erodibility is
dependent on substrate composition and consolidation, and
thus the thickness of the lunar regolith and the consolidation
of either the ejecta associated with the upper segment of
Rima Prinz or the mare basalt substrate can have a significant
effect on the modeled erosion rates. In general, equation (1)
predicts that a mechanically eroded channel will increase in
depth faster as a higher flux of lava flows over a more poorly
consolidated substrate.
[18] In contrast to mechanical erosion, thermal erosion
occurs when the flowing fluid is hot enough to melt the
substrate. The rate of change in channel depth dchan as
the result of thermal erosion is a function of the energy
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ð3Þ
where T g is the initial temperature of the ground or substrate,
cg is the specific heat of the substrate, Lg is the latent heat of
fusion for the substrate, and fmg is the fraction that the substrate must be melted before being carried away by the
flowing fluid [Hulme, 1973; Williams et al., 1998, 2000].
The two terms in equation (3) represent 1) the energy
required to raise the temperature of the substrate to the
melting temperature of the substrate and 2) the energy
required to melt the substrate. The additional heat transfer
coefficient term in equation (2) represents how efficiently
thermal energy can be transferred from the hot flowing lava
to the substrate. Two different approaches have been used to
define the heat transfer coefficient: one by Hulme [1973],
given by
hT ¼
0:017kRe4=5 Pr2=5
;
dlava
ð4Þ
and one by Williams et al. [1998, 2000], given by
0:027kRe4=5 Pr1=3
hT ¼
dlava
mb
mg
!0:14
;
ð5Þ
where k represents the thermal conductivity of the lava,
mb and mg represent the bulk viscosity of the lava and the
viscosity of the substrate, respectively, Re is the Reynolds
number (Re = rvdmlava , turbulent flow that enhances erosion
occurs when Re > 2000), and Pr is the Prandtl number (Pr =
cg m
k ). The difference between these two formulations of the
heat transfer coefficient is subtle, with the formulation by
Williams et al. [1998, 2000] incorporating a slightly higher
weighting of the Prandtl number than the formulation by
Hulme [1973]. This slightly higher weighting is used to
account for the thermal boundary layer, in effect changing the
efficiency at which heat is transferred across this boundary
between the flowing fluid and the substrate. The models
described in equations (2)–(5) indicate that thermal erosion
relies most significantly on the transfer of thermal energy
from the flowing lava to the substrate, but it should be noted
that thermal erosion is also dependent on kinetic and potential energies, factors that are included in the model through
the Re term in the heat transfer coefficient (equations (4) and
(5)). Velocity, a factor in Re, is found by iteratively solving a
model for moderately turbulent flows [Keszthelyi and Self,
1998], given by
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hvlava i2 ¼
gdlava sina
;
Cf
ð6Þ
HURWITZ ET AL.: ORIGIN OF RIMA PRINZ
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Table 2. Lava Compositions, Temperatures, Chemical Parameters, and Physical Parameters
Parameter Symbol
Units
High-Tia
Low-Tia
Komatiitea
Ocean Island Basalta
Initial lava composition
SiO2
TiO2
Al2O3
Fe2O3
FeO
MnO
MgO
CaO
Na2O
K2 O
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
39.7
10
6.63
0
22.5
0.32
12.2
7.67
0.06
na
43.7
2.9
8.2
0
21.9
0.35
12.5
8.4
0.07
na
45
0.3
5.6
1.4
9.2
0.2
32
5.3
0.6
0.03
48.5
1.76
10.2
1.29
1.04
0.17
17.1
8.2
1.51
0.27
Final lava composition
SiO2,f
TiO2,f
Al2O3,f
Fe2O3,f
FeOf
MnOf
MgOf
CaOf
Na2Of
K2 Of
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
wt%
40.5
12
7.9
0
22.3
0.33
7.8
9.1
0.07
na
50.2
4.9
14.1
0
15.5
0.29
0.72
14.1
0.12
na
47
0.5
8.8
2.2
11
0.3
21
8.3
0.9
0.05
52
2.5
14.5
1.8
9.4
0.17
5.2
11.5
2.15
0.38
1338
1322
1338
1150
1150
23
1529
1471
5.87 105
631
1.6 104
4.2 105
5.0 109
2.5 107
4055
3005
2981
0.464
0.83
20
21.15
12.31
7.98
1440
1388
1440
1150
1150
23
1539
1414
6.06 105
679
2.9 105
1.0 104
5.0 1010
2.5 108
4180
2894
2803
0.529
6.05
8
11.99
6.71
5.2
1578
1502
1578
1170
1170
23
1789
1671
6.97 105
1250
3.3 106
3.3 105
5.0 1011
2.5 109
4375
2778
2771
0.103
0.404
12
13.8
10.1
8.87
1408
1358
1408
1050
1050
23
1632
1490
4.20 105
340
9.6 104
4.3 103
5.0 1012
2.5 1010
4390
2726
2683
1.36
15.5
8
10.56
5.99
4.58
Parameter
Initial lava temperature
Final lava temperature
Liquidus temperature
Solidus temperature
Substrate melting temperature
Initial substrate temperature
Initial substrate specific heat
Final substrate specific heat
Substrate latent heat
Heat transfer coefficientb
Initial Reynolds number
Final Reynolds number
Erodibility factorb
Erodibility factorb
Volumetric lava flux
Initial lava density
Final lava density
Initial lava viscosity
Final lava viscosity
Initial lava depth
Final lava depth
Initial lava velocity
Final lava velocity
To
Tf
Tliq
Tsol
Tmg
Tg
cgo
cgf
Lg
hT
Reo
Ref
K
K
Q
rl,o
rl,f
ml,o
ml,f
dl,o
dl,f
vl,o
vl,f
C
C
C
C
C
C
J kg1 K1
J kg1 K1
J kg1
J m2 s1 K1
Pa1
Pa1
m3 s1
kg m3
kg m3
Pa s
Pa s
m
m
m s1
m s1
a
Lava compositions for high-Ti basalt came from Apollo 17 sample 74220 [Longhi et al., 1978], for low-Ti basalt from Apollo 12 sample 12002 [Longhi
et al., 1978], for komatiitic basalt from Kambalda, W. Australia [Lesher and Arndt, 1995], and for ocean island basalt from Kilauea, HI [Clague et al., 1991].
b
Heat Transfer Coefficient calculated from the Williams et al. [1998, 2000] model.
where Cf is a friction factor given by
"
Cf ¼
1
2Re þ 800 0:92
log10 6:15
32
41
!#!2
:
ð7Þ
It should be noted that the full model for thermal erosion
presented by Williams et al. [1998, 2000] and used in analysis of lava composition effects on erosion rate employs
alternative models for velocity and friction factor. The differences are subtle and do not significantly alter the qualitative interpretations made in the current study. For a more
detailed description of the full model, consult Williams et al.
[1998, 2000].
[19] The thermal erosion models presented in equations (2)–
(5) are most significantly affected by temperature, specifically
in the difference between erupted temperature, assumed to be
the liquidus temperature of the erupted lava, and the substrate
melting temperature, assumed to be the solidus temperature of
a lava of the same composition as the erupted lava. Specifically, a 100 K change in the erupted lava temperature T (i.e.,
the approximate difference between the erupted temperatures
of a komatiite-like basalt and a low-Ti basalt) results in a
change in the modeled thermal erosion rate of one order of
magnitude. The temperatures used in the model, as well as
the other considered parameters of thermal conductivity,
specific heat, and latent heat, are all dependent on the lava
composition considered, and each parameter is recalculated
depending on the composition used as an input to the model.
These parameter calculations are described in more detail by
Williams et al. [1998, 2000].
[20] The models presented in equations (1)–(5) are solved
initially to compare erosion rates in all three models. This is
accomplished by first calculating the volume flux of the
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HURWITZ ET AL.: ORIGIN OF RIMA PRINZ
source eruption based on the geometry of the source depression and the density of the lava [Head and Wilson, 1980;
Wilson and Head, 1980]. Second, the width of the lava that
flowed within the observed channel is calculated based on
observed sinuosity, assuming that a fully developed fluid
flow meanders at a wavelength equal to 10.88 times the flow
width [Pelletier, 2008]. Equations (6) and (7) are then used to
solve for flow velocity by iteratively changing the depth of
the lava within the observed channel. This iteration is continued until the volume flux predicted by the width, depth,
and flow velocity calculations match the volume flux calculated independently. Once the lava depth and flow velocity
values are constrained, Re and hT are calculated and the
models in equations (1)–(5) are solved for erosion rate in
each erosion regime considered.
5. Results
[21] The three models discussed in section 4 are used to
simulate the erosion rates expected for the head of Rima
Prinz (at the intersection of the channel and the source
depression) in order to 1) distinguish between mechanical
and thermal erosion origins for the sinuous rille and to
2) compare the erosion rates predicted by the two thermal
erosion models. In order to directly compare model results,
the two thermal erosion models are run for only the head of
the upper segment of Rima Prinz, where no contamination
due to assimilation of melted substrate into the flowing lava
has occurred and thus thermal and geophysical properties of
the lava are assumed to be constant. These models are run for
both terrestrial and lunar gravity conditions at various slopes
to determine how gravity and slope affect predicted erosion
rates. The most relevant model is then used to simulate the
complete formation of Rima Prinz in the presence of different
lavas in order to constrain the conditions present during the
formation of this sinuous rille.
[22] Results for the mechanical and two thermal erosion
models are shown in Figure 6, with results for terrestrial
gravity conditions shown in Figure 6a and results for lunar
gravity conditions shown in Figure 6b. These models were
run assuming a lava composition similar to that of a terrestrial
ocean island basalt (Table 2) because lunar lavas that erupt in
high-effusion rate, high-volume eruptions are expected to
originate from below the lunar crust-mantle interface, and the
lavas erupt at effusion rates similar to those of terrestrial
ocean island basalts [e.g., Head and Wilson, 1992; Wieczorek
et al., 2001]. A lava composition similar to an ocean island
basalt is considered in this study because eruption fluxes
modeled for lunar eruptions and potential source depressions
observed on the lunar surface are similar to those eruption
fluxes and source depressions observed in conjunction with
eruptions of ocean island basalts on Hawaii [e.g., Head and
Wilson, 1980; Wilson and Head, 1980].
[23] Results for the terrestrial case indicate that mechanical
erosion is more efficient than thermal erosion at slopes
greater than about 0.4 . This suggests that at slopes greater
than 0.4 in the terrestrial case, gravitational potential energy
and thus kinetic energy are the dominant forms of energy
acting during channel formation. Alternatively, at slopes less
than 0.4 , potential and kinetic energies are insignificant
compared to the thermal energy stored in the flowing lava,
and thus thermal erosion dominates the formation process. In
E00H14
contrast, results for the lunar case indicate that thermal erosion dominates the channel formation process at slopes less
than about 3.5 . This suggests that the lower gravity characteristic of the Moon provides insufficient potential energy
and thus kinetic energy to contribute significantly to the
formation of Rima Prinz (which has a < 0.7 ). These results
indicate that thermal erosion can dominate the formation of
lunar sinuous rilles that form on consolidated substrates of
basalt at low slopes even though it is not a commonly
observed process in the formation of terrestrial lava channels
that typically form on steeper gradients.
[24] Results shown in Figure 6 also indicate that predicted
erosion rates are similar for both thermal erosion models
considered. While these results certainly depend on the lava
composition and geophysical properties assumed, predicted
erosion rates are typically within 25% for the lava compositions considered as inputs for each model. Because the
results are similar and because the full model developed by
Williams et al. [1998, 2000] incorporates added complexities
that allow for the analysis of affects of lava composition on
channel formation, the full model developed by Williams
et al. [1998, 2000] is used to simulate the detailed formation of Rima Prinz. The full model simulates the formation of
a lava channel as a function of distance from the eruption,
tracing how much of the substrate has been melted and
assimilated into the flowing lava as well as how much olivine
has crystallized in the flowing fluid, then recalculating the
thermal and geophysical properties (such as Reynolds number, Prandtl number, heat transfer coefficient, thermal conductivity, and bulk viscosity) of the new lava composition
[Williams et al. [1998, 2000]. In addition to heat lost to the
substrate, this model also simulates the formation of a fusion
crust at the top of the lava flow, a crust that can be an efficient
insulator for the lava flow [Williams et al. 1998, 2000].
[25] The model developed by Williams et al. [1998, 2000]
is used to determine how fast erosion occurs (i.e., erosion
rate), and from these results and observations of depth in the
head of the upper channel segment, the duration of the
eruption that is required to form this uppermost portion of
Rima Prinz is determined. This calculated eruption duration,
which remains constant for the rest of the channel, is then
used with modeled erosion rates to calculate a predicted
depth for the remainder of the upper, middle, and lower
channel segments, and these predicted erosion depths are
compared with observed depths of Rima Prinz to confirm the
merit of the model (Figure 7). In order to determine effects of
lava composition on erosion rates, four compositions of lava
are considered in this analysis, including compositions similar to a lunar high-Ti basalt (i.e., Apollo 17 sample 74220,
[Longhi et al., 1978]), a lunar low-Ti basalt (i.e., Apollo 12
sample 12002, [Longhi et al., 1978]), a terrestrial komatiite
(i.e., Kambalda, W. Australia [Lesher and Arndt, 1995]), and
a terrestrial ocean island basalt (i.e., Kilauea, HI [Clague
et al., 1991]; see Table 2). The two lunar lava compositions
are considered because they represent lavas that have been
sampled and analyzed directly from the lunar surface, though
the lavas sampled from the lunar surface do not necessarily
represent the lava that flowed through and formed the
observed sinuous rilles. The composition of terrestrial ocean
island basalt is considered because of similarities between
predicted eruption fluxes and observed features associated
with channels for both lunar sinuous rilles and Hawaiian
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Figure 6. Erosion rate versus slope for (a) terrestrial gravity conditions and (b) lunar gravity conditions;
erosion rate is found using one model of mechanical erosion [Sklar and Dietrich, 1998] and two models of
thermal erosion [Hulme, 1973; Williams et al., 1998, 2000] to determine which erosion regime dominates
during channel formation. For the terrestrial case, mechanical erosion is more efficient than thermal erosion
at slopes greater than 0.4 , a result of more significant potential and thus kinetic energies that drive the
erosion process (Figure 6a). In contrast, for the lunar case, the lower gravity conditions contribute insignificant potential and thus kinetic energies, allowing thermal energy to drive the erosion process at slopes
less than 3.5 (Figure 6b). Slopes shown represent the range of slopes over which sinuous rilles are
currently observed on the Moon; thus, thermal erosion is expected to have dominated the formation of lunar
lava channels that formed on consolidated substrates of basalt. It should be noted that mechanical erosion
was still likely to have dominated the initial formation of the sinuous rille as lava flowed over unconsolidated lunar regolith material.
eruptions of ocean island basalt lavas [e.g., Head and Wilson,
1980; Wilson and Head, 1980], and the composition of
terrestrial komatiite is considered because komatiites are
observed to have high liquidus and eruption temperatures,
high Mg- and low Si-content, and thus a very low viscosity;
lavas with a low viscosity are expected to be more efficient
erosion agents [e.g., Huppert and Sparks, 1985].
[26] Results of the comparison between observed and
predicted depths (Figure 7) indicate that the model does follow the trends in channel depth as observed using LOLA
track data (Table 1) for each composition of lava considered.
The gradual decreases in predicted eroded depth are a result
of the decrease in erosion efficiency as lava temperature
decreases and as lava contamination from assimilated substrate and thus lava viscosity increases with distance from the
source vent. The sharp decreases in predicted eroded depth
are artifacts due to the change in observed average channel
slope incorporated into the model at the beginning of each
channel segment. While in reality these slopes would vary
more smoothly along the length of the channel, the predicted
eroded depths adequately follow the trend in channel depths
observed, supporting the earlier interpretation that thermal
erosion is sufficiently simulating the formation of Rima
Prinz.
[27] Model results also indicate that lava composition
has a significant influence on the erosion rate and thus the
eruption duration required to form the observed sinuous rille
(Figure 8). Results are presented for scenarios in which the
composition of the initial, uncontaminated lava is identical to
the composition of the substrate; while the composition of the
lava changes down gradient due to crystallization of olivine
(which will occur as the lava temperature decreases below
the liquidus temperature) and contamination by assimilated
substrate, the substrate composition remains constant. The
gradual decreases in predicted erosion rates mirror those in
the results for predicted eroded depth and are similarly a
result of the decrease in erosion efficiency as lava temperature decreases and lava viscosity increases with distance from
the source vent. The steep decreases in erosion rate are artifacts of the abrupt change in slope used for each channel
segment in the model, though again in reality the slope typically changes more gradually along the channel length.
[28] Results indicate that lava with a composition similar to
that of a terrestrial komatiite will erode the substrate faster
than lava similar to a lunar high-Ti basalt. Lavas with compositions similar to those of lunar low-Ti basalt and terrestrial
ocean island basalt result in intermediate erosion rates.
Lavas producing faster erosion rates require shorter eruption
durations to incise the observed channel. Specifically, a
komatiite-like lava, with erosion rates ranging from about
1.7 m d1 at the head of the channel to 0.80 m d1 at the
channel terminus, requires about 157 Earth days (0.4 Earth
years) to incise Rima Prinz. An ocean island basalt-like lava
(OIB) has erosion rates ranging from about 0.7 m d1 at the
head of the channel to 0.4 m d1 at the channel terminus,
requiring approximately 360 Earth days (1 Earth year) to
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been the dominant process active during channel formation
on the Moon (Figure 6). This dominance is due to the fact that
the low gravity conditions characteristic of the Moon yield
insignificant potential and thus kinetic energies in lava
flowing on the lunar surface. Therefore, thermal energy
contributed by hot lava flowing over a substrate is the dominant form of energy present in lava flowing over a gradually
sloped lunar substrate, and thermal erosion rather than
mechanical erosion was the dominant erosion regime present
during lunar channel formation.
[30] These results are valid for lunar slopes less than about
3.5 and for a well-consolidated basalt substrate with a yield
Figure 7. Eroded depth versus distance from the head of
Rima Prinz. Dots indicate channel depths that were observed
using LOLA track data, and the various lines indicate
modeled depths (using the model by Williams et al. [1998,
2001]) for four types of lava considered, including terrestrial
komatiite, terrestrial ocean island basalt, lunar low-Ti basalt,
and lunar high-Ti basalt. Model results for each lava type
match the observed overall trend of decreasing channel depth
with distance from source. Gradually decreasing trends are
due to an increase in lava assimilation, a process that corresponds to a decrease in lava temperature, an increase in lava
viscosity, and a decrease in erosion efficiency and thus
eroded depth. The steep decreases in eroded depth are artifacts representing abrupt decreases in the average slope
measured for each channel segment. Actual changes in slope
are likely to have been more gradual, leading to a more
gradual decrease in eroded depth.
incise the observed channel. A low-Ti basalt has erosion rates
ranging from about 0.6 m d1 at the head of the channel to
about 0.3 m d1 at the channel terminus, requiring 435 Earth
days (1.2 Earth years) to incise the observed channel.
A high-Ti basalt has the lowest erosion rates ranging from
0.35 m d1 at the channel head to 0.2 m d1 at the channel
terminus, and this lava requires approximately 770 Earth
days (2.2 Earth years), to incise the observed channel.
These times assume a constant eruption flux for the predicted
duration of channel formation and thus represent an average
time required for the formation of Rima Prinz, as eruption
fluxes typically wax and wane over the course of a single
eruption.
6. Discussion
[29] Rima Prinz is a sinuous rille characterized by laterally
continuous walls and a lack of marginal levees, and it is thus
interpreted to be a lava channel that formed as the result of
erosion into the lunar substrate. Analysis of analytical model
results of erosion rate versus slope indicates that thermal
erosion was more likely than mechanical erosion to have
Figure 8. Erosion rate versus distance from the head of
the sinuous rille. Each line represents one of the four lava
types considered: terrestrial komatiite, terrestrial ocean island
basalt, lunar low-Ti basalt, and lunar high-Ti basalt. In each
case, lava of a given initial composition is assumed to erode
a substrate of the same composition. The lava is assumed to
erupt at its associated liquidus temperature, and the substrate
is assumed to melt at its associated solidus temperature.
Results indicate that a komatiite lava flow, with the greatest
difference between its liquidus and solidus temperatures
(see Table 3), erodes a similarly composed substrate at the
fastest rates, from 1.7 m d1 at the channel head to 0.8 m d1
at the channel terminus, and requires the shortest eruption
duration, 157 Earth days, to erode the observed channel. In
contrast, a lunar high-Ti basalt, with the smallest difference
between its liquidus and solidus temperatures, erodes at
the slowest rates, from 0.35 m d1 at the channel head to
0.2 m d1 at the channel terminus, and requires the longest
eruption duration, 766 Earth days, to erode the observed
channel. Results for ocean island basalt and for lunar low-Ti
basalt indicate that these lava types have intermediate erosion
efficiencies (0.7 m d1–0.4 m d1 and 0.6 m d1–0.3 m d1,
respectively). The gradual decrease in erosion rate observed
for each lava composition is due to lava contamination
and associated reduction in erosion efficiency, and the steep
decrease is an artifact due to abrupt changes in the slope
entered into the model for each channel segment.
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Table 3. Summary of Resultsa
Lava
Type
Tliq
( C)
Tsol
( C)
DT
( C)
Q
(m3 s1)
Erosion Rate 1
(m d1)
Erosion Rate 2
(m d1)
Duration
(Earth days)
Vlava
(km3)
Komatiite
Ocean Island Basalt
Low-Ti Basalt (12002)
High-Ti Basalt (74220)
1578
1408
1440
1338
1170
1050
1150
1150
408
358
290
188
4375
4390
4180
4055
1.7
0.75
0.6
0.35
0.8
0.4
0.3
0.2
157
362
435
766
59
137
157
268
a
Erosion Rate 1 represents erosion at the head of Rima Prinz; Erosion Rate 2 represents erosion at the terminus of Rima Prinz.
strength Y of 0.1 MPa [Schultz, 1993] and an erodibility b
of 0.0005 ([Hurwitz et al., 2010] K = Y / b = 5 109 Pa1).
It should be noted that erosion rate is expected to increase in
the presence of a less consolidated substrate such as the lunar
regolith. Specifically for the case of lava composed similarly
to that of an ocean island basalt flowing at the head of Rima
Prinz (a = 0.7 ; see Figure 6), mechanical erosion is expected
to increase from about 1.0 m d1 in the case of a consolidated
basaltic substrate to about 5.0 m d1 in the case of an
unconsolidated regolith substrate (erodibility of 0.0025
[Hurwitz et al., 2010]). This change leads to the interpretation that mechanical erosion is more efficient than thermal
erosion for slopes greater than 0.6 , as is the case at the
head of Rima Prinz (thermal erosion rate = 4.0 m d1 at
a = 0.7 ; see Figure 6). Therefore, mechanical erosion was
likely to have been the dominant process in the initial formation of the channel when the lava is incising through
regolith, but the dominant erosion regime shifted to thermal
erosion once the regolith was removed and a more consolidated basaltic substrate was encountered. This initial period
of more efficient mechanical erosion would be expected to
decrease the duration of channel formation by about 6–10
Earth days, assuming a regolith thickness of 6–10 m [Fa and
Jin, 2010; Kobayashi et al., 2010].
[31] Further analysis of model results indicates that lava
composition has a significant effect on erosion efficiency.
Specifically, komatiite lavas erode a similarly composed
substrate more efficiently than lunar low-Ti basalts, ocean
island basalts, and, most significantly, high-Ti basalts erode
into respectively similarly composed substrates (Figure 8).
The models used to simulate thermal erosion (equations (2)–
(5)) suggest that the most significant parameter involved in
determining erosion efficiency is the difference between the
temperature of the flowing lava and the melting temperature
of the substrate. In the scenarios explored in this study, the
compositions of the initially erupted lava and the substrate
are identical. Therefore, the lava is assumed to erupt at its
corresponding liquidus temperature and the substrate is
assumed to melt at its corresponding solidus temperature
(Table 3). Lava with a composition similar to that of a terrestrial komatiite has the greatest difference between its corresponding liquidus and solidus temperatures (DT = 408 C;
see Table 3), and lava with a composition similar to that of
a lunar high-Ti basalt has the smallest difference between
these two temperatures (DT = 188 C). These observations
are consistent with larger differences between the liquidus
and solidus temperatures resulting in a higher thermal energy
contribution from the flowing lava and thus in higher erosion
rates.
[32] Lavas that erode more efficiently require shorter
eruption durations and thus also require less lava to form the
observed sinuous rille (Figure 8 and Table 3). Specifically,
the fastest eroding komatiite lava requires 157 Earth days to
form the channel, and, assuming a constant eruption flux of
4375 m3 s1 [i.e., Wilson and Head, 1980; Head and Wilson,
1980] over the course of the eruption, the volume of lava that
is expected to be released is 59 km3. This lava volume is
similar to the volume of lava erupted in 43 flows over the
course of 18 eruptions measured on Mauna Loa (25.8 km3
[Malin, 1980]) and about an order of magnitude greater than
the volume of lava erupted in 44 flows over 15 eruptions
measured on Kilauea (2.6 km3 [Malin, 1980]). In contrast,
the slowest eroding high-Ti lunar basalt requires 766 Earth
days to form the channel, and, assuming a constant eruption flux in this case of 4055 m3 s1 over the course of the
eruption, the volume of lava that is expected to be released is
268 km3. This lava volume is significantly larger than those
observed in Hawaii, but this volume is still an order of
magnitude less than the volume of lava that erupted in a
single fissure eruption associated with the emplacement of
the Columbia River flood basalts (>2,000 km3 [Hooper,
1997]). A cursory quantitative analysis of a lava composition similar to a Columbia River basalt [Murase and
McBirney, 1970] indicates that this lava would be very
inefficient at eroding a similarly composed substrate, supporting observations that thermal erosion does not occur in
the Columbia River flood basalts [Greeley et al., 1998]. It
should be noted that the lava volumes reported above represent the entire amount of lava required to form the observed
sinuous rille, but that individual flows may have had smaller
volumes if the channel formed over a series of events similar
to those observed in Kilauea instead of as the result of a
single eruptive event similar to the fissure event in the
Columbia River flood basalt.
[33] The significant volume of lava required to form Rima
Prinz must have been deposited beyond the terminus of the
sinuous rille in Oceanus Procellarum. However, one of
the more enigmatic characteristics of lunar sinuous rilles is
the lack of observed deposits at and beyond the channel termini (Figure 3e). As suggested in section 3, these deposits
may have been embayed by subsequent emplacement of
mare flows that may have flowed back up the channel for
3–5 km from the currently observed channel terminus.
Although the terminal deposits of Rima Prinz are not currently observed, LOLA topography data can be used to estimate the path that the lava may have taken once it left the
confines of the channel (Figure 9). The main assumptions
used in this analysis include, 1) the lava will always flow
down-gradient, 2) on steep slopes (i.e., contours are closely
spaced), lava will flow perpendicular to the contour, 3) on
suddenly gradual slopes (i.e., contours are suddenly spaced
far apart), lava will tend to flow along a contour until a
steeper gradient is reached, 4) lava tends to flow around
topographic boundaries and into basins, and 5) currently
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Figure 9. (a) Proposed deposit area for the volume of erupted lava required to form Rima Prinz, shown
using the LROC WAC global mosaic (100 m pix1 resolution) and (b) LOLA topography data with
20 m contours (120 m pix1). The deposit area was mapped based on five assumptions enumerated in
section 6 of the text. The lava forming the proposed deposit flowed down-gradient, with its flow path
influenced by topography, until it reached a topographic basin 75 km from the terminus of Rima Prinz
and formed a deposit of a depth dependent on the composition of the lava (see Table 3). The deposit then
would have been completely embayed by subsequent mare volcanism, as textural evidence for this lava
flow is not currently observed.
observed topography would have affected the path of the
lava.
[34] An example of a possible lava deposit area is shown in
Figure 9. The flow has a length of 75 km, a length that is
approximately double that of the longer Kilauea flows that
may have been truncated by encountering the ocean [Malin,
1980], and the flow has a surface area of approximately
2450 km2. The proposed deposit would have terminated in a
basin northeast of Rima Prinz, partially but not completely
filling the basin, as the basin is still observed. As previously
discussed, model results indicate that a range of lava volumes
(59 km3–268 km3) may have been required to form Rima
Prinz, dependent on lava composition. These total lava
volumes translate to average deposit depths of 25 m for a
komatiite lava, 55 m for an ocean island basalt, 65 m for
a low-Ti lunar basalt, and 110 m for a high-Ti lunar basalt
over the proposed deposit area. Deposit depths are expected
to decrease for flows deposited on steeper surfaces and
increase for flows deposited on more gradually sloped surfaces or within basins. These depths indicate a minimum
value for the thickness of the subsequent mare flows required
to cover the deposits from Rima Prinz. The composition of
the mare in the western Imbrium region has been identified as
intermediate TiO2 basalts that lack evidence for extensive
mixing [i.e., Zisk et al., 1977; Whitford-Stark and Head,
1980; Giguere et al., 2000; Hiesinger et al., 2003]. While
the depth of the mare fill itself is dependent on the volume
of lava erupted during the emplacement of these deposits,
observations of irregular ‘shorelines’ along the edges of
Oceanus Procellarum suggest that the mare is relatively
shallow along the margins [i.e., Head, 1976]. Therefore,
it might be expected that the mare lava would not be thick
enough to completely embay high-Ti flows from Rima Prinz,
and thus the lava that flowed through and incised Rima Prinz
was most likely to have been composed similarly to lavas
such as komatiites, ocean island basalts, or low-Ti lunar
basalts.
7. Conclusions
[35] The formation of lunar sinuous rilles has long been
considered an enigma, with proposed origin theories including a range of formation mechanisms: 1) origin via construction of levees that channelize flow within a cooling lava
flood, 2) origin via either a constructed, structurally stable
roof over a lava tube or an eroded subsurface lava tube,
and 3) origin via erosion in a surface channel. Our observations of Rima Prinz, a sinuous rille located east of the
Aristarchus Plateau, indicate that this channel has laterally
continuous walls that lack marginal levees, supporting the
theory of origin through erosion of the substrate by a surface
channel. Detailed measurements of channel morphology
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HURWITZ ET AL.: ORIGIN OF RIMA PRINZ
were used as constraints in analytical models in order to
determine whether mechanical or thermal erosion is the
dominant process active during the formation of Rima Prinz.
The most relevant model was then used to determine the
detailed origin of Rima Prinz, including the lava compositions, erosion rates, and eruption durations required to
produce the observed sinuous rille.
[36] The key interpretations of model results presented in
this study indicate that the low gravity characteristic of the
Moon contributes an insignificant amount of potential and
thus kinetic energy to lava flowing on a surface of slopes less
than 3.5 , allowing thermal energy and thus thermal erosion rather than mechanical erosion to dominate during the
formation of a lunar sinuous rille on terrain with these slopes.
Thermal erosion is expected to dominate during sinuous rille
formation on the Moon even though it is not a commonly
observed process in terrestrial lava channel formation, as
terrestrial lava channels form under higher gravity conditions and typically on steeper gradients. Mechanical erosion
remains an important process in the initial stages of lunar
sinuous rille formation, however, as lava initially encounters
the poorly consolidated lunar regolith that is much more
susceptible to mechanical erosion than the more consolidated
underlying basaltic substrate.
[37] Additional analysis of results from a model that
includes lava composition as a model input [Williams et al.,
1998, 2000] indicates that lava composition has a significant effect on erosion rates. In particular, assuming that lava
erupts at its liquidus temperature and melts at its solidus
temperature, and assuming that the erupted lava has the same
composition as the substrate, the lava composition with the
greatest difference between its solidus and liquidus temperatures will contribute the most thermal energy to melting
the substrate and incising a channel. Further analysis of
model results indicates that erosion efficiency increases with
greater liquidus-solidus temperature differences: a lava with
a composition similar to a terrestrial komatiite (DT = 408 C)
results in the highest erosion rates (1.7 m d1–0.8 m d1)
and a lava with a composition similar to a lunar high-Ti
basalt (DT = 188 C) results in the lowest erosion rates
(0.35 m d1–0.2 m d1). Lavas with compositions similar
to terrestrial ocean island basalts (DT = 358 C) and lunar
low-Ti basalts (DT = 290 C) result in intermediate erosion rates (0.7 m d1–0.4 m d1 and 0.6 m d1–0.3 m d1,
respectively).
[38] As expected, greater erosion rates require less time
and thus less lava to carve the observed channel. Results
indicate that a komatiite-like lava would require 157 Earth
days and 59 km3 of lava to form Rima Prinz, an ocean island
basalt-like lava would require 362 Earth days and 137 km3
of lava, a lunar low-Ti basalt would require 435 Earth days
and 157 km3 of lava, and a lunar high-Ti basalt would require
766 Earth days and 268 km3 of lava to form Rima Prinz.
Although lava deposits are not currently observed at the terminus of Rima Prinz, a plausible deposit area of 2450 km2
is proposed based on LOLA topography data. The volumes
of lavas listed above would thus result in komatiite-like lava
deposit depths of 25 m, ocean island basalt deposit depths
of 55 m, lunar low-Ti basalt deposit depths of 65 m, and
lunar high-Ti basalt depths of 110 m. These deposits must
have been completely embayed by subsequent mare flows of
E00H14
intermediate TiO2 content and relatively shallow depths in
order to no longer be visible, suggesting that the most likely
candidates for the composition of lava that formed Rima
Prinz include komatiites, ocean island basalts, and lunar
low-Ti basalts.
[39] Further work is needed to constrain the actual composition of the lava that formed lunar sinuous rilles. The
general lack of deposits within and beyond the currently
observed channel makes this a challenging task. However,
the identification of possible remnant lava lake textures in the
floor of the Rima Prinz source depression provide a possible
starting point for further remote-sensing analyses as well as
a desired destination for future ground-based studies. While
there are certainly outstanding questions as to the detailed
origin of some lunar sinuous rilles, it is clear from this study
that thermal erosion may have played a significant role in the
formation of these features and that the formation of lunar
sinuous rilles represents significant events in the volcanic
history of the Moon.
[40] Acknowledgments. We gratefully acknowledge David Williams
for providing the code used extensively in the analysis presented in this
paper as well as for giving a thorough and critical review of the paper. We
also thank an additional anonymous reviewer for a thoughtful review. This
research was supported financially by the National Aeronautics and Space
Administration through grants NNX09AM54G and NNG07EK00C from
the NASA Lunar Reconnaissance Orbiter project and the LRO Camera
(LROC) and Lunar Orbiter Laser Altimeter (LOLA) experiments.
References
Boyd, A. K., H. Hiesinger, M. S. Robinson, T. Tran, C. H. van der Bogert,
R. V. Wagner, and the LROC Science Team (2011), Lunar pits: Sublunarean voids and the nature of mare emplacement, Lunar Planet. Sci.,
XLII, Abstract 2771.
Carr, M. H. (1974), The role of lava erosion in the formation of lunar
rilles and Martian channels, Icarus, 22, 1–23, doi:10.1016/00191035(74)90162-6.
Chevrel, S. D., P. C. Pinet, Y. Daydou, S. Le Mouélic, Y. Langevin,
F. Costard, and S. Erard (2009), The Aristarchus Plateau on the Moon:
Mineralogical and structural study from integrated Clementine UV–visNIR spectral data, Icarus, 199, 9–24, doi:10.1016/j.icarus.2008.08.005.
Clague, D. A., W. S. Weber, and J. E. Dixon (1991), Picritic glasses from
Hawaii, Nature, 353, 553–556, doi:10.1038/353553a0.
Coombs, C. R., and B. R. Hawke (1988), Kauhako crater and channel,
Kalaupapa, Molokai: A preliminary look at a possible analog to lunar
sinuous rilles, Lunar Planet. Sci., XIV, 207–208.
Coombs, C. R., B. R. Hawke, and L. Wilson (1990), Terrestrial analogs to
lunar sinuous rilles: Kauhako crater and channel, Kalaupapa, Molokai,
and other Hawaiian lava conduit systems, Proc. Lunar Planet. Sci. Conf.,
20th, 195–206.
Fa, W., and Y. Q. Jin (2010), A primary analysis of microwave brightness
temperature of lunar surface from Chang-E 1 multi-channel radiometer
observation and inversion of regolith layer thickness, Icarus, 207,
605–615, doi:10.1016/j.icarus.2009.11.034.
Fagents, S., and R. Greeley (2001), Factors influencing lava-substrate heat
transfer and implications for thermomechanical erosion, Bull. Volcanol.,
62, 519–532, doi:10.1007/s004450000113.
Giguere, T. A., G. J. Taylor, B. R. Hawke, and P. G. Lucey (2000),
The titanium contents of lunar mare basalts, Meteorit. Planet. Sci., 35,
193–200, doi:10.1111/j.1945-5100.2000.tb01985.x.
Greeley, R. (1971), Lunar Hadley Rille: Considerations of its origin,
Science, 172, 722–725, doi:10.1126/science.172.3984.722.
Greeley, R., S. A. Fagents, R. S. Harris, S. D. Kadel, D. A. Williams, and
J. E. Guest (1998), Erosion by flowing lava: Field evidence, J. Geophys.
Res., 103, 27,325–27,345, doi:10.1029/97JB03543.
Gregg, T. K. P., and R. Greeley (1993), Formation of Venusian Canali:
Considerations of lava types and their thermal behaviors, J. Geophys.
Res., 98, 10,873–10,882, doi:10.1029/93JE00692.
Haruyama, J., et al. (2009), Possible lunar lava tube skylight observed
by SELENE cameras, Geophys. Res. Lett., 36, L21206, doi:10.1029/
2009GL040635.
14 of 15
E00H14
HURWITZ ET AL.: ORIGIN OF RIMA PRINZ
Hawke, B. R., C. A. Peterson, C. R. Coombs, P. G. Lucey, G. A. Smith, and
G. J. Taylor (1995), Remote sensing studies of the Aristarchus region of
the Moon, Lunar Planet. Sci. Conf., XXVI, 559–560.
Head, J. W. (1976), Lunar volcanism in space and time, Rev. Geophys., 14,
265–300, doi:10.1029/RG014i002p00265.
Head, J. W., and L. Wilson (1980), The formation of eroded depressions
around the sources of lunar sinuous rilles: Observations, Proc. Lunar
Planet. Sci. Conf., 11th, 426–428.
Head, J. W., and L. Wilson (1981), Lunar sinuous rille formation by thermal
erosion: Eruption conditions, rates and durations, Proc. Lunar Planet.
Sci. Conf., 12th, 427–429.
Head, J. W., and L. Wilson (1992), Lunar mare volcanism: Stratigraphy,
eruption conditions, and the evolution of secondary crusts, Geochim.
Cosmochim. Acta, 56, 2155–2175.
Hiesinger, H., J. W. Head, U. Wolf, R. Jaumann, and G. Neukum (2003),
Ages and stratigraphy of mare basalts in Oceanus Procellarum, Mare
Nubium, Mare Cognitum, and Mare Insularum, J. Geophys. Res.,
108(E7), 5065, doi:10.1029/2002JE001985.
Hooper, P. R. (1997), The Columbia River flood basalt province: Current
status, Geophys. Monogr. Ser., 100, 1–27, doi:10.1029/GM100p0001.
Huang, J., L. Xiao, X. He, L. Qiao, J. Zhao, and H. Li (2011), Geological
characterstics and model ages of Marius Hills on the Moon, J. Earth
Sci., 22, 601–609, doi:10.1007/s12583-011-0211-8.
Hulme, G. (1973), Turbulent lava flow and the formation of lunar sinuous
rilles, Mod. Geol., 4, 107–117.
Hulme, G. (1974), The interpretation of lava flow morphology, Geophys.
J. Int., 39, 361–383, doi:10.1111/j.1365-246X.1974.tb05460.x.
Hulme, G. (1982), A review of lava flow processes related to the formation of lunar sinuous rilles, Surv. Geophys., 5, 245–279, doi:10.1007/
BF01454018.
Hulme, G., and G. Fielder (1977), Effusion rates and rheology of lunar
lavas, Philos. Trans. R. Soc. London, Ser. A, 285, 227–234, doi:10.1098/
rsta.1977.0059.
Huppert, H. E., and R. S. J. Sparks (1985), Komatiites: I. Eruption and flow,
J. Petrol., 26, 694–725.
Hurwitz, D. M., C. I. Fassett, J. W. Head, and L. Wilson (2010), Formation
of an eroded lava channel within an Elysium Planitia impact crater:
Distinguishing between a mechanical and thermal origin, Icarus, 210,
626–634, doi:10.1016/j.icarus.2010.07.024.
Kerr, R. C. (2009), Thermal erosion of felsic ground by the laminar flow of
a basaltic lava, with application to the Cave Basalt, Mount St. Helens,
Washington, J. Geophys. Res., 114, B09204, doi:10.1029/2009JB006430.
Keszthelyi, L., and S. Self (1998), Some physical requirements for the
emplacement of long basaltic lava flows, J. Geophys. Res., 103,
27,447–27,464, doi:10.1029/98JB00606.
Kobayashi, T., J. H. Kim, S. R. Lee, H. Araki, and T. Ono (2010), Simultaneous observation of Lunar Radar Sounder and Laser Altimeter of
Kaguya for lunar regolith layer thickness estimate, Geosci. Remote Sens.
Lett., 7, 435–439.
Komatsu, G., and V. R. Baker (1992), Venusian sinuous rilles, LPI
Contrib., 789, 60–61.
Lesher, C. M., and N. T. Arndt (1995), REE and Nd isotope geochemistry,
petrogenesis and volcanic evolution of contaminated komatiites at
Kambalda, Western Australia, Lithos, 34, 127–157.
Longhi, J., D. Walker, and J. F. Hays (1978), The distribution of Fe and
Mg between olivine and lunar basaltic liquids, Geochim. Cosmochim.
Acta, 42, 1545–1558, doi:10.1016/0016-7037(78)90025-X.
Malin, M. C. (1980), Lengths of Hawaiian lava flows, Geology, 8,
306–308, doi:10.1130/0091-7613(1980)8<306:LOHLF>2.0.CO;2.
McEwen, A. S., M. S. Robinson, E. M. Eliason, P. G. Lucey, T. C.
Duxbury, and P. D. Spudis (1994), Clementine observations of the
Aristarchus region of the Moon, Science, 266, 1858–1862, doi:10.1126/
science.266.5192.1858.
Murase, T., and A. R. McBirney (1970), Viscosity of lunar lavas, Science,
167, 1491–1493, doi:10.1126/science.167.3924.1491.
E00H14
Pelletier, J. D. (2008), Quantitative Modeling of Earth Surface Processes,
Cambridge Univ. Press, New York.
Pinkerton, H., L. Wilson, and G. E. Norton (1990), Thermal erosion: Observations on terrestrial lava flows and implications for planetary volcanism,
Proc. Lunar Planet. Sci. Conf., 21st, 964–965.
Schubert, G., R. E. Lingenfelter, and S. J. Peale (1970), The morphology,
distribution, and origin of lunar sinuous rilles, Rev. Geophys., 8,
199–224, doi:10.1029/RG008i001p00199.
Schultz, R. A. (1993), Strength and deformation properties of basaltic lava
flows on planetary surfaces, Lunar Planet. Sci., XXIV, 1263–1264.
Siewert, J., and C. Ferlito (2008), Mechanical erosion by flowing lava,
Contemp. Phys., 49, 43–54, doi:10.1080/00107510802077388.
Sklar, L., and W. E. Dietrich (1998), River longitudinal profiles and
bedrock incision models: Stream power and the influence of sediment
supply, in Rivers Over Rock: Fluvial Processes in Bedrock Channels,
edited by K. J. Tinkler and E. E. Wohl, pp. 237–260, AGU, Washington,
D. C., doi:10.1029/GM107p0237.
Spudis, P. D., G. A. Swann, and R. Greeley (1988), The formation of
Hadley Rille and implications for the geology of the Apollo 15 region,
Proc. Lunar Planet. Sci. Conf., 18th, 243–254.
Strain, P. L., and F. El-Baz (1977), Topography of sinuous rilles in the
Harbinger Mountains region of the moon, Earth Moon Planets, 16,
221–229.
Whitford-Stark, J. L., and J. W. Head (1977), The Procellarum volcanic
complexes: Contrasting styles of volcanism, Proc. Lunar Sci. Conf.,
8th, 2705–2724.
Whitford-Stark, J. L., and J. W. Head (1980), Stratigraphy of Oceanus
Procellarum basalts: Sources and styles of emplacement, J. Geophys.
Res., 85, 6579–6609, doi:10.1029/JB085iB11p06579.
Wieczorek, M. A., M. T. Zuber, and R. J. Phillips (2001), The role of
magma buoyancy on the eruption of lunar basalts, Earth Planet. Sci. Lett.,
185, 71–83, doi:10.1016/S0012-821X(00)00355-1.
Williams, D. A., R. C. Kerr, and C. M. Lesher (1998), Emplacement
and erosion by Archean komatiite lava flows at Kambalda: Revisited,
J. Geophys. Res., 103, 27,533–27,549, doi:10.1029/97JB03538.
Williams, D. A., S. A. Fagents, and R. Greeley (2000), A reassessment
of the emplacement and erosional potential of turbulent, low-viscosity
lavas on the Moon, J. Geophys. Res., 105, 20,189–20,205, doi:10.1029/
1999JE001220.
Williams, D. A., R. C. Kerr, C. M. Lesher, and S. J. Barnes (2001),
Analytical/numerical modeling of komatiite lava emplacement and thermal erosion at Perseverance, Western Australia, J. Volcanol. Geotherm.
Res., 110, 27–55, doi:10.1016/S0377-0273(01)00206-2.
Wilson, L., and J. W. Head (1980), The formation of eroded depressions
around the sources of lunar sinuous rilles: Theory, Proc. Lunar Planet.
Sci. Conf., 11th, 1260–1262.
Wilson, L., and J. W. Head III (1981), Ascent and eruption of basaltic
magma on the Earth and Moon, J. Geophys. Res., 86, 2971–3001,
doi:10.1029/JB086iB04p02971.
Zisk, S. H., C. A. Hodges, H. J. Moore, R. W. Shorthill, T. W. Thompson,
E. A. Whitaker, and D. E. Wilhelms (1977), The Aristarchus-Harbinger
region of the moon: Surface geology and history from recent remotesensing observations, Earth Moon Planets, 17, 59–99.
J. W. Head and D. M. Hurwitz, Department of Geological Sciences,
Brown University, 324 Brook St., Box 1846, Providence, RI 02912,
USA. (debra_hurwitz@brown.edu)
H. Hiesinger, Institut für Planetologie, Westfälische WilhelmsUniversität Münster, Wilhelm-Klemm-Str. 10, Münster D-48149,
Germany.
L. Wilson, Lancaster Environment Centre, Lancaster University,
Lancaster LA1 4YQ, UK.
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