origin of lunar sinuous rilles: modeling effects of ... · origin of lunar sinuous rilles: modeling...

Origin of lunar sinuous rilles: Modeling effects of gravity,surface slope, and lava composition on erosion rates duringthe 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 resultof 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 andthermal, are considered. Measurements of channel dimensions are used as inputs toanalytical models to constrain the origin of Rima Prinz, including lava compositions,mechanical and thermal erosion rates, eruption durations, and lava volumes required to formthe feature. Key results indicate that Rima Prinz and other large sinuous rilles could haveformed as the result of thermal erosion under the weak gravity and low slope conditionscharacteristic of these lunar features. Further analysis indicates that lava composition hassignificant effects on channel formation. Model results of four considered lava compositionsshow that komatiite-like lava will erode a similarly composed substrate most efficientlywhereas a high-Ti basalt will erode a similarly composed substrate least efficiently; oceanisland 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, depositing50–250 km3 of lava over a plausible deposit area of 2450 km2. Resulting deposit thicknessessuggest that the lava that incised Rima Prinz was most likely similar in composition to aterrestrial komatiite, ocean island basalt, or lunar low-Ti basalt. Further constraints onsinuous rille formation will serve as a window into the nature of volcanic activity of theMoon’s past.

Citation: Hurwitz, D. M., J. W. Head, L. Wilson, and H. Hiesinger (2012), Origin of lunar sinuous rilles: Modeling effectsof 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 widelyaccepted to represent the remains of channels formed bylava that erupted in effusive, high volume volcanic events.The exact mode of channel formation is still debated, asresearchers attempt to distinguish between channels thatformed 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 andFerlito, 2008], due to thermal erosion of the substrate[Hulme, 1973, 1982; Head and Wilson, 1981; Wilson andHead, 1981; Williams et al., 1998, 2000; Kerr, 2009], anddue to thermomechanical erosion of the substrate [Williams

et al., 1998, 2001; Fagents and Greeley, 2001]. Some sinu-ous rilles are contiguous with distinctive source depressions,the geometry of which suggests that the lava flow formingthe rille overflowed from a lava pond fed by pyroclasts fall-ing 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 eruptionconditions, submitted to Journal of Volcanology andGeothermal Research, 2011], with thermal erosion at thebase of the pond as well as at the base of the flow leading tothe observed morphology. In each of the proposed forma-tion mechanisms, the composition of lava that flowedthrough the channel can affect the volume of lava and theamount of time required to form the observed feature. Thecurrent study simulates the formation of Rima Prinz, a lunarsinuous rille interpreted to have an eroded origin, by mod-eling erosion rates and expected erosion depths for fourdistinct lava compositions. Comparisons between expectedand observed channel depths can provide constraints for thecomposition of the lava that formed the observed channel.These interpretations in turn can provide insight into the

1Department of Geological Sciences, Brown University, Providence,Rhode Island, USA.

2Lancaster Environment Centre, Lancaster University, Lancaster, UK.3Institut für Planetologie, Westfälische Wilhelms-Universität Münster,

Munster, Germany.

Copyright 2012 by the American Geophysical Union.0148-0227/12/2011JE004000

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, E00H14, doi:10.1029/2011JE004000, 2012

E00H14 1 of 15

http://dx.doi.org/10.1029/2011JE004000

conditions that were present during the volcanically activeera in lunar history.

2. Background

[3] Sinuous rilles have commonly been identified as con-structed or eroded features, and substantial analysis has beenconducted previously in an attempt to distinguish betweenthese two origins. Constructed channels are typically con-sidered to form as the result of marginal cooling of a broadlava flow. As the flow cools and solidifies inward from themargins, levees form and bound the fastest moving, stillmolten part of the lava flow, forming a channel [i.e., Hulme,1974]. Constructed channels, such as those found in southernImbrium basin lava flows (Figure 1a), tend to be shallowfeatures, forming within the initial sheet lava flow rather thanincising into the substrate.

[4] A constructed mode of origin has also been suggestedfor the formation of larger sinuous rilles identified on theMoon 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, suchas Rima Prinz located east of the Aristarchus Plateau(Figure 1b), are significantly deeper features that appear tolack levees and incise into the substrate, suggesting that thedevelopment of these features is likely to have involvederosion [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 expectedto represent open channels that developed a thin surface crust[i.e., Williams et al., 1998, 2000]. In some cases, channelsmight construct a structurally stable crust that remains intactonce the lava recedes, or channels might form completelysubmerged within the substrate, forming a lava tube [i.e.,Greeley, 1971]. Collapse of a lava tube roof may result inthe 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 ofthe Marius Hills (Figure 1c). Aligned skylights might indi-cate the track of a subsurface lava tube. These skylightsobserved in association with lava tubes represent distinctfeatures from the laterally continuous, nearly parallel wallsobserved in association with the open channels of erodedorigin considered in this study.[5] Two classes of erosion are commonly considered in the

origin of eroded channels: mechanical erosion and thermalerosion. Mechanical erosion occurs when a flowing fluidremoves particles that lay loosely on the ground and involvesparticles suspended in the flowing fluid colliding with thesubstrate, shearing substrate particles and incising into thesubstrate [i.e., Sklar and Dietrich, 1998]. While some workhas been done investigating this erosion regime in the originof lava channels [i.e., Sklar and Dietrich, 1998], this previousapproach assumes that the vertical load of the lava isresponsible for the erosion of the substrate rather than shearstress. However, the low viscosity expected of lunar lavaswould allow for relatively high lava flow velocities, facili-tating erosion by shear. The second type of erosion consid-ered is thermal erosion, a process that involves a flowingfluid whose temperature exceeds the melting temperature ofthe substrate. As the hot fluid comes into contact with thesubstrate, the substrate is melted and assimilated into theflowing fluid, resulting in incision into the substrate. Ana-lytical models must be used to supplement observations ofchannel dimensions and morphology in order to distinguishbetween 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 Aris-tarchus Plateau that is interpreted to have an eroded origin.Remote observations of channel dimensions and morphologydescribed in section 3 are used in conjunction with analyticalmodels discussed in section 4 to calculate the erosion ratesand eruption durations required in each erosion regime toform the observed channel. Effects of gravity, slope, and lavacomposition are explored in sections 5 and 6 to determinewhether Rima Prinz formed as the result of mechanical orthermal erosion. Model results for each of four lava

Figure 1. Lava channels interpreted to form from variousmechanisms observed on the Moon. (a) A channel observedin the southern Imbrium basin that is interpreted to haveformed as the result of construction. The channel is relativelyshallow, and marginal levees are observed along the length ofthe channel (white arrow). In addition, a local source is notevident, indicating that this channel formed concurrentlywith the surrounding lava flows. (b) Rima Prinz, a channelobserved east of the Aristarchus Plateau that is interpretedto have formed as the result of erosion from lava flowingthrough a surface channel. This channel is relatively deep,with laterally continuous, nearly parallel walls that lack mar-ginal levees. Rima Prinz originates in a source depressionthat can be seen in Figures 3 and 4. (c) A channel observedwest of the Marius Hills that is interpreted to have formed asthe result of erosion from lava that flowed through a sub-surface lava tube. The walls are not laterally parallel norcontinuous (white arrow), suggesting the currently observedfeature formed due to collapse of a structurally stable roof.

HURWITZ ET AL.: ORIGIN OF RIMA PRINZ E00H14E00H14

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compositions considered are explored in order to constrainreasonable lava compositions that may have been responsiblefor the formation of the observed sinuous rille. This approachuses sinuous rilles as a window into the lunar interior toprovide constraints for the conditions that were present dur-ing the volcanically active period of lunar history.

3. Geologic Setting

[7] The Aristarchus Plateau (Figure 2) has been identifiedas an uplifted block of lunar crust that shows compositionalevidence for highlands material (excavated by the Aristarchusimpact) that is superposed by Imbrium ejecta material anda regional surface veneer of dark mantle deposits [McEwenet al., 1994; Hawke et al., 1995; Chevrel et al., 2009] andis surrounded to the north and east by mare basalts ofintermediate TiO2 content [Whitford-Stark and Head, 1980;Giguere et al., 2000; Hiesinger et al., 2003]. Nearly 20 vol-canic vents are preserved on the plateau in the form of typi-cally circular depressions that act as the source for sinuousrilles that extend from the plateau into the surrounding marebasalt deposits [i.e., Schubert et al., 1970;Whitford-Stark andHead, 1977]. Many additional sinuous rilles are observedin the area surrounding the plateau, making the AristarchusPlateau – Harbinger Mountain region one of the moredensely concentrated volcanic centers that was likely to havebeen 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 Mountainslocated on a smaller plateau east of the Aristarchus Plateau.

The source depression of Rima Prinz lies on the northernextent of ejecta associated with Prinz crater. The sinuous rilleis characterized by two channels, one larger valley and asmaller, nested sinuous rille that is interpreted to have formedin a second, independent eruption after an initial eruptionformed the larger valley [i.e., Strain and El-Baz, 1977;Wilson and Head, submitted manuscript, 2011]. Both chan-nels were heavily influenced by slope during their formation,with an upper segment forming on Prinz ejecta (Figure 3b), amiddle segment forming in the mare abutting the northernextent of Prinz ejecta (Figure 3c), and a lower segmentforming in the mare (Figure 3d), directed down-grade to thenorth 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 associatedlava channel [Head and Wilson, 1981; Wilson and Head,1981]. A perspective view of Lunar Reconnaissance OrbiterNarrowAngle Camera (LROCNAC) images M104805368LEand M104805368RE (0.5 m pixel�1) overlaid on LunarOrbiter Laser Altimeter (LOLA) data (�120 m pixel�1)shows that the source depression for Rima Prinz has a steep,well-consolidated rim (Figure 4a). The southern depressionwall (image left) is steep down to the depression floor whilethe northern depression wall slopes more gradually to theinterpreted eruption location. This morphology is similar tothat observed in the source crater of Mauna Ulu, Hawaii(Figure 4b), a feature that also has a steep, rocky rim andone wall that slopes more gradually toward the eruptionlocation. Both source depressions are expected to haveformed during a fire fountain eruption due to erosion of thesurface beneath a lava lake [i.e., Head and Wilson, 1981;

Figure 2. Context image of the Aristarchus Plateau –Harbinger Mountain region with LOLA topographydata (�120 m pixel�1 resolution) overlying the LROC WAC global mosaic (100 m pixel�1 resolution).Rima Prinz (white box) has a source depression that is located on the northern ejecta deposits of Prinzcrater, and Rima Prinz extends north into Oceanus Procellarum.


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Wilson and Head, 1981]. Remnant deposits of this lava lakemight still be visible in a long wavelength, hummocky tex-ture on the floor of the source depression of Rima Prinz(Figure 5a), a texture that is similar to that of depositsobserved in the remnant lava lake in Kilauea Iki, Hawaii(Figure 5b). These observations of similar morphologiesbetween terrestrial fire fountain eruption features and lunarsinuous rille source depressions support the theory that lunarsource depressions also formed as the result of fire fountaineruptions [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 themare plains of Oceanus Procellarum to the north. Eachchannel segment is analyzed independently to assess channeldimensions and morphology. Dimensions of interest include1) channel length, which is measured by averaging thelengths of the two bounding channel rims for each channel

segment; 2) channel width, which is measured by averagingrim-to-rim distances along the length of each channel seg-ment; 3) channel depth, which is measured by averaging thedifferences between channel rim elevation and channel floorelevation as documented by LOLA track data; 4) channelsinuosity, which is measured by averaging distances betweenmeander extremes (i.e., meander wavelength) for each chan-nel segment; and 5) regional slope, which is determined bymeasuring the average regional slope along the channel rimusing LOLA gridded data. Sinuosity is measured in order toprovide an estimate of the width of the lava within the cur-rently observed valley, as the valley was unlikely to havebeen filled with lava [Pelletier, 2008]. Uncertainties in thesemeasurements are generally reported as the standard devia-tion of measurements made along the length of each channelsegment, with the exception of the uncertainty in channellength, which is reported as the variation between the rimlength measurements and the length measurement of the

Figure 3. Images and observations of Rima Prinz. (a) Full view of Rima Prinz using the LROC WACglobal mosaic (100 m pixel�1 resolution) with the source depression located on the northern ejecta depositsof Prinz crater in the bottom center of the image (see Figure 4). The channel has been divided into threesegments, with (b) the upper segment extending from the source depression to the northern edge of theejecta deposits, (c) the middle segment following the northern boundary of the ejecta deposits, and (d) thelower segment extending north before (e) terminating in Oceanus Procellarum. Detailed observations ofeach channel segment are discussed in section 3 of the text.


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interpreted channel thalweg. Measurements are summarizedin 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 of1.7 km +/� 0.7 km. This channel segment formed down-gradient at a slope of 0.7� +/� 0.6�; the uncertainty is higherbecause the channel cut through relatively hummocky terrainconsistent with ejecta deposits. The channel is characterizedby steep, nearly parallel walls that lack obvious marginallevees, and the walls appear to be well-preserved, lackingevidence of substantial subsequent slumping. The nestedrille remains clearly visible throughout the channel seg-ment and typically mirrors the sinuosity of the larger outerchannel.

[12] The middle segment of Rima Prinz (Figure 3c) is19 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 of2.4 km +/� 2.0 km. This channel segment formed down-gradient at a slope 0.5� +/� 0.1�, forming along the bottom ofthe northern extent of Prinz crater ejecta. While the northernwall of the middle channel segment remains steep andapparently well-preserved, the southern wall has been sub-jected to substantial slumping, possibly due to the collapse ofPrinz ejecta material during a subsequent impact such as oneresponsible for the formation of Aristarchus crater to thesouthwest. This deformation of the southern wall has resultedin the concealment of the nested rille in many places alongthis channel segment and led to the higher uncertainty valuesin the reported length and depth measurements.

Figure 4. Perspective view of the source depression of Rima Prinz, with LROC NAC imagesM104805368LE and M104805368RE (0.5 m pixel�1) overlying LOLA topography data (�120 m pixel�1).(a) The source depression is characterized by a consolidated rim of highly reflective layers, a relativelysteep southern (left) wall, and a relatively gradually sloped northern (right) wall. This morphology is similarto that of the source depression of Mauna Ulu, Hawaii, shown in Figure 4b. (b) The source depression forMauna Ulu formed as the result of a lava lake fed by a series of fire fountain eruptions, and a similar processis thought to have occurred on the Moon to form the source depression of Rima Prinz.


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[13] The lower segment of Rima Prinz (Figure 3d) is57 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 of2.0 km +/� 1.0 km. This channel segment formed down-gradient at a slope of 0.4� +/� 0.1� and extends northwardinto Oceanus Procellarum. The lower segment of Rima Prinzis characterized by the steep, parallel, and laterally continu-ous walls that are observed in the upper channel segment.This portion of the channel also lacks obvious levees, con-sistent with a channel that formed as the result of erosionprocesses. The nested rille is visible for much of the length ofthe lower channel segment, and whereas the sinuosity of thenested channel mirrors the outer channel along most of thelength of the channel segment, in some places the nestedchannel is significantly more sinuous. This may be a resultof the duration of flow in the nested channel, with a longerduration flow forming more stable, larger meanders, or itmay be the result of the low slope characteristic of this por-tion of the channel segment.[14] Rima Prinz terminates (Figure 3e) in Oceanus Pro-

cellarum at the �1700 m contour, the same elevationat which its neighboring sinuous rille to the east, Rima“Beethoven,” terminates. Rima Prinz appears to increase insinuosity (i.e., decrease in sinuosity wavelength) as it nearsits terminus, and the walls remain nearly parallel and laterally

continuous, though the channel depth has decreased sub-stantially. Deposits are not observed beyond the currentlyobserved channel terminus, indicating either that thesedeposits are too thin to be observed due to the low viscosityof the lava, or that they have been covered by subsequentmare volcanic flows. Because Rima “Beethoven” to the eastterminates at the same elevation as Rima Prinz, embaymentby subsequent mare volcanism is the more likely scenario,and careful inspection of the terminus of Rima Prinz indi-cates that mare lava may have flowed up-gradient through thechannel, partially flooding the observed channel terminus forapproximately 3–5 km (Figure 3e). It should be noted that theembaying lava flows may have covered the distal part ofRima Prinz, leading the length measurement for the lowerchannel segment to represent a minimum value of the actuallength of this channel segment.

4. Theory of Lava Channel Formation by Erosion

[15] The morphology of Rima Prinz, specifically the lateralcontinuity of the channel walls and the lack of leveesobserved along the channel margins, supports the theory thatRima Prinz formed as the result of erosion into the substrate.The observations reported in section 3 represent the currentlyobserved product of this erosion and can thus be used in

Figure 5. (a) The floor of the source depression of Rima Prinz, shown with LROC NAC imageM104805368RE (0.5 m pixel�1), and (b) the floor of Kilauea Iki, Hawaii. The deepest part of the RimaPrinz source depression lies close to the southern steep wall, a wall that is characterized by boulder tracksthat 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 similarto the texture observed in the remnant lava lake on the floor of Kilauea Iki (Figure 5b). These observa-tions suggest that deposits associated with a remnant lava lake may still reside in the floor of the sourcedepression of Rima Prinz.

Table 1. Observations and Measurements of Rima Prinz

ChannelSegment

Length(km) Uncertainty

Width(km)

StandardDeviation

Depth(m)

StandardDeviation

Sinuosity(km)

StandardDeviation

Slope(�)

StandardDeviation

Upper 11 �3 km 1.8 �0.7 km 230 �20 m 1.7 �0.7 km 0.7 �0.6�Middle 19 �8 km 1.0 �0.4 km 210 �40 m 2.4 �2 km 0.5 �2�Lower 57 �3 km 1.0 �0.3 km 145 �30 m 2.0 �1 km 0.4 �1�


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conjunction with analytical models to distinguish betweentwo possible erosion regimes. The analytical models con-sidered 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 betweenparticles in the flowing fluid and the substrate, and the rate ofchange in channel depth dchan as the result of mechanicalerosion is given by

d dchanð Þdt

� �mech

¼ KrgQw sina; ð1Þ

where Qw is the average lava flux per unit width through thechannel in m2 s–1 (Qw = dlava � vlava, as calculated inequations (6) and (7)), r is the lava density (see Table 2 forparameter values), g is the acceleration due to gravity on theMoon, a is the ground slope, and K is a factor with units ofPa�1 that represents the erodibility of the substrate [Sklar andDietrich, 1998; Hurwitz et al., 2010].[16] The model simulating mechanical erosion is most

significantly affected by the erodibility factor K, as explainedin more detail by Hurwitz et al. [2010]. Higher values of thefactor K (�10�7) represent a less consolidated substrate, likethe lunar regolith, that is more susceptible to mechanicalerosion at the lower slopes observed in relation to the lunarsinuous rilles. Lower values of the factor K (�10�9) rep-resent a more consolidated substrate, like lunar basalt, thatis more susceptible to thermal erosion at lower slopes.An unconsolidated surface with an erodibility of �10�7

results in a modeled mechanical erosion rate that is �5 timeshigher than the mechanical erosion rate modeled for a con-solidated substrate with an erodibility of �10�9. Slope alsorepresents a significant parameter in the model of mechanicalerosion, and analysis of how slope affects erosion rates isexplored 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 ofconceptually as modeling the erosion rate as a functionof substrate erodibility and unit stream power, W, whereW = r g Q sin a [Sklar and Dietrich, 1998; Hurwitz et al.,2010]. A different, more fundamental way to think aboutequation (1) is to separate it into different energy compo-nents: the flux term Q is a function of lava velocity and thuskinetic energy, and the term r g sin a represents the potentialenergy stored in the flowing fluid. Equation (1) thereforeindicates that mechanical erosion depends on how efficientlythe kinetic and potential energies stored in the flowing fluidare transferred to the substrate. Substrate erodibility isdependent on substrate composition and consolidation, andthus the thickness of the lunar regolith and the consolidationof either the ejecta associated with the upper segment ofRima Prinz or the mare basalt substrate can have a significanteffect on the modeled erosion rates. In general, equation (1)predicts that a mechanically eroded channel will increase indepth faster as a higher flux of lava flows over a more poorlyconsolidated substrate.[18] In contrast to mechanical erosion, thermal erosion

occurs when the flowing fluid is hot enough to melt thesubstrate. The rate of change in channel depth dchan asthe result of thermal erosion is a function of the energy

provided by the lava flow and the energy required to melt thesubstrate, and is generally defined by

d dchanð Þdt

� �therm

¼ hT T � Tmg

� �Emg

; ð2Þ

where T and Tmg represent the temperature of the lava andthe melting temperature of the substrate, respectively, hT isthe heat transfer coefficient, and Emg is the energy required tomelt the substrate and is given by

Emg ¼ rg cg Tmg � Tg� �þ fmgLg

� �; ð3Þ

where Tg is the initial temperature of the ground or substrate,cg is the specific heat of the substrate, Lg is the latent heat offusion for the substrate, and fmg is the fraction that the sub-strate must be melted before being carried away by theflowing fluid [Hulme, 1973; Williams et al., 1998, 2000].The two terms in equation (3) represent 1) the energyrequired to raise the temperature of the substrate to themelting temperature of the substrate and 2) the energyrequired to melt the substrate. The additional heat transfercoefficient term in equation (2) represents how efficientlythermal energy can be transferred from the hot flowing lavato the substrate. Two different approaches have been used todefine the heat transfer coefficient: one by Hulme [1973],given by

hT ¼ 0:017kRe4=5Pr2=5

dlava; ð4Þ

and one by Williams et al. [1998, 2000], given by

hT ¼ 0:027kRe4=5Pr1=3

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 theviscosity of the substrate, respectively, Re is the Reynoldsnumber (Re = rvdlava

m , turbulent flow that enhances erosionoccurs when Re > 2000), and Pr is the Prandtl number (Pr =cgmk ). The difference between these two formulations of theheat transfer coefficient is subtle, with the formulation byWilliams et al. [1998, 2000] incorporating a slightly higherweighting of the Prandtl number than the formulation byHulme [1973]. This slightly higher weighting is used toaccount for the thermal boundary layer, in effect changing theefficiency at which heat is transferred across this boundarybetween the flowing fluid and the substrate. The modelsdescribed in equations (2)–(5) indicate that thermal erosionrelies most significantly on the transfer of thermal energyfrom the flowing lava to the substrate, but it should be notedthat thermal erosion is also dependent on kinetic and poten-tial energies, factors that are included in the model throughthe Re term in the heat transfer coefficient (equations (4) and(5)). Velocity, a factor in Re, is found by iteratively solving amodel for moderately turbulent flows [Keszthelyi and Self,1998], given by

vlavah i2 ¼ gdlava sinaCf

; ð6Þ


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where Cf is a friction factor given by

Cf ¼ 1

32

� �log10 6:15

2Reþ 800

41

� �0:92 !" # !�2

: ð7Þ

It should be noted that the full model for thermal erosionpresented by Williams et al. [1998, 2000] and used in anal-ysis of lava composition effects on erosion rate employsalternative models for velocity and friction factor. The dif-ferences are subtle and do not significantly alter the qualita-tive interpretations made in the current study. For a moredetailed 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, specificallyin the difference between erupted temperature, assumed to be

the liquidus temperature of the erupted lava, and the substratemelting temperature, assumed to be the solidus temperature ofa lava of the same composition as the erupted lava. Specifi-cally, a 100 K change in the erupted lava temperature T (i.e.,the approximate difference between the erupted temperaturesof a komatiite-like basalt and a low-Ti basalt) results in achange in the modeled thermal erosion rate of one order ofmagnitude. The temperatures used in the model, as well asthe other considered parameters of thermal conductivity,specific heat, and latent heat, are all dependent on the lavacomposition considered, and each parameter is recalculateddepending on the composition used as an input to the model.These parameter calculations are described in more detail byWilliams et al. [1998, 2000].[20] The models presented in equations (1)–(5) are solved

initially to compare erosion rates in all three models. This isaccomplished by first calculating the volume flux of the

Table 2. Lava Compositions, Temperatures, Chemical Parameters, and Physical Parameters

Parameter Parameter Symbol Units High-Tia Low-Tia Komatiitea Ocean Island Basalta

Initial lava composition SiO2 wt% 39.7 43.7 45 48.5TiO2 wt% 10 2.9 0.3 1.76Al2O3 wt% 6.63 8.2 5.6 10.2Fe2O3 wt% 0 0 1.4 1.29FeO wt% 22.5 21.9 9.2 1.04MnO wt% 0.32 0.35 0.2 0.17MgO wt% 12.2 12.5 32 17.1CaO wt% 7.67 8.4 5.3 8.2Na2O wt% 0.06 0.07 0.6 1.51K2O wt% na na 0.03 0.27

Final lava composition SiO2,f wt% 40.5 50.2 47 52TiO2,f wt% 12 4.9 0.5 2.5Al2O3,f wt% 7.9 14.1 8.8 14.5Fe2O3,f wt% 0 0 2.2 1.8FeOf wt% 22.3 15.5 11 9.4MnOf wt% 0.33 0.29 0.3 0.17MgOf wt% 7.8 0.72 21 5.2CaOf wt% 9.1 14.1 8.3 11.5Na2Of wt% 0.07 0.12 0.9 2.15K2Of wt% na na 0.05 0.38

Initial lava temperature To �C 1338 1440 1578 1408Final lava temperature Tf �C 1322 1388 1502 1358Liquidus temperature Tliq �C 1338 1440 1578 1408Solidus temperature Tsol �C 1150 1150 1170 1050Substrate melting temperature Tmg

�C 1150 1150 1170 1050Initial substrate temperature Tg �C �23 �23 �23 �23Initial substrate specific heat cgo J kg�1 K�1 1529 1539 1789 1632Final substrate specific heat cgf J kg�1 K�1 1471 1414 1671 1490Substrate latent heat Lg J kg�1 5.87 � 105 6.06 � 105 6.97 � 105 4.20 � 105

Heat transfer coefficientb hT J m2 s�1 K�1 631 679 1250 340Initial Reynolds number Reo - 1.6 � 104 2.9 � 105 3.3 � 106 9.6 � 104

Final Reynolds number Ref - 4.2 � 105 1.0 � 104 3.3 � 105 4.3 � 103

Erodibility factorb K Pa�1 5.0 � 10�9 5.0 � 10�10 5.0 � 10�11 5.0 � 10�12

Erodibility factorb K Pa�1 2.5 � 10�7 2.5 � 10�8 2.5 � 10�9 2.5 � 10�10

Volumetric lava flux Q m3 s�1 4055 4180 4375 4390Initial lava density rl,o kg m�3 3005 2894 2778 2726Final lava density rl,f kg m�3 2981 2803 2771 2683Initial lava viscosity ml,o Pa s 0.464 0.529 0.103 1.36Final lava viscosity ml,f Pa s 0.83 6.05 0.404 15.5Initial lava depth dl,o m 20 8 12 8Final lava depth dl,f m 21.15 11.99 13.8 10.56Initial lava velocity vl,o m s�1 12.31 6.71 10.1 5.99Final lava velocity vl,f m s�1 7.98 5.2 8.87 4.58

aLava compositions for high-Ti basalt came from Apollo 17 sample 74220 [Longhi et al., 1978], for low-Ti basalt from Apollo 12 sample 12002 [Longhiet 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].

bHeat Transfer Coefficient calculated from the Williams et al. [1998, 2000] model.


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source eruption based on the geometry of the source depres-sion and the density of the lava [Head and Wilson, 1980;Wilson and Head, 1980]. Second, the width of the lava thatflowed within the observed channel is calculated based onobserved sinuosity, assuming that a fully developed fluidflow meanders at a wavelength equal to 10.88 times the flowwidth [Pelletier, 2008]. Equations (6) and (7) are then used tosolve for flow velocity by iteratively changing the depth ofthe lava within the observed channel. This iteration is con-tinued until the volume flux predicted by the width, depth,and flow velocity calculations match the volume flux calcu-lated independently. Once the lava depth and flow velocityvalues are constrained, Re and hT are calculated and themodels in equations (1)–(5) are solved for erosion rate ineach erosion regime considered.

5. Results

[21] The three models discussed in section 4 are used tosimulate the erosion rates expected for the head of RimaPrinz (at the intersection of the channel and the sourcedepression) in order to 1) distinguish between mechanicaland thermal erosion origins for the sinuous rille and to2) compare the erosion rates predicted by the two thermalerosion models. In order to directly compare model results,the two thermal erosion models are run for only the head ofthe upper segment of Rima Prinz, where no contaminationdue to assimilation of melted substrate into the flowing lavahas occurred and thus thermal and geophysical properties ofthe lava are assumed to be constant. These models are run forboth terrestrial and lunar gravity conditions at various slopesto determine how gravity and slope affect predicted erosionrates. The most relevant model is then used to simulate thecomplete formation of Rima Prinz in the presence of differentlavas in order to constrain the conditions present during theformation of this sinuous rille.[22] Results for the mechanical and two thermal erosion

models are shown in Figure 6, with results for terrestrialgravity conditions shown in Figure 6a and results for lunargravity conditions shown in Figure 6b. These models wererun assuming a lava composition similar to that of a terrestrialocean island basalt (Table 2) because lunar lavas that erupt inhigh-effusion rate, high-volume eruptions are expected tooriginate from below the lunar crust-mantle interface, and thelavas erupt at effusion rates similar to those of terrestrialocean island basalts [e.g.,Head andWilson, 1992;Wieczoreket al., 2001]. A lava composition similar to an ocean islandbasalt is considered in this study because eruption fluxesmodeled for lunar eruptions and potential source depressionsobserved on the lunar surface are similar to those eruptionfluxes and source depressions observed in conjunction witheruptions of ocean island basalts on Hawaii [e.g., Head andWilson, 1980; Wilson and Head, 1980].[23] Results for the terrestrial case indicate that mechanical

erosion is more efficient than thermal erosion at slopesgreater than about 0.4�. This suggests that at slopes greaterthan 0.4� in the terrestrial case, gravitational potential energyand thus kinetic energy are the dominant forms of energyacting during channel formation. Alternatively, at slopes lessthan 0.4�, potential and kinetic energies are insignificantcompared to the thermal energy stored in the flowing lava,and thus thermal erosion dominates the formation process. In

contrast, results for the lunar case indicate that thermal ero-sion dominates the channel formation process at slopes lessthan about 3.5�. This suggests that the lower gravity char-acteristic of the Moon provides insufficient potential energyand thus kinetic energy to contribute significantly to theformation of Rima Prinz (which has a < 0.7�). These resultsindicate that thermal erosion can dominate the formation oflunar sinuous rilles that form on consolidated substrates ofbasalt at low slopes even though it is not a commonlyobserved process in the formation of terrestrial lava channelsthat typically form on steeper gradients.[24] Results shown in Figure 6 also indicate that predicted

erosion rates are similar for both thermal erosion modelsconsidered. While these results certainly depend on the lavacomposition and geophysical properties assumed, predictederosion rates are typically within �25% for the lava com-positions considered as inputs for each model. Because theresults are similar and because the full model developed byWilliams et al. [1998, 2000] incorporates added complexitiesthat allow for the analysis of affects of lava composition onchannel formation, the full model developed by Williamset al. [1998, 2000] is used to simulate the detailed forma-tion of Rima Prinz. The full model simulates the formation ofa lava channel as a function of distance from the eruption,tracing how much of the substrate has been melted andassimilated into the flowing lava as well as how much olivinehas crystallized in the flowing fluid, then recalculating thethermal and geophysical properties (such as Reynolds num-ber, Prandtl number, heat transfer coefficient, thermal con-ductivity, and bulk viscosity) of the new lava composition[Williams et al. [1998, 2000]. In addition to heat lost to thesubstrate, this model also simulates the formation of a fusioncrust at the top of the lava flow, a crust that can be an efficientinsulator 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., erosionrate), and from these results and observations of depth in thehead of the upper channel segment, the duration of theeruption that is required to form this uppermost portion ofRima Prinz is determined. This calculated eruption duration,which remains constant for the rest of the channel, is thenused with modeled erosion rates to calculate a predicteddepth for the remainder of the upper, middle, and lowerchannel segments, and these predicted erosion depths arecompared with observed depths of Rima Prinz to confirm themerit of the model (Figure 7). In order to determine effects oflava composition on erosion rates, four compositions of lavaare considered in this analysis, including compositions sim-ilar to a lunar high-Ti basalt (i.e., Apollo 17 sample 74220,[Longhi et al., 1978]), a lunar low-Ti basalt (i.e., Apollo 12sample 12002, [Longhi et al., 1978]), a terrestrial komatiite(i.e., Kambalda, W. Australia [Lesher and Arndt, 1995]), anda terrestrial ocean island basalt (i.e., Kilauea, HI [Clagueet al., 1991]; see Table 2). The two lunar lava compositionsare considered because they represent lavas that have beensampled and analyzed directly from the lunar surface, thoughthe lavas sampled from the lunar surface do not necessarilyrepresent the lava that flowed through and formed theobserved sinuous rilles. The composition of terrestrial oceanisland basalt is considered because of similarities betweenpredicted eruption fluxes and observed features associatedwith channels for both lunar sinuous rilles and Hawaiian


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eruptions of ocean island basalt lavas [e.g.,Head and Wilson,1980; Wilson and Head, 1980], and the composition ofterrestrial komatiite is considered because komatiites areobserved 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 efficienterosion agents [e.g., Huppert and Sparks, 1985].[26] Results of the comparison between observed and

predicted depths (Figure 7) indicate that the model does fol-low the trends in channel depth as observed using LOLAtrack data (Table 1) for each composition of lava considered.The gradual decreases in predicted eroded depth are a resultof the decrease in erosion efficiency as lava temperaturedecreases and as lava contamination from assimilated sub-strate and thus lava viscosity increases with distance from thesource vent. The sharp decreases in predicted eroded depthare artifacts due to the change in observed average channelslope incorporated into the model at the beginning of eachchannel segment. While in reality these slopes would varymore smoothly along the length of the channel, the predictederoded depths adequately follow the trend in channel depthsobserved, supporting the earlier interpretation that thermalerosion is sufficiently simulating the formation of RimaPrinz.[27] Model results also indicate that lava composition

has a significant influence on the erosion rate and thus theeruption 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 tothe composition of the substrate; while the composition of thelava changes down gradient due to crystallization of olivine(which will occur as the lava temperature decreases belowthe liquidus temperature) and contamination by assimilatedsubstrate, the substrate composition remains constant. Thegradual decreases in predicted erosion rates mirror those inthe results for predicted eroded depth and are similarly aresult of the decrease in erosion efficiency as lava tempera-ture decreases and lava viscosity increases with distance fromthe source vent. The steep decreases in erosion rate are arti-facts of the abrupt change in slope used for each channelsegment in the model, though again in reality the slope typ-ically 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 fasterthan lava similar to a lunar high-Ti basalt. Lavas with com-positions similar to those of lunar low-Ti basalt and terrestrialocean island basalt result in intermediate erosion rates.Lavas producing faster erosion rates require shorter eruptiondurations to incise the observed channel. Specifically, akomatiite-like lava, with erosion rates ranging from about1.7 m d�1 at the head of the channel to 0.80 m d�1 at thechannel terminus, requires about 157 Earth days (�0.4 Earthyears) to incise Rima Prinz. An ocean island basalt-like lava(OIB) has erosion rates ranging from about 0.7 m d�1 at thehead of the channel to 0.4 m d�1 at the channel terminus,requiring approximately 360 Earth days (�1 Earth year) to

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 ofthermal erosion [Hulme, 1973; Williams et al., 1998, 2000] to determine which erosion regime dominatesduring channel formation. For the terrestrial case, mechanical erosion is more efficient than thermal erosionat slopes greater than �0.4�, a result of more significant potential and thus kinetic energies that drive theerosion process (Figure 6a). In contrast, for the lunar case, the lower gravity conditions contribute insig-nificant potential and thus kinetic energies, allowing thermal energy to drive the erosion process at slopesless than �3.5� (Figure 6b). Slopes shown represent the range of slopes over which sinuous rilles arecurrently observed on the Moon; thus, thermal erosion is expected to have dominated the formation of lunarlava channels that formed on consolidated substrates of basalt. It should be noted that mechanical erosionwas still likely to have dominated the initial formation of the sinuous rille as lava flowed over unconsoli-dated lunar regolith material.


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incise the observed channel. A low-Ti basalt has erosion ratesranging from about 0.6 m d�1 at the head of the channel toabout 0.3 m d�1 at the channel terminus, requiring 435 Earthdays (�1.2 Earth years) to incise the observed channel.A high-Ti basalt has the lowest erosion rates ranging from0.35 m d�1 at the channel head to 0.2 m d�1 at the channelterminus, and this lava requires approximately 770 Earthdays (�2.2 Earth years), to incise the observed channel.These times assume a constant eruption flux for the predictedduration of channel formation and thus represent an averagetime required for the formation of Rima Prinz, as eruptionfluxes typically wax and wane over the course of a singleeruption.

6. Discussion

[29] Rima Prinz is a sinuous rille characterized by laterallycontinuous walls and a lack of marginal levees, and it is thusinterpreted to be a lava channel that formed as the result oferosion into the lunar substrate. Analysis of analytical modelresults of erosion rate versus slope indicates that thermalerosion was more likely than mechanical erosion to have

been the dominant process active during channel formationon theMoon (Figure 6). This dominance is due to the fact thatthe low gravity conditions characteristic of the Moon yieldinsignificant potential and thus kinetic energies in lavaflowing on the lunar surface. Therefore, thermal energycontributed by hot lava flowing over a substrate is the dom-inant form of energy present in lava flowing over a graduallysloped lunar substrate, and thermal erosion rather thanmechanical erosion was the dominant erosion regime presentduring 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 ofRima Prinz. Dots indicate channel depths that were observedusing LOLA track data, and the various lines indicatemodeled depths (using the model by Williams et al. [1998,2001]) for four types of lava considered, including terrestrialkomatiite, terrestrial ocean island basalt, lunar low-Ti basalt,and lunar high-Ti basalt. Model results for each lava typematch the observed overall trend of decreasing channel depthwith distance from source. Gradually decreasing trends aredue to an increase in lava assimilation, a process that corre-sponds to a decrease in lava temperature, an increase in lavaviscosity, and a decrease in erosion efficiency and thuseroded depth. The steep decreases in eroded depth are arti-facts representing abrupt decreases in the average slopemeasured for each channel segment. Actual changes in slopeare likely to have been more gradual, leading to a moregradual decrease in eroded depth.

Figure 8. Erosion rate versus distance from the head ofthe sinuous rille. Each line represents one of the four lavatypes considered: terrestrial komatiite, terrestrial ocean islandbasalt, lunar low-Ti basalt, and lunar high-Ti basalt. In eachcase, lava of a given initial composition is assumed to erodea substrate of the same composition. The lava is assumed toerupt at its associated liquidus temperature, and the substrateis assumed to melt at its associated solidus temperature.Results indicate that a komatiite lava flow, with the greatestdifference between its liquidus and solidus temperatures(see Table 3), erodes a similarly composed substrate at thefastest rates, from 1.7 m d�1 at the channel head to 0.8 m d�1

at the channel terminus, and requires the shortest eruptionduration, 157 Earth days, to erode the observed channel. Incontrast, a lunar high-Ti basalt, with the smallest differencebetween its liquidus and solidus temperatures, erodes atthe slowest rates, from 0.35 m d�1 at the channel head to0.2 m d�1 at the channel terminus, and requires the longesteruption duration, 766 Earth days, to erode the observedchannel. Results for ocean island basalt and for lunar low-Tibasalt indicate that these lava types have intermediate erosionefficiencies (0.7 m d�1–0.4 m d�1 and 0.6 m d�1–0.3 m d�1,respectively). The gradual decrease in erosion rate observedfor each lava composition is due to lava contaminationand associated reduction in erosion efficiency, and the steepdecrease is an artifact due to abrupt changes in the slopeentered into the model for each channel segment.


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strength Y of 0.1 MPa [Schultz, 1993] and an erodibility bof 0.0005 ([Hurwitz et al., 2010] K = Y / b = 5� 10�9 Pa�1).It should be noted that erosion rate is expected to increase inthe presence of a less consolidated substrate such as the lunarregolith. Specifically for the case of lava composed similarlyto that of an ocean island basalt flowing at the head of RimaPrinz (a = 0.7�; see Figure 6), mechanical erosion is expectedto increase from about 1.0 m d�1 in the case of a consolidatedbasaltic substrate to about 5.0 m d�1 in the case of anunconsolidated regolith substrate (erodibility of 0.0025[Hurwitz et al., 2010]). This change leads to the interpreta-tion that mechanical erosion is more efficient than thermalerosion for slopes greater than �0.6�, as is the case at thehead of Rima Prinz (thermal erosion rate = �4.0 m d�1 ata = 0.7�; see Figure 6). Therefore, mechanical erosion waslikely to have been the dominant process in the initial for-mation of the channel when the lava is incising throughregolith, but the dominant erosion regime shifted to thermalerosion once the regolith was removed and a more consoli-dated basaltic substrate was encountered. This initial periodof more efficient mechanical erosion would be expected todecrease the duration of channel formation by about 6–10Earth days, assuming a regolith thickness of 6–10 m [Fa andJin, 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 composedsubstrate more efficiently than lunar low-Ti basalts, oceanisland basalts, and, most significantly, high-Ti basalts erodeinto respectively similarly composed substrates (Figure 8).The models used to simulate thermal erosion (equations (2)–(5)) suggest that the most significant parameter involved indetermining erosion efficiency is the difference between thetemperature of the flowing lava and the melting temperatureof the substrate. In the scenarios explored in this study, thecompositions of the initially erupted lava and the substrateare identical. Therefore, the lava is assumed to erupt at itscorresponding liquidus temperature and the substrate isassumed to melt at its corresponding solidus temperature(Table 3). Lava with a composition similar to that of a ter-restrial komatiite has the greatest difference between its corre-sponding liquidus and solidus temperatures (DT = 408�C;see Table 3), and lava with a composition similar to that ofa lunar high-Ti basalt has the smallest difference betweenthese two temperatures (DT = 188�C). These observationsare consistent with larger differences between the liquidusand solidus temperatures resulting in a higher thermal energycontribution from the flowing lava and thus in higher erosionrates.[32] Lavas that erode more efficiently require shorter

eruption durations and thus also require less lava to form theobserved sinuous rille (Figure 8 and Table 3). Specifically,

the fastest eroding komatiite lava requires 157 Earth days toform the channel, and, assuming a constant eruption flux of4375 m3 s�1 [i.e.,Wilson and Head, 1980;Head and Wilson,1980] over the course of the eruption, the volume of lava thatis expected to be released is 59 km3. This lava volume issimilar to the volume of lava erupted in 43 flows over thecourse of 18 eruptions measured on Mauna Loa (25.8 km3

[Malin, 1980]) and about an order of magnitude greater thanthe volume of lava erupted in 44 flows over 15 eruptionsmeasured on Kilauea (2.6 km3 [Malin, 1980]). In contrast,the slowest eroding high-Ti lunar basalt requires 766 Earthdays to form the channel, and, assuming a constant erup-tion flux in this case of 4055 m3 s�1 over the course of theeruption, the volume of lava that is expected to be released is268 km3. This lava volume is significantly larger than thoseobserved in Hawaii, but this volume is still an order ofmagnitude less than the volume of lava that erupted in asingle fissure eruption associated with the emplacement ofthe Columbia River flood basalts (>2,000 km3 [Hooper,1997]). A cursory quantitative analysis of a lava com-position similar to a Columbia River basalt [Murase andMcBirney, 1970] indicates that this lava would be veryinefficient at eroding a similarly composed substrate, sup-porting observations that thermal erosion does not occur inthe Columbia River flood basalts [Greeley et al., 1998]. Itshould be noted that the lava volumes reported above repre-sent the entire amount of lava required to form the observedsinuous rille, but that individual flows may have had smallervolumes if the channel formed over a series of events similarto those observed in Kilauea instead of as the result of asingle eruptive event similar to the fissure event in theColumbia River flood basalt.[33] The significant volume of lava required to form Rima

Prinz must have been deposited beyond the terminus of thesinuous rille in Oceanus Procellarum. However, one ofthe more enigmatic characteristics of lunar sinuous rilles isthe lack of observed deposits at and beyond the channel ter-mini (Figure 3e). As suggested in section 3, these depositsmay have been embayed by subsequent emplacement ofmare flows that may have flowed back up the channel for3–5 km from the currently observed channel terminus.Although the terminal deposits of Rima Prinz are not cur-rently observed, LOLA topography data can be used to esti-mate the path that the lava may have taken once it left theconfines of the channel (Figure 9). The main assumptionsused in this analysis include, 1) the lava will always flowdown-gradient, 2) on steep slopes (i.e., contours are closelyspaced), lava will flow perpendicular to the contour, 3) onsuddenly gradual slopes (i.e., contours are suddenly spacedfar apart), lava will tend to flow along a contour until asteeper gradient is reached, 4) lava tends to flow aroundtopographic boundaries and into basins, and 5) currently

Table 3. Summary of Resultsa

LavaType

Tliq(�C)

Tsol(�C)

DT(�C)

Q(m3 s�1)

Erosion Rate 1(m d�1)

Erosion Rate 2(m d�1)

Duration(Earth days)

Vlava

(km3)

Komatiite 1578 1170 408 4375 1.7 0.8 157 59Ocean Island Basalt 1408 1050 358 4390 0.75 0.4 362 137Low-Ti Basalt (12002) 1440 1150 290 4180 0.6 0.3 435 157High-Ti Basalt (74220) 1338 1150 188 4055 0.35 0.2 766 268

aErosion Rate 1 represents erosion at the head of Rima Prinz; Erosion Rate 2 represents erosion at the terminus of Rima Prinz.


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observed topography would have affected the path of thelava.[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 isapproximately double that of the longer Kilauea flows thatmay have been truncated by encountering the ocean [Malin,1980], and the flow has a surface area of approximately2450 km2. The proposed deposit would have terminated in abasin northeast of Rima Prinz, partially but not completelyfilling the basin, as the basin is still observed. As previouslydiscussed, model results indicate that a range of lava volumes(59 km3–268 km3) may have been required to form RimaPrinz, dependent on lava composition. These total lavavolumes translate to average deposit depths of �25 m for akomatiite lava, �55 m for an ocean island basalt, �65 m fora low-Ti lunar basalt, and �110 m for a high-Ti lunar basaltover the proposed deposit area. Deposit depths are expectedto decrease for flows deposited on steeper surfaces andincrease for flows deposited on more gradually sloped sur-faces or within basins. These depths indicate a minimumvalue for the thickness of the subsequent mare flows requiredto cover the deposits from Rima Prinz. The composition ofthe mare in the western Imbrium region has been identified asintermediate TiO2 basalts that lack evidence for extensivemixing [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 volumeof lava erupted during the emplacement of these deposits,observations of irregular ‘shorelines’ along the edges ofOceanus Procellarum suggest that the mare is relativelyshallow along the margins [i.e., Head, 1976]. Therefore,it might be expected that the mare lava would not be thickenough to completely embay high-Ti flows from Rima Prinz,and thus the lava that flowed through and incised Rima Prinzwas most likely to have been composed similarly to lavassuch as komatiites, ocean island basalts, or low-Ti lunarbasalts.

7. Conclusions

[35] The formation of lunar sinuous rilles has long beenconsidered an enigma, with proposed origin theories includ-ing a range of formation mechanisms: 1) origin via con-struction of levees that channelize flow within a cooling lavaflood, 2) origin via either a constructed, structurally stableroof over a lava tube or an eroded subsurface lava tube,and 3) origin via erosion in a surface channel. Our obser-vations of Rima Prinz, a sinuous rille located east of theAristarchus Plateau, indicate that this channel has laterallycontinuous walls that lack marginal levees, supporting thetheory of origin through erosion of the substrate by a surfacechannel. Detailed measurements of channel morphology

Figure 9. (a) Proposed deposit area for the volume of erupted lava required to form Rima Prinz, shownusing the LROC WAC global mosaic (100 m pix�1 resolution) and (b) LOLA topography data with20 m contours (�120 m pix�1). The deposit area was mapped based on five assumptions enumerated insection 6 of the text. The lava forming the proposed deposit flowed down-gradient, with its flow pathinfluenced by topography, until it reached a topographic basin �75 km from the terminus of Rima Prinzand formed a deposit of a depth dependent on the composition of the lava (see Table 3). The deposit thenwould have been completely embayed by subsequent mare volcanism, as textural evidence for this lavaflow is not currently observed.


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were used as constraints in analytical models in order todetermine whether mechanical or thermal erosion is thedominant process active during the formation of Rima Prinz.The most relevant model was then used to determine thedetailed origin of Rima Prinz, including the lava compo-sitions, erosion rates, and eruption durations required toproduce the observed sinuous rille.[36] The key interpretations of model results presented in

this study indicate that the low gravity characteristic of theMoon contributes an insignificant amount of potential andthus kinetic energy to lava flowing on a surface of slopes lessthan �3.5�, allowing thermal energy and thus thermal ero-sion rather than mechanical erosion to dominate during theformation of a lunar sinuous rille on terrain with these slopes.Thermal erosion is expected to dominate during sinuous rilleformation on the Moon even though it is not a commonlyobserved process in terrestrial lava channel formation, asterrestrial lava channels form under higher gravity condi-tions and typically on steeper gradients. Mechanical erosionremains an important process in the initial stages of lunarsinuous rille formation, however, as lava initially encountersthe poorly consolidated lunar regolith that is much moresusceptible to mechanical erosion than the more consolidatedunderlying 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 signifi-cant effect on erosion rates. In particular, assuming that lavaerupts at its liquidus temperature and melts at its solidustemperature, and assuming that the erupted lava has the samecomposition as the substrate, the lava composition with thegreatest difference between its solidus and liquidus tem-peratures will contribute the most thermal energy to meltingthe substrate and incising a channel. Further analysis ofmodel results indicates that erosion efficiency increases withgreater liquidus-solidus temperature differences: a lava witha composition similar to a terrestrial komatiite (DT = 408�C)results in the highest erosion rates (1.7 m d�1–0.8 m d�1)and a lava with a composition similar to a lunar high-Tibasalt (DT = 188�C) results in the lowest erosion rates(0.35 m d�1–0.2 m d�1). Lavas with compositions similarto terrestrial ocean island basalts (DT = 358�C) and lunarlow-Ti basalts (DT = 290�C) result in intermediate ero-sion rates (0.7 m d�1–0.4 m d�1 and 0.6 m d�1–0.3 m d�1,respectively).[38] As expected, greater erosion rates require less time

and thus less lava to carve the observed channel. Resultsindicate that a komatiite-like lava would require 157 Earthdays and 59 km3 of lava to form Rima Prinz, an ocean islandbasalt-like lava would require 362 Earth days and 137 km3

of lava, a lunar low-Ti basalt would require 435 Earth daysand 157 km3 of lava, and a lunar high-Ti basalt would require766 Earth days and 268 km3 of lava to form Rima Prinz.Although lava deposits are not currently observed at the ter-minus of Rima Prinz, a plausible deposit area of �2450 km2

is proposed based on LOLA topography data. The volumesof lavas listed above would thus result in komatiite-like lavadeposit depths of �25 m, ocean island basalt deposit depthsof 55 m, lunar low-Ti basalt deposit depths of �65 m, andlunar high-Ti basalt depths of �110 m. These deposits musthave been completely embayed by subsequent mare flows of

intermediate TiO2 content and relatively shallow depths inorder to no longer be visible, suggesting that the most likelycandidates for the composition of lava that formed RimaPrinz include komatiites, ocean island basalts, and lunarlow-Ti basalts.[39] Further work is needed to constrain the actual com-

position of the lava that formed lunar sinuous rilles. Thegeneral lack of deposits within and beyond the currentlyobserved channel makes this a challenging task. However,the identification of possible remnant lava lake textures in thefloor of the Rima Prinz source depression provide a possiblestarting point for further remote-sensing analyses as well asa desired destination for future ground-based studies. Whilethere are certainly outstanding questions as to the detailedorigin of some lunar sinuous rilles, it is clear from this studythat thermal erosion may have played a significant role in theformation of these features and that the formation of lunarsinuous rilles represents significant events in the volcanichistory of the Moon.

[40] Acknowledgments. We gratefully acknowledge David Williamsfor providing the code used extensively in the analysis presented in thispaper as well as for giving a thorough and critical review of the paper. Wealso thank an additional anonymous reviewer for a thoughtful review. Thisresearch was supported financially by the National Aeronautics and SpaceAdministration through grants NNX09AM54G and NNG07EK00C fromthe NASA Lunar Reconnaissance Orbiter project and the LRO Camera(LROC) and Lunar Orbiter Laser Altimeter (LOLA) experiments.

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Lancaster LA1 4YQ, UK.


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