REPORT◥PLANETARY TOPOGRAPHY

Global drainage patterns and theorigins of topographic relief on
Earth, Mars, and Titan
Benjamin A. Black,1,2* J. Taylor Perron,3 Douglas Hemingway,4 Elizabeth Bailey,5Francis Nimmo,6 Howard Zebker7
Rivers have eroded the topography of Mars, Titan, and Earth, creating diverse landscapes.
However, the dominant processes that generated topography on Titan (and to some extent
on early Mars) are not well known. We analyzed drainage patterns on all three bodies andfound that large drainages, which record interactions between deformation and erosional
modification, conform much better to long-wavelength topography on Titan and Mars
than on Earth. We use a numerical landscape evolution model to demonstrate thatshort-wavelength deformation causes drainage directions to diverge from long-wavelength
topography, as observed on Earth. We attribute the observed differences to ancient
long-wavelength topography on Mars, recent or ongoing generation of long-wavelength
relief on Titan, and the creation of short-wavelength relief by plate tectonics on Earth.

Increasingly detailed observations of rocky
and icy bodies in our solar system reveal
dramatic diversity in surface topographic features. Plate tectonics has shaped topography
extensively on Earth, but on less tectonically
active worlds like Mars (1–5), and icy worlds like
Titan and Pluto (6–8), the origins and history of
the observed surface topography are varied andin some cases unknown. Fluid erosion offers ameans to probe the long-term evolution of topography because drainage patterns interact with
topography as it is uplifted and eroded [e.g., (9)].
Fluid runoff has shaped the surfaces of at least
three bodies in the solar system in the form ofliquid water on Earth and Mars [e.g., (10)] andliquid hydrocarbons on Titan [e.g., (11, 12)], thereby
inscribing a record of how the development oflandscapes has differed on these three worlds.
Earth’s topography is dominated by the dichotomy between continents and ocean basins;
most rivers drain from continental interiors to
the ocean. However, Earth’s topography is also
shaped by deformation concentrated near plateboundaries, such as the formation of collisional
mountain ranges or volcanic arcs above subduc1

Department of Earth and Atmospheric Science, City Collegeof New York, City University of New York, New York, NY,
USA. 2Earth and Environmental Science, The Graduate
Center, City University of New York, New York, NY, USA.
3
Department of Earth, Atmospheric, and Planetary Sciences,
Massachusetts Institute of Technology, Cambridge, MA, USA.
4
Department of Earth and Planetary Science, University ofCalifornia, Berkeley, Berkeley, CA, USA. 5Division of
Geological and Planetary Sciences, California Institute ofTechnology, Pasadena, CA, USA. 6Department of Earth andPlanetary Sciences, University of California, Santa Cruz,
Santa Cruz, CA, USA. 7Department of Geophysics, School ofEarth Sciences, Stanford University, Stanford, CA, USA.
*Corresponding author. Email: bblack@ccny.cuny.edu

Black et al., Science 356, 727–731 (2017)19 May 2017tion zones. These features can divert rivers as they
traverse continents and can thereby displace drainage divides toward active margins, reshaping someof the planet’s richest ecosystems in the process(13). Many terrestrial river basins in tectonically
active regions are continuously reorganized in response to changing tectonic boundary conditions(9). As fluvial erosion (i.e., erosion by surface liquidflow) competes with tectonic deformation toshape Earth’s landscapes, global drainage patterns should come to reflect a combination of
long-wavelength, continent-scale topography andshorter-wavelength features such as mountain
ranges.
Large-scale topography on Mars was established more than 3.5 billion years ago (Ga) in thewake of the formation of Borealis Basin (4, 14)
and the growth of the Tharsis volcanic rise (1).
Most fluvial activity likely occurred early in theplanet’s history (5, 10, 15). On Titan, sparse impact craters and mountainous terrains attest to
active modification of the surface (16), though
the age and origin of relief and the tempo oferosional modification remain to be determined(11). We consider whether global drainage patterns differ on Earth and Mars as a result of
their divergent geologic and surface histories, andwe explore the implications of that comparison
for Titan and other bodies where the erosional
and tectonic history is largely unknown.
Our hypothesis is that on planets or moons
where long-wavelength processes dominate production of relief, drainages should generally flow
parallel to the slope of the long-wavelength topography, and the correlation should improve only
marginally as the resolution of the topography isrefined. We term the agreement between drainage patterns and topography at a given scale the“drainage conformity with topography.” In thiscontext, we consider topography to be longwavelength if it spans at least 1/40 of the planetary circumference—that is, spherical harmonics
up to degree and order 20 (on Earth, ~1000 km).
On bodies shaped by processes like plate tectonics
that generate relief at shorter wavelengths, we
expect reduced correlation at long wavelengths,with gradual improvement as shorter-wavelengthfeatures that deflect rivers are included in thecomparison. We further hypothesize that thetiming of deformation and erosion influences
global drainage patterns. If the establishment ofa planet’s topography is followed by a long periodof tectonic quiescence, rivers will have more time
to adjust to, and alter, that topography, and drainage directions will conform better with the longwavelength component of the altered topography.
On planets where tectonic deformation is more
recent or more intense than fluvial erosion, shorterwavelength topography related to this deformation will have a stronger influence on drainage
directions, and long-wavelength conformity will
be reduced.
To test these hypotheses, we compared global
drainage patterns and long-wavelength topography for Earth, Mars, and Titan (Fig. 1). We focusedon fluvially modified worlds, but we expect volcanic, cryovolcanic, and other fluid-flow features
on bodies such as Venus and Pluto to leave similar signatures. We combined new and existing
maps of drainages on Titan (11, 12), Earth (17),and Mars (18) with spherical harmonic models
for topography (19–22). We computed two proxy
metrics for drainage conformity with topography (fig. S1). The first metric, the downhill percentage (%d), represents the proportion of points
along a river that are at higher elevations than
the next downstream point for a given point spacing and spherical harmonic expansion of topography (Fig. 2A). As topographic resolution becomes
finer—in this case, as topography is expanded tohigher spherical harmonic degrees—%d should
approach 100% for active drainage networks because liquids in open channels flow downhill. The
second metric, the conformity factor (L), is defined as L = median[cos(d)], where d is the angle
between the river drainage direction and thedownslope direction of the topographic expansion(Fig. 2B). Values of L closer to 1 indicate better
agreement between flow directions and longwavelength topography, but we do not expect perfect conformity (L = 1) at any resolution because
we are comparing the steepest descent direction
at a particular point to the flow direction acrossa finite interval.
Our results for topographic conformity as afunction of maximum spherical harmonic degree
are shown in Fig. 2. Conformity is consistently
lower on Earth than on Mars or Titan, whereas
Titan’s conformity factor overlaps within uncertainty with that of Mars. The %d values are
likewise much higher on Mars and Titan than on
Earth. As expected, no body reaches near-perfect
topographic conformity at the long wavelengths
we consider here. These results lead us to thecounterintuitive observation that many of Earth’s
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Fig. 1. Maps of topography referenced to the geoid and expanded
to spherical harmonic degree and order 6, overlain with the fluvial
features employed in this study. (A) Earth. (B) Enlargement of North
America. (C) Titan. Blue outlines show Cassini Synthetic Aperture Radar(SAR) observation swaths. (D) Enlargement of eastern Shangri-La and
Xanadu regions of Titan. T values represent the Cassini SAR swath numbers

rivers appear to flow along contour or uphill withrespect to long-wavelength topography (as shownin Fig. 1B at locations where river traces deviate
from gradient arrows), in contrast to most drainages on Titan and Mars.
On Mars, the strong correlation between valley
network orientations and the present-day longBlack et al., Science 356, 727–731 (2017)19 May 2017(swaths are outlined in blue). (E) Mars. (F) Enlargement of Hellas Basin on
Mars. In (A), (C), and (E), white boxes outline regions enlarged in (B), (D),and (F), where river courses are shown in light blue, black arrows indicate
topographic gradient at each point, and indicated conformity values spanthese enlarged regions, with uncertainties corresponding to the 95%
confidence interval for the median (19).

wavelength topography requires that most largescale topography predates valley network formation in the Noachian era and that this ancient
topography was the dominant influence on valley network orientation (Fig. 1F) (1, 2, 23). Martian
topographic conformity remains imperfect evenwhen shorter wavelengths are considered (fig.

S5). We attribute this persistent, moderate disagreement between drainage directions and topography to the combined effects of impact cratering,
topographic resolution, and deformation after theera of valley network formation (24, 25). Because%d quantifies the proportion of river segmentsthat flow from higher to lower topography (Fig. 2A
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Fig. 2. Topographic conformity differs on Titan andMars versus Earth. (A) The
percent downhill (%d) metricas a function of the spatial
resolution of the sphericalharmonic expansion. (B) The
conformity factor {L =median[cos(d)]}. Angles
corresponding to L values areillustrated on vertical axis.
Uncertainties correspondto the 95% confidence interval for the median (19).

Fig. 3. Deformation history
influences conformity.
Variable-uplift simulations(A) represent plate tectonic–
style–uplift, and uniformuplift simulations (B) represent
dominantly long-wavelength
deformation. Shaded relief
maps in (A) and (B) show
simulations after 10 million
years (My). The model
domain is doubly periodic,
and the lowest 70% of initial
elevations (white) were set as
the base level relative towhich uplift occurs. (C) Mean%d among 10 variable-uplift
simulations and 10 uniformuplift simulations. (D) Mean
topographic conformity
among the same simulations
analyzed in (C). In (C) and(D), error bars represent two
standard errors of the meanacross the simulation
ensembles.

and fig. S5), our results place bounds on theamount of vertical deformation after the era ofvalley network formation. For at least 85% of
the fluvially dissected landscapes on Mars, Hesperian and Amazonian era vertical deformation
has not exceeded the initial relief.
For Titan, a similar analysis suggests that midlatitude and equatorial topography has been stablesince the formation of the fluvial networks. If
present-day topography was shaped by an episode of nonuniform crustal thickening at 0.3 to
1.2 Ga (16, 26), fluvial networks at middle and low
Black et al., Science 356, 727–731 (2017)19 May 2017

latitudes must have formed after that time. In
contrast, many of Titan’s north polar networks
deviate from regional gradients (fig. S3). This result is consistent with recent or ongoing predominantly short-wavelength deformation in the northpolar region.
What processes have shaped the topographic
conformity of Earth, Mars, and Titan? Multiple
factors could plausibly contribute to weak longwavelength topographic conformity, including
little erosion relative to relief and resurfacing, lowamplitude long-wavelength topography, impact

cratering, or vigorous short-wavelength deformation. However, Earth is deeply eroded, the topographic power spectra for the terrestrial planets
are self-affine (i.e., the height of relief features
scales with their wavelength), and topographic
power spectra for Earth and Mars are almost
identical (20, 27). Consequently, neither weak erosion nor contrasts in global static topography canfully explain the low topographic conformity on
Earth relative to Mars.
On Earth, plate tectonics preserves cratons—
broad, flat regions where small changes in
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Fig. 4. Impact cratering can modulate topographic conformity. (A) Shaded relief map of a representative simulation after 60 My of erosion in tandemwith impact cratering. (B) Mean topographic conformity among 10 control simulations, 10 simulations with a cratered initial surface, and 10 simulations
with ongoing cratering in tandem with fluvial erosion. Times refer to model time after initiation (19). Legend shows a typical uncertainty of two standard errorsof the mean within the simulation ensembles.

topography can yield large shifts in conformity—
while driving short-wavelength, spatiotemporally
variable rock uplift at active margins. To explore
the influence of terrestrial plate tectonics on drainage network evolution, we analyzed river network
conformity for a series of numerical landscapeevolution model simulations (19, 28). We completed two sets of ten idealized simulations: thefirst set with spatially uniform uplift to represent
a world in which long-wavelength deformation
dominates the production of relief (Fig. 3A) andthe second set with spatially variable uplift tocapture the effects of short-wavelength deformation on drainage orientations (Fig. 3B). The
simulations with variable uplift are intended toinvestigate the particular influence of plate tectonics. According to both our metrics, drainage
directions in the uniform-uplift simulations conform much better with long-wavelength topography than in the variable-uplift simulations (Fig. 3,
C and D). The absolute magnitudes of L and %d
are higher in the model than in natural drainage
networks, partly because the model lacks cratonsand sedimentary basins, both of which suppress
conformity in nature. Nonetheless, our idealized
model offers qualitative insights into the effectsof variable uplift on drainage patterns. Active,
spatially variable uplift depresses topographic
conformity, but this effect is temporary: once thevariable uplift ceases, the topographic conformity
steadily increases (fig. S4A). Overall, the results
support our hypothesis that short-wavelength active deformation (such as mountain-building on
Earth) interferes with the background pattern ofrivers draining the continents.
Geomorphic mapping shows that drainage
basins on Mars are strongly influenced by preexisting ancient Noachian topography, including
the hemispheric dichotomy, early Noachian impact structures, and subtle ridges of unknown origin located throughout the southern highlands(2, 23). Cratering during and after the Late Heavy
Black et al., Science 356, 727–731 (2017)19 May 2017

Bombardment ~4 Ga further disrupted somedrainage basins (2, 23, 24). To quantify the extent of this disruption and the consequences for
topographic conformity, we conducted additionallandscape evolution simulations (19). We findthat unless impacts obliterate drainages entirely,
they can modify, but do not erase, alignment withpreexisting long-wavelength topography (Fig. 4),
consistent both with mapped relationships between drainage patterns and large-scale slopes(1, 2, 23) and with our measurements showing
relatively high martian topographic conformity.
Crustal magnetization (29) and >3.6-billion-yearold felsic rocks on Mars (30) have been interpreted
as evidence for processes typically associated withplate tectonics on Earth. Our model results andthe high conformity of Martian drainage networks
suggest that at the time of martian river incision,plate tectonics was absent and impact cratering
was insufficiently intense to fully disrupt drainagealignment with ancient long-wavelength topographic gradients (1, 2, 5, 23).
Of the three bodies we consider here, Titan’s
geologic history is the most enigmatic. In contrast
to the ancient long-wavelength topography ofMars (1, 4), Titan shows evidence for recent or
ongoing geologic activity (11, 16, 26). Titan’s longwavelength conformity thus implies that longwavelength mechanisms actively dominate thegeneration of relief in most regions of Titan (thenorth polar region is a possible exception). A mechanism such as global-scale changes in shell thickness due to tidal heating or basal melting andrefreezing would create both long-wavelength
relief and local fractures on Titan (7, 31). Titan’shigh topographic conformity supports geophysicalarguments for substantial sediment transfer from
topographic highs to lows (31). Patterns in Titan’s
atmospheric circulation are expected to result in
net poleward transport of hydrocarbons frommid-latitudes (32). Of the drainages we mappedon Titan that are located poleward of 45°N and

45°S latitudes, and that traverse at least two
degrees of latitude, five out of six drain toward
the poles (Fig. 1 and database S1). This implies that
other hydrocarbon fluxes or transport mechanisms
must balance the net atmospheric and fluvial
transport of hydrocarbons toward Titan’s poles.
Topographic conformity does not reach thenear-perfect %d predicted by the model on anyof the three bodies we consider because of limited
map resolution (19). Modest short-wavelength deformation, impact cratering, or deformation after
the development of drainages (5, 25) have probably also contributed to the imperfect conformity
on Mars and Titan. The improvement of drainage alignment on Earth relative to Mars at very
short wavelengths (24) supports this interpretation for Mars. In a set of landscape evolution simulations in which uplift ceases entirely after aperiod of variable uplift, we find that topographic
gradients on the resulting low-relief surfaces (similar to Earth’s cratons) can eventually grow weakand chaotic at shorter wavelengths, allowing drainage patterns to retain the imprint of past conditions (fig. S4B). On Earth, topographic conformity
dips at scales of 750 to 1500 km, which we attribute to steep gradients in elevation from ocean
basins to convergent margins to low-relief continental interiors.
Earth and Mars share similarly bimodal topography (33) but divergent global geology, provingthat the distribution of elevations alone cannot
reveal geologic evolution. The interaction of rivers
with long-wavelength topography provides analternative record of the generation of planetary
relief. The formation and amalgamation of continental crust are processes that create dominantly long-wavelength topography, as is the processthat built the martian hemispheric dichotomy.
Construction of mountain ranges on Earth has
a dominantly intermediate wavelength, necessarily smaller than the scale of continents. Martiandrainage patterns reflect ancient long-wavelength
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AC KNOWLED GME NTS

We thank E. Chan for spot-checking martian drainages. Threereviewers provided constructive feedback. B.A.B. acknowledges
NASA grant NNX16AR87G. D.H. thanks the Miller Institute for
Basic Research in Science. We thank the Cassini team. The
topography and drainage data used in this paper are available at
http://ddfe.curtin.edu.au/gravitymodels/Earth2012/ and http://
eagle1.umd.edu/flood/DRT/ for Earth, at https://astrogeology.
usgs.gov/search/map/Titan/Cassini/TitanFluvialMapping/
TitanFluvialMapping_July2013 and in database S2 for Titan, andat https://webgis.wr.usgs.gov/pigwad/down/mars_dl.htm andhttp://pds-geosciences.wustl.edu/missions/mgs/megdr.html forMars. The landscape evolution software Tadpole is available athttps://github.com/MITGeomorph/Tadpole.

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topography that predates both valley network
formation and Noachian-Hesperian bombardment(2), confirming that Noachian Mars lacked global plate tectonics and bounding post-Noachianchanges in martian relief. Our results favor dominantly long-wavelength relief-generating mechanisms on Titan such as shell-thickness variations
arising from tidal heating (6, 7) or thermal expansion and contraction (6). Together, the threeriver-worn bodies in our solar system provide a
Rosetta stone for deciphering the imprint of tectonics on landscapes.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/356/6339/727/suppl/DC1
Materials and Methods
Figs. S1 to S8Tables S1 and S2
Databases S1 and S2References (34–55)
1 June 2016; accepted 6 April 201710.1126/science.aag0171

5 of 5Global drainage patterns and the origins of topographic relief
on Earth, Mars, and Titan
Benjamin A. Black, J. Taylor Perron, Douglas Hemingway,
Elizabeth Bailey, Francis Nimmo and Howard Zebker (May 18,
2017)
Science 356 (6339), 727-731. [doi: 10.1126/science.aag0171]

River systems reveal planetary tectonics
Earth, Mars, and Titan have all hosted rivers at some point in their histories. Rivers erode thelandscape, leaving behind signatures that depend on whether the surface topography was in place
before, during, or after the period of liquid flow. Black et al. developed two metrics to measure how
well river channels align with the surrounding large-scale topography (see the Perspective by Burr).
Earth's plate tectonics introduce features such as mountain ranges that cause rivers to divert, processes
that clearly differ from those found on Mars and Titan.
Science, this issue p. 727; see also p. 708

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