J. Taylor Perron

The search for a topographic signature of life

Landscapes are shaped by the uplift, deformation and breakdown of bedrock and the erosion, transport and deposition of sediment. Life is important in all of these processes. Over short timescales, the impact of life is quite apparent: rock weathering, soil formation and erosion, slope stability and river dynamics are directly influenced by biotic processes that mediate chemical reactions, dilate soil, disrupt the ground surface and add strength with a weave of roots. Over geologic time, biotic effects are less obvious but equally important: biota affect climate, and climatic conditions dictate the mechanisms and rates of erosion that control topographic evolution. Apart from the obvious influence of humans, does the resulting landscape bear an unmistakable stamp of life? The influence of life on topography is a topic that has remained largely unexplored. Erosion laws that explicitly include biotic effects are needed to explore how intrinsically small-scale biotic processes can influence the form of entire landscapes, and to determine whether these processes create a distinctive topography.

Formation of evenly spaced ridges and valleys

One of the most striking examples of self-organization in landscapes is the emergence of evenly spaced ridges and valleys. Despite the prevalence of uniform valley spacing, no theory has been shown to predict this fundamental topographic wavelength. Models of long-term landscape evolution can produce landforms that look realistic, but few metrics exist to assess the similarity between models and natural landscapes. Here we show that the ridge–valley wavelength can be predicted from erosional mechanics. From equations of mass conservation and sediment transport, we derive a characteristic length scale at which the timescales for erosion by diffusive soil creep and advective stream incision are equal. This length scale is directly proportional to the valley spacing that emerges in a numerical model of landform evolution, and to the measured valley spacing at five field sites. Our results provide a quantitative explanation for one of the most widely observed characteristics of landscapes. The findings also imply that valley spacing is a fundamental topographic signature that records how material properties and climate regulate erosional processes.

Evidence for an ancient martian ocean in the topography of deformed shorelines

A suite of observations suggests that the northern plains of Mars, which cover nearly one third of the planets surface, may once have contained an ocean. Perhaps the most provocative evidence for an ancient ocean is a set of surface features that ring the plains for thousands of kilometres and that have been interpreted as a series of palaeoshorelines of different age. It has been shown, however, that topographic profiles along the putative shorelines contain long-wavelength trends with amplitudes of up to several kilometres, and these trends have been taken as an argument against the martian shoreline (and ocean) hypothesis. Here we show that the long-wavelength topography of the shorelines is consistent with deformation caused by true polar wander—a change in the orientation of a planet with respect to its rotation pole—and that the inferred pole path has the geometry expected for a true polar wander event that postdates the formation of the massive Tharsis volcanic rise.

Spectral signatures of characteristic spatial scales and nonfractal structure in landscapes

[1] Landscapes are sometimes argued to be scale-invariant or random surfaces, yet qualitative observations suggest that they contain characteristic spatial scales. We quantitatively investigate the existence of characteristic landscape scales by analyzing two-dimensional Fourier power spectra derived from high-resolution topographic maps of two landscapes in California. In both cases, we find that spectral power declines sharply above a frequency that corresponds roughly to hillslope length, implying that the landscape is relatively smooth at finer scales. The spectra also show that both landscapes contain quasiperiodic ridge-and-valley structures, and we derive a robust measure of the ridge-valley wavelength. By comparing the spectra with the statistical properties of spectra derived from randomly generated topography, we show that such uniform valley spacing is unlikely to occur in a random surface. We describe several potential applications of spectral analysis in geomorphology beyond the identification of characteristic spatial scales, including a filtering technique that can be used to measure topographic attributes, such as local relief, at specific scales or in specific orientations.

Can springs cut canyons into rock

Amphitheater-headed valleys on Earth and Mars are often assumed to result from erosion by emerging spring water (i.e., seepage erosion or groundwater sapping) rather than by surface runoff. The origin of such valleys has implications for landscape evolution on Earth and the hydrologic cycle and associated potential for life on other planets. In this paper we explore the evidence for seepage erosion in bedrock to address whether valley morphology can be used as a diagnostic indicator of seepage erosion. Seepage erosion is an important process in loose sediment where hydraulic forces cause grain detachment, often resulting in amphitheater-headed valleys. However, the extension of these processes to resistant rock is uncertain. In sedimentary rocks, groundwater might control the shape and rate of valley formation. It is possible, however, that seepage plays only a secondary role to runoff processes. This seems likely in basaltic valleys on Earth, where little evidence exists for seepage erosion. Since the ability of seepage to erode bedrock valleys remains unclear and because many amphitheater-headed valleys were probably carved by other processes, seepage erosion should not be inferred based solely on valley form.

Formation of amphitheater-headed valleys by waterfall erosion after large-scale slumping on Hawai'i

Amphitheater-headed valleys are common on the surfaces of Earth and Mars. The abrupt terminations of these valleys at their headwalls have been used extensively to argue for valley erosion from springs (i.e., seepage erosion or groundwater sapping) rather than surface runoff. This interpretation has significant implications for Martian hydrology and the associated prospects for life. A connection between channel form and the erosion processes induced by groundwater, however, has not been demonstrated in resistant rock. Perhaps the most widely cited terrestrial analogs for Martian amphitheater-headed valleys in basalt are the spectacular canyons of Kohala, Hawai‘i. Here we present new field observations and topographic analyses of the amphitheater-headed Kohala valleys. We found no evidence for intensively weathered rocks or alcoves around springs at valley headwalls. Instead, valley-head erosion appears to be dominated by waterfall plunge pools. Stream flow from peak annual precipitation events exceeds spring discharge by more than an order of magnitude, and such flow is responsible for evacuation of the coarse sediment that lines the streams. Bathymetric surveys along the Kohala coast have revealed a large submarine landslide, the Polol Slump, directly offshore of the Kohala valleys. We propose that the headscarp of this massive landslide is expressed as the present-day 400 m Kohala sea cliffs. As dominant streams poured over this headscarp as waterfalls, vertical plunge pool erosion and undercutting caused upstream propagation of knickpoints, eventually producing amphitheater-headed valleys. Island subsidence rates and the ages of volcanic eruptions and submarine terraces indicate that the average rate of valley headwall advance is as high as 60 mm/yr. We propose a simple expression for upslope headwall propagation by vertical waterfall erosion based on abrasion by impacting sediment particles in plunge pools. This model indicates that head-wall propagation depends nonlinearly on the sediment flux passing over the waterfall and linearly on the ratio of kinetic versus potential energy of sediment impacts. After the Polol Slump, many streams did not form upslope-propagating waterfalls because they had smaller discharges due to a radial drainage pattern and fault-bounded drainage divides, which prevented runoff from the wetter summit of the volcano. A threshold for headwall propagation due to sediment supply or sediment-transport capacity is consistent with the model. Island subsidence following valley formation has resulted in alluviation of the valley floors, which has created the observed U-shaped valley cross sections. Our interpretation implies that surface runoff can carve amphitheater-headed valleys and that seepage erosion cannot be inferred based solely on valley form on Earth, Mars, or other planets.

Climatic control of bedrock river incision

Bedrock river incision drives the development of much of Earth’s surface topography, and thereby shapes the structure of mountain belts and modulates Earth’s habitability through its effects on soil erosion, nutrient fluxes and global climate. Although it has long been expected that river incision rates should depend strongly on precipitation rates, quantifying the effects of precipitation rates on bedrock river incision rates has proved difficult, partly because river incision rates are difficult to measure and partly because non-climatic factors can obscure climatic effects at sites where river incision rates have been measured. Here we present measurements of river incision rates across one of Earth’s steepest rainfall gradients, which show that precipitation rates do indeed influence long-term bedrock river incision rates. We apply a widely used empirical law for bedrock river incision to a series of rivers on the Hawaiian island of Kaua‘i, where mean annual precipitation ranges from 0.5 metres to 9.5 metres (ref. 12)—over 70 per cent of the global range—and river incision rates averaged over millions of years can be inferred from the depth of river canyons and the age of the volcanic bedrock. Both a time-averaged analysis and numerical modelling of transient river incision reveal that the long-term efficiency of bedrock river incision across Kaua‘i is positively correlated with upstream-averaged mean annual precipitation rates. We provide theoretical context for this result by demonstrating that our measurements are consistent with a linear dependence of river incision rates on stream power, the rate of energy expenditure by the flow on the riverbed. These observations provide rare empirical evidence for the long-proposed coupling between climate and river incision, suggesting that previously proposed feedbacks among topography, climate and tectonics may occur.

Valley formation and methane precipitation rates on Titan

Branching valley networks near the landing site of the Huygens probe on Titan imply that fluid has eroded the surface. The fluid was most likely methane, which forms several percent of Titans atmosphere and can exist as a liquid at the surface. The morphology of the valley networks and the nature of Titans surface environment are inconsistent with a primary valley formation process involving thermal, chemical, or seepage erosion. The valleys were more likely eroded mechanically by surface runoff associated with methane precipitation. If mechanical erosion did occur, the flows must first have been able to mobilize any sediment accumulated in the valleys. We develop a model that links precipitation, open-channel flow, and sediment transport to calculate the minimum precipitation rate required to mobilize sediment and initiate erosion. Using data from two monitored watersheds in the Alps, we show that the model is able to predict precipitation rates in small drainage basins on Earth. The calculated precipitation rate is most sensitive to the sediment grain size. For a grain diameter of 1–10 cm, a range that brackets the median size observed at the Huygens landing site, the minimum precipitation rate required to mobilize sediment in the nearby branching networks is 0.5–15 mm hr^(−1). We show that this range is reasonable given the abundance of methane in Titans atmosphere. These minimum precipitation rates can be compared with observations of tropospheric cloud activity and estimates of long-term methane precipitation rates to further test the hypothesis that runoff eroded the valleys.

Fluvial features on Titan: Insights from morphology and modeling

Fluvial features on Titan have been identified in synthetic aperture radar (SAR) data taken during spacecraft flybys by the Cassini Titan Radar Mapper (RADAR) and in Descent Imager/Spectral Radiometer (DISR) images taken during descent of the Huygens probe to the surface. Interpretations using terrestrial analogs and process mechanics extend our perspective on fluvial geomorphology to another world and offer insight into their formative processes. At the landscape scale, the varied morphologies of Titan’s fluvial networks imply a variety of mechanical controls, including structural influence, on channelized flows. At the reach scale, the various morphologies of individual fluvial features, implying a broad range of fluvial processes, suggest that (paleo-)flows did not occupy the entire observed width of the features. DISR images provide a spatially limited view of uplands dissected by valley networks, also likely formed by overland flows, which are not visible in lower-resolution SAR data. This high-resolution snapshot suggests that some fluvial features observed in SAR data may be river valleys rather than channels, and that uplands elsewhere on Titan may also have fine-scale fluvial dissection that is not resolved in SAR data. Radar-bright terrain with crenulated bright and dark bands is hypothesized here to be a signature of fine-scale fluvial dissection. Fluvial deposition is inferred to occur in braided channels, in (paleo)lake basins, and on SAR-dark plains, and DISR images at the surface indicate the presence of fluvial sediment. Flow sufficient to move sediment is inferred from observations and modeling of atmospheric processes, which support the inference from surface morphology of precipitation-fed fluvial processes. With material properties appropriate for Titan, terrestrial hydraulic equations are applicable to flow on Titan for fully turbulent flow and rough boundaries. For low-Reynolds-number flow over smooth boundaries, however, knowledge of fluid kinematic viscosity is necessary. Sediment movement and bed form development should occur at lower bed shear stress on Titan than on Earth. Scaling bedrock erosion, however, is hampered by uncertainties regarding Titan material properties. Overall, observations of Titan point to a world pervasively influenced by fluvial processes, for which appropriate terrestrial analogs and formulations may provide insight.

The root of branching river networks

Branching river networks are one of the most widespread and recognizable features of Earth’s landscapes and have also been discovered elsewhere in the Solar System. But the mechanisms that create these patterns and control their spatial scales are poorly understood. Theories based on probability or optimality have proven useful, but do not explain how river networks develop over time through erosion and sediment transport. Here we show that branching at the uppermost reaches of river networks is rooted in two coupled instabilities: first, valleys widen at the expense of their smaller neighbours, and second, side slopes of the widening valleys become susceptible to channel incision. Each instability occurs at a critical ratio of the characteristic timescales for soil transport and channel incision. Measurements from two field sites demonstrate that our theory correctly predicts the size of the smallest valleys with tributaries. We also show that the dominant control on the scale of landscape dissection in these sites is the strength of channel incision, which correlates with aridity and rock weakness, rather than the strength of soil transport. These results imply that the fine-scale structure of branching river networks is an organized signature of erosional mechanics, not a consequence of random topology.