If you have ever gazed out of the window when flying over particularly barren landscapes you will have noticed that ridges and valleys seem to crop up at remarkably uniform spacing. This feature of the Earth’s surface has long since been recognized by geographers but they have always struggled to identify the underlying physical factors that control the distribution of these landforms. Now, however, a team of researchers in the US and Switzerland have developed the first general theory to describe and predict the mechanics of this natural phenomenon.

Taylor Perron at Massachusetts Institute of Technology (MIT) and his colleagues argue that ridge spacing represents a fundamental balance in nature between the slow “creep” of soil and the branching of water channels over the Earth’s surface. To verify their theory, the MIT scientists compared figures from their numerical model with high resolution images taken of the Earth from above. The researchers believe that a quantitative understanding of valley evolution could also yield valuable information about the nature of localized climates throughout Earth history.

Historical landscapes

Some of the early work on landscape morphology from the late 19th century was already focusing on the segmentation of landscapes into ridges and valleys. But until recently, most studies have remained qualitative, largely because we have lacked the topographic maps with sufficient resolution. Another barrier to developing numerical models is that erosion acts very slowly — just a tenth of a millimetre per year on average — and often in fits and starts, so it's almost impossible to measure directly.

Perron and his team have overcome the mapping problem by using a relatively new technology called LiDAR, which combines GPS with aircraft-mounted lasers. This has been used to produce digital topographic maps covering large areas with resolutions of 1 m per pixel. Another useful feature of LiDAR is it can filter out the laser signals returned from vegetation, and keep only the ones that hit the exposed ground. “We can virtually deforest the landscape, and measure the ridge-valley wavelengths that were previously obscured by trees,” Perron told physicsworld.com.

The researchers have also managed get around the difficulty of measuring erosion rates in order to confirm the river incision and creep parameters in their equations. They achieved this by developing a new technique for calibrating those parameters using only the topography, so we were able to directly compare the wavelength that emerges in model landscapes observed in the field.

Shared geography

The researchers focused on regions that are soil-covered and “low relief”. These landscapes are relatively free of vegetation and the vertical height of the ridges and valleys is not too large relative to their horizontal dimensions. “Basically, this is a disclaimer that our model does not apply to landscapes that are so steep that landslides and debris flows occur frequently,” said Perron. The study was based on sites mostly in the western US but these landscapes are also common in many other regions of the world including the north-eastern US and the UK.

The purpose of collecting these images was to compare them with a numerical model put forward by the same researchers last year. To their delight the MIT scientists found strong agreement between the two sets of data and this led them to a non-dimensional quantity that gauges the balance between soil creep and channel incision — a trade-off that governs the size of ridge spacing. Their model also confirms the long-held rule of thumb that drier climates and weaker rocks are associated with closely spaced valleys in which river incision dominates over creep.

What’s more these findings could help earth scientists to develop historic climate records. “We evaluate how the time-averaged climate has varied among regions by comparing their wavelengths,” said Perron. “By comparing the topography with independent climate records, we can also start to approach the question of which aspects of a variable climate have the strongest effect on long-term erosion and sediment transport,” he added.

Kelin Whipple, an earth scientist at Arizona State University believes the impact of this research will be felt across a range of disciplines. “I think this study of ridge-valley spacing will drive further and deeper analysis of the relations among climate, climate change, and landform morphology in general.” However, he also cautions against viewing this as a key to understanding the full details of past climates. “It is certainly part of the puzzle in trying to determine how climate and climate history is reflected in the shape of landforms — there is promise here, but it’s a complex problem and not fully resolved.”

This research was published in the latest edition of Nature.