MIT Research News' Journal

A “pacemaker” for North African climate

The Sahara desert is one of the harshest, most inhospitable places on the planet, covering much of North Africa in some 3.6 million square miles of rock and windswept dunes. But it wasn’t always so desolate and parched. Primitive rock paintings and fossils excavated from the region suggest that the Sahara was once a relatively verdant oasis, where human settlements and a diversity of plants and animals thrived.

Now researchers at MIT have analyzed dust deposited off the coast of west Africa over the the last 240,000 years, and found that the Sahara, and North Africa in general, has swung between wet and dry climates every 20,000 years. They say that this climatic pendulum is mainly driven by changes to the Earth’s axis as the planet orbits the sun, which in turn affect the distribution of sunlight between seasons — every 20,000 years, the Earth swings from more sunlight in summer to less, and back again.

For North Africa, it is likely that, when the Earth is tilted to receive maximum summer sunlight with each orbit around the sun, this increased solar flux intensifies the region’s monsoon activity, which in turn makes for a wetter, “greener” Sahara. When the planet’s axis swings toward an angle that reduces the amount of incoming summer sunlight, monsoon activity weakens, producing a drier climate similar to what we see today.

“Our results suggest the story of North African climate is dominantly this 20,000-year beat, going back and forth between a green and dry Sahara,” says David McGee, an associate professor in MIT’s Department of Earth, Atmospheric and Planetary Sciences. “We feel this is a useful time series to examine in order to understand the history of the Sahara desert and what times could have been good for humans to settle the Sahara desert and cross it to disperse out of Africa, versus times that would be inhospitable like today.”

McGee and his colleagues have published their results today in Science Advances.

A puzzling pattern

Each year, winds from the northeast sweep up hundreds of millions of tons of Saharan dust, depositing much of this sediment into the Atlantic Ocean, off the coast of West Africa. Layers of this dust, built up over hundreds of thousands of years, can serve as a geologic chronicle of North Africa’s climate history: Layers thick with dust may indicate arid periods, whereas those containing less dust may signal wetter eras.

Scientists have analyzed sediment cores dug up from the ocean bottom off the coast of West Africa, for clues to the Sahara’s climate history. These cores contain layers of ancient sediment deposited over millions of years. Each layer can contain traces of Saharan dust as well as the remains of life forms, such as the tiny shells of plankton.

Past analyses of these sediment cores have unearthed a puzzling pattern: It would appear that the Sahara shifts between wet and dry periods every 100,000 years — a geologic beat that scientists have linked to the Earth’s ice age cycles, which seem to also come and go every 100,000 years. Layers with a larger fraction of dust seem to coincide with periods when the Earth is covered in ice, whereas less dusty layers appear during interglacial periods, such as today, when ice has largely receded.

But McGee says this interpretation of the sediment cores chafes against climate models, which show that Saharan climate should be driven by the region’s monsoon season, the strength of which is determined by the tilt of the Earth’s axis and the amount of sunlight that can fuel monsoons in the summer.

“We were puzzled by the fact that this 20,000-year beat of local summer insolation seems like it should be the dominant thing controlling monsoon strength, and yet in dust records you see ice age cycles of 100,000 years,” McGee says.

Beats in sync

To get to the bottom of this contradiction, the researchers used their own techniques to analyze a sediment core obtained off the coast of West Africa by colleagues from the University of Bordeaux — which was drilled only a few kilometers from cores in which others had previously identified a 100,000-year pattern.

The researchers, led by first author Charlotte Skonieczny, a former MIT postdoc and now a professor at Paris-Sud University, examined layers of sediment deposited over the last 240,000 years. They analyzed each layer for traces of dust and measured the concentrations of a rare isotope of thorium, to determine how rapidly dust was accumulating on the seafloor.

Thorium is produced at a constant rate in the ocean by very small amounts of radioactive uranium dissolved in seawater, and it quickly attaches itself to sinking sediments. As a result, scientists can use the concentration of thorium in the sediments to determine how quickly dust and other sediments were accumulating on the seafloor in the past: During times of slow accumulation, thorium is more concentrated, while at times of rapid accumulation, thorium is diluted. The pattern that emerged was very different from what others had found in the same sediment cores.

“What we found was that some of the peaks of dust in the cores were due to increases in dust deposition in the ocean, but other peaks were simply because of carbonate dissolution and the fact that during ice ages, in this region of the ocean, the ocean was more acidic and corrosive to calcium carbonate,” McGee says. “It might look like there’s more dust deposited in the ocean, when really, there isn’t.”

Once the researchers removed this confounding effect, they found that what emerged was primarily a new “beat,” in which the Sahara vacillated between wet and dry climates every 20,000 years, in sync with the region’s monsoon activity and the periodic tilting of the Earth.

“We can now produce a record that sees through the biases of these older records, and so doing, tells a different story,” McGee says. “We’ve assumed that ice ages have been the key thing in making the Sahara dry versus wet. Now we show that it’s primarily these cyclic changes in Earth’s orbit that have driven wet versus dry periods. It seems like such an impenetrable, inhospitable landscape, and yet it’s come and gone many times, and shifted between grasslands and a much wetter environment, and back to dry climates, even over the last quarter million years.”

This research was funded, in part, by the National Science Foundation.

Customizing computer-aided design

MIT researchers have devised a technique that “reverse engineers” complex 3-D computer-aided design (CAD) models, making them far easier for users to customize for manufacturing and 3-D printing applications.

Nearly all commercial products start as a CAD file, a 2-D or 3-D model with the product’s design specifications. One method that’s widely used to represent today’s 3-D models is constructive solid geometry (CSG), a technique where numerous basic shapes, or “primitives,” with a few adjustable parameters can be assembled in various ways to form a single object. When finalized, the compiled digital object is converted to a mesh of 3-D triangles that defines the object’s shape. These meshes are used as input for many applications, including 3-D printing and virtual simulation.

Customizing that mesh, however, is no easy task. For example, adjusting the radius in one portion of the object requires individually tweaking the vertices and edges of each affected triangle. With complex models comprising thousands of triangles, customization becomes daunting and time consuming. Traditional techniques to convert triangle meshes back into shapes don’t scale well to complex models or work accurately on low-resolution, noisy files.

In a paper presented at the recent AMC SIGGRAPH Asia conference, MIT researchers describe a system that applies a technique called “program synthesis” to break down CAD models into their primitive shapes, such as spheres and cuboids. Program synthesis automatically constructs computer programs based on a set of instructions.

Essentially, to build CAD models, designers assemble individual shapes into a final object; the researchers’ method does the reverse, disassembling the CAD models into individual shapes that can be edited. As input, the system takes a 3-D triangle mesh and first determines the individual shapes that make it up. Program synthesis crawls through the shapes, trying to figure out how the shapes were put together and assembled into the final model. In doing so, it breaks down the mesh into a tree of nodes that represent the primitive shapes and other nodes detailing the steps for how those shapes fit together. The final shapes contain editable parameters for users to tweak that can be reuploaded to the mesh.

Foundational shapes

The researchers built a dataset of 50 3-D CAD models of varying complexity. In experiments, the researchers demonstrated their system could reverse engineer CAD files composed of up to 100 primitive shapes. Simpler models can be broken down in around a minute. While run times can be quick, the key advantage of the system is its ability to distill very complex models into simple, foundational shapes, the researchers say.

“At a high level, the problem is reverse engineering a triangle mesh into a simple tree,” says Tao Du, a PhD student in the Computational Fabrication group of MIT’s Computer Science and Artificial Intelligence Laboratory (CSAIL). “Ideally, if you want to customize an object, it would be best to have access to the original shapes — what their dimensions are and how they’re combined. But once you combine everything into a triangle mesh, you have nothing but a list of triangles to work with, and that information is lost. Once we recover the metadata, it’s easier for other people to modify designs.”

The process could be useful in manufacturing or when combined with 3-D printing software, Du says. This is especially important in the age of design sharing, where amateur 3-D-printer users upload 3-D-print models to websites for online communities to download and modify. Uploads are mostly triangle meshes, because meshes are far more universally accepted across platforms than the original CSG-based CAD files.

“We have tons of mesh models, but comparatively few CAD files behind them,” Du says. “If users want to reproduce the design at home and customize it a little, then this technique could be useful.”

Trees and triangles

Program synthesis automatically finds candidate computer programs given a specific “grammar,” meaning the structure it must work within, such as trees, and mathematical specifications. Using those constraints, program synthesis works its way back and fills in the blanks to construct an algorithm that satisfies those specifications, given new input. The technique is used, for example, for simple components of software engineering.

In the researchers’ work, the grammar is CSG, represented as trees. Each final node (with no branching nodes) represents a primitive shape with clearly defined parameters, and intermediate nodes represent basic ways the shapes converge and relate.

The researchers developed a method that lets program synthesis scan an entire 3-D mesh and, essentially, think of each possible CSG tree it could create as a new candidate program.

After the system receives an input mesh, a preprocessing step detects the possible locations, orientations, and parameters of all primitive shapes. This process creates a massive point cloud across the surface of the triangle mesh. A special “primitive-detection” algorithm infers from these points the dimensions for each primitive shape that makes up the mesh.

The researchers then sample tons of points in the entire 3-D space and flag them as either inside or outside the mesh. This helps determine how the shapes converge or relate to one another. A simple example is a mesh consisting of two spheres, A and B, merged together. If one sampled point falls inside sphere A, one inside sphere B, and one at the intersection of the two (inside both A and B), it’s most likely a union of the two shapes.

Given this information, along with the primitive dimensions, program synthesis could potentially create a CGS tree. But, 3-D meshes of even low complexity would require program synthesis to sample tens of thousands of points. This would create a massive search space that’s computationally impractical to handle. “Directly feeding all the samples will choke the program synthesizer,” Du says.

To ensure the system worked efficiently, the researchers designed a sampling method that creates several small subsets of point samples across the 3-D space, which is much easier for program synthesis to compute. By sampling these subsets, it creates a new candidate “program,” or CGS tree, that could be considered correct. After numerous iterations — and using techniques to eliminate certain points and trees — the system lands on the correct CGS tree for each shape, with correct intermediate steps and final parameters. Any edited shapes are fed back into the mesh as the system computationally follows the intermediate steps back to the final object.

Currently, the system only handles four primitive shapes — spheres, cylinders, cuboids, and tori (donut shapes). Next, the researchers aim to increase the complexity of CSG grammar to handle fare more shapes and more modifiers outside just Boolean operators.