During Earth's last glacial period, temperatures on the planet periodically spiked dramatically and rapidly. Data in layers of ice of Greenland and Antarctica show that these warming events - called Dansgaard-Oeschger and Antarctic Isotope Maximum events -- occurred at least 25 times. Each time, in a matter of decades, temperatures climbed 5-10 degrees Celsius, then cooled again, gradually. While there remain several competing theories for the still-unexplained mechanisms behind these spikes, a new paper in the journal Chaos suggests that mathematics from information theory could offer a powerful tool for analyzing and understanding them.

"In many systems, before an extreme event, information dynamics become disordered," says Joshua Garland, a postdoctoral fellow at the Santa Fe Institute and lead author on the new paper. For instance, information-theoretic tools have been used to anticipate seizure events from disturbances in EEG readings.

Initially, the authors anticipated they would see a signal - a destabilization in the climate record similar to those seen in pre-seizure EEGs - just before the warming events. But those signals never appeared. "Around these events, you have the same amount of information production," says Garland. And this, suggest the authors, indicates that Dansgaard-Oeschger and Antarctic Isotope Maximum events were most likely regular and predictable patterns of the climate of the last glacial period rather than the results of unexpected events. {module In-article}

Also, information theory could improve how scientists calculate accumulation - how much snow fell in any given year. "It's very challenging. Many people are working on this, and they are using sophisticated math, combined with expert knowledge and known features, to figure out the accumulation," says Garland. Currently, fine pollen signatures are some of the best differentiators between years in ice that is tens of thousands of years old, compressed under the weight of each subsequent snowfall. Information theory, and specifically a statistical approach called permutation entropy, offers a different approach. "This could be a fast and efficient tool for the experts to corroborate their work," says Garland.

"When you're dealing with a time-series, you want to know what meaningful information is present. You want to extract it and use it, and to not use information that isn't useful," says Garland. "We hope this tool can help scientists do this with ancient climate records."

Information theory is already being used to identify anomalies in the climate record - particularly, to flag anomalies introduced during the collection and observation of the ice cores.

This paper follows on the heels of two related studies published in Entropy and Advances in Intelligent Data Analysis XV.

"These information-theoretic calculations are not only useful for revealing hidden problems with the data, but also potentially powerful in suggesting new and sometimes surprising geoscience," write the authors in the new paper.

Researchers have modeled the fluid dynamics of multi-rotor wind turbines, and how they interact in wind farms; the research demonstrates a clear advantage for a turbine model with four rotors

Researchers have modeled the fluid dynamics of multi-rotor wind turbines, and how they interact in wind farms. The research demonstrates a clear advantage for a turbine model with four rotors.

With their 220-meter diameter, the wind turbines at the future Dogger Bank wind farm in the North Sea are the world's largest yet. But large, larger, largest is not necessarily the best when it comes to wind turbines.

Researchers from Aarhus University and Durham University in the UK have now modeled the fluid dynamics of multi-rotor wind turbines via high-resolution numerical simulations, and it turns out that wind turbines with four rotors on one foundation have a number of advantages.

A wind turbine harvests energy from the incoming wind, but when the wind passes through the blades of the turbine, a region with lower wind speeds and higher turbulence is created called wind turbine wake. A second wind turbine downstream is affected by this turbulence in several ways. First of all, it produces less energy, and secondly, the structural load is increased. {module In-article}

"In the study, we found that turbulence and currents in the wake of the turbines recover much faster with multi-rotor turbines. This means that, with multi-rotors, a second turbine downstream will produce more energy and will be subjected to less load and stress, because the turbulence is correspondingly smaller," says Mahdi Abkar, assistant professor at the Department of Engineering, Aarhus University and an expert in flow physics and turbulence.

Less cost, less hassle, more energy

A wind turbine with more than one rotor creates less turbulence, and the wind is "restored" faster, which means a higher energy output. And this is important knowledge at a time when wind turbines are becoming increasingly larger, and thereby also increasingly expensive.

"You can always increase your energy output by increasing the diameter of the rotor blades, but there are major structural challenges in building these massive constructions with diameters exceeding 150 meters. The material requirements increase, the transport of the structures is cumbersome and expensive, and it becomes more costly to maintain the wind turbines," says Mahdi Abkar.

A turbine with four rotors costs approx. 15% less to construct than a turbine with one rotor, even though the blades cover the same area in total. At the same time, a construction with four rotors is much lighter and therefore easier to transport. And if one of the rotors stops working, the rest of the turbine will still produce energy, unlike ordinary wind turbines.

In addition, the researchers have found that individual multi-rotor turbines actually produce slightly more energy than single-rotor turbines: approx. 2% more.

"We've explored several different geometries and dynamics of multi-rotor turbines and have found that the optimum construction is a turbine with four rotors as far apart as possible. The latter results in less downstream turbulence and a faster stabilization of the wake behind the wind turbines" says Assistant Professor Mahdi Abkar.