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Boundary-layer physicists: when perseverance pays off

Sea ice forecast Sea ice models Science Arctic

Optimising climate models is definitely not the ideal task for people who need to see quick results.

It takes perseverance, a love for detail, and a tremendous amount of stamina, as the findings of a joint German-Russian project now show. In the project, experts from the Alfred Wegener Institute and their Russian peers succeeded in substantially improving the AWI’s regional climate model for the Arctic – with the help of simplified equations for simulating heat and momentum transfer in the boundary layer.

Although most people may not know it, the lowest layer of the atmosphere – that is, the layer in which we are born, live and die – is constantly changing. And not simply because the wind shifts, the seasons change, birds fly, or motors and smokestacks pump emissions into the atmosphere; but because this atmospheric layer is greatly influenced by the Earth’s surface.

Just one example: when the sun rises in the morning, its rays warm the planet’s surface. In turn, like a stovetop burner, the surface gives off heat to the lowest atmospheric layer, so that its air masses warm and start to rise in small, funnel-shaped turbulences. “As a result of these rising air masses, the entire lower atmospheric layer is mixed, and heat and moisture are transported. In other words, processes are set in motion that have a major influence on our weather and climate,” says Dr Christof Lüpkes, an atmospheric physicist at the Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research in Bremerhaven.

For more than 30 years, Lüpkes has been investigating the boundary layer in our atmosphere – i.e., the lowest atmospheric layer, which is influenced by the Earth’s surface, be it through the transfer of heat or momentum. Physics enthusiasts may know the latter phenomenon from the well-known example of Newton’s cradle: here, a ball suspended on a string collides with several other balls at rest, transferring a part of its kinetic force – or momentum, as the experts call it – to them. As a result, the outermost ball begins to swing. “In the same way, high-altitude air currents transfer their momentum to underlying atmospheric layers, which pass it on to the sea ice or the ground. Consequently, the transfer of momentum plays a critical part in boundary-layer processes,” says Lüpkes.

The boundary layer: stable or unstable? A vital question for climate models

In Central Europe, on a warm day the atmospheric boundary layer can extend up to 1,000 metres and be permeated by numerous turbulences. In such cases, meteorologists speak of convective or unstable layering. Over the Arctic ice, the boundary layer often extends to between 30 and 400 metres; elsewhere, it’s only a few metres thick, practically lying on the ice itself. But at the same time, its structure remains exceptionally stable for the longest part of the year. In other words, the atmospheric layer is barely affected by rising turbulences because, given the cold surface, the air temperature rises with increasing elevation. As a result, a rising pocket of air rapidly loses its surplus heat in comparison to its surroundings, preventing it from rising further. Consequently, turbulences that are set off in a thermally stable boundary layer soon dissipate again, producing no effects. In this way, a stable boundary layer prevents heat and momentum transfers between the ice, ocean and atmosphere.

These physical peculiarities of the Arctic boundary layer have preoccupied Christof Lüpkes for decades – both in detail, and in the context of climate change. When the boundary layer is stable and lies atop the ice and ocean like a giant lid, how can heat, moisture and momentum be transferred between the ice, ocean and upper atmosphere? In this regard, which environmental parameters are most important? Is it the temperature differences between the ice (minus 20 degrees Celsius) and open water (minus 1.8 degrees Celsius) – or are the features of the ice’s surface more important? Formations known as pressure ridges, which can redirect surface currents and produce turbulences, are now becoming more common, because the ice is generally becoming thinner and therefore more mobile. “This changes the surface drag of the ice,” Lüpkes explains.

Another aspect that remains unclear is how, under stable boundary-layer conditions, heat from the middle latitudes that reaches the Arctic at high altitudes manages to reach the surface of the ice, causing snow and ice to melt. “What processes allow the heat to bypass the boundary layer, and how quickly does this downward heat transport take place? There was an urgent need to find answers to these questions, since neither regional nor global climate models were capable of reflecting the conditions and processes in a stable boundary layer, which made it virtually impossible to investigate how changes in the Arctic affect the weather and climate in the middle latitudes in the long term,” Lüpkes relates.

Shortcomings of previous global climate models

There are two main drawbacks to conventional global climate models. Firstly, they lack the spatial resolution to depict boundary-layer turbulences with a diameter of several decimetres to several decametres. These models use grids with a scale of 50 to 100 kilometres per square – far too coarse to reflect small-scale momentum and energy flows on the surface of the ice. Secondly, to date boundary-layer processes have only been described using approximations in climate modelling.  “These equations don’t have a clear, mathematical solution like two plus two equals four. Instead, the computer has to run several iterations, one after the other, to find an approximate solution – and has to do so for every single grid point in the model. This approach costs considerable computing power and time, making it fairly expensive,” says AWI climate modeller Dr Dörthe Handorf.

POLEX: Two birds with one stone

With these aspects in mind, four years ago the AWI experts set themselves an ambitious goal: by working together with Russian colleagues in a joint project (POLEX*), they hoped to improve the representation of small-scale changes in the Arctic in global climate models. But to succeed, they would have to kill two birds with one stone. The first step: simplifying the complex quagmire of equations used to simulate boundary-layer processes, using actual observational data to do so. Lüpkes and Russian theoretical physicist Dr Vladimir Gryanik took on this challenge.

In the second step, they would need to integrate the simplified equations into both a regional and a global climate model and run a number of test simulations to determine whether the models were now capable of simulating Arctic meteorological and climatic processes more accurately. This task fell to Dörthe Handorf and her colleagues Dr Annette Rinke and Dr Wolfgang Dorn at the AWI Potsdam, with additional support provided by a doctoral student and a master’s student.

What may sound like a simple two-point plan soon turned out to be a Herculean task, especially when it came to replacing the complex boundary-layer equations using simpler equations or parameterization. “In climate modelling, parameterization means representing an unknown process as a function of a known parameter,” Lüpkes explains.

Yet the difficulty with energy flows in the atmospheric boundary layer is that they depend on so many different parameters. “You have to determine the surface drag and the windspeed. Plus, you need to at least know the temperature and its distribution. After all, the equation should ultimately take into account virtually all laws of physics and should function for all possible combinations of values. That’s anything but easy,” says the atmospheric physicist. But giving up wasn’t an option! 

Using teamwork to catch lightning in a bottle

Instead, Lüpkes and Gryanik split up the work amongst themselves and used one of the best-known Arctic datasets – field data from the Surface Heat Budget of the Arctic Ocean (SHEBA) expedition, gathered by US researchers in the Beaufort Sea in the winter of 1997/1998 – to check their simulations.

“In fact, we tried out a wide range of approaches and only slowly got closer to the solution,” Lüpkes recalls. “When either of us had an idea for an equation, we quickly jotted it down and sent it to the other to check, since in our work, we couldn’t simply assume that idealised mathematical formulas described nature with sufficient accuracy. The formulas had to be checked and put to the test.”

Once the equation had been corrected, its solutions had to be compared with the SHEBA field data. “We used self-written computer programs to calculate the solutions and compare them with observational data from the Arctic – and of course, first of all these programs had to be written. In this project, Vladimir focused more on developing the equations, while I checked and optimised them, and did the programming work and calculations. We constantly checked each other’s work to try to weed out mistakes.”

The breakthrough they ultimately made: pursuing a strategy predicated on a simple relation between two stability parameters in the bottom ten metres of the boundary layer. One of these parameters is what is referred to as the stability length: it depends on the energy flows in the bottommost boundary layer. In contrast, the second stability parameter, known as the Richardson number, depends on  the difference in temperature at the Earth’s surface and at ten metres; on the windspeed at ten metres; on the difference in moisture at the surface and at ten metres, and on the elevation itself.

According to Lüpkes: “Our approach establishes a simple, functional relation between two stability parameters – a solution that many experts had been searching for in vain for many years. Another new aspect is that our parameterizations work not only for the SHEBA dataset, but for many other forms of observational data. They’re essentially universally applicable for the bottom ten metres of the boundary layer; in other words, they work anywhere on the globe, not just in the Arctic.”

For example, if an atmospheric physicist wants to model the bottom ten metres of the boundary layer over the Sahara Desert, they no longer need to modify large, complex tables. “We do this with a small, simple table, since in our approach, everything ultimately depends on two parameters. All the other parameters are generated automatically. That’s the trick,” says Lüpkes.

Minor headway or major advance?

Meanwhile, at the AWI Potsdam Dörthe Handorf, Annette Rinke, Wolfgang Dorn and master’s student Thea Schneider also got down to work. They integrated the new parameterizations for surface drag, heat and momentum flows in a stable boundary layer into their regional Arctic climate model, which simulates processes from the Arctic Circle to the North Pole at a resolution of between ten and twenty kilometres. They then programmed the model to simulate the atmospheric conditions at the time of the SHEBA expedition and a Russian ice-drift expedition in a number of test runs. Did the outcomes now offer a better match with the actual observational data?

“We can clearly see the effects of the new parameterizations. For instance, our regional model now reflects the surface atmospheric pressure far more realistically than in the past, which means a major step forward for us,” says Dörthe Handorf. She had secretly hoped that the new parameterizations would also produce improved simulation outcomes for other parameters. But the climate processes in the model itself kept that from happening: “Our regional Arctic model now reflects heat transfer in stable boundary layers considerably more realistically; that’s for certain. But when these stable conditions occur too infrequently in the modelled reality, the new parameterizations ultimately have little effect, or only in specific parts of the model,” she explains.

You can hear a bit of disappointment in her voice. Yet the insights gleaned in POLEX and the initial simulations using a global climate model, which were run and analysed by doctoral student Sara Khosravi, also give her grounds for optimism. According to Handorf: “We’re now seeing the first indications that, thanks to the new parameterizations for surface drag and boundary-layer processes, global circulation patterns like blocking high-pressure systems are more frequently appearing in our global atmospheric simulations.”

If further test runs confirm this observation, the AWI experts will have achieved a major advance after all. Why? Because the frequency of blocking high-pressure systems – as is generally agreed – is rarely depicted accurately in global climate models. And when they do manifest, these circulation patterns have massive effects on the weather in Central Europe. A prime example: the blocking high-pressure systems that reached from the North Atlantic to Scandinavia and Eastern Europe in April and May 2018, which kept rainclouds from reaching Central Europe, producing prolonged droughts and major crop losses in northern and eastern Germany.

The outcomes of the regional modelling in the context of the German-Russian joint project POLEX were released as a study in the journal Atmospheric Science Letters in August 2021  under the following title:

Thea Schneider, Christof Lüpkes, Wolfgang Dorn, Dmitry Chechin, Dörthe Handorf, Sara  Khosravi, Vladimir M. Gryanik, Irina Makhotina, Annette Rinke (2021). Sensitivity to changes in the surface-layer turbulence parameterization for stable conditions in winter: A case study with a regional climate model over the Arctic. Atmospheric Science Letters, doi.org/10.1002/asl.1066

The POLEX project was funded by the German Research Foundation, the Russian Science Foundation and the Helmholtz Association. In addition, the work used resources of the Deutsches Klimarechenzentrum (DKRZ) granted by its Scientific Steering Committee (WLA) under project ID 238.

Dr. Christof Lüpkes heads the Polar Meteorology Working Group at the Alfred Wegener Institute in Bremerhaven and is a respected authority on the observation and modelling of small-scale processes in the Arctic. For decades, and in various research projects, he has worked to better understand heat and momentum transfers in the atmospheric boundary layer, as well as the role of clouds for atmospheric processes, and to reflect these aspects in climate models using simple equations.

Dr. Dörthe Handorf is an atmospheric physicist and climate modeller at the Alfred Wegener Institute in Potsdam. Her current focus is on the AWI’s regional Arctic climate model, which she is using in various projects to determine how changes in the Arctic are impacting the weather and climate in the middle latitudes.

Pressure ridges increase the surface drag of the Arctic sea ice.

Pressure ridges increase the surface drag of the Arctic sea ice, and in turn affect flows in the boundary layer. These ridges are formed when ice floes collide. (photo: Alfred Wegener Institute / Mario Hoppmann CC-BY 4.0)