Rethinking Surface-Layer Parameterization: A Turbulence-Based Framework Without Using Similarity Functions and Its Impacts on Surface–Atmosphere Coupling

The air we breathe is never truly still. Even on a calm day, invisible eddies and swirls constantly mix the atmosphere, carrying heat, moisture, and pollutants between the ground and the sky. For more than fifty years, scientists have relied on a specific set of rules to describe this mixing, particularly in the lowest layer of the atmosphere where we live. These rules, known as similarity functions, act like a translation guide, helping computer models convert the complex, churning reality of wind and temperature into numbers that can be calculated. They work by comparing the current state of the air to a standard, idealized state, adjusting the calculations based on whether the air is stable or unstable. While these rules have been the backbone of weather forecasting and climate modeling, they are built on empirical relationships derived from specific experiments decades ago. As models have grown more powerful, scientists have begun to wonder if these old translation guides are still the best way to describe the ever-changing dance of the atmosphere, or if they introduce errors that ripple through our predictions of storms, heatwaves, and air quality.

A new study led by researchers at the National Center for Atmospheric Research and NOAA proposes a different way to think about this problem. Instead of relying on those established translation guides, the team developed a framework that lets the turbulence speak for itself. They created a new method, implemented in the widely used Weather Research and Forecasting model, that calculates how the air moves based directly on the energy of the swirling eddies near the surface. In this approach, the stability of the atmosphere is not forced into the calculation through a separate correction formula. Instead, the stability is built into the very measure of how fast the air is moving and mixing. The researchers tested this new system against the standard method by running five-day simulations over the entire United States during a typical winter and a typical summer. They found that by removing the old rules and letting the turbulence drive the exchange, the model produced more realistic wind speeds, especially at night, and altered how heat and moisture were shared between the ground and the air in ways that changed the behavior of summer storms.

The standard approach has long been the default for weather models because it provides a consistent way to handle the transition between day and night, when the atmosphere shifts from being well-mixed and turbulent to calm and stable. However, the choice of which specific rule to use can significantly change the outcome of a forecast. Different formulas can lead to different predictions for how much heat rises from the ground or how fast the wind blows near the surface. These differences are not just minor tweaks; they can alter the height of the boundary layer, the thickness of the air mass that mixes with the surface, and even the intensity of rainfall. The new study suggests that by anchoring the calculations in the actual velocity of the turbulence, rather than in a pre-set formula, the model can adapt more naturally to these changing conditions.

In their simulations, the researchers compared the new turbulence-based method, which they call ESTAR, against the standard method, known as BASE. During the winter simulations, which featured cold, stable air and weak winds, the new method showed a clear advantage. It reduced the error in predicted wind speeds by approximately 0.5 to 1 meter per second. More importantly, it smoothed out the daily cycle of errors. The standard method tended to overestimate wind speeds significantly at night and underestimate them during the day, creating a jagged, unrealistic pattern. The new method produced a much flatter, more consistent bias, suggesting it handles the tricky transition of stable, calm air better than the traditional rules. This improvement is crucial because accurate wind predictions are essential for everything from aviation safety to understanding how pollutants disperse in the air.

The results were different, yet still significant, during the summer simulations. When the sun heats the ground, the air becomes unstable and rises in powerful currents, creating deep, turbulent layers. In these conditions, the new method changed how the surface shared energy with the atmosphere. It increased the amount of sensible heat, the warmth you feel on your skin, rising from the ground by roughly 50 to 150 watts per square meter during the day. This shift in energy partitioning meant that the boundary layer grew taller and the air near the surface became slightly warmer. While the standard method and the new method produced similar results for moisture and temperature in some areas, the new approach fundamentally altered the balance between heating the air and evaporating water. This change in the surface energy budget had a direct impact on how storms developed.

Perhaps the most striking finding was how these changes in the lowest layer of the atmosphere influenced the weather above. The new method consistently reduced the intensity of excessive rainfall in the simulations. In several regions, the new model produced rainfall that was 20 to 40 millimeters per day less intense than the standard model, which had a tendency to over-predict the strength of storms. Instead of a few intense, concentrated downpours, the new method generated rainfall that was more spread out across the landscape. This suggests that by better representing how heat and moisture are mixed near the ground, the model creates a more realistic environment for storms to form, preventing them from becoming too concentrated and violent. However, the study also noted that while the intensity improved, the location of the storms did not necessarily become more accurate, indicating that other factors in the model still control where rain falls.

The researchers also looked at how these changes played out in different environments, such as cities versus rural areas. They found that the new method was particularly sensitive to the differences between urban and rural surfaces during hot, sunny days. In these conditions, the new model amplified the contrast in heat exchange between the city and the countryside, reflecting the stronger influence of buoyancy and turbulence in a convective atmosphere. This sensitivity suggests that the new framework captures the physical reality of how different surfaces interact with the air more effectively than the old rules, which often treat these interactions with a one-size-fits-all approach.

Despite these successes, the study does not claim that the new method is a perfect replacement for all situations. The improvements were most pronounced in variables directly controlled by turbulent exchange, like wind speed, while the effects on temperature and moisture were more conditional, depending on the season and the specific location. The vertical structure of the atmosphere, the layers of air above the surface, showed that the biggest differences between the two methods remained confined to the lowest kilometer. This makes sense, as the new method is designed to fix the surface layer, and its influence naturally fades as you move higher into the atmosphere, where other forces take over.

The work represents a significant step toward a more physically consistent way of modeling the atmosphere. For decades, the field has relied on a set of formulas that, while useful, are essentially approximations of a much more complex reality. By shifting the focus to the turbulence itself, the researchers have shown that it is possible to build a model that does not need those external correction factors to function. The results suggest that when the atmosphere is calm and stable, or when it is churning with summer heat, letting the turbulence drive the exchange leads to a more realistic picture of how the ground and the sky interact. While the new method still requires further testing across different climates and model configurations, it offers a promising path forward for reducing the uncertainties that have long plagued weather and climate predictions. The study concludes that surface-layer exchange can indeed be represented without the traditional similarity functions, producing a system that is both physically realistic and aware of the changing conditions of the atmosphere.