Friction and the atmospheric boundary layer

The atmospheric boundary layer (ABL), also known as the planetary boundary layer (PBL), is the lowest part of the troposphere, directly affected by the Earth's surface. Its depth can range from a few tens of metres at night over land to several kilometres during a sunny afternoon over land or in unstable conditions over the ocean. Within this layer, processes like friction, heating, and cooling from the surface play a dominant role in shaping the wind, temperature, and moisture profiles.

Above the ABL is the free atmosphere, where the wind is largely uninfluenced by surface drag and tends to flow more closely to the geostrophic balance, parallel to the isobars. The transition between these two layers is often marked by an inversion or a sharp change in wind speed and direction.

Understanding the ABL's behaviour is crucial because all human activities occur within it. From wind turbine operations to drone flights, crane work, and marine navigation, the wind conditions experienced are fundamentally governed by the physics of this layer. Its dynamic nature means that wind at a given height can vary significantly over short periods due to changes in surface heating, roughness, and the overall synoptic weather pattern.

The Earth's surface exerts a frictional drag on the moving air. This drag is caused by obstacles like vegetation, buildings, and terrain features, or by the roughness of the water surface. The effect of this friction is strongest at the surface and diminishes with height, leading to a vertical gradient in wind speed known as wind shear.

Friction not only slows the wind but also alters its direction. In the free atmosphere, the wind is largely in geostrophic balance, flowing parallel to the isobars. However, within the ABL, the reduction in wind speed due to friction weakens the Coriolis force. With a reduced Coriolis force, the pressure gradient force becomes relatively stronger, causing the wind to turn across the isobars towards lower pressure.

This turning is typically observed as a veering (clockwise shift) of wind direction with increasing height in the Northern Hemisphere. Conversely, the wind at the surface backs (turns anticlockwise) relative to the wind aloft. The magnitude of this turning depends on surface roughness and atmospheric stability. Over very rough terrain, the turning can be substantial, while over smooth surfaces like open water, it is less pronounced.

The Ekman spiral is an idealised theoretical model that describes the turning of wind with height within the atmospheric boundary layer, resulting from the balance between the pressure gradient force, the Coriolis force, and frictional drag. It assumes a horizontally uniform pressure gradient, a constant eddy viscosity (a measure of turbulent mixing), and a steady state.

In this model, the wind vector traces a spiral shape when plotted on a hodograph, starting from the surface and extending upwards. At the surface, the wind is significantly slowed and turned across the isobars towards lower pressure. As height increases, frictional effects diminish, the wind speed increases, and the direction gradually veers (in the Northern Hemisphere) until it aligns with the geostrophic wind in the free atmosphere above the ABL.

While the real atmosphere is more complex, with variations in stability, roughness, and pressure gradients, the Ekman spiral provides a fundamental intuition for why wind veers with height. It explains the observed backing of surface winds relative to those aloft and the general increase in speed with altitude within the ABL. Modern numerical weather prediction models use more sophisticated parameterisations but build upon these foundational concepts to represent ABL processes.

The most direct consequence of surface friction within the ABL is the reduction of wind speed compared to the geostrophic wind aloft. The geostrophic wind, a theoretical wind that flows parallel to isobars, is a balance between the pressure gradient force and the Coriolis force, neglecting friction. However, at the surface, friction acts as an additional force opposing motion, disrupting this balance.

Because friction slows the air, the Coriolis force (which is proportional to wind speed) also weakens. This allows the pressure gradient force to dominate slightly, pulling the wind across the isobars towards lower pressure. The net effect is a significant reduction in wind speed. Commonly cited figures suggest that the 10 m wind speed over land is typically 40–60% of the geostrophic wind speed, while over open water it can be 60–80%.

For example, if the geostrophic wind is 20 m/s (approximately 39 knots or 72 km/h), the 10 m surface wind over a rural land area might be 8 to 12 m/s (16 to 23 knots or 29 to 43 km/h). This difference is not constant; it varies with:

• Surface roughness: Rougher surfaces cause more drag and a greater reduction in speed.
• Atmospheric stability: In stable conditions (e.g., clear nights), friction can penetrate higher, leading to a greater speed reduction near the surface.
• Wind speed: Higher wind speeds generally lead to more effective momentum transfer downwards, but the relative reduction can still be substantial.

This reduction is a primary reason why wind forecasts for surface operations must account for the ABL, rather than simply relying on geostrophic wind calculations.

The depth and characteristics of the atmospheric boundary layer undergo a significant diurnal (daily) cycle, especially over land. This cycle is primarily driven by the sun's heating and the Earth's radiative cooling.

Daytime: As the sun heats the ground, the surface warms and transfers heat to the overlying air. This creates convective turbulence, with warm air parcels rising and cooler air sinking. This vigorous mixing deepens the ABL, typically reaching its maximum depth in the late afternoon, often 1–3 km. During this time, momentum from higher levels is mixed downwards, leading to a more uniform wind profile and often gustier conditions at the surface due to the downward transport of higher-speed air.

Night-time: After sunset, the ground cools rapidly by radiating heat away. This cools the air immediately above it, leading to a stable boundary layer. Convective mixing ceases, and turbulence is primarily mechanical (generated by wind shear). The stable layer effectively decouples the surface from the air aloft, leading to a shallow ABL (often less than 100–300 m deep). Within this shallow layer, surface winds can become very light or even calm, while a strong low-level jet (a band of high wind speed) can form just above it, where friction is reduced but the pressure gradient force is still active.

This diurnal variation means that wind conditions, particularly shear and gustiness, can change dramatically between day and night, even under the same synoptic pressure pattern.

The degree of frictional drag exerted by the surface is highly dependent on its characteristics, specifically its roughness length (z₀). This parameter quantifies the effective height at which the wind speed would theoretically become zero due to surface obstacles. Different surfaces have vastly different roughness lengths, leading to varied impacts on the ABL.

• Open Sea: The ocean surface is relatively smooth, especially in calm conditions. Its roughness length is very small, typically in the order of 0.0001 to 0.001 metres. This results in minimal frictional drag, allowing surface winds to be a higher percentage of the geostrophic wind and exhibiting less shear and turning with height compared to land.
• Open Land (Grassland, Farmland): These surfaces present more obstacles than the sea but are generally less rough than urban areas or forests. Roughness lengths typically range from 0.01 to 0.1 metres. Friction here causes a more noticeable reduction in wind speed and greater turning with height.
• Forests and Urban Areas: These are very rough surfaces. Forests, with their tall, dense canopy, and urban areas, with buildings of varying heights, create significant drag. Roughness lengths can be 0.5 metres or more. This leads to a substantial reduction in surface wind speed, strong shear, and considerable turbulence within and above the canopy or urban canyon.

Worked Example: Consider a geostrophic wind of 15 m/s. Over the open sea, the 10 m wind might be 75% of this, or 11.25 m/s. Over open grassland (e.g., Co. Kildare), it could be 50%, or 7.5 m/s. Over a dense forest (e.g., Co. Wicklow), it might drop to 35%, or 5.25 m/s. These are approximate values, but they illustrate the significant impact of surface type on observed wind speeds.

Numerical weather prediction (NWP) models, such as those used by Met Éireann or ECMWF, cannot explicitly resolve every eddy and small-scale process within the atmospheric boundary layer. The grid spacing of global and even regional models (typically kilometres to tens of kilometres) is too coarse to capture these fine-scale interactions directly. Instead, they use parameterisation schemes.

Parameterisation is the process of representing the effects of sub-grid scale physical processes (like turbulence, friction, and convection within the ABL) through their interaction with the larger-scale, resolved atmospheric state. These schemes use mathematical relationships and empirical observations to estimate how the ABL influences the momentum, heat, and moisture budgets of the model's grid cells.

Key aspects parameterised include:

• Vertical mixing of momentum: How effectively friction and turbulence transfer wind speed from higher levels down to the surface.
• Heat and moisture transfer: How the surface exchanges heat and moisture with the atmosphere, influencing stability.
• Cloud formation: ABL processes are crucial for initiating shallow convection and fog.

The choice and complexity of ABL parameterisation schemes are critical for the accuracy of surface and low-level wind forecasts. Different models use different schemes, which can lead to variations in their predictions, especially for phenomena like low-level jets, fog, and surface gusts. The Wind Agent's Agreement Spine helps to visualise these model differences.