The atmospheric boundary layer (ABL) is the lowest part of the troposphere directly influenced by Earth's surface. Its characteristics play a crucial role in weather, climate, and air pollution dispersion. The ABL's structure and dynamics are governed by turbulence, surface interactions, and diurnal variations.
Turbulence in the ABL is generated by wind shear and buoyancy forces, with eddies ranging from millimeters to kilometers. The wind speed generally increases with height due to reduced surface friction. The ABL undergoes a distinct diurnal cycle driven by solar heating and surface cooling.
Atmospheric boundary layer characteristics
- The atmospheric boundary layer (ABL) is the lowest part of the troposphere directly influenced by Earth's surface
- ABL characteristics play a crucial role in weather, climate, and air pollution dispersion
- The structure and dynamics of the ABL are governed by turbulence, surface interactions, and diurnal variations
Turbulence in atmospheric boundary layer
- Turbulence in the ABL is primarily generated by wind shear and buoyancy forces
- Turbulent eddies in the ABL range in size from millimeters to kilometers, facilitating the vertical transport of heat, moisture, and momentum
- The intensity of turbulence in the ABL varies with height, stability, and surface roughness
- Turbulent kinetic energy (TKE) is a measure of the intensity of turbulence, defined as $TKE = \frac{1}{2}(u'^2 + v'^2 + w'^2)$, where $u'$, $v'$, and $w'$ are the fluctuating components of velocity
Velocity profile near Earth's surface
- The wind speed in the ABL generally increases with height due to reduced friction from the surface
- The logarithmic wind profile describes the vertical variation of wind speed in the surface layer under neutral stability conditions: $U(z) = \frac{u_}{\kappa} ln(\frac{z}{z_0})$, where $U(z)$ is the wind speed at height $z$, $u_$ is the friction velocity, $\kappa$ is the von Karman constant (≈0.4), and $z_0$ is the aerodynamic roughness length
- The wind profile deviates from the logarithmic form under non-neutral stability conditions, with stronger shear in stable conditions and weaker shear in unstable conditions
Diurnal cycle of atmospheric boundary layer
- The ABL undergoes a distinct diurnal cycle driven by solar heating and surface cooling
- During the day, solar heating of the surface leads to the development of a convective boundary layer (CBL) characterized by strong turbulent mixing and a well-mixed vertical structure
- At night, surface cooling creates a stable boundary layer (SBL) with suppressed turbulence and a shallower depth compared to the daytime CBL
- The morning and evening transitions between the CBL and SBL are characterized by rapid changes in ABL structure and dynamics
Stability effects on boundary layer
- Atmospheric stability strongly influences the structure and dynamics of the ABL
- In unstable conditions (surface warmer than air), buoyancy-driven turbulence enhances vertical mixing, leading to a deeper and well-mixed ABL
- Stable conditions (surface cooler than air) suppress turbulence, resulting in a shallower ABL with limited vertical mixing and stronger vertical gradients of wind, temperature, and other variables
- Neutral stability occurs when the surface and air temperatures are similar, and mechanical turbulence dominates over buoyancy effects
Surface roughness impact
- Surface roughness plays a critical role in determining the structure and dynamics of the ABL
- Rougher surfaces (forests, cities) enhance turbulence and vertical mixing, while smoother surfaces (grasslands, oceans) have less impact on the ABL
Aerodynamic roughness length
- The aerodynamic roughness length ($z_0$) is a key parameter that characterizes the effect of surface roughness on the ABL
- $z_0$ represents the height above the surface where the wind speed theoretically becomes zero, accounting for the drag exerted by surface elements
- Typical values of $z_0$ range from millimeters for smooth surfaces (sand, snow) to meters for rough surfaces (forests, urban areas)
Displacement height for obstacles
- For surfaces with tall obstacles (trees, buildings), the displacement height ($d$) is introduced to account for the vertical shift in the effective surface level
- The wind profile is modified to: $U(z) = \frac{u_*}{\kappa} ln(\frac{z-d}{z_0})$, where $d$ is the displacement height
- The displacement height is typically about 2/3 to 3/4 of the average obstacle height
Urban vs rural surface roughness
- Urban areas have significantly higher surface roughness compared to rural areas due to the presence of buildings and other structures
- The increased roughness in urban areas leads to enhanced turbulence, stronger vertical mixing, and a deeper ABL
- Urban surface roughness also affects the wind flow patterns, creating complex circulations such as urban heat islands and street canyon effects
Monin-Obukhov similarity theory
- Monin-Obukhov similarity theory (MOST) is a framework for describing the vertical structure of the ABL under different stability conditions
- MOST assumes that the turbulent fluxes and gradients in the surface layer are determined by a few key parameters: friction velocity ($u_*$), surface heat flux ($Q_0$), and buoyancy flux ($\frac{g}{\theta_v} \overline{w'\theta_v'}$)
Dimensionless parameters in similarity theory
- MOST introduces dimensionless parameters to characterize the ABL structure:
- Stability parameter: $\zeta = \frac{z}{L}$, where $L$ is the Obukhov length, a measure of the relative importance of buoyancy and shear in generating turbulence
- Dimensionless wind shear: $\phi_m = \frac{\kappa z}{u_*} \frac{\partial U}{\partial z}$
- Dimensionless temperature gradient: $\phi_h = \frac{\kappa z}{\theta_} \frac{\partial \theta}{\partial z}$, where $\theta_$ is the surface temperature scale
- The stability parameter $\zeta$ is positive for stable conditions, negative for unstable conditions, and zero for neutral conditions
Flux-profile relationships
- MOST provides flux-profile relationships that relate the dimensionless gradients to the stability parameter:
- Wind shear: $\phi_m = (1 - \gamma_m \zeta)^{-1/4}$ for unstable conditions, $\phi_m = 1 + \beta_m \zeta$ for stable conditions
- Temperature gradient: $\phi_h = (1 - \gamma_h \zeta)^{-1/2}$ for unstable conditions, $\phi_h = 1 + \beta_h \zeta$ for stable conditions
- The coefficients $\gamma_m$, $\gamma_h$, $\beta_m$, and $\beta_h$ are empirically determined constants
- These relationships allow the estimation of turbulent fluxes from mean gradients and vice versa
Limitations of similarity theory
- MOST assumes horizontal homogeneity and stationarity, which may not always hold in real-world conditions
- The theory is strictly applicable only to the surface layer (lowest 10% of the ABL) and may not capture the complexity of the entire ABL
- MOST does not account for the effects of advection, subsidence, or other mesoscale processes that can influence the ABL structure
Boundary layer height estimation
- The boundary layer height (or mixing height) is a critical parameter for air pollution dispersion, weather forecasting, and climate modeling
- The boundary layer height varies diurnally and with atmospheric stability, ranging from a few hundred meters to several kilometers
Daytime convective boundary layer height
- The daytime convective boundary layer (CBL) height can be estimated using the parcel method, which considers the vertical profile of potential temperature
- The CBL height is determined as the level where a hypothetical air parcel rising adiabatically from the surface becomes neutrally buoyant
- Other methods for estimating the CBL height include the use of vertical profiles of turbulence, aerosols, or humidity
Nocturnal stable boundary layer height
- The nocturnal stable boundary layer (SBL) height is typically much shallower than the daytime CBL and more challenging to estimate
- The SBL height can be estimated using the Richardson number criterion, which compares the relative importance of buoyancy and shear in suppressing turbulence
- The SBL height is often defined as the level where the Richardson number exceeds a critical value (e.g., 0.25)
Boundary layer height measurement techniques
- Various measurement techniques are used to determine the boundary layer height:
- Radiosondes: Provide vertical profiles of temperature, humidity, and wind, allowing the estimation of the boundary layer height based on the vertical structure of these variables
- Lidar: Measures the vertical profile of aerosol backscatter, which can be used to identify the top of the boundary layer as a sharp decrease in aerosol concentration
- Sodar: Measures the vertical profile of acoustic backscatter, which is related to the turbulence structure of the ABL and can be used to estimate the boundary layer height
- Wind profilers: Provide vertical profiles of wind speed and direction, allowing the identification of the boundary layer height based on changes in wind characteristics
Numerical modeling considerations
- Accurate representation of the ABL in numerical weather prediction (NWP) and climate models is crucial for simulating surface-atmosphere interactions, turbulent mixing, and the transport of heat, moisture, and pollutants
- NWP and climate models employ various parameterization schemes to represent the subgrid-scale processes in the ABL
Boundary layer parameterization schemes
- ABL parameterization schemes in numerical models aim to represent the effects of turbulent mixing and surface-atmosphere interactions on the resolved-scale variables
- Common ABL parameterization approaches include:
- First-order closure schemes (e.g., YSU, MYJ): Relate turbulent fluxes to mean gradients using eddy diffusivity coefficients
- Higher-order closure schemes (e.g., MYNN): Solve additional prognostic equations for turbulent quantities, providing a more detailed representation of turbulence
- Large-eddy simulation (LES) schemes: Explicitly resolve large-scale turbulent eddies while parameterizing smaller-scale eddies, offering a high-resolution simulation of ABL processes
Surface energy balance in models
- The surface energy balance plays a critical role in determining the surface fluxes of heat, moisture, and momentum that drive ABL processes
- Numerical models include land surface models (LSMs) to represent the surface energy balance and the exchange of energy and mass between the land surface and the atmosphere
- LSMs account for various processes, such as radiative transfer, soil heat conduction, vegetation dynamics, and snow cover, to provide lower boundary conditions for the ABL parameterization schemes
Challenges in simulating boundary layer processes
- Despite advancements in ABL parameterization schemes and LSMs, several challenges remain in accurately simulating boundary layer processes in numerical models:
- Representing the complex interactions between the surface, turbulence, and atmospheric stability
- Capturing the diurnal cycle of the ABL and the transitions between the CBL and SBL
- Simulating the effects of heterogeneous land surfaces and urban environments on the ABL structure
- Representing the feedback between the ABL and other atmospheric processes, such as clouds, precipitation, and radiation
- Ongoing research focuses on improving ABL parameterization schemes, developing higher-resolution models, and incorporating observational data to better understand and simulate boundary layer processes