E5 Turbulence and Atmospheric Boundary Layer

Topic

The atmospheric boundary layer is the lowest layer of the troposphere—directly influenced by the Earth's surface—with a thickness ranging from one hundred to two thousand meters depending on the time of day. During the day, surface heating generates thermal convection, which vigorously mixes the entire atmospheric boundary layer from top to bottom; conversely, at night, radiative cooling of the surface creates a stable nocturnal layer in which turbulence is suppressed. Thus, the atmospheric boundary layer alternates daily between a turbulent, mixed state during daylight hours and a stable, calm state during hours of darkness—a cycle that repeats with each new round of surface heating and cooling.

The turbulence dominating the atmospheric boundary layer during the day does more than just mix the air; it also transports momentum, sensible heat, and latent heat from the surface into the atmosphere, carrying upward the momentum, heat, and moisture that the surface transfers to the boundary layer.

Monin-Obukhov similarity theory serves as the standard theoretical framework for describing this turbulence in the lowest section of the atmospheric boundary layer—the ten to fifty meters closest to the ground. This theory defines the Obukhov length, a height scale at which the production of turbulence due to mechanical wind effects becomes comparable to that caused by thermal effects from surface heating or cooling. Comparing the measurement height against this Obukhov length allows for the classification of the layer's state: a negative result indicates an unstable state dominated by thermal convection, while a positive result indicates a stable state with suppressed turbulence, as occurs at night. Based on that same comparison between height and the Obukhov length, wind and temperature profiles within this surface layer follow similarity functions that depend on that ratio; these similarity functions modify the logarithmic profile that wind and temperature would exhibit if the layer were in a neutral state—neither unstable nor stable.

In numerical models, turbulence occurring at scales smaller than the model's resolution must still be represented in some way; this is the role of parameterizations for unresolved turbulence. The simplest schemes—first-order schemes—describe turbulent flux as proportional to the gradient of the transported quantity, multiplied by a turbulent diffusivity that encapsulates the entire effect of unresolved turbulence in a single number. Higher-order schemes, by contrast, explicitly solve an equation predicting the evolution of turbulent kinetic energy itself, using that energy to calculate turbulent flux in greater detail than a simple first-order scheme allows.

Two quantities, more than any others, summarize the state of the entire atmospheric boundary layer at any given moment: friction velocity—which measures the strength of the wind's agitation of the surface—and the turbulent heat flux rising from the surface, which measures the amount of heat the surface transfers to the atmospheric boundary layer at that instant. These two quantities are the fundamental parameters controlling the structure of the atmospheric boundary layer; they underpin both Monin-Obukhov similarity theory and parameterizations of unresolved turbulence, serving, in essence, as the summarized, measurable manifestation of the diurnal heating, nocturnal cooling, and turbulence described earlier.

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