Chatper 5: Wind

Chatper 5: Wind
The role of turbulence in environmental mass and energy fluxes
Agron/Mteor 405/505 – February 7, 2013
Goal: Understand what eddy covariance is, how eddy covariance relates to Agron/Meteor
405/505, and how to use eddy covariance data.
Wind as a Vector
A vector has two components: magnitude (i.e. speed) and direction. A three dimensional vector,
such as wind, can be broken down in to x (east/west), y (north/south), and z (vertical) components.
Meteorologists usually use u, v, and w when referring to the x, y, and z components of wind,
respectively. The u-wind is the east/west component and is positive when from the west/going towards the east. The v-wind is the north/south component and is positive when from the south/going
towards the north. The w-wind is the vertical component and is positive when air is lifting and
negative when air is sinking.
In this course, the direction of the horizontal components of the wind (u and v) are usually not
important, so u usually refers to the total magnitude of the horizontal wind.
√ If you are given 3-D
wind data, the total magnitude of the horizontal wind can be computed as u2 + v 2 .
When talking about the movement of energy and mass in and out of an ecosystem, the important
wind component is the vertical wind, w. The rising or sinking of an air parcel carries and mixes
the heat and mass concentration properties of the parcel with the air above or below.
Turbulence and Eddies
Turbulence is the erratic, swirling motion of a fluid, in our case, air, that is generated when the
air moves over a rough boundary and/or the air is thermally unstable. An eddy is simply a single
swirl of air.
Eddies are generated by wind moving over a rough surface, such as the land surface, and by
convection, such as when the land surface heats the air and makes it warmer than the air above.
Eddies can be any size between a few millimeters and the height of the atmospheric boundary layer.
It is the combination of eddies, large and small, that creates turbulence in the (vertical) wind
and the turbulent mixing of energy and mass. We can “see” turbulence by measuring wind speeds
at high frequency, such as with a sonic anemometer. An example of high frequency wind speed
data is shown in Figure 1
Mean, Variance, and Covariance
For a timeseries of some quantity a, we denote the time-averaged mean of a as a. We then remove
the mean from a and call the timeseries’ residual values a� :
a� = a − a
Figure 1: An example of five minutes of vertical wind speeds captured at high frequency (20 Hz)
by a sonic anemometer. The erraticness of the plot suggests that the air is very turbulent.
For this discussion, we will call a� the variance of a (technically the variance is a�2 ). The
covariance of a and b is then a� b� . Covariances are also typically averaged over time, and so we
write the covariance of a and b as a� b� .
While in class we are modeling the transfer of heat and mass as a function of conductances
and gradients, in reality, heat and mass is usually transported by turbulence. We can calculate the
vertical flux of anything (say a) by covarying it with w� :
Flux of a = w� a�
We can write equations for sensible heat flux and latent heat flux this way by taking covariances
with temperature and vapor concentration:
H = ρ̂cp w� T �
λE = λρ̂w� Cv�