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Abstract:

The subject of this chapter is the zonally averaged circulation of the atmosphere, which occurs, of course, in the latitude-height domain. In Chapter 2, we briefly discussed the stream function of the mean meridional circulation, and identified the Hadley and Ferrel cells. We also described the associated zonally averaged distributions of the temperature, zonal and meridional wind, and water vapor mixing ratio, as well as the zonally averaged precipitation rate. Now we take a closer look. As a first step, we adopt the following definitions: In the following discussion, we consider various statistics derived from the three-dimensional fields of v and T. Here v and T can stand for any variables. They could be the same variable. The temporal covariance of v and T is Randall 605 Book Title 111 time mean departure from time mean, or “transient component” zonal mean departure from zonal mean, or “eddy component” vT = ( v + v ′ ) ( T + T ′) v T + v′T ′ + vT ′ + v′T v T + v′T′. (4.1) The last line of (4.1) is only approximate, unless the averaging interval is infinite. Now decompose the first term of (4.1) into its zonal mean and eddy components: It follows that Similarly, Finally, substitution gives Some statistics of interest are: 1. v, T Time mean fields 2. vT Temporal covariance 3. [ v] [ T] Total symmetric 4. v T Total stationary 5. v′T ′ = vT – v T Total transient Randall 605 Book Title v T [ v] v * ( +) [ T] T * [ v]

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