## Further analysis of Fwan 331 The components of Fwall

Overland and Turet (1994) undertook a detailed analysis of the components of Fwall using an expanded GFDL data set for a 25-year period. Here we review some of these results. Recall from Equation (3.6) that Fwall contains three terms: (1) sensible heat, (2) latent heat and (3) potential energy, which collectively represent moist static energy. The three terms can themselves be expanded into four components: the transient eddy flux (TE), the stationary eddy flux (SE), the mean meridional circulation flux (MMC) and the net mass flux (NMF). The meridional sensible heat flux can be used as an example:

{[VT]} = {[VT7]} + {[VT]} + {[V]"[T ]"} + {[v]}{[T]} (3.9)

### TE SE MMC NMF

The term on the left is the total meridional sensible heat flux with the overbars denoting the time mean, the brackets [ ] denoting the zonal mean and the braces {} denoting the mass-weighted vertical average. Regarding the terms on the right, the single primes indicate a departure from the time mean while the asterisks represent a departure from the zonal mean. The double primes mean a departure from the vertical average.

In studies of the general circulation, eddies represent departures of a field from the zonal mean of that field. A transient eddy is the component of the eddy field (that is, a field of zonal departures) that varies with time. Transient eddies are those that we generally associate with migratory cyclones and anticyclones. The TE meridional (north-south) sensible heat flux at a given location and level is associated with the covariance between time departures of the meridional wind and temperature. Positive

(poleward) departures from the time-averaged meridional wind tend to be associated with positive departures from the time-averaged temperature. Negative (equatorward) departures of the meridional wind tend to be associated with negative departures of temperature. The net result is a poleward flux of eddy sensible heat. The TE sensible heat flux in Equation (3.9) relates to the zonal and mass-weighted average. Stationary (or standing) eddies, by contrast, refer to the time-averaged (or time-invariant) component of the eddy field, which we associate with the standing planetary waves. Areas with positive time-mean departures of v from its zonal average tend to be associated with those for which corresponding departures of T are also positive, and vice versa.

A mean meridional circulation in the atmosphere is a circulation that is represented in a time-averaged vertical cross section of the wind field along a line of longitude. It consists of the meridional and vertical components of the circulation only. A zonal-mean meridional circulation is the mean meridional circulation averaged over all longitudes (the most obvious example being the Hadley cell). By extension, one can use Equation (3.9) to compute the net poleward sensible heat transport associated with the MMC at any latitude through consideration of the vertical dependency of the time-mean, zonal-averaged v wind and temperature.

The final term of Equation (3.9) is the NMF. It relates to the net sensible heat flux associated with the net transport of atmospheric mass. If the time-mean, zonal-mean, vertically averaged v wind is positive, this means a net poleward sensible heat flux and a corresponding increase in surface pressure over the polar cap. In other words, an import (export) of mass is associated with an increase (decrease) in the sensible heat transport. There is seasonality in the atmospheric mass over the polar cap (see Chapter 4), but on time scales of a month or longer, to a good approximation {[V]} is zero. The NMF term can therefore be ignored.

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