## Info

Aerosol Surface Area (¡imz/cm3)

Figure 2.3 Sulfate aerosol surface area density versus pressure. The dashed line is an estimate of the background aerosol amount. The solid line is a high-latitude northern hemisphere profile obtained in March 1992, and shows enhanced aerosol amounts resulting from the eruption of Mount Pinatubo. (After Dessler ct ul. [46], Figure lc.)

conditions and after the eruption of Mount Pinatubo. Most of the impact on SAD was in the lower stratosphere, with the volcanic enhancement rapidly decreasing with altitude. We will discuss the implications of this on the chemistry of the stratosphere in Chapter 6.

There are -10 aerosol particles cm"1 in the lower stratosphere [47|. Under background conditions these aerosol particles have typical radii of 0.1-0.2 mm [39,45,48], After the eruption of Mount Pinatubo the typical radii of the particles increased to -0.5 jim [45,48 ]. The distribution of particle sizes around these typical sizes is usually described by unimodal or bimodal lognormal distributions [49,50]. These are simple analytic functions of the total number of aerosol particles and one or two "effective radii". The effective radius is the third moment of the size distribution divided by the second moment, and can be thought of as a typical value for the distribution.

PSCs are found in the polar regions during the winter and early spring. The cold temperatures there (less than -196 K) permit the condensation of water vapor and nitric acid into various liquid and solid forms. These clouds serve as sites for heterogeneous reactions that are necessary for polar O, destruction and the formation of the Antarctic ozone hole. We will discuss PSCs in detail in Chapter 7.

### 2.2 The Continuity Equation

In order to understand the chemistry of the stratosphere, one must understand the continuity equation. At a given point in the stratosphere, the continuity equation for a constituent X is

P is the photochemical production term—the amount of X produced per unit volume per second. Photochemical loss is written as the product of a loss frequency L, typically with units of inverse seconds, and the abundance of X. This convention is adopted because the rate of destruction of X is generally proportional to its abundance (there are exceptions to this, however). Production, on the other hand, is generally independent of the abundance of X. The far-right term on the right-hand side of Equation (2.22) is the divergence of the flux of X. This term represents net transport of X in or out of the unit volume by the wind. Typically, each term in Equation (2.22) (P, LfX], etc.) will have units of molecules per cubic centimeter per second or VMR per second.

The continuity equation is the atmospheric equivalent of balancing a checkbook. The terms on the right-hand side of the equation represent the sources and sinks of X in the unit volume. If the sources and sinks balance, then there is no net change in the abundance of X, and d[X j/d? is zero. If, on the other hand, the sources and sinks of X do not balance, then the abundance of X must be changing in response. Note that photochemical production (P) always leads to a positive time rate of change, while loss (L[XJ) always leads to a negative time rate of change. The transport term, however, can be either positive or negative.

Depending on the location, time of year, and species in question, the right-hand side of the continuity equation might be dominated by one or two of the terms—and the remaining term(s) can be neglected. A common situation in stratospheric chemistry is the case where the photochemistry terms (P and L[X|) are much larger than the transport term (V • (VfX'])). In this case, the transport of X can be neglected, and Equation (2.22) can be written as

Let us further assume that P = /^(l+siniftK)), where P„ (molecules cm 3 s ') is a constant, and L (s ') is a constant. In other words, the production varies over the time period I/o», while the loss frequency L is constant. In the real atmosphere, production and loss will often vary over periods of 24 h (although in this example only production is varying), so a typical value of (O is 2jt/(24 h). The general solution to Equation (2.23) is then

The right-hand side of Equation (2.24) has two terms: a perturbation term (C,e ") and a "steady-state" term ((Pua)' + .. .)/(L(L2 + ft)2». The steady-state term represents the abundance of X that is consistent with the photochemical production and loss rates—it is important to realize that this term is not necessarily constant with time. The perturbation term accounts for departures of [X] from its steady-state abundance. Note that the value of the perturbation, initially C., is reduced by a factor of \/e every 1 /L units of time, i.e. l/L is the "^-folding time" of the perturbation. As

>», the perturbation term goes to zero, and X achieves its steady-state abundance.

The c-folcling time I/L turns out to be a crucial parameter for understanding the behavior of [X] as a function of time. The perturbation term does not change significantly over time periods much shorter than l/L; we will show later in this section that the steady-state term will also not change significantly over time periods much less than l/L. As a result—and this is an important point - the abundance of X does not change significantly over lengths of time much shorter than l/L. For these time-scales, we say that constituent X is "conserved". On the other hand, over lengths of time much longer than l/L, the concentration of [X] can change significantly.

The implications of this are important. For example, l/L for ClONO, in the lower stratosphere is a few hours. If two measurements of [C10N02] are made in the same air parcel a few minutes apart, the abundance of C10N02 will be about the same, regardless of what happens to the air parcel between the measurements—the chemistry is simply not fast enough to change [ClONO,]. However, if the time between measurements is a few days, then we cannot expect [ClONO,] to be unchanged. We define T = l/L to be the "lifetime" of the constituent. As we will discuss in the next section, this quantity is widely used in stratospheric chemistry. Note that this lifetime is the same as that derived for first-order reactions (Equation

There are two limiting cases for the steady-state term of Equation (2.24). If L » ft), then the lifetime of X is much shorter than the time scale for production to vary. From Equation (2.24), [Xjss, the steady-state abundance of X, is

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