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Figure 2.6 Zonal-average contours of N20 VMR (ppbv) for December 1992. Data are from the UARS Reference Atmosphere Project (W. J. Randel, personal communication, 1998).

Problems

1. Equation (2.24) was derived based on production rate P = P,(sm(CiW)+1) and loss rate L = L„[X], where P„ (molecules cm 1 s ') and L0 (s !) are constants. The first term on the right-hand side is the "steady-state" part of the solution. The second term (C, exp(-L0/)) is the perturbation term that damps with a lifetime of 1 //,„. For the rest of this problem, we will assume that C, is 0.

(a) What is the time-scale for the production of X to vary? (In other words, the average production is P„, but instantaneous production varies about this average value. What is the characteristic time-scale for P to vary about Pn7)

(b) What is the time-scale of the loss chemistry of X? (In other words, what is the lifetime of X with respect to loss processes?)

From the form of Equation (2.24) it should be obvious that [X| is a sinusoid that shows no long-term trends. Thus, it must be in some form of steady state.

(c) To satisfy yourself of this, calculate 3[X](/)/3f and show that the long-time average of this quantity is zero (by long time, I mean that the time over which we average 1/tu). Also, calculate the long-time average production and loss rates of X. Are they equal?

The next thing you're probably asking yourself is: is the system in "photochemical steady state" in the strictest sense? In oilier words, docs the production equal loss at all points in time, or just in the average?

Let's look at two cases: first, assume that Lu > (0.

(d) In words, what does this condition mean?

(e) Calculate the loss rate for this condition. Is it equal to production? Does this make sense?

(f) In words, what does this condition mean?

(g) Calculate the loss rate for this condition. Is it equal to production? Does this make sense?

(h) Explain, in a few sentences, under what conditions a system is in the strict photochemical steady state—i.e. instantaneous production equals loss at all points in time.

2. Under certain conditions, the reactive uptake coefficient y for loss of CIONO-, on an aerosol is 0.05. What is the lifetime of lower-stratospheric C10N02 for background and volcanically perturbed conditions with respect to reaction on an aerosol? How do these lifetimes compare with the lifetime of C10N02 with respect to photolysis?

3. Which constituents in Figure. 2.1 are primarily photolyzed by visible radiation? Which are primarily photolyzed by ultraviolet radiation?

4. Assume there is some constituent X which is produced at a constant rate of P = 10" molecules cm 1 s Constituent X is lost through photolysis, and the photolysis rate constant J, is 0.1 s

(a) What is the steady-state concentration (neglecting transport)?

(b) What are the replacement lifetimes with respect to production and loss at the steady state?

(c) Suppose that the J value for loss of X suddenly doubles to 0.2 s 1 (for example, if the air parcel goes over a reflective cloud). What is the new steady-state concentration of X?

(d) The concentration of X cannot instantaneously achieve this new steady-state value. Instead, after the./ value changes the concentration of X will tend toward its new steady-state value. Write the equation that describes how the abundance of X achieves its new steady-state value. How long does it take for X to achieve its new steady-state value?

5. The atmospheric lifetime of a constituent was defined in Equation (2.30). The stratospheric lifetime is defined (by analogy ) to be where the integral in the numerator is over the entire atmosphere, and the integral in the denominator is over the stratosphere.

(a) The atmospheric lifetime of CH, is -10 years, while the stratospheric lifetime is -100 years. What does this tell you about where in the atmosphere CH., is destroyed?

(b) The main loss process of CH, is through reaction with OH radicals. This reaction has a large temperature dependence. How does this explain the answer to (a)? Assume [OH] is approximately constant throughout the atmosphere.

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