Error Analysis in Spectrophotometric Determinations and the Environmental Consequences of a Reduction in the Ozone Layer John W. Larson Marshall University, Huntington, WV 25701
A standard and important part of teaching spectrophotometric analysis ( I ) involves consideration of the intrinsic error in the method assuming a constant relative uncertainty in the measurement of the power output of the detector, dP1 P, due to either reading error or thermal noise. The central point in this analysis may he summarized by eq 1. The relative uncertainty in the determined concentration, dclc, goes through a minimum for a given uncertainty in the relative detector error when the transmittance of the solution, P I P , is 0.37 and increases to very large values when the transmittance approaches either 0 or 1. I t is therefore desirable to design spectrophotometric procedures so that the analvsis is carried out in the region a t which eq 1 is a t a . minimum. An important new application of eq 1 is to consider the relative change in the amount of UV radiation (dP/P) that reaches the surface of the earth as a consequence of a change in the relative concentration of ozone (dclc). Much of the literature concerning the increase in UV radiation resulting from a decrease in ozone ( 2 5 ) (that in turn results from the increase in chlorofluorocarbon use) indicates that the percent increase in UV radiation is ereater than the ~ e r c e n t No explanation ~ f t h i s a m ~ ~ i f i c a t&i ousualn decrease in 0,. Iveiven, and one might easily infer that this wan the result of amode1dependent &alysis-of the complex photochemistry that is involved in the upper atmosphere. That is not the case. The principle that leads to this amplification can he easily understood hy rewriting eq 1in the form dPIP = In (PlP)(dclc)
(2)
where In ( P I P ) is the "amplification factor" that indicates the relative increase in UV radiation for a relative decrease in concentration of ozone. This function is shown in the figure for ground-level solar radiation in the ultraviolet range. It is clear from eq 2 that the amplification factor increases rapidly as the transmittance drops. Thus, if 99%of the radiation a t any wavelength is absorbed, a 1% change in the concentration of the absorbing chemical will lead to a 4.6% change in the residual radiation. Application of eq 2 to the case of solar UV radiation requires knowledge of the relative biological effectiveness of the radiation. The effective range of UV radiation that causes sunburn, properly termed erythema, is from 310 to 295 nm (6). The center of this region a t 303 nm corresponds to an ozone transmittance of 0.14. This yields an amplification factor ln (PIP') of 2, which is the commonly quoted EPA value (2-5) of the % increase in harmful W radiation for each 1% decrease in ozone and is assumed to he a least a rough guide to the % increase in skin cancer for every 1%decrease in stratospheric
-....-.
""l " " P ~
Equation 2 also describes accurately the regional and reasonal variation (7)in the "amplification factor." At low lati-
Erythema1 Photons PIPO
0
5
0
4
P/PU
I,[PIPO)
2-
0 3 0
2
Values of VansmMBncB d me atmosphere from r e f Band values o f -In ( P I P ) In the UV-8 region.
tudes where the ozone concentration is lower and the solar radiation path length through the atmosphere is short, the transmittance of UV radiation is high and in ( P I P ) becomes less than 1. At higher latitudes, the ozone concentration doubles. and the oath leneth increases because of the anele of the ridiation through atmosphere, and the transmittance d r o ~ swith a corres~ondine " increase in the "am~lification factor" to over 5. * A major source of uncertainty in evaluating the harm due to a change in the ozone layer may also he understood from eq 2 and the figure. The value of in ( P I P ) changes rapidly in the region from 320 nm to 280 nm. Because the action spectrum that results in skin cancers is not well defined, an estimate of the damage resulting from a given reduction in the ozone layer would involve large uncertainties even if the reduction ii the ozone layer wereknown accurately. Lltereture Clbd R. A,, Jr; Undowood, A. L. Quenfifotiue Anolysia, 5th ed.: PrenticeHall: E n g l e w d Cliffs. NJ,1986; p 448. Skoog. D. A. Plinciples oflrufrumanlo1 A ~ i l y r i s :Ssundera: Philadelphia, 1984 p 168. Christian. G. D.Anolyficol Chrmlstry, 3rd ed.; Wiley: New York, 1980: p 399. Flaschka. H,A.; Barnard, A. J.: Sturroek, P. E. Quonritotiva Andyticd Chemistry. 2nd ed.; Grant: Boaton, 1980: p
1. See for sxample Day.
A2Z
2. Couneil on Environmental Quality. "Phoraearbona and the Environment"; USPO: Wsshington.DC, 1975. 3. Hively, W. Am. Sci. 1989, 77,219. 4. Midden, W.R.Spacfrum 1989.2,13. 5. Hammon, A. L.:Maugh, T. H.Science 1974,186,335. M. Energy and fha Atmosphere. A PhyaicoCChomiral Approoeh: Wiley: 6. Campbell. I. London, 1977. 7. Pyle, J. A,; Demanf P. G.Noture 1980,286,373.
Volume 67
Number 11 November 1990
943
