10. ATMOSPHERIC SCATTERING10.1 Introduction
The atmosphere scatters part of the radiation of the solar direct beam, and in doing so, attenuates the direct beam intensity and creates skylight. It is principally the effect of the attenuation on the direct beam measurements that is considered here, though some comment also will be made on the measurement of the scattered light of tile zenith sky. Errors in the direct beam measurements due to skylight scattered into tile Dobson instrument's field of view are considered in Section 4 on stray light. The scattering processes divide conveniently into scattering by molecules of the air (Rayleigh scattering), by aerosols (particles of approximately 0.05 to 5µ in diameter), and by clouds (water droplets or ice crystals of approximately 5µ to 500µ in diameter). Virtually all the attenuation by particles is due to scattering, i.e., is energy conserving.
The physics of the scattering processes is well known. However, the great temporal and spatial variation in the concentrations and characteristics of the scattering media make it virtually impossible to calculate the scattering effects for any one situation. Aerosols vary greatly in composition, concentration, size distribution and refractive index, and clouds are notoriously variable and transitory. The exception, of course, is Rayleigh scattering, which essentially depends only on surface air pressure, and which can be calculated accurately. The only means available to cope with the effects of aerosols and clouds on ozone measurements are those of optimum experiment design and of empirical correction. In both cases the methods must be tested not only by their effect on actual observation sets, but more importantly, by their consistency with physically well based models of atmospheric scattering.
10.2 Rayleigh scattering
Rayleigh scattering is approximately proportional to the inverse fourth power of wavelength, and a simple approximation for the base 10 scattering coefficients used in the Dobson instrument equation is:
β = 1.787 x 1010 λ-4.25 (10.1)where λ is the wavelength in nm. The approximation is accurate to 0.2% and the coefficients themselves are thought to be accurate to about 1%. Further discussion and tabulations of Rayleigh scattering coefficients may be found in Penndorf (1957). Hoyt (1977) and Frohlich and Shaw (1980) have claimed that these coefficients are in error by two or three percent, but this has been strongly disputed by Young (1980 and 1981) on the grounds of incorrect definitions.
From the equations of Section 1 it can be calculated that the Rayleigh scattering contribution to an estimation of ozone column amount using direct sunlight is equivalent to about 0.066, 0.138, and 0.009 atm cm for the A, C and AD band combinations respectively. The standard AD estimation is clearly insensitive to error in the Rayleigh scattering coefficient, and even for the C bandpair an accuracy of 1% would be acceptable. At the same time, it is desirable that the controversy referred to above be resolved and the coefficient error reduced to below the 1% level. It should be noted that the Rayleigh scattering coefficients for the Dobson instrument given by equation 10.1 and by Table 1.1 apply to a mean sea level pressure of po = 1013 mb, and that at other pressures, p, which may be due to natural air pressure variations or to the elevation of the Dobson station, the coefficients must be corrected in proportion to p/po. Generally, the corrections are significant only for a single bandpair combinations, and even then, only for pressure deviation of 1% or more.
Measurements of the light of the zenith blue sky can be used to estimate ozone column amounts, and to estimate an approximate profile of the ozone concentration with height using the Umkehr method. The zenith light is the integral with height of the light produced principally by Rayleigh scattering, but also by aerosol scattering. Because most of the molecular atmosphere lies below the bulk of the ozone layer, the absorption path for zenith light is similar to that of direct sunlight, and the zenith log intensity ratio is therefore closely related to the direct solar log intensity ratio. The relationship does depend on the zenith angle of the sun and the column amount and height distribution of the ozone concentration owing to their effect on the absorption components of the above integral. In practice, large numbers of near-simultaneous measurements of direct sun and zenith blue log intensity ratios are used to construct tables or charts which can then be used for empirically estimating the ozone column amounts (for examples of charts, see Figures 2 and 3 in Appendix A).
The accuracies of the zenith blue and zenith cloudy estimations of ozone amount are affected by natural variations in ozone profiles and surface albedo, and may be poor, i.e., worse than 10%, in conditions of high airmass, high ozone and high albedo (Mateer et al, 1977). Other systematic errors such as stray light may cause errors. Errors due to aerosol extinction along the beam, as distinct from aerosol scattering into the beam, will be similar for zenith sky and direct solar radiation and so should not contribute significant additional aerosol error. Accuracies can be estimated from the comparison data used to create the empirical charts or tabulations. Dobson and Normand (1962) indicate an RMS deviation in the difference of direct sun and zenith blue sky estimations of 0.005 atm cm or about 1.5% for the AD band combination. Komhyr (1960) reports differences equivalent to a 1.5% RMS deviation also, and Farkas (private communication) finds a similar value for her AD measurements at Invercargill. These will be the minimum errors. Under routine operational conditions, larger errors, perhaps two times larger, should be expected owing to variations of the error with airmass, with instrument adjustment and with observational practice. Extracts from Komhyr (1960) concerning his study of the accuracy of both clear and cloudy zenith measurements are presented in Appendix A, in order to make the results of this useful study more accessible.
The consideration of error sources associated with ozone profile estimations using the Umkehr method and the Dobson instrument is beyond the scope of the present work. However, most of the error sources discussed here for ozone column measurements will have a direct effect on the accuracy of the Umkehr estimations, and because the technique provides a limited information content and is sensitive to input parameters and the accuracy of the raw measurements, some of the error effects are likely to be significant. For further information on the Umkehr technique see DeLuisi and Mateer (1971), DeLuisi (1979), Mateer and DeLuisi (1981), and Dave et al. (1981). It can be noted that the modelling of Umkehr zenith intensities also provides the means for analysing the accuracy of the zenith blue sky estimation of ozone column amount.
10.3 Aerosol scattering
Aerosol scattering coefficients (i.e., coefficients to base 10 of attenuation or extinction) experimentally measured in the visible at 500 nm range from 0.02 for very clear conditions to 0.5 for particularly hazy conditions (Flowers et al., 1969). Monthly average values in the United States in summer have maxima that range from 0.1 to 0.3. A value of 0.3 usually gives a milky sky in which clouds are difficult to discern. In the 300 to 340 nm region, the figures are likely to be one to two times these values.
The principal defences of the Dobson instrument against the effects of aerosol scattering lie in, firstly, its optical design, and secondly, the variability of aerosol characteristics, which can be expected to result in a spectrally smooth extinction spectrum. By making only relative and not absolute measurements, and by siting the bands close together and in a spectral region where the ozone absorption changes rapidly with wavelength, Dobson was able to discriminate strongly against a smooth and flat aerosol attenuation. From the work of Rat'kov (1971) it seems that the maximum ozone errors due to aerosols for the A, C and D bandpairs are about ±0.029, ±0.065 and ±0.156 atm cm respectively. Shah's (1968) work indicates maxima of about two-thirds of these values. When the aerosol extinction spectrum is constant, there will be no error. Further, by combining the measurements of two bandpairs, such as in the standard AD method, it is possible to discriminate against aerosol error for the more general case of a linearly varying extinction spectrum.
If, as is reasonable, one assumes that the aerosol error contribution to XAD is a few percent or less, it is possible, with accurately calibrated instruments, to use the differences between the single bandpair ozone estimations and XAD :
- to determine corrections to the single bandpair ozone estimations (Shah, 1968; see also Ramanathan and Karandikar, 1949);- to determine trends in this aerosol error correction (Kulkarni, 1973);
- to determine the gradient of the assumed linear aerosol spectral attenuation function (Basher, 1976).
Kulkarni (1973) went further and attempted to determine, using XA and XD, the aerosol error contribution to the long term trend in XAD, but the method was shown by Basher (1976) to be invalid owing to a lack of independence in the equations used.
In an attempt to better describe the aerosol extinction spectrum and its effects, Basher (1976) expressed the spectrum explicitly as a quadratic polynomial:
δ(λ) = δ(λ0) + g1(λ - λ0) + g2(λ - λ0)2 (10.2)and obtained expressions for the "true" ozone and the coefficients g1 and g2. The approximation was found to explain very well the systematic and previously unexplained differences amongst a set of double bandpair measurements given by Dobson and Normand (1962) and gave an ozone estimation about 4% higher than the XAD value. However Gardiner (1978) challenged this approach on mathematical grounds, pointing out that the restriction of the polynomial to a quadratic was arbitrary unless well supported by independent knowledge of the extinction spectrum, and worse, that the inclusion of higher orders of polynomial increases the sensitivity of the ozone determination to experimental uncertainty, to the extent that any possible improvement in accuracy due to a more complete representation of the aerosol extinction spectrum could be swamped by the increase in the effect of experimental uncertainty. It is worth noting that Shah (1979) proposed a power law approximation which may be criticised on exactly the same grounds.
The situation at that time was quite unsatisfactory in that the questions as to which was the best estimation method and what the aerosol error was in each case remained unanswered. A simple answer to the second question was given by Basher and Thomas (1979). They considered the Mie extinction efficiency spectrum for a nominal aerosol particle and calculated the maximum efficiency difference for the bands of a Dobson instrument bandpair, firstly for a monodisperse aerosol, and secondly for aerosols of realistic polydispersion and optical depth. Of note is the way the variability in aerosol size and refractive index results in a relatively smooth extinction spectrum with at most two or three spectral features over the small range of wavelength of interest. The authors concluded that the maximum errors for the particularly hazy conditions of δ = 0.5 are about 0.022, 0.048, 0.0106 and 0.009 atm cm respectively for the A, C, D and AD band combinations (cf. above-noted figures of Rat'kov, 1971; and Shah, 1968.) Most sites do not encounter such hazy conditions, and certainly for averages over periods of one month or more the error in the standard AD estimation will be 1% or less.
Mateer and Asbridge (1981) analysed a sample of 252 A, C and D band pair data in terms of the Basher (1976) and the Shah (1979) approaches as well as by a simple least square method. They note the four-fold increase in the sensitivity of the Basher and Shah methods to measurement uncertainty and conclude that the standard AD method is to be preferred, presumably on the grounds of simplicity and greater stability. Of course, there was no way of knowing which of the estimation methods had the least systematic aerosol error. Basher and Thomas (1980) calculated the propagation of nominal uncertainties in the A, B, C and D bandpair measurements through to the various multi-bandpair ozone estimations for various polynomial orders. They concluded that the uncertainties magnify rapidly as the polynomial order is increased, i.e., the equations rapidly become poorly conditioned, that for a given order there is little advantage in using more than the minimum number of bandpairs needed (in agreement with the above Mateer and Asbridge study), that the most practical combinations are those of the standard AD method and the quadratic ACD method, and most importantly, that the expected aerosol errors as determined by Basher and Thomas (1979) will rarely justify the use of more than the linear polynomial standard AD method.
Further insight into the effect of aerosol extinction can be gained from the calculation reported by Thomas and Basher (1981) of Mie extinction efficiencies for monodisperse aerosols of constant optical depth, and the presentation of the resulting ozone errors as a function of particle diameter. This work shows clearly how the use of the polynomial models reduces the lower frequency components of the error spectrum (with respect to particle diameter) but at the expense of increasing the magnitude of the higher frequency components, how the polynomial methods magnify not only errors of measurement, but also errors in the appropriateness or accuracy of the polynomial model itself, and how, relative to the single wavelength pairs, the standard AD method serves to reduce markedly the error due to particles in the 0.0 to 1.0 um diameter range. Of particular note is the confirmation that for realistic size distributions and especially hazy conditions (δ = 0.5), the maximum error in the AD estimation is about 0.010 atm cm.
10.4 Cloud attenuation
Very little of substance can be said about the effect of clouds on the measurement of ozone. Two measurement types are possible, the first being of the direct solar beam when the cloud is relatively thin, i.e., sufficiently thin that the measurements are not significantly affected, and the second being the zenith light from a cloudy sky, in which the log intensity measurement is empirically related to the measurement of the zenith blue sky and thence to the measurement of the direct solar beam. The empirical charts which are used are built up from years of simultaneous pair measurements. Further information on the methods may be found in Appendix A. When the cloud is optically thin, there will be uncertainty about the cloud-induced errors and about when to change the observation type from the direct sun type. On occasion, optically thin clouds may not be obvious to an observer, especially when the clouds are near the solar position, though the author's experience suggests that the AD ozone estimation is little affected even by quite noticeable amounts of cirrus and other thin cloud.
It may be useful to note a few theoretical considerations. From Mie theory it can be shown that for the large droplets of clouds the scattering efficiency is essentially spectrally flat, and hence, apart from minor refraction and reflection effects within the droplet, the spectral character of a solar beam passing through a cloud is largely unchanged. However, the intensity of the scattered light received by an instrument's field of view does have a small spectral dependence, owing to the spectral dependence of the angular distribution of the scattered light (cf. visible coloured rings around the moon). The intense scattering that occurs in clouds can quickly extinguish any beam and create in its place a very diffuse radiation flux. The mean optical path of the diffuse flux is greater than that of a direct zenith beam so there will be a small increase in absorption due to the presence of the tropospheric ozone within the cloud. The spectral character of the radiation emanating from the bottom of the cloud also depends on the spectral character of the radiation illuminating the cloud, both at the bottom from the irradiance of the ground, and at the top from the direct attenuated solar radiation and the Rayleigh scattered skylight. Its intensity and spectral character therefore will depend on the surface albedo, the cloud thickness and type and the solar zenith angle. It is possible to model these factors and their effect on column ozone measurements. The study by Mateer et al. (1977) is a worthwhile step in this direction.
The accuracy of measurements of ozone under cloudy conditions may be assessed through the comparison of quasi-simultaneous measurements under cloudy and clear conditions. Dobson and Normand (1962) indicate that RMS differences of about 0.010 atm cm, or approximately 3%, occur both for the comparison of AD measurements under zenith cloud and direct sunlight, and for the comparison of CCl cloud measurements and AD direct sun measurements. For the same measurement types, Komhyr (1960) found similar values, of about 2.5% and 2% respectively. Further details of this work by Komhyr may be found in Appendix A. When the cloud thickness is great the differences can be greater, and on occasion differences as large as 0.200 atm cm have been found (Dobson et al., 1946, Dobson and Normand, 19621 and Kerr, 1973). Such unexplained large differences have been termed the "cumulus effect". The accuracy of any cloud measurement will depend on the quality of the empirical correction charts used, and on the constancy of the zenith light during the sequence of bandpair measurements. Under cloudy conditions this zenith light is frequently not constant, and this, together with the virtual impossibility of obtaining comparisons of cloudy sky and zenith clear sky measurements for some cloud types, means that often the cloudy sky ozone estimations will have relatively large errors.
Brewer and Kerr (1973) proposed the use of a polarizing filter to improve cloudy sky measurements. The filter is oriented to eliminate the clear sky's singly scattered and strongly polarised component of Rayleigh scattering, and hence to greatly reduce the difference between the clear sky and cloudy sky measurements due to this component. They reported encouraging results using the Brewer grating spectrophotometer and subsequently Dobson (in Walshaw, 1975) and Mateer et al. (1977) supported the method's use with the Dobson instrument. However, Dziewulska-Losiowa's (1978) experiments with it were quite unsuccessful, and the method is not described in the WMO Dobson Operations Handbook (Komhyr, 1980b).
Owing to the difficulty of properly accounting for all the known sources of systematic error and for the uncertainties of observational practice, it would seem that the best means of assessing the accuracy of cloudy-sky measurements, and possibly also zenith blue sky measurements and focussed-image measurements, is by analysis of actual data sets, such as was done by Komhyr (1960 - see Appendix A also), and Dobson and Normand (1962). It is likely that further studies of this sort already exist in unpublished form. Bearing in mind the large contribution of these measurement types to the column ozone data archives, it is highly desirable that any such existing studies be reviewed and circulated, and that further studies be initiated by those familiar with the data and with good access to suitable data sets. Better methods or improvements to the old methods might also be devised.
10.5 Summary
(i) Although the physics of atmospheric scattering processes is well known, the great temporal and spatial variations of aerosol and cloud characteristics prevent the exact calculation of their effects on column ozone measurements. Instead, empirical methods must be used.(ii) The current debate about the accuracy of the Rayleigh scattering coefficients needs to be quickly resolved. The coefficients now used with the Dobson instrument are probably accurate to 1%, which gives negligible error for the AD and CD ozone estimations and perhaps up to 0.5% error for the C ozone estimation.
(iii) The standard sea level Rayleigh scattering coefficients need to be corrected in proportion to a station's mean pressure altitude, and to its daily pressure variations. Usually this is only important for single bandpair combinations.
(iv) The RMS accuracy of the AD ozone estimations derived from measurements of zenith skylight is at best 0.005 atm cm, or about 1.5%, and may in general be twice this value.
(v) Maximum ozone errors for direct sun and zenith sky estimations due to aerosol extinction alone, and for the particularly hazy conditions of δ = 0.5 are about 0.022, 0.048, 0.106 and 0.009 atm cm respectively for the A, C, D and AD band combinations. Very few sites ever experience such strong haziness and certainly for averages of one month or more the errors in AD estimations will be less than 1%.
(vi) The use of non-linear representations of the aerosol extinction spectrum, and hence of combinations of the A, B, C and D bandpairs which are more elaborate than the standard AD combination, leads to the magnification of experimental errors and is rarely, if ever, justified by the expected magnitude of the aerosol extinction error.
(vii) The RMS accuracy of the AD ozone estimation derived from measurements of the cloudy zenith sky is at best about 0.010 atm cm, or 2 to 3 per cent, and will be greater under thick or variable cloud. Under cumulonimbus clouds, and in the vicinity of thunderstorms, very large deviations, of up to 0.200 atm cm or over 50% may be encountered, but this may be due to a real ozone increase rather than to any error.
(viii) There is little readily accessible information on the accuracy of the zenith blue and cloudy zenith sky methods. It is desirable that any relevant unpublished atmospheric modelling studies or data analyses be circulated and that further studies be initiated. The possibility of improvements to the methods should be considered.
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