Radiation Amplification Factor

An alternate method for the estimation of long-term changes in UV-B irradiance can be devised by combining measured ozone values with radiative transfer calculations. These calculations can be simplified for estimating irradiance change by neglecting scattering effects. For clear-sky, constant cloud, and constant aerosol conditions, changes in monochromatic UV-B irradiance dF show a well-defined inverse relation with changes in the amount of ozone d^ in the atmosphere based on laboratory measurements of the ozone UV absorption coefficient a (e.g., Zerefos et al., 2001). This has been most clearly demonstrated using a spectroradiometer measuring ozone and erythemally weighted irradiance (300 nm - 400 nm) at Mauna Loa, Hawaii on 132 clear mornings between July 1995 and July 1996 (WMO report, 1999). The relationship of a change in irradiance dF at a single wavelength to a small change in column ozone amount d£?is approximately given in Eq. (5.1).

The differential relationship is derived from the standard Beer's Law of irradiance

F attenuation in an absorbing atmosphere, F = Fo exp( -aQ sec(#)), where

Q= the ozone column amount in DU (1 DU = 1 milli-atm-cm or 2.69x 1016 2 —1 molecules/cm ), a=the ozone absorption coefficient (in cm ), d = the SZA, and

Fo is the irradiance at the top of the atmosphere. The quantity ail sec(#) is the slant path optical depth, which was also named the Radiation Amplification

Factor, or RAF(£?,#) (Madronich, 1993) when Eq. (5.1) was used for estimating irradiance change. When varying cloud reflectivity d^ is included, F=Fo exp

(-ailsec(#)) (1 -R)/(1 -RG) and the fractional change in irradiance is dF/F = -dn/n aQ sec(#) + dCj/Cj (5.2)

where CT = the cloud + aerosol transmission = (1 -R)/(1 - RG), and R = the reflectivity of the ground RG + cloud RC system (RG < R < 1).

Equation (5.2) has proven to be quite accurate for estimating monochromatic irradiance changes for small changes in Q under a wide variety of conditions, especially for cloud-free conditions. A comparison was run between radiative transfer solutions RTS and Eq. (5.1) for 1% change from three ozone values, 275 DU, 375 DU, and 475 DU for the wavelength range 290 nm to 350 nm, and SZA = 30° (Herman et al., 1999). The largest difference between the RTS and Eq. (5.1) was 0.2% at 290 nm for 275 DU, and less than 0.1% for wavelengths larger than 310 nm.

Figure 5.5 shows a specific example of the cloud-free monochromatic RAF for Q = 0.33 atmosphere-cm = 330 DU and SZA = 45°,and shows the ozone absorption coefficient (cm-1) for the wavelength range from 240 nm to 340 nm. The RAF method accurately estimates small monochromatic UV irradiance changes compared to clear-sky radiative transfer (Herman et al., 1999). For example, radiative transfer shows that a 1% decrease in O3 produces a 2.115% increase in 305 nm irradiance, while the RAF method estimates a 2.064% increase (Q = 375 DU, d = 30°). There are wavelength dependent deviations from Eqs. (5.1) and (5.2) under optically thick clouds caused by multiple scattering increasing the optical path for ozone absorption. If there is a 1% change in ground reflectivity from a



-----r —i -----r"

RAFw=aPsee (45°)

0=0.33 aim cm

t_____' ' ... 'x.


- * X

_.Photons reach the


s earth's surface

RAFA\aicm"'5 -

; Few photons at the

11In A

: earth's surface

\ ■ 1 L t

. , . U ti

280 300 Wavelength (nm)

Figure 5.5 Ozone absorption coefficient a (cm ') and the RAF45 for an SZA = 45° and ozone amount of 330 DU (O =0.330 atm cm). Note that at 310 nm, the RAF45~1, so that a 1% increase in O3 would produce a 1% decrease in 310 nm irradiance

280 300 Wavelength (nm)

Figure 5.5 Ozone absorption coefficient a (cm ') and the RAF45 for an SZA = 45° and ozone amount of 330 DU (O =0.330 atm cm). Note that at 310 nm, the RAF45~1, so that a 1% increase in O3 would produce a 1% decrease in 310 nm irradiance nominal reflectivity of RG = 5 RU (RG = 0.05) for clear skies, the change in downward irradiance is less than 0.35% due to backscattering from the atmosphere. If there is optically thick cloud cover, the change increases to about 0.8%.

The RAF method has also been validated using measurements of ozone and UV irradiance at Mauna Loa, Hawaii. Figure 5.6 shows that when clear-sky measurements of monochromatic irradiance are carefully made for a 1% change in ozone amounts, but no change in aerosols, the measured and calculated changes agree quite well. Later, it is shown that an empirical power-law RAF method agrees with monochromatic Eq. (5.1) for small ozone changes, but also applies for action spectrum weighted irradiances with larger ozone changes. The empirical power law can be obtained (numerically) from Beer's Law (see Section 5.7).

Figure 5.6 Validation of RAF method using the measured (dark circles) changes in ozone and UV irradiance from Mauna Loa, Hawaii (WMO, 1999)

Fioletov et al. (1997) reported an extensive analysis of UV-B irradiance and its dependence on total ozone. The analysis provides an empirical wavelength-by-wavelength measure of the increase of UV-B irradiance for a 1% decrease of total ozone. The values for UV change with ozone change were found to be essentially the same for clear and cloudy conditions (except for very heavy clouds), and are in good agreement with model results for longer wavelengths and moderate SZA. The conclusion is in agreement with the approximation in Eqs. (5.1) and (5.2).

Both theory and observations show that reductions in ozone lead to increases in UV erythemal and UV-B monochromatic radiation at the earth's surface. For mid-latitudes, changes in measured erythemal irradiance can be approximated using Eq. (5.1) with the monochromatic RAF = 1.3 to 1.4 at mid-latitudes when the ozone amount changes by 1%. However, an empirical power law form gives a better approximation to erythemal irradiance change with ozone than Eq. (5.1). A detailed discussion of RAF is given in Section 5.7.

Satellite estimates of ozone and reflectivity are retrieved separately, each with its own error budget. Ozone is retrieved with about 1% accuracy, especially on a zonal average basis. Zonal average reflectivity is retrieved with an accuracy of about 2 RU or 0.02 (0 < R < 1). The differences d^and dR have the same accuracy as Q and R, since they are simply the difference from a fixed reference value. When Eqs. (5.1) and (5.2) are used for estimating UV trends in this study (see Section 5.3.7), the reference values used are the average value of ozone or reflectivity in the first year as a function of latitude.

The implication of this and following sections is that it may be easier to measure changes in ozone amounts and cloud plus aerosol transmission combined with radiative transfer calculations of UV irradiance change than it is to measure the changes in UV irradiance with very stable and well-calibrated instrumentation. This method will miss some features of UV irradiance, such as the momentary increase above clear sky amounts caused by reflections from the sides of clouds and will not be accurate in mountainous regions where the terrain reflectivity affects the irradiance more than in relatively flat regions. Even in mountainous regions, Eq. (5.2) will still represent the change in irradiance caused by satellite-detected changes in stratospheric and tropospheric ozone amounts. However, changes in scene reflectivity from the sides of mountains can affect the amount of UV irradiance in a manner that is usually not detected by ozone-measuring satellites. The method will also miss any absorption effects (usually small) caused by other trace gases (e.g., NO2 and SO2) and absorbing aerosols. Currently there are no long-term measurements of these quantities and their changes over wide areas.

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