## Reduction of UV Irradiance by Clouds and Aerosols

A measured daily cycle of UV reaching the surface will show large UV irradiance reductions from clear-sky conditions as clouds pass over a site while blocking the view of the sun. These reductions are frequently in excess of those caused by measured ozone changes from climatological values for wavelengths longer than 305 nm. In general, the effect of clouds and aerosols reduces the UV and VIS amounts at all wavelengths reaching the earth's surface. When using satellite data to estimate the amount of UV reaching the surface, the average amount of UV radiation reduction caused by clouds, plus scattering aerosols, can be estimated from the Lambert Equivalent scene Reflectivity (LER), which varies significantly between locations on the coarse resolution scale of the satellite instrument (50 km to 100 km). The cloud reflectivity estimation can only be done for snow and ice-free conditions,

The LER of a scene is calculated by requiring that the measured radiance ISM match the calculated radiance IS at the observing position of the satellite by adjusting a single free parameter R in the formal solution of the radiative transfer equation in Eq. (5.5).

Is(A0, R, Po) = RId(/1,6R PYn(p f Po) + IdO(A0, Po) = Ism (5.5)

Q = column ozone amount

0 = viewing geometry (SZA, satellite look angle, azimuth angle) R = LER at PO, 0 < R < 1

PO=pressure of the reflecting surface (e.g., ground or cloud) Sb = fraction scattered back to PO from the atmosphere Id = sum of direct and diffuse irradiance reaching PO f = fraction of radiation reflected from PO reaching the satellite IdO = radiance scattered back from the atmosphere for R = RG = 0 at P = PO The quantities Sb, Id, f, and IdO are calculated from a radiative transfer solution and stored in tables. From Eq. (5.5), r =-Ism -1dO--(5.6)

The quantities in Eq. (5.6) are calculated from the TOMRAD vector radiative transfer program for a pure Rayleigh atmosphere for different values of R and PO to create a table lookup capability. The details of the implementation are given in the paper written by Dave (1964) from which TOMRAD was developed. Essentially, the quantities Sb and f are calculated for unit upward irradiance leaving the surface at PO. In the case of Sb, it is the fraction that scatters back to the surface, and in the case off, it is the fraction that reaches the satellite. IdO is computed for the case Rg = 0.

The earth's reflectivity as represented by the LER is not the same as the angularly dependent reflectivity of a surface containing structures (grass, vegetation, mountains, clouds, etc.). The angular effects caused by structures in the surface and in clouds are minimized by scene averaging from the coarse resolution of the observations. In order to use the LER to estimate change in reflectivity, the observing geometry must be approximately constant over the life of the satellite, or corrections must be made to account for the change in angular dependence of the observations. Most of the satellites used to construct the reflectivity time series were in near-noon sun-synchronous orbits. This means that any location on the earth's surface was observed at approximately the same angle for the same day of each year. Long-term changes in LER represent changes in the scene reflectivity (clouds, aerosols, and surface) for each location. Comparisons of LER between seasons contain an angular effect caused by the seasonal change in the noontime SZA from the changing solar declination angle ± 23.3°.

The Nimbus-7/TOMS instrument obtained daily global coverage for ozone and LER for over 13 years at a spatial resolution that varied between 50 x 50 km to 100 x 100 km2. For any given location on the earth's surface, frequency of occurrence histograms were constructed from satellite derived reflectivity values (Fig. 5.7) (Herman et al., 2001b). These histograms showed that the most commonly occurring values of R were about 3 RU - 5 RU greater than the surface reflectivity, and represent haze or very sparse cloud cover. Central Europe, represented by Germany, is quite different from North American sites in that the most frequent values are around 10 RU (127 days; 3.9%) or around 50 RU (128 days; 3.9%), with almost the same number of days (80 to 128 days; 2.4% to 3.9%) having 10 RU to 70 RU. Greenland is another extreme, where the reflectivity is always high because of the ice cover. Nevada and Virginia are similar, except that Nevada has a lower average reflectivity representing less cloud cover. Another extreme case is represented by Australia, where the average reflectivity (due to cloud cover) is very low, and cumulative UV exposure is high compared to the same latitude in the U.S.

Satellite observations of reflected UV indicate that reflectivities for typical mid-latitude cloud covered scenes have a wide range of values, which can reach 90 RU over high altitude cloud tops, which most frequently occurs in the tropics. Under snow-free conditions, the surface reflectivity RG is usually between 2 RU and 4 RU, reaching about 10 RU in the Libyan Desert and similar small areas (e.g., Andes Mountain high deserts). Area-averaged clear-sky UV surface irradiance is then approximately reduced as a linear function of the cloud plus aerosol reflectivity, which can be written in terms of effective transmission. The cloud transmission is approximately given by CT = (1 - R)/(1 - RG), where RG < R < 1. Figure 5.7 Frequency of occurrence of reflectivity values 1979 - 1987 (3285 days) for six different locations. The mean and standard deviation (SD) are in RU (1 RU = 1%). Based on Herman et al. (2001b)

A satellite viewing the earth's surface observes a combined reflectivity R = RSYSTEM from the clouds and the ground. Assume that the cloud-ground system can be approximated by a two-layer Stokes problem with atmospheric effects neglected. Assume that the clouds have different transmission and reflections properties for diffuse Td, Rd and direct-sun TC, RC. The arrows in Fig. 5.8 represent the partial contributions to the upward and downward fluxes. Figure 5.8 Stokes diagram for CT for unit irradiance incident on a cloud of transmittance TC over a surface of reflectance RG. The cloud and surface have diffuse transmittance and reflectivity of TD and RD

RSYSTEM " RC + RGTCTD [1 + RGRD + (RGRD)2 + "' ]

CT = Tc [1 + Rg Rd + (Rg Rd)2 + "'] = Tc/(1 - Rg Rd) (5.8)

1 "RSYSTEM = 1 "RC "RGTDTC/(1 "RGRD) = 1 "RC "RGTDCT (5.9)

Assume TC = 1 -RC and TD = 1 -RD, rewrite (5.8) as CT (1 -RGRD) = 1 -RC.

Now Eq. (5.9) becomes 1 -RSYSTEM = CT (1 -RGRD) -RGCT (1 -RD)

where

Rg = Reflectivity of the ground RC=Direct beam cloud reflectivity Rd = Diffuse flux cloud reflectivity

RSYSTEM = Reflectivity of the combined ground-cloud system TC and TD are the corresponding cloud transmissivities Assume R = RSYSTEM as an approximation of the reflectivity seen by the satellite A problem exists for high reflectivity scenes observed by UV/VIS satellite instruments, such as those covered by snow or ice. Snow/ice covered scenes cannot be distinguished from cloud cover by radiance observations in the UV wavelengths. Because of this, the use of CT to estimate the amount of UV radiation at the surface in the presence of snow is likely to be in error. For example, the very high reflectivity values observed in Greenland (Fig. 5.7) are almost independent of the cloud cover. Radiative transfer solutions for clouds over snow/ice surfaces show that the maximum reflectivity is obtained for clear-sky scenes, which is reduced somewhat in the presence of clouds over snow/ice (Krotkov et al., 1998).

Long-term changes in regional cloud and aerosol reflectivity must be considered when estimating long-term changes in UV irradiance. However, for most populated regions of the earth, long-term (decadal) cloud and aerosol scattering changes have been shown to be small, even where they are statistically significant (Herman et al., 2001a; Herman et al., 2009b). Local values of aerosol amounts and absorption are currently estimated from the widely distributed AERONET network of ground-based sunphotometers (Holben et al., 2001), and for clear-sky scenes, from satellite data (Torres et al., 2002a, b).