Cloud reflectivity R is calculated to support the ozone, aerosol, and UV irradiance algorithms. For ozone, it is necessary to estimate the amount of ozone beneath the clouds, when present, and to account directly for the additional backscattered radiance in the ozone absorbing wavelengths. The amount of aerosols can only be estimated for cloud-free pixels. This means that the aerosol index can only be converted into optical depth when the reflectivity is about 15% or less. Aerosol plumes (smoke or dust) frequently have reflectivities of about 15%. The presence of clouds is the largest factor in reducing the amount of UV reaching the ground at a given location. To first order, the UV irradiance is reduced by the fraction 1- R.
In addition to its support role, the reflectivity values can be converted into effective cloud optical depth for each pixel. As with any remote sensing instrument, the cloud fraction within a pixel cannot be determined so that only an effective optical depth can be calculated for that pixel.
The 340 or 388 nm LER (Lambert Equivalent Reflectivity) is calculated by requiring that the measured TOMS radiance ISM match the calculated radiance IS (see Equation 1) by adjusting a single free parameter R in the formal solution of the radiative transfer equation
Is(Q,R, Po)=RId(Q,R,Po)f(Po) / 1-RSb(Po)
where
Q = viewing geometry (solar zenith angle, satellite zenith angle, azimuth angle, etc.)
R = LER (the combined effect of the surface, clouds, water haze, and aerosols)
Po = reflecting surface pressure
Sb = fraction scattered back to PO from the atmosphere
Id = sum of direct and diffuse radiation reaching Po
f = fraction of radiation reflected from Po reaching the satellite
The resulting values of R represent the LER of the scene from measured backscattered radiances originating from the ground, aerosols, and clouds as components of the reflectivity. Certain scenes, such as those containing ice or specular reflection, are distinctly non-Lambertian, as are clouds observed at large solar zenith angles.
In magnitude, R ranges from 0 to 1, but can be negative or greater than 1 if there are absorbing aerosols that are not taken into account or the reflecting surfaces are sufficiently non-Lambertian (e.g., sun-glint from ice). Another possibility for errors in R can occur if the phase functions of aerosols present in the atmosphere are not adequately approximated. In practice, the values of R are usually between 0 and 1 for the Nimbus-7/TOMS observations. Most exceptions are over regions of ocean sun-glint and after injection of volcanic aerosols into the stratosphere (e.g., after the 1983 El Chichon and 1991 Mt. Pinatubo eruptions). Corrections can be applied for these effects (Torres et al., 1995; Herman et al., 1993). When clouds are present, the scene reflectivity R is frequently composed of a mixture of sub-pixel clouds, the surface reflectivity, and possible aerosol backscatter. The approximation of the scene albedo by the LER (instead of the more complicated bi-directional reflectivity distribution) is improved by having a field of view (8-10 km) large enough to help average out the effects of individual clouds or surface features.
It is important to note that the cloud transmission of UV irradiance to the ground is approximately given by 1-R with corrections that can be derived for solar zenith angle and satellite zenith angle (Herman et al., 1999a; Krotkov et al., 1999). These angles are approximately equal for Triana observations and fall between 165° and 177°. The Triana spacecraft cannot get nearer to the Earth-Sun line than about 3° before solar radio noise interferes with the telemetry transmission back to Earth.