2. Strategy of Simulateneous Remote sensing of atmospheric aerosol optical depth and average surface reflectance.

2.1 Parameterization and separation of contribution of atmospheric scattering scattering and surface reflectance.

For horizontally homogeneous atmosphere and homogeneous lambertain surface, RT model codes such as DISORT, 6S, et al. have been widely used to obtain numerical results with enough accuracy. An approximate expression is also commonly used [3,4]

I(t,m₀,m_s, j_os) = I_a( t,m₀,m_s, j_os) + F_d(t,m₀)T (t,m_s) A([1-s(t)A] (1)
Taking r_s(t,A,m_o, m_s, j_os) = pI / m0F, Eq. (1) Can be simply expressed as the following form (omitting m0,ms,pos)

r_s(l,t,A) = a(l,t) + b(l,t) A +c(l,t)A² (2)
Figure 1 shows the calculated results of r_s - (t,A) relationship by DISORT code, atmospheric condition is mid-latitude summer and rural aerosol of LOWTRAN7.


Fig.1 Relationship of rs-(t,A) each line represents rs-(t,A) relationship for fixed values of A, value of A are from 0.0 (the leftest) to 1.0 (the rightest) with interval of 0.1.
After making a series of computation with wide range of t and A and wavelength l, for specific view angles by using RT code, we may establish empirical polynomial approximation of a, b and c as






In [4] we have shown the detailed results a_ij, b_ij, and c_ij of these parameterization. There is very accurate fitting, the maximum error is less than 2% in most cases.

2.2 simultaneous Remote Sensing of Atmospheric Aerosol Optical Depth and Surface Reflectance.
Eqs.(2)-(4) consist of the explicit expression of r_s-(t,A) relationship for different wavelength. We need complementary information of the form of spectral dependence of t(l) and A(l).

For atmospheric scattering, we may use molecular scattering ts-(l) and exponential relationship for aerosol optical depth ts-(l) as

t(l)= t_m (l) + ta(l) = tm(l₀)(l₀)^-4 (5)
where l₀ is certain reference wavelength, where t_m(l₀) is known, so

tm(l) =t(l) -tm(l) =(l₀) l/l₀)^-a (6)
for surface reflectance, we need to establish specific relationship for different classes of surface. In certain land surface such as soil and vegetation, in some wavelength interval in visible and infrared band, linear relationship is existed.

A(l) = A(l) + C(l-l₀) (7)
Eqs. (2)-(7) consist of basic equations for simultaneous remote sensing of t(l). In [2] we have given some numerical results for these retrieval. These equations are solved by a hybrid method.

3. Straegy of Atmospheric Correction for Inhomogeneous Surface
For inhomogeneous (but Lambertaion) surface, atmospheric correction consists of reduction of intrinsic atmospheric scattering and adjacency effect. In this case, the following approximate expression can be used [3]

r(t,A(₀),A_b) =r₀(t) +T(q0)A(0)exp(-t/t_v) +T(t_o)A_bd(t_v) (8)
Here A(0) is the reflectance of some target pixel, A_b is the average reflectance for background surface surrounding the target pixel. T(q₀) is the atmospheric transmittance (direct plus diffuse) to the surface, d(q_v) is the upward diffuse transmittance. A_b is expressed as the weighting integration of background surface reflectance A(L,f), L and f are distance and azimuth angle between background pixel to the center of target pixel. The weighing function D(L) is called atmospheric spread function.


In fact, the effective average area is determined by D(L).