Problem#4: Interpretation of satellite image
Xiaofeng Wang
The two figures above (drawn by myself when I was in Beijing) are the cloud
parameter product from MODIS. The bands involved in the retrievals of cloud
optical thickness and cloud droplets effective radius includes 0.645µm (used for
land surface) / 0.858µm (ocean surface)/ 1.24µm (ice & snow surface), 1.64µm,
2.13µm, 3.75µm.
Cloud optical thickness is defined as the vertical integration of extinction over the
whole cloud physical thickness. And cloud droplet effective radius is the ratio of the
third moment of size distribution to the second moment of size distribution.
In order to get the retrievals, first we need to know the reflectance of a specific band
in a finite interval, expressed as:
𝑅(𝜏𝑐 , 𝑟𝑒 ; 𝜇, 𝜇0 , 𝜙) =
∫𝜆 𝑅 𝜆 (𝜏𝑐 , 𝑟𝑒 ; 𝜇, 𝜇0 , 𝜙)𝑓(𝜆)𝐹0 (𝜆)𝑑𝜆
∫𝜆 𝑓(𝜆)𝐹0 (𝜆)𝑑𝜆
Where, 𝜏𝑐 cloud optical depth; 𝑟𝑒 effective radius; µ cosine of absolute value of zenith
angle; 𝜇0 cosine of solar radiation zenith angle; 𝜙 the relative azimuth angle
between the direction of reflected radiation and the incident solar direction; f(λ)
band’s spectral response; 𝐹0 (𝜆) incoming solar flux; 𝑅 𝜆 reflectance function at a
certain wavelength.
From Figure 1, we find that (1) at shortwave band, reflection function is much more
sensitive to cloud optical depth; (2) at long wave bands, reflection function is much
more sensitive to effective radius, especially at larger optical depth.
In practice, we usually use another diagram to illustrate the aforementioned
sensitivity relationship (Figure 2). From Figure 2, we know that if we have a pair of
reflection value, we can get corresponding value of cloud optical thickness and
effective radius through interpolation.
With this knowledge and the reflection function, after calculating different reflection
value under diverse angles, cloud optical thickness and effective radius, a look-up
table for cloud parameter can be generated. So when we know the reflection
function at a band in satellite, through some interpolation processes in the look-up
table, we will get the cloud optical thickness and effective radius simultaneously.
The 2.13 band retrievals of effective radius and optical thickness in combination
with shortwave band are set as default in MODIS cloud products. Effective radii from
the 1.64 and 3.75 band are usually reported as differences in effective radius
relative to 2.13 band.
(Figure 1: From King et al., 1997, Page 16)
(Figure 2: From Liou 1997, Page 374)
References:
King, M. D., S. C. Tsay, S. E. Platnick, M. Wang, and K. N. Liou. Cloud retrieval algorithms for
MODIS: optical thickness, effective particle radius, and thermodynamic phase, MODIS
Algorithm Theoretical Basis Document No. ATBD-MOD-05, Dec. 23, 1997, Version 5
Liou, K. N.. An Introduction to Atmospheric Radiation, Academic Press, 2002, 2nd Edition
Platnick, S., M. D. King, Member IEEE, S. A. Ackerman, W. P. Menzel, B. A. Baum, J. C. Riédi,
and R. A. Frey. The MODIS Cloud Products: Algorithms and Examples From Terra, IEEE
Transactions on Geoscience and Remote Sensing, 2003, 41(2), 459-473