This procedure, translated into approximately 10,000 lines of code,
gives the MYSTIC radiative transfer solver. If you are interested in
more details you may have a look at
[Mayer, 1999],
[Mayer, 2000]
where some technical details of the model are given. A good source
of information are the
extended abstracts of the
Intercomparison of 3D radiation codes (I3RC)
as well as the
reference list provided there.
If you went through the quick overview given in this slide show, you may
already have recognized the main advantages of the Monte Carlo method
compared to other RTE solvers:
- It is a plain and straightforward way to calculate the
radiation field.
- No simplifying assumptions are required. Each atmospheric process
is simulated individually and exactly.
- Each quantity of the radiation field is easily accessible,
including not only irradiance, actinic flux, and radiance,
but also for example photon pathlength statistics.
With that many advantages, there is of course also a disadvantage:
While the Monte Carlo method is very efficient for area-averaged
quantities, calculations with high output resolution usually are
computationally very demanding. As a rule of thumb,
- Monte Carlo is a statistical method; hence the relative
uncertainty of a result is directly proportional to the
inverse square root of the number of photons that went into
the result.
- In other words, to improve the precision by a factor of 10
one needs 100 times more photons.
- The computational time is obviously directly proportional
to the number of photons traced. A typical number for MYSTIC
is 20,000 photons per second in a cloudless atmosphere
(on a decent PC, Pentium III, 600 MHz). This number decreases in
presence of clouds, as more scatterings are encountered along the
photon's path.
As an example, consider the calculation of surface irradiance on a
100 x 100 pixels grid. In order to reach a standard deviation
of 1% for each pixel, 10,000 photons need to be sampled in each grid
cell. With a typical atmospheric transmittance of 0.5 one needs to
trace
100 x 100 x 10,000 / 0.5 = 200,000,000
photons
which takes
about 5 hours in a moderately cloudy atmosphere, on a single
processor. For the area average, on the other hand, only about
10,000 / 0.5 = 20,000 photons
are required which are traced in a matter of seconds.
