I was hoping someone could tell me (or point me to) exactly how the SeaWiFS L3 Monthly bins that are available via the DAAC are calculated.  Is it an arithmetic mean, geometric mean (log transformed or root), etc?  Thanks!

Ryan,

The short and simple answer is that the L3 data values are arithmetic
means.   To get the much longer and more detailed answer, consult
Volume 32 of the SeaWiFS Prelaunch Technical Report Series: 
"Level-3 SeaWiFS Data Products:  Spatial and Temporal Binning
Algorithms".   The Project has just completed putting all of the Prelaunch
TM series online in PDF format, so you can get that volume here:

http://seawifs.gsfc.nasa.gov/cgi/tech_memo.pl

I hope you'll find that information useful!

Jim Acker

Ryan,

Be advised that, although the technical report
mentioned by Jim does provide a good description
of the binning methodology for SeaWiFS, it does
contain one significant departure from the method
actually used.

Volume 32 indicates that SeaWiFS data are
log-transformed before being accumulated into
equal-area bins.  That strategy was abandoned
before launch because it was discovered that
the maximum likelihood estimator based on the
log-transformed values was unstable.

If you read Volume 32 and ignore the parts
about log-transforming the data, then you will
have a good understanding of how our level-3
products are produced.

Norman

Jim and Norman,

Thanks for your replies!  I have one clarification question: Jim you mentioned that the L3 are a arithmetic mean, yet Norman and Vol 32 describe a maximum likelihood estimator (sans log transforming).   When I run both methods on a small sample data set, I get (not surprisingly) different results.     Which method is used in the L3?  I'm guessing that the maximum likelihood method was used, but I wanted to make sure.

Thanks again,
Ryan

Jim,

As far as I know, a correction to Volume 32
has not been published anywhere.

This would be a good thing to do.

Ryan,

I was unclear in my previous message.

We do not use the maximum likelihood
estimator for SeaWiFS data.  We do use
the arithmetic mean when accumulating
spatial averages and a weighted mean
for combining spatial averages into
temporal averages (see Section 2.2.4
and Appendix B of Volume 32, replacing
x with X everywhere i.e. don't do the
log transform).

Norman

I have to agree on the correction statement;  I initially checked
the Archive Product Specifications document, which doesn't describe
what the value in the binned/SMI products is (i.e., pursuant to Ryan's
question, an arithmetic or geometric mean, or something else).  The
Archive Product Specs refer the reader to the TM series, which is
obviously where I went next.   So, if there isn't a defining statement on
the "identity" of the value obtained in the binning procedure available
somewhere in the current documentation, we should perhaps
consider creating one.   Since these products are so popular, this
is useful information.

I checked to see what we have at the DAAC in the SeaWiFS Level 3
Dataset Guide Document, and though it adds a bit more information,
it's still too vague.   It says this:

"For the 8-day, monthly, and annual Level 3 products, all of the
valid measurements for the given time period and grid square
are compiled in the same bin and the weighted mean of all
observations is generated. The weight is based on the number
of valid pixels used in the binning process. The binning procedure
is described in detail in Volume 32 of the SeaWiFS Technical
Memorandum Series," ...

So at least it says "mean", which excludes the MLE, but it doesn't
specify the arithmetic or geometric mean.

I can add this to our "Recently Asked Questions" page (which hasn't
had a recently asked question for a couple of years).    That can be
a temporary solution for reference purposes until a more permanent
and comprehensive  treatment can be created.  Of course, we can
now also refer similar questions to this oceancolor discussion.