Log errors are defined:

1

The Chlorophyll Algorithm Revisited Results of
the OCBAM Workshop
J. Campbell1, D. Aurin, S. Bailey, P. Bontempi,
M. Dowell, R. Frouin, H. Feng, P. Lyon, C.
McClain, S. Maritorena, T. Moore, R. Morrison, J.
OReilly, H. Sosik, C. Trees, J. Werdell
Abstract (OS24R-15)
Adjusting for Differences in the Distribution of
NOMAD Data vs. Global Climatology
The Ocean Color Bio-optical Algorithm Mini
Workshop (OCBAM)
The Ocean Color Bio-optical Algorithm Mini
Workshop (OCBAM) was held at the University of
New Hampshire on September 27-29, 2005. The
purpose of the workshop was to evaluate
chlorophyll algorithms in light of a newly
published bio-optical database (NOMAD) and to
consider whether improved accuracy can be
achieved by accounting for other optically active
constituents. It was concluded that any
significant improvement to the chlorophyll
algorithm can only be achieved by accounting for
the effects of other constituents. The time has
come to begin pushing the envelope toward
algorithms that yield information about dissolved
and particulate materials as well as the
chlorophyll concentration. Such information might
be derived inherent optical properties rather
than the materials themselves. Model-based
algorithms that relate the apparent optical
properties of radiance and reflectance to the
inherent optical properties are likely to be the
solution. In this poster, we describe a process
whereby new model-based algorithms will be
evaluated and potentially selected to replace the
current empirical algorithms used by NASA for
SeaWiFS and MODIS data processing.
Goals
Error statistics were calculated within bins of
log C (right). The mean and mean square errors
were weighted by the frequency in the global
SeaWiFS climatology (red).
Evaluate ocean color algorithms that produce
chlorophyll retrievals. Algorithms tested may
also retrieve other constituents and / or related
inherent optical properties. Compare new
algorithms to the operational empirical
algorithms used for SeaWiFS (OC4.v4) and MODIS
(OC3M).
Can accuracy be improved by accounting for other
optically active constituents?
Quantifying the Uncertainty in a Chlorophyll
Algorithm
Motivation
Log errors are defined where is the
algorithm CHL and C is the in situ CHL. These
are the errors minimized by the 4th-order
polynomial algorithms (right).

• NOMAD. We have a new data set to use in
  evaluating algorithms.

Global climatological CHL distribution
Table 3. Results of weighting error statistics by the global SeaWiFS climatology (1997-2005) (right columns). Unweighted statistics (Tables 1 and 2) are listed for comparison. Table 3. Results of weighting error statistics by the global SeaWiFS climatology (1997-2005) (right columns). Unweighted statistics (Tables 1 and 2) are listed for comparison. Table 3. Results of weighting error statistics by the global SeaWiFS climatology (1997-2005) (right columns). Unweighted statistics (Tables 1 and 2) are listed for comparison. Table 3. Results of weighting error statistics by the global SeaWiFS climatology (1997-2005) (right columns). Unweighted statistics (Tables 1 and 2) are listed for comparison. Table 3. Results of weighting error statistics by the global SeaWiFS climatology (1997-2005) (right columns). Unweighted statistics (Tables 1 and 2) are listed for comparison.
unweighted statistics unweighted statistics weighted statistics weighted statistics
OC4.v4 OC3M OC4.v4 OC3M
d (log units) d (log units) d (log units) d (log units) d (log units)
bias -0.047 -0.045 -0.006 -0.020
RMSE 0.256 0.266 0.193 0.196
relerr () relerr () relerr () relerr () relerr ()
mean 6 8 9 6
median -10 -10 -1 -4
std dev 67 72 51 50

lower 0.50 0.49 0.63 0.61
median 0.90 0.90 0.99 0.96
upper 1.60 1.65 1.54 1.50
di
For the two operational algorithms, log errors
are approximately normally distributed

• A recent paper (Siegel et al. 2005) argues for
  the importance of accounting for the effects of
  colored dissolved organic matter.

The performance measures derived from NOMAD or
any database are influenced by the distribution
of the stations in the database. Often theres
an over abundance of high chlorophyll stations.
The figure below compares the distribution of
chlorophyll in the SeaWiFS climatology
(1997-2005) (red) with that in NOMAD (blue).
The GSM01 algorithm (Maritorena et al. 2000) was
applied to global SeaWiFS data, and the derived
chlorophyll distributions were compared with maps
derived by the standard algorithm (OC4).
Differences are quite significant and related
to the Colored Dissolved Organic Matter (CDOM)
absorption as derived by the GSM01 algorithm.
Log error (d)
Table 1. Log error statistics based on NOMAD. Table 1. Log error statistics based on NOMAD. Table 1. Log error statistics based on NOMAD. Table 1. Log error statistics based on NOMAD. Table 1. Log error statistics based on NOMAD.
algorithm N mean stdev RMSE
OC4.v4 2208 -0.047 0.252 0.256
OC3M 2208 -0.045 0.262 0.266
Relative errors are defined
Conclusions

• The log error is the basic
  measure of uncertainty. Relative error statistics
  can be derived assuming normal log errors.
• Uncertainty in OC4 and OC3M algorithms has been
  quantified in log CHL bins for single retrievals.
  This enables the creation of uncertainty maps
  for level-2 and level-3 products.
• The operational chlorophyll algorithms used by
  SeaWiFS (OC4) and MODIS (OC3M) are not
  accurate to within 35. Globally, the
  uncertainty is 50 about the median.
• OCBAM participants concluded that little
  improvement can be achieved without accounting
  for other optically active constituents.
• The Ocean Biology Data Processing Group at NASA
  Goddard is prepared to run algorithm codes and
  produce metrics for anyone wishing to have an
  algorithm considered for the next generation of
  ocean color algorithms.

Attendees
The red curves are the global chlorophyll
distribution based on the SeaWiFS climatology
(1997-2005).
This relationship between the log error and
relative error holds only for individual points.
Statistics of relative errors can be derived
assuming normal distribution of log errors.
Dirk Aurin University of Connecticut Sean
Bailey NASA Goddard Space Flight Center Shane
Bradt University of New Hampshire Paula
Bontempi NASA Headquarters Janet Campbell Ocean
Process Analysis Lab, UNH Mark Dowell Joint
Research Center, Ispra, Italy Robert Frouin
University of California - San Diego Carol
Fairfield NMFS Visiting Scientist, UNH Hui
Feng Ocean Process Analysis Lab, UNH Paul
Lyons ORBIMAGE, Inc. Haymarket, VA Chuck
McClain NASA Goddard Space Flight Center
Stephane Maritorena University of California -
Santa Barbara Timothy Moore Ocean Process
Analysis Lab, UNH Ru Morrison Ocean Process
Analysis Lab, UNH Jay O'Reilly NMFS
Narragansett Laboratory Heidi Sosik Woods Hole
Oceanographic Institution Chuck Trees San Diego
State University Jeremy Werdell NASA Goddard
Space Flight Center
Table 2. Relative error statistics based on NOMAD. Table 2. Relative error statistics based on NOMAD. Table 2. Relative error statistics based on NOMAD. Table 2. Relative error statistics based on NOMAD. Table 2. Relative error statistics based on NOMAD.
Lognormal Lognormal Empirical Empirical
relerr () OC4.v4 OC3M OC4.v4 OC3M
mean 6 8 6 9
median -10 -10 -8 -8
std dev 67 72 66 76
median 1 std dev median 1 std dev based on percentiles based on percentiles
lower 0.50 0.49 0.50 0.51
median 0.90 0.90 0.92 0.92
upper 1.60 1.65 1.54 1.56
Log errors (di) for OC4.v4
1Ocean Process Analysis Laboratory, Institute for
the Study of Earth, Oceans, and Space, University
of New Hampshire, Durham, NH 03824. Email
janet.campbell_at_unh.edu. This work was supported
by a NASA MODIS Science Team award to J. Campbell
(NNG04HZ37C).