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Daily High-Resolution-Blended Analyses for Sea Surface Temperature

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Two new high-resolution sea surface temperature (SST) analysis products have been developed using optimum interpolation (OI). The analyses have a spatial grid resolution of 0.25° and a temporal resolution of 1 day. One product uses the Advanced Very High Resolution Radiometer (AVHRR) infrared satellite SST data. The other uses AVHRR and Advanced Microwave Scanning Radiometer (AMSR) on the NASA Earth Observing System satellite SST data. Both products also use in situ data from ships and buoys and include a large-scale adjustment of satellite biases with respect to the in situ data. Because of AMSR’s near-all-weather coverage, there is an increase in OI signal variance when AMSR is added to AVHRR. Thus, two products are needed to avoid an analysis variance jump when AMSR became available in June 2002. For both products, the results show improved spatial and temporal resolution compared to previous weekly 1° OI analyses. The AVHRR-only product uses Pathfinder AVHRR data (currently available from January 1985 to December 2005) and operational AVHRR data for 2006 onward. Pathfinder AVHRR was chosen over operational AVHRR, when available, because Pathfinder agrees better with the in situ data. The AMSR– AVHRR product begins with the start of AMSR data in June 2002. In this product, the primary AVHRR contribution is in regions near land where AMSR is not available. However, in cloud-free regions, use of both infrared and microwave instruments can reduce systematic biases because their error characteristics are independent.
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Daily High-Resolution-Blended Analyses for Sea Surface Temperature
RICHARD W. REYNOLDS,* THOMAS M. SMITH,CHUNYING LIU,* DUDLEY B. CHELTON,#
KENNETH S. CASEY,@AND MICHAEL G. SCHLAX#
* NOAA/National Climatic Data Center, Asheville, North Carolina
NOAA/NESDIS, CICS/ESSIC, University of Maryland, College Park, College Park, Maryland
#College of Oceanic and Atmospheric Sciences, and Cooperative Institute for Oceanographic Satellite Studies,
Oregon State University, Corvallis, Oregon
@NOAA/National Oceanographic Data Center, Silver Spring, Maryland
(Manuscript received 18 December 2006, in final form 12 April 2007)
ABSTRACT
Two new high-resolution sea surface temperature (SST) analysis products have been developed using
optimum interpolation (OI). The analyses have a spatial grid resolution of 0.25° and a temporal resolution
of 1 day. One product uses the Advanced Very High Resolution Radiometer (AVHRR) infrared satellite
SST data. The other uses AVHRR and Advanced Microwave Scanning Radiometer (AMSR) on the NASA
Earth Observing System satellite SST data. Both products also use in situ data from ships and buoys and
include a large-scale adjustment of satellite biases with respect to the in situ data. Because of AMSR’s
near-all-weather coverage, there is an increase in OI signal variance when AMSR is added to AVHRR.
Thus, two products are needed to avoid an analysis variance jump when AMSR became available in June
2002. For both products, the results show improved spatial and temporal resolution compared to previous
weekly 1° OI analyses.
The AVHRR-only product uses Pathfinder AVHRR data (currently available from January 1985 to
December 2005) and operational AVHRR data for 2006 onward. Pathfinder AVHRR was chosen over
operational AVHRR, when available, because Pathfinder agrees better with the in situ data. The AMSR–
AVHRR product begins with the start of AMSR data in June 2002. In this product, the primary AVHRR
contribution is in regions near land where AMSR is not available. However, in cloud-free regions, use of
both infrared and microwave instruments can reduce systematic biases because their error characteristics
are independent.
1. Introduction
Sea surface temperature (SST) is an important vari-
able to better understand interactions between the
ocean and the atmosphere. SST analyses convert ir-
regularly spaced SST data to a regular grid and have
been used for many purposes from climate monitoring
and prediction (e.g., Smith and Reynolds 2003) to fea-
ture tracking (e.g., Quartly and Srokosz 2002). Often
the planned purpose for the analysis strongly influences
the analysis resolution and accuracy. Thus, for example,
a SST analysis designed for climate research may have
reduced spatial and temporal resolution in order to re-
duce sampling errors. This can occur (as discussed be-
low) in the western boundary current regions in winter
where clouds can reduce high-resolution infrared (IR)
satellite sampling while lower-resolution microwave
satellite data is not impacted.
In this paper the focus is on improving the resolution
of the climate-scale SST analyses produced at the Na-
tional Oceanic and Atmospheric Administration
(NOAA) as described by Reynolds and Smith (1994)
and Reynolds et al. (2002). These older analyses use IR
satellite data from the Advanced Very High Resolution
Radiometer (AVHRR) and in situ data from ships and
buoys. The analyses are performed weekly on a 1° spa-
tial grid from November 1981 to present by optimum
interpolation (OI) with a separate step to correct any
large-scale satellite biases relative to the in situ data.
The Reynolds and Smith (1994) and Reynolds et al.
(2002) weekly OI will henceforth be referred to as OI
version 1 (OI.v1) and OI version 2 (OI.v2), respec-
tively. The techniques for these analyses were originally
Corresponding author address: Richard W. Reynolds, NOAA/
National Climatic Data Center, 151 Patton Ave., Asheville, NC
28801-5001.
E-mail: Richard.W.Reynolds@noaa.gov
VOLUME 20 JOURNAL OF CLIMATE 15 NOVEMBER 2007
DOI: 10.1175/2007JCLI1824.1
© 2007 American Meteorological Society 5473
JCLI4331
designed in the late 1980s and early 1990s when there
was only one AVHRR satellite instrument producing
SSTs. Thus, the spatial scales of the OI were designed
conservatively.
Since the late 1990s, more satellite datasets have be-
come available and there have been frequent compari-
sons of other data and analyses with the OI.v2. These
results have strongly suggested that spatial and tempo-
ral improvements were needed. Perhaps the most con-
vincing study was the work of Chelton and Wentz
(2005), hereafter CW05, which focused on six regions in
the World Ocean with strong SST fronts. In these com-
parisons, data from the Advanced Microwave Scanning
Radiometer (AMSR) on the NASA Earth Observing
System satellite were used. AMSR is the first micro-
wave (MW) sensor that can retrieve SSTs from a sat-
ellite with global coverage. The data record begins in
June 2002. CW05 also used AVHRR data from the
version 5 Pathfinder reanalysis project in the compari-
son and two analyses: the OI.v2 and the National Cen-
ters for Environmental Prediction (NCEP) daily Real
Time Global SST (RTG_SST) analysis (Thiébaux et al.
2003). The RTG_SST analysis is based on the same
data used in the OI.v2. However, the RTG_SST has
been produced daily since 30 January 2001 on a
1
2
° grid,
and it uses smaller spatial error correlation scales than
those used in the OI.v2. (A higher resolution
1
12
° daily
analysis was implemented on 27 September 2005.)
CW05 showed that the gradients in RTG_SST analysis
agreed better with AMSR than the OI.v2. Because the
RTG_SST and OI.v2 use AVHRR and in situ data that
are independent of AMSR, this is strong evidence that
the OI.v2 analysis can be improved even in the 1980s
when only AVHRR data were available.
The objective of this study is to refine the OI.v2
analysis procedure to produce a higher-resolution re-
analysis product dating back to January 1985 and main-
tained operationally in real time. The analysis will be
designed to better resolve features such as the strong
fronts described in CW05. This analysis will be more
useful for hurricane forecasting, fisheries (through bet-
ter location of isotherms and the fish that follow them),
and as a boundary condition for atmospheric models. In
particular the impact of AVHRR and AMSR SST data
will be assessed.
The new analysis that will be developed here is based
on OI. This is partly because of the success of the OI.v2.
However, there are many similar methods. For example
Thiébaux et al. (2003) uses a variational method that
iterates a solution based on steepest descent. Reynolds
et al. (2002) investigated this method and found the
resulting solution to be almost identical to the OI. The
variational method was computationally more efficient.
However, it required some constraints of the error sta-
tistics that were not required for the OI. Kriging is
another technique that is equivalent to the OI, as dis-
cussed by Hock and Jensen (1999). They mention that
kriging and OI were developed for geology and meteo-
rology, respectively, and that the initial papers on the
analysis methods were first published in 1963.
As discussed in CW05, clouds are essentially trans-
parent to MW radiation and AMSR SSTs can be ob-
tained in all conditions free of precipitation. Infrared
measurements can only be obtained in clear-sky condi-
tions, and cloud-contaminated data are often difficult
to identify (e.g., Cayula and Cornillon 1996; Stowe et al.
1999). As shown by CW05, combined daytime and
nighttime MW coverage in 3-day averages is greater
than 95% over most of the World Ocean while IR cov-
erage is less than 25% in cloudy regions. Because of the
resolution and sampling limitations of MW and IR
measurements of SST, a 0.25° latitude/longitude grid
was selected. This choice will simplify comparisons of
analysis products using IR and MW satellite products.
The temporal resolution for the analysis was selected
to be daily. This selection ignores the diurnal cycle,
which cannot be properly resolved using only one polar
orbiting instrument. Furthermore, as discussed in sec-
tion 3 all satellite data are bias adjusted relative to 7
days of in situ data, which further reduces any diurnal
signal. Thus, the OI analysis is a daily average SST that
is bias adjusted using a spatially smoothed 7-day in situ
SST average.
Potential users of satellite data should be aware that
there are now many additional data products and analy-
ses that are operational or under development (Donlon
et al. 2002). Many of these are part of the Global Ocean
Data Assimilation Experiment (GODAE) high-resolu-
tion sea surface temperature pilot project (GHRSST,
more information available online at http://www.ghrsst-
pp.org/, see in particular “Data Access”). These include
estimates of the diurnal cycle and analyses using both
geostationary and polar orbiting satellite data. The
analyses are computed over a variety of regions and
time periods with different spatial and temporal reso-
lutions. Users have a choice of analyses that was never
possible before GHRSST was established.
Many analyses use as many data input files as pos-
sible to obtain the most accurate product at a given
time (Kawai et al. 2006). However, this choice may lead
to abrupt jumps in the resolution of the analyses at
times when new satellite instruments become available
or old instruments are terminated. This nonstationarity
of the mapping error complicates the accuracy and
resolution of the SST for climate variability. To avoid
this, each satellite product should be compared sepa-
5474 JOURNAL OF CLIMATE VOLUME 20
rately before combining them. This is most important
when data are obtained from satellites in very different
orbits such as geostationary versus polar, or from in-
struments with very different resolution and sampling
such as IR and MW.
Anomalies in this paper are computed relative to the
Xue et al. (2003) monthly climatology, which has a base
period of 19712000 and a spatial resolution of 1°. The
finer spatial and temporal resolution required for the
daily OI is computed by linear interpolation.
In the sections that follow, the data used in this ver-
sion of the daily OI will first be discussed. This is fol-
lowed by a short discussion of the OI analysis proce-
dure with error statistics appropriate for the daily OI
analysis. A new satellite bias correction method is then
discussed along with a more complete analysis error
estimate that includes sampling, random, and bias er-
rors. This discussion is followed by detailed analysis
intercomparisons showing progress and problems. The
analyses used in the comparison will be limited to the
analyses presented here and those presented in CW05.
The paper ends with a summary of conclusions and
future plans.
2. Data
The two new daily OI SST products presented in this
study use satellite SST retrievals, SST observations
from ships and buoys, and proxy SSTs generated from
sea ice concentrations. Each of these data sources is
summarized in this section.
a. Satellite SST retrievals
At this time there are a number of different polar and
geostationary satellites that produce SST retrievals. For
the daily OI, AVHRR and AMSR instruments were
selected as the initial set of satellite instruments. They
represent the longest global record of IR and MW re-
trievals.
As described by CW05, AMSR SST retrievals are
made along with several other variables including wind
speed and precipitation. The AMSR SST retrievals
have a footprint size of 56 km and are contaminated
within about 75 km of land or ice and during precipi-
tation events. The primary advantage of AMSR data is
the near-all-weather measurement capability. Except in
the intertropical convergence zone (ITCZ) where pre-
cipitation is persistent, only a few percent of MW SSTs
are lost due to precipitation contamination. AMSR
data, version 5, are obtained from Remote Sensing Sys-
tems as twice daily gridded averages on a 0.25°grid
(more information available online at http://www.ssmi.
com/amsr/amsr_browse.html).
In the OI.v1 and OI.v2 analyses, an operational
AVHRR product was used. Details on the algorithm
can be found in May et al. (1998): only a brief sketch is
presented here. The biggest challenge in retrieving SST
from an IR instrument is the previously mentioned
cloud detection problem. Once clouds have been elimi-
nated, the SST retrieval algorithm is designed to mini-
mize the effects of atmospheric water vapor using two
or three IR channels. The SST algorithms are tuned
using regression of SST against quality-controlled buoy
data. This procedure converts the retrieval of the tem-
perature of the skin(roughly a micron in depth) to a
bulk(roughly 0.5 m in depth) SST. To make this
procedure as stable as possible, the tuning procedure is
done globally with several weeks of data. In this pro-
cedure it is important that the SST range of the buoy
and satellite data be roughly similar. If, for example,
buoy SSTs were not available above 20°C, then tuned
satellite retrievals above 20°C would not be properly
corrected (Emery et al. 2001). Furthermore, if the sat-
ellite SST retrievals are partially contaminated by
clouds, they have a negative bias because cloud tem-
peratures are nearly always colder than the SSTs. Nega-
tive biases can also be caused by atmospheric aerosols,
especially stratospheric aerosols from large volcanic
eruptions (see Reynolds et al. 1989; Reynolds 1993). In
addition, biases of either sign can be due to other prob-
lems including instrument design and instrument aging.
AVHRR instruments with multichannel capabilities
have been available on NOAA polar orbiters since No-
vember 1981. However, the data from the Pathfinder
AVHRR reanalysis project begins in January 1985.
1
The Pathfinder version 5 AVHRR data are based on
one satellite instrument with twice-daily gridded aver-
ages on a 4.6-km grid (more information available on-
line at http://pathfinder.nodc.noaa.gov). These data are
produced by the University of Miami and the NOAA/
National Oceanographic Data Center, and represent an
improvement over the previously available Pathfinder
version 4 AVHRR data (Kilpatrick et al. 2001). Path-
finder data have the potential of being better than the
operational product because a reanalysis allows correc-
tions to the AVHRR dataset in a delayed mode. Thus,
for example, correction of the operational satellite re-
trievals following a volcanic eruption would be delayed
by the response time to modify the algorithm.
1
Five-channel AVHRR NOAA-7 data began in November
1981 and ended in January 1985. Pathfinder did not process
NOAA-7 data because buoy data, which are used to tune the
algorithm, were sparse during this time period. Experiments are
being conducted now, however, to extend the Pathfinder time
series to include these early years.
15 NOVEMBER 2007 REYNOLDS ET AL. 5475
To examine differences between Pathfinder and op-
erational SST retrievals, the zonal monthly averages of
the satellite minus in situ SST anomaly differences
were computed on a 1°latitude grid for both AVHRR
Pathfinder and AVHRR operational products. (Details
on the in situ data follow in section 2b.) Figure 1 shows
the nighttime and daytime satellite differences with re-
spect to all in situ data (day and night combined). The
same in situ reference is used in all panels. Pathfinder
nighttime and daytime differences are less variable over
time than the corresponding operational daytime and
nighttime differences. There are also clear seasonal
cycles in the northern midlatitudes where the daytime
operational product is warmer than the in situ data in
summer and both the nighttime and daytime Pathfinder
products are cooler in winter. There are some other
large operational differences near the beginning of 1988
and 2001 that may be due to instrumental problems that
FIG. 1. Zonal-averaged differences of AVHRR data products minus in situ data. (top to
bottom) The AVHRR data products are operational night, Pathfinder night, operational day,
and Pathfinder day. Zonal monthly averaged satellite and in situ data anomalies are generated
on a 1°latitude grid and then differenced. Pathfinder AVHRR was selected for the OI.
5476 JOURNAL OF CLIMATE VOLUME 20
Fig 1 live 4/C
occurred near the end of the lifetimes of the NOAA-9
and NOAA-14 instruments, respectively. In addition,
negative biases related to Mt. Pinatubo (199192) are
less extensive in the Pathfinder differences. Unfortu-
nately, Pathfinder does have a nighttime residual nega-
tive bias, especially in the Tropics. A spatial map of the
differences (as will be shown later) indicates that these
differences occur over regions that are generally cloudy
[e.g., the ITCZ and the South Pacific convergence zone
(SPCZ)]. These differences occur even though only
Pathfinder data with the lowest errors (quality control
flag 7) were used.
It is useful to also examine the data coverage of
AMSR and the two AVHRR versions. Figure 2 shows
the percentage of daily oceanic
1
4
°grid boxes that have
either daytime or nighttime observations for 2003. The
results for AVHRR use the same satellite instrument.
For the AVHRR, the results show that the average day
and night operational AVHRR coverage is 8%, while
the day and night Pathfinder coverage is 13% and 12%,
respectively. (If day and night are combined, the op-
erational and Pathfinder AVHRR coverage increases
to 16% and 25%, respectively.) Because this is the same
sensor, the different coverage is evidently due to dif-
ferent cloud masking. The tropical negative biases in
Pathfinder SSTs (Fig. 1) may therefore be an indication
of cloud detection errors. Because the overall Path-
finder AVHRR minus in situ month-to-month variabil-
ity is lower than the operational AVHRR minus in situ
variability, Pathfinder will be used in the daily OI when
available. As Pathfinder processing is not done in real
time, the operational AVHRR product will be used
for the most recent data period (presently beginning
1 January 2006). This is not an ideal solution. However,
the bias correction, as discussed in the next section, will
take care of most large-scale biases on temporal scales
of 7 days or longer. During the operational AVHRR
record, biases occurred as satellite instruments failed or
as the atmosphere changed (e.g., due to addition of
volcanic aerosols). Thus, the reanalysis of Pathfinder
AVHRR is a better choice. In addition, the bias cor-
rection with respect to the in situ data (discussed
in section 3b) eliminates any transition between
Pathfinder and operational AVHRR except south of
40°–50°S where in situ data are sparse. The potential
bias error south of 40°–50°S is defined in section 3b and
demonstrated through analysis intercomparisons in sec-
tion 4. Note that the ocean grid boxes include coastal
regions, the Great Lakes, and the Caspian Sea, as well
as Arctic and Antarctic regions that may be covered by
sea ice. If ocean regions poleward of 70°latitude are
excluded, the percentages given above and shown in
Fig. 2 increase by a factor of 1.2.
AMSR coverage has a clear advantage over AVHRR
(Fig. 2), as expected. AMSR raises the daily coverage
for day and night to 40% and 46%, respectively. (If day
and night are combined, the average AMSR coverage
increases to 86%.) Note that the daytime AMSR has a
gradual decrease in observations from April through
August. This occurs every year due to contamination of
measurements by daytime sun glint between 50°and
10°S (C. Gentemann 2006, personal communication).
Also there are periods where AMSR data are missing.
The largest one occurred between 30 October and 5
November 2003 due to a spacecraft problem during
which none of the onboard sensors were operational.
This reduction of data results in a noticeable drop in the
daily OI gradient, which will be discussed later.
For the analyses in section 4, daytime AVHRR,
nighttime AVHRR, daytime AMSR, and nighttime
AMSR were separately averaged onto a
1
4
°grid. Sepa-
rate analyses will be produced using AVHHR alone,
FIG. 2. Daily percentage of
1
4
°ocean grid boxes with day and
nighttime satellite data. The types of data are Pathfinder
AVHRR, operational AVHRR, and AMSR. The maximum num-
ber of ocean boxes is 691 454. The AMSR data were completely
missing from 30 Oct to 5 Nov 2003.
15 NOVEMBER 2007 REYNOLDS ET AL. 5477
AMSR alone, and AVHRR and AMSR combined. All
analyses use in situ data and proxy estimates of SSTs
obtained from sea ice as discussed below.
b. In situ data
The in situ SST data are from observations from
ships and buoys (both moored and drifting) obtained
from the International Comprehensive OceanAtmo-
sphere Dataset (ICOADS: e.g., Worley et al. 2005).
Most ship observations in the 19852006 period were
made from insulated buckets, hull contact sensors, and
engine condenser intakes at depths of one to several
meters. Although selected SST observations can be
very accurate (see Kent et al. 1999; Kent and Taylor
2006), typical rms errors of individual observations
from ships are larger than 1°C and may have biases of
a few tenths of a degree Celsius. SST observations from
drifting and moored buoys are typically made by a ther-
mistor or hull contact sensor and usually are obtained
in real time by satellites. Although the accuracy of the
buoy SST observations varies, the random error is usu-
ally smaller than 0.5°C, which is significantly smaller
than ship SST errors.
c. Sea ice to SST conversion algorithms
In situ and satellite observations tend to be sparse in
the marginal ice zone (MIZ). Thus, as was done in the
OI.v2, sea ice data were used to obtain proxy estimates
of SST. Operationally the OI.v2 uses real-time sea ice
concentrations generated from microwave satellite data
by Grumbine (1996) with delayed sea ice concentra-
tions by Cavalieri et al. (1999). The Grumbine product
has been gathered from different sources and has not
been reanalyzed to produce a consistent long-term
dataset. This problem can be clearly seen in Fig. 3,
which compares Northern and Southern Hemisphere
coverage for the two sets of sea ice data. In particular,
the Southern Hemisphere shows a seasonal amplitude
change after 1991 with several temporary jumps in
199596. [R. W. Grumbine (2006, personal communi-
cation) is planning to correct this]. For the daily OI
presented in this study, the Cavalieri sea ice is used
through December 2004 and the Grumbine sea ice is
used after 2004. Use of one consistent product available
in real time would be preferable to avoid potential in-
consistencies between products such as the difference
in the Northern Hemisphere winter maxima (Fig. 3). At
this time, however, a consistent real-time, long-term set
does not exist.
In the OI.v2 based on Rayner et al. (2003) a qua-
dratic relationship was defined between sea ice concen-
tration and SST:
T
I
aI
2
bI cI I
0
,1
where T
I
is the simulated SST, Iis the ice concentration
fraction, which varies from 0 (0%) to 1 (100%), and I
0
is the minimum value of Iused to simulate SSTs. The
coefficients are assumed to be locally constant by
month and by region. A simpler linear version
T
I
bIc,II
0
2
is also considered here. The coefficients a,b,c,b, and
cin the empirical relationships (1) and (2) are deter-
mined by regression for 30°wide longitude bands (or
sectors) for the Northern and Southern Hemispheres.
For both equations the coefficients are constrained so
that T
I
is equal to the freezing point of water (1.8°C
for seawater and 0°C for freshwater) for ice concentra-
tions of I1.
In appendix A, (1) and (2) are evaluated. The pro-
cedure is carried out by determining the coefficients for
a 10-yr dependent period and then evaluating the rms
and bias differences between the simulated and actual
FIG. 3. Daily percentage of
1
4
°ocean grid boxes with sea ice
coverage from two products: Cavalieri et al. (1999) and Grumbine
(1996). The period is 1 Jan 19901 Jan 1997. Note the irregulari-
ties in the Grumbine dataset.
5478 JOURNAL OF CLIMATE VOLUME 20
SSTs for a 10-yr independent period. The rms differ-
ences increased in both fits with decreasing ice concen-
tration. In addition, the absolute biases were typically
smaller for the linear fit for ice concentrations 0.5 and
smaller for the quadratic fit for ice concentrations 0.5.
For some quadratic fits (not shown) data were sparse
and the quadratic fit occasionally generated SSTs that
were unstable at low sea ice concentrations. As a con-
servative approach, I
o
was set to 0.5 and the linear fit
(2) was selected over the quadratic fit. This selec-
tion avoided the problem of the unstable quadratic
fit. It seemed better to let the OI fill in the values
between the actual SST data and the simulated sea ice
for I0.5, rather than simulating SSTs where rms
differences were large. Thus, SSTs were simulated from
ice concentrations for I0.5 using (2): no SSTs were
simulated for I0.5.
For actual use in the daily OI, the coefficients were
recomputed for the entire 20-yr period (19852004).
The sea ice data indicated the presence of summer sea
ice in the Great Lakes in 2003. This resulted in sea-ice-
simulated SSTs that led to 18°C anomalies in Lake
Ontario. The sea ice algorithms were not designed for
low salinity water (D. J. Cavalieri 2006, personal com-
munication). Simulated SSTs for sea ice were therefore
not used in the Baltic nor in the Great Lakes. (Sea ice
concentrations are not produced regularly for the Cas-
pian Sea, so no ice simulated SSTs were generated
there.) In addition, occasional 1-day noise events were
noted in both the Cavalieri and Grumbine ice fields.
During these events, the ice concentrations increased
dramatically, especially in coastal regions, resulting in
spikes in the daily OI from the sea-ice-simulated SSTs.
To eliminate this problem, a 7-day median filter was
applied temporally to all daily ice fields, and the simu-
lated SSTs were computed from the median smoothed
sea ice data.
3. Analysis
The OI.v2 analysis includes a preliminary correction
of the AVHRR satellite data with respect to the in situ
data before they are used in the OI (Reynolds et al.
2002). This initial step is necessary because the OI
method assumes that the data do not contain long-term
biases. For comparisons, the daily OI is processed with
and without this bias correction. In sections 3ac, the
OI procedure is discussed first, followed by the satellite
bias correction procedure.
a. The OI analysis
The OI analysis is performed on a regular grid using
irregularly spaced data. The analysis is formed by a
weighted sum of the data, using the OI linear weights,
w
ik
, determined by regression. In this section, the indi-
ces iand jwill be used for data while kwill be used for
analysis grid points. The relationship can be expressed
(see Reynolds and Smith 1994, for details) as
r
k
i1
N
w
ik
q
i
,3
where q
i
are the SST data values, Nis the number of
data values, r
k
is the analyzed SST, and normally qand
rare differences from a first-guess reference system,
which is defined here as the analysis from the previous
time step. Thus, in the daily OI, qand rare the SST
data and analysis increments, defined as the difference
from the analysis at the previous time step.
The weights are formally defined following Reynolds
and Smith (1994). Here the ensemble average of the
analysis correlation error
i
j
is assumed Gaussian,
expressed as
i
j
exp
x
i
x
j
2
x
2
y
i
y
j
2
y
2
.4
The variables xand yare the zonal and meridional data
and analysis locations, and
x
and
y
are the zonal and
meridional spatial scales, discussed below. The weights
can then be defined (following Reynolds and Smith
1994) by
i1
N
i
j
i
2
ij
w
ik
j
k
,5
where
i
is the noise-to-signal standard deviation ratio,
which also needs to be determined. The ensemble av-
erages of the data errors are assumed uncorrelated be-
tween different observations. Thus, the data correlation
error is
ij
1 for ijand
ij
0, otherwise.
It is important to note that the actual SSTs (data and
analysis) only appear in (3). The remaining equations
to determine the weights depend only on the distance
via (4) and noise-to-signal ratios for the available SST
data. For each analysis grid point,
i
,
x
, and
y
are
assumed locally constant and the set of equations are
solved to determine the weights and the analyzed SST,
r
k
. Spatial functions are defined for each of these quan-
tities with different fields of
i
for each type of data.
Presently, the data types are ships, buoys, SST simu-
lated for sea ice, and day and night satellite data for
each instrument.
The set of linear equations defined by (5) is solved at
each grid point, k. To reduce computing time, only data
points near the analyzed grid point are used. This ap-
proach is reasonable because (4) approaches zero with
15 NOVEMBER 2007 REYNOLDS ET AL. 5479
increasing data-to-gridpoint distance. Furthermore, the
solution of the set of linear equations becomes more
difficult to solve when data points approach each other
because the rows defining
i
j
典⫹
2
i
ij
become closer
to each other, leading to a degenerate solution (i.e., the
determinant approaches zero). To avoid this possibility,
each type of observation within a grid box is averaged
into a superobservation for the grid box, which is as-
sumed to be at the center of the box. Next, all super-
observations within each box are combined. The com-
bination is carried out using a simplified optimum av-
eraging technique (Kagan 1979) assuming that the local
error correlations within each box can be approximated
as 1. This method performs an optimal combination of
all superobservations values, q
i
, and the super noise-to-
signal ratios,
i
, within a grid box into a combined ob-
servation and reduced combined noise-to-signal ratio
(see appendix B for details). The combined observa-
tions and noise-to-signal ratios are the variables actu-
ally used in (3)(5). This method is a two step process,
an OA followed by an OI, which approximates an
OI-only procedure. However, the two step process is
computationally more efficient.
To solve (5), a box centered on each grid point was
defined that contains all the observations to be used for
that grid point. Recall that the OA method will com-
bine all observations within a grid box, 0.25°. Thus, Nis
not only the number of observations; Nis also the num-
ber of grid boxes with data. The box size is defined to
be R
max
and the maximum number of observations was
limited to a specified value of N,N
max
. Next, rough
weights were computed for the special case where off-
diagonal elements in (5) were zero. In that case, the
rough weights would be w
jk
⫽具
j
k
/(1 ⫹␧
2
i
). The
rough weights were ordered by decreasing magnitude
and only data points corresponding to the largest ones
were selected such that NN
max
. The algorithm to
solve (5) includes a parameter to show when the deter-
minate is close to zero. In that case, N
max
is reduced for
that grid point and a reduced set of observations is
selected using the ordered rough weights. For the daily
OI, R
max
was set to 400 km and N
max
to 22.
It is necessary to determine the spatial correlation
scales and noise-to-signal ratios. These scales are spe-
cific to the first-guess reference system used to define q
and rin (3) and here are based on the previous daysOI
as first guess. The scales computed for the weekly OI.v1
and Oi.v2 could not therefore be used. Following Rey-
nolds and Smith (1994), spatial lagged correlations
where computed zonally and meridionally for each grid
point. Fitting procedures yield average
x
and
y
for
AMSR and AVHRR and for each type of data. For
operational AVHRR, the day and night algorithms are
different. However, the day and night algorithms are
the same for AMSR and Pathfinder AVHRR. Thus, for
each satellite instrument the same values of were used
for both day and night.
The results of these statistical estimates are summa-
rized in Table 1 for the average values (60°S60°N) for
both the OI.v1 and the new daily OI. (The OI.v2 used
values that were slightly modified from those of the
OI.v1.) The noise-to-signal ratios are much smaller for
the daily OI than the OI.v1. The biggest change occurs
in the spatial correlation scales, which are greatly re-
duced for the daily OI (Fig. 4). In the Oi.v2, the aver-
age zonal and meridional spatial scales were 850 and
615 km, respectively. Note that the overall zonal and
meridional scales in Fig. 4 are similar and could be
made isotropic. These scales vary somewhat geographi-
cally: they are larger in the Tropics (150200 km) than
at higher latitudes (100150 km) and smallest (50100
km) primarily in the regions of western boundary cur-
rents. The much smaller correlation scales for the new
daily OI compared to those used for the OI.v1 and
OI.v2 allow much finer spatial resolution of the SST
field.
The choice of the spatial error scales,
, partially de-
termines the spatial smoothing. If
is equal to the size
of the grid box, then each grid box is analyzed indepen-
dently. This would make the analysis very noisy be-
cause many grid boxes (see Fig. 2) would have no data
prior to the availability of AMSR SST data. However,
if
were very large (e.g., 1000 km) many of the finer
gradient details would be reduced, as there are in the
OI.v2.
To illustrate the impact of
, the daily OI analysis was
produced using the scales in Fig. 4 and using a constant
scale of
50 km. The analyses were run using
AVHRR-only and AMSR and AVHRR combined
data. The SST anomalies are shown for 1 July 2003 in
Fig. 5. Because the differences are relatively small, the
TABLE 1. Noise-to-signal standard deviation ratios and spatial
correlation scales as used in the weekly OI.v1 and in the high-
resolution daily OI.
Variable OI.v1 Daily OI
ship 3.90 1.94
buoy 1.50 0.50
ice 1.00 0.50
day AVHRR 1.46 0.50
night AVHRR 0.88 0.50
day AMSR —– 0.35
night AMSR —– 0.35
zonal 859 km 151 km
meridional 608 km 155 km
5480 JOURNAL OF CLIMATE VOLUME 20
anomalies are shown for part of the Southern Hemi-
sphere. This region and date were selected to empha-
size the impact of winter clouds on the analyses. The
results show that the difference in
makes almost no
difference between the two AMSR and AVHRR analy-
ses. This is because most grid points have AMSR data.
Thus, the N
max
limit of 22 grid points is more important
than the change in
. If the two AMSR and AVHRR
analyses are now compared with the AVHRR-only
analysis with variable
, the AVHRR-only anomalies
appear similar but are a little weaker and smoother
especially in the Falkland Current region near 40°S,
50°W. This weakening of the anomalies is due to the
limited AVHRR data compared to AMSR. However,
the AVHRR-only anomalies using the constant
50
km are reduced even more, especially in the Falkland
Current region. In this region AVHRR retrievals tend
to be missing due to cloud cover. Here the value of
is
more important than N
max
. In the AVHRR-only analy-
sis with constant
, the smaller values of
limit spatial
smoothing, which reduces the large-scale impact of
AVHRR data.
FIG. 4. Zonal and meridional error correlation scales used in the daily OI. The smallest
scales are in the western boundary current regions; the largest are in the Tropics. Missing data
limited computations south of 60°S and north of 70°N; these values were filled by the southern
and northern midlatitude averages, respectively.
15 NOVEMBER 2007 REYNOLDS ET AL. 5481
Fig 4 live 4/C
The final requirement is to determine the OI random
and sampling error, E
2
k
. (The bias error will be com-
puted in the bias correction step that follows.) It is
determined following Reynolds and Smith (1994) for
the OI.v1:
E
k
2
V
k
2
1
i1
N
w
ik
i
k
,6
where V
2
k
is the AVHRR OI analysis increment vari-
ance. [Note that the final subscript in (6) has been cor-
rected; there was a typographical error in the equiva-
lent equation in Reynolds and Smith (1994).] The ex-
pected random and sampling error defined by (6)
reduces V
2
k
by the observations used in the OI. The
standard deviation, V
k
, (see Fig. 6) is largest in western
boundary current regions and smallest in the subtropi-
cal convergence areas and at high latitudes.
b. The bias correction
In the OI.v1 and OI.v2, satellite biases are corrected
relative to the in situ data using Poissons equation
(
2
⌽⫽
), where
⫽ⵜ
2
,is the initial satellite field,
and is the corrected satellite field. Here is set equal
to the value of the in situ field, T, wherever Tis con-
sidered sufficiently accurate. All variables were defined
weekly on a 2°spatial grid and Twas defined to be of
sufficient accuracy when the number of in situ gridded
observations during the week was at least five. This
method determined at each time step. A problem
with this method is that the threshold of five for suffi-
cient accuracy of Tis arbitrary, and is either deter-
mined by Poissons equation or set to T. This makes the
corrected satellite field noisy in both time and space.
This was better tolerated in the weekly OI than in a
higher-resolution product such as the daily OI devel-
oped in this study.
An alternative method would be to use empirical or-
thogonal functions (EOFs) to fill in the sparse in situ
data (e.g., see Smith et al. 1996). As described there, the
spatial modes S
i
(x) (of order i) are determined from a
SST analysis for a well-observed period. These modes
are then fit to the observed data for each time tto
FIG. 5. Daily OI anomalies for 1 Jul 2003. (left) The bias-corrected AVHRR-only daily OI. (right) The bias-corrected
AMSR and AVHRR combined daily OI. (top) The variable correlation scales,
, shown in Fig. 4, and (bottom) a constant
correlation scale of
50 km.
5482 JOURNAL OF CLIMATE VOLUME 20
Fig 5 live 4/C
determine the weights W
i
(t) of each mode. The problem
with this procedure (Smith et al. 1996) is that data tends
to become sparser in the early part of the record. Thus,
a mode can be generated with artificially large weights
if the data coverage is poor for that particular mode.
Smith et al. (1998) developed a method that objectively
determines which modes can be supported by any des-
ignated data coverage. However, this method may fail if
the mode has large spatial teleconnections. For ex-
ample, if the magnitude of S
i
(x) is large in both the
Atlantic and the Pacific, the mode could be adequately
sampled in Atlantic but not in the Pacific. If this prob-
lem occurred, the Pacific part of the mode would be
extrapolated and may not be accurate. Because the
EOF method demands orthogonality between modes,
higher order modes tend to be spatial complex over
large regions. Rotated modes are generally more local-
ized and more closely resemble observed structures
than unrotated modes (Richman 1986). Empirical or-
thogonal teleconnection (EOT) functions (Van den
Dool et al. 2000) also produce modes with localized
spatial functions. Furthermore, as discussed below,
EOTs can be tuned to eliminate large teleconnections.
A new bias correction method was designed using
EOTs. These functions were determined for a dataset,
(x,t), a function of space and time, by finding the
location with the largest spatial covariance with respect
to all the other points (see Van den Dool et al. 2000 for
details). The time series at that point is defined as T
1
(t).
By regression, the corresponding spatial function, X
1
(x),
is then computed. The product of X
1
(x)T
1
(t) is sub-
tracted from (x,t) and the process is repeated. This
yields a set of modes such that (x,t)⬇兺
M
i1
X
i
(x)T
i
(t),
where Mis the maximum number of modes.
Smith and Reynolds (2003) used the OI.v2 SST
anomalies to define (x,t) and determined a set of
X
i
(x) spatial modes, where Mwas set to 130. The num-
ber of modes, M, and the spatial functions, X
i
(x), was
determined by Smith and Reynolds (2004). The value
was of Mwas selected subjectively to account for most
of the global anomaly variations. Because of the way
the modes were selected, the higher order modes tend
to be spatially more coherent than unrotated EOFs.
This can be seen in Fig. 7 where three modes (1, 4, and
100) are shown. Note that the spatial scale of mode 100
is roughly similar to the other modes. The major ad-
vantage of EOTs is that modes are determined one at a
time. Thus, the individual modes can be tapered so that
the maximum spatial extent of the mode is limited.
Smith and Reynolds used linear tapering to limit the
maximum extent of their functions to 800 km to avoid
large spatial teleconnections.
To avoid situations in which a mode is only sampled
outside of its center of action, Smith and Reynolds
(2003) defined a mode selection criteria, C
i
, given by
C
i
x
xX
x
2
x
x
x
X
x
2
x
x,7
FIG. 6. Analysis increment standard deviation for 19852005 for the AVHRR-only daily OI.
The analysis increment is the analysis minus the first guess. The standard deviation is assumed
to be the OI sampling and random error if there are no observations.
15 NOVEMBER 2007 REYNOLDS ET AL. 5483
Fig 6 live 4/C
where
(x) is 1, if there are observations at grid location
x, or 0, otherwise, and
(x) is the cosine weighting of
the area associated with each 2°grid box. If C
i
is below
a critical threshold, the data are considered to be inad-
equate and the mode is not used. Smith and Reynolds
carried out cross-validation studies and determined that
this critical threshold must be at least 15% for adequate
sampling. The modes that satisfy this critical sampling
test are used and are fit to in situ SST data as described
in Smith et al. (1996) to define the anomalies; other-
wise, the modes are not used.
The EOT spatial modes of SST anomalies were used
to bias correct the satellite data. In this procedure seven
days of in situ data and satellite data were converted
into anomalies and then separately averaged onto a 2°
grid. Because it is important to use the same modes for
both sets, modes were only selected if C
i
for both sets
was greater than 15%. In almost all cases, modes like
mode 4 (Fig. 7) were not used. Mode 4 could be rep-
resented by the satellite data but not by the in situ data
because of the lack the in situ data there. (If, for ex-
ample, mode 4 were used, the large-scale in situ
anomaly from the mode would be zero, and the large-
scale smoothed satellite anomaly would be treated as a
bias and eliminated.) Next, the temporal factors were
determined for the modes used for each set of anoma-
lies. The difference between the two reconstructed
EOT fitted fields was then computed as the bias adjust-
ment. The adjustment was interpolated to the OI
1
4
°
grid and used to correct each satellite superobservation.
This method was applied separately for day and night
and for each satellite instrument. The corrected satel-
lite data were then used in the daily OI.
The EOT bias adjustment method has the additional
important advantage that it can be used to define an
estimate of the bias error. This is done by assuming that
the satellite bias error is related to satellite EOT modes
, which could not be corrected by the in situ data plus a
residual. The individual EOT bias variance, E
2
Bj
,is
E
Bj
2
i1
M
ij
X
i
2
x
i
2
,8
where jis an index for the number of satellite sources
used. The factor
ij
is 1 if the mode was not adequately
sampled by either the satellite or the in situ data; oth-
erwise, it is 0. The bias variance associated with each
mode is
2
i
, which was estimated by computing the sat-
ellite reconstructed anomaly modes for 19852005 and
then determining the variance of each mode. The
anomaly variance was found to be similar to the bias
variance for those modes adequately sampled, allowing
the bias variance of those modes to be computed. The
values of
2
i
generally decrease with increasing value of
the index i. Equation (8) is probably an overestimate of
the EOT bias error because the modes are almost, but
not completely, orthogonal. Thus, the nonorthogonal
overlap of modes can count the variance in some re-
gions more than once, giving an overestimate.
The total bias error E
2
B
can be expressed as
E
B
2
E
B0
2
1
mn
j1
N
E
Bj
2
,9
where nis the total number of sets of satellite data used
for which biases are estimated by (8), mis the number
FIG. 7. Empirical orthogonal teleconnection spatial modes:
modes 1, 4, and 100. The EOT method used here avoids basin-
scale teleconnections.
5484 JOURNAL OF CLIMATE VOLUME 20
Fig 7 live 4/C
of independent satellite instruments, and E
2
B0
is the re-
sidual error variance for the bias not resolved by the
modes. The value of E
2
B0
was set equal to 0.01°C
2
. This
value was estimated by examining residual differences
between AMSR and AVHRR and by the residual dif-
ference between ships and buoys.
In (9), day and night observations from the same
satellite have been assumed to be dependent data,
while observations from different satellite are indepen-
dent. Thus, if just AVHRR day and AVHRR night are
used, m1 and 2, and E
2
Bj
from the two satellite
sources is simply averaged. However, if AMSR day,
AMSR night, AVHRR day, and AVHRR night are
used, m2, n4, and E
2
Bj
from all four satellite
sources is averaged and then divided by 2. In this case
the average bias is reduced because two independent
satellite sources are used. Note that the modes defined
by
ij
in (8) may be different at the same time step
because the satellite data distribution can vary even
though the in situ distribution is the same. However, for
the 7-day period used for the bias adjustment, all modes
can usually be expressed by the satellite data alone;
thus,
ij
is usually the same.
The total error variance assumes that the random
and sampling error and the bias error are independent
and is therefore simply the sum of E
2
from (6) and E
2
B
from (9) at each grid point. The total error (standard
deviation) is shown in Fig. 8. The large scale patterns
south of 40°S are primarily due to the bias errors due to
limited in situ data. The bias errors are lower for
AMSR and AVHRR than for AVHRR only because
two independent satellite instruments were used in the
AMSR and AVHRR OI. The random and sampling
errors are indicated in the figure by north/south bands
in the error magnitude. Here the higher values occur in
regions between the satellite swaths. In the regions with
data, the random and sampling errors are very small
because of the dense satellite coverage. The sampling
and random errors are even lower when AMSR is
added to AVHRR data, as also shown in Fig. 8.
c. The computation
With the EOT bias and OI steps complete, the daily
OI was run with EOT bias correction using Pathfinder
AVHRR data (3 January 198531 December 2005) and
operational AVHRR data (1 January 2006 to present).
The second daily OI product used the AVHRR data
plus the AMSR data, which began in June 2002. These
two daily OI products are designated as the daily OI,
version 1. (The version number is not continued from
the weekly OI because the daily OI has greatly ex-
panded temporal and spatial resolution compared to
the weekly product.) Other special products were also
run for the comparisons that follow. These include the
above analyses using uncorrected satellite data as well
as a special AMSR-only analysis.
4. Results
In this section, the new daily OI analyses products
are intercompared with themselves and other products.
a. SST gradient intercomparisons
The first step was to recompute the SSTs and SST
gradients for the six regions considered by CW05 with
the addition of the daily OI using AVHRR and AMSR
and AVHRR. Because gradients are computed from
spatial differences, they are useful in showing how well
analyses can resolve strong coherent features.
Figure 9 shows the magnitude of the 3-day mean Gulf
Stream SST gradients centered on 1 October 2003.
AVHRR data show high-resolution details in cloud-
free regions, although the coverage for AVHRR data is
less than half of the possible number of ocean grid
points. AMSR data show smoother details because of
the coarser footprint but with the expected better cov-
erage except near land as AMSR SSTs cannot be re-
trieved within 75 km of land. The analyses fill in the
missing AMSR and AVHRR data gaps with different
smoothing. In particular, note the region of missing
AMSR data due to precipitation contamination be-
tween 35°and 45°N along 60°W. Here the AMSR and
AVHRR daily OI correctly fills in the missing data.
This procedure is not always done correctly, as will be
shown below. In the comparison, the OI.v2 is heavily
smoothed, as reported by CW05. The RTG_SST and
AVHRR OI are similar, showing much more detail.
Here the RTG_SST is slightly smoother than the
AVHRR OI. The highest resolution is obtained by the
AMSR and AVHRR OI, which is similar to the AMSR
data in most of the offshore regions. The improvement
in the AMSR and AVHRR analysis resolution is due to
the better AMSR coverage compared to AVHRR. The
results for other western boundary currents (e.g., the
Agulhas, the Kuroshio, and Falkland Current regions,
not shown) show the same rankings of gradients for the
SST products and data.
The mean SST gradient is shown for the tropical east-
ern Pacific region for the 3-day period centered on
28 May 2003 (Fig. 10). The overall analysis gradient
ranking is again the same. In this case, the AVHRR-
only OI gradient resolution is almost as good as the
AMSRAVHRR OI. This is because the overall per-
cent of AVHRR oceanic data coverage in Fig. 10 is
larger than the AVHRR coverage in Fig. 9.
15 NOVEMBER 2007 REYNOLDS ET AL. 5485
At first it may seem surprising that the OI AVHRR
gradients are as accurate as is shown, given the rela-
tively sparse availability of AVHRR data due to cloud
cover. Examination of the daily OI over time using
AMSR data shows that most of the SST gradient fea-
tures in western boundary currents vary relatively
slowly. Because of the persistence built into the OI
procedure by using the previous analysis as the first
guess for each new analysis, the daily OI using
AVHRR alone does a credible job of determining
much of the signal with only limited observations, even
in winter. However, in some high-gradient regions, such
as the eastern tropical Pacific region (Fig. 10), the SST
gradient patterns vary on shorter time scales and are
not well resolved in the AVHRR-only OI during peri-
ods of persistent cloud cover.
FIG. 8. Total error (standard deviation) for 1 Jan 2003 for (top) the AVHRR-only and
(bottom) AMSR and AVHRR combined analyses. The total error is derived from the ran-
dom, sampling, and bias error (see text).
5486 JOURNAL OF CLIMATE VOLUME 20
Fig 8 live 4/C
To investigate the gradients over time, gradient indi-
ces were computed. The index for the Gulf Stream was
computed from the daily magnitude of the SST gradi-
ents from June 2002 through December 2004 for three
daily OI runs: AVHRR-only, AMSR-only, and
AMSRAVHRR, and for the OI.v2 and RTG_SST
analyses. For the Gulf Stream, the maximum gradient
value was determined along lines of longitudes from 70°
to 40°W at intervals of 0.25°between 35°and 50°N;
these maximum values were then averaged over longi-
tude and daily indices created (Fig. 11). The AMSR-
only OI is not plotted because the differences between
the AMSR and AMSR and AVHRR combined OI are
very small and could not be distinguished. The results
show that the OI.v2 SST gradients are consistently
much weaker than the others, as expected (Fig. 9). Also
as expected, the AVHRR-only and the RTG_SST in-
dices are generally quite similar. Perhaps the most in-
FIG. 9. Three-day averages of SST gradient magnitudes for analyses and data centered on 1 Oct 2003 for the Gulf
Stream region. The data products are AVHRR and AMSR. The analyses are OI.v2, RTG_SST, and the daily OI for
AVHRR-only and AMSR and AVHRR. The analysis gradients are weakest for the OI.v2 and strongest for the daily OI
using AMSR and AVHRR.
15 NOVEMBER 2007 REYNOLDS ET AL. 5487
Fig 9 live 4/C
teresting difference occurs between the AVHRR-only
and AMSR and AVHRR gradient indices. These indi-
ces are similar in August and September, with the
AMSR and AVHRR gradient index only slightly stron-
ger. The differences gradually increase from September
to roughly March and then decrease again to the Au-
gust minima. In winter, the AMSR and AVHRR gra-
dient index is almost double the AVHRR-only index.
The results show that the seasonal cycle of the index is
underrepresented by AVHRR alone because cloud
cover tends to be more pervasive in winter.
b. AMSR limitations
The benefits of the improved sampling from the
near-all-weather measurement capability for MW are
clear. Of course every satellite instrument has limita-
tions, and it is useful to show a problem with the AMSR
data. One such problem is shown (Fig. 12) for the daily
OI AVHRR and AMSR and AVHRR combined
analyses and for AMSR data. The top panels show the
SST and the bottom the gradients for a 3-day-average
centered on 9 February 2003. There is a region of miss-
ing AMSR data near 25°N, 130°W. Because of the
3-day average and the irregular shape, the pattern is
most likely due to precipitation, which contaminates
the AMSR SST retrievals. The AMSR and AVHRR
OI analysis fills in the missing data. In this case,
AVHRR data cannot compensate for the missing
AMSR data because of the associated cloud cover. The
problem is most evident in the SST gradient panels
because the spatial derivatives magnify the edge ef-
fectsof the precipitation contamination. To correct
this problem, AMSR data near the edge of regions with
precipitation contamination data should be excluded in
future versions of the OI.
FIG. 10. Three-day average of SST gradient magnitudes for analyses and data centered on 28 May 2003 for the eastern Tropical
Pacific; otherwise as in Fig. 9.
5488 JOURNAL OF CLIMATE VOLUME 20
Fig 10 live 4/C
c. Day-to-day differences
Both versions of the daily OI show day-to-day differ-
ences. These differences are especially evident in re-
gions of high variability (e.g., the Gulf Stream region in
winter). Figure 13 shows one day of AMSR and
AVHRR day and night data anomalies on a 0.25°spa-
tial grid for 11 January 2003. The figure shows the im-
proved coverage of AMSR over AVHRR. Cloud cover
restricts the potential AVHRR coverage, while precipi-
tation restricts the AMSR coverage. However, all data
anomalies show sampling difficulties. In particular, the
AMSR daytime anomalies are warmer than for AMSR
night south of 30°N, suggesting a diurnal warming.
However, north of 50°N between 50°and 40°W, night-
time AMSR is warmer than daytime. Given four snap-
shots of a complex and variable SST field over one day,
it should not be surprising that four partly obscured
snapshots show inconsistencies when compared with
each other. To reduce these differences, a 3-day data
window with appropriate temporal e-folding error cor-
relation scales may need to be added to a future version
of the daily OI.
d. SST bias adjustments
Finally, the large-scale biases for the January 2003
December 2005 period are now examined where the
AMSR and AVHRR combined daily OI analysis is
used as a reference. The average difference with re-
spect to the AMSR and AVHRR is computed for this
period for the OI.v2, the AVHRR-only daily OI with
and without bias correction, and the AMSR and
AVHRR daily OI without bias correction. For this
comparison, the OI.v2 is linearly interpolated to the
daily OI grid. The OI.v2 (top-left panel in Fig. 14)
shows that the biggest difference with respect to the
AMSR and AVHRR daily OI occurs between 60°and
40°S, with largest values in the Pacific east of the date
line. This is the region of the World Ocean with the
poorest in situ data coverage (see Reynolds et al. 2002);
thus, the true bias is not well known. Many of the other
differences in the western boundary current regions
(e.g., in the Gulf Stream and Kuroshio) and in the east-
ern Pacific equatorial region are due to the increased
resolution of the daily OI. The AVHRR-only OI with
bias correction (top-right panel) shows some residual
biases with respect to the AMSR only AVHRR daily
OI primarily along the ITCZ and SPCZ, a reminder
that residual biases can survive the bias correction step
if the biases persist (Fig. 1).
The AVHRR-only OI analysis without bias correc-
tion (bottom-left panel in Fig. 14) shows the largest
biases with respect to the AMSR and AVHRR com-
bined analysis with bias correction. The biases are es-
pecially evident in tropical oceans. Comparison with
the AVHRR-only OI analysis with bias correction (top-
right panel) shows the necessity of the bias correction.
The AMSR and AVHRR OI analysis without bias cor-
rection (bottom-right panel) with respect to the AMSR
and AVHRR analysis with bias correction shows
smaller long-term biases although some biases remain
as discussed below.
The daily OI biases in the Tropics can be evaluated
using the Tropical AtmosphereOcean (TAO) moored
buoy array (McPhaden et al. 1998). These data are used
in all daily OI analyses and in the RTG_SST and the
OI.v2. Zonal sections of the average analysis anomalies
for 200305 (Fig. 15) along 5°N show the daily
AVHRR-only and AMSR and AVHRR OI analyses
with and without bias correction where the OI.v2 analy-
sis is shown for reference. The AMSR and AVHRR
combined analyses generally agree with the OI.v2. The
two AVHRR-only OI analyses show the original bias
from the uncorrected AVHRR Pathfinder data and a
residual bias from the corrected Pathfinder data. In ad-
dition to the expected results (Fig. 15), positive spikes
can be seen in the two AVHRR-only analyses. Locally
these spikes tend to move the analysis toward the OI.v2
and the AMSR and AVHRR analyses. The spikes are
due to the combination of in situ data from the TAO
array and the AVHRR pathfinder data. Near the loca-
tion of the mooring, both types of observations are
FIG. 11. Analysis SST gradient index (see text) for the Gulf
Stream region for 1 Jun 200231 Dec 2004. The analyses are the
OI.v2, the RTG_SST, and the daily OI using AVHRR-only and
AMSR and AVHRR. Gradients are weakest for the OI.v2. The
near-all-weather coverage of AMSR improves the winter and
spring gradients of the daily AMSR and AVHRR OI over analy-
ses using AVHRR alone.
15 NOVEMBER 2007 REYNOLDS ET AL. 5489
5490 JOURNAL OF CLIMATE VOLUME 20
Fig 12 live 4/C
used: away from these locations, the moored data have
little impact, as can be expected from the spatial scales
in Fig. 4. The amplitudes of the spikes are roughly
0.10°–0.15°C for the AVHRR-only analysis with cor-
rected AVHRR data and 0.20°–0.40°C for the AVHRR-
only OI analysis without bias correction. It is important
to note that these spikes would have been smoothed in
the OI.v2 if they had occurred. For the user of any
high-resolution SST analysis, it is critical to realize that
a high-resolution analysis shows both an increased sig-
nal and a greater susceptibility to noise. Furthermore,
the analysis differences shown in the top panel (Fig. 15)
help justify the 0.01°C
2
residual bias variance assumed
in section 3.
Both the AVHRR-only and the AMSR and AVHRR
daily OI analyses without bias correction have a mid-
latitude Northern Hemisphere bias (Fig. 14) with re-
spect to the AMSR and AVHRR daily OI with bias
correction. Although biases are corrected, the fact that
both uncorrected IR and MW products have similar
biases suggests that these biases may be due to biases
within the in situ data, themselves.
5. Summary and discussion
A set of higher resolution SST analyses have been
produced using OI. The analyses have a spatial grid
resolution of 0.25°and a temporal resolution of 1 day.
FIG. 12. Three-day averages of analyses and data centered on 9 Feb 2003 for an area off the west coast of North America: (top) The
daily OI SSTS for AVHRR-only and AMSR and AVHRR and for AMSR data and (bottom) the associated SST gradient magnitudes.
Precipitation reduces the AMSR data coverage over a region centered on 25°N, 130°W. Contamination of AMSR SSTs near the edge
of the precipitation boundary leads to interpolation errors in the daily OI.
FIG. 13. Daily daytime and nighttime data anomalies for (left) AVHRR Pathfinder and (right) AMSR for 11 Jan 2003.
Note the sampling variability among the four panels. The same climatological field is used to compute all the anomalies
shown because the climatology does not include any diurnal signal.
15 NOVEMBER 2007 REYNOLDS ET AL. 5491
Fig 13 live 4/C
One product uses satellite IR data from AVHRR. The
other uses AVHRR and satellite MW data from
AMSR. Both products use in situ data and include a
large-scale adjustment of the satellite biases with re-
spect to the in situ data. The results show that both
products have dramatically improved spatial and tem-
poral resolution compared to the weekly OI.v2 analysis
(Reynolds et al. 2002). Infrared instruments can pro-
duce SST retrievals only during cloud-free periods,
while MW can produce SST retrievals except within 75
km of land and during precipitation events. The mid-
and high-latitude MW coverage, especially in winter, is
far superior to the IR coverage, although the IR spatial
resolution is much better than MW when skies are
clear. Because of the improved coverage of the MW
data, the analyses show a strong increase in variance
and SST gradient resolution when AMSR became
available in June 2002. Therefore, two products have
been produced: an AVHRR-only product dating back
to January 1985 and an AMSR and AVHRR combined
product dating back to June 2002.
The AVHRR-only product uses Pathfinder AVHRR
data (currently available from January 1985 to Decem-
ber 2005) and Operational U.S. Navy AVHRR data
from 2006 onward. Pathfinder AVHRR data were cho-
sen over operational AVHRR data because they had
lower large-scale variability with respect to in situ data.
Systematic biases nonetheless remain in the Pathfinder
AVHRR data, which are not completely corrected by
the EOT bias correction procedure applied here (Figs.
1 and 14). Furthermore, the operational AVHRR data
used in 2006 includes multiple AVHRR instruments,
whereas Pathfinder AVHRR presently includes only
one instrument for any given part of the record. Path-
finder AVHRR data could be improved in the later
part of the record by providing Pathfinder products for
all available AVHRR instruments. Also, the Pathfinder
AVHRR data do not include the local time of the obser-
vation since they are produced by binning observa-
tions into a temporal (as well as spatial) grid. Further
improvement in AVHRR data would be useful for im-
proving the accuracies of the OI analyses produced here.
FIG. 14. Average analysis differences for 200305 with respect to the daily OI AMSR and AVHRR with bias correction.
(top) The analyses compared with bias correction are the AVHRR-only daily OI and the OI.v2. (bottom) The analyses
without bias correction are the AVHRR-only and the AMSR and AVHRR daily OI. Noin the title indicates no bias
correction. (bottom left) The daily OI AVHRR-only without bias correction shows the largest difference with respect to
the daily OI AMSR and AVHRR with bias correction.
5492 JOURNAL OF CLIMATE VOLUME 20
Fig 14 live 4/C
The AMSR and AVHRR combined product begins
with the start of the AMSR data record in June 2002.
The improved coverage from AMSR leads to improved
spatial resolution of SST gradient features compared
with the AVHRR-only product (Figs. 911). In the
AMSR and AVHRR product, the primary AVHRR
contribution is near land. Of course AVHRR could
further improve the resolution in cloud-free regions.
However, the resolution of an AVHRR-only analysis is
degraded during cloudy periods (Fig. 11).
Because their error characteristics are independent
and systematic biases may tend to cancel each other,
there is an important advantage in using both IR and
MW instruments. However, problems remain near
edges of precipitation boundaries where errors in
AMSR SST retrievals cannot be compensated by IR
data because of cloud cover (Fig. 12).
(The daily OI SST analyses are presently available
via FTP at ftp://eclipse.ncdc.noaa.gov/pub/OI-daily/,
TDS at http://nomads.ncdc.noaa.gov:8085/thredds/
catalog.html, and LAS at http://nomads.ncdc.noaa.
gov:8085/las/servlets/dataset. The Web server address is
http://www.ncdc.noaa.gov/oa/climate/research/sst/oi-
daily.php.)
Further work is needed and will continue. One of the
most important steps is to develop a method to improve
the bias correction and to correct ship and buoy biases.
In addition, the data time window may need to be opened
to 3 days to eliminate day-to-day noise (Fig. 12).
[C. Gentemann (2006, personal communication) has
recently added additional precipitation flags to the
AMSR data that may mitigate the precipitation
edge effects noted above.] As improved satellite
AMSR and AVHRR datasets become available, the
analyses will be reprocessed. One of the most impor-
tant potential improvements would occur due to the
addition of new satellite datasets. The next daily OI
product will include the MW Tropical Rainfall Mea-
suring Mission (TRMM) Microwave Imager (TMI)
(which samples between 38°S and 38°N) and the global
Along Track Scanning Radiometer (ATSR) series of
IR instruments. Later additions will include other polar
and geostationary data. Each of these satellite datasets
will first be examined separately using an independent
analysis. It is hoped that the number of final products
will not have to be expanded. New products will only be
added when, as expected, the SST analyses show a sig-
nificant improvement with the addition of new satellite.
Improvements with updated documentation will be
added as needed.
Acknowledgments. We are grateful to NCDC and the
NOAA/Office of Global Programs, which provided
partial support for this work. The graphics were com-
puted using the Grid Analysis and Display System
(GrADS, available online at http://grads.iges.org/grads),
Center for OceanLandAtmosphere Studies. We
thank the following people for help with the data: Di-
ane Stokes for providing information and access to real-
time in situ data and sea ice data, Chelle Gentemann
for providing information about the AMSR-E data, and
John Sapper for providing real time access to the
AVHRR data. Reynolds thanks the Cooperative Insti-
tute for Oceanographic Satellite Studies at Oregon
State University (OSU) for contributing part of his
travel costs towards a visit to OSU in July 2005. NOAA
reviewers Sharon LeDuc, Gary Wick, and Huai-Min
Zhang provided helpful editorial comments. Further
constructive comments were obtained from an anony-
mous reviewer, as well as Chris Folland, and Alexey
Kaplan.
FIG. 15. Average analysis anomalies for 200305 along 5°Nin
the Pacific. The daily analyses are the AVHRR-only and AMSR
and AVHRR (top) with and (bottom) without bias correction.
The OI.v2 analysis is shown for reference. The spikes in the daily
OI AVHRR-only analyses show the local balance of the TAO
buoy and satellite SSTs on the analysis.
15 NOVEMBER 2007 REYNOLDS ET AL. 5493
APPENDIX A
Simulating SSTs from Sea Ice Concentration
The quadratic (1) and linear (2) equations defined in
section 2c express the relationship between sea ice con-
centration and SST. In this appendix the two equations
were examined to determine the differences between
the equations and to estimate a minimum sea ice con-
centration for use with (1) and (2). The coefficients a,b,
c,b, and cin (1) and (2) were determined by regres-
sion for 30°wide longitude bands (or sectors) for each
month for the Northern and Southern Hemispheres. In
addition, there were four separate 30°wide bands for
the North Pacific south of 66°N and one each for the
Baltic Sea and Great Lakes. These extra regions were
necessary because the sea ice in these regions behaves
differently than the general Northern Hemisphere
bands at the same longitudes. Both the linear and qua-
dratic constants were determined by a climatological
least squares fitting procedure using collocated SST
data (AVHRR and in situ) and sea ice concentrations
with the constraint that the simulated SST is set to the
freezing point of water (1.8°C for the ocean or 0°C for
the Great Lakes) when the sea ice concentration is 1.
Once this is done, the sea ice concentration, location,
and month can be used to generate the simulated SST.
In the OI.v2, sea ice concentrations were bias ad-
justed following the procedure in Rayner et al. (2003)
to account for melt pond summer biases. This adjust-
ment was done to smooth the transition between satel-
lite and in situderived ice concentrations in the OI.v2.
However, it was not needed here because in situ
derived sea ice concentrations were not used and be-
cause the fitting procedure in (1) and (2) accounts for
any local biases via the derived coefficients.
To determine whether Eq. (1) or (2) is more accurate
and to determine the minimum value the coefficients
were determined by a regression of observed SSTs (sat-
ellite and in situ) onto observed sea ice concentrations
for a 10-yr-dependent period (198594). The accuracy
of the regression was evaluated for an independent pe-
riod (19952004). For this independent period, biases
and rms differences were computed between simulated
SSTs generated from sea ice concentrations and actual
observed SSTs. These biases and rms differences were
computed for ice concentration bins with widths of 0.1
centered on multiples of 0.1.
Figure A1 shows a summary of the rms differences
and biases averaged over all months and all Northern
Hemisphere regions. The rms differences are noisy and
not very useful in determining whether (1) or (2) is
more accurate. The results do show that rms errors
increase with decreasing concentration. This should not
be surprising since climatology is used to generate the
SSTs and the only constraint in the fit occurs at high
concentrations (i.e., at the freezing point of the water).
However, the differences in the biases did have useful
information. A perfect fit would have zero biases. The
results indicate that the absolute biases are smaller for
the linear fit for ice concentration bins between 0.6 and
0.7 and smaller for the quadratic fit for the 0.9 bin and
for bins less than 0.5. At bins of 0.5 and 0.8, the fits are
about equal. Furthermore, for some quadratic fits (not
shown) data are sparse and the quadratic fit may gen-
erate SSTs that are unstable at low sea ice concentra-
tions and may generate extreme SSTs there. As a con-
servative approach, the minimum sea ice concentration
for use of (1) or (2) was set to 0.5 and the linear fit (2)
was selected over the quadratic fit. This limits the maxi-
FIG. A1. Northern Hemisphere average (top) rms difference
and (bottom) bias between measured SSTs minus SSTs simulated
from sea ice concentration for all months for quadratic and linear
fits. The period for the comparison is 19952004, an independent
period.
5494 JOURNAL OF CLIMATE VOLUME 20
mum rms error to less than 1.5°C. Thus, SSTs were
simulated for sea ice concentrations 0.5 using (2); no
SSTs were simulated for sea ice concentrations 0.5.
APPENDIX B
Combining Observations Using Simplified
Optimum Averaging
This appendix discusses a simplified optimum aver-
aging (OA) appropriate for combining observations,
and also for computing the error estimate of the com-
bination. For reference and background, see section 3.3
in Kagan (1979).
To begin, Kagans Eq. (3.3.2) is used and rewritten
here as
i1
n
w
i
C
ij
w
j
E
j
2
C
jA
,j1,...,n,B1
where C
ij
is the covariance between observations iand
j,C
jA
is the covariance between observation jand the
average value, and E
2
j
is the noise error variance of
observation j. The OA weights for the nobservations
are w
j
.
Here the averaging region is assumed to be the OI
analysis 0.25°spatial box. For this box it is assumed that
the averaging region is small enough that all correla-
tions within the region are equal to 1 and that the vari-
ance,
2
, is constant within the region. With these as-
sumptions, the OA weights for the nindividual obser-
vations are found by solving
j
2
w
j
i1
n
w
i
1, j1,...,n.B2
In (B2),
2
j
E
2
j
/
2
is the noise-to-signal variance ratio
of observation, j.
From (B2) the weights can be expressed as
w
j
1
i1
n
w
i
j
2
.B3
The sum of the weights is then
nw
i1
n
w
i
1nw
j1
n
1Ⲑ␧
j
2
.B4
Defining H⫽兺
n
i1
1/
2
i
, then by algebraic manipulation
of (B4) the sum of the weights as a function of the
normalized error variances becomes
nwH
1H.B5
The weights are then defined as
w
j
1
1H
j
2
.B6
Using these same assumptions, the combined noise-to-
signal variance ratio is
0
2
1nw 1
1H.B7
Note that these OA weights may cause damping of
the solution in situations when the noise is large. To
avoid this damping the weights can be normalized, giv-
ing the solution
q
i
1
H
i
2
.B8
Here the sum of the normalized weights, q
i
, is equal to
1. Using Kagans Eq. (3.3.10), it can be shown that the
error using normalized weights is
q
2
0
2
1nw
2
nw 1
H.B9
Note that this error reduces to the error from (B7) as
the sum of the weights approaches 1. Otherwise it is
slightly larger. The normalization has been imple-
mented in the current OI SST processing.
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5496 JOURNAL OF CLIMATE VOLUME 20
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... The daily OISST product is constructed by using satellite SST maps from Advanced Very High-Resolution Radiometer (AVHRR) (data.nodc.noaa.gov (accessed on 15 August 2022)) [36,37]. This study used 29 years of the OISST product from January 1993 through December 2021. ...
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SST predictions are usually issued in terms of anomalies and standardized anomalies relative to a 30-yr normal: climatological mean (CM) and standard deviation (SD). The World Meteorological Organization (WMO) suggests updating the 30-yr normal every 10 yr. In complying with the WMO's suggestion, a new 30-yr normal for the 1971-2000 base period is constructed. To put the new 30-yr normal in historical perspective, all the 30-yr normals since 1871 are investigated, starting from the beginning of each decade (1871-1900, 1881-1910, , 1971-2000). Using the extended reconstructed sea surface temperature (ERSST) on a 2° grid for 1854-2000 and the Hadley Centre Sea Ice and SST dataset (HadISST) on a 1° grid for 1870-1999, eleven 30-yr normals are calculated, and the interdecadal changes of seasonal CM, seasonal SD, and seasonal persistence (P) are discussed. The interdecadal changes of seasonal CM are prominent (0.3°-0.6°) in the tropical Indian Ocean, the midlatitude North Pacific, the midlatitude North Atlantic, most of the South Atlantic, and the sub-Antarctic front. Four SST indices are used to represent the key regions of the interdecadal changes: the Indian Ocean (`INDIAN'; 10°S-25°N, 45°-100°E), the Pacific decadal oscillation (PDO; 35°-45°N, 160°E-160°W), the North Atlantic Oscillation (NAO; 40°-60°N, 20°-60°W), and the South Atlantic (SATL; 22°S-2°N, 35°W-10°E). Both INDIAN and SATL show a warming trend that is consistent between ERSST and HadISST. Both PDO and NAO show a multidecadal oscillation that is consistent between ERSST and HadISST except that HadISST is biased toward warm in summer and cold in winter relative to ERSST. The interdecadal changes in Niño-3 (5°S-5°N, 90°-150°W) are small (0.2°) and are inconsistent between ERSST and HadISST. The seasonal SD is prominent in the eastern equatorial Pacific, the North Pacific, and North Atlantic. The seasonal SD in Niño-3 varies interdecadally: intermediate during 1885-1910, small during 1910-65, and large during 1965-2000. These interdecadal changes of ENSO variance are further verified by the Darwin sea level pressure. The seasonality of ENSO variance (smallest in spring and largest in winter) also varies interdecadally: moderate during 1885-1910, weak during 1910-65, and strong during 1965-2000. The interdecadal changes of the seasonal SD of other indices are weak and cannot be determined well by the datasets. The seasonal P, measured by the autocorrelation of seasonal anomalies at a two-season lag, is largest in the eastern equatorial Pacific, the tropical Indian, and the tropical North and South Atlantic Oceans. It is also seasonally dependent. The `spring barrier' of P in Niño-3 (largest in summer and smallest in winter) varies interdecadally: relatively weak during 1885-1910, moderate during 1910-55, strong during 1955-75, and moderate during 1975-2000. The interdecadal changes of SD and P not only have important implications for SST forecasts but also have significant scientific values to be explored.
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To assess climatic changes in sea surface temperature (SST), changes in the measurement method with time and the effect of these changes on the mean SST must be quantified. Observations from the International Comprehensive Ocean–Atmosphere Data Set (ICOADS) have been analyzed for the period from 1970 to 1997 using both SST measurement metadata contained within the dataset and a World Meteorological Organization (WMO) catalog of observing ships. The WMO metadata were particularly important in identifying engine-intake SSTs during the 1970s, but increased method identification over the entire period. There are strong regional variations in the preferred SST measurement method, with engine-intake SST most common in the Pacific and bucket SST preferred by countries bordering the Atlantic. The number of engine-intake SSTs increases over time and becomes more numerous than buckets by the early 1980s. There are significant differences between SST observations made by different methods. The rounding of reports is more common for engine-intake SST than for either bucket or hull sensor SST, which degrades its quality. Significant time-varying biases exist between SST derived from buckets and from engine intakes. The SST difference has a strong seasonal signal with bucket SST being relatively cold in winter, probably resulting from heat loss from the buckets, and warm in summer, probably resulting from solar warming or the sampling of a shallow warm layer. There is also a long-term trend with engine-intake SST being relatively warm in the early period but with a small annual mean difference between the two methods by 1990.
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We have generated consistent sea ice extent and area data records spanning 18.2 years from passive-microwave radiances obtained with the Nimbus 7 scanning multichannel microwave radiometer and with the Defense Meteorological Satellite Program F8, F11, and F13 special sensor microwave/imagers. The goal in the creation of these data was to produce a long-term, consistent set of sea ice extents and areas that provides the means for reliably determining sea ice variability over the 18.2-year period and also serves as a baseline for future measurements. We describe the method used to match the sea ice extents and areas from these four multichannel sensors and summarize the problems encountered when working with radiances from sensors having different frequencies, different footprint sizes, different visit times, and different calibrations. A major obstacle to adjusting for these differences is the lack of a complete year of overlapping data from sequential sensors. Nonetheless, our procedure reduced ice extent differences during periods of sensor overlap to less than 0.05% and ice area differences to 0.6% or less.