Objective analysis of monthly temperature and salinity for the world
ocean in the 21^st^ century: Comparison with WOA and application to
assimilation validation

You-Soon Chang\*^1,2^, Anthony J. Rosati^1^, Shaoqing Zhang^1^ and
Matthew J. Harrison^1^

*^1^Geophysical Fluid Dynamics Laboratory, Princeton, New Jersey, USA*

*^2^National Institute of Meteorological Research, Seoul, Korea*

Final version on November 24, 2008

to JGR-Oceans

\*Corresponding author: You-Soon Chang, GFDL/NOAA, Princeton University
Forrestal Campus, 201 Forrestal Road, Princeton, NJ 08542, USA. E-mail:
You-Soon.Chang@noaa.gov Tel: (609) 452-5318 Fax: (609) 987-5063

**Abstract**

A new world ocean atlas of monthly temperature and salinity, based on
individual profiles for 2003-2007 (WOA21c), is constructed and compared
with the World Ocean Atlas 2001 (WOA01), the World Ocean Atlas 2005
(WOA05) and the data assimilation analysis from the Coupled Data
Assimilation (CDA) system developed by the Geophysical Fluid Dynamics
Laboratory (GFDL). First, we established a global data management system
for quality control (QC) of oceanic observed data both in real time and
delayed mode. Delayed mode QC of Argo floats identified about 8.5% (3%)
of the total floats (profiles) up to December 2007 as having a
significant salinity offset of more than 0.05. Second, all QCed data
were gridded at 1° by 1° horizontal resolution and 23 standard depth
levels using six spatial scales (large and small longitudinal,
latitudinal, and cross-isobath) and a temporal scale. Analyzed mean
temperature in WOA21c is warm with respect to WOA01 and WOA05, while
salinity difference is less evident. Consistent differences among WOA01,
WOA05, and WOA21c are found both in the fully and sub-sampled dataset,
which indicates a large impact of recent observations on the existing
climatologies. Root mean square temperature and salinity differences and
offsets of the GFDL's CDA results significantly decrease in the order of
WOA01, WOA05, and WOA21c in most oceans and depths as well. This result
suggests that the WOA21c is of use for the collocated assessment
approach especially for high-performance assimilation models on the
global scale.

**1. Introduction**

The gridded World Ocean Atlas (WOA) of the National Oceanographic Data
Center (NODC) has been widely used in the ocean modeling community as
initial and boundary conditions and as verification data for numerical
models. The original WOA product \[*Levitus,* 1982\] was updated in 1994
(WOA94), 1998 (WOA98), 2001 (WOA01), and 2005 (WOA05) as new data,
particularly Argo profiling floats since the 21^st^ century, became
available \[*Boyer et al*., 2006\].

Black dots of Figure 1 show the horizontal distribution of observation
data at 700 m depth in August for the recent 5 years. It is evident that
areas where the data are insufficient to produce a reliable analysis
field have been decreasing over time, thanks to the successful
international Argo project
\[[*http://www.argo.net*](http://www.argo.net/)\]. The Argo array
includes more than 3000 robotic floats and is currently providing over
100,000 temperature and salinity profiles worldwide each year. This high
density profile array, without seasonal and spatial bias, makes it
possible to produce the 3 dimensional oceanic state in near real time.
*Schmid et al.* \[2007\] described the real time data management
methodologies for the global Argo array and pointed out the great
potential of Argo profiles for an improved climatology. *Ingleby and
Huddleston* \[2007\] also developed their new historical database
including recent Argo profiles and emphasized the importance of the
quality control (QC) process.

The Argo data covering most of the global oceanic database in the 21^st^
century should be used with the higher QC called "delayed mode" because
the data cannot be calibrated during their 4-5 year observation period.
However, most of the researchers including NODC have used the Argo data
with their own mid level quality checks, even though two algorithms for
delayed mode QC had already been developed by *Wong et al.,* \[2003\]
(hereafter "WJO03") and *Böhme and Send* \[2005\] (hereafter "BS05") and
recommended by the Argo community. This means that there have been no
corrections for salinity sensor drift in most previous analyses and
climatologies using Argo data. As for the temperature, there are almost
no differences between real time and delayed mode Argo data, so analyses
using temperature data in real time are not seriously compromised.
However, some systematic pressure sensor problems affecting temperature
and salinity analyses are being reported \[*Willis et al*., 2007; *Argo
Steering Team*, 2008\], which will be discussed later in this
manuscript.

Coriolis (one of the Argo Global Data Assembly Center (GDAC)) has
operated the Coriolis Analysis System (CAS). This system produces weekly
gridded fields of global temperature and salinity. It also considers the
sensor drift with QC algorithms as described by *Gaillard et al.*
\[2008\], however their analysis is only limited in the Atlantic Ocean.
In this study, we documented a global oceanic data management system
mostly based on the delayed mode Argo dataset, and produced monthly mean
gridded fields of temperature and salinity for 2003-2007. This global
objective estimate (hereafter "WOA21c") will be an important database in
determining the accurate rate of the oceanic change as well as the
quantitative assessment of numerical models. This study is organized as
follows: section 2 describes the data used in this study; methodologies
for QC and optimal interpolation (OI) are followed in section 3; section
4 analyzes WOA21c comparing with WOA01 and WOA05; section 5 deals with
the assimilation assessment. As a target model for our validation, we
used the latest results for 2003-2007 from the state-of-the-art fully
CDA system developed at GFDL \[*Zhang et al.*, 2007, 2008\]. A summary
and conclusion are given in section 6.

### 

### 2. Data 

The Global Temperature-Salinity Profile Program (GTSPP) has assembled
and distributed the up-to-date global temperature and salinity data
transmitted by the Global Telecommunication System (GTS). In this study,
we used "best-copy" data from the GTSPP Continuously Managed Database
(CMD). This "best-copy" data file replaces the real time low resolution
(accuracy) one when NODC provides the full resolution, or fully
processed and QC data
\[[*http://www.nodc.noaa.gov/GTSPP/gtspp-home.html*](http://www.nodc.noaa.gov/GTSPP/gtspp-home.html)\].

As we mentioned in the introduction, autonomous profiling data observed
from Argo floats should be used with higher quality delayed mode. In the
Argo data which have been transmitted via GTS within 24 hours and stored
in the GTSPP CMD, there are no enough information for the delayed mode
QC \[*Argo Data Management*, 2006a\]. Therefore, we constructed another
data-mirroring system from the GDAC in charge of the global Argo data
assembling and distribution in NetCDF format with a full salinity
accuracy and QC flag. We identified all PFL (autonomous profiling Argo
floats) types from the mixed GTSPP dataset and then replaced them with
the new Argo dataset from GDAC.

We also excluded all BT (Bathythermograph) data types (mostly MBT
(Mechanical Bathythermograph) and XBT (Expendable Bathythermograph))
from the mixed GTSPP dataset; that is, we used only data types with both
temperature and salinity profiles. Moreover, this new dataset does not
show the systematic warm bias found in XBT, which will be discussed in
chapter 4. As shown in Figure 4, 25.6% of total profiles used in this
study are from GTSPP. MRB (moored ocean buoys) data are taking up the
large part of our GTSPP dataset that had been separated from all PFL and
BT types. Most of them are from the Tropical Atmosphere Ocean (TAO)
project and restricted around the particular observation points with
relatively high temporal observation intervals. The important
contribution of this GTSPP data is that they fill in data sparse regions
especially around the equatorial Atlantic Ocean where many of the Argo
floats with incorrect pressure sensor removed in our analysis were
distributed.

We will use this database based on both temperature and salinity
profiles in a series of follow-up studies investigating the global
variability of density, steric height, and velocity (transport) fields
as well as the corresponding model assessments. We also expect that the
GTSPP data identified from Argo and XBT data could be used for checking
any systematic biases of in situ data in separate studies.

# 

# 3. Methods

# 3.1. Quality Control

The QC system for the global temperature and salinity profile data has
been developed. First, we carried out the initial data processing with
conventional QC based on the NODC technical report \[*Boyer and
Levitus*, 1994\] and Argo's real time QC manual \[*Argo Data
Management*, 2006b\]. This conventional QC consists of the real time QC
flag check, duplication check for pressure and cycle, impossible value
check for position and date, monotonically increasing check for
pressure, range/spike/gradient check for temperature and salinity, and
visual inspection for suspect data. The majority of profiles (87.3%)
passed this conventional QC test (Figure 4).

For the autonomous profiling data observed from Argo floats, we applied
another separate QC process (delayed mode QC) investigating an
artificial salinity offset (including drift). By comparing Argo floats
to neighboring hydrographic data, every float with significant salinity
offset has been eliminated or corrected. First, we excluded all floats
(2.1% of total Argo floats that passed the conventional QC) observed in
marginal seas (East/Japan Sea and Mediterranean Sea) from our study,
since they should be investigated with a specified regionally adapted QC
system \[*Park and Kim*, 2007\]. Recently, systematic biases associated
with incorrect pressure have been discovered in the some fraction of
Argo floats mainly in SOLO (Sounding Oceanographic Lagrangian Observer)
floats with FSI (Falmouth Scientific, Inc.) or SBE (SeaBird Electronics,
Inc.) CTD (Conductivity-Temperature-Depth) sensors
\[[*http://www-argo.ucsd.edu/Acpres_offset2.html*](http://www.argo.ucsd.edu/)\].
We checked them again based on the Argo grey list provided by Argo
community. Argo grey list contains float information with pressure
sensor problem as well as other problems such as battery, location and
frozen profiling. In this study these profiles were almost completely
removed through the QC flag check in our conventional QC routine. We
also excluded the premature floats younger than about 100 days (in case
the total cycle number is less than 10) since they can not provide the
reliable salinity trend for the delayed mode QC and some of them show
the serious biocide wash off problem as well. The recommendation of the
Argo community is that there needs to be 6 months of data to be able to
quantify the pattern in salinity drift for delayed mode QC. For most of
the floats used in this study, a 21-profile criterion has been applied
to calculate the time evolution of the potential conductivity slope
correction term. We used smaller criteria started from 11-profile series
only for some particular rapid biocide wash-off case suggested by WJO03.

Up to December in 2007, only 25% of total Argo floats have completed a
delayed mode QC at each Argo Data Assembly Center (DAC). For about 75%
remaining Argo floats that have not been undergone (or completed) the
delayed mode QC, we employed the WJO03 method except for some cases. For
the floats observed in the North Atlantic (15.8% of total Argo floats
that need delayed mode QC), we applied BS05 method that considers the
hydrographic structure following the large-scale contours of the
potential vorticity only in the North Atlantic. Finally we carried out
the visual inspection again based on the historical database and
neighboring recent floats. This final process takes a long time, but it
is very necessary in order to confirm if the calibrated salinities are
artificial offsets or natural variability.

Figure 2 is an example of our delayed mode QC result. Two Argo floats
(WMO ID: 1900073 and 1900075) with APEX CTD sensors were deployed in
March 2003 and drifted by May 2006. For more than one and half years,
the measurements from these floats are in agreement with the
climatological estimates. After approximately 100 cycles (700 days),
however, the float measurements gradually drifted toward higher values
owing to a biofouling or unknown sensor problem judging from the
neighboring hydrography and climatology. Our calibrations are in line
with the climatology estimates as well as the GDAC result, even though
GDAC provides the delayed mode QC of the 1900073 float only until
September 2005. As shown the case of 190073 and 190075 floats in Figure
2, many floats with artificial salinity offsets have not completed the
delayed mode QC at the respective DACs. In this study, all floats
showing artificial salinity offset were calibrated up to December 2007.

Among the 3,937 floats (328,841 profiles), which have passed the
conventional QC, 336 floats (9,861 profiles) show a salinity offset of
more than 0.05. This is about 8.5% (3%) of the total floats (profiles).
Figure 3(a) shows the spatial distribution of Argo profiles with
salinity offset. This offset has been simply calculated by the
difference between the conventional QCed salinity and the delayed mode
QCed one averaged from the surface to the parking depth of each profile.
Most floats with salinity offset have been found around the costal areas
associated with high levels of biological activity causing the
biofouling. The Atlantic Ocean also shows the high density of Argo
floats with salinity offsets comparing to other oceans, which might be
related to the floats age (Most autonomous floats in the early stage of
Argo project were deployed around the Atlantic Ocean). Figure 3(b) shows
the same distribution with Figure 3(a) except on the basis of Argo float
types with different CTD sensors. Salinity offsets of more than 0.05
have been found to all float types; that is, there is no significant
relationship between salinity drift and particular sensor problems
discovered in the some fraction of SOLO floats.

We have summarized all QC procedures with every single rejection
percentage using the flow chart in Figure 4.

# 3.2. Optimal Interpolation

QCed data for global temperature and salinity profiles have been
optimally interpolated to monthly 1 grid after the linear vertical
interpolation for the 23 standard depths from 10 m to 1500 m. The
Optimal Interpolation (OI) method used in this study is originally based
on the Gauss-Markov theorem which gives a linear estimate that is
unbiased and optimal in the least square sense. This provides an
estimate of the uncertainty (error variance) that takes into account the
distribution of the data used \[*Bretherton et al.*, 1976; *McIntosh*,
1990\]. Following is the overall OI algorithms that were similarly used
in this study during the delayed mode QC. Observation data used for this
OI version are also selected by three-step criteria guaranteeing no
spatial bias, which would be efficient for the objective analysis
studies dealing with autonomous float data. Therefore, we picked up and
modified this approach.

The covariance of the data is assumed to be Gaussian with the decay
scales determined by four different parameters following *Hadfield et
al.* \[2007\]: a longitudinal scale (Lx), a latitudinal scale (Ly), a
cross-isobath scale (), and a temporal scale (). In this study, each
spatial scale consists of large (Lx~1~, Ly~1~, ~1~) and small scales
(Lx~2~, Ly~2~, ~2~), respectively. We determined the scale values at
Lx~1~=10, Ly~1~=5, ~1~=0.5, Lx~2~=5, Ly~2~=3, ~2~=0.25, =35 days with
careful consideration based on the number of the data within the
selected correlation scales. The spatial scales are anisotropic, with Lx
greater than Ly to reflect the predominant zonal currents in the ocean
interior.

The objective estimate (T(S) ^obj^) of the temperature (salinity) at
each grid point of standard depths is given by

T(S)^obj^ = \<d\> + ω·(d-\<d\>) (1)

where d = \[d~1~,..., d~N~\] denotes the set of selected "N" temperature
(salinity) profiles to the grid point being interpolated to and \<d\>
denotes the mean value of the set d. For the insufficient observed data
and smoothing effect, most of the previously documented mapping methods
have taken the climatology such as WOA01 as a mean value \<d\>. In this
study, we use the mean value of "N" based on observed dataset instead of
climatology in order to avoid any contamination of ocean state in the
21^st^ century from the climatology based on the historical dataset,
mainly in the 20^th^ century.

N is selected based on three criteria, following both WJO03 and BS05:

\(1\) One-third of total data points within
Dx^2^~i,g~/Lx~1~^2^+Dy^2^~i,g~/Ly~1~^2^+F^2^~i,g~/~1~^2^ \< 1 (i.e.
within the e-folding distance of the covariance function to be used) are
randomly selected. Dx and Dy are the spatial distances between the
observed data (subscripts i) and the grid point (subscripts g) in zonal
and meridional directions, respectively. F is the fractional distance in
potential vorticity representing the cross-isobath separation. F is
calculated using the following formula,

![](media/image1.wmf){width="1.69375in" height="0.5138888888888888in"}

where PV is the barotropic potential vorticity, f/H, f is the Coriolis
parameter and H is the full ocean depth. The inclusion of the
cross-isobath separation considers the tendency of ocean currents to
follow the bathymetry (BS05). We did not make any estimated value at the
grid point where the total data points within the e-folding distance of
the covariance function are less than 10 (See the blank areas in Figure
1).

\(2\) From the remaining data points, one-third of the profile data
within the shortest generalized distance scaled by the large length
scales, Dx^2^~i,g~/Lx~1~^2^+Dy^2^~i,g~/Ly~1~^2^+F^2^~i,g~/~1~^2^ are
selected.

\(3\) Again from the remaining data points, one-third are selected that
have the shortest spatial and temporal separation factor using the short
length scales and the temporal scale,
Dx^2^~i,g~/Lx~2~^2^+Dy^2^~i,g~/Ly~2~^2^+F^2^~i,g~/~2~^2^+Dt^2^~i,g~/^2^.
Dt is the temporal difference between the observed date and 15^th^ day
of each month to be mapped. Using these three-step criteria, a set of
profiling data is provided, which is not spatially biased (WJO03 and
BS05).

ω is the weighing matrix (ω=Cdg· \[Cdd+I·\<^2^\>\]^-1^) including
data-grid (Cdg) and data-data (Cdd) covariance matrix and random noise
(\<^2^\>). As in WJO03 and BS05, a two-stage mapping is also employed.
In the first stage, the covariance is a function of the large-scale
spatial separation only:

Cdg~i~(x,y)=\<s^2^\>·exp{-\[
Dx^2^~i,g~/Lx~1~^2^+Dy^2^~i,g~/Ly~1~^2^+F^2^~i,g~/~1~^2^\]}

Cdd~i,j~(x,y)=\<s^2^\>·exp{-\[
Dx^2^~i,j~/Lx~1~^2^+Dy^2^~i,j~/Ly~1~^2^+F^2^~i,j~/~1~^2^\]}

\<s^2^\>=(1/N)$\sum_{i}^{}{(d_{i} - d > )^{2}}$

\<^2^\>=(1/2N)$\sum_{i}^{}{(d_{i} - d_{n})^{2}}$

\<s^2^\> and \<^2^\> are the signal and noise variance of the observed
data set. \<d\> and d~n~ denote the mean value of the set d, and the
data value at the points that has the shortest distance from d~i~,
respectively. The first-stage estimate at each grid point, T(S)^obj(1)^
is a large-scale estimate without respect to temporal variability or
small-scale features.

In the second stage, the residuals from the first stages are mapped to
the grid point using (1), but with a covariance that is a function of
the small-scale spatial and temporal separation.

Cdg~i~(x,y,t)= \<s^2^\>·exp{-\[
Dx^2^~i,g~/Lx~2~^2^+Dy^2^~i,g~/Ly~2~^2^+F^2^~i,g~/~2~^2^+Dt^2^~i,g~/^2^\]}

Cdg~i,j~(x,y,t)= \<s^2^\>·exp{-\[
Dx^2^~i,j~/Lx~2~^2^+Dy^2^~i,j~/Ly~2~^2^+F^2^~i,j~/~2~^2^+Dt^2^~i,j~
/^2^\]}

The second stage estimate T(S)^obj(2)^ thus resolves the small scale
features.

The final objective estimate at each grid point is then the sum of the
two stage of mapping (T(S)^obj^ = T(S)^obj(1)^ + T(S)^obj(2)^ ).
Therefore this objective estimate is composed of selected observed data
close to the grid point in space and time relative to the spatial
(Lx~1~, Ly~1~, ~1~, Lx~2~, Ly~2~, ~2~) and temporal () scales. The final
error variance of the objective estimate is taken form the second-stage
mapping \[*McIntosh*, 1990\]:

$\sigma_{\text{obj}}^{2}(T(S)^{\text{obj}}) = \overline{(T(S)^{\text{obj}(2)} - \overline{T(S)^{\text{obj}(2)}})^{2}} - \text{Cdg}(x,y,t) \times \text{Cdd}(x,y,t)^{- 1} \times \text{Cdg}(x,y,t)^{T}$where
the overbar is an average over all mapped residuals.

# 4. Comparison with WOA

The WOA21c analysis, based on the high quality profile dataset for
2003-2007, has been compared to WOA01 and WOA05 on global and basin
scales.

Figure 5a shows the horizontal distribution of annual temperature and
salinity fields at 10 m depth. WOA21c clearly depicts the large-scale
gradient patterns associated with temperature and salinity fronts and a
large pool of homogenous water. The error variance of temperature is
large in the Kuroshio, Gulf stream, Agulhas, and Brazil current regions.
In addition to the strong western boundary currents, the variability of
fresh water flux makes the error variance of salinity increase near the
equatorial ocean and major run off regions. At the 1500 m depth as shown
in Figure 5b, Mediterranean outflow can be found both in temperature and
salinity fields. The horizontal distribution of a water mass (salinity
range from 34.2 to 34.5) is very clear both in WOA01 and WOA21c. Large
error variance at 1500 m depth is shown around the Mediterranean outflow
and Antarctic circumpolar current regions.

Overall horizontal distribution patterns of temperature and salinity of
WOA21c is in agreement with the WOA01. However, there are significant
differences between the WOA21c and WOA01. Overall warming in WOA21c is
apparent. Freshening (Salting) at 10 m depth is seen throughout the
North Pacific (Atlantic). Another freshening signal is found throughout
the Western Pacific, while salting is shown over the South Pacific
Ocean. These results are in agreement with previous studies focusing on
the (multi-) decadal variation of salinity in global or basin scale
\[*Boyer et al.,* 2005; *Polyakov et al.*, 2005; *Boyer et al.,* 2007;
*Delcroix et al.,* 2007\].

Most likely, the primary reason for this difference between WOA21c and
WOA01 is related to the water mass variability on interannual, decadal,
or longer time scale. For instance, ocean surface water during 2003 to
2007 happened to be particularly warm and fresh over much of the North
Pacific. Another potential issue is related to the sampling bias of
observation data and the discrepancy of analysis methods between WOA21c
and WOA01. In this study, a sampling experiment was carried out using
additional climatology, WOA05. WOA05 employed very similar methods on
the data QC and objective analysis compared to WOA01, but WOA05 used
more recent observation up to February 2005 (WOA01 is up to August 2001)
\[*Locarnini et al.,* 2006; *Antonov et al.*, 2006\].

Left panels of Figure 6 shows the global mean (0-360, 60S-60N)
temperature and salinity in the upper ocean (10 m - 700 m) estimated by
WOA01, WOA05, and WOA21c, respectively. Dotted lines are fully-sampled
annual cycle of WOA01 (black) and WOA05 (green). Solid lines are
sub-sampled WOA01 (black) and WOA05 (green) data based on the
distribution of WOA21c (red) spatially and monthly from 2003 to 2007, in
which grid points where the observation data are insufficient to produce
reliable OI mapping estimates were excluded. Although monthly
discrepancies between two curves (solid and dotted) are decreasing due
to the number of observations increasing in time (See that data-sparse
areas are gradually decreasing in Figure 1), significant differences
still exist. Sub-sampled WOAs (solid lines) have no seasonal amplitude
as well. The fully-sampled annual phase reflects the peak warming in
Austral summer since two-thirds of the world's oceans lie in the
Southern Hemisphere. Therefore, under-sampling around the Southern
Hemisphere appears to be the primary cause of the discrepancy in the
global ocean scale. Other data-sparse regions around marginal seas and
the central Atlantic Ocean where most of the SOLO floats with FSI and
SBE CTD sensors had been deployed could be other sources for
discrepancy, even though GTSPP data somewhat filled these data-sparse
areas as mentioned in chapter 2. This result suggests that the
observation data density for 2003-2007 is not adequate to resolve the
absolute global temperature and salinity.

However, the difference among WOAs shows the consistent variability in
time regardless of the sampling issue. Dotted black lines in the right
panels of Figure 6 indicate the difference between fully-sampled WOA05
and WOA01. Solid black lines show the same information for sub-sampled
data. In general, temperature of WOA05 is higher than that of WOA01.
This warming difference is apparent during boreal summer both in fully-
and sub-sampled data. For the salinity difference, salting is dominant
during boreal summer and vise versa both in fully- and sub-sampled data.
It is also important that the consistent trend have been found at the
difference result between WOA21c and WOA01 (solid red line). In this
study, our emphasis is not a investigating the absolute temperature and
salinity of individual ocean but the relative difference among WOAs, so
that hereafter we will deal with only sub-sampled WOAs.

Figure 7 shows the vertical difference of the annual mean temperature
and salinity among WOA21c, WOA01, and WOA05 for each ocean basin from 10
m to 1500 m depth. Over most of the major ocean basins, warm differences
in WOA21c are dominant over all depths except for the mid (100 m -- 1000
m) layer of the South Pacific and the Indian Ocean. For the salinity,
the North Pacific exhibits a strong freshening around upper layer. In
contrast, all other areas experience salting biases, while slight
freshening is evident below mid (200 -- 800 m) layer. When the
difference between the WOA21c and WOA05 is calculated (blue lines in
Figure 7), it is obviously smaller than the result between WOA21c and
WOA01 (red lines in Figure 7) in all regions and all depths. Statistical
values such as bias and Root Mean Square Error (RMSE) dramatically
decrease as well (blue bins in Figure 8). This implies that the mean
state of temperature and salinity in WOA21c (January 2003 to December
2007) follows the consistent trend of oceanic climate change since the
20^th^ century. The significant difference between WOA01 and WOA05 also
indicates the large impact of recent observations used in only WOA05
(September 2001 to February 2005) on the existing oceanic climatology,
mainly based on the 20^th^ century observations.

Recently, two kinds of instrument biases that might cause the difference
between WOA21c and WOA01 (WOA05) have been reported. One is the warm
bias in XBT data associated with the fall-rate equations \[*Gouretski
and Koltermann*, 2007; *Willis et al*., 2007; *Wijffels et al.,* 2008\].
These XBT data were already used in WOA01 and WOA05 (not in WOA21c). As
shown in this study, WOA21c is warmer than WOA01 and WOA05 in general.
Without the XBT bias in existing climatologies, presumably, WOA21c would
be warmer than the others. The other bias is the large scale cold bias
in Argo data that is related to the systematic pressure sensor error
\[*Argo Steering Team*, 2008\]. This case is in addition to the SOLO
floats as mentioned in previous chapter. Since the observation in the
21^st^ century is relying mainly on Argo floats, this case causes a
negative bias on the global heat content and steric height as well as
our WOA21c. When this Argo systematic bias would be identified and
corrected again, WOA21c would be warmer than WOA01 (WOA05), too. Even
though we consider these two possible systematic biases, it is apparent
that the analyzed mean temperature in WOA21c is warm with respect to
WOA01 (WOA05). We expect that more detailed analyses unveiling these
instrument biases will be completed by further studies.

# 5. Assimilation validation

In this section, we present the collocated assimilation model assessment
approach by using WOA01, WOA05, and WOA21c, respectively. So far, most
large-scale assimilation studies have applied their assimilation systems
in the perfect model (twin experiment) context in which an arbitrary
model simulation result is considered as a true status. One of the
reasons for this perfect model assumption is that assimilation
performance is hard to validate using real observations because a
reasonable true status based on observations have been unknown due to
the data density and quality problems on a global scale. However, most
oceanographic communities want to check the base model performance and
assimilation results in the real oceanic state by applying the real
interannual forcing. Therefore, they have used WOA01 (WOA05) as a data
source for their large-scale data-model comparison. In this study, we
developed the monthly 3 dimensional gridded fields (WOA21c) representing
the global ocean state in the 21^st^ century, so that it will be
interesting and meaningful to address the direct model-data comparison
result using WOAs.

As a target model for our validation, we used the latest results for
2003-2007 from the fully CDA system developed at GFDL (hereafter
"GFDL~CDA~21c"). Since GFDL~CDA~21c used no flux restoring based on
climatology, this validation using WOAs will be meaningful. This
assimilation system employed two-step data assimilation procedure for an
Ensemble Kalman Filter under a local least squares framework with
super-parallelized technique applied to GFDL's coupled climate model
(CM2) (See the Figure 2 in *Zhang et al.* \[2007\]). The ocean component
of CDA is the fourth version of the Modular Ocean Model (MOM4)
configured with 50 vertical levels (22 levels of 10-m thickness each in
the top 220 m) and 1° by 1° horizontal B-grid resolution, telescoping to
1/3° meridional spacing near the equator. A totally independent ensemble
initial condition for CDA is formed by combining the atmosphere and land
states at 00UTC 1 January of years 1973, 1974, 1975, 1976, 1977, 1978
with the ocean and ice state at 00UTC 1 January 1976 of the GFDL IPCC
historical run using temporally-varying Green House Gas and Natural
Aerosol (CHGNA) radiative forcing from 1861. The IPCC control and
historical runs themselves were initialized by spinning up the CM2 for
380 years from the previous integration \[*Stouffer et al.,* 2004\] with
1860 fixed-year radiative forcing. Since 1976, oceanic observations
(World Ocean Database (WOD) for the 20^th^ century assimilation and Argo
profiles for the 21^st^ century assimilation) were assimilated into the
CDA with careful consideration of temperature and salinity covariance
(See the Figure 5 and Figure 6 in *Zhang et al.* \[2008\]). A
significant improvement in the data assimilation's skill is seen when
the Argo observation data is included, which is strongly related to the
data coverage of Argo network since the sampling coverage has a large
impact on the inferred temperature variability as pointed out by
*AchutaRao et al.* \[2006\]. More details about CDA system and previous
assimilation results in the 20^th^ and 21^st^ century can be found in
*Zhang et al.* \[2007, 2008\].

In this section, we will show the latest CDA results using a direct
comparison with our new gridded dataset. In order to undertake the
model-data comparison, all WOAs with 1° by 1° horizontal resolution and
23 standard depth levels were projected to the model grids. We converted
in situ temperatures of all WOAs into potential temperatures as well.

Figure 9 shows the vertical structure of the potential temperature and
salinity averaged over individual ocean basins for 2003-2007, and the
corresponding time series at 15 m, 205 m, 618 m, and 1364 m depth,
respectively. As we mentioned in Figure 6, it should be noted that grid
points where the observation data are insufficient to produce reliable
mapping estimates have been excluded from the box average in the same
manner for WOA21c, WOA01, WOA05, and GFDL~CDA~21c.

In general, GFDL~CDA~21c is in line with WOAs. However, GFDL~CDA~21c has
systematic bias underestimating the salinity below 205 m depth except
for the Atlantic Ocean (The North Atlantic (Figure 9c) shows no
significant model bias and the South Atlantic (Figure 9d) overestimates
the salinity below 600 m depth). These freshening biases gradually
decrease in time associate with the dynamic adjustment process. This
tendency can be clearly found at the 205 m depth in the Southern
Hemisphere (South Pacific (Figure 9b), South Atlantic (Figure 9d), South
Indian (Figure 9f), Antarctic Ocean (Figure 9g) and World Ocean (Figure
9h)). In the 21^st^ century, we have almost same amount of salinity
profiles compared to the temperature from Argo floats (In the 20^th^
century, only temperatures profiles were dominant mainly from MBT and
XBT). Increase of uniform salinity profiles makes it possible for
assimilation system to adjust the simulated salinity field to the
observation especially below the surface layer in the Southern
Hemisphere over time. For the surface, there is little tendency of
salinity adjustment because the fresh water flux (precipitation minus
evaporation) from the atmospheric data assimilation strongly affects the
oceanic condition as a surface boundary condition. Adjustment for the
temperature has already been reached before 2003 year due to high
sampling from MBT and XBT in the 20^th^ century (See the Figure 7 of
*Zhang et al.* \[2007\]).

GFDL~CDA~21c shows the consistent biases with WOA21c when it compared to
the WOA01 and WOA05 as shown in the previous section (Warming in all
oceans, freshening in the North Pacific and the Antarctic Ocean, and
salting in the North Atlantic). This result reflects the large
assimilation effects for 2003-2007. Figure 10 shows the vertical
difference of the annual mean temperature and salinity for individual
ocean basins in 2007. Red lines are mean differences between
GFDL~CDA~21c and WOA21c in 2007, which exactly represents the model
biases. Figure 11 shows the root mean square temperature and salinity
difference and offset of GFDL's CDA result compared to the WOA21c,
WOA01, and WOA05 averaged from 10 m to 1500 m depth over the individual
oceans in 2007. It is evident that statistical values dramatically
decrease when we used WOA21c for the assimilation validation. These
differences significantly decrease in the order of WOA01, WOA05, and
WOA21c, which reflects the consistent trend of oceanic climate change as
discussed in the previous section. In general, it should be noted that
it is likely to underestimate the assimilation performance from the
GFDL's CDA when we use the climatology such as the WOA01 or WOA05 as the
dataset for the model assessment. However, there are some areas where
the model agreement is better with WOA01 (WOA05) than with WOA21c. For
instance, when we take a look at the temperature (salinity) at 100 m
depth of the Antarctic Ocean (North Indian) in 2007 (Figure 10), model
seems to have no bias compared to WOA01 (WOA05), even though there is an
apparent cold (fresh) bias compared to the WOA21c. We claim that this is
an over-estimating case when we use the existing climatologies for the
model assessment.

# 

# 6. Summary and Conclusions 

We have presented and analyzed a new monthly gridded dataset of global
temperature and salinity. The product is based on the compilation of the
identified GTSPP and Argo data from 2003 to 2007. The main improvement
of our climatology as compared to previous studies is that is based on
the high quality profile dataset with no systematic errors (XBT
fall-rate equation problem, Argo pressure sensor (SOLO floats identified
to date) and salinity offset problem). In this study we employed WJO03
and BS05 methods to complete delayed mode QC for 3,937 Argo floats that
have not undergone (or completed) the delayed mode QC at the respective
DACs. 8.5% (3%) of total Argo floats (profiles) show the significant
salinity offset of more than 0.05 and they are mostly found around the
coastal areas and the Atlantic Ocean.

In order to undertake the comparison with existing climatology and
assimilation result, the observed data were optimally interpolated in
space and time using six spatial scales (large and small longitudinal,
latitudinal, and cross-isobath) and one temporal scale. This
three-dimensional gridded field retains more realistic and detailed
structures, since no merging with background fields such as
climatological mean or model outputs has been applied. The warm
difference in the 21^st^ century is apparent from 10 m to 1500 m depth,
while salinity change is different in every ocean and depth. At 10 m
depth, large scale freshening is seen throughout the North and western
Pacific, while salting is shown over the subtropical South Pacific and
the North Atlantic. The North Pacific exhibits a strong freshening up to
600 m depth. In contrast, all other areas experience a salting period
with slight freshening below mid (200 - 800 m) layer. We expect that
physical interpretations on the oceanic variability in the 21^st^
century will be followed in further studies.

Our new dataset has been applied to the assimilation assessment. The CDA
system based on GFDL's climate model is clearly in line with WOAs except
for some systematic salinity bias below the surface layer. However,
these biases gradually decrease over time associated with the increasing
of salinity profiles especially in the Southern Hemisphere. The best fit
with model results is WOA21c in most ocean and depth, which indicates
the assimilation effects for 2003-2007. Bias and RMSE of temperature and
salinity difference significantly decreases from WOA01 to WOA21c in most
ocean basins.

In this study, we emphasized the large impact of recent observation on
the existing climatology and the success of the CDA system developed at
GFDL. Our new dataset based on individual profiles from Argo and GTSPP
in near real time will be updated every month. This updated WOA21c will
be used for an operational prediction model as their initial and
boundary condition as well as their validation source in the 21^st^
century simulation, while WOA01 (WOA05) will be continuously used for
model spin-up and validation source for the hindcasting studies
including a numerical scheme development. This high quality dataset both
in temperature and salinity field makes various follow-up studies
possible as well. Our next multi-decadal CDA will be consistently
compared against the same dataset, and more detail assessments will be
addressed around ocean basins where model biases are conspicuous. We
will investigate the variability of not only temperature and salinity
fields, but also density and velocity (transport) by using additional
sea level data. This must precisely quantify the model sensitivities to
resolve the physical processes, numerical choices, and assimilation
effects. These studies can also help evaluate existing or future ocean
observing systems in terms of advanced quality control especially for in
situ data biases associated with the particular sensor problem, sampling
errors, objective analysis methods, and a strong link between the
observational and numerical oceanographic communities, which is very
important.

# 

# Acknowledgements

#  This research was supported by the Visiting Scientist Program at the National Oceanic and Atmospheric Administration's Geophysical Fluid Dynamics Laboratory (NOAA/GFDL), administered by the University Corporation for Atmospheric Research (UCAR). We would like to acknowledge the international Argo and GTSPP Program for the rich publicly available databases. We are grateful to Drs. A. T. Wittenberg and H.-C. Lee for their comments on the earlier version of this manuscript. Suggestions made by anonymous reviewers were very constructive in the revision of the manuscript.

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**Lists of Figures**

Figure 1. Horizontal distribution of the gridded temperature fields with
the observation data (black dots) at 700 m depth in August from 2003 to
2007. Areas where the data are insufficient to produce reliable mapping
estimates are left blank.

Figure 2. Example of delayed mode QC results. Left panels show
trajectories of two Argo floats (WMO ID: 1900073 (red line) and 1900075
(blue line)) with the annual mean ocean salinity (color shading) derived
from WOA01 at 550 m (upper panel) and 1750 m (low panel), respectively.
Middle panel indicates the salinity variability of the 1900073 float for
about 5 years at both depths. Right panel shows the same information for
1900075 float. Black (Blue) dots denote the real time (delayed mode) QC
data provided by GDAC. Green bars indicate the error variance of the
objective estimates and red lines are final QC results from this study.
GDAC provides the delayed mode QC of the 1900073 float only until
September 2005; there is no delayed model QC for 1900075 float provided
by GDAC as of January 2008.

Figure 3. (a) Spatial distribution of Argo profiles showing the salinity
offset of more than 0.05 averaged from surface to parking depths up to
December 2007. (b) The same as (a) but on the basis of float types with
different CTD sensors.

Figure 4. Flow chart for the quality control of the global temperature
and salinity data used in this study. The percentages represent the
profiles that passed (or failed) during every single QC process.

Figure 5a. Annual mean of the global temperature (top) and salinity
(bottom) at 10 m depth from the WOA01 (first columns) and WOA21c (second
columns) for 2003-2007. Third columns indicate the error variances of
objective estimates for WOA21c, and the last columns are the horizontal
differences between WOA21c and WOA01, respectively.

Figure 5b. Same as Figure 5a but for the 1500 m depth.

Figure 6. Upper panels shows the global mean (0-360, 60S-60N)
temperature in the upper ocean (10 m -- 700 m) estimated by WOA01 (black
lines), WOA05 (green lines) and WOA21c (red line), respectively. Black
lines (Red line) on the right panels show the difference between WOA05
(WOA21c) and WOA01. Dotted (Solid) lines represent the fully-sampled
(sub-sampled) results. Discrepancies between these two curves (dotted
and solid lines) are caused by the under-sampling of observations during
the mapping procedure. Lower panels show the same information for
salinity.

Figure 7. Vertical difference of the annual mean temperature and
salinity among the WOA01, WOA05, and WOA21c averaged over individual
oceans (NP: North Pacific, SP: South Pacific, NA: North Atlantic, SA:
South Atlantic, NI: North Indian, SI: South Indian, AO: Antarctic Ocean,
WO: World Ocean) for 2003-2007. Red (Blue) lines indicate the mean
differences between WOA21c and WOA01 (WOA05). Dotted green lines denote
the range of error variances of objective estimates for WOA21c.

Figure 8. Statistics for the temperature (left panels) and salinity
(right panels) averaged from 10 m to 1500 m depth over individual oceans
as shown in Figure 7. Red (Blue) bins indicate the bias (upper panels)
and RMSE (lower panels) calculated between WOA21c and WOA01 (WOA05).

Figure 9a. Vertical structure of the potential temperature (left panels)
and salinity (right panels) averaged over the North Pacific for
2003-2007, and the corresponding time series at 15 m, 205 m, 618 m, and
1364 m depth, respectively. Blue (Black, Green, and Red) lines indicate
the results from GFDL~CDA~21c (WOA01, WOA05, and WOA21c). All time
series averaged around the North Pacific have been calculated
considering the variability of data-sparse regions of WOA21c as shown in
Figure 1.

Figure 9b. Same as Figure 9a but for the South Pacific.

Figure 9c. Same as Figure 9a but for the North Atlantic.

Figure 9d. Same as Figure 9a but for the South Atlantic.

Figure 9e. Same as Figure 9a but for the North Indian.

Figure 9f. Same as Figure 9a but for the South Indian.

Figure 9g. Same as Figure 9a but for the Antarctic Ocean.

Figure 9h. Same as Figure 9a but for the World Ocean.

Figure 10. Vertical difference of the annual mean potential temperature
and salinity between GFDL~CDA~21c and WOAs averaged over each region.
Red (Black, Green) lines indicate the mean differences between
GFDL~CDA~21c and WOA21c (WOA01, WOA05) in 2007.

Figure 11. Statistics for the potential temperature (left panels) and
salinity (right panels) averaged from 10 m to 1500 m depth over
individual oceans as shown in Figure 10. Red (Black, Green) bins
indicate the bias (upper panels) and RMSE (lower panels) calculated
between GFDL~CDA~21c and WOA21c (WOA01, WOA05) in 2007.