OSOcean ScienceOSOcean Sci.1812-0792Copernicus GmbHGöttingen, Germany10.5194/os-11-195-2015Argo data assimilation into HYCOM with an EnOI method in the Atlantic
OceanMignacD.davi.mignac@gmail.comTanajuraC. A. S.SantanaA. N.LimaL. N.XieJ.https://orcid.org/0000-0002-8602-2774Graduate Program in Geophysics, Physics Institute and Geosciences
Institute, Federal University of Bahia, Salvador, BrazilOceanographic Modeling and Observation Network,
Center for Research in Geophysics and Geology, Federal University of Bahia, Salvador, BrazilPhysics Institute, Federal University of Bahia, Salvador, BrazilOcean Sciences Department, University of California, Santa Cruz, CA, USAInstitute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, ChinaD. Mignac (davi.mignac@gmail.com)11February20151111952138April20142July201418December20148January2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.ocean-sci.net/11/195/2015/os-11-195-2015.htmlThe full text article is available as a PDF file from https://www.ocean-sci.net/11/195/2015/os-11-195-2015.pdf
An ocean data assimilation system to assimilate Argo temperature (T) and
salinity (S) profiles into the HYbrid Coordinate Ocean Model (HYCOM) was
constructed, implemented and evaluated for the first time in the Atlantic
Ocean (78∘ S to 50∘ N and 98∘ W to 20∘ E). The system
is based on the ensemble optimal interpolation (EnOI) algorithm proposed by
Xie and Zhu (2010), especially made to deal with the hybrid nature of the HYCOM
vertical coordinate system with multiple steps. The Argo T–S profiles were
projected to the model vertical space to create pseudo-observed layer
thicknesses (Δpobs), which correspond to the model target densities. The
first step was to assimilate Δpobs considering the sub-state vector
composed by the model layer thickness (Δp) and the baroclinic velocity
components. After that, T and S were assimilated separately. Finally, T was
diagnosed below the mixed layer to preserve the density of the model
isopycnal layers. Five experiments were performed from 1 January 2010 to
31 December 2012: a control run without assimilation, and four assimilation
runs considering the different vertical localizations of T, S and Δp. The
assimilation experiments were able to significantly improve the thermohaline
structure produced by the control run. They reduced the root mean square
deviation (RMSD) of T and S calculated with respect to Argo independent data
in 34 and 44 %, respectively, in comparison to the control run. In
some regions, such as the western North Atlantic, substantial corrections in
the 20 ∘C isotherm depth and the upper ocean heat content towards
climatological states were achieved. The runs with a vertical localization of
Δp showed positive impacts in the correction of the thermohaline structure
and reduced the RMSD of T (S) from 0.993 ∘C (0.149 psu) to 0.905 ∘C
(0.138 psu) for the whole domain with respect to the other assimilation
runs.
Introduction
Many ocean circulation models include highly sophisticated numerical schemes
and a large set of physical parameterizations. However, these are
approximations of the governing equations and therefore they are sources of
errors or discrepancies with respect to observations. Also, errors may be
produced due to inaccuracies of the initial conditions, atmospheric forcing
and lateral boundary conditions (Kalnay et al., 1996; Chassignet et al.,
2009). For these reasons, data assimilation methods are important scientific
tools in oceanography and other fields. They combine model outputs with
observational data in a mathematically optimal or sub-optimal way and
produce an objective analysis with smaller errors than the model output
alone (Daley, 1991; Kalnay, 2003). The analysis is used as the model initial
condition for weather and climate forecasts (Kalnay, 2003), and more
recently for ocean weather forecasts under the framework of operational
oceanography (Dombrowsky et al., 2009; Chassignet et al., 2009; Schiller and
Brassington, 2011). Data assimilation methods are also applied to produce
long-term series of analyses for climate diagnostics studies and they
contribute to a better understanding of the physical mechanisms that are
responsible for the ocean variability. For example, the depth of the mixed
layer and the heat content can be better represented by analyses than by
model simulations without assimilation (Carton and Giese, 2008).
A major obstacle in ocean data assimilation is the relatively small volume
of observed ocean data available for assimilation and validation. Most of
the spatial and high-frequency temporal variability from the ocean surface
is acquired by satellite measurements such as the sea surface height (SSH)
and sea surface temperature (SST). However, these observations are available
for only a few decades and they are insufficient to determine the
sub-surface variability (Ezer and Mellor, 1994; Chassignet et al., 2006).
Therefore, the implementation of the Argo network with more than 3300
profilers freely reporting temperature and salinity data down to 2000 m
has transformed the in situ ocean observing system in the new millennium (Schiller
and Brassington, 2011). For the first time it is possible to have continuous
measurements of the temperature, salinity and velocity of the upper ocean
which makes the Argo network indispensable for any global or regional data
assimilation system (Chassignet et al., 2007; Oke et al., 2008; Xie and Zhu,
2010). For example, Oke and Schiller (2007) showed that the assimilation of
SST and SSH should be complemented with Argo profiles since the assimilation
of this component plays a crucial role in improving the model thermohaline
state, especially for salinity.
Among all data assimilation methods, the ensemble-based methods use a set of
different model states to estimate the model errors (Evensen, 2003; Oke et
al., 2005). One widely used is the ensemble optimal interpolation (EnOI)
(Oke et al., 2005) in which the ensemble members are derived from an
existing model run. This reduces the computational cost of the assimilation
and makes this method suitable for operational purposes. It is already
verified that the EnOI is able to effectively constrain the model towards
observations. For instance, it was successfully applied to assimilate Argo
data in the Pacific Ocean (Xie and Zhu, 2010), sea level anomaly (SLA) data
in the South China Sea (Xie et al., 2011) and in the Gulf of Mexico
(Counillon and Bertino, 2009), and SLA, SST and Argo data in the Australian
region (Oke et al., 2008) and in the Indo-Pacific Ocean (Yan et al., 2010).
Considering the importance of the model in the construction of the analysis,
several state-of-the-art, publically available ocean circulation models
should be evaluated in order to develop an operational ocean forecasting
system with data assimilation. One choice is the HYbrid Coordinate Ocean
Model (HYCOM). It is formulated in terms of target densities and employs a
hybrid vertical coordinate system to combine the best features of each
vertical coordinate in specific oceanic regions (Bleck, 2002). The model has
fixed z-levels to better represent the mixed layer, isopycnal layers to
discretize the deep stratified ocean and σ-levels to better
reproduce the bathymetry in shallow areas. Because of the hybrid nature of
the model, the best way to assimilate vertical profile data into HYCOM is
still an open question. A choice of the model prognostic variables should be
made a priori since only two of the three state variables – temperature,
salinity and potential density – are independent. Furthermore, the layer
thickness, which is a key model variable, varies spatially and temporally
according to the evolution of temperature, salinity and density.
Taking into account these characteristics, Thacker and Esenkov (2002;
hereafter TE) proposed a method to assimilate expendable bathythermographic
(XBT) data into HYCOM with a three-dimensional variational scheme (3-D Var).
In this work, the XBT profiles are converted into observed layer
thicknesses that respect the target densities of each model layer, and the
temperature and salinity of the XBTs are projected to each observed
layer thickness. Xie and Zhu (2010; hereafter XZ) used an EnOI scheme to
assimilate Argo data, and showed that the TE approach produced significant
improvements in relation to simpler schemes, in which the innovation is
calculated in the observational space.
Very little has been published to evaluate the impact of in situ profile data
assimilation into HYCOM with a focus on the Atlantic Ocean (e.g., Thacker et
al., 2004; Belyaev et al., 2012). In the present work, a data assimilation
system for HYCOM was constructed, implemented and realized for the Atlantic
Ocean for the first time. The data assimilation algorithm follows the EnOI scheme suggested by XZ very
closely. The present system was developed
within the Brazilian Oceanographic Modeling and Observation Network (REMO)
to be a component of an operational ocean forecasting system for the
Atlantic Ocean (www.rederemo.org) (Tanajura and Belyaev, 2009; Lima et al.,
2013; Tanajura et al., 2013). In this paper, the focus is on the impact of
Argo data assimilation over the Atlantic Ocean and on a sensitivity study of
the analysis run, considering different vertical localizations of the model
error co-variance matrix involving temperature, salinity and especially the
layer thickness. The REMO forecasting system uses a nested model approach
based on HYCOM. The present work deals with the construction of large-scale
analyses over almost the whole Atlantic Ocean. This domain was conceived and
configured to provide reasonable boundary conditions to higher-resolution
grids of greater interest to REMO over the South Atlantic. In the near
future, the present data assimilation methodology will be used in the
Atlantic domain, and in the higher-resolution grids over the Metarea V (from
35.5 ∘S to 7 ∘N, west of 20 ∘W to Brazil) and sub-regions off
the Brazilian coast of particular interest to the Brazilian Navy and the
active petroleum industry located there.
This paper is organized as follows. In Sect. 2, HYCOM and the
configuration used in this study are briefly described. In Sect. 3, the
EnOI scheme to assimilate Argo data is presented. Section 4 shows the design
of the assimilation experiments and Sect. 5 presents their results.
Section 6 contains discussion and conclusions.
HYCOM and its configuration
HYCOM is a primitive equation general circulation model, which has evolved
from the Miami Isopycnic Coordinate Ocean Model (MICOM) (Bleck and Smith,
1990). The main advantage of the isopycnal coordinate is its ability to
maintain the properties of water masses which do not communicate directly
with the mixed layer. In HYCOM, with the advection of layer thicknesses by
the continuity equation, the isopycnal coordinates smoothly transform into
the z-coordinate in the weakly stratified upper ocean mixed layer and into
the terrain-following σ-coordinate in the shallow water regions (Bleck,
2002; Chassignet et al., 2007). The freedom to adjust the vertical spacing
of the coordinate surfaces in HYCOM simplifies the numerical implementation
of several physical processes, such as turbulence in the mixed layer,
detrainment and convective adjustment. Also, the capability of assigning
additional coordinate surfaces to the oceanic mixed layer in HYCOM allows
the option of implementing sophisticated vertical mixing turbulence closure
schemes (Halliwell, 2004). Hence, HYCOM is considered to be a suitable model
for operational ocean forecasting systems and climate studies (Chassignet et
al., 2007, 2009). In this work, the version 2.2.14 of
HYCOM was used.
The model grid in the present configuration has 760×480 horizontal grid
points, with a spatial resolution of 0.25∘, which remains constant in
longitude, but varies in latitude attaining higher resolution towards the
poles. The computational model domain covered almost all the Atlantic Ocean
from 78 ∘S to 50 ∘N and from 100 ∘W to 20 ∘E, excluding the
Pacific Ocean, the Mediterranean Sea and the North Atlantic subpolar region.
The choice for the northern limit at 50 ∘N was based on two facts.
First, the surface currents are primarily zonal at this latitude (Gabioux et
al., 2013). Second, the purpose of this grid is to provide reasonable
boundary conditions to higher-resolution grids that will soon be configured
along the Brazilian coast, which is the area of main interest to REMO and
far away from the northern boundary. On the lateral boundaries, relaxation
to monthly climatological temperature and salinity from Levitus (1982) was
applied considering the outermost 10 grid cells and the timescale of 30
days. This approach attempts to preserve climatological shear through
geostrophic adjustment and has been successfully used in previous works
(e.g., Paiva and Chassignet, 2001; Gabioux et al., 2013). Constant barotropic
volume fluxes were imposed: zero flux in the north, eastward flux of 110 Sv
in the Drake Passage, westward flux of 10 Sv in 12 grid points adjacent to
South Africa along 20 ∘E, and eastward flux of 120 Sv further south to
Antarctica.
The model was configured to use surface pressure as reference for potential
density, aiming for improved representation of near-surface fields, at the
cost of not representing accurately the Antarctic Bottom Water (Chassignet
et al., 2003). The vertical domain was discretized in 21 vertical layers.
The chosen target potential densities were 19.50, 20.25, 21.00, 21.75,
22.50, 23.25, 24.00, 24.70, 25.28, 25.77, 26.18, 26.52, 26.80, 27.03, 27.22,
27.38, 27.52, 27.64, 27.74, 27.82 and 27.88. To obtain the volumetric
density in kg m-3, 1000 should be added to each target
density. The first layers have a few light target density values that ensure
a minimum of three fixed-depth layers near the surface of the ocean.
The vertical mixing scheme is the K-profile parameterization (KPP) (Large et
al., 1994). The model bathymetry was interpolated from the Earth Topography 1
(ETOPO1) with 1 min resolution. The model was initialized from the state of
rest with climatological thermohaline structure, and a 30-year spin-up was
performed using monthly climatological forcing fields from the Comprehensive
Ocean and Atmosphere data set (COADS) (Woodruff et al., 1987). Then, from
January 1995 to December 2009, the model was forced on the ocean surface
with 6-hourly atmospheric reanalysis version 1 by the National Centers for
Environmental Prediction/National Centers for Atmospheric Research
(NCEP/NCAR) (Kalnay et al., 1996), including precipitation, wind speed at 10 m,
short- and long-wave radiation fluxes at the surface, air temperature and
humidity at 2 m. The result of this simulation was used as the initial condition
for the Argo data assimilation experiments starting on 1 January 2010.
Mean temperature (∘C) and salinity (psu) in the upper 1000 m along
25∘ W for (a) averaged simulated temperature from January 1997
to December 2008, (b) climatological temperature from WOA13, (c) averaged simulated
salinity from January 1997 to December 2008, and (d) climatological
salinity from WOA13.
Figure 1 shows the mean state of temperature and salinity simulated by HYCOM
from 1 January 1997 to 31 December 2008 and its comparison with the World
Ocean Atlas 2013 Climatology (WOA13) (Boyer and Mishonov, 2013) along
25 ∘W for the upper 1000 m. WOA13 climatology shown in Fig. 1 spans the
period from 1995 to 2012. In general, the pattern of the simulated
temperature and salinity is similar to the WOA13 climatology, particularly in
the South Atlantic, which is the main target area for REMO. In the North
Atlantic large differences are seen between 25 and 50 ∘N below 400 m.
The Mediterranean water (MW) is more saline, warmer and found further
north in comparison with WOA13. The Mediterranean Sea is not simulated in
this grid and is imposed as a relaxation towards monthly climatological
temperature and salinity at the boundary without mass flux. In addition, the
simulated temperature is higher than WOA13 in the upper 300 m of the
equatorial region, while the values of high-salinity cores in the subtropical
gyres are smaller than the values found in the climatology. It is worth
noting that this resolution of 1/4∘ is not enough for HYCOM to
properly solve the Gulf Stream and its associated dynamics (Hulburt and
Hogan, 2000), which may also contribute to some of the model discrepancies in
comparison to WOA13 in the mid-latitudes of the North Atlantic. It is
expected that assimilation of Argo data will improve the model state and
reduce the existing differences in the thermohaline structure with respect to
the WOA13 climatology.
The data assimilation scheme
The analysis (Xa) according to the EnOI scheme is given by the formula
(Evensen, 2003)
Xa=Xb+K(Y-HXb),
where Xb∈RN is the model background state or the prior,
K is the gain matrix, Y is the vector of observations, Y∈RNOBS, and HXb is the projection of
the prior onto the observational space by the observational operator H. The term
(Y-HXb) is called the innovation vector and the term
K(Y-HXb) is the analysis increment. The gain matrix
K is calculated from the equation
K=α(σ∘B)HT[αH(σ∘B)HT+R]-1,
where B is the co-variance matrix of the model errors and R is the diagonal
variance matrix of the observational error. The term α∈(0,1] is a scalar that can tune
the magnitude of the analysis increment and σ denotes the localization operator applied over
B by a Schur product represented by the symbol ∘. Equation () is used by
many data assimilation schemes such as the optimal interpolation, the ensemble Kalman filter (EnKF)
or the EnOI. In the EnOI scheme, B is estimated from the equation
B=A′A′T(M-1),
where A′=[A′1A′2,…,A′M], A′k=(Xk-1M∑m=1MXm), Xk∈RN
is the model state vector of the kth ensemble member with k varying from 1 to M, and M=132 is the number of
ensemble members used in all assimilation steps in this study. This ensemble of model anomalies can
be taken from a long-term model run (Evensen, 2003) or a spin-up run (Oke et al., 2008) in order to
capture the model variability at certain scales. Thus, even being stationary in time, this ensemble
of model anomalies allows for the description of the spatial correlations and the anisotropic nature of ocean
circulation, keeping the analysis dynamically consistent and substantially reducing the
computational cost. Details on how the B matrix was calculated here regarding the high-frequency variability of the model are described below.
Calculation of the innovation vector
Basically, there are two ways to calculate the innovation vector. The first
one projects the model state vector into the observational space. In this
case, the temperature, salinity and layer thicknesses of HYCOM are projected
into the vertical levels of the Argo profiles, which provide almost
vertically continuous measurements of temperature and salinity, ranging from
near surface to 2000 m. This procedure makes the H operator
become
complex and non-linear. Since Eq. (1) is linear, the use of a
non-linear operator may cause problems in the linear analysis update and may
contribute to a sub-optimal assimilation performance (Xie and Zhu, 2010). A
second way to calculate the innovation follows the strategy adopted by TE and
by XZ for HYCOM. In this approach, temperature (T) and salinity
(S) data profiles are projected into the model vertical space to create
pseudo-observed layer thicknesses (Δpobs). This is done following the
hybrid nature of the model's layers: each layer is required to have a minimum
thickness and, after that requirement is satisfied, it should be as close as
possible to its specified target value of potential density. Thus, each Argo
profile is processed as follows. Based on a pair of profiles of potential
temperature and salinity, the profile of potential density can be calculated
by an equation of state for seawater (Brydon et al., 1999). The estimated
surface density from the Argo profile is compared to the top layer target
density to decide whether any sufficiently low-density water was observed. If
not, the minimum thickness is assigned to the layer and the procedure is
repeated for the layer below. Once water with the target density is
encountered, the remainder of the potential density profile can be
partitioned and the layer averages will correspond to the model target densities down to the maximum depth of the Argo profile.
Figure 2 shows the vertical profiles of potential temperature, salinity and
potential density at z-levels and the new synthetic observations defined at
model layers for an Argo float located at 4.04∘ N and 23∘ W on 1
January 2010. In Fig. 2, each Δpobs respects the target densities of
the model as soon as the first target density is found in the potential
density profile of the Argo data. Also, the averages for all the
observational variables are computed for each layer, as shown by the
discretized profiles of potential temperature and salinity in the model
layers. The step functions of T, S and Δpobs are the data that will
be actually assimilated by the EnOI scheme.
Profile of potential temperature (∘C), salinity (psu) and potential density
(kg m-3) from an Argo float located at 4.04∘ N and 23∘ W on 1 January 2010 plotted
against its approximation for HYCOM as layer averages. The model target density
is indicated by the solid black vertical lines.
The modified EnOI to assimilate profile data into HYCOM
After the observation is defined in the HYCOM layers, the observed layer
thicknesses are assimilated in a first step by Eqs. (1) and (2), and the
analysis update is carried out for the model control state vector
(Δpi,Ui,Vi);i=1,…,nz, where Δpi,Ui and Vi are the layer thicknesses and the baroclinic
velocity components, respectively, defined at the nz model layers
for a single time step. To avoid the analyzed layer thicknesses occasionally
becoming negative, a computationally efficient scheme based on Sakov et al. (2012)
is used. If the thickness of a layer becomes negative, it is reset to
zero and the thickness deficit is added to the neighboring layers. The
layers are traversed twice, once from top to bottom, and a second time from
bottom to top. Finally, the sum of the layer thicknesses should be equal to
the initial bottom pressure (or local depth).
In the next step, temperature and salinity are assimilated separately and in
a univariate way also according to Eqs. (1) and (2), but now with the
previously adjusted layer thicknesses. Finally, T or S is diagnosed below
the mixed layer by the seawater equation of state. According to TE, “within
the context of HYCOM, when correcting temperature, it is necessary to decide
whether to move interfaces, keeping potential densities of the layers
unchanged, or to correct the densities, leaving the interfaces unchanged”.
Therefore, when the assimilation of layer thicknesses is performed, the
potential density should be kept constant in the ocean simulated with
isopycnal coordinates. Considering that most of the T corrections in the
experiments of XZ were due to changes in the layer thicknesses by the
assimilation of Δpobs, T was chosen to be diagnosed below the mixed
layer in the present work, instead of S.
Generation of a running ensemble
Many authors have shown how sensitive the EnOI and EnKF schemes are to the
ensemble size (Mitchell et al., 2002; Evensen, 2003; Oke et al., 2007). In
the EnOI scheme, the propagation of the observational information is highly
dependent on the size and the quality of the ensemble, because the final
analysis can be regarded as a combination of the ensemble anomalies whose
relative weight is determined by the co-variances. In this work, 132
ensemble members were used. They were selected from the model free run for
each assimilation day, regarding the intra-seasonal variability and the high-frequency model dynamics. This number of ensemble members was chosen after a
few sensitivity experiments considering a reasonable representation of the
model's anomalies without high computational cost, and is in agreement with
the numbers used in recent works (e.g., Counillon and Bertino, 2009; Xie and
Zhu, 2010; Xie et al., 2011).
The long-term model run that was used to select the ensemble members
corresponded to the 12-year period from 1 January 1997 to 31 December
2008. For each assimilation step, a different model co-variance matrix was
calculated. Considering the assimilation day, 11 ensemble members for each
year of the 12-year period were selected around the date of the
corresponding assimilation day. For instance, to perform assimilation on 15
March 2010, 11 members centered on 15 March of each year from 1997 to 2008
were taken 8 days apart, which gives a time window of 80 days for each
year. However, the computational code developed here is flexible to use
another number of ensemble members and to select different intervals between
each ensemble member.
Localization
The localization technique is a feasible solution to reduce the effect of
the sampling error in the ensemble-based methods, especially when the
ensemble size is small (Hamill et al., 2001; Oke et al., 2007). The
significance range of a measurement is a critical question in assimilation.
In the present case, it should be unreasonable that a measurement in the
Gulf Stream contributes to resolving the mesoscale features of the
circulation of the Brazil Current. Therefore, the localization aims to
delete long-distance correlations that may appear in the gain matrix and to
limit the influence of a single observation by the Kalman update equation
within a fixed region around the observation location. However, a drawback
of the localization is that it can breakdown the geostrophic balance. Oke et
al. (2007) showed that localization conserves the geostrophic balance when the
radius of the localization is equal to or larger than the radius of
decorrelation, which is the scale in which the correlations become
negligible.
For many EnKF and EnOI schemes, localization is only applied in the
horizontal direction (Oke et al., 2008; Sakov et al., 2012). However, some
works have already investigated the vertical localization and its impact on
the analysis, such as in XZ. They presented a vertical localization scheme
for T and S when assimilating Argo profiles into HYCOM. Here, localization
in the vertical direction is also investigated, but differently from XZ, as
the focus is on Δp.
The operator σ∘ in Eq. (2) defines the implementation of
the localization by a Schur product, i.e., a product between elements with
the same index in the arrays. The notation σ∘B denotes the
Schur product of a correlation matrix σ with the B matrix, and
this approach is used in many works (Oke et al., 2007, 2008; Xie
and Zhu, 2010). Here, the localization operator is separated into a
horizontal component (σh) and a vertical component (σv),
and it is defined as σ=σhσv.
Horizontal localization
In order to define the horizontal correlation matrix σh, a
fifth-order function is used as in Gaspari and Cohn (1999):
σhIij,L=-14IijL5+12IijL4+58IijL3-53IijL2+1,0≤Iij≤L112IijL5-12IijL4+58IijL3+53IijL2-5IijL+4-23IijL-1,L<Iij≤2L0,Iij>2L
In this function, Iij is defined as the Euclidean distance between any
two arbitrary points in the horizontal space and L is the horizontal scale
of influence defined as 150 km for all the assimilated variables. It is
similar to a Gaussian function in physical space but more compact. The
correlation function σh forces the model error co-variance matrix
B to decrease to zero when Iij reaches 300 km. Thus, the radius of
localization is defined as 300 km.
The horizontal scale of influence was chosen to be 150 km because this
number roughly matches the scales of boundary currents (Ezer and Mellor,
1994; Carton and Giese, 2008). Since the present work was the first REMO
effort to implement an EnOI scheme to assimilate Argo data into HYCOM, the
horizontal scale of influence was fixed for the entire model domain and for
all depths. In this case, the choice of 150 km was conservative in order to
avoid capturing co-variances that could damage the analysis in
high-variability regions, such as the Gulf Stream and the Brazil–Malvinas
Confluence.
Vertical localization
Concerning the vertical localization, XZ found considerable off-diagonal
correlations for temperature and salinity between different HYCOM layers.
However, there was no significant impact in the analysis when those
co-variances were filtered and no significant differences in the experiments
with and without vertical localization were reported. However, in the
present work the vertical localization of co-variances between the layer
thicknesses was investigated. They showed considerable off-diagonal
correlations of above 0.4 or below -0.4 from the seventh layer to the bottom
(Fig. 3). In the formulation of the vertical localization operator, the
vertical distance between the layers was measured by the water column
stratification, rather than by the Euclidian distance. Thus, in order to
define the correlation matrix σv, the following function was
used:
σv(i,j)=exp-(Δρ(i,j)/Lρ)2,
where Δρ(i,j) is the density
difference between the HYCOM layers i and j, and
Lρ is a vertical-scale factor defined as 0.5 kg m-3 according to XZ.
As shown by Fig. 3, when applying
the vertical localization, the elements a few entries away from the diagonal
in the co-variance matrix are almost canceled, but the correlations between
the adjacent layers remain.
Vertical correlations of layer thickness between different layers at the location
of an Argo float (69.95∘ W and 30.14∘ N) in the model domain: (a) calculated directly
from the model ensembles (M=132) and (b) after applying the vertical localization of
layer thickness according to Eq. (5) and Lρ defined as 0.5 kg m-3. The white lines denote correlations above 0.4 and below -0.4.
Observational errors
Since the observations that are actually assimilated are defined in the
model vertical space, the observational errors of T and S in the model
layers are calculated as a function of the depth D in meters,
respectively, as in XZ:
SDT(D)=0.05+0.45exp(-0.002D),SDS(D)=0.02+0.10exp(-0.008D).
The standard deviations of the observational errors of T vary in the
vertical from 0.5 ∘C on the surface to 0.05 ∘C in the deep ocean.
For S, they vary from 0.12 to 0.02 psu. According to Eqs. (6) and (7),
the observational errors are assumed Gaussian with zero mean and
uncorrelated.
In case of layer thickness, according to TE, the standard deviation of
Δpobs is calculated depending on the oceanic region.
For example, in the mixed layer, the layer thickness is assigned to the
minimum layer thickness allowed by the model configuration, and the standard
deviation is defined as 0.05Δpk, where Δpk represents
the layer thickness at the kth layer calculated from the observed profiles.
In the isopycnal layers, the standard deviation is defined by the formula
SD(Δpk)=max0.5δpk,max0.05Δpk,Δpk0.05+(0.5-0.05)sdσ(k)SDσ(k),
where δpk is the minimum layer thickness specified by the model
configuration for the kth layer, sdσ(k) is the minimum standard
deviation of the potential density defined as 0.001 kg m-3 ,
and SDσ(k) is the standard deviation of the potential density
from observations. The latter should be small when the potential density
from the observed layer thickness has values close to its target
density.
Assimilation experiments Argo data and quality control
The Argo data employed in the assimilation were collected from a global data
center (available at: ftp://ftp.ifremer.fr/ifremer/argo/geo/atlantic_ocean/). All
those observations were required to step into a data quality control (QC)
procedure, which is an essential part to any oceanic data assimilation
system since spurious data can compromise the analysis quality and introduce
artificial trends in the assimilation results (Yan and Zhu, 2010). The QC
used in this work was both developed by REMO together with the Brazilian Navy
and tests the date, the location and the temperature and salinity of each Argo
profile previously collected. The validation of T and S profiles was made
according to all criteria and references established by the Global
Temperature and Salinity Pilot Program from the Intergovernmental Oceanographic
Commission (IOC, 1990) and from the database of the National Oceanographic
Data Center (NODC).
From January 2010 to December 2012, 47 999 valid Argo profiles were
assimilated into HYCOM in the Atlantic Ocean. These profilers covered almost
the entire model domain, and were especially dense in the North Atlantic, as
shown in Fig. 4.
Configuration and evaluation of the assimilation experiments
Five integrations were performed from 1 January 2010 to 31 December 2012
to evaluate the impact of the Argo data assimilation and the vertical
localization in the correction of the ocean state and circulation. The first
one was a control run without assimilation (CTL). The other runs were
assimilation runs, namely, (i) assimilation without vertical localization
(ASSIM), (ii) assimilation with vertical localization of layer thickness
(VL_DP), (iii) assimilation with vertical localization of
temperature and salinity (VL_TS) and (iv) assimilation with
vertical localization of all the assimilated variables (VL_DPTS). In all experiments with data assimilation, a 3-day observational
window was considered in order to select all the valid profiles collected 3
days before the assimilation day. The interval between each assimilation
step was also 3 days and the scalar α in Eq. (2) was defined as 0.3.
The Argo daily data were also used to validate the results of the experiments
on a daily basis, despite the fact that assimilation was performed only
every 3 days. However, the prior state was always considered in the evaluation of
the assimilation runs. The prior is the model state immediately before the
assimilation step. Considering each assimilation cycle, the ocean states at
24, 48 and 72 h after assimilation were assessed in the assimilation runs.
Therefore, the validation of the prior is done with independent data, since all
the Argo profiles employed in the validation were used only in the next
assimilation cycle. This procedure is analogous to the evaluation of
forecasts. Moreover, 16 fixed moorings from the Prediction and Research
Moored Array in the Tropical Atlantic (PIRATA) were used as another
independent data set for validation. Their locations are represented by red
dots in Fig. 4. Also, the domain was split into 12 sub-regions from a to l, as
shown in Fig. 4, in order to evaluate the regional impact of the
assimilation. These sub-regions and their coordinates were selected taking
into account the spatial distribution of the surface mean kinetic energy and
the mean standard deviations of SSH, SST and sea surface salinity (SSS) from
1997 to 2008. The numbers of Argo profiles assimilated in the experiments
in the 12 sub-regions a–l were 3085, 2352, 2522, 540, 1463, 2750, 2475,
1849, 1560, 1597, 2536 and 3067.
Locations of the 47 999 valid Argo profiles (blue dots) assimilated
and also used to validate the prior state of each experiment from 2010 to
2012 in the model domain (100∘ W–20∘ E, 78∘ S–50∘ N), which excludes the Pacific Ocean, the
Mediterranean Sea, and the North Atlantic subpolar region. The 16 fixed moorings from PIRATA used in
the experiment's validation are represented by red dots. The numbers of valid
Argo profiles in the 12 sub-regions (a–l) were 3085, 2352,
2522, 540, 1463, 2750, 2475, 1849, 1560, 1597, 2536 and 3067.
Outputs from the HYCOM Navy Coupled Ocean Data Assimilation (HYCOM + NCODA)
(Chassignet et al., 2007, 2009) system available in
z-levels and fields from the Ocean Surface Current Analyses Real Time
(OSCAR) (Johnson et al., 2007) were employed to compare the velocity fields
produced by the assimilation runs. Also, WOA13 climatology for the period
from 2005 to 2012 was used to evaluate the mean state of T, S and heat
content of the upper 300 m (HC300) in all experiments. In this period, WOA13
includes the global coverage of Argo floats to compose the climatological
gridded fields of T and S in 1/4∘ of spatial resolution.
ResultsComparison of mean states
The first comparison is conducted with the WOA13 climatology along 25∘ W
for the upper 1000 m (Fig. 5). It was already verified that the free model
run mean from 1997 to 2008 showed substantial differences with respect to
the WOA13 climatology (Fig. 1). According to Chen et al. (2000), ocean
circulation models can naturally present large and systematic biases in T and
S due to their initialization and configuration. This is also shown by the
control run, particularly in the North Atlantic. As mentioned before, to
simulate the MW in the Atlantic, relaxation of T and S in the boundary
condition is imposed without mass flux. Moreover, the resolution of 1/4∘
could also be a limitation to accurately solve the Gulf Stream and its
associated dynamics in the mid-latitudes of the North Atlantic (Hulburt and
Hogan, 2000). The main purpose of this grid is to provide boundary conditions
for higher-resolution grids focusing on the Metarea V. However, even with
these limitations, the assimilation schemes are able to substantially reduce
these differences and correct the ocean state towards WOA13. For example, the
positive temperature bias up to 3 ∘C and the negative salinity bias up to
0.4 psu in the upper 300 m of the control run are not produced in any
assimilation run. Moreover, all the discrepancies found in the MW are
remarkably diminished in the data assimilation runs, which are able to
decrease the differences in 0.6 psu and more than 2 ∘C towards WOA13
between 20 and 40∘ N in the sub-surface, especially below 400 m.
This correction is very effective in the VL_DP and
VL_DPTS runs, which adopt the vertical localization of
Δp. The VL_DPTS run is able to more efficiently
improve the mean T and S states in the North Atlantic along the entire water
column by further reducing the differences of 1 ∘C and 0.1 psu found in
the other assimilation runs with respect to WOA13. Also, at 300 m near
25∘ S, only the VL_DPTS run decreases the differences
towards WOA13 from more than 3 to almost 1 ∘C, while the ASSIM and
VL_TS runs are not able to reduce these differences with
respect to the control run. But, south of 30∘ S, the improvements of T
and S in the VL_DPTS are considerably smaller than those
obtained by the other assimilation runs.
The model mean minus WOA13 along 25∘ W in the upper 1000 m for
temperature (∘C) on the left and salinity (psu) on the right from 1 January 2010
to 31 December 2012 according to the CTL run and the prior state of the ASSIM, VL_TS and
VL_DPTS runs.
Near 50∘ S, the control run does not well represent the formation of the
Antarctic Intermediate Water Mass (AAIW). The experiments with data
assimilation can correct the negative biases shown by
the control run by up to 2 ∘C and 0.3 psu, except for in experiment VL_DPTS. Since
this is a region of water mass formation, it seems that the vertical
correlations between model layers are very important in order to represent
physical processes. In the experiments with vertical localization of
Δp, much of this information between layers is lost (Fig. 3), and
the experiment VL_DPTS was not efficient at improving the
model state for this region in particular.
In order to investigate how stratification was modified by Argo data
assimilation in the upper 300 m, Fig. 6 shows the meridional section along
25∘ W of the mean potential density and the position of the layers
interfaces for the experiments CTL, ASSIM and VL_DPTS. In
general, as already shown in Fig. 5, the assimilation runs tend to decrease
the temperature and increase the salinity in the upper 300 m, driving the
model towards WOA13. This is associated with a general increase of the mean
potential density in the sub-surface in all the assimilation experiments,
especially between 30∘ S and 30∘ N. This increase of the potential
density can reach more than 0.5 kg m-3 near the equator and
in the subtropical gyres. According to Bleck (2002), the implementation of
the isopycnal vertical coordinate in HYCOM follows the theoretical
formulation that each isopycnal layer will move to be as close as possible to
its target density. Therefore, in the assimilation experiments the deeper
layers will move towards the surface to encompass the density increase
produced by the T and S increments and satisfy their target densities. For
example, near the equator and in the subtropical gyre of the South Atlantic,
there is a displacement of 25 m or more of the deeper layer interfaces
towards the surface. In the North Atlantic, this displacement is even larger
and it can reach 150 m, as can be seen by the behavior of the lowermost
white dashed line in Fig. 6 that represents the interface between the 11th
and 12th layer. Large et al. (1997) showed that the warm temperature bias
near the equator is a common feature of coarse-resolution models and it is
related to weak zonal currents and weak zonal slopes of the isotherms.
However, all the data assimilation experiments are able to force the present
low-resolution model to stack the layer interfaces in the upper 300 m and
correct the model bias of temperature and salinity not only at the equator
but also at all latitudes, especially between 30∘ S and 30∘ N.
The depth of the 20 ∘C isotherm is also evaluated for the experiments and
the WOA13 climatology in two longitudinal sections, one along the equator and
the other along 30∘ N (Fig. 7). In the WOA13, the depth of 20 ∘C
isotherm along equator is about 120 m in the west and it gets shallower in
the east with a value of almost 50 m. The control run is clearly warmer than
WOA13 in the upper ocean with temperatures higher than 28 ∘C in the first
100 m, so that the position of 20 ∘C isotherm is deeper, especially in
the east of the section with values close to 100 m. All the assimilation
experiments reduce the warm bias in the upper ocean, and the depth of
20 ∘C isotherm is lifted to a shallower position in much better agreement
with the WOA13 climatology. In the North Atlantic, the control run has an
even stronger bias of more than 4 ∘C in the upper 300 m. Hence, the
depth of 20 ∘C isotherm of the control run is deeper than WOA13,
attaining more than 300 m in the west of the section. Again, the experiments
with data assimilation are able to significantly reduce the warm bias by
moving the position of the 20 ∘C isotherm more than 150 m towards the
surface. This agrees very well with the large displacement of the layer
interfaces in the North Atlantic shown in Fig. 6, and also with the WOA13
climatology. Along 30∘ N, between 75 and 65∘ W and between
40 and 25∘ W, the experiment VL_DPTS is able to
bring the 20 ∘C isotherm up to 50 m closer to the surface in comparison
with the other runs without the vertical localization of layer thickness. On
the other hand, the experiment VL_DPTS is the only
assimilation experiment that does not represent very well the upwelling in
the east margin of the Atlantic Ocean at 30∘ N in Fig. 7. Probably, this
is because there is a strong vertical correlation among several model layers
in the upwelling region that is not considered by the vertical localization
of layer thickness in the VL_DPTS run. Similar behavior was
observed in the region of AAIW formation shown in Fig. 5.
Potential density (kg m-3) and the position of the layer interfaces
along 25∘ W in the upper 300 m for the (a) CTL run and the prior state of the
(b) ASSIM and (c) VL_DPTS runs from 1 January 2010 to 31 December 2012. The white dashed lines
represent the interface between the 5th and the 6th, between the 8th and the 9th, and
between the 11th and the 12th isopycnal layers, from top to bottom.
To further assess the impact of the assimilation in the upper ocean thermal
structure, the spatial distribution of the HC300 between 50∘ S and
50∘ N is presented in Fig. 8 for the WOA13 together with the differences
(model mean minus WOA13) for each run. In general, the control run has a
larger HC300 in comparison with the WOA13 climatology. Vast areas of the
North and South Atlantic have more than 50 MJ m-2 of HC300 excess over
the climatology. The largest differences are attained in the Gulf Stream
region (about 400 MJ m-2), since it is misplaced northward
with respect to observations, and in the southwest Atlantic around
40∘ S, associated with a misrepresentation of the Brazil–Malvinas
Confluence. When Argo data are assimilated, the model temperature is
constrained towards WOA13 and there is a strong impact on the HC300. All the
assimilation experiments decrease the HC300 difference with respect to WOA13
by more than 150 MJ m-2 for large areas of the subtropical
North Atlantic and 50 MJ m-2 in the equatorial and South
Atlantic. However, large differences still remain in the simulated Gulf
Stream region. No Argo data were available in this shelf region – to the
north of the observed Gulf Stream – to constrain the model (Fig. 4);
therefore,
the assimilation runs could not correct this discrepancy. Also, no SST and
SLA were assimilated and the assimilation of Argo only could not completely
modify this important circulation feature.
Comparison with Argo profilers and PIRATA moorings
The root mean square deviation (RMSD) is calculated on a daily basis against
Argo and PIRATA observations to objectively evaluate the temperature and
salinity produced by the experiments. This comparison is done with
independent data, since the 24 h, the 48 h and the 72 h simulations
after each analysis cycle is assessed. The 72 h simulations correspond to
the prior or background states used in the assimilation steps.
Temperature (∘C) along the Equator (left) and along 30∘ N (right) in
the upper 300 m for the WOA13 climatology, the CTL run and the prior state of the ASSIM,
VL_TS and VL_DPTS runs from 1 January 2010 to 31 December 2012.
The depth averaged RMSD of T and S above 2000 m against the Argo profilers
in the model domain from 1 January 2010 to 31 December 2012 is shown in
Fig. 9. The RMSDs of the ASSIM and VL_DPTS runs are
substantially reduced from 1.75 ∘C and 0.30 psu in the beginning of the
runs to 1 ∘C and 0.14 psu by the end of the runs. In Fig. 9, the only
assimilation runs presented are the ASSIM and VL_DPTS, since
the other two assimilation runs produced similar curves. The first year of
integration has the greatest RMSD reduction for the assimilation experiments.
From the second year on, especially in the last year, the RMSD reduction is
smaller and the RMSD values tend to oscillate around a stable mean. This
indicates that the analysis error is close to saturation and that changes in
the assimilation parameters such as α may be necessary to better
constrain the model towards observations. Here, α is equal to 0.3.
However, care should be taken when increasing α. The relatively small
value chosen here considered two aspects. First, a small value of α
helps avoiding abrupt changes in the model state and numerical instability
considering the relatively large discrepancies between the model background
and observations in certain regions. Also, the model resolution is relatively
low and the use of high values of α could overfit the data and try to
introduce mesoscale patterns that cannot be resolved by the model.
Heat content (MJ m-2) to 300 m of the WOA13 climatology and the
model mean minus WOA13 for the CTL run and the prior state of the ASSIM and
VL_DPTS runs over the period from 1 January 2010 to 31 December 2012.
Regions shallower than 300 m were not considered.
The VL_DPTS run produces smaller RMSDs than the ASSIM run.
The RMSD of the VL_DPTS is about 86 % (69 %) of the ASSIM
RMSD for temperature (salinity). However, this improvement is mainly due to
the vertical localization of the layer thickness. It was found that when
applying the vertical localization of the layer thickness, the number of
grid points with negative Δp after assimilation and before the
post-processing was greatly reduced. In the 365 assimilation steps from 1
January 2010 to 31 December 2012, more than 235 000 grid points with
negative Δp were generated and needed post-processing in the ASSIM
run. This number was decreased to less than 80 000 in the VL_DP and VL_DPTS runs, which means a reduction of 66 %. The
improvement caused by the vertical localization of Δp, rather than
the vertical localization of T and S, will be discussed in detail below.
The vertical profiles of the mean RMSD of all runs against Argo and PIRATA
data over the whole model domain are presented in Fig. 10. The largest
temperature and salinity RMSD of the control run are attained in the top
700 m with respect to Argo data and in the top 200 m with respect to PIRATA
data. This is associated with difficulties that models have with representing the
thermocline and pycnocline regions of sharp vertical gradients (Oke and
Schiller, 2007; Xie and Zhu, 2010). When Argo data are assimilated, the
vertical thermohaline structure is very much improved. With respect to Argo
data, the experiment ASSIM decreases the RMSD of the control run in the top
600 m from 2 to 1.3 ∘C and from almost 0.4 to 0.19 psu.
Regarding PIRATA data, the experiment ASSIM reduces the RMSD values of the
control run by up to 1 ∘C and 0.13 psu in the first 120 m. Gains with
the vertical localization of Δp are seen from 200 to 800 m and
from 1200 to 2000 m. In these ranges, the experiment VL_DPTS is able to further decrease the RMSD by 0.15 ∘C and 0.025 psu with
respect to the other assimilation runs. The vertical localization of only T
and S had almost no positive impacts on the RMSD, and contributed to slightly
degrading S near the surface when the runs were compared to PIRATA data. This is
mainly because the most important HYCOM variable to determine the thermohaline
structure is the model layer thickness (Thacker and Esenkov, 2002; Thacker et
al., 2004; Xie and Zhu, 2010). For instance, according to HYCOM formulation,
if the analysis increments of T and S decrease the density of a specific
layer in comparison to its target density, the model attempts to move the
lower interface downward, so that the flux of denser water across this
interface increases the layer density (Bleck, 2002). The opposite happens if
there is an increase of the layer density compared to its target density.
Therefore, the analysis increments of T and S will try to indirectly change
the model layer thicknesses in order to adjust the layer densities to their
target densities. However, in the EnOI scheme proposed here, the assimilation
of Δpobs is realized before the assimilation of T and S, and is very
effective in changing the model layer thicknesses. This may explain why the
model thermohaline structure is much more sensitive to the vertical
localization of Δp rather than to the vertical localization of T and S. The
latter was studied by XZ and they also did not find any significant impact in
their assimilation experiments.
Depth-averaged RMSD of temperature (∘C) and salinity (psu)
to 2000 m against 47 999 Argo profilers in the model domain (100∘ W–20∘ E,
78∘ S–50∘ N) from 1 January 2010 to 31 December 2012 according to the
control run (black) and the prior state of the experiment ASSIM (red) and
VL_DPTS (light blue).
Vertical distribution of the RMSD of temperature (∘C) and salinity (psu)
against 47 999 Argo profilers and 16 PIRATA fixed moorings in the model domain
(100∘ W–20∘ E, 78∘ S–50∘ N) from 1 January 2010 to 31 December 2012 according to
the control run (black) and the prior state of the experiment ASSIM (red), VL_TS (dark
dashed blue), VL_DP (dark dashed yellow) and VL_DPTS (light blue).
(a) and (b) correspond to the RMSD of T and S with respect to Argo observations while
(c) and (d) correspond to the RMSD of T and S with respect to PIRATA data,
respectively.
According to Fig. 10, the vertical localization of Δp seems to be
a good approach to better improve the model state, especially when
correlations of the ensemble members come from a free model run that
contains large discrepancies in certain regions in comparison with
climatology and observations. Since the co-variance matrix of the model
errors in the EnOI scheme is calculated by many snapshots of the model
state, the performance of the assimilation is quite dependent on the
accuracy of the error co-variances (Oke et al., 2005; Xie and Zhu, 2010).
Due to the biases of the ensemble members used in this work, many vertical
correlations might not be well represented, especially between distant
layers. Thus, since the vertical localization of layer thickness mostly
keeps the correlations between adjacent layers, this strategy avoids the
generation of many grid points with negative Δp during the
assimilation process and makes this approach a safer way to produce a more
physically consistent and reliable analysis.
To investigate the spatial distribution of the RMSD of T and S with respect
to Argo data above 2000 m, Table 1 contains the deviations for all the 12
sub-regions previously defined in Fig. 4. In the control run, the largest
RMSDs of T and S are attained in the sub-regions a, b and d with values
greater than 1.6 ∘C and 0.27 psu. All those sub-regions are found in the
North Atlantic, where the model has the largest differences in comparison
with the WOA13 climatology and with Argo observations. This is particularly
clear for sub-region a corresponding to the Gulf Stream region with RMSD of
2.3 ∘C, and for sub-region d in the Gulf of Mexico with RMSD of
0.368 psu. It should be reinforced that this grid configuration was prepared to
provide boundary conditions for higher-resolution grids focusing on the
Metarea V. Hence, the control run is better adjusted with smaller RMSDs in
the South Atlantic than in the North Atlantic as shown in Table 1. The
maximum RMSD in the South Atlantic is attained in the sub-region i
corresponding to the Brazil–Malvinas Confluence with values of 1.29 ∘C and
0.207 psu. For all the sub-regions, the different EnOI runs are able to
reduce the RMSD values of T and S in comparison with the control run. The
greatest impact of data assimilation is in the North Atlantic, where
approximately 60 % of the assimilated Argo profiles are found and where the
control run has its largest RMSDs. For example, the experiment ASSIM
decreases the RMSD of the control run about 1 ∘C in the sub-regions a and b,
and more than 0.17 psu for the sub-regions b, c and d. In the
Gulf of Mexico, this reduction is up to 0.2 psu. On other hand, the RMSD
reductions by the ASSIM run in the South Atlantic are only about 0.2 ∘C
and 0.04 psu. Even with the large impact of the Argo data assimilation, some
regions still remain with large RMSDs. This is the case with the Gulf Stream, the
Gulf of Mexico and the Brazil–Malvinas Confluence in the sub-regions a, d
and i, respectively, where the experiments still have RMSDs greater than
1 ∘C and 0.145 psu. These are regions of strong gradients, variability
and mesoscale eddy activity. The Gulf Stream is highly influenced by
mesoscale circulation and the growth of baroclinic instability after its
separation from the North American coast (Robinson et al., 1989; Spall and
Robinson, 1990; Lee and Mellor, 2003). Also, the Brazil–Malvinas Confluence
is characterized by a weak and warm southward Brazil Current meeting a
strong, cold and less saline northward Malvinas Current, which results in
large contrasts in stratification and strong eddy activity (Gordon, 1989;
Garzoli and Garrafo, 1989; Goni et al., 1996). Thus, the large RMSD still
found in the assimilation runs in these regions can be due to lack of data,
inaccuracies in the ensemble members, and limitation of the model resolution
to solve the mesoscale circulation patterns. Similarly, XZ found that the
assimilation of Argo profiles did not capture the mesoscale activities in the
Pacific Ocean due to the coarse model resolution, and the Kuroshio System
remained with large RMSDs in their assimilation run.
RMSD of temperature (∘C) and salinity (psu) to 2000 m
with respect to Argo data for the prior state of each experiment from 1 January 2010
to 31 December 2012. The calculations were performed for the
whole model domain (100∘ W–20∘ E, 78∘ S–50∘ N)
and for each one of the 12
sub-regions previously defined in Fig. 4.
RMSD CTL ASSIM VL_DPTS VL_DP VL_TS TSTSTSTSTS(∘C)(psu)(∘C)(psu)(∘C)(psu)(∘C)(psu)(∘C)(psu)A2.3020.2791.3000.1661.1800.1481.1530.1471.2680.157B1.7220.2830.7280.1130.6470.1070.6740.1100.7070.109C1.2140.2870.8130.1160.6650.1120.6520.1110.8150.142D1.6630.3681.0890.1600.9950.1751.0160.1701.0340.175E0.9720.2270.6780.1190.6550.1150.6330.1140.6620.119F1.1770.1630.7610.0970.7290.0940.7290.0940.7650.098G1.1390.1610.8000.1070.7590.1050.7590.1050.7640.106H0.7560.1660.6330.1250.5500.1150.5540.1090.6510.132I1.2900.2071.0480.1791.0350.1791.0380.1781.0360.180J0.9200.1580.6700.1240.7000.1270.7090.1290.6730.124K0.8450.1510.5940.1060.5960.1130.5990.1120.6380.110L0.7860.1400.5750.0900.5490.0820.5480.0790.5950.092All1.5070.2640.9930.1490.9050.1390.9150.1380.9720.147
In Table 1, the assimilation experiments with the best performances are the
ones with vertical localization of layer thickness. This is particularly
clear in the sub-regions a, b and c, where the experiments VL_DPTS and VL_DP are able to reduce the RMSD values up to
0.12 ∘C and 0.018 psu with respect to the ASSIM and VL_TS
runs. These three sub-regions are located in the North Atlantic, where the model
free run has its largest bias in comparison with WOA13 (Fig. 1). They are
sub-regions where the ensemble vertical correlations might not be well
represented. Therefore, relaxing the vertical constraints by vertical
localization should improve the model state. Small gains can also be seen in
the South Atlantic when applying the vertical localization of layer
thickness, for example, in the sub-region h corresponding to the Brazil
Current. The only regions where the experiments VL_DP and
VL_DPTS are just a little bit worse than the experiment ASSIM
is the Gulf of Mexico, sub-region d, for salinity, and the sub-regions j and
k in the mid-latitudes close to the AAIW formation. In general, the pairs of
experiments ASSIM and VL_TS, and VL_DP and
VL_DPTS, produced similar results in all sub-regions, and the
strategies with vertical localization of layer thickness attained smaller
RMSDs of T and S. It corroborates the conclusion that the vertical localization
of Δp was more important than the vertical localization of T and S
for the present experiments.
Analysis increments after assimilating an Argo profile located at
30.72∘ N and 31.98∘ W on 1 January 2010 of: (a) layer thickness (unit: m) and
current components (unit: m s-1) in the 12th layer for the experiment ASSIM,
(b) layer thickness (unit: m) and current components (unit: m s-1) in the
12th layer for the experiment VL_DP and (c) SSH (unit: m) along 30.72∘ N for
the experiment ASSIM (red) and VL_DP (dark dashed yellow). The pink dot
represents the location of the Argo float.
Adjustment of the altimetry and velocity fields
As shown above, the EnOI scheme used in this work adjusts the baroclinic
velocity fields via their co-variance with layer thickness in the analysis
increments. This is a physically consistent adjustment, since the horizontal
velocity fields are dominated by the slope of the isopycnal layers, which in
turn generates the pressure gradient force. XZ showed that around the
assimilated Argo profiles in the mid-latitudes, cyclonic and anti-cyclonic
circulations develop, consistent with the large local modifications of the
model layer thicknesses and geostrophy. This is due to the nature of the
co-variances, which come from an ensemble of model states and allow for the
description of the anisotropic patterns of the circulation (Oke et al., 2005, 2008;
Xie and Zhu, 2010). Figure 11 shows the analysis increment of
layer thickness and the circulation originating in the 12th layer around an
Argo profile located in the mid-latitudes of the North Atlantic on 1 January 2010
regarding the experiments ASSIM and VL_DP. The experiment
ASSIM robustly induces thinning of layer thickness up to 200 m, and then a
stronger and more anisotropic cyclonic pattern is imposed with velocity
increments reaching 0.5 m s-1. Both experiments develop a cyclonic circulation
around this mid-latitude Argo profile. This is coherent with the negative
analysis increment of layer thickness and the negative SSH increment also
shown in Fig. 11. Thus, the geostrophic balance was preserved in both
experiments. Since the experiment VL_DP has limited influence
between distant layers, the analysis increments are smoothed and smaller
velocity increments of about 0.1 m s-1 are produced. The cyclonic gyre is
better represented in the VL_DP and VL_DPTS
(not shown) runs, which show a more negative and more continuous increment of
SSH than the ASSIM run. The analysis constructed by this increment may be
more suitable to initialize a model than the analysis by the ASSIM strategy
considering the present background state and ensemble members. However,
further adjustment of the velocity fields is made by the model itself during
further integration to balance the analysis increments after assimilation of
Δp, T and S.
30-day running SSH mean (m) of the control run (black) and the
prior state of the experiment ASSIM (red), VL_TS (dark blue), VL_DP (dark
yellow) and VL_DPTS (light blue) from 1 January 2010 to 31 December 2012.
The markers represent the 30-day running mean values of SSH, while the bars
correspond to the standard deviations of each run.
The trend of SSH reduction by Argo data assimilation in the present
experiments is confirmed in Fig. 12. It shows the 30-day SSH running mean of
all experiments considering the model domain between 50∘ S and 50∘ N.
From the beginning of the integration to December 2012, SSH is reduced
from 0.22 to 0.12 m in the experiments ASSIM and VL_TS,
which is compatible with the largest impact found in the first year of
assimilation in Fig. 9. The VL_DP and VL_DPTS
runs produce a larger reduction from 0.22 to 0.08 m. From this period on,
the SSH of all assimilation experiments stabilize around these values and
different SSH means are achieved in the experiments with and without vertical
localization of layer thickness, but with variability very close to the
control run. The diagnostic model SSH varies due to the barotropic pressure
mode and especially due to the deviations in temperature and salinity caused
by changes in the structure of the layer thicknesses (Chin et al., 2002).
Hence, this lower SSH mean in the assimilation experiments reflects the new
thermohaline state and stratification achieved when Argo data are
assimilated. The thermal expansion of seawater constitutes a very important
component of SSH and then the reduction of the temperature and the heat
content in the assimilation experiments contribute strongly to the SSH
decrease. For example, the heat content is positively correlated with SSH
(Chambers et al., 1998; Willis et al., 2004; Dong et al., 2007). In this
work, mean correlation values of 0.802, 0.815 and 0.812 between the HC and
SSH are found for the experiments CTL, ASSIM and VL_DPTS,
respectively. When comparing the monthly means of all the experiments with
the WOA13 monthly means over the entire domain (not shown), the experiments
VL_DP and VL_DPTS are able to decrease the HC
by more than 7 MJ m-2 towards the climatology. This could
explain why there is a larger decrease of the mean SSH in the experiments
with vertical localization of layer thickness.
In order to evaluate how the local changes in layer thickness, SSH and
velocity fields affect the large-scale circulation, the zonal velocity along
25∘ W in the upper 300 m for all the experiments and HYCOM + NCODA
analysis is shown in Fig. 13. Some observed features are clearly represented
in the HYCOM + NCODA analysis, such as the South Atlantic Current (SAC) south
of 40∘ S, the branches of the westward South Equatorial Current (SEC),
the eastward equatorial undercurrent (EUC) and the North Equatorial
Countercurrent (NECC). Modifications with respect to the control run were
imposed by assimilation. However, some can be considered improvements towards
the HYCOM + NCODA analysis, and some cannot. For example, there is a strong
zonal current in the control run up to 0.6 m s-1 between 30 and
40∘ N associated with the Gulf Stream recirculation path, which is much
more intense than in the HYCOM + NCODA analysis. This zonal current is
reduced to 0.1–0.2 m s-1 in the experiments VL_TS and
VL_DPTS. However, it is displaced further south in comparison
with HYCOM + NCODA analysis, especially in the VL_TS run. In
the experiment ASSIM, this recirculation path is even weaker and merges in
the broader eastward flow. Also, in all assimilation experiments the EUC
velocity decreases from 0.6 to 0.4 m s-1 and gets closer to the magnitude
of the HYCOM + NCODA analysis, but the shape of its core remains the same as
in the control run and is not as elongated as in the HYCOM + NCODA analysis.
On the other hand, all data assimilation runs constrain the SAC near to the
surface, while it reaches more than 300 m in the HYCOM + NCODA analysis.
Finally, assimilation is not able to reduce the magnitude of the SEC and to
increase the intensity of the NECC simulated by the control run.
Zonal velocity fields (m s-1) in the upper 300 m along 25∘ W of
the HYCOM + NCODA analysis, the CTL run and the prior state of the ASSIM,
VL_TS and VL_DPTS runs from 1 January 2010 to 31 December 2012. The black solid and black dashed lines
denote the contours of 0.1 m s-1 and -0.1 m s-1, respectively.
XZ could observe modifications in the equatorial Pacific current system due
to Argo data assimilation, but they were not always positive when compared
to the Tropical Atmosphere Ocean (TAO) array data. For instance, a too deep
undercurrent maximum in the east and a too thick and strong westward current
in the west were produced. In the present work, a few modifications were
observed in the equatorial Atlantic region as well, but with smaller
intensity than in the mid-latitudes. It should be noted that the geostrophic
balance that holds in most of the ocean interior loses importance close to
the equator. Therefore, the equatorial current system should be less
sensitive to analysis increments by Argo data assimilation, so that changes
in this region may be mostly attributed to remote impacts from the
assimilation in extra-equatorial regions.
In the present work, the discrepancies of the model free run and its
variability with respect to climatology and observations are an important
limitation for the assimilation to produce the correct analysis increments,
particularly for the large-scale circulation. For this reason, many works
point out that the model biases should be considered during the assimilation
process (Reynolds et al., 1996; Dee and Silva, 1998; Bell et al., 2004; Dee,
2005; Xie and Zhu, 2010). Also, improving the co-variances of the ensemble
members may lead to more accurate analyses (Oke et al., 2008; Xie and Zhu,
2010). In addition to the comparison with the HYCOM + NCODA analysis, the
surface velocity fields of the assimilation runs were compared to the OSCAR
fields. Again, the results did not provide a clear signal about the impact
of Argo data assimilation on the surface currents. The RMSD of U and V with
respect to OSCAR were reduced by less than 5 % in comparison to the
control run.
Conclusions and discussion
In this work, an EnOI scheme to assimilate Argo data into HYCOM was
successfully constructed and implemented. The first results were evaluated
against observations and analyses over the Atlantic Ocean. The EnOI scheme
was based mostly on the work of XZ. A key variable in the assimilation
algorithm was the observed model layer thickness, Δpobs,
constructed from the Argo temperature (T) and salinity (S) profiles,
according to TE. First, Δpobs was assimilated and the analysis state
vector considered not only the model layer thickness, but also the
baroclinic velocities. This procedure is physically consistent, since the
horizontal velocity fields are dominated by the difference between the layer
depths, which will be the responsible for the pressure gradient force. After
that, with the previously adjusted model layer thicknesses, T and S were
assimilated in separate steps. Finally, T was diagnosed below the mixed
layer through the seawater equation of state following the best results
found in XZ. Thus, this EnOI scheme respects the hybrid nature of the HYCOM
vertical coordinate system and allows for the restructuring of the isopycnal layer
thicknesses and velocities with the assimilation of Δpobs. Also, a
sensitivity study was performed considering different vertical localizations
of the model error co-variance matrix, involving the variables T, S and
especially Δp. Five integrations were realized from 1 January 2010
to 31 December 2012. The study of the impact of the vertical localization
of Δp is an original contribution of this work.
The thermohaline structure of the experiments with assimilation was
significantly improved above 2000 m, the maximum depth of the Argo data. The
RMSDs with respect to Argo observations in the assimilation runs were reduced
in at least 34 % (44 %) for T (S), regarding the control run over the
whole domain. Spatially, the RMSD of T and S decreased for all the 12
selected sub-regions of the domain with remarkable corrections in the depth
of the 20 ∘C isotherm and heat content in the upper 300 m towards WOA13,
particularly in the North Atlantic. Also, the reorganization of the isopycnal
layers by the assimilation of Δpobs has provided a large reduction of
the diagnosed SSH in the model, reflecting the new thermohaline state
achieved by Argo data assimilation. Indeed, the correction of layer thickness
played a role in correcting the model thermohaline structure and
stratification, as stated in previous data assimilation works with HYCOM
(Thacker and Esenkov, 2002; Chin et al., 2002; Thacker et al., 2004; Xie and
Zhu, 2010).
The vertical localization of T and S did not produce any significant impact
in the assimilation experiments, which is consistent with the results found
in XZ. However, the experiments VL_DP and VL_DPTS with vertical localization of Δp were able to decrease the
RMSD of T (S) from 0.993 ∘C (0.149 psu) to 0.905 ∘C (0.138 psu) in
the whole model domain with respect to the other assimilation runs. This
improvement was especially seen in the North Atlantic, where the ensemble
members and background had their largest biases with respect to observations
and climatology. The experiments with vertical localization of Δp
decreased by 66 % the number of grid points with negative Δp
generated during the assimilation process by constraining the vertical
co-variances between more distant layers, and then reducing the degrees of
freedom offered by the ensemble members. This result reinforces how
important the quality of the ensemble members is in order to improve the
performance of the assimilation, particularly in the EnOI scheme, in which
the ensemble is stationary in time and does not evolve with the model
integration as in the EnKF (Evensen, 2003; Oke et al., 2005, 2008).
In future works with EnOI, the quality of the ensemble members should
be taken into account. For example, long reanalysis with Argo data
assimilation should be performed first to provide new and better ensemble
members and, therefore, improve the accuracy of the model error co-variance
to be employed in a new assimilation run. If more accurate ensemble members
are employed, it is expected that the strong vertical localization of
Δp will not lead to improvements in the analysis.
Despite the evidence that the assimilation experiments caused a strong SSH
reduction in the model domain and that the analysis increments of
Δp and velocities were locally consistent, there was not a clear
improvement in the large-scale circulation. The assimilation schemes were
simply bias blind here. The model biases should be considered in future
studies to better analyze the impact of Argo data assimilation in the
large-scale circulation. According to Oke and Schiller (2007), the role of
Argo data assimilation is mainly to constrain the thermohaline structure of
the model, especially for salinity, and this was obtained in the present
work. To constrain the SST and T in the mixed layer, the assimilation of SST
should be performed, and to correct the upper mesoscale circulation, the
assimilation of SLA is needed.
The present work was a key step forward in two major directions. First, it
was the basis for the future implementation of assimilation in the other
REMO higher-resolution grids. For the current domain with 760 × 480
horizontal grid points, the Argo data assimilation code took around 12 min
of CPU on 32 2 GHz processors to assimilate approximately 150 Argo
T–S profiles. Therefore, it can be easily used in operational mode. Second,
it served as the backbone to construct the assimilation code for along-track
satellite altimetry data and SST analyses that will form the REMO Ocean Data
Assimilation System into HYCOM (RODAS_H) for operational and
research purposes (Tanajura et al., 2014).
Acknowledgements
This work was financially supported by PETROBRAS and
Agência Nacional de Petróleo, Gás Natural e Biocombustíveis
(ANP), Brazil, via the Oceanographic Modeling and Observation Network
(REMO). The authors of this manuscript would like to acknowledge the support of the National
Research Council (CNPq), Ministry of Science, Technology and Innovation of
Brazil (proc. 130032/2012-3), and the support of the CAPES
Foundation, Ministry of Education of Brazil (proc. BEX 3957/13-6).
Edited by: N. Wells
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