As with other Western Boundary Currents globally, the East Australian Current
(EAC) is highly variable making it a challenge to model and predict. For the
EAC region, we combine a high-resolution state-of-the-art numerical ocean
model with a variety of traditional and newly available observations using an
advanced variational data assimilation scheme. The numerical model is
configured using the Regional Ocean Modelling System (ROMS 3.4) and takes
boundary forcing from the BlueLink ReANalysis (BRAN3). For the data
assimilation, we use an Incremental Strong-Constraint 4-Dimensional Variational (IS4D-Var) scheme, which uses the model dynamics to perturb the
initial conditions, atmospheric forcing, and boundary conditions, such that
the modelled ocean state better fits and is in balance with the observations.
This paper describes the data assimilative model configuration that achieves
a significant reduction of the difference between the modelled solution and
the observations to give a dynamically consistent “best estimate” of the
ocean state over a 2-year period. The reanalysis is shown to represent both
assimilated and non-assimilated observations well. It achieves mean
spatially averaged root mean squared (rms) residuals with the observations of 7.6 cm for sea surface height (SSH) and
0.4

The East Australian Current (EAC) is the Western Boundary Current (WBC) of
the South Pacific subtropical gyre, flowing poleward along the east coast of
Australia. The EAC has the weakest mean flow of the WBCs associated with the
subtropical gyres

Model domain and bathymetry with the 100, 200, (bold) and 2000 m contours. Australian states are labelled and main towns are labelled and shown by the red diamonds. A sketch of the EAC is overlain showing the typical separation latitude and the Tasman Front.

In general, the kinetic energy of the ocean is dominated by submesoscale and
mesoscale eddies that fluctuate on timescales of days to months and on
spatial scales of tens to hundreds of kilometres and exceeds the mean flow by
1
order of magnitude or more

In this work we use Incremental Strong-constraint 4-Dimensional Variational
data assimilation (IS4D-Var), which generates increments to adjust the model
initial conditions, boundary and surface forcings such that the difference
between the model solution of the time-evolving flow and all available
observations is minimised over an assimilation interval. The 4D-Var scheme
uses the linearised model equations and their adjoint to compute the
increment adjustments, such that the model is adjusted in a dynamically
consistent way to minimise the difference between the observations and the
modelled time-evolving ocean state. Using the linearised equations allows
dynamical connections between state variables to propagate information from
observed variables to unobserved, dynamically linked variables. Because the
linearised version of the governing equations is used, rather than the full
nonlinear version, the assimilation interval length is limited such that the
linear assumption remains reasonably valid and the nonlinearities do not grow
too large. The state estimate is a solution of the model equations, and the
minimisation process can be used to understand the sensitivity of the
modelled ocean circulation to initial conditions, boundary and surface
forcing, and model parameters (e.g.

Combining a state-of-the-art numerical ocean model with a variety of
traditional and newly available observations, we generate a high-resolution
ocean state estimate of the EAC region over a 2-year period
(January 2012-December 2013). This paper describes the development and
evaluation of the data assimilative model configuration. We begin by
configuring a numerical model of the EAC region that is capable of
representing the mean ocean circulation and its eddy variability. The model
is configured to resolve the continental shelf, which is 15 km wide at its
narrowest point and may be important in accelerating the EAC and driving the
current's separation

We show that the assimilation configuration developed in this work results in
a
significant reduction of the differences between the modelled solution and
the observations. As such, the reanalysis provides us with a “best
estimate” of the ocean state that is dynamically consistent within each
assimilation time window. The reanalysis is being used to study the
variability and separation dynamics of the EAC. Furthermore, the 4D-Var
method allows us to use the reanalysis to quantify the impact of particular
data streams on circulation estimates, which has the potential to provide
important information for assessing and improving the observing system
design. The product is also being used as boundary forcing for a variety of
downscaling studies in coastal south-eastern Australia. This data assimilative
model represents a significant improvement on previous modelling work in the
EAC for these purposes: e.g.

The reanalysis development and evaluation is presented as follows. In Sect. 2, we describe the numerical model configuration, including validation of a 10-year free-running simulation to provide confidence that the model is correctly representing the region's circulation dynamics. In Sect. 3, we describe the development of the reanalysis, including the data assimilation scheme used, the assimilation configuration and the observations. The reanalysis performance is evaluated in Sect. 4 using a variety of metrics to illustrate the system's skill. A summary and conclusions are presented in Sect. 5.

We use the Regional Ocean Modeling System (ROMS, version 3.4) to simulate the
atmospherically forced eddying ocean circulation off the south-eastern coast
of Australia. ROMS is a free-surface, hydrostatic, primitive equation ocean
model solved on a curvilinear grid with a terrain-following vertical
coordinate system

Sub-grid-scale horizontal mixing of momentum and tracers uses a harmonic
(3-point stencil) mixing operator

Root mean squared (rms) SSH anomaly over 10-year period from AVISO

The model domain (shown in Fig.

In models using terrain-following coordinate systems, steep topographic
gradients generate numerical errors associated with the computation of the
pressure gradient term resulting in artificial along-slope flows

The model uses initial conditions and boundary forcing from the BlueLink ReANalysis version 3p5 (BRAN3;

We begin by configuring a 10-year free-running simulation (hereafter referred
to as the “10 yr free run”) to ensure that the model is capable of
representing the mean ocean circulation and its variability. The 10 yr free
run is also used to provide estimates of background variability to compute
background error covariances for the assimilation scheme, and the 10-year-mean SSH field is used for addition of sea level anomaly
(SLA) observations for assimilation into the model. For the 10 yr free run,
we use atmospheric forcing from the National Center for Environmental
Prediction (NCEP) reanalysis atmospheric model

The 10 yr free run is performed from 2002 to 2011 as this is the most recent
period over which BRAN3 data were available at the time of model development
for use as initial and boundary forcing (BRAN3 more recently became available
for the reanalysis period, 2012–2013). Comparison of the 10 yr free run
with observations provides validation of the ability of the model to
represent the ocean dynamics in the region. The model reproduces well the
spatial patterns of the time mean and variability of the mesoscale SSH;
however, it is not expected to be in phase with the observations (e.g. the
time and location of mesoscale eddies do not match).
Figure

Mean alongshore velocity from the ROMS 10 yr free run at the
cross-shore sections that cross the coast at the EAC transport array
(27.5

Mean cross-shore sections of alongshore velocity and temperature for the
10-year modelled period reveal a southward flowing EAC and the associated
upslope thermocline tilt (Fig.

Total full-water-column alongshore transport (Sv) through
27.5

Alongshore transport through the same three cross-shore sections for the full
water column is computed daily and the mean, standard deviation, minimum and
maximum transports are shown in Table

The model configuration is capable of producing the mean dynamical features of the EAC and representing the SSH variability. Thus, using 4D-Var data assimilation, we aim to constrain the model with 2 years of observational data to examine the evolution of the EAC during this period.

The reanalysis is configured for the 2-year period of 2012–2013 because of
the availability of significant observational resources during this time; in
particular, a mooring array deployed to capture the transport of the EAC (as
detailed in the next section). The reanalysis model uses initial conditions
and boundary forcing from BRAN3 and atmospheric forcing provided by the
12 km resolution BOM ACCESS analysis, which was not available over the
10 yr free-run testing period described above. The simulation is spun-up
over a 1-month period before we begin assimilation on 1 January 2012. A
surface heat flux correction was applied such that the new atmospheric
surface forcing is in balance with SST from BRAN3 for each month. To ensure
that the higher-resolution atmospheric forcing did not significantly alter
the previous model comparison, we integrated the model for two years without
assimilation (hereafter referred to as the “2 yr free run”) and compared
the model-derived SST with those from the advanced very-high-resolution
radiometer (AVHRR) satellite data. The 2 yr free-run model spatially
averaged SST and the spatially-averaged SST observations exhibit a small net
bias over the 2012–2013 period (0.28

To generate the full reanalysis, we combine the model with the observations
in a way that uses the model physics to compute increments in initial
conditions, boundary, and surface forcing to generate a state estimate that
better fits the observations. In this regard, we are looking for the model to
represent the observations, not replicate the observations. If the model is
capable of representing all of the observations in time and space using the
physics of the model, then we should have the most complete description of
the ocean state available. To accomplish this, we use IS4D-Var.
IS4D-Var uses variational calculus to solve for increments in model initial
conditions, boundary conditions, and forcing such that the difference between
the modelled solution and all available observations is minimised – in a
least-squares sense – over the assimilation window. This is achieved by
minimising an objective cost function,

Temperature–salinity diagram for the Argo observations and corresponding values from the 2 yr free run for 2012–2013.

The forward integration of the nonlinear model equations, given a prior
estimate of the initial conditions, surface, and boundary forcings, provides
an estimate of the background state. The evolution of the state vector,

where

The first step of the assimilation procedure is the forward integration of
the nonlinear model equations to estimate the background state (referred to
as the first

An advantage of this assimilation method is that it makes use of the
dynamical connections between the model fields, such that observed variables
propagate information to unobserved, dynamically linked variables. Because
the linearised model equations are used for the cost function minimisation,
the length of the assimilation window is limited by the time over which the
tangent-linear assumption remains reasonable. For a thorough description of
the IS4D-Var formulation, the reader is referred to

The goal of the assimilation is to combine an uncertain model with uncertain
observations to generate a circulation estimate that has reduced uncertainty
and better represents the observations. To do this we solve for the nonlinear
ocean solution that is dynamically consistent with the observations and is
free within the uncertainties in the system. As such, specification of the
prior model and observation uncertainties is important. These uncertainties
are prescribed in the background and observation error covariance matrices and are important scaling factors in the cost function,

The minimisation of

The ROMS 4D-Var allows for controlling both the initial conditions and the time-varying atmospheric and boundary forcing. We adjust the atmospheric forcing every 12 h and the open-boundary conditions every 24 h. The heat flux is the dominant adjustment in the atmospheric forcing over most of the domain, with the wind adjustment dominating in the vicinity of the HF radar.

The reanalysis time period (2012–2013) was chosen because it contains the
greatest number of available observations, including a full-depth mooring
array that resolves the EAC transport, which was deployed from 1 April 2012 to
26 August 2013. Other available subsurface observations and satellite-derived
surface observations are also sourced for this time period.
Figure

Argo observations coloured by time of occurrence

Number of observations (after processing) used in each 5-day
assimilation window; for each observation type

The uncertainties in the observations are specified to prevent
“over-fitting” the solution to uncertain observations. The observation
uncertainty is a combination of the uncertainty in the observation itself and
just as significantly, the uncertainty in the model's ability to represent
that observation (referred to as representation error). The observational
uncertainties are prescribed in the observation error covariance matrix,

We describe the observations used in the section below, and detail the observation uncertainties specified for each. The consistency of these uncertainty estimates is checked in Sect. 4.1.

AVISO, France, produce global, daily, gridded
(

The gridded AVISO product is used to constrain SSH, rather than the along-track altimetry, to ensure that the constraint is projected into the baroclinic ocean state solution. The use of along-track SSH data successfully with 4D-Var relies on the prescription of balanced terms in the background error covariance matrix to describe the covariance between SSH and the subsurface ocean (refer to Sect. 3.5). This is a topic of further research.

We use SST from the US Naval Oceanographic Office Global Area Coverage
Advanced Very High Resolution Radiometer level-2 product (NAVOCEANO GAC
AVHRR L2P SST). The product does not provide observations through clouds but
contains useful observations close to the coast. Data are available 2–3 times
per day. A product error is specified in the NAVOOCEANO SST product

SSS was observed from space for the first time by
the National Aeronautics and Space Administrations (NASA) Aquarius
satellite (

Argo is an international program consisting of nearly 4000 free-drifting
profiling floats that measure the temperature and salinity of the upper
2000 m of the global ocean (

Uncertainty profiles are defined to specify the nominal minimal uncertainties
for subsurface temperature and salinity. To devise the profile shapes,
temperature and salinity variance is computed for each month of the year from
the 10 yr free run. The monthly variances are spatially averaged over the
model domain and averaged in time to give a single variance profile for both
temperature and salinity. The profiles are then scaled to provide variance
profiles appropriate for the nominal minimum observation error variance,
based on preliminary assimilations and checks against the diagnostics
described in Sect. 4.1 (computed throughout the water column). The
uncertainty profiles are shown in Fig.

XBT collect temperature profiles along repeat
lines sampled by merchant ships. Two transects intersect our model domain:
PX34, which is the Sydney–Wellington route, and PX30, which is the
Brisbane–Fiji route (only a small portion of this transect is within our
model domain). Five PX30 lines took place over the assimilation period
(16 December 2011, 8–9 March 2012, 13 September 2012, 7 June 2013, and
1 November 2013) and seven PX34 lines (3–4 February 2012, 23–24 May 2012,
22–23 September 2012, 26–27 November 2012, 16–18 February 2013,
12–13 May 2013, and 24–26 August 2013). The sections are sampled at 10 km
intervals. The XBT data points are averaged to the model grid and a 5 min
time step. The same nominal minimal uncertainty profile used for the Argo
temperature observations (Fig.

The Coffs Harbour high-frequency (HF) ocean radar is part of the IMOS and is
managed by the Australian Coastal Ocean Radar Network (ACORN;

The HF radar broadcasts and receives along defined angles in a phased-array
set-up and the surface current speed (towards and away from the radar site) is
measured. The overlapping coverage from the two radar sites allows for the
surface current (

Nominal minimum observation uncertainty profiles applied to subsurface temperature and salinity observations offshore of the continental shelf.

Radial data are available from 1 March 2012 to the end of the reanalysis
period. The areas of HF radar coverage are shown in Fig.

Radial speed standard error is given in the data files provided by ACORN,
calculated from the mean width of the two Bragg peaks weighted by their
maximum power

Data collected from three moorings located along the NSW continental shelf
are
used in this assimilation study. The moorings collect temperature and
velocity data at high sampling frequencies and are located off the coast of Coffs
Harbour, 30

Mooring information for the EAC deep water array moorings (EAC1-5), South East Queensland shelf moorings (SEQ200, SEQ400) and the NSW shelf moorings (CH100, SYD100, SYD140).

All temperature observations taken from moorings at high sampling frequencies
are low-pass filtered to remove variability at periods shorter than the
inertial period (23.8 h for Coffs Harbour and 21.5 h for Sydney), and the
observations are applied 6 hourly. For latitudes south of 30

For all observations on the continental shelf, different nominal minimum
observation error variance profiles are adopted (to those used offshore for
Argo and XBT) to account for increased variability due to finer-scale
processes that occur on the shelf that are not resolved in the model.
Variance profiles for the shelf observations were computed by comparing all
of the shelf observations (NSW moorings, SEQ moorings, and gliders) to the
2 yr free run for the 2012–2013 assimilation period to generate a nominal
uncertainty profile on the shelf. Profiles were generated for all observed
in situ variables:

The observation error variance is specified as the maximum of the nominal minimum error variance and the variance from averaging observations within the same model grid cell. For velocities, the high density of the ADCP depth bins means several velocity measurements are often available for a single vertical grid layer, which can result in variances that exceed the specified nominal minimum uncertainty.

The EAC transport array was deployed as part of IMOS to understand the
variability of the EAC, and it is comprised of five deep water moorings (EAC
1–5), which measure temperature, salinity, and velocities. The array was
positioned where the EAC is predicted to be most coherent and was designed to
measure the mean and time-varying EAC transport

All temperature and salinity observations are low-pass filtered to remove
variability at periods shorter than the inertial period (26.0 h), and the
observations are applied 6 hourly. The vertical uncertainty profile used for
the other off-shelf temperature and salinity observations
(Fig.

Autonomous ocean gliders (both SeaGliders and Slocum) were deployed as part
of the IMOS by the Australian National Facility for Ocean Gliders
(

The background error covariance matrix,

Initial nonlinear cost function and the reduction achieved in the
final (14th) tangent-linear model

In the horizontal, the characteristic length scales chosen for the background
error covariances are 100 km for SSH, temperature, and salinity, and 70 km
for velocities. These values were chosen based on analysis of
cross-correlation of SSH and complex correlation of surface velocities
between points in the eddy rich Tasman Sea region from the 2 yr free run.
The length scale of 100 km for SSH is consistent with the decorrelation
scales estimated from along-track satellite data for the area by

For the vertical, semivariogram analysis of glider data on the NSW shelf by

Analysis of correlations between velocities measured by the moorings found vertical decorrelation length scales of 20–50 m for the shelf moorings (NSW moorings, SEQ 200), 70 m for SEQ 400, and 100–200 m for the EAC deep water array moorings (EAC 1–5). Because the deep water moorings span the core of the EAC, we reduced the de-correlation length scale value to 50 m in the vertical for velocity to ensure consistency when assimilating velocities outside of the EAC and/or on the shelf.

The background error covariance matrix plays an important role in determining the spatial structure of the analysis increment and, in this oceanic region, the horizontal and vertical scales of variability differ between the mesoscale eddy field in the Tasman Sea and the smaller-scale shelf processes. Further research on the impact of applying anisotropic correlation length scales on system performance is warranted.

The background error standard deviations were estimated from the average of 5-day variances from the 10 yr free run described above. These climatological variances provide an estimate of the uncertainty associated with each state variable and surface forcing field, based on the assumption that background errors are likely to be the largest in regions of strong ocean variability. We choose 5-day variances as the model is nested in BRAN3, which assimilates large-scale data, so we expect our model prior boundary and initial conditions to be accurate to within the typical changes to the ocean state that occur over 5 days. The same background error covariance matrix is used for each assimilation cycle.

In this section, we evaluate the performance of the assimilation procedure in terms of the consistency of the prior uncertainty assumptions, comparison with the assimilated observations, and comparison to unassimilated observations. Overall, the assimilation performs well in minimising the cost function over each assimilation interval and the corresponding reanalysis provides a good match to observations.

The analysis generated by the IS4D-Var system is dependent on the prior
assumptions of the background and observation uncertainties, and the validity
of these assumptions is important in determining the optimality of the
analysis. A measure of the consistency of the assimilation system given the
prior uncertainty assumptions can be made using a set of diagnostics based on
the innovation statistics, presented in

The rms SSH observation anomaly

The rms SST observation anomaly, including seasonal cycle,

The rms difference between the free run and observations, the free run
and the bias-adjusted observations, and the analysis and observations for
Argo

For SSH, square-root of the spatially averaged diagnosed observation error
variance ranges from 4.1 to 8.4 cm with a mean value of 5.8 cm, which matches
the square root of the prior observation error variance of 6 cm very well.
The SSH prior and diagnosed model error variances are also consistent. For
subsurface temperature, the prior and diagnosed model error variances match
very well. The prior observation error variances are greater than the
diagnosed observation error variances for subsurface temperature; the
time mean of the square root of the spatially averaged prior error variances
is 0.88

The rms potential density observation anomaly and rms difference between the free run and observations, and the analysis and observations for Argo float observations. Observations are grouped into nominal depth bins of 25 mm from the surface to 200 and 50 m below 200 m.

Complex correlation between observed velocities and free-run and analysis velocities at mooring locations.

Complex correlation of surface velocities computed from the
assimilated HF radar radials, and surface velocities computed from the
corresponding free run

Another simple diagnostic to check the validity of

Overall, the prior assumptions of observation and model background uncertainties are considered reasonable and the assimilation achieves reduced analysis uncertainty by reduction of the cost function for each assimilation interval. The cost function reduction and convergence properties are detailed in the following section.

Linear minimisation of the cost function,

The rms observation anomaly for a particular observation location describes the variability in the observation with respect to its time mean. This is compared to the rms differences between the observations and the free-running model (the 2 yr free run), as well as the observations and the analysis (i.e. the analysis error), to provide an assessment of how well the free run and the analysis match the observations relative to their typical variability. A skilful state estimate will have residuals with the observations that are much lower that the observation's typical variability.

The observation anomaly for an observed variable

Figure

The free-running model shows some skill in prediction of the SST due to the
accuracy of the surface forcing; however, significant improvement is achieved
in the analyses. The rms SST observation anomalies describe the variability
in SST over the 2-year assimilation period, including the seasonal cycle, and
are shown in Fig.

The Aquarius SSS data were included but for this assimilation configuration
provides little constraint. The rms

Subsurface observations are spatially and/or temporally sparse in comparison
to satellite observations of the sea surface. The dynamical connections
between surface and subsurface variables are taken into account by the
adjoint and tangent-linear model such that the time-evolving model physics
are used to perform the cost function minimisation. While these connections
allow for the surface observations to impact state estimates of the subsurface
properties, subsurface observations are invaluable in improving estimates of
the subsurface (e.g.

We show the improvement in subsurface temperature as measured by the Argo
floats, XBTs and ocean gliders by computing the
RMSD

To investigate the relative contribution of improved representation of
dynamical features and reduction in bias to the RMSD reduction between the
free run and the analysis, we also compute the RMSD between the free run and
the “bias-adjusted observations”. The bias-adjusted observations have
the bias between the observations and the free run removed and, for each
depth bin, are given by

As the Argo profiling floats measure both temperature and salinity at each
observation time we are able to assess the residual reduction in terms of
potential density throughout the water column (Fig.

Profiles of the complex correlation between the velocities from the
free-running model and the analyses at the mooring velocity measurement
locations are shown in Fig.

Here we choose to present the results in terms of surface velocities (rather
than the scalar radial current speeds) as they are more meaningful in terms
of the ocean surface currents. The observed surface velocities are computed
from the assimilated radials and the corresponding values computed from the
radial values extracted from the free-running model and the analyses. The
complex correlations between these observed surface velocities and the
surface velocities computed from the free-running model and the analysis are
shown in Fig.

In terms of the radial current speeds measured from both NNB and RRK sites,
the RMSD

Because IS4D-Var uses the model dynamics to solve for the increment adjustments, information from observed variables can propagate to unobserved regions such that the ocean state better fits and is in balance with the observations. Comparison of the reanalysis with independent, non-assimilated, observations allows us to assess the performance of the state estimate away from assimilated observations. As the principal aim of this work was to assimilate the maximum number of available observations in the region in order to provide a “best estimate” of the ocean state over the 2-year period, few independent observations remain available for this comparison.

The available independent observations are from shipboard conductivity–temperature–depth (CTD) casts that were
taken on three separate cruises within the model domain over the 2-year
period; 15 CTD casts were taken as part of the deployment of the EAC array,
along the EAC array transect from 21 to 27 April 2012 (blue diamonds in
Fig.

The rms potential density observation anomaly and rms difference between
the free run and observations, and the analysis and observations for
independent CTD cast observations mapped to model vertical
levels

Note that the profiles of Argo RMSD

We have presented the development of a data assimilating model of the EAC
region and assessed the performance of the corresponding reanalysis over a
2-year period. We use an advanced variational data assimilation scheme to
integrate a state-of-the-art coastal ocean model with an unprecedented
observational data for the south-east Australian region. We show that the
free-running numerical model reproduces the long-term mean surface and
subsurface ocean properties and represents the eddying circulation as
expressed by the sea surface variability well. For the reanalysis, we show
that the SSH and SST have mean rms residuals with the observations of 7.6 cm
and 0.4

The performance of the reanalysis is dependent on prior assumptions of the model background and observation error covariances. We processed the observations to be assimilated to eliminate fine-scale processes not resolved by the model, and carefully specified the prior observation and model background uncertainties. Overall, the prior uncertainty assumptions are considered reasonable and the assimilation achieves reduced analysis uncertainty by reduction of the cost function for each assimilation interval.

Not only does the reanalysis provide a good fit to observations, it is the
first reanalysis of the EAC region that resolves the continental shelf along
south-east Australia (BRAN3 has a resolution of 10 km

The reanalysis is being used to study the three-dimensional structure of the current and the processes that drive its separation from the coast and eddy formation. Several modelling studies of coastal regions in south-eastern Australia are making use of the reanalysis for boundary forcing. Output from the adjoint model integrations performed in each assimilation interval is being used to directly assess the impact of specific observations on the estimates of circulation dynamics of interest. Through this we hope to understand which observations are most effective at improving our state estimates and which locations are most effective to observe, providing valuable information on how we might improve the observing system to ultimately improve prediction.

Model initial conditions and boundary forcing come from the Bluelink
ReANalysis version 3p5 (BRAN3;

The reanalysis output is saved as snapshots of three-dimensional fields of ocean properties (sea-level, temperature, salinity, velocities) every 4 h over the 2-year period (2012–2013). The data are archived at UNSW Australia and can be made available for research purposes (contact the corresponding author of this paper).

This research and C. Kerry were supported by an Australian Research Council Discovery project no. 140102337. Data were primarily sourced from the Integrated Marine Observing System (IMOS) – IMOS is a national collaborative research infrastructure, supported by the Australian Government. We thank Holly Sims from the BOM for making ACCESS available to us and Gary Brassington, also from the BOM, for providing data in the preliminary phases of this work and for his useful discussions. The XBT data were kindly provided by Ken Ridgway of CSIRO Hobart.Edited by: R. Marsh Reviewed by: two anonymous referees