A series of observing system simulation experiments
(OSSEs) is carried out with a global data assimilation system at
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Observing system simulation experiments (OSSEs) are powerful tools to evaluate the impact, relative merits and complementarities of the different components of the global ocean observing system. They allow for the assessment of existing elements of the global ocean observing system and are essential to evaluate revised or new designs (e.g. evolution of sampling characteristics, addition of a new observing system component). OSSEs rely on models that realistically represent the space–time variability of the essential ocean variables to be monitored and data assimilation to optimally merge in situ from satellite observations and models. OSSEs typically use two different models. One model is used to perform a “truth” or “nature” run, and it is treated as if it were the real ocean. The nature run is sampled in a manner that mimics either an existing or future observing system – yielding synthetic observations. The synthetic observations are assimilated into the second model (assimilated run) and the model performance is evaluated by comparing it against the nature run. This in turn quantifies the impact of observations. OSSEs are also important tools for testing the capability of global data assimilation systems to effectively merge different types of observations with models to produce improved ocean analyses and forecasts. OSSEs are complementary to OSEs (observing system evaluations). OSEs analyse the impact of real data for ocean analysis and forecasting generally by comparing a run assimilating all available data with a run assimilating all the data except for the data type to be investigated. OSSEs allow, however, a more comprehensive assessment of errors on analyses and forecasts at all depths and for all parameters through the comparison with the nature run (the truth). On the other hand, results for existing observing systems must be consistent with those derived from OSSEs. This issue of calibration of OSSEs with respect to OSEs is actually an important element for the proper design of OSSEs (e.g. Halliwell et al., 2014). Choice of the nature run, assimilated run, data assimilation scheme and errors to apply to synthetic observations should be carefully analysed to avoid under or overestimations of forecast and analysis errors in OSSEs.
In this study, an assessment of the impact of multiple altimeters and Argo
profiling floats is carried out with the Mercator Ocean global
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The paper is organised as follows. Section 2 provides a description of the OSSE methodology and modelling and data assimilation system. Section 3 analyses the impact of assimilating one, two or three altimeters. The complementary role of Argo is discussed in Sect. 4. Main conclusions and future prospects are given in Sect. 5.
This section describes the methodologies used to perform the different OSSEs. The Mercator Ocean data assimilation system is first presented. The nature run and the free run used to initialise the assimilated run, the simulation of observations and the characteristics of OSSEs are then described.
Commonly called SAM2, the current protocol for data assimilation at Mercator Ocean (Lellouche et al., 2013) computes correction over a 7-day assimilation window and is based on a modified Kalman filter named SEEK (singular evolutive ensemble Kalman filter) first introduced by Pham et al. (1998). Analysis is calculated at the middle of the assimilation window, i.e. the fourth day. The SEEK filter means, as explained by Brasseur and Verron (2006), that covariance error matrices are forced at a low rank (“Singular”) and that it computes model error covariances propagation (“Evolutive”) following the model dynamics.
The filter used in SAM2 is not evolutive in the same way as SEEK. Indeed, instead of using
empirical orthogonal functions to build its error covariance matrix that will be propagated onto the
model along time steps, SAM2 takes a fixed base of smoothed model anomaly
fields (349 in the following experiments). This approach allows the system
to get a covariance matrix that is realistic with the climatological
statistics of the ocean model at the time step and saves computation time
as this matrix will not be propagated in the model unlike the SEEK.
Anomalies for the five control variables (sea level,
In this study, both the nature run (NR) and the assimilated run (AR) are
based on the NEMO model (Nucleus for European Modelling of the Ocean; Madec
et al., 1998) with a global coverage and 50 vertical levels, with 22 levels
within the upper 100 m and with 1 m resolution from the first level, increasing with depth up to 450 m for the last one. The system uses the OPA (Océan Parallélisé) model coupled
with the LIM2 ice model (Fichefet and Morales Maqueda, 1997). The difference
between the two configurations is that the NR uses a 1
The OSSEs were started from 7 January 2009 over an almost 1-year
time period. Two different initial conditions (i.e. 7 January 2009) for the
NR and for the AR are required so that we can quantify the impact of
assimilating pseudo-observations of the NR in the AR. This was achieved by
running the two free-run NEMO configurations initialised from climatology
but at different times. The NR simulation was started in 2003 and forced
with ECMWF (European Centre of Medium Weather Forecasting) operational 3 h
atmospheric data and the AR was initialised from a 1
To assess the impact of the number of altimeter data, three satellites have been considered: Jason-1, Jason-2 and Envisat (Fig. 1a). Jason-1 and Jason-2 have a 10-day repeat cycle and Envisat a 35-day repeat cycle. Jason-1 was in its interleaved orbit with its ground tracks just in between Jason-2 tracks and with a time shift of 5 days. This orbit was chosen to optimise mesoscale variability sampling by Jason-1 and Jason-2. The OSSEs were carried out over the year 2009. Jason-1, Jason-2 and Envisat simulated observations were derived from the NR with a resolution of 7 km between two points along the tracks. An observation white noise of 3 cm rms was simulated and added to these pseudo-observations.
Mercator Ocean operational systems assimilate SLA
observations. The absolute sea level (i.e. sea level relative to the geoid)
is obtained by using an external mean dynamic topography (MDT) based on the
CNES-CLS MDT. In our case, the nature and assimilated runs have different
MDTs because of the grid resolution, the model parametrisations and
different initialisation procedures. We thus chose to assimilate the
absolute sea level (which include the MDT and the SLA) from the NR at
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Argo in situ temperature and salinity observations from the surface down to 2000 m were simulated using the 2009 Argo profile positions in the Coriolis CORA3.2 database (Fig. 1b).
Computed simulations and assimilated data set.
The four different OSSEs that have been carried out are summarised in Table 1. The first three simulations address the question of the number of altimeters required to constrain ocean analyses and forecasts. There are three experiments with one (Jason-2), two (Envisat and Jason-2) and three (Jason-1, Envisat and Jason-2) assimilated satellite data sets. They are respectively called Sat1, Sat2 and Sat3 experiments. The other OSSE addresses the impact of Argo profiling floats together with the three satellite data sets.
All the assimilated experiments start on 7 January 2009 and end 30 December 2009. The difference between a given simulation and the NR are used to derive statistics on errors on analyses and forecasts over the last 7 months (June–December 2009). For each assimilation experiment, time series of errors on analyses and forecasts (up to 7 days) are obtained. Seven-day forecast errors will be used in this study.
The impact of assimilation of altimeter data is first analysed on sea level
(SL). A wavenumber spectral characterisation of the error is also carried
out. Errors on surface zonal (
Global mean square error (MSE) of the relative SL in cm
Figure 2 shows the mean square error (MSE) for the free run (FR) and for the analyses and forecasts of the three different assimilation runs (Sat1, Sat2 and Sat3) estimated as the difference with the NR. As expected, the FR shows large differences with the NR as they provide two uncorrelated mesoscale variability fields. Assimilation of one satellite leads to a significant reduction of both analysis and 7-day forecast errors due to a strong correction of the mean sea level. Adding a second altimeter significantly reduces the errors. The impact of assimilating a third altimeter remains positive but not as large as the addition of a second altimeter. Moreover, errors are largely reduced between the 7-day forecast and the analysis for each of the three assimilation runs.
Time evolution of the global MSE of SL in cm
The evolution in time of the global MSE of sea level for both the analysis
and 7-day forecast fields is shown in Fig. 3. The system constrained by the
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GS 7-day forecast MSE of SL in cm
GS analyses MSE of SL in cm
AC 7-day forecast MSE of SL in cm
AC analyses MSE of SL in cm
KU 7-day forecast MSE of SL in cm
KU analyses MSE of SL in cm
To analyse further the structure of errors in areas of high mesoscale variability, MSEs for analyses and 7-day forecasts are shown for the GS (Figs. 4 and 5), AC (Figs. 6 and 7) and KU (Figs. 8 and 9) regions. Diamond-like structures can be seen on the analysis error maps for all regions when only one altimeter is assimilated revealing the repetitive spatial sampling of Jason-2. Adding Envisat observations suppresses this effect. In those energetic regions, the MSE for the free run is very high in the core of the main current. The increase in the number of assimilated altimeter data sets allows for a clear reduction of both 7-day forecast and analysis errors.
To summarise results shown on the different maps, the following score is defined as the MSE for a given AR in percentage of the free-run MSE:
Assimilated simulation relative sea level MSE in percent of the free-run MSE.
Sea level error energy spectrum in the GS
Sea level variance preserving error spectrum in the GS
Global MSE in cm
These statistics are presented in Table 2.
The greatest impact is made with the assimilation of the first altimeter which strongly reduces the large-scale biases existing between the NR and FR. Sat1 sea level global analysis MSE reaches 21 % of the free-run MSE. Adding a second satellite (Sat2) reduces the analysis errors by 6 %. The third satellite (Sat3) reduces further the errors by about 2 %.
Compared to Sat1 global analysis MSE, Sat2 analysis MSE is reduced by 28 % and for Sat3 compared to Sat2 error is reduced by 11 %. In high-eddy-energy regions this ratio can reach respectively 42 and 22 %.
For the same assimilation experiment, the analysis error is always lower than the 7-day forecast error. The error level of the analysis with one altimeter is close to the 7-day forecast error level when two or three altimeter data sets are assimilated. This is true for all of the considered regions and globally (Table 2). The largest error reduction due to data assimilation occurs in the Agulhas and Kuroshio regions.
The error increase between the analysis and 7-day forecast for each experiment highlights the “model predictability” in the different regions. The relative MSE in percent between analysis and forecast increase is 28 % globally for Sat1, 35 % for Sat2 and 37 % for Sat3. In western boundary currents (WBCs), values are around 34 % for Sat1, around 49 % for Sat2 and 54 % for Sat3. The error increase is thus the largest when more altimeter data are assimilated. Analyses are thus better constrained, but this does not fully translate into improved forecasts.
Note that as the NR and the AR use the same atmospheric forcing, 7-day forecast errors are only related to internal mesoscale dynamics and initialisation issues.
Estimation of the sea level wavenumber spectrum from altimetry data (e.g. Le Traon et al., 1990; Stammer, 1997; Le Traon and Dibarboure, 2008) has allowed major progresses in the characterisation of ocean mesoscale dynamics. Wavenumber spectra are used here to characterise sea level analysis and 7-day forecast errors in the Gulf Stream, the Agulhas Current and the Kuroshio regions.
Wavenumber spectra were calculated from the sea level model error fields
using fast Fourier transform (FFT). The FFT was applied in 10
The error reduction due to altimeter data assimilation is visible for all of
the three selected regions: the free model run error spectrum is higher at
all wavelengths larger than 100 km. The assimilation corrects the
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As seen before, the error is reduced each time an additional altimeter is assimilated, for all wavelengths larger than 100 km and up to 1000 km. It is also the case for the analysis compared to the 7-day forecast. Analysis of spectra in a variance preserving form (Fig. 11) shows that, compared to analysis errors, 7-day forecast errors occur at larger wavelengths; they have a maximum variance at wavelengths of 300–500 km, while it is about 200–300 km for analysis errors.
Compared to the free-run errors, adding one satellite (Sat1) reduces analysis errors for all wavelengths larger than 250 km. Addition of a second (Sat2) and third (Sat3) altimeter allows for the reduction of analysis errors down to 150 km wavelength. In the KU and the GS regions, the Sat2 and Sat3 analysis errors are similar for most of the length scale. In the AG region, the assimilation of the third satellite still allows for significant analysis error reduction.
In most cases, the 7-day forecast error spectrum for the Sat3 experiment is lower than the analysis error for the Sat1 experiment for wavelengths smaller than 300 km.
To assess the system ability to reproduce the nature run, it is necessary to
analyse how non-assimilated model variables are improved when assimilating
sea level altimeter data. The unobserved variables are impacted by
assimilating only sea level observation through two mechanisms. The first
one is the multivariate characteristic of the analysis corrections computed
by SAM2. The model error covariance matrix is defined with a collection of
model anomalies used to calculate increment for all the model prognostic
variables, SL,
Because of geostrophy, we expect, in particular, that assimilating more
altimetry data will better constrain surface velocity fields. Figure 12
presents the MSE of analysis and 7-day forecast for the surface zonal
velocity
Assimilated simulation relative zonal velocity (
Table 3 shows the same score as the one used for the sea level but for the
MSE of the analysis and 7-day forecast errors of the zonal and meridional
velocity components in cm
Global 7-day forecast RMSE of
Global 7-day forecast RMSE of
Global 7-day forecast RMSE of
Global 7-day forecast RMSE of
The absolute MSEs decrease from Sat1 to Sat3, and are much lower than the free run. For each experiment, the analysis error is again reduced compared to the 7-day forecast error. The level of error for the 7-day forecast of Sat3 is, in most regions, comparable to the level of the analysis error of Sat1. The assimilation of a second satellite leads to a higher error reduction than the third one, for both analysis and 7-day forecast and in all regions.
Sat1 global analysis velocity MSEs represent 55 % of the free-run MSEs. Additional error reductions of 10 and 4 % occur for Sat2 and Sat3. In high-eddy-energy regions (GS, AC, KU), the analysis MSEs are smaller and can reach 35 % of the free-run MSE for Sat1; they continue to be reduced by 13 and 4 % for Sat2 and Sat3 (on average in the WBCs).
Seven-day forecast surface velocity errors are less reduced when an additional altimeter data set is assimilated. They globally represent 64, 56 and 53 % of the free-run MSE for respectively Sat1, Sat2 and Sat3.
Assimilation of multiple altimeter data does not only improve the surface
velocity; it also improves velocity fields at depth. Figure 13 shows global
RMSE
profiles for
Assimilating sea level altimeter data also improves the temperature and
salinity at depths as shown on RMSE profiles for temperature (
Assimilating altimeter data only improves temperature fields (and marginally
salinity fields), but errors remain large. This leads to the next part of the
study concerning the Argo1 experiments. This experiment has been designed to
answer how a simulated Argo profiles data set allows for correcting large scales
when they are assimilated with altimetry compared to the Sat3 experiment.
Argo floats are designed to monitor large-scale and low-frequency
variability as described in Roemmich et al. (2009) and the complementarity
between remote sensing observation and in situ profiles has been studied in
the North Atlantic using OSSE-like simulations by Guinehut et al. (2004).
They showed how well the estimation of 200 m
Profiles in Fig. 15 represent the RMSE of
It is then expected that scores may differ from one set of experiments to the other. Moreover there are no reasons for the nature run to be similar to the ocean state estimated by OSEs or for the results to be exactly the same.
First, Argo profiles go up to 2000 m depth and allow for a good large-scale
constraint of the first 1500 m of the ocean, complementary to altimetry:
RMSEs of the innovation in Argo1 are smaller than in FR and Sat3. The increase
in
the error at depth in Argo1 shows a weakness of the assimilation scheme in that
it does not find the right correction at depth that will give a good fit to both
in situ and altimetry data. Assimilation of a
Then, considering these OSE and OSSE results, we see that the given profiles
are very similar. As explained in the previous section, temperature fields
at depth are improved compared to the free run when altimetric sea level
observations are assimilated, and this conclusion can also be made when
looking at the OSEs results when analysing the corresponding free run and
RunNa (meaning no Argo) OSEs of Turpin et al. (2016). In the OSSEs, maxima
of RMSEs drop from 1.2
Improvement brought by the Argo float assimilation is explained by the
comparison between Argo1 and Sat3 for OSSEs and the RunOP (for operational
run) and RunNa for Turpin et al. (2016) OSEs. Temperature RMSE maximum
reaches 0.6
This comparison helps to validate the results of the OSSE experiments. The similarity of the error profiles for both OSE and OSSE is a good indication of the realism of the OSSE experimental context, at least in terms of errors relative to the nature run for the OSSE and the real ocean for OSEs.
The Fig. 16 maps give a better understanding of how and where the improvements are made in Argo1 compared to Sat3. They represent the RMSE of temperature at the surface and at 318, 902 and 1941 m altitude. Those depths correspond to model vertical level. Only fields in the upper 2000 m are shown because it is the maximum depth for Argo profiles.
Sat3 RMSE maps show larger-scale patterns compared to the Argo1 fields
where much smaller structures are visible. At the surface, in situ data
assimilation is the most effective in the Southern Ocean, where RMSEs
are strongly driven back to a much smaller value (from more than
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The 318 m depth is the level most impacted by the assimilation presented here. The strong RMSE in the Atlantic is efficiently corrected in Argo1 and values are reduced everywhere else. Errors show smaller structures and only remain high in the WBCs.
The last two maps (at 902 and 1941 m) give similar results but in a much less significant way. Big patterns in Sat3 are corrected and lead to small RMSE structures in Argo1.
Finally we did not comment on the impact of Argo observations on the sea level since the differences are not significant between Argo1 and Sat3.
A series of observing system simulation experiments (OSSEs) was carried out
with a global data assimilation system at 1
The study is now being extended to analyse the impact of the extension of Argo (deep Argo, improved coverage in western boundary currents and in the tropics), the evolution of the altimeter constellation like the use of synthetic aperture radar altimeters with a reduced measurement error compared to the low-resolution mode (LRM) classic observations and the impact of other elements of global in situ observing systems (e.g. moorings, gliders).
No data sets were used in this article.
The authors declare that they have no conflict of interest.
This study was funded as part of a CNES–Mercator Ocean collaboration. The PhD grant of Simon Verrier was co-funded by Ifremer and Mercator Ocean. Edited by: Markus Meier Reviewed by: three anonymous referees