Reduced-order Optimal Interpolation Research Articles

Effect of circulation at early life stages of European anchovy in the Bay of Biscay from observational data and a Lagrangian approach

Coastal circulation influences the distribution of European anchovy (Engraulis encrasicolus) at early life stages (ELS) in the Bay of Biscay (BoB). However, how this happens is not yet fully understood. In this work, further insight is provided by performing Lagrangian diagnostics based on observations of ELS anchovies' initial distributions and currents. Surface diagnostics were obtained by using high-frequency radar (HFR) currents and were applied to analyse multiyear variability and detect the coastal processes that affect the distribution. Since ELS anchovies are also located at subsurface levels, subsurface diagnostics were obtained by using currents reconstructed from HFR and ADCP observations with a reduced order optimal interpolation (ROOI) method. The analyses included transport computations as well as the analysis of flow properties by Lagrangian Coherent Structures and chlorophyll-a satellite images.Results suggest that ELS anchovies are mostly retained over the shelf and slope, and that transport patterns highly vary across different periods. Mesoscale structures such as eddies, fronts and along-slope currents within the slope and the Capbreton canyon area, as well as strong and persistent winds, could significantly impact the distribution of ELS anchovies. In some periods, the resulting distribution might be due to a combination of these processes. Circulation can also play a key role in ELS anchovy aggregation within short time scales (20 days). This work showcases the potential of observation-based approaches and emphasizes the relevance of coastal observatories for integrated studies.

3D reconstruction of ocean velocity from high-frequency radar and acoustic Doppler current profiler: a model-based assessment study

Abstract. The effective monitoring and understanding of the dynamics of coastal currents is crucial for the development of environmentally sustainable coastal activities in order to preserve marine ecosystems as well as to support marine and navigation safety. This need is driving the set-up of a growing number of multiplatform operational observing systems, aiming for the continuous monitoring of the coastal ocean. A significant percentage of the existing observatories is equipped with land-based high-frequency radars (HFRs), which provide real-time currents with high spatio-temporal coverage and resolutions. Several approaches have been used in the past to expand the surface current velocity measurements provided by HFR to subsurface levels, since this can expand the application of the technology to other fields, like marine ecology or fisheries. The possibility of obtaining 3D velocity current fields from the combination of data from HFRs with complementary data, such as the velocity current profiles provided by in situ acoustic Doppler current profiler (ADCP) moorings is explored here. To that end, two different methods to reconstruct the 3D current velocity fields are assessed by a standard approach conceptually similar to OSSEs (observing system simulation experiments), where 3D numerical simulations are used as true ocean in order to evaluate the performance of the data-reconstruction methods. The observations of currents from a HFR and ADCP moorings are emulated by extracting the corresponding data from the 3D true ocean, and used as input for the methods. Then, the 3D reconstructed fields (outputs of the methods) are compared to the true ocean to assess the skills of the data-reconstruction methods. These methods are based on different approaches: on the one hand, the reduced order optimal interpolation uses an approximation to the velocity covariances (which can be obtained from historical data or a realistic numerical simulation) and on the other hand, the discrete cosine transform penalized least square is based on penalized least squares regression that balances fidelity to the data and smoothness of the solution. This study, which is based on the configuration of a real observatory located in the south-eastern Bay of Biscay (SE-BoB), is a first step towards the application of the data-reconstruction methods to real data, since it explores their skills and limitations. In the SE-BoB, where the coastal observatory includes a long-range HFR and two ADCP moorings inside the HFR footprint area, the results show satisfactory 3D reconstructions with mean spatial (for each depth level) errors between 0.55 and 7 cm s−1 for the first 150 m depth and mean relative errors of 0.07–1.2 times the rms value for most of the cases. The data-reconstruction methods perform better in well-sampled areas, and both show promising skills for the 3D reconstruction of currents as well as for the computation of new operational products integrating complementary observations, broadening the applications of the in situ observational data in the study area.

Reconstruction of transports through the Strait of Gibraltar from limited observations

Observing the water transports through the Strait of Gibraltar is a difficult task. Here we present a methodology aimed to obtain the inflow, outflow and net transport of water from the limited set of available observations, currently consisting of an upward looking ADCP deployed at Espartel sill, two tide gauges located at each side of the Strait and radars monitoring the surface velocities. More precisely, we reconstruct the velocity field over a vertical section across the Strait using a reduced order optimal interpolation technique fed with the spatial covariance patterns deduced from high resolution numerical simulations. As a first step we carry out some sensitivity experiments with synthetic data that demonstrate the high potential of the approach. The reconstruction methodology can reproduce very satisfactorily the variability of the transports with estimated correlations for the inflow, outflow and net over 0.9 in all the cases and estimated RMS errors of 0.03, 0.08 and 0.05 Sv, respectively. However, we have also found that the reconstruction is sensible to bias problems, mostly due to the sensitivity of the method to the differences between the statistics of the actual and modeled velocity profiles. The sensitivity experiments have been used to tune the parameters of the method and a reconstruction of actual monthly transports has been performed for the period 2004–2010 along with an estimate of the associated uncertainty. This reconstruction provides for the first time a multiannual time series of the inflow and the net transports solely based on in situ observations. Therefore it can be used as an independent estimate for the validation of numerical models and surface freshwater fluxes in the Mediterranean.

Quality Assessment of a 1985–2007 Mediterranean Sea Reanalysis

Abstract A simulation and two reanalyses from 1985 to 2007 have been produced for the Mediterranean Sea using different assimilation schemes: a reduced-order optimal interpolation [System for Ocean Forecast and Analysis (SOFA)] and a three-dimensional variational scheme (OceanVar). The observational dataset consists of vertical temperature and salinity in situ profiles and along-track satellite sea level anomalies; daily mean fields of satellite sea surface temperature are used for correcting the air–sea fluxes. This paper assesses the quality of the reanalyses with respect to observations and the simulation. Both the SOFA and OceanVar schemes give very similar root-mean-square errors and biases for temperature and salinity fields compared with the assimilated observations. The largest errors are at the thermocline level and in regions of large eddy field variability. However, OceanVar gives 20% better results for sea level anomaly root-mean-square error.

The INGV–CMCC Seasonal Prediction System: Improved Ocean Initial Conditions

Abstract The development of the Istituto Nazionale di Geofisica e Vulcanologia (INGV)–Centro Euro-Mediterraneo per i Cambiamenti Climatici (CMCC) Seasonal Prediction System (SPS) is documented. In this SPS the ocean initial-conditions estimation includes a reduced-order optimal interpolation procedure for the assimilation of temperature and salinity profiles at the global scale. Nine-member ensemble forecasts have been produced for the period 1991–2003 for two starting dates per year in order to assess the impact of the subsurface assimilation in the ocean for initialization. Comparing the results with control simulations (i.e., without assimilation of subsurface profiles during ocean initialization), it is shown that the improved ocean initialization increases the skill in the prediction of tropical Pacific sea surface temperatures of the system for boreal winter forecasts. Considering the forecast of the 1997/98 El Niño, the data assimilation in the ocean initial conditions leads to a considerable improvement in the representation of its onset and development. The results presented in this paper indicate a better prediction of global-scale surface climate anomalies for the forecasts started in November, probably because of the improvement in the tropical Pacific. For boreal winter, significant increases in the capability of the system to discriminate above-normal and below-normal temperature anomalies are shown in both the tropics and extratropics.

Characterization of error dynamics in a 3D coastal model of the Catalan sea using stochastic modelling

The structure and dynamics of errors in a 3D coastal model of the Catalan sea is characterized through stochastic modelling. Wind forcing and large scale circulation are identified as the main sources of model errors. Ensemble simulations perturbing the wind field and the model initial and open boundary conditions are performed. The dispersion of model trajectories in the ensemble allows us to characterize the errors structure and dynamics. Model errors induced by errors in the wind forcing are linear but non-stationary, while those induced by errors in the description of the large scale circulation are non-linear but stationary. The ensemble results are also used to characterize the error covariance spatial patterns through the use of multivariate EOFs. The capability of this EOF decomposition to control the model evolution is investigated using a reduced order optimal interpolation (ROOI) data assimilation scheme.

The CMCC-INGV Global Ocean Data Assimilation System (CIGODAS)

Centro Euro-Mediterraneo per i Cambiamenti Climatici, Bologna, Italy Istituto Nazionale di Geofisica e Vulcanologia, Bologna, Italy

Multivariate assimilation in MERCATOR project: New statistical parameters from forecast error estimation

The new operational prototype of Mercator (french Global Ocean Data Assimilation Experiment contribution) is composed of a North Atlantic primitive equation ocean model OPA (Ocean Parallel Algorithm between 20°S and 70°N, [Madec, G., P. Delecluse, M. Imbard and C. Lévy (1998). OPA8.1 ocean general circulation model reference manuel. Notes du pôle de modélisation IPSL. n°11: 91p]) and of a multivariate and multidata assimilation scheme [De Mey, P. and M. Benkiran (2002). “A multivariate reduced-order optimal interpolation method and its application in Mediterranean basin-scale circulation.” Ocean Forecasting : Conceptual basis and application, Pinardi, N., Springer Verlag.] This system has already given some significant improvements from previous Mercator configurations (M. Benkiran, personal communication). However some biases on ocean state still remain in the tropics where the reduced-order optimal interpolation scheme is suspected to be ill-parameted in the model forecast error. Indeed the guess error covariance matrix is decomposed into an error variance value and a spatio-temporal correlation function which are assumed to have some “good” properties (spatial homogeneity of the correlation function, constant ratio between signal and error variance). This study shows how we can use ensemble methods to validate these assumptions. We can see that the correlation function can reach negative values locally, mostly in regions of high variability contradictory with the homogeneous hypothesis. The reduced space used in the operational configuration is based on the signal seasonal Empirical Orthogonal Functions (EOFs). An empirical relationship between signal and error variance has been set and the correlation function is the same on every dimension of the reduced space. By projection of the estimated guess error variance onto the reduced space, we find a repartition of this quantity quite different to what was set in the system. The error statistics is found to be inhomogeneous compared to hypothesis made in the assimilation scheme. These two new parameters tested separately in the assimilation scheme gives significant improvements of the forecast and analysis results. This is particularly obvious in the tropics. But relationship between signal and error statistics (as assumed in the optimal interpolation) is found to be complex.

Simulating biomass assimilation in a Mediterranean ecosystem model using SOFA: setup and identical twin experiments

Abstract. Assessing the potential improvement of basin scale ecosystem forecasting for the Mediterranean Sea requires biochemical data assimilation techniques. To this aim, a feasibility study of surface biomass assimilation is performed following an identical twin experiment approach. NPZD ecosystem data generator, embedded in one eighth degree general circulation model, is integrated with the reduced-order optimal interpolation System for Ocean Forecasting and Analysis. The synthetic "sea-truth" data are winter daily averages obtained from the control run (CR). The twin experiments consist in performing two runs: the free run (FR) with summer-depleted phytoplankton initial conditions and the assimilated run (AR), in which, starting from the same FR phytoplankton concentrations, weekly surface biomasses averaged from the CR data are assimilated. The FR and AR initial conditions modify the winter bloom state of the phytoplankton all over the basin and reduce the total nitrogen, i.e. the energy of the biochemical ecosystem. The results of this feasibility study shows good performance of the system in the case of phytoplankton, zooplankton, detritus and surface inorganic nitrogen. The weak results in the case of basin inorganic nitrogen and total nitrogen, the latter nonperformant at surface, are discussed.

Estimation of the optimal interpolation parameters in a quasi-geostrophic model of the Northeast Atlantic using ensemble methods

The SOPRANE operational forecasting system is based on a quasi-geostrophic (QG) model of the Northeast Atlantic. The assimilation scheme used to constrain the model consists of a Reduced Order Optimal Interpolation (ROOI) using an Extended Kalman Filter (EKF) formulation. Corrections to the model fields at the surface are consistent with satellite along track data and a priori statistical information on the forecast error. The required forecast error variance is updated using an estimation of the time evolution of the analysis error variance (taken as the initial condition error variance). A correlation function C then leads to the forecast error covariance matrix. However, our knowledge on these statistics is poor. We then achieve ensemble forecast experiments based on perturbed initial condition fields so as to estimate initial condition error growth and check if the ROOI hypothesis is relevant. Tests on six different initial ensembles of 140 members, integrated over 35 days, have been performed to correctly determine characteristics of the initial condition statistics. We can clearly show the strong correlation between local dynamics and spatial repartition of the error growth, which concentrates on the most energetic regions. Some interannual variability patterns can also be found. This leads to the computation of a new ensemble, with statistics consistent with what is observed in the previous experiments. Time propagation of the initial condition error variance, the C matrix and its parameters are estimated. It shows a northward decrease of the error correlation radii and a westward propagation of the errors. There is an interannual and spatial variation of C, on the contrary to what is stated in the SOPRANE ROOI scheme. Moreover, the increase error variance in time is also correlated with the dynamics.

Assimilation scheme of the Mediterranean Forecasting System: operational implementation

Abstract. This paper describes the operational implementation of the data assimilation scheme for the Mediterranean Forecasting System Pilot Project (MFSPP). The assimilation scheme, System for Ocean Forecast and Analysis (SOFA), is a reduced order Optimal Interpolation (OI) scheme. The order reduction is achieved by projection of the state vector into vertical Empirical Orthogonal Functions (EOF). The data assimilated are Sea Level Anomaly (SLA) and temperature profiles from Expandable Bathy Termographs (XBT). The data collection, quality control, assimilation and forecast procedures are all done in Near Real Time (NRT). The OI is used intermittently with an assimilation cycle of one week so that an analysis is produced once a week. The forecast is then done for ten days following the analysis day. The root mean square (RMS) between the model forecast and the analysis (the forecast RMS) is below 0.7°C in the surface layers and below 0.2°C in the layers deeper than 200 m for all the ten forecast days. The RMS between forecast and initial condition (persistence RMS) is higher than forecast RMS after the first day. This means that the model improves forecast with respect to persistence. The calculation of the misfit between the forecast and the satellite data suggests that the model solution represents well the main space and time variability of the SLA except for a relatively short period of three – four weeks during the summer when the data show a fast transition between the cyclonic winter and anti-cyclonic summer regimes. This occurs in the surface layers that are not corrected by our assimilation scheme hypothesis. On the basis of the forecast skill scores analysis, conclusions are drawn about future improvements. Key words. Oceanography; general (marginal and semi-enclosed seas; numerical modeling; ocean prediction)

The Mediterranean ocean forecasting system: first phase of implementation (1998–2001)

Abstract. The Mediterranean Forecasting system Pilot Project has concluded its activities in 2001, achieving the following goals: 1. Realization of the first high-frequency (twice a month) Voluntary Observing Ship (VOS) system for the Mediterranean Sea with XBT profiles for the upper thermocline (0–700 m) and 12 n.m. along track nominal resolution; 2. Realization of the first Mediterranean Multidisciplinary Moored Array (M3A) system for the Near-Real-Time (NRT) acquisition of physical and biochemical observations. The actual observations consists of: air-sea interaction parameters, upper thermocline (0–500 m) temperature, salinity, oxygen and currents, euphotic zone (0–100 m) chlorophyll, nutrients, Photosinthetically Available Radiation (PAR) and turbidity; 3. Analysis and NRT dissemination of high quality along track Sea Level Anomaly (SLA), Sea Surface Temperature (SST) data from satellite sensors to be assimilated into the forecasting model; 4. Assembly and implementation of a multivariate Reduced Order Optimal Interpolation scheme (ROOI) for assimilation in NRT of all available data, in particular, SLA and VOS-XBT profiles; 5. Demonstration of the practical feasibility of NRT ten day forecasts at the Mediterranean basin scale with resolution of 0.125° in latitude and longitude. The analysis or nowcast is done once a week; 6. Development and implementation of nested regional (5 km) and shelf (2–3 km) models to simulate the seasonal variability. Four regional and nine shelf models were implemented successfully, nested within the forecasting model. The implementation exercise was carried out in different region/shelf dynamical regimes and it was demonstrated that one-way nesting is practical and accurate; 7. Validation and calibration of a complex ecosystem model in data reach shelf areas, to prepare for forecasting in a future phase. The same ecosystem model is capable of reproducing the major features of the primary producers’ carbon cycle in different regions and shelf areas. The model simulations were compared with the multidisciplinary M3A buoy observations and assimilation techniques were developed for the biochemical data. This paper overviews the methodological aspects of the research done, from the NRT observing system to the forecasting/modelling components and to the extensive validation/calibration experiments carried out with regional/shelf and ecosystem models. Key words. Oceanography: general (ocean prediction; instruments and techniques) Oceanography: physical (currents)

Assimilation of satellite altimeter data in a primitive-equation model of the Azores–Madeira region

Abstract The aim of this study is to implement satellite altimetric assimilation into a high-resolution primitive-equation ocean model and check the validity and sensitivity of the results. Beyond this paper, the remote objective is to get a dynamical tool capable of simulating the surface ocean processes linked to the air–sea interactions as well as to perform mesoscale ocean forecasting. For computational cost and practical reasons, this study takes place in a 1000 by 1000 sq km open domain of the Canary basin. The assimilation experiments are carried out with the combined TOPEX/POSEIDON and ERS-1 data sets between June 1993 and December 1993. The space–time domain overlaps with in situ data collected during the SEMAPHORE experiment and thus enables an objective validation of the results. A special boundary treatment is applied to the model by creating a surrounding recirculating area separated from the interior by a buffer zone. The altimetric assimilation is done by implementing a reduced-order optimal interpolation algorithm with a special vertical projection of the surface model/data misfits. We perform a first experiment with a vertical projection onto an isopycnal EOF representing the Azores Current vertical variability. An objective validation of the model's velocities with Lagrangian float data shows good results (the correlation is 0.715 at 150 dbar). The question of the sensitivity to the vertical projection is addressed by performing similar experiments using a method for lifting/lowering of the water column, and using an EOF in Z -coordinates. Some comparisons with in situ temperature data do not show any significant difference between the three projections, after five months of assimilation. However, in order to preserve the large-scale water characteristics, we felt that the isopycnal projection was a more physically consistent choice. Then, the complementary character of the two satellites is assessed with two additional experiments which use each altimeter data sets separately. There is an evidence of the benefit of combining the two data sets. Otherwise, an experiment assimilating long-wavelength bias-corrected CLS altimetric maps every 10 days exhibits the best correlation scores and emphasizes the importance of reducing the orbit error and biases in the altimetric data sets. The surface layers of the model are forced using realistic daily wind stress values computed from ECMWF analyses. Although we resolve small space and time scales, in our limited domain the wind stress does not significantly influence the quality of the results obtained with the altimetric assimilation. Finally, the relative effects of the data selection procedure and of the integration times (cycle lengths) is explored by performing data window experiments. A value of 10 days seems to be the most satisfactory cycle length.