Data Assimilation In Oceanography Research Articles

Ensemble-based data assimilation for predictable zones and application for non-linear deep-water waves

The ensemble-based variational method is easier to implement and parallelize than the adjoint method. For circumstances in which observed data are too limited and sparse for oceanographic data assimilation, the surface wave reconstruction by ensemble adjoint-free data assimilation (SWEAD) method was developed in a previous study. SWEAD generates ensembles of search directions from Fourier modes to numerically differentiate the squared error between observed data and a physical model. However, Fourier modes are global bases and could be redundant for a narrow predictable zone confined by a dispersion relationship. To concentrate ensembles on the predictable zone, we propose using singular value decomposition (SVD) of the approximated Jacobian of the squared error. Here, the Jacobian was first approximated by the linear dispersion relationship and successively updated to consider the non-linearity of the physical system. A new criterion for reusing the ensemble was also devised for this new method, increasing the dimension of search directions. A twin experiment was conducted for non-linear deep-water waves, and the optimization efficiency of the new method—SWEAD using SVD (SWEAD-S)—was significantly greater than that of SWEAD. Expansion of the predictable zone caused by the effect of non-linearity on the wave group velocity is thought to be essential for this improvement.

An Embedded Tactical Decision Aid Framework for Environmentally Adaptive Autonomous Underwater Vehicle Communication and Navigation

Motivated by a changing acoustic environment in the Arctic Beaufort Sea, in this article, we present a tactical decision aid framework for a human decision-maker collaborating with an autonomous underwater vehicle (AUV) to integrate the vertical sound-speed profile for underwater navigation and communication. In a predeployment phase, using modeled and real oceanographic data, we load basis function representations of the sound-speed perturbations onto one or more AUVs on deck, where a handful of weights can estimate a sound-speed profile. During deployment, these weights are updated on an AUV through a digital acoustic message to improve navigation and reciprocal communication throughout the duration of an under-ice mission. Field work applying this framework in the Beaufort Sea is presented, highlighting key decisions regarding predeployment oceanographic data assimilation, CTD cast collection, and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> weight choice. Selected examples evaluate the framework’s ability to adapt to a depth-limited CTD cast and the appearance of an anomalous microlens feature in the profile. We show that the framework effectively balances the need to adapt in a changing acoustic environment in real time while maintaining operator trust in an AUV’s embedded intelligence.

Study and application of an improved four-dimensional variational assimilation system based on the physical-space statistical analysis for the South China Sea

The four-dimensional variational assimilation (4D-Var) has been widely used in meteorological and oceanographic data assimilation. This method is usually implemented in the model space, known as primal approach (P4D-Var). Alternatively, physical space analysis system (4D-PSAS) is proposed to reduce the computation cost, in which the 4D-Var problem is solved in physical space (i.e., observation space). In this study, the conjugate gradient (CG) algorithm, implemented in the 4D-PSAS system is evaluated and it is found that the non-monotonic change of the gradient norm of 4D-PSAS cost function causes artificial oscillations of cost function in the iteration process. The reason of non-monotonic variation of gradient norm in 4D-PSAS is then analyzed. In order to overcome the non-monotonic variation of gradient norm, a new algorithm, Minimum Residual (MINRES) algorithm, is implemented in the process of assimilation iteration in this study. Our experimental results show that the improved 4D-PSAS with the MINRES algorithm guarantees the monotonic reduction of gradient norm of cost function, greatly improves the convergence properties of 4D-PSAS as well, and significantly restrains the numerical noises associated with the traditional 4D-PSAS system.

Assessing the Impact of Different Ocean Analysis Schemes on Oceanic and Underwater Acoustic Predictions

AbstractAssimilating oceanic observations into prediction systems is an advantageous approach for real‐time ocean environment characterization. However, its benefits to underwater acoustic predictions are not trivial due to the nonlinearity and sensitivity of underwater acoustic propagation to small‐scale oceanic features. In order to assess the potential of oceanic data assimilation, integrated ocean‐acoustic Observing System Simulation Experiments are conducted. Synthetic altimetry and in situ data were assimilated through a variational oceanographic data assimilation system. The predicted sound speed fields are then ingested in a range‐dependent acoustic model for transmission loss (TL) predictions. The predicted TLs are analyzed for the purpose of (i) evaluating the contributions of different sources to the uncertainties of oceanic and acoustic forecasts and (ii) comparing the impact of different oceanic analysis schemes on the TL prediction accuracy. Using ensemble member clustering techniques, the contributions of boundary conditions, ocean parameterizations, and geoacoustic characterization to acoustic prediction uncertainties are addressed. Subsequently, the impact of three‐dimensional variational (3DVAR), 4DVAR, and hybrid ensemble‐3DVAR data assimilation on acoustic TL prediction at two signal frequencies (75 and 2,500 Hz) and different ranges (30 and 60 km) are compared. 3DVAR significantly improves the predicted TL accuracy compared to the control run. Promisingly, 4DVAR and hybrid data assimilation further improve the TL forecasts, the hybrid scheme achieving the highest skill scores for all cases, while being the most computationally intensive scheme. The optimal scheme choice thus depends on requirements on the accuracy and computational constraints. These findings foster developments of coupled data assimilation for operational underwater acoustic propagation.

An optimal data assimilation method and its application to the numerical simulation of the ocean dynamics

ABSTRACTAn original data assimilation (DA) scheme with a general dynamics model is considered. It is shown that this scheme can be approximated by the stochastic diffusion process. The sufficient conditions to provide this approximation are formulated. Based on this algorithm a new DA method is developed. The method combines variational and statistical approaches commonly used in DA theory and minimizes the variance of the trajectory of a diffusion process in conjunction with a dynamics numerical model. In this sense the method is optimal in contrast to other DA approaches. The proposed scheme takes the model dynamics into account and in this way it differs from the well-known Kalman filter. Furthermore, the derived DA method can be applied to a very wide field of dynamical systems, for example, gas dynamics, fluid dynamics and other disciplines. However, the current study deals with oceanography and DA in oceanography specifically. Then the method is applied to the HYbrid Coordinate Ocean Model and assimilates satellite sea level anomaly data from the Archiving, Validating and Interpolating Satellite Oceanography Data over the Atlantic Ocean to correct the model state. Several numerical experiments have been performed. The experiments show that the method substantially changes the synoptic and mesoscale structure of ocean dynamics. Also, the distribution of the obtained result is estimated through the solution of the Fokker–Planck–Kolmogorov equation.

Application of 3-D ensemble variational data assimilation to a Baltic Sea reanalysis 1989–2013

A 3-D ensemble variational (3DEnVar) data assimilation method has been implemented and tested for oceanographic data assimilation of sea surface temperature (SST), sea surface salinity (SSS), sea ice concentration (SIC), and salinity and temperature profiles. To damp spurious long-range correlations in the ensemble statistics, horizontal and vertical localisation was implemented using empirical orthogonal functions. The results show that the 3DEnVar method is indeed possible to use in oceanographic data assimilation. So far, only a seasonally dependent ensemble has been used, based on historical model simulations. Near-surface experiments showed that the ensemble statistics gave inhomogeneous and anisotropic horizontal structure functions, and assimilation of real SST and SIC fields gave smooth, realistic increment fields. The implementation was multivariate, and results showed that the cross-correlations between variables work in an intuitive way, for example, decreasing SST where SIC was increased and vice versa. The profile data assimilation also gave good results. The results from a 25-year reanalysis showed that the vertical salinity and temperature structure were significantly improved, compared to both dependent and independent data.

On adaptive filtering for high dimensional systems under parameter uncertainty and its application to satellite data assimilation in oceanography

In this paper, the adaptive filtering theory, recently proposed and developed the authors of present work [1-9] for stochastic, encountered in the field of data as simulation in meteorology and oceanography, is reviewed. Several important questions on numerical estimation og the gain matrix, model reduction, structural choices for the gain, filter stability… are discussed. We show the connections of present approach with a standard Kalman filtering. Adaptive filter is implemented along with a Kalman filtering. Adaptive filter is implemented along with a Kalman filter and standard Newton relation method on the four-layer adiabatic Miami Isopycnical Co-ordinate Ocean Model (MICOM) to produce the estimate for the deep oceanic circulation using assimilate synthetic observations of surface height. Numerical results justify high efficiency of the adaptive filter whose performance is slightly better than that of a Kalman filter due to impossibility to correctly specify the error statistics in a Kalman filter.

Towards a parallel component in a GPU–CUDA environment: a case study with the L-BFGS Harwell routine

Modern graphics processing units (GPUs) have been at the leading edge of increasing parallelism over the last 10 years. This fact has encouraged the use of GPUs in a broader range of applications, where developers are required to lever age this technology with new programming models which ease the task of writing programs to run efficiently on GPUs. In this paper, we discuss the main guidelines to assist the developer when porting sequential scientific code on modern GPUs. These guidelines were carried out by porting the L-BFGS, the (Limited memory-) BFGS algorithm for large scale optimization, available as Harwell routine VA15. The specific interest in the L-BFGS algorithm arises from the fact that this is the computational module with the longest running time of a Oceanographic Data Assimilation application software, on which some of the authors are working.

Robust control problems for primitive equations of the ocean

In this article, we study some robust control problems associatedwith the primitive equations of the ocean and related to dataassimilation in oceanography. We prove the existence and uniquenessof solutions to these control problems.

Ensemble data assimilation with the CNMCA regional forecasting system

AbstractThe Ensemble Kalman Filter (EnKF) is likely to become a viable alternative to variational methods for the next generation of meteorological and oceanographic data assimilation systems. In this work we present results from real‐data assimilation experiments using the CNMCA regional numerical weather prediction (NWP) forecasting system and compare them to the currently operational variational‐based analysis. The set of observations used is the same as the one ingested in the operational data stream, with the exception of satellite radiances and scatterometer winds. Results show that the EnKF‐based assimilation cycle is capable of producing analyses and forecasts of consistently superior skill in the root mean square error metric than CNMCA operational 3D‐Var.One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. To combat this problem a number of different parametrizations of the model error unaccounted for in the assimilation cycle have been proposed. In the CNMCA system a combination of adaptive multiplicative and additive background covariance inflations has been found to give adequate results and to be capable of avoiding filter divergence in extended assimilation trials. The additive component of the covariance inflation has been implemented through the use of scaled forecast differences.Following suggestions that ensemble square‐root filters can violate the gaussianity assumption when used with nonlinear prognostic models, the statistical distribution of the forecast and analysis ensembles has been studied. No sign of the ensemble collapsing onto one or a few model states has been found, and the forecast and analysis ensembles appear to stay remarkably close to the assumed probability distribution functions. Copyright © 2010 Royal Meteorological Society

The interannual and decadal variability of the sea level in the Japan/East Sea

Sea level observed by altimeter during the 1993–2007 period and the thermosteric sea level from 1945 through 2005 obtained by using the global ocean temperature data sets recently published are used to investigate the interannual and decadal variability of the sea level in the Japan/East Sea (JES) and its response to El Nino and Southern Oscillation (ENSO). Both the interannual variations of the sea level observed by altimeter and those of the thermosteric sea level obtained from reanalyzed data in the JES are closely related to ENSO. As a result, one important consequence is that the sea level trends are mainly caused by the thermal expansion in the JES. An ‘enigma’ is revealed that the correlation between the thermosteric sea level and ENSO during the PDO (Pacific Decadal Oscillation) warm phase (post mid-1970s) is inconsistent with that during the cold phase (pre mid-1970s) in the JES. The thermosteric sea level trends and the Southern Oscillation Index (SOI) suggest a strong negative correlation during the period 1977–1998, whereas there appears a relatively weak positive correlation during the period 1945–1976 in the JES. Based on the SODA (Simple Oceanographic Data Assimilation) datasets, possible mechanisms of the interannual and decadal variability of the sea level in the JES are discussed. Comprehensive analysis reveals that the negative anomalies of SOI correspond to the positive anomalies of the southeast wind stress, the net advective heat flux and the sea level in the JES during the PDO warm phase. During the PDO cold phase, the negative anomalies of SOI correspond to the positive anomalies of the southwest wind stress, the negative anomalies of the net advective heat flux and the sea level in the JES.

A Sequential Variational Algorithm for Data Assimilation in Oceanography and Meteorology

Abstract This study theoretically establishes a sequential variational (SVAR) method for the data assimilation in oceanography and meteorology defined on the model space. Requiring a significantly smaller amount of computer memory, theoretically SVAR gives the same optimal model state estimate as the four-dimensional variational data assimilation method. Its computational cost is similar to that of the four-dimensional variational data assimilation and representer methods. In addition to the optimal state estimates, SVAR computes error covariances at the end of the assimilation window. These advantageous properties of the new algorithm are obtained by combining the sequential methodology with suitable definitions of several new l2 norms, which implicitly provide required estimates.

The ensemble Kalman filter in an operational regional NWP system: preliminary results with real observations

AbstractThe ensemble Kalman filter (EnKF) has been widely tested as a possible candidate for the next generation of meteorological and oceanographic data assimilation algorithms. While a number of tests with models of varying realism have been successfully performed, the EnKF has been seldom evaluated in an operational regional NWP environment at realistic spatial resolution. In this work one particular EnKF implementation (Local Ensemble Transform Kalman Filter, LETKF) has been implemented and its performance evaluated in comparison with CNMCA operational 3D‐Var.One of the most important issues in EnKF implementations lies in the filter tendency to become underdispersive for practical ensemble sizes. While multiplicative (or additive) covariance inflation has been used to deal with this problem, tuning its values is an expensive and possibly never‐ending task. Following ideas from linear estimation theory, we test an adaptive estimation procedure to evaluate forecast covariance inflation factors and observation errors. Our results show that, differently from previous experiences, the online estimation technique can be successfully employed in a realistic state‐of‐the‐art NWP system. More generally the LETKF analysis is shown to be of superior quality with respect to the operational 3D‐Var and a likely candidate for its replacement in the not‐too‐distant future. Copyright © 2008 Royal Meteorological Society

On the key role of nutrient data to constrain a coupled physical–biogeochemical assimilative model of the North Atlantic Ocean

A sequential assimilative system has been implemented into a coupled physical–biogeochemical model (CPBM) of the North Atlantic basin at eddy-permitting resolution (1/4°), with the long-term goal of estimating the basin scale patterns of the oceanic primary production and their seasonal variability. The assimilation system, which is based on the SEEK filter [Brasseur, P., Verron, J., 2006. The SEEK filter method for data assimilation in oceanography: a synthesis. Ocean Dynamics. doi: 10.1007/s10236-006-0080-3], has been adapted to this CPBM in order to control the physical and biogeochemical components of the coupled model separately or in combination. The assimilated data are the satellite Topex/Poseidon and ERS altimetric data, the AVHRR Sea Surface Temperature observations, and the Levitus climatology for salinity, temperature and nitrate. In the present study, different assimilation experiments are conducted to assess the relative usefulness of the assimilated data to improve the representation of the primary production by the CPBM. Consistently with the results obtained by Berline et al. [Berline, L., Brankart, J-M., Brasseur, P., Ourmières, Y., Verron, J., 2007. Improving the physics of a coupled physical–biogeochemical model of the North Atlantic through data assimilation: impact on the ecosystem. J. Mar. Syst. 64 (1–4), 153–172] with a comparable assimilative model, it is shown that the assimilation of physical data alone can improve the representation of the mixed layer depth, but the impact on the ecosystem is rather weak. In some situations, the physical data assimilation can even worsen the ecosystem response for areas where the prior nutrient distribution is significantly incorrect. However, these experiments also show that the combined assimilation of physical and nutrient data has a positive impact on the phytoplankton patterns by comparison with SeaWiFS ocean colour data, demonstrating the good complementarity between SST, altimetry and in situ nutrient data. These results suggest that more intensive in situ measurements of biogeochemical nutrients are urgently needed at basin scale to initiate a permanent monitoring of oceanic ecosystems.

Experiments of one-dimensional soil moisture assimilation system based on ensemble Kalman filter

Ensemble Kalman filter is a new sequential data assimilation algorithm which was originally developed for atmospheric and oceanographic data assimilation. It can be applied to calculate error covariance matrix through Monte-Carlo simulation. This approach is able to resolve the nonlinearity and discontinuity existed within model operator and observation operator. When observation data are assimilated at each time step, error covariances are estimated from the phase-space distribution of an ensemble of model states. The error statistics is then used to calculate Kalman gain matrix and analysis increments. In this study, we develop a one-dimensional soil moisture data assimilation system based on ensemble Kalman filter, the Simple Biosphere Model (SiB2) and microwave radiation transfer model (AIEM, advanced integration equation model). We conduct numerical experiments to assimilate in situ soil surface moisture measurements and low-frequency passive microwave remote sensing data into a land surface model, respectively. The results indicate that data assimilation can significantly improve the soil surface moisture estimation. The improvement in root zone is related to the model bias errors at surface layer and root zone. The soil moisture does not vary significantly in deep layer. Additionally, the ensemble Kalman filter is predominant in dealing with the nonlinearity of model operator and observation operator. It is practical and effective for assimilating observations in situ and remotely sensed data into land surface models.

Robust control problems for the multilayer quasi-geostrophic system

In this article, we study some robust control problems associated with the multilayer quasi-geostrophic equations of the ocean and related to data assimilation in oceanography. We consider higher norms (compared to [T. Tachim Medjo, Robust control problems associated with the multilayer quasi-geostrophic equations of the ocean, Appl. Math. Optim. 51(3) (2005) 333–360]) in the definition of the cost functionals. We prove the existence and uniqueness of solutions. The result relies on better a priori estimates on the solutions to the multilayer quasi-geostrophic system obtained using a new formulation that we introduce for the multilayer quasi-geostrophic equation of the ocean. The new formulation replaces the non-homogenous boundary conditions (and the non-local constraint) on the stream-function by a simple homogenous Dirichlet boundary condition.

Problems and Techniques

This issues features papers about mathematical genetics, data compression, and data assimilation in oceanography. 1. Computer algebra can help to predict the genetic makeup of a population. This is what we can conclude from the first paper, “Buchberger's Algorithm and the Two-Locus, Two-Allele Model.” With reproduction rates and probability of chromosome recombination as parameters, and one variable for each chromosome type, one can set up a system of polynomial equations. The solution value for a variable indicates how often this chromosome type occurs in the population. The question is now, over all parameter choices, how many different equilibrium solutions can there be? In other words, in the long term, can a chromosome type occur with any possible frequency? Arthur Copeland's answer is no: the number of solutions is almost always finite (and conjectured to be 15) in the special case when a population contains at most four different chromosome types. He arrives at his answer by means of affine varieties, ideals, and Gröbner bases. He also shows that the equilibrium solutions vary smoothly with the parameters. 2. The second paper, “A Direct Formulation for Sparse PCA Using Semidefinite Programming,” by Alexandre d'Aspremont, Laurent El Ghaoui, Michael I. Jordan, and Gert R. G. Lanckriet, is concerned with principal component analysis (PCA), a technique for compressing data so that as little information as possible is lost. PCA accomplishes this by finding directions of maximum variance in the data. In data analysis of gene expressions, for instance, different elements of a direction vector correspond to different genes. However, interpreting the meaning of a direction is much easier if only a few genes contribute to the direction. Such a direction vector has many zero elements and is called sparse. The authors propose a semidefinite programming method that maximizes variance as well as sparsity. The method is computationally efficient and robust. 3. The topic of the third paper, “A Reduced-Order Kalman Filter for Data Assimilation in Physical Oceanography,” by D. Rozier, F. Birol, E. Cosme, P. Brasseur, J. M. Brankart, and J. Verron, is a technique used by oceanographers to increase the accuracy of numerical models for predicting ocean circulation. Data assimilation combines the output of a simulation step with observed data and error statistics and then returns this “corrected” output to the simulation as the basis for the next step. Data assimilation based on Kalman filters assumes that measurement and model errors are unbiased and Gaussian. This is expensive, however, because an error covariance matrix must be constructed at every step. A reduced-order Kalman filter (called SEEK) is a cheaper version that reduces (or compresses) the size of the covariance matrix—the same key idea as in the paper described above. The authors give a very readable account of the issues associated with so-called ocean global circulation models: choice of vertical coordinate system (depending on the ocean region: shallow coastal shelf, steeply sloping ocean floors, stratified regions); limitations of models for ocean circulation simulations; sequential data assimilation techniques; adaptation of Kalman filters to geophysical applications; and modes of data acquisition (via satellites, ships, floats, mooring networks). The effectiveness of the SEEK filter is illustrated with numerical simulations of the Gulf Stream and the Bay of Biscay.

The SEEK filter method for data assimilation in oceanography: a synthesis

This paper reviews the developments of the singular evolutive extended Kalman (SEEK) filter method used for data assimilation in oceanography, since the original paper by Pham et al. (J Mar Syst 16:3–4, 323–340 1998a). First, a short review is presented of the context of data assimilation in oceanography and of the variety of numerical ocean codes and configurations in which the SEEK filter has been implemented using different data sets for assimilation. Then, the paper provides an exposition of the different versions of the SEEK filter developed during the past 10 years and discusses their relative merits for scientific or operational implementations. A classification of the algorithmic variants is proposed, and several possible improvements of the generic methodology are mentioned in the perspective of new assimilation challenges.

PALM: a computational framework for assembling high‐performance computing applications

AbstractThe PALM project aims to implement a general tool allowing the easy integration of high‐performance computing applications in a flexible and evolutive way. It was originally designed for oceanographic data assimilation algorithms, but its application domain extends to multiple scientific applications. In the framework of PALM, applications are split into elementary components that can exchange data. The main features of PALM are the dynamic launching of the coupled components, the full independence of the components from the application algorithm, the parallel data exchanges with redistribution and the separation of the physics from the algebraic manipulations performed by the PALM algebra toolbox. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Robust Control Problems Associated with the Multilayer Quasi-Geostrophic Equations of the Ocean

In this article we study some robust control problems associated with the multilayer quasi-geostrophic equations of the ocean and related to data assimilation in oceanography. We prove the existence and uniqueness of solutions using a general framework given in [6].