scholarly journals Generalized Kalman Filter and Ensemble Optimal Interpolation, Their Comparison and Application to the Hybrid Coordinate Ocean Model

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2371
Author(s):  
Konstantin Belyaev ◽  
Andrey Kuleshov ◽  
Ilya Smirnov ◽  
Clemente A. S. Tanajura
Keyword(s):  
Kalman Filter ◽  
Data Assimilation ◽  
Ocean Circulation ◽  
Ocean Model ◽  
Computational Effort ◽  
Optimal Interpolation ◽  
State Variables ◽  
Ensemble Optimal Interpolation ◽  
Hybrid Coordinate Ocean Model ◽  
Generalized Kalman Filter

In this paper, we consider a recently developed data assimilation method, the Generalized Kalman Filter (GKF), which is a generalization of the widely-used Ensemble Optimal Interpolation (EnOI) method. Both methods are applied for modeling the Atlantic Ocean circulation using the known Hybrid Coordinate Ocean Model. The along-track altimetry data taken from the Archiving, Validating and Interpolating Satellite Oceanography Data (AVISO) were used for data assimilation and other data from independent archives of observations; particularly, the temperature and salinity data from the Pilot Research Array in the Tropical Atlantic were used for independent comparison. Several numerical experiments were performed with their results discussed and analyzed. It is shown that values of the ocean state variables obtained in the calculations using the GKF method are closer to the observations in terms of standard metrics in comparison with the calculations using the standard data assimilation method EnOI. Furthermore, the GKF method requires less computational effort compared to the EnOI method.

scholarly journals A STUDY OF THE IMPACT OF ALTIMETRY DATA ASSIMILATION ON SHORT-TERM PREDICTABILITY OF THE HYCOM OCEAN MODEL IN REGIONS OF THE TROPICAL AND SOUTH ATLANTIC OCEAN

2013 ◽  
Vol 31 (2) ◽  
pp. 271 ◽  
Author(s):  
Leonardo Nascimento Lima ◽  
Clemente Augusto Souza Tanajura
Keyword(s):  
Data Assimilation ◽  
Sea Surface Height ◽  
Ocean Model ◽  
South Atlantic ◽  
Sea Surface ◽  
Optimal Interpolation ◽  
Altimetry Data ◽  
Hybrid Coordinate Ocean Model ◽  
Along Track ◽  
The Impact

ABSTRACT. In this study, assimilation of Jason-1 and Jason-2 along-track sea level anomaly (SLA) data was conducted in a region of the tropical and South Atlantic (7◦N-36◦S, 20◦W up to the Brazilian coast) using an optimal interpolation method and the HYCOM (Hybrid Coordinate Ocean Model). Four 24 h-forecast experiments were performed daily from January 1 until March 31, 2011 considering different SLA assimilation data windows (1 day and 2 days) and different coefficients in the parameterization of the SLA covariance matrix model. The model horizontal resolution was 1/12◦ and the number of vertical layers was 21. The SLA analyses added to the mean sea surface height were projected to the subsurface with the Cooper & Haines (1996) scheme. The results showed that the experiment with 2-day window of along-track data and with specific parameterizations of the model SLA covariance error for sub-regions of the METAREA V was the most accurate. It completely reconstructed the model sea surface height and important improvements in the circulation were produced. For instance, there was a substantial improvement in the representation of the Brazil Current and North Brazil Undercurrent. However, since no assimilation of vertical profiles of temperature and salinity and of sea surface temperature was performed, the methodology employed here should be considered only as a step towards a high quality analysis for operational forecasting systems.   Keywords: data assimilation, optimal interpolation, Cooper & Haines scheme, altimetry data.   RESUMO. Neste estudo, a assimilação de dados de anomalia da altura da superfície do mar (AASM) ao longo da trilha dos satélites Jason-1 e Jason-2 foi conduzida em uma região do Atlântico tropical e Sul (7◦N-36◦S, 20◦W até a costa do Brasil) com o método de interpolação ótima e o modelo oceânico HYCOM (Hybrid Coordinate Ocean Model). Foram realizados quatro experimentos de previsão de 24 h entre 1 de janeiro e 31 de março de 2011, considerando diferentes janelas de assimilação de AASM (1 dia e 2 dias) e diferentes coeficientes na parametrização da matriz de covariância dos erros de AASM do modelo. A resolução horizontal empregada no HYCOM foi 1/12◦ para 21 camadas verticais. As correções de altura da superfície do mar devido à assimilação de AASM foram projetadas abaixo da camada de mistura através da técnica de Cooper & Haines (1996). Os resultados mostraram que o experimento com assimilação de dados ao longo da trilha dos satélites com a janela de 2 dias e com parametrizações da matriz de covariância específicas para sub-regiões da METAREA V foi o mais acurado. Ele reconstruiu completamente a altura da superfície do mar e também proporcionou melhorias na circulação oceânica reproduzida pelo modelo. Por exemplo, houve substancial melhoria da representação nos campos da Corrente do Brasil e Subcorrente Norte do Brasil. Entretanto, tendo em vista que não foi realizada a assimilação de perfis verticais de temperatura e de salinidade e da temperatura da superfície do mar, a metodologia apresentada deve ser considerada apenas como um passo na conquista de uma análise oceânica e de um sistema previsor de qualidade para fins operacionais.   Palavras-chave: assimilação de dados, interpolação ótima, técnica de Cooper & Haines, dados de altimetria.

scholarly journals Data Assimilation Method, its Application and Stability

2019 ◽  
Vol 292 ◽  
pp. 03012
Author(s):  
Konstantin Belyaev ◽  
Andrey Kuleshov ◽  
Ilya Smirnov ◽  
Natalia Tuchkova
Keyword(s):  
Markov Chain ◽  
Kalman Filter ◽  
Data Assimilation ◽  
Dynamic System ◽  
Numerical Experiments ◽  
Sufficient Conditions ◽  
Ocean Model ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Kalman Filter

The authors data assimilation method, namely, generalized Kalman filter (GKF) method, its application and stability is considered. The problem of stability of a dynamic system with data assimilation formulated for a sequence of random variables forming a Markov chain is considered. The stability formulation for this problem is suggested as the problem of the convergence of the corresponding Markov chain when the number of its members goes to infinity. Necessary and sufficient conditions of this convergence are proved. A number of numerical experiments with the specific dynamic system, namely with the ocean model circulation HYCOM and the GKF method are conducted and discussed. The stability of the GKF method was proofed.

scholarly journals A hybrid data assimilation method and its comparison with an Ensemble Optimal Interpolation scheme in conjunction with the numerical ocean model using altimetry data

2019 ◽  
Author(s):  
Konstantin Belyaev ◽  
Andrey Kuleshov ◽  
Ilya Smirnov ◽  
Clemente A. S. Tanajura
Keyword(s):  
Data Assimilation ◽  
Computational Cost ◽  
Ocean Model ◽  
Optimal Interpolation ◽  
Altimetry Data ◽  
Interpolation Scheme ◽  
Hybrid Data Assimilation ◽  
Ensemble Optimal Interpolation ◽  
Numerical Ocean Model ◽  
Hybrid Data

Abstract. An original hybrid data assimilation scheme recently developed is presented and tested. The scheme is based on the application of the theory of diffusion random processes. It is applied here in conjunction with the Hybrid-Coordinate Ocean Model (HYCOM) to assimilate altimetry data from the Archiving, Validating and Interpolating Satellite Oceanography Data (AVISO) in the Atlantic. Several numerical experiments were conducted and their results were analyzed. It is shown that the method is able to assimilate data and to produce analyses closer to observations. It also conserves the model balance. This method allows calculating the confidence range of the analyses by estimating their errors The presented method is compared with the Ensemble Optimal Interpolation scheme (EnOI) and it is shown that it has several advantages, in particular, it provides a better forecast and requires less computational cost.

scholarly journals Argo data assimilation into HYCOM with an EnOI method in the Atlantic Ocean

Ocean Science ◽  
2015 ◽  
Vol 11 (1) ◽  
pp. 195-213 ◽  
Author(s):  
D. Mignac ◽  
C. A. S. Tanajura ◽  
A. N. Santana ◽  
L. N. Lima ◽  
J. Xie
Keyword(s):  
Data Assimilation ◽  
Atlantic Ocean ◽  
Heat Content ◽  
Ocean Model ◽  
Optimal Interpolation ◽  
Argo Data ◽  
Thermohaline Structure ◽  
Vertical Coordinate ◽  
Ocean Data Assimilation ◽  
Hybrid Coordinate Ocean Model

Abstract. An ocean data assimilation system to assimilate Argo temperature (T) and salinity (S) profiles into the HYbrid Coordinate Ocean Model (HYCOM) was constructed, implemented and evaluated for the first time in the Atlantic Ocean (78° S to 50° N and 98° W to 20° E). The system is based on the ensemble optimal interpolation (EnOI) algorithm proposed by Xie and Zhu (2010), especially made to deal with the hybrid nature of the HYCOM vertical coordinate system with multiple steps. The Argo T–S profiles were projected to the model vertical space to create pseudo-observed layer thicknesses (Δ pobs), which correspond to the model target densities. The first step was to assimilate Δ pobs considering the sub-state vector composed by the model layer thickness (Δ p) and the baroclinic velocity components. After that, T and S were assimilated separately. Finally, T was diagnosed below the mixed layer to preserve the density of the model isopycnal layers. Five experiments were performed from 1 January 2010 to 31 December 2012: a control run without assimilation, and four assimilation runs considering the different vertical localizations of T, S and Δ p. The assimilation experiments were able to significantly improve the thermohaline structure produced by the control run. They reduced the root mean square deviation (RMSD) of T and S calculated with respect to Argo independent data in 34 and 44%, respectively, in comparison to the control run. In some regions, such as the western North Atlantic, substantial corrections in the 20 °C isotherm depth and the upper ocean heat content towards climatological states were achieved. The runs with a vertical localization of Δ p showed positive impacts in the correction of the thermohaline structure and reduced the RMSD of T (S) from 0.993 °C (0.149 psu) to 0.905 °C (0.138 psu) for the whole domain with respect to the other assimilation runs.

A New Solar Radiation Penetration Scheme for Use in Ocean Mixed Layer Studies: An Application to the Black Sea Using a Fine-Resolution Hybrid Coordinate Ocean Model (HYCOM)*

2005 ◽  
Vol 35 (1) ◽  
pp. 13-32 ◽  
Author(s):  
A. Birol Kara ◽  
Alan J. Wallcraft ◽  
Harley E. Hurlburt
Keyword(s):  
Solar Radiation ◽  
Optical Depth ◽  
Black Sea ◽  
Ocean Circulation ◽  
Mixed Layer ◽  
Ocean Model ◽  
The Black Sea ◽  
Atmospheric Forcing ◽  
Model Simulations ◽  
Hybrid Coordinate Ocean Model

Abstract A 1/25° × 1/25° cos(lat) (longitude × latitude) (≈3.2-km resolution) eddy-resolving Hybrid Coordinate Ocean Model (HYCOM) is introduced for the Black Sea and used to examine the effects of ocean turbidity on upper-ocean circulation features including sea surface height and mixed layer depth (MLD) on annual mean climatological time scales. The model is a primitive equation model with a K-profile parameterization (KPP) mixed layer submodel. It uses a hybrid vertical coordinate that combines the advantages of isopycnal, σ, and z-level coordinates in optimally simulating coastal and open-ocean circulation features. This model approach is applied to the Black Sea for the first time. HYCOM uses a newly developed time-varying solar penetration scheme that treats attenuation as a continuous quantity. This scheme includes two bands of solar radiation penetration, one that is needed in the top 10 m of the water column and another that penetrates to greater depths depending on the turbidity. Thus, it is suitable for any ocean general circulation model that has fine vertical resolution near the surface. With this scheme, the optical depth–dependent attenuation of subsurface heating in HYCOM is given by monthly mean fields for the attenuation of photosynthetically active radiation (kPAR) during 1997–2001. These satellite-based climatological kPAR fields are derived from Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) data for the spectral diffuse attenuation coefficient at 490 nm (k490) and have been processed to have the smoothly varying and continuous coverage necessary for use in the Black Sea model applications. HYCOM simulations are driven by two sets of high-frequency climatological forcing, but no assimilation of ocean data is then used to demonstrate the importance of including spatial and temporal varying attenuation depths for the annual mean prediction of upper-ocean quantities in the Black Sea, which is very turbid (kPAR > 0.15 m−1, in general). Results are reported from three model simulations driven by each atmospheric forcing set using different values for the kPAR. A constant solar-attenuation optical depth of ≈17 m (clear water assumption), as opposed to using spatially and temporally varying attenuation depths, changes the surface circulation, especially in the eastern Black Sea. Unrealistic sub–mixed layer heating in the former results in weaker stratification at the base of the mixed layer and a deeper MLD than observed. As a result, the deep MLD off Sinop (at around 42.5°N, 35.5°E) weakens the surface currents regardless of the atmospheric forcing used in the model simulations. Using the SeaWiFS-based monthly turbidity climatology gives a shallower MLD with much stronger stratification at the base and much better agreement with observations. Because of the high Black Sea turbidity, the simulation with all solar radiation absorbed at the surface case gives results similar to the simulations using turbidity from SeaWiFS in the annual means, the aspect of the results investigated in this paper.

Evaluating Effects of Observational Data Assimilation in General Ocean Circulation Model by Ensemble Kalman Filtering: Numerical Experiments with Synthetic Observations

2021 ◽  
pp. 50-66
Author(s):  
V. N. Stepanov ◽  
◽  
Yu. D. Resnyanskii ◽  
B. S. Strukov ◽  
A. A. Zelen’ko ◽  
...  
Keyword(s):  
Data Assimilation ◽  
Observational Data ◽  
Ocean Circulation ◽  
Numerical Experiments ◽  
Turbulent Viscosity ◽  
Bottom Topography ◽  
Synthetic Data ◽  
Circulation Model ◽  
Ocean Model ◽  
Global Ocean

The quality of simulation of model fields is analyzed depending on the assimilation of various types of data using the PDAF software product assimilating synthetic data into the NEMO global ocean model. Several numerical experiments are performed to simulate the ocean–sea ice system. Initially, free model was run with different values of the coefficients of horizontal turbulent viscosity and diffusion, but with the same atmospheric forcing. The model output obtained with higher values of these coefficients was used to determine the first guess fields in subsequent experiments with data assimilation, while the model results with lower values of the coefficients were assumed to be true states, and a part of these results was used as synthetic observations. The results are analyzed that are assimilation of various types of observational data using the Kalman filter included through the PDAF to the NEMO model with real bottom topography. It is shown that a degree of improving model fields in the process of data assimilation is highly dependent on the structure of data at the input of the assimilation procedure.

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