Data Assimilation by Neural Network for Ocean Circulation: Parallel Implementation


  • Haroldo F. Campos Velho National Institute for Space Research, São José dos Campos, Brazil
  • Helaine C. M. Furtado Federal University of Western Pará, Santarém, Brazil
  • Sabrina B. M. Sambatti Independent researcher, São José dos Campos, Brazil
  • Carla Barros Osthoff Ferreira de Barros National Laboratory for Scientific Computing, Petrópolis, Brazil
  • Maria E. S. Welter National Laboratory for Scientific Computing, Petrópolis, Brazil
  • Roberto P. Souto National Laboratory for Scientific Computing, Petrópolis, Brazil
  • Diego Carvalho Federal Center for Technological Education Celso Suckow da Fonseca, Rio de Janeiro, Brazil
  • Douglas O. Cardoso Federal Center for Technological Education Celso Suckow da Fonseca, Petrópolis, Brazil; Polytechnic Institute of Tomar, Tomar, Portugal



data assimilation, artificial neural network, shallow water equations, parallel processing


Data assimilation (DA) is an essential issue for operational prediction centers, where a computer code is applied to simulate physical phenomena by solving differential equations. The procedure to determine the best initial condition combining data from observation and previous forecasting (background) is carried out by a data assimilation method. The Kalman filter (KF) is a technique for data assimilation, but it is computationally expensive. An approach to reduce the computational effort for DA is to emulate the KF by a neural network. The multi-layer perceptron neural network (MLP-NN) is employed to emulate the Kalman in a 2D ocean circulation model, and algorithmic complexity to KF and NN is presented. A shallow-water system models the ocean dynamics. Synthetic measurements are used for evaluating the MLP-NN for the data assimilation process. Here, a parallel version for the DA procedure by the neural network is described and tested, showing the performance improvement for a parallel version of the NN-DA.


Anochi, J.A., Campos Velho, H.F., Hernandez Torres, R.: Two geoscience applications by optimal neural network architecture. Pure and Applied Geophysics 1776(1), 1–21 (2019).

Bennett, A.F.: Inverse Modeling of The Ocean and Atmosphere. Cambridge University Press (2002)

Boucher, M.A., Quilty, J., Adamowski, J.: Data assimilation for streamflow forecasting using extreme learning machines and multilayer perceptrons. Water Resources Research 56 (2020).

Campos Velho, H.F., Härter, F.P., Rempel, E.L., Chian, A.: Neural networks in auroral data assimilation. Journal of Atmospheric and Solar-Terrestrial Physics 70(10), 1243–1250 (2008).

Cintra, R.C., Campos Velho, H.F., Todling, R.: Redes neurais artificiais na melhoria de desempenho de métodos de assimilação de dados: filtro de Kalman. TEMA: Trends in Computational and Applied Mathematics 11(1), 29–39 (2010).

Cintra, R.S.C., Campos Velho, H.F.: Data assimilation by artificial neural networks for an atmospheric general circulation model. In: El-Shahat, A. (ed.) Advanced Applications for Artificial Neural Networks, chap. 14, pp. 265–285. Intech (2018).

Cintra, R.S.C., Campos Velho, H.F., Cocke, S.: Tracking the model: data assimilation by artificial neural network. In: IEEE International Joint Conference on Neural Networks – IJCNN, Vancouver, Canada, July 24-29, 2016. vol. 4, pp. 403–410 (2016).

Daley, R.: Atmospheric Data Analysis. Cambridge University Press (1993)

Furtado, H.C., Cintra, R.S.C., Campos Velho, H.F., et al.: Neural network for data assimilation method applied to shallow water equation. In: 2nd International Symposium on Uncertainty Quantification and Stochastic Modeling, Rouen, France, July 7-11, 2014. pp. 299–311 (2014)

Haykin, S.: Neural Networks: A Comprehensive Foundation. Prentice Hall Inc. (1994)

Kalnay, E.: Atmospheric Modeling, Data Assimilation, and Predictability. Cambridge University Press (2003)

Luz, E.F.P., Becceneri, J.C., de Campos Velho, H.F.: A new multi-particle collision algorithm for optimization in a high performance environment. Journal of Computational Interdisciplinary Sciences 1(1), 3–10 (2008).

Mendel, J.: Computational requirements for a discrete Kalman filter. IEEE Transactions on Automatic Control 16(6), 748–758 (1971).

Mesinger, F., Arakawa, A.: Numerical methods used in atmospheric models. Global Atmospheric Research Program – World Meteorological Organization (1976)

Reich, S., Cotter, C.: Probabilistic Forecasting and Baysian Data Assimilation. Cambridge University Press (2015)

Sambatti, S.B.M., Campos Velho, H.F., Furtado, H.C.M., et al.: Self-configured neural network for data assimilation using FPGA for ocean circulation. In: 3Conference of Computational Interdisciplinary Science (CCIS 2016), São José dos Campos (SP), Brazil (2016)

Vaidehi, V., Krishnan, C.N.: Computational complexity of the Kalman tracking algorithm. IETE Journal of Researcht 44(3), 125–134 (1998).




How to Cite

Campos Velho, H. F., Furtado, H. C. M., Sambatti, S. B. M., Osthoff Ferreira de Barros, C. B., Welter, M. E. S., Souto, R. P., Carvalho, D. ., & Cardoso, D. O. (2022). Data Assimilation by Neural Network for Ocean Circulation: Parallel Implementation. Supercomputing Frontiers and Innovations, 9(1), 74–86.