Post-processing of Numerical Forecasts Using Polynomial Networks with the Operational Calculus PDE Substitution

  • Ladislav ZjavkaEmail author
  • Stanislav Mišák
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 874)


Large-scale weather forecast models are based on the numerical integration of systems of differential equation which can describe atmospheric processes in light of physical patterns. Meso-scale weather forecast systems need to define the initial and lateral boundary conditions which can be supplied by global numerical models. Their overall solutions, using a large number of data variables in several atmospheric layers, represent the weather dynamics on the earth scale. Post-processing methods using local measurements were developed in order to adapt numerical weather prediction model outputs for local conditions with surface details. The proposed forecasts correction procedure is based on the 2-stage approach of the Perfect Prog method using data observations to derive a model which is applied to the forecasts of input variables to predict 24-h series of the target output. The post-processing model formation requires an additional initial estimation of the optimal number of training days in consideration of the latest test data. Differential polynomial network is a recent machine learning technique using a polynomial PDE substitution of Operational calculus to form the test and prediction models. It decomposes the general PDE into the 2nd order sub-PDEs in its nodes, being able to describe the local weather dynamics in the surface level. The PDE sum models represent the current local data relations in a sort of settled weather which allow improvements in local forecasts corrected with NWP utilities in the majority of days.


Polynomial neural network General partial differential equation Polynomial substitution Operational calculus Post-processing model 



This paper was supported by the following projects: LO1404: Sustainable Development of ENET Centre; CZ.1.05/2.1.00/19.0389 Development of the ENET Centre Research Infrastructure; SP2018/58 and SP2018/78 Student Grant Competition and TACR TS777701, Czech Republic.


  1. 1.
    Durai, V.R., Bhradwaj, R.: Evaluation of statistical bias correction methods for numerical weather prediction model forecasts of maximum and minimum temperatures. Nat. Hazards 73, 1229–1254 (2014)CrossRefGoogle Scholar
  2. 2.
    Klein, W., Glahn, H.: Forecasting local weather by means of model output statistics. Bull. Am. Meteorol. Soc. 55, 1217–1227 (1974)CrossRefGoogle Scholar
  3. 3.
    Marzban, C., Leyton, S., Colman, B.: Ceiling and visibility forecasts via neural networks. Weather Forecast. 22, 466–479 (2007)CrossRefGoogle Scholar
  4. 4.
    Marzban, C., Sandgathe, S., Kalnay, E.: MOS, perfect prog, and reanalysis. Mon. Weather Rev. 134, 657–663 (2006)CrossRefGoogle Scholar
  5. 5.
    Nikolaev, N.Y., Iba, H.: Adaptive Learning of Polynomial Networks. Genetic and Evolutionary Computation. Springer, New York (2006)zbMATHGoogle Scholar
  6. 6.
    Shao, A.M., Xi, S., Qiu, C.J.: A variational method for correcting non-systematic errors in numerical weather prediction. Earth Sci. 52, 1650–1660 (2009)Google Scholar
  7. 7.
    Vannitsem, S.: Dynamical properties of MOS forecasts: analysis of the ECMWF operational forecasting system. Weather Forecast. 23, 1032–1043 (2008)CrossRefGoogle Scholar
  8. 8.
    Xue, H.-L., Shen, X.-S., Chou, J.-F.: A forecast error correction method in numerical weather prediction by using recent multiple-time evolution data. Adv. Atmos. Sci. 30, 1249–1259 (2013)CrossRefGoogle Scholar
  9. 9.
    Zjavka, L.: Wind speed forecast correction models using polynomial neural networks. Renew. Energy 83, 998–1006 (2015)CrossRefGoogle Scholar
  10. 10.
    Zjavka, L.: Numerical weather prediction revisions using the locally trained differential polynomial network. Expert Syst. Appl. 44, 265–274 (2016)CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.ENET CentreVŠB-Technical University of OstravaOstravaCzech Republic

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