Nonlinear Methodologies for Climate Studies in the Peruvian Northeast Coast

  • Huber Nieto-ChaupisEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 833)


We use in an explicit manner the well-known input-output methodology used in the Volterra theory to the concrete case to estimate the risks that are continuously expected due to the climatic variations in the Peruvian Northeast Coast as consequence of the arrival of phenomena such as the well-known “El Niño”. We have interpreted the Volterra series as a methodological tool to calculate probabilities of risk. Thus the resulting Volterra output is therefore seen as a type of risk’s probability by which a peripheral area of a large city might be affected by flooding. Under this view, the estimation of the risk depends entirely on the calculation of the parameters of the Volterra theory. The full estimation of the risk’s level has used a family of input functions focused on Lorentzian and Gaussian profiles. For this end we used Google images by which we have focused our attention to that populations located near to rivers that are under permanent risk in summer times. This methodology can be finally seen as a scheme for disaster anticipation. We paid attention in those zones located in Tumbes city which have been affected by river overflow along the north coast of Peru in previous summer times.


System identification Nonlinear systems Climate 


  1. 1.
    Gorder, P.F.: Modeling El Niño: a force behind world weather. Comput. Sci. Eng. 7(1), 5–7 (2005)CrossRefGoogle Scholar
  2. 2.
    Takahashi, K., Martínez, A.G.: The very strong coastal El Niño in 1925 in the far-eastern Pacific. Clim. Dyn. 2017, 1–27 (2017). Scholar
  3. 3.
    Rugh, W.J.: Nonlinear System Theory, The Volterra/Wiener Approach. Johns Hopkins University Press, Baltimore (1981)zbMATHGoogle Scholar
  4. 4.
    Boyd, S., Chua, L.: Fading memory and the problem of approximating nonlinear operators with Volterra series. IEEE Trans. Circ. Syst. CAS–32(11), 1150–1161 (1985)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Boyd, S., Chua, L.O., Desoer, C.A.: Analytical foundations of Volterra series. J. Math. Control Inf. 1, 243–282 (1984)CrossRefGoogle Scholar
  6. 6.
    Boyd, S.P.: Volterra series: engineering fundamentals. Ph.D. dissertation, Department of Electrical Engineering and Computer Science, University of California, Berkeley, CA (1985)Google Scholar
  7. 7.
    Brockett, R.W.: Convergence of Volterra series on infinite intervals and bilinear approximations. In: Lakshmikanthan, V. (ed.) Nonlinear Systems and Applications, pp. 39–46. Academic, New York (1977)CrossRefGoogle Scholar
  8. 8.
    Antzoulakos, D.: Derivation of the probability distribution functions for succession quota random variables. Ann. Inst. Stat. Math. 48(3), 551–561 (1996)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Casti, J.L.: Nonlinear System Theory. Mathematics in Science and Engineering, vol. 175. Academic, Orlando (1985)Google Scholar
  10. 10.
  11. 11.
    Shaikhet, L.: Stability in probability of nonlinear stochastic Volterra difference equations with continuous variable. In: Stochastic Analysis and Applications, vol. 25, no. 6, pp. 1151–1165 (2007)Google Scholar
  12. 12.
    Crouch, P.E., Collingwood, P.C.: The observation space and realizations of finite Volterra series. SIAM J. Control Optim. 25(2), 316–333 (1987)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Google Maps:
  14. 14.
    Jing, X.J., Lang, Z.Q., Billings, S.A.: Magnitude bounds of generalized frequency response functions for nonlinear Volterra systems described by Narx model. Automatica 44, 838–845 (2008)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Gilbert, E.G.: Functional expansions for the response of nonlinear differential systems. IEEE Trans. Autom. Control AC-22(6), 909–921 (1977)MathSciNetCrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Center of Research eHealthUniversidad de Ciencias y HumanidadesLima39Peru

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