TY - GEN

T1 - Diffusion model to predict coastal profile evolutions

AU - Baramiya, Denis

AU - Gorbenko, Nikolay

AU - Lavrentiev, Mikhail

AU - Spigler, Renato

N1 - Publisher Copyright: © 2019 IEEE. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2019/6

Y1 - 2019/6

N2 - In this paper we study the possibility to predict the so-called long-term coastal profile evolution, based on the several years' measurements. Prediction is done by calibrating and then solving numerically a diffusion type model, earlier proposed in literature to describe this phenomenon. Model coefficients, say diffusion and transport, are calibrated according to the available measured data, and then a prediction is provided by the numerical solution to a diffusion equation with the so-obtained (by calibration) values of the equation coefficients. Earlier, we studied the model in the 'frequency-type' domain, applying Laplace transforms to the model equation, and applying a sort of discrete Laplace transform to the set of measured data. Observations made over more then 20 years were needed for accomplishiong the model calibration in this case. In this paper, we study the diffusion model directly in the time-space domain. Observations of the depth profile dynamics just over 10 years suffice to make predictions on the evolution of the coastal profile for 1 year ahead, with a relative error less than 10 percent. It is also possible to predict the depth profile evolution for 2 and 3 years ahead at the price of a slightly larger integrated relative error.

AB - In this paper we study the possibility to predict the so-called long-term coastal profile evolution, based on the several years' measurements. Prediction is done by calibrating and then solving numerically a diffusion type model, earlier proposed in literature to describe this phenomenon. Model coefficients, say diffusion and transport, are calibrated according to the available measured data, and then a prediction is provided by the numerical solution to a diffusion equation with the so-obtained (by calibration) values of the equation coefficients. Earlier, we studied the model in the 'frequency-type' domain, applying Laplace transforms to the model equation, and applying a sort of discrete Laplace transform to the set of measured data. Observations made over more then 20 years were needed for accomplishiong the model calibration in this case. In this paper, we study the diffusion model directly in the time-space domain. Observations of the depth profile dynamics just over 10 years suffice to make predictions on the evolution of the coastal profile for 1 year ahead, with a relative error less than 10 percent. It is also possible to predict the depth profile evolution for 2 and 3 years ahead at the price of a slightly larger integrated relative error.

KW - coastal evolution prediction

KW - depth profile evolution

KW - diffusion model

UR - http://www.scopus.com/inward/record.url?scp=85103836632&partnerID=8YFLogxK

U2 - 10.1109/OCEANSE.2019.8867524

DO - 10.1109/OCEANSE.2019.8867524

M3 - Conference contribution

AN - SCOPUS:85103836632

T3 - OCEANS 2019 - Marseille, OCEANS Marseille 2019

BT - OCEANS 2019 - Marseille, OCEANS Marseille 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 OCEANS - Marseille, OCEANS Marseille 2019

Y2 - 17 June 2019 through 20 June 2019

ER -