×

zbMATH — the first resource for mathematics

Global optimization for data assimilation in landslide tsunami models. (English) Zbl 1453.86028
Summary: The goal of this article is to make automatic data assimilation for a landslide tsunami model, given by the coupling between a non-hydrostatic multi-layer shallow-water and a Savage-Hutter granular landslide model for submarine avalanches. The coupled model is discretized using a positivity preserving second-order path-conservative finite volume scheme. Then, the data assimilation problem is posed in a global optimization framework. Later, multi-path parallel metaheuristic stochastic global optimization algorithms are developed. More precisely, a multi-path Simulated Annealing algorithm is compared with a multi-path hybrid global optimization algorithm based on coupling Simulated Annealing with gradient local searchers.
MSC:
86A15 Seismology (including tsunami modeling), earthquakes
65K10 Numerical optimization and variational techniques
86A05 Hydrology, hydrography, oceanography
86-08 Computational methods for problems pertaining to geophysics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65Y05 Parallel numerical computation
65Z05 Applications to the sciences
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Grilli, S. T.; Watts, P., Tsunami generation by submarine mass failure. I: Modeling, experimental validation, and sensitivity analyses, J. Waterw. Port Coast., 131, 6, 283-297 (2005)
[2] Fine, I. V.; Rabinovich, A. B.; Bornhold, B. D.; Thomson, R. E.; Kulikov, E. A., The Grand Banks landslide-generated tsunami of November 18, 1929: preliminary analysis and numerical modeling, Mar. Geol., 215, 1, 45-57 (2005)
[3] Skvortsov, A.; Bornhold, B., Numerical simulation of the landslide-generated tsunami in Kitimat Arm, British Columbia, Canada, 27 April 1975, J. Geophys. Res., Earth, 112, F2, 1-12 (2007)
[4] Abadie, S. M.; Harris, J. C.; Grilli, S. T.; Fabre, R., Numerical modeling of tsunami waves generated by the flank collapse of the Cumbre Vieja Volcano (La Palma, Canary Islands): tsunami source and near field effects, J. Geophys. Res., Oceans, 117, C5, 1-26 (2012)
[5] Horrillo, J.; Wood, A.; Kim, G.-B.; Parambath, A., A simplified 3-D Navier-Stokes numerical model for landslide-tsunami: application to the Gulf of Mexico, J. Geophys. Res., Oceans, 118, 12, 6934-6950 (2013)
[6] Assier Rzadkiewicz, S.; Mariotti, C.; Heinrich, P., Numerical simulation of submarine landslides and their hydraulic effects, J. Waterw. Port Coast., 123, 4, 149-157 (1997)
[7] Ma, G.; Kirby, J. T.; Shi, F., Numerical simulation of tsunami waves generated by deformable submarine landslides, Ocean Model., 69, 146-165 (2013)
[8] Iverson, R. M., The physics of debris flows, Rev. Geophys., 35, 3, 245-296 (1997)
[9] Savage, S. B.; Hutter, K., The motion of a finite mass of granular material down a rough incline, J. Fluid Mech., 199, 177-215 (1989) · Zbl 0659.76044
[10] Fernández-Nieto, E.; Bouchut, F.; Bresch, D.; Díaz, M. C.; Mangeney, A., A new Savage-Hutter type model for submarine avalanches and generated tsunami, J. Comput. Phys., 227, 16, 7720-7754 (2008) · Zbl 1156.76015
[11] Ma, G.; Kirby, J. T.; Hsu, T.-J.; Shi, F., A two-layer granular landslide model for tsunami wave generation: theory and computation, Ocean Model., 93, 40-55 (2015)
[12] Fernández-Nieto, E.; Parisot, M.; Penel, Y.; Sainte-Marie, J., A hierarchy of dispersive layer-averaged approximations of Euler equations for free surface flows, Commun. Math. Sci., 16, 5, 1169-1202 (2018) · Zbl 1408.35136
[13] Kalnay, E., Atmospheric Modeling, Data Assimilation and Predictability (2003), Cambridge University Press: Cambridge University Press Cambridge
[14] Blum, J.; Dimet, F.-X. L.; Navon, I. M., Data assimilation for geophysical fluids, (Temam, R. M.; Tribbia, J. J., Special Volume: Computational Methods for the Atmosphere and the Oceans. Special Volume: Computational Methods for the Atmosphere and the Oceans, Handb. Numer. Anal., vol. 14 (2009), Elsevier), 385-441
[15] Lions, J., Optimal Control of Systems Governed by Partial Differential Equations (1971), Springer Verlag · Zbl 0203.09001
[16] Vrugt, J. A.; Diks, C. G.H.; Gupta, H. V.; Bouten, W.; Verstraten, J. M., Improved treatment of uncertainty in hydrologic modeling: combining the strengths of global optimization and data assimilation, Water Resour. Res., 41, 1, 1-17 (2005)
[17] Beven, K.; Binley, A., The future of distributed models: model calibration and uncertainty prediction, Hydrol. Process., 6, 3, 279-298 (1992)
[18] Thiemann, M.; Trosset, M.; Gupta, H.; Sorooshian, S., Bayesian recursive parameter estimation for hydrologic models, Water Resour. Res., 37, 10, 2521-2535 (2001)
[19] Vrugt, J. A.; Bouten, W.; Gupta, H. V.; Sorooshian, S., Toward improved identifiability of hydrologic model parameters: the information content of experimental data, Water Resour. Res., 38, 12, 48-1-48-13 (2002)
[20] Vrugt, J. A.; Gupta, H. V.; Bouten, W.; Sorooshian, S., A Shuffled Complex Evolution Metropolis algorithm for optimization and uncertainty assessment of hydrologic model parameters, Water Resour. Res., 39, 8, 1-14 (2003)
[21] Yapo, P. O.; Gupta, H. V.; Sorooshian, S., Multi-objective global optimization for hydrologic models, J. Hydrol., 204, 1, 83-97 (1998)
[22] Yin, X.; Wang, B.; Liu, J.; Tan, X., Evaluation of conditional non-linear optimal perturbation obtained by an ensemble-based approach using the Lorenz-63 model, Tellus, Ser. A Dyn. Meteorol. Oceanol., 66, 1, Article 22773 pp. (2014)
[23] Yuan, S.; Zhang, H.; Li, M.; Mu, B., CNOP-P-based parameter sensitivity for double-gyre variation in ROMS with simulated annealing algorithm, J. Oceanol. Limnol., 37, 3, 957-967 (2019)
[24] Haidvogel, D. B.; Arango, H. G.; Hedstrom, K.; Beckmann, A.; Malanotte-Rizzoli, P.; Shchepetkin, A. F., Model evaluation experiments in the North Atlantic Basin: simulations in nonlinear terrain-following coordinates, Dyn. Atmos. Ocean., 32, 239-281 (2000)
[25] Mu, M.; Duan, W.; Wang, Q.; Zhang, R., An extension of conditional nonlinear optimal perturbation approach and its applications, Nonlinear Process. Geophys., 17, 2, 211-220 (2010)
[26] Sánchez-Linares, C.; de la Asunción, M.; Castro, M.; Mishra, S.; Šukys, J., Multi-level Monte Carlo finite volume method for shallow water equations with uncertain parameters applied to landslides-generated tsunamis, Appl. Math. Model., 39, 23, 7211-7226 (2015)
[27] Kirkpatrick, S.; Gelatt, C. D.; Vecchi, M. P., Optimization by simulated annealing, Science, 220, 671-680 (1983) · Zbl 1225.90162
[28] Aarts, E.; van Laarhoven, P., Statistical cooling: a general approach to combinatorial optimization problems, Philips J. Res., 40, 193-226 (1985)
[29] Vaz, A. I.F.; Vicente, L. N., A particle swarm pattern search method for bound constrained global optimization, Int. J. Comput. Math., 39, 2, 197-219 (2007) · Zbl 1180.90252
[30] Vaz, A. I.F.; Vicente, L. N., PSwarm: a hybrid solver for linearly constrained global derivative-free optimization, Optim. Methods Softw., 24, 4-5, 669-685 (2009) · Zbl 1177.90327
[31] Storn, R.; Price, K., Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces, J. Glob. Optim., 11, 4, 341-359 (1997) · Zbl 0888.90135
[32] Hooke, R.; Jeeves, T. A., “Direct Search” solution of numerical and statistical problems, J. ACM, 8, 2, 212-229 (1961) · Zbl 0111.12501
[33] Nelder, J. A.; Mead, R., A simplex method for function minimization, Comput. J., 7, 308-313 (1965) · Zbl 0229.65053
[34] Fletcher, R.; Reeves, C. M., Function minimization by conjugate gradients, Comput. J., 7, 149-154 (1964) · Zbl 0132.11701
[35] Polak, R. G.E., Note sur la convergence de méthodes de directions conjuguées, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 3, R1, 35-43 (1969) · Zbl 0174.48001
[36] Broyden, C. G., The convergence of a class of double rank minimization algorithms: 2. The new algorithm, IMA J. Appl. Math., 6, 3, 222-231 (1970) · Zbl 0207.17401
[37] Fletcher, R., A new approach to variable metric algorithms, Comput. J., 13, 317-322 (1970) · Zbl 0207.17402
[38] Goldfarb, D., A family of variable metric methods derived by variational means, Math. Comput., 24, 109, 23-26 (1970) · Zbl 0196.18002
[39] Shanno, D. F., Conditioning of quasi-Newton methods for function minimization, Math. Comput., 24, 111, 647-650 (1970) · Zbl 0225.65073
[40] Liu, D. C.; Nocedal, J., On the limited memory method for large scale optimization, Math. Program., 45, 1-3, 503-528 (1989) · Zbl 0696.90048
[41] Byrd, R. H.; Lu, P.; Nocedal, J.; Zhu, C., A limited memory algorithm for bound constrained optimization, SIAM J. Sci. Comput., 16, 5, 1190-1208 (1995) · Zbl 0836.65080
[42] Robertson, D.; Brown, B.; Navon, I., Determination of the structure of mixed argon-xenon clusters using a finite-temperature, Lattice-Based Monte-Carlo method, J. Chem. Phys., 90, 3221-3229 (1989)
[43] Navon, I.; Brown, F.; Robertson, D., A combined simulated-annealing and quasi-Newton-like conjugate gradient method for determining the structure of mixed argon-xenon clusters, Comput. Chem., 14, 305-311 (1990)
[44] Wales, D. J.; Doye, J. P.K., Global optimization by Basin-Hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 Atoms, J. Phys. Chem. A, 101, 5111-5116 (1997)
[45] Wengert, R. E., A simple automatic derivative evaluation program, Commun. ACM, 7, 8, 463-464 (1964) · Zbl 0131.34602
[46] Automatic differentiation engine, TAPENADE (“2019)
[47] Ding, Y.; Jia, Y.; Wang, S. S.Y., Identification of Manning’s roughness coefficients in shallow water flows, J. Hydraul. Eng., 130, 6, 501-510 (2004)
[48] Bélanger, E.; Vincent, A., Data assimilation (4D-VAR) to forecast flood in shallow-waters with sediment erosion, J. Hydrol., 300, 1, 114-125 (2005)
[49] Lai, X.; Monnier, J., Assimilation of spatially distributed water levels into a shallow-water flood model. Part I: mathematical method and test case, J. Hydrol., 377, 1, 1-11 (2009)
[50] Hostache, R.; Lai, X.; Monnier, J.; Puech, C., Assimilation of spatially distributed water levels into a shallow-water flood model. Part II: use of a remote sensing image of Mosel River, J. Hydrol., 390, 3, 257-268 (2010)
[51] Honnorat, M.; Monnier, J.; Le Dimet, F.-X., Lagrangian data assimilation for river hydraulics simulations, Comput. Vis. Sci., 12, 5, 235-246 (2009) · Zbl 1426.86005
[52] Bernard, E.; Titov, V., Evolution of tsunami warning systems and products, Philos. Trans. R. Soc. A-Math. Phys. Eng. Sci., 373, Article 20140371 pp. (2015)
[53] Wang, Y.; Satake, K.; Maeda, T.; Gusman, A. R., Data assimilation with dispersive tsunami model: a test for the Nankai Trough, Earth Planets Space, 70, 131, 1-9 (2018)
[54] Wang, Y.; Satake, K.; Maeda, T.; Gusman, A. R., Green’s function-based tsunami data assimilation: a fast data assimilation approach toward tsunami early warning, Geophys. Res. Lett., 44, 20, 10282-10289 (2017)
[55] Li, J.; Xiu, D., On numerical properties of the ensemble Kalman filter for data assimilation, Comput. Methods Appl. Mech. Eng., 197, 43-44, 3574-3583 (2008) · Zbl 1195.93137
[56] Narayan, A.; Marzouk, Y.; Xiu, D., Sequential data assimilation with multiple models, J. Comput. Phys., 231, 19, 6401-6418 (2012) · Zbl 1284.62801
[57] Yang, Y.; Dunham, E. M.; Barnier, G.; Almquist, M., Tsunami wavefield reconstruction and forecasting using the ensemble Kalman filter, Geophys. Res. Lett., 46, 2, 853-860 (2019)
[58] Takagi, T.; Inamoto, K.; Kawahara, M., Estimation of wave propagation using a Kalman filter, Int. J. Comput. Fluid Dyn., 9, 1, 77-84 (1998) · Zbl 0906.76041
[59] Wang, Y.; Maeda, T.; Satake, K.; Heidarzadeh, M.; Su, H.; Sheehan, A. F.; Gusman, A. R., Tsunami data assimilation without a dense observation network, Geophys. Res. Lett., 46, 4, 2045-2053 (2019)
[60] Gusman, A. R.; Sheehan, A. F.; Satake, K.; Heidarzadeh, M.; Mulia, I. E.; Maeda, T., Tsunami data assimilation of Cascadia seafloor pressure gauge records from the 2012 Haida Gwaii earthquake, Geophys. Res. Lett., 43, 9, 4189-4196 (2016)
[61] Nodet, Maëlle, Variational assimilation of lagrangian data in oceanography, Inverse Probl., 22, 1, 245-263 (2006) · Zbl 1089.86002
[62] Tsushima, H.; Hirata, K.; Hayashi, Y.; Tanioka, Y.; Kimura, K.; Sakai, S.; Shinohara, M.; Kanazawa, T.; Hino, R.; Maeda, K., Near-field tsunami forecasting using offshore tsunami data from the 2011 off the Pacific coast of Tohoku Earthquake, Earth Planets Space, 63, 7, 56 (2011)
[63] Sumata, H.; Kauker, F.; Gerdes, R.; Köberle, C.; Karcher, M., A comparison between gradient descent and stochastic approaches for parameter optimization of a sea ice model, Ocean Sci., 9, 4, 609-630 (2013)
[64] Sumata, H.; Kauker, F.; Karcher, M.; Gerdes, R., Simultaneous parameter optimization of an Arctic sea ice-ocean model by a genetic algorithm, Mon. Weather Rev., 147, 6, 1899-1926 (2019)
[65] Ferreiro, A. M.; García-Rodríguez, J. A.; López-Salas, J. G.; Vázquez, C., An efficient implementation of parallel Simulated Annealing algorithm in GPUs, J. Glob. Optim., 57, 3, 863-890 (2013) · Zbl 1286.90115
[66] Ferreiro, A. M.; García-Rodríguez, J. A.; Souto, L.; Vázquez, C., Basin Hopping with synched multi L-BFGS local searches. Parallel implementation in multi-CPU and GPUs, Appl. Math. Comput., 356, 282-298 (2019) · Zbl 1428.90131
[67] Ferreiro, A. M.; García-Rodríguez, J. A.; López-Salas, J. G.; Vázquez, C., SABR/LIBOR market models: pricing and calibration for some interest rate derivatives, Appl. Math. Comput., 242, 65-89 (2014) · Zbl 1335.91093
[68] Mangeney, A.; Bouchut, F.; Thomas, N.; Vilotte, J. P.; Bristeau, M. O., Numerical modeling of self-channeling granular flows and of their levee-channel deposits, J. Geophys. Res., Earth Surf., 112, F2, 1-21 (2007)
[69] Pirulli, M.; Mangeney, A., Results of back-analysis of the propagation of rock avalanches as a function of the assumed rheology, Rock Mech. Rock Eng., 41, 1, 59-84 (2008)
[70] Pouliquen, O., Scaling laws in granular flows down rough inclined planes, Phys. Fluids, 11, 3, 542-548 (1999) · Zbl 1147.76477
[71] Brunet, M.; Moretti, L.; Le Friant, A.; Mangeney, A.; Fernández Nieto, E. D.; Bouchut, F., Numerical simulation of the 30-45 ka debris avalanche flow of Montagne Pelée volcano, Martinique: from volcano flank collapse to submarine emplacement, Nat. Hazards, 87, 2, 1189-1222 (2017)
[72] Escalante, C.; Morales, T.; Castro, M., Non-hydrostatic pressure shallow flows: GPU implementation using finite-volume and finite-difference scheme, Appl. Math. Comput., 338, 631-659 (2018) · Zbl 1427.76160
[73] Escalante, C.; Fernández-Nieto, E. D.; Morales de Luna, T.; Castro, M. J., An efficient two-layer non-hydrostatic approach for dispersive water waves, J. Sci. Comput., 79, 1, 273-320 (2019) · Zbl 1444.76032
[74] Castro Díaz, M.; Fernández-Nieto, E., A class of computationally fast first order finite volume solvers: PVM methods, SIAM J. Sci. Comput., 34, 4, A2173-A2196 (2012) · Zbl 1253.65167
[75] Adsuara, J.; Cordero-Carrión, I.; Cerdá-Durán, P.; Aloy, M., Scheduled relaxation Jacobi method: improvements and applications, J. Comput. Phys., 321, 369-413 (2016) · Zbl 1349.65114
[76] Locatelli, M., On the multilevel structure of global optimization problems, Comput. Optim. Appl., 30, 5-22 (2005) · Zbl 1130.90035
[77] Locatelli, M.; Schoen, F., Global Optimization: Theory, Algorithms, and Applications, MOS-SIAM Series on Optimization (2013), SIAM
[78] Addis, B.; Locatelli, M.; Schoen, F., Local optima smoothing for global optimizations, Optim. Methods Softw., 20, 417-437 (2005) · Zbl 1134.90035
[79] Addis, B., Global Optimization Using Local Searches (2004), Universitá degli Studi di Firenze, Ph.D. thesis
[80] Leary, R. H., Global optimization on funneling landscapes, J. Glob. Optim., 18, 4, 367-383 (2000) · Zbl 0986.90038
[81] Goffe, W. L., SIMANN: a global optimization algorithm using simulated annealing, Stud. Nonlinear Dyn. Econom., 1, 3, 1-9 (1996) · Zbl 1078.91519
[82] Zhu, C.; Byrd, R. H.; Lu, P.; Nocedal, J., Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization, ACM Trans. Math. Softw., 23, 4, 550-560 (1997) · Zbl 0912.65057
[83] Grilli, S. T.; Shelby, M.; Kimmoun, O.; Dupont, G.; Nicolsky, D.; Ma, G.; Kirby, J. T.; Shi, F., Modeling coastal tsunami hazard from submarine mass failures: effect of slide rheology, experimental validation, and case studies off the US East Coast, Nat. Hazards, 86, 1, 353-391 (2017)
[84] Landslide tsunami model benchmarking workshop (“2019)
[85] Macías, J.; Castro, M. J.; Ortega, S.; Escalante, C.; González-Vida, J. M., Performance benchmarking of tsunami-HySEA model for NTHMP’s inundation mapping activities, Pure Appl. Geophys., 174, 8, 3147-3183 (2017)
[86] Navon, I. M., Practical and theoretical aspects of adjoint parameter estimation and identifiability in meteorology and oceanography, Dyn. Atmos. Ocean., 27, 1-4, 55-79 (1998)
[87] Cacuci, D. G.; Navon, I. M.; Ionescu-Bujor, M., Computational Methods for Data Evaluation and Assimilation (2013), Chapman and Hall/CRC
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.