Abstract
This study aims at analyzing the combined impact of uncertainties in initial conditions and wind forcing fields in ocean general circulation models (OGCM) using polynomial chaos (PC) expansions. Empirical orthogonal functions (EOF) are used to formulate both spatial perturbations to initial conditions and space-time wind forcing perturbations, namely in the form of a superposition of modal components with uniformly distributed random amplitudes. The forward deterministic HYbrid Coordinate Ocean Model (HYCOM) is used to propagate input uncertainties in the Gulf of Mexico (GoM) in spring 2010, during the Deepwater Horizon oil spill, and to generate the ensemble of model realizations based on which PC surrogate models are constructed for both localized and field quantities of interest (QoIs), focusing specifically on sea surface height (SSH) and mixed layer depth (MLD). These PC surrogate models are constructed using basis pursuit denoising methodology, and their performance is assessed through various statistical measures. A global sensitivity analysis is then performed to quantify the impact of individual modes as well as their interactions. It shows that the local SSH at the edge of the GoM main current—the Loop Current—is mostly sensitive to perturbations of the initial conditions affecting the current front, whereas the local MLD in the area of the Deepwater Horizon oil spill is more sensitive to wind forcing perturbations. At the basin scale, the SSH in the deep GoM is mostly sensitive to initial condition perturbations, while over the shelf it is sensitive to wind forcing perturbations. On the other hand, the basin MLD is almost exclusively sensitive to wind perturbations. For both quantities, the two sources of uncertainty have limited interactions. Finally, the computations indicate that whereas local quantities can exhibit complex behavior that necessitates a large number of realizations, the modal analysis of field sensitivities can be suitably achieved with a moderate size ensemble.
Similar content being viewed by others
References
Alexanderian, A., Winokur, J., Sraj, I., Srinivasan, A., Iskandarani, M., Thacker, W.C., Knio, O.M.: Global sensitivity analysis in an ocean general circulation model: a sparse spectral projection approach. Comput. Geosci. 16(3), 757–778 (2012)
Alvera-Azcárate, A., Barth, A., Rixen, M., Beckers, J.M.: Reconstruction of incomplete oceanographic data sets using empirical orthogonal functions: application to the adriatic sea surface temperature. Ocean Model. 9 (4), 325–346 (2005)
Blatman, G., Sudret, B.: Adaptive sparse polynomial chaos expansion based on least angle regression. J. Comput. Phys. 230(6), 2345–2367 (2011)
Bleck, R.: An oceanic general circulation model framed in hybrid isopycnic cartesian coordinates. Ocean Modell. 4(1), 55–88 (2002). doi:10.1016/S1463-5003(01)00012-9
Chassignet, E.P., Hurlburt, H.E., Smedstad, O.M., Halliwell, G.R., Hogan, P.J., Wallcraft, A.J., Baraille, R., Bleck, R.: The hycom (hybrid coordinate ocean model) data assimilative system. J. Mar. Syst. 65(1-4), 60–83 (2007). doi:10.1016/j.jmarsys.2005.09.016
Chen, S.S., Curcic, M.: Ocean surface waves in hurricane ike (2008) and superstorm sandy (2012): Coupled model predictions and observations Ocean Modelling (2015)
Conrad, P.R., Marzouk, Y.M.: Adaptive smolyak pseudospectral approximations. SIAM J. Sci. Comput. 35(6), A2643–A2670 (2013)
Constantine, P.G., Eldred, M.S., Phipps, E.T.: Sparse pseudospectral approximation method. Comput. Methods Appl. Mech. Eng. 229, 1–12 (2012)
Crestaux, T., Le Maître, O., Martinez, J.M.: Polynomial chaos expansion for sensitivity analysis. Reliab. Eng. Syst. Saf. 94(7), 1161–1172 (2009)
Doostan, A., Owhadi, H.: A non-adapted sparse approximation of pdes with stochastic inputs. J. Comput. Phys. 230(8), 3015–3034 (2011)
Efron, B., Hastie, T., Johnstone, I., Tibshirani, R., et al.: Least angle regression. Ann. Stat. 32(2), 407–499 (2004)
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res 99(C5), 10,143–10,162 (1994)
Gerstner, T., Griebel, M.: Dimension-adaptive tensor—product quadrature. Computing 71(1), 65–87 (2003)
Ghanem, R.G., Spanos, P.D.: Stochastic finite elements: a spectral approach. Springer-Verlag, New York (1991)
Hodur, R.M.: The naval research laboratorys coupled ocean/atmosphere mesoscale prediction system (coamps). Mon. Weather Rev. 125, 1414–1430 (1997). doi:10.1175/1520-0493(1997)125%3C1414:TNRLSC%3E2.0.CO;2
Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of nonlinear models. Reliab. Eng. Syst. Saf. 52(1), 1–17 (1996)
Ichiye, T.: Circulation and water mass distribution in the gulf of Mexico. Geofis. Int. 2(3), 47–76 (1962)
Kac, M., Siegert, A.: An explicit representation of a stationary gaussian process. Annals of Mathematical Statistics, 438–442 (1947)
Karhunen, K.: Über lineare Methoden in der Wahrscheinlichkeitsrechnung, vol. 37. Universitat Helsinki (1947)
Keppenne, C., Rienecker, M.: Initial testing of a massively parallel ensemble Kalman filter with the Poseidon isopycnal ocean general circulation model. Mon. Weather. Rev. 130(12), 2951–2965 (2002)
Knio, O.M., Najm, H.N., Ghanem, R.G., et al.: A stochastic projection method for fluid flow: i. basic formulation. J. Comput. Phys. 173(2), 481–511 (2001)
Le Hénaff, M., Kourafalou, V.H., Paris, C., Helgers, J., Aman, Z.M., Hogan, P.J., Srinivasan, A.: Surface evolution of the deepwater horizon oil spill patch: combined effects of circulation and wind-induced drift. Environ. Sci. Tech. 46(13), 7267–7273 (2012)
Le Maître, O.P., Knio, O.M.: Spectral methods for uncertainty quantification: with applications to computational fluid dynamics. Springer Science & Business Media (2010)
Le Maître, O.P., Najm, H.N., Pébay, P.P., Ghanem, R.G., Knio, O.M.: Multi-resolution-analysis scheme for uncertainty quantification in chemical systems. SIAM J. Sci. Comput. 29(2), 864–889 (2007)
Le Maître, O.P., Reagan, M.T., Najm, H.N., Ghanem, R.G., Knio, O.M.: A stochastic projection method for fluid flow: Ii. random process. J. Comput. Phys. 181(1), 9–44 (2002)
Loève, P.: Fonctions Aléatoires Du Second Ordre, a Note in P. Lévy, Processus Stochastiques Et Mouvement Brownien. Gauthier-Villars, Paris (1948)
Marzouk, Y.M., Najm, H.N.: Dimensionality reduction and polynomial chaos acceleration of bayesian inference in inverse problems. J. Comput. Phys. 228(6), 1862–1902 (2009)
McKay, M.D., Beckman, R.J., Conover, W.J.: Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)
Najm, H.N., Debusschere, B.J., Marzouk, Y.M., Widmer, S., Le Maître, O.: Uncertainty quantification in chemical systems. Int. J. Numer. Methods Eng. 80(6), 789 (2009)
Peng, J., Hampton, J., Doostan, A.: A weighted l1-minimization approach for sparse polynomial chaos expansions. J. Comput. Phys. 267, 92–111 (2014)
Schmitz, W.J.: Cyclones and Westward Propagation in the Shedding of Anticyclonic Rings from the Loop Current. In: Sturges, W., Lugo-Fernandez, A. (eds.) Circulation in the Gulf of Mexico: Observations and Models, Geophysical Monograph Series, vol. 161, pp 241–261. American Geophysical Union, Washington, D.C (2005)
Sheather, S.J., Jones, M.C.: A reliable data-based bandwidth selection method for kernel density estimation. J. Royal Stat. Soc. Ser. B (Methodological) 53(3), 683–690 (1991). http://www.jstor.org/stable/2345597
Sobol, I.: Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp. 1, 407–414 (1993)
Sraj, I., Iskandarani, M., Srinivasan, A., Thacker, W.C., Winokur, J., Alexanderian, A., Lee, C.Y., Chen, S.S., Knio, O.M.: Bayesian inference of drag parameters using axbt data from typhoon fanapi. Mon. Weather. Rev. 141(7), 2347–2367 (2013)
Sraj, I., Maître, O.P.L., Knio, O.M., Hoteit, I.: Coordinates transformation and polynomial chaos for the bayesian inference of a gaussian process with parametrized prior covariance function. arXiv preprint arXiv:1501.03323 (2015)
Thacker, W.C., Srinivasan, A., Iskandarani, M., Knio, O.M., Le Henaff, M.: Propagating boundary uncertainties using polynomial expansions. Ocean Model. 43, 52–63 (2012)
Van Den Berg, E., Friedlander, M.: Spgl1: a solver for large-scale sparse reconstruction (2007)
Van Den Berg, E., Friedlander, M.P.: Probing the Pareto frontier for basis pursuit solutions. SIAM J. Sci. Comput. 31(2), 890–912 (2008)
Winokur, J., Conrad, P., Sraj, I., Knio, O., Srinivasan, A., Thacker, W.C., Marzouk, Y., Iskandarani, M.: A priori testing of sparse adaptive polynomial chaos expansions using an ocean general circulation model database. Comput. Geosci. 17(6), 899–911 (2013)
Winokur, J.G.: Adaptive sparse grid approaches to polynomial chaos expansions for uncertainty quantification. Ph.D. thesis Duke University (2015)
Xiu, D., Karniadakis, G.E.: The wiener–askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24(2), 619–644 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, G., Iskandarani, M., Hénaff, M.L. et al. Quantifying initial and wind forcing uncertainties in the Gulf of Mexico. Comput Geosci 20, 1133–1153 (2016). https://doi.org/10.1007/s10596-016-9581-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-016-9581-4