Variance-based sensitivity analysis: An illustration on the lorenz'63 model

Monthly Weather Review

Volumn 141, Issue 11, 2013, Pages 4069-4079

  Marzban, Caren ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DATA ASSIMILATION; DIMENSIONALITY REDUCTION; INITIAL STATE VARIABLES; LATIN HYPERCUBE SAMPLING; SENSITIVITY MEASURES; SIMPLE RANDOM SAMPLING; STATE VARIABLES; VARIANCE-BASED SENSITIVITY ANALYSIS;

DATA PROCESSING; NUMERICAL MODELS;

SENSITIVITY ANALYSIS;

DATA ASSIMILATION; NUMERICAL MODEL; SENSITIVITY ANALYSIS; VARIANCE ANALYSIS; WEATHER FORECASTING;

EID: 84888405502     PISSN: 00270644     EISSN: 15200493     Source Type: Journal    
DOI: 10.1175/MWR-D-13-00032.1     Document Type: Article

References (53)

1. Alapaty, K., S. Raman, and D. Niyogi, 1997: Uncertainty in the specification of surface characteristics: A study of prediction errors in the boundary layer. Bound.-Layer Meteor., 82, 473-500.
2. Ancell, B., and G. Hakim, 2007: Comparing adjoint-and ensemblesensitivity analysis with applications to observation targeting. Mon. Wea. Rev., 135, 4117-4134.
3. Bellomo, N., and L. Preziosi, 1995: Modelling Mathematical Methods and Scientific Computation. CRC Press, 497 pp.
4. Bishop, C. M., 1996: Neural Networks for Pattern Recognition. Clarendon Press, 482 pp.
5. Bolado-Lavin, R., and A. C. Badea, 2008: Review of sensitivity analysis methods and experience for geological disposal of radioactive waste and spent nuclear fuel. JRC Scientific Tech. Rep. LD-NA-23712-EN-C, 81 pp.
6. Bowman, K. P., J. Sacks, and Y.-F. Chang, 1993: Design and analysis of numerical experiments. J. Atmos. Sci., 50, 1267-1278.
7. Busby, D., 2009: Hierarchical adaptive experimental design for Gaussian process emulators. Reliab. Eng. Syst. Saf., 94 (7), 1183-1193.
8. Cacuci, D. G., 2003: Sensitivity and Uncertainty Analysis. Chapman and Hall/CRC, 285 pp.
9. Chaloner, K., and I. Verdinelli, 1995: Bayesian experimental design: A review. Stat. Sci., 10 (3), 273-304.
10. Chowdhury, R., B.N. Rao, and A. M. Prasad, 2008: High dimensional model representation for piece-wise continuous function approximation. Commun. Numer. Methods Eng., 24, 1587-1609.
11. Cioppa, T., and T. Lucas, 2007: Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics, 49 (1), 45-55.
12. Davis, C. A., and K. Emanuel, 1991: Potential vorticity diagnostics of cyclogenesis. Mon. Wea. Rev., 119, 1929-1953.
13. Douglas, C. M., 2005: Design and Analysis of Experiments. John Wiley & Sons, 643 pp.
14. Dusby, D., 2009: Hierarchical adaptive experimental design for Gaussian process emulators. Reliab. Eng. Syst. Saf., 94 (7), 1183-1193.
15. Errico, R. M., 1997: What is an adjoint model? Bull. Amer. Meteor. Soc., 78, 2577-2591.
16. Fang, K.-T., R. Li, and A. Sudjianto, 2006: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, 290 pp.
17. Fasso, A., 2006: Sensitivity analysis for environmental models and monitoring networks. Proceedings of the iEMSs Third Biennial Meeting: Summit on Environmental Modelling and Software, A. Voinov, A. J. Jakeman, and A. E. Rizzoli, Eds., International Environmental Modelling and Software Society, 6 pp. [Available online at http://www.iemss.org/iemss2006/sessions/all.html.]
18. Golaz, J.-C., V. E. Larson, J. A. Hansen, D. P. Schanen, and B. M. Griffin, 2007: Elucidating model inadequacies in a cloud parameterization by use of an ensemble-based calibration framework. Mon. Wea. Rev., 135, 4077-4096.
19. Gombos, D., and J. A. Hansen, 2008: Potential vorticity regression and its relationship to dynamical piecewise inversion. Mon. Wea. Rev., 136, 2668-2682.
20. Hacker, J. P., C. Snyder, S.-Y. Ha, and M. Pocernich, 2011: Linear and non-linear response to parameter variations in a mesoscale model. Tellus, 63A, 429-444, doi:10.1111/j.1600-0870.2010.00505.x.
21. Hakim, G. J., and R. D. Torn, 2008: Ensemble synoptic analysis. Synoptic-Dynamic Meteorology and Weather Analysis and Forecasting: A Tribute to Fred Sanders, Meteor. Monogr., No. 55, Amer. Meteor. Soc., 147-162.
22. Hall, M. C. G., 1986: Application of adjoint sensitivity theory to an atmospheric general circulation model. J. Atmos. Sci., 43, 2644-2651.
23. Hsieh, W., 2009: Machine Learning Methods in the Environmental Sciences: Neural Network and Kernels. Cambridge University Press, 349 pp.
24. Jimenez, L., and D. Landgrebe, 1998: Supervised classification in high dimensional space: Geometrical, statistical, and asymptotical properties of multivariate data. IEEE Trans. Syst. Man Cybern., 28C, 39-54, doi:10.1109/5326.661089.
25. Lorenz, E. N., 1963: Deterministic non-periodic flow. J. Atmos. Sci., 20, 130-141.
26. Magnusson, L., M. Leutbecher, and E. Källén, 2008: Comparison between singular vectors and breeding vectors as initial perturbations for the ECMWFensemble prediction system. Mon. Wea. Rev., 136, 4092-4104.
27. Marzban, C., 2011: Sensitivity analysis in linear and nonlinear models: A review. Preprints, Ninth Conf. on Artificial Intelligence, Seattle, WA, Amer. Meteor. Soc., 2.2. [Available online at https://ams.confex.com/ams/91Annual/webprogram/Paper187333.html.]
28. McKay, M. D., R. J. Beckman, and W. J. Conover, 1979: A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21 (2), 239-245.
29. Miller, R. N., 2007: Numerical Modeling of Ocean Circulation. Cambridge University Press, 242 pp.
30. Mishra, V., K. A. Cherkauer, and L. C. Bowling, 2010: Parameterization of lakes and wetlands for energy and water balance studies in the Great Lakes region. J. Hydrometeor., 11, 1057-1082.
31. Morris, M. D., 1991: Factorial sampling plans for preliminary computational experiments. Technometrics, 33, 161-174.
32. Murphy, J. M., D. M. H. Sexton, D. N. Barnett, G. S. Jones, M. J. Webb, M. Collins, and D. A. Stainforth, 2004: Quantification of modelling uncertainties in a large ensemble of climate change simulations. Nature, 430, 768-772.
33. Niyogi, D. S., S. Raman, and K. Alapaty, 1999: Uncertainty in the specification of surface characteristics. Part II: Hierarchy of interaction-explicit statistical analysis. Bound.-Layer Meteor., 91, 341-366.
34. Oakley, J. E., and A. O'Hagan, 2004: Probabilistic sensitivity analysis of complex models: ABayesian approach. J. Roy. Stat. Soc., 66B (3), 751-769.
35. Richardson, L. F., 2007: Weather Prediction by Numerical Process. 2nd ed. Cambridge University Press, 250 pp.
36. Rougier, J. C., 2008: Efficient emulators for multivariate deterministic functions. J. Comput. Graph. Stat., 17 (4), 827-843.
37. Rougier, J. C., S. Guillas, A. Maute, and A. Richmond, 2009: Expert knowledge and multivariate emulation: The Thermosphere-Ionosphere Electrodynamics General Circulation Model (TIE-GCM). Technometrics, 51 (4), 414-424.
38. Rushton, K. R., 2003: Groundwater Hydrology: Conceptual and Computational Models. John Wiley and Sons Ltd., 416 pp.
39. Sacks, J., S. B. Schiller, and W. J. Welch, 1989a: Designs for computer experiments. Technometrics, 31 (1), 41-47.
40. Sacks, J., W. J. Welch, T. J. Mitchell, and H. P. Wynn, 1989b: Design and analysis of computer experiments. Stat. Sci., 4, 409-423.
41. Saltelli, A., M. Ratto, T. Andres, F. Campolongo, J. Cariboni, M. Saisana, and S. Tarantola, 2008: Global Sensitivity Analysis: The Primer. Wiley Publishing, 304 pp.
42. Saltelli, A., P. Annoni, I. Azzini, F. Campolongo, M. Ratto, and S. Tarantola, 2010: Variance based sensitivity analysis of model output: Design and estimator for the total sensitivity index. Comput. Phys. Commun., 181, 259-270.
43. Sanderson, B. M., 2011: A multimodel study of parametric uncertainty in predictions of climate response to rising greenhouse gas concentrations. J. Climate, 24, 1362-1377.
44. Santner, T. J., B. J. Williams, and W. I. Notz, 2003: The Design and Analysis of Computer Experiments. Springer, 299 pp.
45. Scott, D. W., 1992: Multivariate Density Estimation; Theory, Practice, and Visualization. John Wiley & Sons, 325 pp.
46. Sobol, I. M., 1993: Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Exp., 1, 407-414.
47. Stein, U., and P. Alpert, 1993: Factor seperation in numerical simulations. J. Atmos. Sci., 50, 2107-2115.
48. Storlie, C. B., L. P. Swiler, J. C. Helton, and C. J. Sallaberry, 2009: Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demandingmodels. Reliab. Eng. Syst. Saf., 94, 1735-1763.
49. Torn, R. D., and G. Hakim, 2008: Ensemble-based sensitivity analysis. Mon. Wea. Rev., 136, 663-677.
50. Urban, N. M., and T. E. Fricker, 2010: A comparison of Latin hypercube and grid ensemble designs for the multivariate emulation of an Earth system model. Comput. Geosci., 36, 746-755.
51. Weiss, N. A., 2005: A Course in Probability. Addison-Wesley, 789 pp.
52. Welch, W. J., R. J. Buck, J. Sacks, H. P. Wynn, T. J. Mitchell, and M. D. Morris, 1992: Screening, predicting, and computer experiments. Technometrics, 34 (1), 15-25.
53. Zhao, J., and C. Tiede, 2011: Using a variance-based sensitivity analysis for analyzing the relation between measurements and unknown parameters of a physical model. Nonlinear Processes Geophys., 18, 269-276.