Skip to main content
SpringerLink
Log in

Sensitivity Analysis of Spatial and/or Temporal Phenomena

  • Reference work entry
  • First Online:
Handbook of Uncertainty Quantification

Abstract

This section presents several sensitivity analysis methods to deal with spatial and/or temporal models. Focusing on the variance-based approach, solutions are proposed to perform global sensitivity analysis with functional inputs and outputs. Some of these solutions are illustrated on two industrial case studies: an environmental model for flood risk assessment and an atmospheric dispersion model for radionuclide release. These test cases are fully described at the beginning of the paper. Then a section is dedicated to spatiotemporal inputs and proposes several sensitivity analysis methods. The use of metamodels is also addressed. Pros and cons of the various methods are then discussed. In a subsequent section, solutions to deal with spatiotemporal outputs are proposed: aggregated, site, and block indices are described. The use of functional metamodels for sensitivity analysis purpose is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 1,099.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 1,399.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Bayarri, M., Berger, J., Cafeo, J., Garcia-Donato, G., Liu, F., Palomo, J., Parthasarathy, R., Paulo, R., Sacks, J., Walsh, D.: Computer model validation with functional output. Ann. Stat. 35, 1874–1906 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bonin, O.: Sensitivity analysis and uncertainty analysis for vector geographical applications. In: 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Lisbon, 5–7 July 2006

    Google Scholar 

  3. Caers, J.: Modeling Uncertainty in the Earth Sciences. Wiley-Blackwell, Hoboken (2011)

    Book  MATH  Google Scholar 

  4. Caers, J., Park, K., Scheidt, C.: Modeling uncertainty of complex earth systems in metric space. In: Handbook of Geomathematics, pp. 865–889. Springer, Berlin/New York (2010)

    Google Scholar 

  5. Campbell, K., McKay, M.D., Williams, B.J.: Sensitivity analysis when model outputs are functions. Reliab. Eng. Syst. Saf. 91(10), 1468–1472 (2006)

    Article  Google Scholar 

  6. Chatterjee, A.: An introduction to the proper orthogonal decomposition. Curr. Sci. 78(7), 808–817 (2000)

    Google Scholar 

  7. Crosetto, M., Tarantola, S.: Uncertainty and sensitivity analysis: tools for GIS-based model implementation. Int. J. Geogr. Inf. Sci. 15, 415–437 (2001)

    Article  Google Scholar 

  8. Da Veiga, S.: Global sensitivity analysis with dependence measures. J. Stat. Comput. Simul. 85(7), 1283–1305 (2014)

    Article  MathSciNet  Google Scholar 

  9. De Lozzo, M., Marrel, A.: New improvements in the use of dependence measures for sensitivity analysis and screening. J. Stat. Comput. Simul. (2015, submitted) doi:https://hal.archives-ouvertes.fr/hal-01090475

  10. Doury, A.: Pratiques françaises en matiére de prévision quantitative de la pollution atmosphérique potentielle liée aux activités nucléaires. In: Seminar on radioactive releases and their dispersion in the atmosphere following a hypothetical reactor accident, vol. I, pp. 403–448 (1980)

    Google Scholar 

  11. Erdlenbruch, K., Gilbert, E., Grelot, F., Lescouliers, C.: Une analyse coût-bénéfice spatialisée de la protection contre les inondations: application de la méthode des dommages évités à la basse vallée de l’Orb. Ingénieries Eau-Agriculture-Territoires 53, 3–20 (2008)

    Google Scholar 

  12. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis. Springer Series in Statistics, Springer, New York (2006)

    MATH  Google Scholar 

  13. Fisher, P.F.: Modelling soil map-unit inclusions by Monte Carlo simulation. Int. J. Geogr. Inf. Sci. 5(2), 193–208 (1991)

    Article  Google Scholar 

  14. Fort, J.C., Klein, T., Lagnoux, A., Laurent, B.: Estimation of the Sobol indices in a linear functional multidimensional model. J. Stat. Plan. Inference 143, 1590–1605 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  15. Francos, A., Elorza, F.J., Bouraoui, F., Bidoglio, G., Galbiati, L.: Sensitivity analysis of distributed environmental simulation models: understanding the model behaviour in hydrological studies at the catchment scale. Reliab. Eng. Syst. Saf. 79(2), 205–218 (2003)

    Article  Google Scholar 

  16. Gamboa, F., Janon, A., Klein, T., Lagnoux, A., et al.: (2014) Sensitivity analysis for multidimensional and functional outputs. Electron. J. Stat. 8, 575–603

    Article  MathSciNet  MATH  Google Scholar 

  17. Gijbels, I., Prosdocimi, I., Claeskens, G.: Nonparametric estimation of mean and dispersion functions in extended generalized linear models. Test 19(3), 580–608 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  18. Ginsbourger, D., Rosspopoff, B., Pirot, G., Durrande, N., Renard, P.: Distance-based kriging relying on proxy simulations for inverse conditioning. Adv. Water Resour. 52, 275–291 (2013)

    Article  Google Scholar 

  19. Gretton, A., Bousquet, O., Smola, A., Schölkopf, B.: Measuring statistical dependence with Hilbert-Schmidt norms. In: Algorithmic Learning Theory, vol. 3734, pp. 63–77. Springer, Berlin/Heidelberg (2005)

    Google Scholar 

  20. Hengl, T.: Finding the right pixel size. Comput. Geosci. 32, 1283–1298 (2006)

    Article  Google Scholar 

  21. Heuvelink, G.B.M., Brus, D.J., Reinds, G.: Accounting for spatial sampling effects in regional uncertainty propagation analysis. In: Proceedings of the Ninth International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, Leicester, pp. 85–88, 20–23 July 2010

    Google Scholar 

  22. Heuvelink, G.B.M., Burgers SLGE, Tiktak, A., Den Berg, F.V.: Uncertainty and stochastic sensitivity analysis of the GeoPEARL pesticide leaching model. Geoderma 155(3–4), 186–192 (2010)

    Article  Google Scholar 

  23. Iooss, B.: Treatment of spatially dependent input variables in sensitivity analysis of model output methods. Technical report, European project PAMINA (Performance assessment methodologies in application to guide the development of the safety case) (2008)

    Google Scholar 

  24. Iooss, B., Ribatet, M.: Global sensitivity analysis of computer models with functional inputs. Reliab. Eng. Syst. Saf. 94, 1194–1204 (2009)

    Article  Google Scholar 

  25. Jacques, J., Lavergne, C., Devictor, N.: Sensitivity analysis in presence of model uncertainty and correlated inputs. Reliab. Eng. Syst. Saf. 91(10–11), 1126–1134 (2006)

    Article  Google Scholar 

  26. Lamboni, M., Monod, H., Makowski, D.: Multivariate sensitivity analysis to measure global contribution of input factors in dynamic models. Reliab. Eng. Syst. Saf. 96(4), 450–459 (2011)

    Article  Google Scholar 

  27. Lilburne, L., Tarantola, S.: Sensitivity analysis of spatial models. Int. J. Geogr. Inf. Sci. 23(2), 151–168 (2009)

    Article  Google Scholar 

  28. Marrel, A., Iooss, B., Jullien, M., Laurent, B., Volkova, E.: Global sensitivity analysis for models with spatially dependent outputs. Environmetrics 22(3), 383–397 (2011)

    Article  MathSciNet  Google Scholar 

  29. Marrel, A., Iooss, B., Da Veiga, S., Ribatet, M.: Global sensitivity analysis of stochastic computer models with joint metamodels. Stat. Comput. 22(3), 833–847 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Marrel, A., Perot, N., Mottet, C.: Development of a surrogate model and sensitivity analysis for spatio-temporal numerical simulators. Stoch. Environ. Res. Risk Assess. 29(3), 959–974 (2015)

    Article  Google Scholar 

  31. McCullagh, P., Nelder, J.A., McCullagh, P.: Generalized Linear Models, vol. 2. Chapman and Hall, London (1989)

    Book  MATH  Google Scholar 

  32. Monfort, M., Patryl, L., Armand, P.: Presentation of the ceres platform used to evaluate the consequences of the emissions of radionuclides in the environment. HARMO 13, 1–4 (2010)

    Google Scholar 

  33. Morris, M.D.: Gaussian surrogates for computer models with time-varying inputs and outputs. Technometrics 54(1), 42–50 (2012)

    Article  MathSciNet  Google Scholar 

  34. Romary, T.: Heterogeneous media stochastic model inversion. PhD thesis, Université Pierre et Marie Curie – Paris VI (2008)

    Google Scholar 

  35. Ruffo, P., Bazzana, L., Consonni, A., Corradi, A., Saltelli, A., Tarantola, S.: Hydrocarbon exploration risk evaluation through uncertainty and sensitivity analyses techniques. Reliab. Eng. Syst. Saf. 91(10–11), 1155–1162 (2006)

    Article  Google Scholar 

  36. Saint-Geours, N.: Sensitivity analysis of spatial models: application to cost-benefit analysis of flood risk management plans. PhD thesis, Université Montpellier 2, http://tel.archives-ouvertes.fr/tel-00761032 (2012)

  37. Saint-Geours, N., Lavergne, C., Bailly, J.S., Grelot, F.: Change of support in variance-based spatial sensitivity analysis. Math. Geosci. 44(8), 945–958 (2012)

    Article  MATH  Google Scholar 

  38. Saint-Geours, N., Bailly, J.S., Grelot, F., Lavergne, C.: Multi-scale spatial sensitivity analysis of a flood damage assessment model. Environ. Model. Softw. 60, 153–166 (2014). http://dx.doi.org/10.1016/j.envsoft.2014.06.012

    Article  MATH  Google Scholar 

  39. Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S.: Variance based sensitivity analysis of model output. design and estimator for the total sensitivity index. Comput. Phys. Commun. 181(2), 259–270 (2010)

    Google Scholar 

  40. Scheidt, C., Caers, J.: Representing spatial uncertainty using distances and kernels. Math. Geosci. 41(4), 397–419 (2009)

    Article  MATH  Google Scholar 

  41. Shi, J.Q., Wang, B., Murray-Smith, R., Titterington, D.M.: Gaussian process functional regression modeling for batch data. Biometrics 63(3), 714–723 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  42. SMVOL: Programme d’actions de prévention des inondations sur les bassins de l’Orb et du Libron (34) pour les années 2011–2015. Note de présentation, Syndicat Mixte des Vallées de l’Orb et du Libron (2011)

    Google Scholar 

  43. Smyth, G.K.: Generalized linear models with varying dispersion. J. R. Stat. Soc. Ser. B (Methodol.) 51, 47–60 (1989)

    MathSciNet  Google Scholar 

  44. Suzuki, S., Caers, J.: A distance-based prior model parameterization for constraining solutions of spatial inverse problems. Math. Geosci. 40(4), 445–469 (2008)

    Article  MATH  Google Scholar 

  45. Suzuki, S., Caumon, G., Caers, J.: Dynamic data integration for structural modeling: model screening approach using a distance-based model parameterization. Comput. Geosci. 12(1), 105–119 (2008)

    Article  MATH  Google Scholar 

  46. Volkova, E., Iooss, B., Van Dorpe, F.: Global sensitivity analysis for a numerical model of radionuclide migration from the RRC Kurchatov Institute radwaste disposal site. Stoch. Environ. Res. Risk A 22(1), 17–31 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  47. Wechsler, S.: Uncertainties associated with digital elevation models for hydrologic applications: a review. Hydrol. Earth Syst. Sci. 11(4), 1481–1500 (2007)

    Article  Google Scholar 

  48. Zabalza, I., Dejean, J.P., Collombier, D.: Prediction and density estimation of a horizontal well productivity index using generalized linear models. In: 6th European Conference on the Mathematics of Oil Recovery. Peebles, Scotland (1998)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CEA, DEN, DER, F-13108, Saint-Paul-lez-Durance, France

    Amandine Marrel & Matthias De Lozzo

  2. ITK - Predict & Decide, F-34830, Clapiers, France

    Nathalie Saint-Geours

Authors
  1. Amandine Marrel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nathalie Saint-Geours
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Matthias De Lozzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Amandine Marrel .

Editor information

Editors and Affiliations

  1. Department of Civil and Environmental Engineering, University of Southern California, Los Angeles, California, USA

    Roger Ghanem

  2. Social and Decision Analytics Laboratory, Virginia Bioinformatics Institute, Virginia Tech University, Arlington, Virginia, USA

    David Higdon

  3. Computing and Mathematical Sciences, California Institute of Technology, Pasadena, California, USA

    Houman Owhadi

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this entry

Cite this entry

Marrel, A., Saint-Geours, N., De Lozzo, M. (2017). Sensitivity Analysis of Spatial and/or Temporal Phenomena. In: Ghanem, R., Higdon, D., Owhadi, H. (eds) Handbook of Uncertainty Quantification. Springer, Cham. https://doi.org/10.1007/978-3-319-12385-1_39

Download citation

Publish with us

Policies and ethics

Search

Navigation