In any model, Sensitivity Analysis (SA) is a fundamental process to improve the robustness and credibility of the results, as part of validation procedure. Generally, SA determined how the variation in the model output can be apportioned to different sources of variations, and how the given model depends upon the information fed into it. Many complex techniques of SA have been developed within the field of numerical modeling; however, they have limited applications for spatial models, as they do not consider variations in the spatial distributions of the variables included. In this research, a variation in the implementation of a Global Sensitivity Analysis (E-FAST) is proposed in order to include the spatial level. For this purpose the conventional tools available in a raster Geographical Information System (GIS) are used. The procedure has been tested in a simulation of urban growth for the Madrid Region (Spain) based on Multi-Criteria Evaluation (MCE) techniques. The results suggest that the inclusion of the spatial perspective in the application of the SA is necessary, because it can modify the factors that have a decisive influence on the results.
KeywordsSensitivity AnalysisGeographical Information SystemMulti-Criteria EvaluationSimulation of Urban GrowthMadrid Region (Spain)
J. I. Barredo and M. D. Gómez “Towards a Set of IPCC SRES Urban Land-Use Scenarios: Modeling Urban LandUse in the Madrid Region,” In: M. Paegelow and M. T. C. Olmedo, Eds., Modeling Environmental Dynamics. Advances in Geomatics Solution, Springer, Berlin, 2008, pp. 363-385.
P. H. Verburg, P. P. Schot, M. J. Dijst and A. Veldkamp, “Land Use Change Modeling: Current Practice and Research Priorities,” GeoJournal, Vol. 61, No. 4, 2004, pp. 309-324. doi:10.1007/s10708-004-4946
M. G. Delgado and J. Bosque Sendra, “Validation of GIS-performed analysis,” In: P. K. Joshi, P. Pani and S. N. Mohapatra, Eds., Geoinformatics for Natural Resource Management, Nova Science Publishers, Hauppauge, 2009, pp. 179-208.
M. Paegelow and M. T. C. Olmedo, “Modeling Environmental Dynamics,” Springer-Verlag, Berlin, 2008.
M. E. Qureshi, S. R. Harrison and M. K. Wegener, “Validation of Multi-Criteria Analysis Models,” Agricultural Systems, Vol. 62, No. 2, 1999, pp. 105-116. doi:10.1016/S0308-521X(99)00059-1
M. L. Chu-Agor, R. Mu?oz-Carpena, G. Kiker, A. Emanuelsson and I. Linkov, “Exploring Vulnerability of Coastal Habitats to Sea Level Rise through Global Sensitivity and Uncertainty Analyses,” Environmental Modeling & Software, Vol. 26, No. 5, 2011, pp. 593-604. doi:10.1016/j.envsoft.2010.12.003
M. Crosetto, S. Tarantola and A. Saltelli, “Sensitivity and Uncertainty Analysis in Spatial Modeling Based on GIS,” Agriculture, Ecosystems and Environment, Vol. 81, No. 1, 2000, pp. 71-79. doi:10.1016/S0167-8809(00)169-9
A. Saltelli, K. Chan and E. M. Scott “Sensitivity Analysis,” Wiley, LTD., Chichester, 2000.
A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana and S. Tarantola, “Global Sensitivity Analysis: The Primer,” Wiley, LTD., Chichester, 2008.
A. Saltelli, S. Tarantola and K. Chan, “A Role for Sensitivity Analysis in Presenting the Results from MCDA studies to Decision Makers,” Journal of Multi-Criteria Decision Analysis, Vol. 8, No. 3, 1999, pp. 139-145. doi:10.1002/(SICI)1099-1360(199905)
M. G. Delgado and J. B. Sendra, “Sensitivity Analysis in Multi-Criteria Spatial Decision-Making: A Review,” Human and Ecological Risk Assessment, Vol. 10, No. 6, 2004, pp. 1173-1187. doi:10.1080/10807030490887221
C. J. Pettit, “Land Use Planning Scenarios for Urban Growth: A Case Study Approach,” Ph.D. Thesis, University of Queensland, Queensland, 2002.
N. B. Chang, G. Parvathinathan and J. B. Breeden, “Combining GIS with Fuzzy Multi-Criteria Decision-Making for Landfill Sitting in a Fast-Growing Urban Region,” Journal of Environmental Management, Vol. 87, No. 1, 2008, pp. 139-153.
P. Jankowski, “Integrating Geographic Information Systems and Multiple Criteria Decision Making Methods,” International Journal of Geographical Information Systems, Vol. 9, No. 3, 1995, pp. 251-273. doi:10.1080/02693799508902036
S. Baja, D. M. Chapman and D. Dragovich, “Spatial Based Compromise Programming for Multiple Criteria Decision Making in Land Use Planning,” Environmental Model & Assessment, Vol. 12, No. 3, 2007, pp. 171-184. doi:10.1007/s10666-006-9059-1
D. Geneletti and I. van Duren, “Protected Area Zoning for Conservation and Use: A Combination of Spatial MultiCriteria and Multi-Objective Evaluation,” Landscape and Urban Planning, Vol. 85, No. 2, 2008, pp. 97-110. doi:10.1016/j.landurbplan.2007.10.004
L. Lilburne and S. Tarantola, “Sensitivity Analysis of Models with Spatially-Distributed Input,” International Journal of Geographic Information Systems, Vol. 23, No. 2, 2009, pp. 151-168.
M. Crosetto and S. Tarantola, “Uncertainty and Sensitivity Analysis: Tools for GIS-Based Model Implementation,” International Journal of Geographical Information Science, Vol. 15, No. 5, 2001, pp. 415-437. doi:10.1080/13658810110053125
M. G. Delgado and S. Tarantola, “Global Sensitivity Analysis, GIS and Multi-Criteria Evaluation for a Sustainable Planning of Hazardous Waste Disposal Site in Spain,” International Journal of Geographical Information Science, Vol. 20, No. 4, 2006, pp. 449-466. doi:10.1080/13658810600607709
T. Wagener and J. Kollat, “Numerical and Visual Evaluation of Hydrological and Environmental Models Using the Monte Carlo Analysis Toolbox,” Environmental Modeling & Software, Vol. 22, No. 7, 2007, pp. 1021-1033. doi:10.1016/j.envsoft.2006.06.017
Y. Tang, P. Reed, T. Wagener and K. van Werkhoven, “Comparing Sensitivity Analysis Methods to Advance Lumped Watershed Model Identification and Evaluation”, Hydrology and Earth system Sciences, Vol. 11, No. 2, 2007, pp. 793-817. www.hydrol-earth-syst-sci.net/11/793/2007/
H. Varella, M. Guèrif and S. Buis “Global Sensitivity Analysis Measures the Quality of Parameter Estimation: The Case of Soil Parameters and a Crop Model,” Environmental Modeling & Software, Vol. 25, No. 3, 2010, pp. 310-319. doi:10.1016/j.envsoft.2009.09.012
European Environment Agency (EEA), “Urban Sprawl in Europe, the Ignored Challenge,” EEA Report 10, Luxemburg, 2006.
W. P. Rocha, M. G. Delgado and J. B. Sendra, “Land Use Changes and Urban Expansion in the Community of Madrid (1990-2000),” Scripta-Nova, Vol. XIII, No. 293, 2009. http://www.ub.es/geocrit/sn/sn-293.htm
W. P. Rocha, M. G. Delgado and J. B. Sendra, “Development of Optimal Urban Growth Models for the Community of Madrid applying Multicriteria Evaluation Techniques and Geographic Information Systems,” GeoFocus (International Journal of Science and Technology of Geographic Information), Vol. 10, 2010, pp. 103-134. http://geofocus.rediris.es/2010/Articulo5_2010.pdf
W. P. Rocha, M. G. Delgado and J. B. Sendra, “Simulating Urban Growth Scenarios Using GIS and Multi-Criteria Evaluation Techniques. Case Study: Madrid Region, Spain,” Environment and Planning B, Vol. 38, No. 6, 2011, pp. 1012-1031. doi:10.1068/b37061
F. A. Benavente, W. P. Rocha, J. B. Sendra and M. G. Delgado, “Design and Simulation of Scenarios of Urban Land Demand in Metropolitan Areas,” International Journal of Sustainability, Technology and Humanism, Vol. 4, 2009, pp. 57-80. http://hdl.handle.net/2099/8535
A. Saltelli, S. Tarantola and K. K. Chan, “A Quantitative Model Independent Method for Global Sensitivity Analysis of Model Output,” Technometrics, Vol. 41, No. 1, 1999, pp. 39-56. doi:10.2307/1270993
R. I. Cukier, C. M. Fortuin, K. E. Schuler, A. G. Petschek and J. H. Schaibly, “Study of the Sensitivity of Coupled Reaction Systems to Uncertainties in Rate Coefficients. Part I: Theory,” Journal of Chemical Physics, Vol. 59, No. 8, 1975, pp. 3873-3878. doi:10.1063/1.431440
M. Crosetto, J. A. M. Ruiz and B. Crippa, “Uncertainty Propagation in Models Driven by Remotely Sensed Data,” Remote Sensing of Environment, Vol. 76, No. 3, 2001, pp. 373-437. doi:10.1016/S0034-4257(01)00184-5
M. Crosetto, F. Crosetto and S. Tarantola, “Optimized Resource Allocation for GIS-Based Model Implementation,” Photogrammetric Engineering & Remote Sensing, Vol. 68, No. 3, 2003, pp. 225-232.