A meta-modeling approach for spatio-temporal uncertainty and sensitivity analysis: an application for a cellular automata-based Urban growth and land-use change model

References

• Abily, M., et al., 2016. Spatial global sensitivity analysis of high resolution classified topographic data use in 2D urban flood modelling. Environmental Modelling and Software, 77, 183–195. doi:10.1016/j.envsoft.2015.12.002
   Web of Science ®Google Scholar
• Armstrong, M. and Matheron, G., 1986. Isofactorial models for granulodensimetric data. Mathematical Geology, 18 (8), 743–757. doi:10.1007/BF00899741
   Google Scholar
• Bilotta, G., et al., 2012. Sensitivity analysis of the MAGFLOW cellular automaton model for lava flow simulation. Environmental Modelling & Software, 35, 122–131. doi:10.1016/j.envsoft.2012.02.015
   Web of Science ®Google Scholar
• Burnaev, E., Panin, I., and Sudret, B., 2017. Efficient design of experiments for sensitivity analysis based on polynomial chaos expansions. Annals of Mathematics and Artificial Intelligence, 81 (1–2), 187–207. doi:10.1007/s10472-017-9542-1
   Web of Science ®Google Scholar
• Candau, J., Rasmussen, S., and Clarke, K.C., 2000. A coupled cellular automaton model for land use/land cover dynamics. In 4th International Conference on Integrating GIS and Environmental Modeling. Banff, Alberta.Canada.
   Google Scholar
• Chaudhuri, G. and Clarke, K.C., 2013. The SLEUTH land use change model: a review. The International Journal of Environmental Resources Research, 1 (1), 88–104.
   Google Scholar
• Chen, Q. and Mynett, A.E., 2003. Effects of cell size and configuration in cellular automata based prey-predator modelling. Simulation Modelling Practice and Theory, 11 (7–8), 609–625. doi:10.1016/j.simpat.2003.08.006
   Web of Science ®Google Scholar
• Chen, Y., Yu, J., and Khan, S., 2010. Spatial sensitivity analysis of multi-criteria weights in GIS-based land suitability evaluation. Environmental Modelling and Software, 25 (12), 1582–1591. doi:10.1016/j.envsoft.2010.06.001
   Web of Science ®Google Scholar
• Chiles, J.P. and Delfiner, P., 1999. Geostatistics: modeling spatial uncertainty. New York: Wiley.
   Google Scholar
• Clarke, K.C., et al., 2007. A decade of SLEUTHing: lessons learned from applications of a cellular automaton land use change model. In: P. Fisher, ed. Classics in IJGIS Twenty Years of the International Journal of Geographical Information Science and Systems. Boca Raton, FL: Taylor and Francis, CRC, 413–425.
   Google Scholar
• Clarke, K.C., 2008. A decade of cellular urban modeling with SLEUTH: unresolved issues and problems. In: R.K. Brail, ed. Planning support systems for cities and regions. Cambridge, MA: Lincoln Institute of Land Policy, Chapter 3, 47–60.
   Google Scholar
• Clarke, K.C., Gaydos, L., and Hoppen, S., 1997. A self-modifying cellular automaton model of historical urbanization in the San Francisco bay area. Environment and Planning B, 24, 247–261. doi:10.1068/b240247
   Web of Science ®Google Scholar
• Couclelis, H., 1985. Cellular worlds: a framework for modeling micro - macro dynamics. Environment and Planning A, 17 (5), 585–596. doi:10.1068/a170585
   Web of Science ®Google Scholar
• Crestaux, T., Le Maître, O., and Martinez, J.M., 2009. Polynomial chaos expansion for sensitivity analysis. Reliability Engineering and System Safety, 94 (7), 1161–1172. doi:10.1016/j.ress.2008.10.008
   Web of Science ®Google Scholar
• Crosetto, M. and Tarantola, S., 2001. Uncertainty and sensitivity analysis: tools for GIS-based model implementation. International Journal of Geographical Information Science, 15 (5), 415–437. doi:10.1080/13658810110053125
   Web of Science ®Google Scholar
• Crosetto, M., Tarantola, S., and Saltelli, A., 2000. Sensitivity and uncertainty analysis in spatial modelling based on GIS. Agriculture, Ecosystems & Environment, 81 (1), 71–79. doi:10.1016/S0167-8809(00)00169-9
   Web of Science ®Google Scholar
• Cukier, R.I., et al. 1973. Study of the sensitivity of coupled reaction systems to uncertainties in rate coefficients: I theory. The Journal of Chemical Physics, 59 (8), 3873–3878. doi:10.1063/1.1680571
   Web of Science ®Google Scholar
• Dahal, K.R. and Chow, T.E., 2015. Characterization of neighborhood sensitivity of an irregular cellular automata model of urban growth. International Journal of Geographical Information Science, 29 (3), 475–497. doi:10.1080/13658816.2014.987779
   Web of Science ®Google Scholar
• De Almeida, C.M., et al. 2003. Stochastic cellular automata modeling of urban land use dynamics: empirical development and estimation. Computers, Environment and Urban Systems, 27 (5), 481–509. doi:10.1016/S0198-9715(02)00042-X
   Google Scholar
• Deman, G., et al., 2016. Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model. Reliability Engineering and System Safety, 147, 156–169. doi:10.1016/j.ress.2015.11.005
   Web of Science ®Google Scholar
• Erlacher, C., et al. 2017. A GPU-based parallelization approach to conduct spatially-explicit uncertainty and sensitivity analysis in the application domain of landscape assessment. GI_Forum, (1), 44–58. doi:10.1553/giscience2017_01_s44
   Google Scholar
• Gómez‐Delgado, M. and Tarantola, S., 2006. GLOBAL sensitivity analysis, GIS and multi‐criteria evaluation for a sustainable planning of a hazardous waste disposal site in Spain. International Journal of Geographical Information Science, 20 (4), 449–466. doi:10.1080/13658810600607709
   Web of Science ®Google Scholar
• Halls, J.N., 2002. A spatial sensitivity analysis of land use characteristics and phosphorus levels in small tidal creek estuaries of North Carolina, USA. Journal of Coastal Research, Special Issue (36), 340–351.
   Google Scholar
• Helton, J.C., 1993. Uncertainty and sensitivity analysis techniques for use in performance assessment for radioactive waste disposal. Reliability Engineering & System Safety, 42 (2–3), 327–367. doi:10.1016/0951-8320(93)90097-I
   Web of Science ®Google Scholar
• Helton, J.C. and Davis, F.J., 2002. Illustration of sampling based methods for uncertainty and sensitivity analysis. Risk Analysis, 22 (3), 591–622. doi:10.1111/risk.2002.22.issue-3
   PubMed Web of Science ®Google Scholar
• Herman, J.D., et al. 2013. From maps to movies: high-resolution time-varying sensitivity analysis for spatially distributed watershed models. Hydrology and Earth System Sciences, 17 (12), 5109–5125. doi:10.5194/hess-17-5109-2013
   Web of Science ®Google Scholar
• Heuvelink, G.B.M., 1989. Propagation of errors in spatial modelling with GIS. International Journal of Geographical Information Systems, 3 (4), 303–322. doi:10.1080/02693798908941518
   Google Scholar
• Heuvelink, G.B.M., 1998. Uncertainty analysis in environmental modelling under a change of spatial scale. Nutrient Cycling in Agroecosystems, 50, 255–264. doi:10.1023/A:1009700614041
   Web of Science ®Google Scholar
• Heuvelink, G.B.M., 2003. Analysis uncertainty propagation in GIS: why is it not that simple?. In: G.M. Foody and P.M. Atkinson, eds. Uncertainty in remote sensing and GIS. West Sussex, England: John Wiley & Sons, Ltd, 155–165.
   Google Scholar
• Heuvelink, G.B.M. and Burrough, P.A., 1993. Error propagation in cartographic modelling using Boolean logic and continuous classification. International Journal of Geographical Information Systems, 7 (3), 231–246. doi:10.1080/02693799308901954
   Web of Science ®Google Scholar
• Heuvelink, G.B.M. and Burrough, P.A., 2002. Developments in statistical approaches to spatial uncertainty and its propagation. International Journal of Geographical Information Science, 16 (2), 111–113. doi:10.1080/13658810110099071
   Web of Science ®Google Scholar
• Holland, J., 1999. Emergence : from chaos to order. Cambridge, MA: Perseus Book.
   Google Scholar
• Hu, Y., et al. 2015. Global sensitivity analysis for large-scale socio-hydrological models using Hadoop. Environmental Modelling & Software, 73 (2015), 231–243. doi:10.1016/j.envsoft.2015.08.015
   Google Scholar
• Jantz, C.A. and Goetz, S.J., 2005. Analysis of scale dependencies in an urban land-use‐change model. International Journal of Geographical Information Science, 19 (2), 217–241. doi:10.1080/13658810410001713425
   Web of Science ®Google Scholar
• Jantz, C.A., Goetz, S.J., and Shelley, M.K., 2003. Using the SLEUTH urban growth model to simulate the impacts of future policy scenarios on urban land use in the Baltimore-Washington metropolitan area. Environment and Planning B: Planning and Design, 31 (2), 251–271. doi:10.1068/b2983
   Web of Science ®Google Scholar
• Kim, J.H., 2013. Spatiotemporal scale dependency and other sensitivities in dynamic land-use change simulations. International Journal of Geographical Information Science, 27 (9), 1782–1803. doi:10.1080/13658816.2013.787145
   Web of Science ®Google Scholar
• Kocabas, V. and Dragićević, S., 2006. Assessing cellular automata model behaviour using a sensitivity analysis approach. Computers, Environment and Urban Systems, 30 (6), 921–953. doi:10.1016/j.compenvurbsys.2006.01.001
   Web of Science ®Google Scholar
• Kyriakidis, P.C. and Goodchild, M.F., 2006. On the prediction error variance of three common spatial interpolation schemes. International Journal of Geographical Information Science, 20 (8), 823–855. doi:10.1080/13658810600711279
   Web of Science ®Google Scholar
• Lamboni, M., et al. 2009. Multivariate global sensitivity analysis for dynamic crop models. Field Crops Research, 113 (3), 312–320. doi:10.1016/j.fcr.2009.06.007
   Web of Science ®Google Scholar
• Li, X., Liu, X., and Yu, L., 2014. A systematic sensitivity analysis of constrained cellular automata model for urban growth simulation based on different transition rules. International Journal of Geographical Information Science, 28 (7), 1317–1335. doi:10.1080/13658816.2014.883079
   Web of Science ®Google Scholar
• Ligmann-Zielinska, A., 2013. Spatially-explicit sensitivity analysis of an agent-based model of land use change. International Journal of Geographical Information Science, 27 (9), 1764–1781. doi:10.1080/13658816.2013.782613
   Web of Science ®Google Scholar
• Ligmann-Zielinska, A. and Jankowski, P., 2014. Spatially-explicit integrated uncertainty and sensitivity analysis of criteria weights in multicriteria land suitability evaluation. Environmental Modelling and Software, 57, 235–247. doi:10.1016/j.envsoft.2014.03.007
   Web of Science ®Google Scholar
• Lilburne, L. and Tarantola, S., 2009. Sensitivity analysis of spatial models. International Journal of Geographical Information Science, 23 (February 2015), 151–168. doi:10.1080/13658810802094995
   Google Scholar
• Marrel, A., et al. 2011. Global sensitivity analysis for models with spatially dependent outputs. Environmetrics, 22 (3), 383–397. doi:10.1002/env.1071
   Web of Science ®Google Scholar
• Ménard, A. and Marceau, D.J., 2005. Exploration of spatial scale sensitivity in geographic cellular automata. Environment and Planning B: Planning and Design, 32 (5), 693–714. doi:10.1068/b31163
   Web of Science ®Google Scholar
• Metropolis, N. and Ulam, S., 1949. The Monte Carlo method. Journal of American Statistical Association, 44 (247), 335–341. doi:10.1080/01621459.1949.10483310
   PubMed Web of Science ®Google Scholar
• Moreau, P., et al., 2013. An approach for global sensitivity analysis of a complex environmental model to spatial inputs and parameters: a case study of an agro-hydrological model. Environmental Modelling and Software, 47, 74–87. doi:10.1016/j.envsoft.2013.04.006
   Web of Science ®Google Scholar
• Moreno, N., Wang, F., and Marceau, D., 2008. An object-based land-use cellular automata model to overcome cell size and neighborhood sensitivity. Proceedings of GEOBIA 2008–pixels, objects, intelligence GEOgraphic object based image analysis for the 21st century, 5–8 August, Calgary. Available from: http://www.isprs.org/proceedings/XXXVIII/4-C1/Sessions/Session6/6753_Marceau_Proc_pap.pdf [Accessed 2 September 2016].
   Google Scholar
• Najm, H.N., 2009. Uncertainty quantification and polynomial chaos techniques in computational fluid dynamics. Annual Review of Fluid Mechanics, 41 (1), 35–52. doi:10.1146/annurev.fluid.010908.165248
   Web of Science ®Google Scholar
• NCGIA. SLEUTH - Project Gigapolis. Available at: http://www.ncgia.ucsb.edu/projects/gig/ [Accessed 2 September 2016].
   Google Scholar
• O’Hagan, A., 2011. Polynomial chaos: a tutorial and critique from a statistician’s perspective. SIAM/ASA J. Uncertainty Quantification, 20 (2013), 1–20.
   Google Scholar
• Oakley, J. and Hagan, A.O., 2000. Bayesian inference for the uncertainty distribution of computer model outputs. Biometrika, 89 (4), 769–784. doi:10.1093/biomet/89.4.769
   Web of Science ®Google Scholar
• Pan, Y., et al. 2010. The impact of variation in scale on the behavior of a cellular automata used for land use change modeling. Computers, Environment and Urban Systems, 34 (5), 400–408. doi:10.1016/j.compenvurbsys.2010.03.003
   Web of Science ®Google Scholar
• Pontius, R.G. and Neeti, N., 2010. Uncertainty in the difference between maps of future land change scenarios. Sustainability Science, 5 (1), 39–50. doi:10.1007/s11625-009-0095-z
   Web of Science ®Google Scholar
• Rajabi, M.M., Ataie-Ashtiani, B., and Simmons, C.T., 2015. Polynomial chaos expansions for uncertainty propagation and moment independent sensitivity analysis of seawater intrusion simulations. Journal of Hydrology, 520, 101–122. doi:10.1016/j.jhydrol.2014.11.020
   Web of Science ®Google Scholar
• Ratto, M. and Pagano, A., 2012. State dependent regressions: from sensitivity analysis to meta-modeling. In L. Wang, H. Garnier, eds. Environmental modeling, and control system design. London: Springer. 171–190.
   Google Scholar
• Roura-Pascual, N., et al. 2010. Spatially-explicit sensitivity analysis for conservation management: exploring the influence of decisions in invasive alien plant management. Diversity and Distributions, 16 (3), 426–438. doi:10.1111/j.1472-4642.2010.00659.x
   Web of Science ®Google Scholar
• Rutherford, M.J., Crowther, M.J., and Lambert, P.C., 2015. The use of restricted cubic splines to approximate complex hazard functions in the analysis of time-to-event data: a simulation study. Journal of Statistical Computation and Simulation, 85 (4), 777–793. Available at. doi:10.1080/00949655.2013.845890
   Web of Science ®Google Scholar
• Saint-Geours, N., et al., 2014. Multi-scale spatial sensitivity analysis of a model for economic appraisal of flood risk management policies. Environmental Modelling & Software, 60, 153–166. doi:10.1016/j.envsoft.2014.06.012
   Web of Science ®Google Scholar
• Şalap-Ayça, S. and Jankowski, P., 2016. Integrating local multi-criteria evaluation with spatially explicit uncertainty-sensitivity analysis. Spatial Cognition & Computation, 16 (2), 106–132. doi:10.1080/13875868.2015.1137578
   Web of Science ®Google Scholar
• Saltelli, A., et al. 2010. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181 (2), 259–270. doi:10.1016/j.cpc.2009.09.018
   Web of Science ®Google Scholar
• Saltelli, A., Chan, K., and Scott, E.M., 2000. Sensitivity analysis. New York: Wiley.
   Google Scholar
• Saltelli, A., Tarantola, S., and Chan, K.P.S., 1999. A quantiative model-independent method for global sensitivity analysis of model output. Techniques, 41 (1), 39–56. doi:10.1080/00401706.1999.10485594
   Web of Science ®Google Scholar
• Samat, N., 2006. Characterizing the scale sensitivity of the cellular automata simulated urban growth: a case study of the Seberang Perai Region, Penang State, Malaysia. Computers, Environment and Urban Systems, 30 (6), 905–920. doi:10.1016/j.compenvurbsys.2005.11.002
   Web of Science ®Google Scholar
• Sobol’, I.M., 1993. Sensitivity analysis for non-linear mathematical models. Mathematical Modeling & Computational Experiments, 1, 407–414.
   Google Scholar
• Sobol’, I.M., 2001. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Mathematics and Computers in Simulation, 55 (1–3), 271–280. doi:10.1016/S0378-4754(00)00270-6
   Web of Science ®Google Scholar
• Sudret, B., 2008. Global sensitivity analysis using polynomial chaos expansions. Reliability Engineering and System Safety, 93 (7), 964–979. doi:10.1016/j.ress.2007.04.002
   Web of Science ®Google Scholar
• Sudret, B., 2014. Polynomial chaos expansions and stochastic finite element methods. In: K. Phoon and J. Ching, eds. Risk and reliability in geotechnical engineering. Boca Raton, FL: CRC Press, 265–300.
   Google Scholar
• Tang, W. and Jia, M., 2014. Global sensitivity analysis of a large agent-based model of spatial opinion exchange: a heterogeneous multi-GPU acceleration approach. Annals of the Association of American Geographers, 104 (3), 485–509. doi:10.1080/00045608.2014.892342
   Web of Science ®Google Scholar
• Tobler, W.R., 1979. Cellular geography. In: S. Gale and G. Olsson, eds. Philosophy in Geography. Dortrecht, NL: Dortrecht Reidel, 379–386.
   Google Scholar
• Torrens, P.M. and Nara, A., 2007. Modeling gentrification dynamics: a hybrid approach. Computers, Environment and Urban Systems, 31 (3), 337–361. doi:10.1016/j.compenvurbsys.2006.07.004
   Web of Science ®Google Scholar
• Torrens, P.M. and O’Sullivan, D., 2000. Cities, cells, and complexity: developing a research agenda for urban geocomputation. In 5th international conference on GeoComputation. University of Greenwich, UK, pp. 1–14.
   Google Scholar
• Ulam, S., 1952. Random processes and transformations. Proceedings of the International Congress of Mathematics, 2, 264–275.
   Google Scholar
• van Vliet, J., et al. 2016. A review of current calibration and validation practises in land-change modeling. Environmental Modelling and Software, (82), 174–182. doi:10.1016/j.envsoft.2016.04.017
   Google Scholar
• Villa-Vialaneix, N., et al. 2012. A comparison of eight metamodeling techniques for the simulation of N 2O fluxes and N leaching from corn crops. Environmental Modelling and Software, 34 (August 2017), 51–66. doi:10.1016/j.envsoft.2011.05.003
   Google Scholar
• Von Neumann, J., 1966. In: A.W. Burks, ed. Theory of self-reproducing automata. Champaign, IL: University of Illinois Press.
   Google Scholar
• Wackernagel, H., 2003. Multivariate geostatistics: an introduction with applications. New York: Springer Berlin Heidelberg.
   Google Scholar
• White, R. and Engelen, G., 1993. Cellular automata and fractal urban form: a cellular modelling approach to the evolution of urban land-use patterns. Environment and Planning A, 25 (8), 1175–1199. doi:10.1068/a251175
   Web of Science ®Google Scholar
• White, R. and Engelen, G., 1994. Urban systems dynamics and cellular automata: fractal structures between order and chaos. Chaos, Solitons and Fractals, 4 (4), 563–583. doi:10.1016/0960-0779(94)90066-3
   Web of Science ®Google Scholar
• White, R., Engelen, G., and Uljee, I., 1997. The use of constrained cellular automata for high-resolution modelling of urban land-use dynamics. Environment and Planning B: Urban Analytics and City Science, 24 (3), 323–343. doi:10.1068/b240323
   Google Scholar
• Wiener, N., 1938. The homogenous chaos. American Journal of Mathematics, 60 (4), 897–936. doi:10.2307/2371268
   Google Scholar
• Xiu, D., et al. 2002. Stochastic modeling of flow-structure interactions using generalized polynomial chaos. Journal of Fluids Engineering, 124 (1), 51. doi:10.1115/1.1436089
   Web of Science ®Google Scholar
• Xiu, D. and Karniadakis, G.E., 2002. The Wiener-Askey polynomial chaos for stochastic differential equations. Society for Industrial and Applied Mathematics Journal of Scientific Computing, 24 (2), 619–644.
   Google Scholar
• Xu, E. and Zhang, H., 2013. Spatially-explicit sensitivity analysis for land suitability evaluation. Applied Geography, 45, 1–9. doi:10.1016/j.apgeog.2013.08.005
   Web of Science ®Google Scholar
• Yeh, A.G.-O. and Li, X., 2006. Error propagation and model uncertainties of cellular automata in urban simulation with GIS. Computers, Environment and Urban Systems, 30 (1), 10–28. doi:10.1016/j.compenvurbsys.2004.05.007
   Web of Science ®Google Scholar