A Class-Kriging Predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers

详细信息    查看全文

• 作者：Alessandra Menafoglio ; Piercesare Secchi ; Alberto Guadagnini
• 关键词：Geostatistics ; Functional compositions ; Clustering ; Particle ; size curves ; Groundwater ; Hydrogeology
• 刊名：Mathematical Geosciences
• 出版年：2016
• 出版时间：May 2016
• 年：2016
• 卷：48
• 期：4
• 页码：463-485
• 全文大小：5,791 KB
• 参考文献：Aitchison J (1982) The statistical analysis of compositional data. J R Stat Soc B 44(2):139–177
  Aitchison J (1986) The statistical analysis of compositional data. Chapman and Hall, London
  Cressie N (1993) Statistics for spatial data. Wiley, New York
  Delicado P (2011) Dimensionality reduction when data are density functions. Comput Stat Data Anal 55(1):401–420CrossRef
  Egozcue JJ (2009) Reply to “On the Harker Variation Diagrams; ...” by J.A. Cortés. Math Geosci 41(7): 829-834
  Egozcue JJ, Díaz-Barrero JL, Pawlowsky-Glahn V (2006) Hilbert space of probability density functions based on aitchison geometry. Acta Math Sin 22(4):1175-1182
  Egozcue JJ, Pawlowsky-Glahn V, Tolosana-Delgado R, Ortego M, van den Boogaart K (2013) Bayes spaces: use of improper distributions and exponential families. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales Serie A Matematicas 107(2):475-486
  Franco-Villoria M, Ignaccolo R (2014) Uncertainty evaluation in functional kriging with external drift. In: Bongiorno EG, Salinelli E, Goia A, Vieu P (eds) Contributions in infinite-dimensional statistics and related topics. Esculapio Pub Co., Bologna, pp 191–196
  Fréchet M (1948) Les éléments Aléatoires de Nature Quelconque dans une Espace Distancié. Annales de L’Institut Henri Poincaré 10(4):215–308
  Horváth L, Kokoszka P (2012) Inference for functional data with applications. Springer series in statistics. Springer, BerlinCrossRef
  Hron K, Menafoglio A, Templ M, Hruzova K, Filzmoser P (2015) Simplicial principal component analysis for density functions in Bayes spaces. Comput Stat Data Anal. doi:10.​1016/​j.​csda.​2015.​07.​007
  Marron JS, Alonso AM (2014) Overview of object oriented data analysis. Biom J 56(5):732–753CrossRef
  Martìn MA, Rey JM, Taguas FJ (2005) An entropy-based heterogeneity index for mass-size distributions in earth science. Ecol Model 182:221–228CrossRef
  McQueen J (1967) Some methods for classification and analysis of multivariate observations. 5th Berkeley symposium on mathematics. Statistics and probability, vol 1, pp 281-298
  Menafoglio A, Guadagnini A, Secchi P (2014) A Kriging approach based on Aitchison geometry for the characterization of particle-size curves in heterogeneous aquifers. Stoch Environ Res Risk Assess 28(7):1835–1851CrossRef
  Menafoglio A, Secchi P, Dalla Rosa M (2013) A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space. Electron J Stat 7:2209–2240CrossRef
  Nerini D, Ghattas B (2007) Classifying densities using functional regression trees: applications in oceanology. Comput Stat Data Anal 51(10):4984–4993CrossRef
  Pawlowsky-Glahn V, Buccianti A (2011) Compositional data analysis. Theory and applications. Wiley, New York
  Pawlowsky-Glahn V, Egozcue JJ (2001) Geometric approach to statistical analysis in the symplex. Stoch Environ Res Risk Assess 15:384–398CrossRef
  Pawlowsky-Glahn V, Egozcue JJ, Tolosana-Delgado R (2015) Modeling and analysis of compositional data. Statistics in practice. Wiley, New York
  Pigoli D, Menafoglio A, Secchi P (2013) Kriging prediction for manifold-valued random field. CRiSM Paper No. 13-18, University of Warwick
  Ramsay J, Silverman B (2005) Functional data analysis, 2nd edn. Springer, New York
  Riva M, Guadagnini A, Fernández-García D, Sánchez-Vila X, Ptak T (2008) Relative importance of geostatistical and transport models in describing heavily tailed breakthrough curves at the Lauswiesen site. J Contam Hydrol 101:1–13CrossRef
  Riva M, Guadagnini L, Guadagnini A (2010) Effects of uncertainty of lithofacies, conductivity and porosity distributions on stochastic interpretations of a field scale tracer test. Stoch Environ Res Risk Assess 24:955–970. doi:10.​1007/​s00477-010-0399-7 CrossRef
  Riva M, Guadagnini L, Guadagnini A, Ptak T, Martac E (2006) Probabilistic study of well capture zones distributions at the Lauswiesen field site. J Contam Hydrol 88:92–118CrossRef
  Riva M, Sánchez-Vila X, Guadagnini A (2014) Estimation of spatial covariance of log-conductivity from particle-size data. Water Resour Res 50(6):5298–5308. doi:10.​1002/​2014WR015566 CrossRef
  Sangalli LM, Secchi P, Vantini S (2014) Object oriented data analysis: a few methodological challenges. Biom J 56(5):774–777CrossRef
  Tolosana-Delgado R, Pawlowsky-Glahn V, Egozcue JJ (2008a) Indicator kriging without order relation violations. Math Geosci 40(3):327–347CrossRef
  Tolosana-Delgado R, Pawlowsky-Glahn V, Egozcue JJ (2008b) Simplicial indicator kriging. J China Univ Geosci 19(1):65–71CrossRef
  Tolosana-Delgado R, van den Boogaart KG, Pawlowsky-Glahn V (2011) Geostatistics for compositions. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, Chichester. doi:10.​1002/​9781119976462.​ch6
  van den Boogaart K, Egozcue JJ, Pawlowsky-Glahn V (2010) Bayes linear spaces. SORT 34(2):201–222
  van den Boogaart KG, Egozcue JJ, Pawlowsky-Glahn V (2014) Bayes Hilbert spaces. Aust NZ J Stat 56:171–194CrossRef
  Vukovic M, Soro A (1992) Determination of hydraulic conductivity of porous media from grain-size composition. Water Resources Publications, Littleton
  
• 作者单位：Alessandra Menafoglio (1)
  Piercesare Secchi (1)
  Alberto Guadagnini (2) (3)
  
  1. MOX-Department of Mathematics, Politecnico di Milano, Milano, Italy
  2. Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Milano, Italy
  3. Department of Hydrology and Water Resources, The University of Arizona, Tucson, 85721, USA
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Earth sciences
  Mathematical Applications in Geosciences
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Geotechnical Engineering
  Hydrogeology
  
• 出版者：Springer Berlin Heidelberg
• ISSN：1874-8953

文摘

This work addresses the problem of characterizing the spatial field of soil particle-size distributions within a heterogeneous aquifer system. The medium is conceptualized as a composite system, characterized by spatially varying soil textural properties associated with diverse geomaterials. The heterogeneity of the system is modeled through an original hierarchical model for particle-size distributions that are here interpreted as points in the Bayes space of functional compositions. This theoretical framework allows performing spatial prediction of functional compositions through a functional compositional Class-Kriging predictor. To tackle the problem of lack of information arising when the spatial arrangement of soil types is unobserved, a novel clustering method is proposed, allowing to infer a grouping structure from sampled particle-size distributions. The proposed methodology enables one to project the complete information content embedded in the set of heterogeneous particle-size distributions to unsampled locations in the system. These developments are tested on a field application relying on a set of particle-size data observed within an alluvial aquifer in the Neckar river valley, in Germany.