Advertisement

Environmental and Ecological Statistics

, Volume 25, Issue 2, pp 277–304 | Cite as

Functional regression on remote sensing data in oceanography

  • Nihan Acar-DenizliEmail author
  • Pedro Delicado
  • Gülay Başarır
  • Isabel Caballero
Article

Abstract

The aim of this study is to propose the use of a functional data analysis approach as an alternative to the classical statistical methods most commonly used in oceanography and water quality management. In particular we consider the prediction of total suspended solids (TSS) based on remote sensing (RS) data. For this purpose several functional linear regression models and classical non-functional regression models are applied to 10 years of RS data obtained from medium resolution imaging spectrometer sensor to predict the TSS concentration in the coastal zone of the Guadalquivir estuary. The results of functional and classical approaches are compared in terms of their mean square prediction error values and the superiority of the functional models is established. A simulation study has been designed in order to support these findings and to determine the best prediction model for the TSS parameter in more general contexts.

Keywords

Exponential regression models Functional linear regression models Functional partial least squares Functional principal components Remote sensing data 

References

  1. Acar-Denizli N, Delicado P, Başarır G, Caballero I (2017) Functional linear regression models for scalar responses on remote sensing data: an application to oceanography. In: Functional statistics and related fields, Springer, Brelin, pp 15–21Google Scholar
  2. Aguilera AM, Escabias M, Preda C, Saporta G (2010) Using basis expansions for estimating functional PLS regression: applications with chemometric data. Chemom Intell Lab Syst 104(2):289–305CrossRefGoogle Scholar
  3. Bernardello R, Serrano E, Coma R, Ribes M, Bahamon N (2016) A comparison of remote-sensing sst and in situ seawater temperature in near-shore habitats in the western mediterranean sea. Mar Ecol Prog Ser 559:21–34CrossRefGoogle Scholar
  4. Besse PC, Cardot H, Faivre R, Goulard M (2005) Statistical modelling of functional data. Appl Stoch Models Bus Ind 21(2):165–173CrossRefGoogle Scholar
  5. Binding C, Bowers D, Mitchelson-Jacob E (2003) An algorithm for the retrieval of suspended sediment concentrations in the irish sea from seawifs ocean colour satellite imagery. Int J Remote Sens 24(19):3791–3806CrossRefGoogle Scholar
  6. Binding C, Bowers D, Mitchelson-Jacob E (2005) Estimating suspended sediment concentrations from ocean colour measurements in moderately turbid waters; the impact of variable particle scattering properties. Remote Sens Environ 94(3):373–383CrossRefGoogle Scholar
  7. Björn-Helge M, Wehrens R (2007) The pls package: principal component and partial least squares regression in R. J Stat Softw 18(2):1–23.  https://doi.org/10.18637/jss.v018.i02. https://www.jstatsoft.org/v018/i02
  8. Caballero I, Navarro G (2016) Análisis multisensor para el estudio de los patrones de turbidez en el estuario del guadalquivir. Revista de teledetección: Revista de la Asociación Española de Teledetección 46:1–17CrossRefGoogle Scholar
  9. Caballero I, Morris E, Prieto L, Navarro G (2014a) The influence of the Guadalquivir River on the spatio-temporal variability of suspended solids and chlorophyll in the Eastern Gulf of Cadiz. Mediter Mar Sci 15(4):721–738CrossRefGoogle Scholar
  10. Caballero I, Morris EP, Ruiz J, Navarro G (2014b) Assessment of suspended solids in the Guadalquivir estuary using new DEIMOS-1 medium spatial resolution imagery. Remote Sens Environ 146:148–158CrossRefGoogle Scholar
  11. Cardot H, Ferraty F, Sarda P (1999) Functional linear model. Stat Probab Lett 45(1):11–22CrossRefGoogle Scholar
  12. Cardot H, Faivre R, Goulard M (2003) Functional approaches for predicting land use with the temporal evolution of coarse resolution remote sensing data. J Appl Stat 30(10):1185–1199CrossRefGoogle Scholar
  13. Chen X, Han X, Feng L (2015) Towards a practical remote-sensing model of suspended sediment concentrations in turbid waters using MERIS measurements. Int J Remote Sens 36(15):3875–3889CrossRefGoogle Scholar
  14. Clarke E, Speirs D, Heath M, Wood S, Gurney W, Holmes S (2006) Calibrating remotely sensed chlorophyll-\(a\) data by using penalized regression splines. J R Stat Soc: Ser C (Appl Stat) 55(3):331–353CrossRefGoogle Scholar
  15. Delaigle A, Hall P et al (2012) Methodology and theory for partial least squares applied to functional data. Ann Stat 40(1):322–352CrossRefGoogle Scholar
  16. Everson R, Cornillon P, Sirovich L, Webber A (1997) An empirical eigenfunction analysis of sea surface temperatures in the western North Atlantic. J Phys Oceanogr 27(3):468–479CrossRefGoogle Scholar
  17. Faivre R, Fischer A (1997) Predicting crop reflectances using satellite data observing mixed pixels. J Agric Biol Environ Stat 2(1):87–107CrossRefGoogle Scholar
  18. Febrero-Bande M, Oviedo de la Fuente M (2012) Statistical computing in functional data analysis: the R package fda.usc. J Stat Softw 51(4):1–28 http://www.jstatsoft.org/v51/i04/
  19. Febrero-Bande M, Galeano P, González-Manteiga W (2015) Functional principal component regression and functional partial least-squares regression: an overview and a comparative study. Int Stat Rev.  https://doi.org/10.1111/insr.12116 CrossRefGoogle Scholar
  20. Ferraty F, Zullo A, Fauvel M (2017) Nonparametric regression on contaminated functional predictor with application to hyperspectral data. Econom Stat.  https://doi.org/10.1016/j.ecosta.2017.02.004
  21. Fettweis MP, Nechad B (2011) Evaluation of in situ and remote sensing sampling methods for SPM concentrations, Belgian continental shelf (Southern North sea). Ocean Dyn 61(2–3):157–171CrossRefGoogle Scholar
  22. Friedman J, Hastie T, Tibshirani R (2010) Regularization paths for generalized linear models via coordinate descent. J Stat Softw 33(1):1–22 http://www.jstatsoft.org/v33/i01/
  23. Gitelson AA, Peng Y, Arkebauer TJ, Suyker AE (2015) Productivity, absorbed photosynthetically active radiation, and light use efficiency in crops: implications for remote sensing of crop primary production. J Plant Physiol 177:100–109CrossRefPubMedGoogle Scholar
  24. Goldsmith J, Bobb J, Crainiceanu C, Caffo B, Reich D (2011) Penalized functional regression. J Comput Graph Stat 20:830–851CrossRefPubMedPubMedCentralGoogle Scholar
  25. Gong M, Miller C, Scott E (2015) Functional pca for remotely sensed lake surface water temperature data. Procedia Environ Sci 26:127–130CrossRefGoogle Scholar
  26. Hastie T, Tibshirani R, Wainwright M (2015) Statistical learning with sparsity. CRC Press, HoeffdingCrossRefGoogle Scholar
  27. Horváth L, Kokoszka P (2012) Inference for functional data with applications, vol 200. Springer, BerlinGoogle Scholar
  28. James GM (2002) Generalized linear models with functional predictors. J R Stat Soc Ser B (Stat Methodol) 64(3):411–432CrossRefGoogle Scholar
  29. Kokoszka P, Reimherr M (2017) Introduction to functional data analysis. CRC Press, HoeffdingGoogle Scholar
  30. Lahet F, Ouillon S, Forget P (2001) Colour classification of coastal waters of the Ebro river plume from spectral reflectances. Int J Remote Sens 22(9):1639–1664CrossRefGoogle Scholar
  31. Le C, Hu C, Cannizzaro J, English D, Muller-Karger F, Lee Z (2013) Evaluation of chlorophyll-\(a\) remote sensing algorithms for an optically complex estuary. Remote Sens Environ 129:75–89CrossRefGoogle Scholar
  32. Liu C, Ray S, Hooker G, Friedl M (2012) Functional factor analysis for periodic remote sensing data. Ann Appl Stat 6(2):601–624CrossRefGoogle Scholar
  33. Marx BD, Eilers PHC (1999) Generalized linear regression on sampled signals and curves: a P-spline approach. Technometrics 41(1):1–13CrossRefGoogle Scholar
  34. MATLAB (2011) Version 7.10.0 (R2010a). The MathWorks Inc., NatickGoogle Scholar
  35. Morris JS (2015) Functional regression. Ann Rev Stat Appl 2:321–359CrossRefGoogle Scholar
  36. Navarro G, Ruiz J (2006) Spatial and temporal variability of phytoplankton in the Gulf of Cádiz through remote sensing images. Deep Sea Res Part II 53(11):1241–1260CrossRefGoogle Scholar
  37. Navarro G, Huertas IE, Costas E, Flecha S, Díez-Minguito M, Caballero I, López-Rodas V, Prieto L, Ruiz J (2012) Use of a real-time remote monitoring network (RTRM) to characterize the guadalquivir estuary (Spain). Sensors 12(2):1398–1421CrossRefPubMedPubMedCentralGoogle Scholar
  38. Nechad B, Ruddick K, Park Y (2010) Calibration and validation of a generic multisensor algorithm for mapping of total suspended matter in turbid waters. Remote Sens Environ 114(4):854–866CrossRefGoogle Scholar
  39. Nezlin NP, DiGiacomo PM (2005) Satellite ocean color observations of stormwater runoff plumes along the San Pedro Shelf (Southern California) during 1997–2003. Cont Shelf Res 25(14):1692–1711CrossRefGoogle Scholar
  40. Preda C, Saporta G (2005) PLS regression on a stochastic process. Comput Stat Data Anal 48(1):149–158CrossRefGoogle Scholar
  41. R Core Team (2017) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna. https://www.R-project.org
  42. Ramsay J, Silverman B (2005) Functional data analysis. Springer, New YorkCrossRefGoogle Scholar
  43. Ramsay JO, Wickham H, Graves S, Hooker G (2017) FDA: functional data analysis. R package version 2.4.7. http://CRAN.R-project.org/package=fda
  44. Rawat J, Kumar M (2015) Monitoring land use/cover change using remote sensing and GIS techniques: a case study of Hawalbagh block, district Almora, Uttarakhand, India. Egypt J Remote Sens Space Sci 18(1):77–84Google Scholar
  45. Reiss PT, Goldsmith J, Shang HL, Ogden RT (2017) Methods for scalar-on-function regression. Int Stat Rev 85(2):228–249CrossRefPubMedGoogle Scholar
  46. Ruiz J, Polo MJ, Díez-Minguito M, Navarro G, Morris EP, Huertas E, Caballero I, Contreras E, Losada MA (2014) The Guadalquivir estuary: a hot spot for environmental and human conflicts. In: Environmental management and governance, Springer, Berlin pp 199–232Google Scholar
  47. Wang JL, Chiou JM, Mueller HG (2016) Functional data analysis. Ann Rev Stat Appl 3(2):257–295CrossRefGoogle Scholar
  48. Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc B 67:301–320CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsMimar Sinan Güzel Sanatlar ÜniversitesiIstanbulTurkey
  2. 2.Department of Statistics and Operational ResearchUniversitat Politècnica de CatalunyaBarcelonaSpain
  3. 3.Department of Ecology and Coastal ManagementInstitute of Marine Sciences of Andalusia (ICMAN), National Research Council (CSIC)Puerto RealSpain
  4. 4.National Centers for Coastal Ocean ScienceNOAA National Ocean ServiceSilver SpringUSA

Personalised recommendations