Abstract
Mountain glacier retreat is an important problem related to temperature increase caused by global climate change. The retreat of mountain glaciers has been studied from the ground, but there exists a need for automated methods to catalog glacial change with a wider scope. A viable approach is to extract intensity profiles from Landsat images along the glacial flowline and follow the terminus location over time. We propose a new robust and accurate statistical algorithm to estimate the movement of glacial termini over time from these extracted image intensity profiles. The method we propose first uses regression splines to smooth the image intensity profiles. For each profile, the glacial terminus location is assumed to lie near a point of high negative change in the smoothed profiles. An approximate path of termini locations over time is obtained by an algorithm that seeks to minimize the cumulative first derivative value across the profiles. Spline smoothing is applied to this pilot path for estimation of long-term terminus movement. The predictions from the method are evaluated on simulated data and compared to available ground measurements for the Nigardsbreen, Gorner, Rhone, and Franz Josef glaciers.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bintanja, R., van de Wal, R. S., and Oerlemans, J. (2005) “Modelled atmospheric temperatures and global sea levels over the past million years,” Nature, 437(7055):125–128.
Bradley, R. S., Mann, M., and Hughes, M. K. (1999) “Northern hemisphere temperatures during the past millennium: inferences, uncertainties, and limitations,” Geophysical Research Letters, 26(6):759–762.
Eilers, P. H. and Marx, B. D. (1996) "Flexible smoothing with b-splines and penalties," Statistical Science, 11:89–102.
Golub, G. H., Heath, M., and Wahba, G. (1979) “Generalized cross-validation as a method for choosing a good ridge parameter,” Technometrics, 21(2):215–223.
Irish, R. R. (2000) “Landsat 7 automatic cloud cover assessment,” In AeroSense 2000. International Society for Optics and Photonics. pp. 348–355.
Joo, J.-H., Qiu, P. (2009) “Jump detection in a regression curve and its derivative,” Technometrics, 51(3):289–305.
Kachouie, N. N., Gerke, T., Huybers, P., and Schwartzman, A. (2014) “Non-parametric regression for estimation of spatiotemporal mountain glacier retreat from satellite images,” IEEE Transactions on Geosciences and Remote Sensing, 53:1135–1145.
Kachouie, N. N., Huybers, P., and Schwartzman, A. (2012) “Localization of mountain glacier termini in landsat multi-spectral images,” Pattern Recognition Letters, 34:94–104.
Landsat.org. http://landat.org/.
Landsat-US National Aeronautics and Space Administration (NASA). http://landsat.gsfc.nasa.gov/.
Loader, C. R. (1996) “Change point estimation using non-parametric regression,” The Annals of Statistics, 24(4):1667–1678.
Marra, G. and Wood, S. N. (2012) “Coverage properties of confidence intervals for generalized additive model components,” Scandinavian Journal of Statistics, 39(1):53–74.
Muller, H.-G. (1992) “Change-points in non-parametric regression analysis,” The Annals of Statistics, 20(2):737–761.
Nychka, D. (1988) “Bayesian confidence intervals for smoothing splines,” Journal of the American Statistical Association, 83(404):1134–1143.
Oerlemans, J. (2000) “Holocene glacier fluctuations: Is the current rate of retreat exceptional?,” Annals of Glaciology, 31(1):39–44.
Oerlemans, J. and van de Wal, R. (1995) “Response of valley glaciers to climate change and kinematic waves: A study with a numerical ice-flow model,” Journal of Glaciology, 41(137):142–152.
Ruppert, D. (2002) “Selecting the number of knots for penalized splines, ” Journal of Computational and Graphical Statistics, 11(4):735–757.
Salomonson, V. and Appel, I. (2004) “Estimating fractional snow cover from modis using the normalized difference snow index,” Remote Sensing of Environment, 89(3):351–360.
Seidel, K. and Martinec, J. (2004) Remote Sensing in Snow Hydrology: Runoff Modelling, Effect of Climate Change, Springer: Berlin.
The Swiss Glacier Inventory 2000 (SGI 2000). http://www.geo.unizh.ch/fpaul/SGI2000/.
US Geographical Survey (USGS). http://landat.usgs.gov/.
Wahba, G. (1983) "Bayesian “confidence intervals" for the cross-validated smoothing spline”, Journal of the Royal Statistical Society. Series B (Methodological), 45:133–150.
Wood, S. N. (2006) Generalized Additive Models: An Introduction with R, Chapman and Hall/CRC: Boca Raton, Florida.
World Glacier Monitoring Service. http://www.wgms.ch/.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Usset, J., Maity, A., Staicu, AM. et al. Glacier Terminus Estimation from Landsat Image Intensity Profiles. JABES 20, 279–298 (2015). https://doi.org/10.1007/s13253-015-0207-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13253-015-0207-4