Submitted as: development and technical paper
19 Jul 2022
Submitted as: development and technical paper | 19 Jul 2022
Status: a revised version of this preprint is currently under review for the journal GMD.

A new bootstrap technique to quantify uncertainty in estimates of ground surface temperature and ground heat flux histories from geothermal data

Francisco José Cuesta-Valero1,2, Hugo Beltrami3, Stephan Gruber4, Almudena García-García1,2, and J. Fidel González-Rouco5 Francisco José Cuesta-Valero et al.
  • 1Department of Remote Sensing, Helmholtz Centre for Environmental Research (UFZ), Permoserstraße 15, Leipzig, 04318, Saxony, Germany
  • 2Remote Sensing Centre for Earth System Research, Leipzig University, 04103, Leipzig, Germany
  • 3Climate & Atmospheric Sciences Institute, St. Francis Xavier University, 5009 Chapel Square, Antigonish, B2G 2W5, NS, Canada
  • 4Department of Geography and Environmental Studies, Carleton University, 1125 Colonel By Dr, Ottawa, K1S 5B6, ON, Canada
  • 5Instituto de Geociencias, Consejo Superior de Investigaciones Científicas - Universidad Complutense de Madrid, Madrid, Spain

Abstract. Estimates of the past thermal state of the land surface are crucial to assess the magnitude of current anthropogenic climate change, as well as to assess the ability of Earth System Models to forecast the evolution of the climate near the ground, not included in standard meteorological records. Subsurface temperature data are able to retrieve long-term changes in surface energy balance –from decadal to millennial time scales, thus constituting an important record of the dynamics of the climate system that contributes low-frequency information to proxy-based paleoclimatic reconstructions. A broadly used technique to retrieve past temperature and heat flux histories from subsurface temperature profiles based on a Singular Value Decomposition (SVD) algorithm was able to take into account a limited number of sources of uncertainty, with recent works attempting to increase the number of factors considered in uncertainty estimates. Nevertheless, the SVD methodology did not define a statistical framework for aggregating inversions of individual profiles to derive global results, which lead to estimates of global and regional uncertainties that are difficult to interpret. To alleviate the lack of a conceptual framework for estimating uncertainties in past temperature and heat flux histories at regional and global scales, we combine a new bootstrapping sampling strategy with the broadly used SVD algorithm, and assess its performance against the original SVD technique and another technique based on generating perturbed parameter ensembles of inversions. The new bootstrap approach is able to reproduce the prescribed surface temperature series used to derive an artificial profile. Bootstrap results are also in agreement with the global mean surface temperature history and the global mean heat flux history retrieved in previous studies. Furthermore, the new bootstrap technique provides with a meaningful uncertainty range for the inversion of large sets of subsurface temperature profiles. We suggest the use of this new approach particularly for aggregating results from a number of individual profiles, and to this end, we release the programs used to derive all inversions in this study as a suite of codes labelled CIBOR 1.0: Codes for Inverting BORholes, version 1.0.

Francisco José Cuesta-Valero et al.

Status: final response (author comments only)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2022-178', Anonymous Referee #1, 01 Aug 2022
    • AC2: 'Reply on RC1', Francisco José Cuesta-Valero, 21 Sep 2022
  • RC2: 'Comment on gmd-2022-178', Anonymous Referee #2, 11 Aug 2022
    • AC3: 'Reply on RC2', Francisco José Cuesta-Valero, 21 Sep 2022
  • CEC1: 'Comment on gmd-2022-178', Juan Antonio Añel, 23 Aug 2022
    • AC1: 'Reply on CEC1', Francisco José Cuesta-Valero, 23 Aug 2022
      • CEC2: 'Reply on AC1', Juan Antonio Añel, 24 Aug 2022

Francisco José Cuesta-Valero et al.

Francisco José Cuesta-Valero et al.


Total article views: 354 (including HTML, PDF, and XML)
HTML PDF XML Total BibTeX EndNote
248 87 19 354 7 4
  • HTML: 248
  • PDF: 87
  • XML: 19
  • Total: 354
  • BibTeX: 7
  • EndNote: 4
Views and downloads (calculated since 19 Jul 2022)
Cumulative views and downloads (calculated since 19 Jul 2022)

Viewed (geographical distribution)

Total article views: 323 (including HTML, PDF, and XML) Thereof 323 with geography defined and 0 with unknown origin.
Country # Views %
  • 1
Latest update: 28 Sep 2022
Short summary
Inversions of subsurface temperature profiles provide past long-term estimates of ground surface temperature histories and ground heat flux histories at time scales of decades to millennia. Theses estimates complement high-frequency proxy temperature reconstructions and are the basis to study continental heat storage. We develop and release a new bootstrap method to derive meaningful confidence intervals for the average surface temperature and heat flux histories from any number of profiles.