Long-term global ground heat flux and continental heat storage from geothermal data

Abstract

Abstract. Energy exchanges among climate subsystems are of critical importance to determine the climate sensitivity of the Earth's system to greenhouse gases, to quantify the magnitude and evolution of the Earth's energy imbalance, and to project the evolution of future climate. Thus, ascertaining the magnitude of and change in the Earth's energy partition within climate subsystems has become urgent in recent years. Here, we provide new global estimates of changes in ground surface temperature, ground surface heat flux, and continental heat storage derived from geothermal data using an expanded database and new techniques. Results reveal markedly higher changes in ground heat flux and heat storage within the continental subsurface than previously reported, with land temperature changes of 1 K and continental heat gains of around 12 ZJ during the last part of the 20th century relative to preindustrial times. Half of the heat gain by the continental subsurface since 1960 has occurred in the last 20 years.

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

“…Most global estimates of continental heat storage have been inferred from subsurface temperature profiles (STPs) (Beltrami et al, 2002;Beltrami, 2002;von Schuckmann et al, 2020;Cuesta-Valero et al, 2021c), which allow to estimate past ground surface temperature and ground heat flux changes at decadal to centennial time scales (e.g., Shen et al, 1992;Beltrami et al, 2002;Beltrami, 2002;Hopcroft et al, 2007;Demezhko and Gornostaeva, 2015a;Kukkonen et al, 2020). These long-term estimates of surface temperature and ground heat flux changes have also been used to evaluate the ability of general circulation models (GCMs) to reproduce past changes in the conditions of the shallow continental subsurface, which has increased our knowledge of the Earth System and the confidence in future projections (González-Rouco et al, 2006;González-Rouco et al, 2009;García-García et al, 2016;Cuesta-Valero et al, 2019;Melo-Aguilar et al, 2020).…”

“…Several techniques exist to retrieve the evolution of ground surface temperature changes from STPs, all yielding similar results (Beltrami and Mareschal, 1992;Shen et al, 1992;Hartmann and Rath, 2005;Hopcroft et al, 2007;Cuesta-Valero et al, 2021c). These techniques solve the inversion problem, that is, estimating the surface temperature that generated the observed profile, with two main strategies to retrieve STP inversions: Bayesian methods (Shen et al, 1992;Woodbury and Ferguson, 2006;Hopcroft et al, 2007Hopcroft et al, , 2009, and methods based on a Singular Value Decomposition (SVD) algorithm (Beltrami et al, 1992;Beltrami and Mareschal, 1992;Clauser and Mareschal, 1995;Hartmann and Rath, 2005;Jaume-Santero et al, 2016;Cuesta-Valero et al, 2021c).…”

“…Several techniques exist to retrieve the evolution of ground surface temperature changes from STPs, all yielding similar results (Beltrami and Mareschal, 1992;Shen et al, 1992;Hartmann and Rath, 2005;Hopcroft et al, 2007;Cuesta-Valero et al, 2021c). These techniques solve the inversion problem, that is, estimating the surface temperature that generated the observed profile, with two main strategies to retrieve STP inversions: Bayesian methods (Shen et al, 1992;Woodbury and Ferguson, 2006;Hopcroft et al, 2007Hopcroft et al, , 2009, and methods based on a Singular Value Decomposition (SVD) algorithm (Beltrami et al, 1992;Beltrami and Mareschal, 1992;Clauser and Mareschal, 1995;Hartmann and Rath, 2005;Jaume-Santero et al, 2016;Cuesta-Valero et al, 2021c). Nevertheless, several sources of uncertainty arise in the inversion process, being the most important the unknown thermal properties at most sites, the determination of the quasi-equilibrium temperature profile at each site, and the value of several parameters in the inversion framework, such as the number and length of the time steps for mod-elling the retrieved surface temperature series, and the number of eigenvalues retained in the SVD algorithm to obtain stable solutions.…”

“…Nevertheless, including the uncertainty due to unknown thermal properties in the ground into SVD inversions required the development a different approach. This new approach was labelled Perturbed Parameter Inversion (PPI), because it was based on estimating a large ensemble of SVD inversions by changing the value of the inversion parameters for each iteration, including the value of thermal properties (Cuesta-Valero et al, 2021c). After generating the ensemble, the 2.5th, 50th and 97.5th percentile of all solutions was computed in order to obtain a best estimate and a 95% confidence interval.…”

“…Estimates of ground heat flux histories have been retrieved from STPs using two main methods: inversion of subsurface heat flux profiles, and from ground surface temperature histories. Subsurface heat flux profiles can be estimated directly from measured STPs using the Fourier equation, and due to the nature of heat diffusion through the ground, these heat flux profiles can be inverted following the same SVD approach used to invert subsurface temperature profiles (Beltrami, 2001;Turcotte and Schubert, 2002;Cuesta-Valero et al, 2021c). Nevertheless, subsurface heat flux profiles are noisier than STPs, thus the uncertainty in the retrieved ground heat flux histories is large.…”