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Reconstructions of long-term ground surface heat flux changes from deep-borehole temperature data
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ScienceDirect Russian Geology and Geophysics 55 (2014) 1471–1475 www.elsevier.com/locate/rgg
Reconstructions of long-term ground surface heat flux changes from deep-borehole temperature data D.Yu. Demezhko *, A.A. Gornostaeva Institute of Geophysics, Ural Branch of the Russian Academy of Sciences, ul. Amundsena 100, Yekaterinburg, 620016, Russia Received 22 July 2013; accepted 11 October 2013
Abstract Based on analysis of geothermal data from the Ural superdeep borehole (SG-4) and Onega parametric borehole, the first reconstructions of ground surface heat flux changes for the last 40 kyr have been made. The increase in heat flux during the Pleistocene–Holocene warming (20–10 ka) proceeded ~2 kyr earlier than the growth in surface temperature; reaching the maximum value of 0.08–0.13 W/m2 at ~13 ka, the heat flux was reduced. The coordinated changes in heat flux and average annual insolation at 60º N at 5–24 ka indicate that the orbital factors were the main cause of climatic changes in this period. The correlations between the changes in heat flux and CO2 content in the Antarctic ice cores and the temperature changes are analyzed. © 2014, V.S. Sobolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. Keywords: geothermy; paleoclimatic reconstructions; heat flux; energy balance of the Earth’s surface; Pleistocene; Holocene; Urals; Karelia
Introduction Geothermal reconstructions of the ground surface temperature history have long been used in the paleoclimatological methods (Cermak, 1971; Dahl-Jensen et al., 1998; Demezhko and Golovanova, 2007; Lachenbruch and Marshall, 1986; Majorowicz et al., 2002; Pollack et al., 1998). They are based on analysis of the present-day distribution of rock temperatures throughout a borehole and on the solution of heat equation with respect to the upper boundary condition—changes in the ground surface temperature. The reconstructions give an idea of the long-period components of temperature fluctuations, which are poorly reproduced (or are not reproduced at all) by other proxies (Krenke et al., 1995). This problem admits another boundary condition—ground surface heat flux changes. Reconstructions of long-period variations in climatecaused heat flux are of crucial importance for estimating the energy of climatic processes and the factors determining the natural and anthropogenic components of climatic variations. The climate-caused variations in heat flux, in contrast to geothermal heat flow, lead to variations in lithospheric heat content. These fluxes, together with net radiation and radiant sensible and latent heat fluxes, form the energy balance of the planet. * Corresponding author. E-mail address: [email protected] (D.Yu. Demezhko)
Despite the urgency of this problem, there are still only a few publications implementing the above approach. This research problem was put forward earlier, the ways of its solution were proposed, reconstructions of the heat flux were made, and the heat content in the upper lithosphere in the period from several centuries (Northern Hemisphere) to thousand years ago (Eastern Canada) was estimated (Beltrami, 2001; Beltrami et al., 2002). It is obvious that these few studies do not show the method potentialities in full measure. A considerable part of the existing borehole temperatures database has not been analyzed. Changes in heat flux and in the heat content of rocks in the period of global restructuring of the climatic system at the Holocene/Pleistocene boundary (~10 ka) have not been studied. In this paper we make the first reconstructions of ground surface heat flux changes for the last 40 kyr, based on analysis of geothermal data from the Ural superdeep borehole (SG-4) and Onega parametric borehole.
Methods Reconstruction of the ground surface temperature history from borehole temperatures (inversion) is based on the solution of nonstationary one-dimensional heat equation in a homogeneous or horizontally layered medium in the absence of heat sources and convective factors of heat transfer.
1068-7971/$ - see front matter D 201 4 , V . S. So bolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.rgg.2014.11.011
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D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475
Fluctuations in surface temperature T(z = 0, t), where z is depth and t is time, are specified as a boundary condition in the form of a sum of simple functions (harmonic oscillations, step, and linear temperature change), for which the heat equation has an explicit solution. Since this solution is linear with respect to the unknown parameters of the boundary condition, we can make an equation containing m + 2 unknown parameters (m parameters of the temperature history, initial temperature, and unperturbed temperature gradient) for each point of the temperature profile. In this case, the inversion problem is reduced to the solution of a system of linear equations and is formulated as a search for a set of the parameter values that would provide the least discrepancy between the observed and model temperatures in the specified metrics. The known methods of inversion of geothermal data differ in the ways of specifying functions approximating the temperature history and in the way of solution of ill-posed problems. For this purpose, various methods are used to limit the family of equivalent solutions, which are based on the involvement of additional information, smoothing, and restriction of the amplitudes of temperatures to be reconstructed. Heat flux q(z = 0, t) can also be specified as a surface boundary condition. The techniques of the thermal-history reconstruction are similar to the techniques of temperature reconstruction. There is a functional relationship between the two solutions, with respect to temperature and flux. In the simplest case of the specified harmonic temperature oscillations with amplitude A, frequency ω, and initial phase ϕ at the surface, T (0, t) = A sin (ωt + ϕ),
(1)
the propagation of temperature waves in a homogeneous half-space with thermal diffusivity a is described by the expression ⎯⎯⎯⎯⎯ ω / 2a . T (z, t) = A e−kz sin (ωt − kz + ϕ), k = √
(2)
Differentiating (2) with respect to z, we find the change in ground surface heat flux q: q (0, t) = − λ
⎛ ⎪ ∂ = AE √ ⎯⎯ω sin ⎜ωt + ϕ + T (z, t)⎪ ∂z ⎝ ⎪z = 0
π⎞ 4 ⎟⎠
π⎞ ⎛ =E√ (3) ⎯⎯ω T ⎜0, t + ⎟ , 4⎠ ⎝ where λ is the thermal conductivity and E is the thermal effusivity (thermal inertia) of the medium, expressed via thermal conductivity, thermal diffusivity, and volumetric heat capacity of rocks, ρC: E = (λρC)1/2 = λ/(a)1/2 = ρC(a)1/2. The heat flux changes are ahead of temperature changes by π/4, i.e., one-eighth of the oscillation period. The physical meaning of this shift is clear: It is the flux changes that determine the temperature change, and not vice versa. These relationships describe well the diurnal temperature fluctuations at the Earth’s surface under the effect of varying insolation. The maximum insolation falls on the solar noon, and the maximum surface temperature is observed ~3 hours later. Note that E, despite its second name “thermal inertia”, defines not the
temperature lag but only the ratio between the amplitudes of the flux and temperature oscillations. General integral relation between the changes in surface temperature and heat flux was obtained by Wang and Bras (1999). Beltrami et al. (2002) presented its finite-difference approximation for the case when the temperature history is expressed by a continuous piecewise linear function defined at the nodes of a uniform grid: q (0, ti) =
2E
i
∑
⎯⎯⎯ ⎡Tj − Tj−1⎤ ⋅ ⎡√ ⎯⎯⎯⎯⎯⎯⎯⎯ i −⎯ j ⎤ . i − (j − 1) − √ ⎦ ⎦ ⎣
πΔ ⎯⎯⎯ √ ⎯tj=1 ⎣
(4)
Here, T is the surface temperature specified at regular intervals Δt, ti = iΔt, i = 1...n, j = 1...i. This formula is conveniently used when it is necessary to assess the thermal ground surface history from earlier reconstructed temperature histories.
Results and discussion Figure 1 shows reconstructions of the ground surface thermal history in the Urals and in Karelia, made using formula (4) and the results of our earlier temperature history reconstructions (Demezhko and Shchapov, 2001; Demezhko et al., 2013). The shapes of the curves T(0, t) and q(0, t) differ considerably. Changes in heat flux precede changes in the surface temperature, reaching a maximum (0.08–0.13 W/m2) at the time of the maximum rate of warming and then decreasing. The temperature and flux changes in the Urals and in Karelia differ in chronology. In the Urals, the maximum heat flux was reached at 10 ka, and in Karelia, at 14 ka. These differences might be due to the fact that the thermal diffusivity of rocks in the Ural superdeep borehole SG-4 was taken equal to a = 1.0 × 10–6 m2/s (Demezhko and Shchapov, 2001) and that in the Onega parametric borehole, to a = 0.75 × 10–6 m2/s (Demezhko et al., 2013). The choice of the thermal diffusivity coefficient is often very subjective because of the lack of experimental data, which leads to serious uncertainties in the assessment of the chronology of reconstructed events. More reasonable tie of the reconstructions to the time scale is possible on the assumption that the heat flux changes are related to radiative forcing. The Pleistocene glacial–interglacial climatic variations were caused by an insolation change related to variations in the eccentricity, inclination of the Earth’s orbit, and precession of the Earth’s axis. Figure 2 shows a theoretical curve for the average annual insolation I for 60º N in the last 40 kyr (Berger and Loutre, 1991). In the period 24–5 ka it correlates well with the reconstructed heat flux for Karelia. The absence of a peak at ~35 ka on the reconstructed curve is due to the natural limitations of the geothermal method, namely, the loss in its resolution power when following backward in the past (Demezhko and Shchapov, 2001). The ratio of the amplitudes of the heat flux and insolation changes is Δq/ΔI = 1.1%. The maximum correlation between the reconstructed Ural heat flux and insolation is reached when the initial thermal
D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475
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Fig. 2. Comparison of the insolation changes I(t) (1) at 60º N (Berger and Loutre, 1991) and the reconstructed changes in ground surface heat flux, q(0, t), in Karelia (2) and in the Urals (3, 4). Curve 3 corresponds to the thermal diffusivity of rocks equal to a = 1.0 × 10–6 m2/s, and curve 4, to a = 0.7 × 10–6 m2/s (E = 3.0 × 103 J/(m2⋅K⋅s1/2)).
Fig. 1. Temperature (T(0, t), solid lines) and heat (q(0, t), dashed lines) histories of the Earth’s surface in the Urals (a) and in Karelia (b). Calculation conditions: a = 1.0 × 10–6 m2/s, λ = 2.5 W/(m⋅K), E = 2.5 × 103 J/(m2⋅K⋅s1/2) (Urals); a = 0.75 × 10–6 m2/s, λ = 2.5 W/(m⋅K), E = 2.9 × 103 J/(m2⋅K⋅s1/2) (Karelia).
diffusivity decreases by 30% to a = 0.7 × 10–6 m2/s (Fig. 2). This correction shifts the curve q(0, t) further to the past, and its amplitude increases to 0.09 W/m2 as a result of the increased thermal effusivity related to the thermal-diffusivity decrease. The ratio of the amplitudes of the heat flux and insolation changes is Δq/ΔI = 0.8%. The consistent insolation and heat flux changes indicate that the changes in the Earth’s surface temperature in the period 24–5 ka were determined mainly by the orbital factors. However, only about 1% extra radiation has been spent for the Earth’s heat content increase. In Karelia, the heat content in this period increased by 4.1 × 1010 J/m2, and in the Urals, by 2.9 × 1010 J/m2. These estimates characterize the amount of heat adsorbed in the rock column with a cross section of 1 m2, limited in vertical by the depth of propagation of the Pleistocene–Holocene warming anomaly of about 2 km. For comparison, at the stationary geothermal heat flow of 0.040– 0.045 W/m2 in the studied areas (Golovanova et al., 2008; Majorowicz and Wybraniec, 2011), the lithospheric heat loss in this period was (2.4–2.7) × 1010 J/m2, which, however, was compensated by the inner heat sources. Thus, the energy effect of warming at the Pleistocene/Holocene boundary is commensurate with the generation of heat by the inner Earth’s sources, mostly, radioactive ones. In models of the Earth’s energy balance, the reconstructed heat flux is described as the difference q = QN – QH – QE, where QN is net radiation at the Earth’s surface and QH and
QE are sensible and latent heat fluxes, respectively. The flux value is usually estimated as a portion of net radiation flux. For the annual cycle it is 3–30% (Choudhury et al., 1987; Krapez et al., 2009) and is determined by the value of the parameter LAI (leaf area index). Our estimates Δq/ΔI ≈ 1% are even lower, since they take into account the portion of the energy that passed through the atmosphere and transformed in it. It is also of interest to compare the geothermal reconstructions of temperatures and heat fluxes with data on changes in CO2 content in the Antarctic ice cores (Barnola et al., 2003; Blunier et al., 1998; Pedro et al., 2012). Usually, data on the changes in CO2 content during the last deglaciation are compared with the global or hemispheric temperatures to assess the cause–effect relationship between these factors (Shakun et al., 2012, and references therein). If the increase in CO2 content is faster than the temperature growth, this indicates the existence of an additional forcing caused by the greenhouse effect in the warming mechanism. In contrast, the faster temperature growth points to the subordinate role of carbon dioxide in the warming. In our opinion, the conclusions drawn from such comparisons are rather unreliable because the estimated CO2 content as well as the estimated age of air bubbles obtained by different authors are strongly different. To confirm the hypothesis of the primacy of CO2 and the greenhouse effect, it would be more logical to compare these data not with temperatures but with heat flux changes. Figure 3 shows the average (over the Urals and Karelia) T(0, t) and q(0, t) curves together with data on the changes in CO2 content. Comparison of the curves shows that the changes in CO2 content are much closer in shape and chronology to temperature changes than to the heat flux changes. The increase in heat flux started earlier and proceeded at a higher rate; at 12 ka, the heat flux began to decrease. The CO2 content increased till 10 ka nearly with the same rate as the
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D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475
Fig. 3. Comparison of the average changes in ground surface temperature (1) and heat flux (2) in the Urals and in Karelia and the changes in CO2 content in the Antarctic ice cores (3–5): 3, (Blunier et al., 1998); 4, (Barnola et al., 2003); 5, (Pedro et al., 2012).
temperature growth. These differences are clearly seen even despite the uncertainties in the estimates of CO2 content. If the greenhouse effect caused by the increase in CO2 content played a significant role in the Pleistocene–Holocene warming, this would inevitably affect the shape of the heat flux curve. The latter, however, reflects only the changes in the average annual insolation. The performed studies confirmed the high paleoclimatic information provided by the geothermal data and proposed a new tool for climatic analysis. We have first reconstructed changes in ground surface heat flux during the last, most global, natural restructuring of the climatic system at the Pleistocene/Holocene boundary. These data indicate that the warming was mainly due to the external (orbital) factors. This work was supported by grant 13-05-00724-a from the Russian Foundation for Basic Research.
References Barnola, J.-M., Raynaud, D., Lorius, C., Barkov, N.I., 2003. Historical CO2 record from the Vostok ice core, in: Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. Beltrami, H., 2001. Surface heat flux histories from geothermal data: inferences from inversion. Geophys. Res. Lett. 28 (4), 655–658. Beltrami, H., Smerdon, J., Pollack, H., Huang, S., 2002. Continental heat gain in the global climate system. Geophys. Res. Lett. 29 (8), doi:10.1029/ 2001GL014310. Berger, A., Loutre, M.F., 1991. Insolation values for the climate of the last 10 million years. Quat. Sci. Rev. 10 (4), 297–317.
Blunier, T., Chappellaz, J., Schwander, J., Dällenbach, A., Stauffer, B., Stocker, T., Raynaud, D., Jouzel, J., Clausen, H.B., Hammer, C.U., Johnsen, S.J., 1998. Asynchrony of Antarctic and Greenland climate change during the last glacial period. Nature 394, 739–743. Cermak, V., 1971. Underground temperature and inferred climatic temperature of the past millennium. Palaeogeogr. Palaeoclim. Palaeoecol. 10, 1– 19. Choudhury, B.J., Idso, S.B., Reginato, R.J., 1987. Analysis of an empirical model for soil heat flux under a growing wheat crop for estimating evaporation by an infrared-temperature based energy balance equation. Agric. For. Meteorol. 39, 283–297. Dahl-Jensen, D., Mosegaard, K., Gundestrup, N., Clow, G.D., Johnsen, S.J., Hansen, A.W., Balling, N., 1998. Past temperatures directly from the Greenland Ice Sheet. Science 282, 268–271. Demezhko, D.Yu., Golovanova, I.V., 2007. Climatic changes in the Urals over the past millennium—an analysis of geothermal and meteorological data. Climate of the Past 3, 237–242. Demezhko, D.Yu., Shchapov, V.A., 2001. 80,000 years ground surface temperature history inferred from the temperature-depth log measured in the superdeep hole SG-4 (the Urals, Russia). Global Planet. Change 29 (1–2), 219–230. Demezhko, D.Yu., Gornostaeva, A.A., Tarkhanov, G.V., Esipko, O.A., 2013. Ground surface temperature reconstruction over the last 30,000 years from the Onega parametric-borehole temperature data. Geofizicheskie Issledovaniya 14 (2), 38–48. Golovanova, I.V., Puchkov, V.N., Sal’manova, R.Y., Demezhko, D.Y., 2008. A new version of the heat flow map of the Urals with paleoclimatic corrections. Dokl. Earth Sci. 422 (1), 1153–1156. Krapez, J.-C., Oliosob, A., Coudertc, B., 2009. Comparison of three methods based on the Temperature–NDVI diagram for soil moisture characterization. Proc. SPIE 7472, 74720Y, 1–12, doi: 10.1117/12.830451. Krenke, A.N., Chernavskaya, M.M., Brázdil, R., Rauner, Yu.L., Zolotokrylin, A.N., 1995. The European Climatic Variability in the Historical Past [in Russian]. Nauka, Moscow. Lachenbruch, A.H., Marshall, B.V., 1986. Changing climate: geothermal evidence from permafrost in the Alaskan Arctic. Science 234, 689–696.
D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475 Majorowicz, J., Wybraniec, S., 2011. New terrestrial heat flow map of Europe after regional paleoclimatic correction application. Int. J. Earth Sci. 100 (4), 881–887. Majorowicz, J., Safanda, J., Skinner, W., 2002. East to west retardation in the onset of the recent warming across Canada inferred from inversions of temperature logs. J. Geoph. Res. 107 (B10), 2227, doi:10.1029/2001 JB000519. Pedro, J.B., Rasmussen, S.O., van Ommen, T.D., 2012. Tightened constraints on the time-lag between Antarctic temperature and CO2 during the last
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deglaciation. Climate of the Past 8, 1213–1221, doi:10.5194/cp-8-12132012. Pollack, H.N., Huang, S., Shen, P.Yu., 1998. Climate change record in subsurface temperatures: a global perspective. Science 282, 279–281. Shakun, J.D., Clark, P.U., He, F., Marcott, S.A., Mix, A.C., Liu, Z., Otto-Bliesner, B., Schmittner, A., Bard, E., 2012. Global warming preceded by increasing carbon dioxide concentrations during the last deglaciation. Nature 484 (7392), 49–54. Wang, J., Bras, R.L., 1999. Ground heat flux estimated from surface soil temperature. J. Hydrol. 216 (3–4), 214–226.
Editorial responsibility: A.D. Duchkov
ScienceDirect Russian Geology and Geophysics 55 (2014) 1471–1475 www.elsevier.com/locate/rgg
Reconstructions of long-term ground surface heat flux changes from deep-borehole temperature data D.Yu. Demezhko *, A.A. Gornostaeva Institute of Geophysics, Ural Branch of the Russian Academy of Sciences, ul. Amundsena 100, Yekaterinburg, 620016, Russia Received 22 July 2013; accepted 11 October 2013
Abstract Based on analysis of geothermal data from the Ural superdeep borehole (SG-4) and Onega parametric borehole, the first reconstructions of ground surface heat flux changes for the last 40 kyr have been made. The increase in heat flux during the Pleistocene–Holocene warming (20–10 ka) proceeded ~2 kyr earlier than the growth in surface temperature; reaching the maximum value of 0.08–0.13 W/m2 at ~13 ka, the heat flux was reduced. The coordinated changes in heat flux and average annual insolation at 60º N at 5–24 ka indicate that the orbital factors were the main cause of climatic changes in this period. The correlations between the changes in heat flux and CO2 content in the Antarctic ice cores and the temperature changes are analyzed. © 2014, V.S. Sobolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. Keywords: geothermy; paleoclimatic reconstructions; heat flux; energy balance of the Earth’s surface; Pleistocene; Holocene; Urals; Karelia
Introduction Geothermal reconstructions of the ground surface temperature history have long been used in the paleoclimatological methods (Cermak, 1971; Dahl-Jensen et al., 1998; Demezhko and Golovanova, 2007; Lachenbruch and Marshall, 1986; Majorowicz et al., 2002; Pollack et al., 1998). They are based on analysis of the present-day distribution of rock temperatures throughout a borehole and on the solution of heat equation with respect to the upper boundary condition—changes in the ground surface temperature. The reconstructions give an idea of the long-period components of temperature fluctuations, which are poorly reproduced (or are not reproduced at all) by other proxies (Krenke et al., 1995). This problem admits another boundary condition—ground surface heat flux changes. Reconstructions of long-period variations in climatecaused heat flux are of crucial importance for estimating the energy of climatic processes and the factors determining the natural and anthropogenic components of climatic variations. The climate-caused variations in heat flux, in contrast to geothermal heat flow, lead to variations in lithospheric heat content. These fluxes, together with net radiation and radiant sensible and latent heat fluxes, form the energy balance of the planet. * Corresponding author. E-mail address: [email protected] (D.Yu. Demezhko)
Despite the urgency of this problem, there are still only a few publications implementing the above approach. This research problem was put forward earlier, the ways of its solution were proposed, reconstructions of the heat flux were made, and the heat content in the upper lithosphere in the period from several centuries (Northern Hemisphere) to thousand years ago (Eastern Canada) was estimated (Beltrami, 2001; Beltrami et al., 2002). It is obvious that these few studies do not show the method potentialities in full measure. A considerable part of the existing borehole temperatures database has not been analyzed. Changes in heat flux and in the heat content of rocks in the period of global restructuring of the climatic system at the Holocene/Pleistocene boundary (~10 ka) have not been studied. In this paper we make the first reconstructions of ground surface heat flux changes for the last 40 kyr, based on analysis of geothermal data from the Ural superdeep borehole (SG-4) and Onega parametric borehole.
Methods Reconstruction of the ground surface temperature history from borehole temperatures (inversion) is based on the solution of nonstationary one-dimensional heat equation in a homogeneous or horizontally layered medium in the absence of heat sources and convective factors of heat transfer.
1068-7971/$ - see front matter D 201 4 , V . S. So bolev IGM, Siberian Branch of the RAS. Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.rgg.2014.11.011
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D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475
Fluctuations in surface temperature T(z = 0, t), where z is depth and t is time, are specified as a boundary condition in the form of a sum of simple functions (harmonic oscillations, step, and linear temperature change), for which the heat equation has an explicit solution. Since this solution is linear with respect to the unknown parameters of the boundary condition, we can make an equation containing m + 2 unknown parameters (m parameters of the temperature history, initial temperature, and unperturbed temperature gradient) for each point of the temperature profile. In this case, the inversion problem is reduced to the solution of a system of linear equations and is formulated as a search for a set of the parameter values that would provide the least discrepancy between the observed and model temperatures in the specified metrics. The known methods of inversion of geothermal data differ in the ways of specifying functions approximating the temperature history and in the way of solution of ill-posed problems. For this purpose, various methods are used to limit the family of equivalent solutions, which are based on the involvement of additional information, smoothing, and restriction of the amplitudes of temperatures to be reconstructed. Heat flux q(z = 0, t) can also be specified as a surface boundary condition. The techniques of the thermal-history reconstruction are similar to the techniques of temperature reconstruction. There is a functional relationship between the two solutions, with respect to temperature and flux. In the simplest case of the specified harmonic temperature oscillations with amplitude A, frequency ω, and initial phase ϕ at the surface, T (0, t) = A sin (ωt + ϕ),
(1)
the propagation of temperature waves in a homogeneous half-space with thermal diffusivity a is described by the expression ⎯⎯⎯⎯⎯ ω / 2a . T (z, t) = A e−kz sin (ωt − kz + ϕ), k = √
(2)
Differentiating (2) with respect to z, we find the change in ground surface heat flux q: q (0, t) = − λ
⎛ ⎪ ∂ = AE √ ⎯⎯ω sin ⎜ωt + ϕ + T (z, t)⎪ ∂z ⎝ ⎪z = 0
π⎞ 4 ⎟⎠
π⎞ ⎛ =E√ (3) ⎯⎯ω T ⎜0, t + ⎟ , 4⎠ ⎝ where λ is the thermal conductivity and E is the thermal effusivity (thermal inertia) of the medium, expressed via thermal conductivity, thermal diffusivity, and volumetric heat capacity of rocks, ρC: E = (λρC)1/2 = λ/(a)1/2 = ρC(a)1/2. The heat flux changes are ahead of temperature changes by π/4, i.e., one-eighth of the oscillation period. The physical meaning of this shift is clear: It is the flux changes that determine the temperature change, and not vice versa. These relationships describe well the diurnal temperature fluctuations at the Earth’s surface under the effect of varying insolation. The maximum insolation falls on the solar noon, and the maximum surface temperature is observed ~3 hours later. Note that E, despite its second name “thermal inertia”, defines not the
temperature lag but only the ratio between the amplitudes of the flux and temperature oscillations. General integral relation between the changes in surface temperature and heat flux was obtained by Wang and Bras (1999). Beltrami et al. (2002) presented its finite-difference approximation for the case when the temperature history is expressed by a continuous piecewise linear function defined at the nodes of a uniform grid: q (0, ti) =
2E
i
∑
⎯⎯⎯ ⎡Tj − Tj−1⎤ ⋅ ⎡√ ⎯⎯⎯⎯⎯⎯⎯⎯ i −⎯ j ⎤ . i − (j − 1) − √ ⎦ ⎦ ⎣
πΔ ⎯⎯⎯ √ ⎯tj=1 ⎣
(4)
Here, T is the surface temperature specified at regular intervals Δt, ti = iΔt, i = 1...n, j = 1...i. This formula is conveniently used when it is necessary to assess the thermal ground surface history from earlier reconstructed temperature histories.
Results and discussion Figure 1 shows reconstructions of the ground surface thermal history in the Urals and in Karelia, made using formula (4) and the results of our earlier temperature history reconstructions (Demezhko and Shchapov, 2001; Demezhko et al., 2013). The shapes of the curves T(0, t) and q(0, t) differ considerably. Changes in heat flux precede changes in the surface temperature, reaching a maximum (0.08–0.13 W/m2) at the time of the maximum rate of warming and then decreasing. The temperature and flux changes in the Urals and in Karelia differ in chronology. In the Urals, the maximum heat flux was reached at 10 ka, and in Karelia, at 14 ka. These differences might be due to the fact that the thermal diffusivity of rocks in the Ural superdeep borehole SG-4 was taken equal to a = 1.0 × 10–6 m2/s (Demezhko and Shchapov, 2001) and that in the Onega parametric borehole, to a = 0.75 × 10–6 m2/s (Demezhko et al., 2013). The choice of the thermal diffusivity coefficient is often very subjective because of the lack of experimental data, which leads to serious uncertainties in the assessment of the chronology of reconstructed events. More reasonable tie of the reconstructions to the time scale is possible on the assumption that the heat flux changes are related to radiative forcing. The Pleistocene glacial–interglacial climatic variations were caused by an insolation change related to variations in the eccentricity, inclination of the Earth’s orbit, and precession of the Earth’s axis. Figure 2 shows a theoretical curve for the average annual insolation I for 60º N in the last 40 kyr (Berger and Loutre, 1991). In the period 24–5 ka it correlates well with the reconstructed heat flux for Karelia. The absence of a peak at ~35 ka on the reconstructed curve is due to the natural limitations of the geothermal method, namely, the loss in its resolution power when following backward in the past (Demezhko and Shchapov, 2001). The ratio of the amplitudes of the heat flux and insolation changes is Δq/ΔI = 1.1%. The maximum correlation between the reconstructed Ural heat flux and insolation is reached when the initial thermal
D.Yu. Demezhko and A.A. Gornostaeva / Russian Geology and Geophysics 55 (2014) 1471–1475
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Fig. 2. Comparison of the insolation changes I(t) (1) at 60º N (Berger and Loutre, 1991) and the reconstructed changes in ground surface heat flux, q(0, t), in Karelia (2) and in the Urals (3, 4). Curve 3 corresponds to the thermal diffusivity of rocks equal to a = 1.0 × 10–6 m2/s, and curve 4, to a = 0.7 × 10–6 m2/s (E = 3.0 × 103 J/(m2⋅K⋅s1/2)).
Fig. 1. Temperature (T(0, t), solid lines) and heat (q(0, t), dashed lines) histories of the Earth’s surface in the Urals (a) and in Karelia (b). Calculation conditions: a = 1.0 × 10–6 m2/s, λ = 2.5 W/(m⋅K), E = 2.5 × 103 J/(m2⋅K⋅s1/2) (Urals); a = 0.75 × 10–6 m2/s, λ = 2.5 W/(m⋅K), E = 2.9 × 103 J/(m2⋅K⋅s1/2) (Karelia).
diffusivity decreases by 30% to a = 0.7 × 10–6 m2/s (Fig. 2). This correction shifts the curve q(0, t) further to the past, and its amplitude increases to 0.09 W/m2 as a result of the increased thermal effusivity related to the thermal-diffusivity decrease. The ratio of the amplitudes of the heat flux and insolation changes is Δq/ΔI = 0.8%. The consistent insolation and heat flux changes indicate that the changes in the Earth’s surface temperature in the period 24–5 ka were determined mainly by the orbital factors. However, only about 1% extra radiation has been spent for the Earth’s heat content increase. In Karelia, the heat content in this period increased by 4.1 × 1010 J/m2, and in the Urals, by 2.9 × 1010 J/m2. These estimates characterize the amount of heat adsorbed in the rock column with a cross section of 1 m2, limited in vertical by the depth of propagation of the Pleistocene–Holocene warming anomaly of about 2 km. For comparison, at the stationary geothermal heat flow of 0.040– 0.045 W/m2 in the studied areas (Golovanova et al., 2008; Majorowicz and Wybraniec, 2011), the lithospheric heat loss in this period was (2.4–2.7) × 1010 J/m2, which, however, was compensated by the inner heat sources. Thus, the energy effect of warming at the Pleistocene/Holocene boundary is commensurate with the generation of heat by the inner Earth’s sources, mostly, radioactive ones. In models of the Earth’s energy balance, the reconstructed heat flux is described as the difference q = QN – QH – QE, where QN is net radiation at the Earth’s surface and QH and
QE are sensible and latent heat fluxes, respectively. The flux value is usually estimated as a portion of net radiation flux. For the annual cycle it is 3–30% (Choudhury et al., 1987; Krapez et al., 2009) and is determined by the value of the parameter LAI (leaf area index). Our estimates Δq/ΔI ≈ 1% are even lower, since they take into account the portion of the energy that passed through the atmosphere and transformed in it. It is also of interest to compare the geothermal reconstructions of temperatures and heat fluxes with data on changes in CO2 content in the Antarctic ice cores (Barnola et al., 2003; Blunier et al., 1998; Pedro et al., 2012). Usually, data on the changes in CO2 content during the last deglaciation are compared with the global or hemispheric temperatures to assess the cause–effect relationship between these factors (Shakun et al., 2012, and references therein). If the increase in CO2 content is faster than the temperature growth, this indicates the existence of an additional forcing caused by the greenhouse effect in the warming mechanism. In contrast, the faster temperature growth points to the subordinate role of carbon dioxide in the warming. In our opinion, the conclusions drawn from such comparisons are rather unreliable because the estimated CO2 content as well as the estimated age of air bubbles obtained by different authors are strongly different. To confirm the hypothesis of the primacy of CO2 and the greenhouse effect, it would be more logical to compare these data not with temperatures but with heat flux changes. Figure 3 shows the average (over the Urals and Karelia) T(0, t) and q(0, t) curves together with data on the changes in CO2 content. Comparison of the curves shows that the changes in CO2 content are much closer in shape and chronology to temperature changes than to the heat flux changes. The increase in heat flux started earlier and proceeded at a higher rate; at 12 ka, the heat flux began to decrease. The CO2 content increased till 10 ka nearly with the same rate as the
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Fig. 3. Comparison of the average changes in ground surface temperature (1) and heat flux (2) in the Urals and in Karelia and the changes in CO2 content in the Antarctic ice cores (3–5): 3, (Blunier et al., 1998); 4, (Barnola et al., 2003); 5, (Pedro et al., 2012).
temperature growth. These differences are clearly seen even despite the uncertainties in the estimates of CO2 content. If the greenhouse effect caused by the increase in CO2 content played a significant role in the Pleistocene–Holocene warming, this would inevitably affect the shape of the heat flux curve. The latter, however, reflects only the changes in the average annual insolation. The performed studies confirmed the high paleoclimatic information provided by the geothermal data and proposed a new tool for climatic analysis. We have first reconstructed changes in ground surface heat flux during the last, most global, natural restructuring of the climatic system at the Pleistocene/Holocene boundary. These data indicate that the warming was mainly due to the external (orbital) factors. This work was supported by grant 13-05-00724-a from the Russian Foundation for Basic Research.
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Editorial responsibility: A.D. Duchkov