The Post-Glacial Warming Signal in Heat Flow IUGG Perugia, It, 6/7/2007 Will Gosnold and Jacek Majorowicz University of North Dakota Grand Forks, ND USA

Outline Introduction to the problem The signal is subtle and difficult to detect Test of warming signals Impact on heat flow and crustal temperature analyses Summary

Introduction Much of our understanding of the thermal state of Earth’s crust derives from a mere scratch of the surface. Most direct measurements of the temperature distribution in the continents come from boreholes less than 500 m deep. Fewer than 4 percent of heat flow measurements in North America and only slightly more than 14 percent of all continental heat flow measurements were made at depths greater than 2 km.

20,201 heat flow sites recognized by the International Heat Flow Commission

How then, one might ask, is it that we can use this “scratch of the surface” to calculate temperature profiles for the crust and to confidently apply these calculations in a variety of geological, geochemical and geophysical investigations? We assume the thermal state of the crust is conductive, in thermal equilibrium, and that we know with reasonable certainty the thermal properties of the rocks that comprise the crust. In general, these assumptions are valid for the deeper part of the crust, and heat flow researchers take precautions to avoid non- conductive regimes and transient disturbances in the near-surface measurements.

What if the heat flow data acquired from shallow boreholes contain a systematic error? Would the error lead to inaccurate projections of temperatures deeper in the crust?

Recent heat flow studies in Europe and Russia lead us to hypothesize that post- glacial warming in northern hemisphere continents may have been of the order of 10° to15° C rather than 3° to 5° C as is generally accepted in terrestrial heat flow research. If this hypothesis is correct, some northern hemisphere heat flow values may require revision by as much as 30 to 60 percent. A significant challenge is that the signal is difficult to detect and to quantify.

Conductive heat flow at the surface is described by Fourier’s Law of heat conduction and common practice is to use a portion of the T-z profile in which the gradient is linear for heat flow calculations. q = 70 mW m -2 λ= 1.3 W/m/K

The effect of postglacial warming on the thermal gradient is subtle.

100 – 200 m 200 – 300 m 300 – 400 m 400 – 500 m 500 – 600 m 600 – 700 m How detectable is the disturbance to the temperature gradient? ΔT-z for a 15º temperature change at 10 ka Answer: Not at all! y = x R 2 = y = x R 2 = y = x R 2 = y = x R 2 = y = x R 2 = y = x R 2 = Suppose we calculate a linear least squares fit to the temperature gradient at 100 meter intervals. Will the postglacial warming signal be detected?

Revision of some data may be needed even if warming at the end of the last glaciation was only 3 to 5 °C. This range of warming may be appropriate globally, but we now know that the temperature trends associated with climate change increase toward the poles. For example global temperatures have warmed about 1°C during the past century, but high latitude temperatures (e.g.,Alaska) have warmed by up to 5 °C. Could we determine an appropriate scale for post glacial warming in high latitudes?

How can the hypothesis be tested? Empirical evidence from existing sites. Data from deep boreholes in which continuous temperature logs can be matched with continuous thermal conductivity measurements.

Empirical evidence for large magnitude postglacial warming T-z measurements in parts of Europe and North America show a systematic increase in heat flow with depth.

Heat flow increases with depth in Europe

Heat flow increases with depth in the North American craton

Empirical evidence for large magnitude postglacial warming Heat flow in southern hemisphere shields averages approximately 61.4 mWm -2, but heat flow in northern hemisphere shields averages 37 mWm -2.

Differences by Craton Brazil 64.8 ± ? mW m -2 (86) Africa52.3 ± ? mW m -2 (145) Australia 68.1 ± ? mW m -2 (157) N. America 33.1 ± ? mW m -2 (315) Fennoscandia and East European Craton mW m -2 (1,352)

Optimum sites would be in periglacial regions in rocks having minimal variability in λ.

The Tertiary and Upper Cretaceous sections of the Williston basin consist of continuously deposited marine shales. These units have a thermal conductivity of 1.1 to 1.2 W/m/K.

Theoretical and empirical studies suggest that as porosity is reduced by compaction, thermal conductivity increases. If heat flow is constant, the temperature gradient should decrease with depth and the T-z curve should be convex up.

LSQ analyses of 200 m segments of a temperature log from the Williston basin all appear linear. The geothermal gradient increases systematically with depth. The surface intercept on the temperature scale decreases systematically with depth. Does the change in surface temperature show the amount of warming that has occurred at the surface? If so, the minimum warming has been at least 12 K.

Three T-z profiles from the Williston basin exhibit an increase in heat flow with depth. The synthetic T-z shows an expected profile for constant heat flow with the effects of compaction on thermal conductivity. The 15 degree signal is a modeled curve for warming since 10 ka. The Glacx curve results from superposition of 3 glacial/interglacial cycles (90 ka/10) ka warming signal on the steady-state synthetic T-z. It appears to match closely the observed T-z profiles.

Detection of the signal from variable conductivity strata is more difficult.

Curve fits to six sites in periglacial regions in North America

Knowledge of Earth’s internal temperature is applied in a variety of geological, geochemical and geophysical investigations including but not limited to: Geodynamics Tectonics Rheology Seismology Curie Temperature Groundwater Flow Radioactive Waste Petrology Mineralogy Volcanology Geothermal Energy Maturation of Oil and Gas Reservoirs Paleoclimatology

Percentage of q vs. depth as a result of warming

Summary Evidence for large magnitude post-glacial warming in northern Europe and Asia is growing. Some North American sites show indications of large magnitude post- glacial warming. Many northern hemisphere heat flow values may require revision by as much as 60 percent because they were determined from boreholes too shallow for recognition of the gradient disturbance caused by a large post-glacial warming signal. The hypothesis requires further testing with data from deep boreholes in periglacial regions. If the hypothesis holds, can a general correction to heat flow measurements be determined?

Low heat flow in North American craton Mareschal and Jaupart (2004)

Low heat flow in North America (Blackwell and Richards, 2004). Note that the low heat flow area in the Canadian Shield is coincident with the center of the Wisconsinan ice sheet.