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Temperature: Borehole Temperatures

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We next turn our attention to a very different means of reconstructing the temperature — studies of the temperatures measured in boreholes (i.e., holes drilled into the ground) at various locations around the Earth. The temperature profiles (how temperature changes with depth) for three representative boreholes in eastern Canada are shown in the figure below:

The temperature profiles (how temperature changes with depth) for 3 representative boreholes in eastern Canada
Temperature profiles from three representative boreholes showing the unexpected curvature towards higher temperatures near the tops of the boreholes.
Credit: David Bice

Note that in all three cases, the temperature curves around to higher temperatures near the surface — this reflects a response of soil and bedrock to warming from the atmosphere. In the absence of warming at the surface due to climate change, these temperature profiles would tend to follow the trends represented in the lower few hundreds of meters, and this would intersect the surface at around 3-4°C.

The basic idea here is a surprising one — that the way temperature changes down a borehole at the present time tells us something about how the surface temperature has changed in the past. This is indeed a remarkable and useful reality of some fairly basic physics of heat flow. It also provides us with an excellent way to filter out the “noise” in the climate record and focus on the main trends.

Heat is just a measure of the kinetic or vibrational energy of the atoms in some substance. If something is hot, its atoms are vibrating very fast, and because vibrating atoms affect neighboring atoms, heat can be transmitted; we often talk about this heat transmission as heat flow. Heat flows from hot regions to cold regions and the rate of heat flow is proportional to what we call the thermal gradient — the rate of temperature change with distance. In our case, for distance, we are talking about depth in the Earth, and the center of the Earth is very hot — about 5000°C. The surface, instead, is quite cool at 15°C, so heat from the Earth tends to flow out to the surface, and this process is cooling the Earth very slowly. This situation leads to a geothermal gradient (rate of change of temperature with depth) that tends to be more or less steady at around 20 or 30°C per kilometer. The heat released to the surface is tiny compared to the energy coming from the Sun, so this geothermal heat, on a global basis, does not affect the climate.

When the surface temperature rises and becomes hotter than the temperature just below the surface, heat moves down into the ground, but it does this quite slowly. When the surface temperature becomes colder, heat flows up from the ground, cooling the ground, and this cooling is transmitted downward slowly. This general idea is illustrated schematically in the figure below:

Four graphs showing the variation of temperature with depth above and below the surface at four different times
Schematic illustration of how the temperature below the surface responds to an abrupt increase in the surface temperature.
Credit: David Bice

Each of the four rectangles shows the variation of temperature with depth above and below the surface at different times. At the beginning (Time 1), the temperature below the surface increases steadily, while it is constant above the surface. Then at Time 2, the surface temperature suddenly rises and is hotter than the ground right at the surface. By Time 3, the ground temperature right near the surface warms, but that warming does not penetrate very deeply. At Time 4, the surface temperature has continued to remain high, and the heat flowing down into the ground has reached a greater depth.

This process of thermal diffusion is quite well-known thanks to a famous Frenchman named Joseph Fourier, who in 1822 wrote a seminal treatise on heat flow. Using his theory, we can calculate how the surface temperature history is transmitted downward into the Earth. An example is shown in the figure below for a case where there is a sudden increase in surface temperature of 1°C above a region where the surface temperature was 0°C and the geothermal gradient was 0°C/km (this is clearly not a realistic starting condition, but it makes the calculations simpler).

Graph of downward propagation of a step increase in surface temperature
This figure shows the calculated evolution of the temperature
profile over time, with times in years following a sudden temperature increase.
Credit: David Bice

Here, you can see that after 10 years, the effects of the sudden rise in temperature are felt in the upper 50 meters or so and that as time passes, the depth of penetration increases — about 100 meters after 50 years, and 150 meters after 150 years. The adjustment is slower as time progresses since the key feature that affects the rate of change in temperature is the rate at which the slope of the temperature profile changes; where it changes rapidly, the temperature change over time is also high.

Rocks have a very low thermal conductivity (conductivity is the term used to describe the way heat is transported at the molecular level) compared to many other materials, which means that it can take a long time for rocks underground to respond to changes in surface temperatures. Because of the way that the heat flows through rocks, short-term changes are smoothed out as the heat diffuses through the rocks. This means that the borehole temperature profiles provide information only about changes in the long-term average temperature.

Unlike most other methods for studying paleoclimate, borehole thermometry does not need to be calibrated against the instrumental record. Hence, borehole thermometry provides an independent record of paleoclimate against which other paleoclimate techniques can be validated. Below, we see the results of the analysis of a global data set of borehole temperatures, which give us an estimate of the global temperature change.

Graph comparing the instrumental temp record of Mann et al with the Borehole record of Huang et al
The globally averaged temperature reconstruction for borehole temperature profiles around the world, compared to an instrumental global temperature reconstruction paired with a multi-proxy temperature reconstruction. The temperatures are anomalies relative to the 1961-1990 mean.
Credit: David Bice

Clearly, the shapes of the curves, or the rates of temperature change over this time period, are in close agreement, which is important since they come from very different, independent data sources. The borehole temperature reconstruction does not match the last bit of this time period in part because the measurements begin further down the hole, and many of the measurements were made in the 1980s and 1990s before the instrumental record ends.