# Earth's internal heat budget

Global map of the flux of heat, in mW/m2, from Earth's interior to the surface.[1] The largest values of heat flux coincide with mid ocean ridges, and the smallest values of heat flux occur in stable continental interiors.

Earth's internal heat budget is fundamental to the thermal history of the Earth. The flow of heat from Earth's interior to the surface is estimated at ${\displaystyle 47\pm 2}$ terawatts (TW)[1] and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of the Earth.[2]

Earth's internal heat powers most geological processes[3] and drives plate tectonics.[2] Despite its geological significance, this heat energy coming from Earth's interior is actually only 0.03% of Earth's total energy budget at the surface, which is dominated by 173,000 TW of incoming solar radiation.[4] The insolation that eventually, after reflection, reaches the surface penetrates only several tens of centimeters on the daily cycle and only several tens of meters on the annual cycle. This renders solar radiation minimally relevant for internal processes.[5]

## Heat and early estimate of Earth's age

Based on calculations of Earth's cooling rate, which assumed constant conductivity in the Earth's interior, in 1862 William Thomson (later made Lord Kelvin) estimated the age of the Earth at 98 million years,[6] which contrasts with the age of 4.5 billion years obtained in the 20th century by radiometric dating.[7] As pointed out by John Perry in 1895[8] a variable conductivity in the Earth's interior could expand the computed age of the Earth to billions of years, as later confirmed by radiometric dating. Contrary to the usual representation of Kelvin's argument, the observed thermal gradient of the Earth's crust would not be explained by the addition of radioactivity as a heat source. More significantly, mantle convection alters how heat is transported within the Earth, invalidating Kelvin's assumption of purely conductive cooling.

## Global internal heat flow

Cross section of the Earth showing its main divisions and their approximate contributions to Earth's total internal heat flow to the surface, and the dominant heat transport mechanisms within the Earth.

Estimates of the total heat flow from Earth’s interior to surface span a range of 43 to 49 terawatts (TW) (a terawatt is 1012 watts).[9] One recent estimate is 47 TW,[1] equivalent to an average heat flux of 91.6 mW/m2, and is based on more than 38,000 measurements. The respective mean heat flows of continental and oceanic crust are 70.9 and 105.4 mW/m2.[1]

While the total internal Earth heat flow to the surface is well constrained, the relative contribution of the two main sources of Earth's heat, radiogenic and primordial heat, are highly uncertain because their direct measurement is difficult. Chemical and physical models give estimated ranges of 15–41 TW and 12–30 TW for radiogenic heat and primordial heat, respectively.[9]

The structure of the Earth is a rigid outer crust that is composed of thicker continental crust and thinner oceanic crust, solid but plastically flowing mantle, a liquid outer core, and a solid inner core. The fluidity of a material is proportional to temperature; thus, the solid mantle can still flow on long time scales, as a function of its temperature[2] and therefore as a function of the flow of Earth's internal heat. The mantle convects in response to heat escaping from Earth's interior, with hotter and more buoyant mantle rising and cooler, and therefore denser, mantle sinking. This convective flow of the mantle drives the movement of Earth's lithospheric plates; thus, an additional reservoir of heat in the lower mantle is critical for the operation of plate tectonics and one possible source is an enrichment of radioactive elements in the lower mantle.[10]

Earth heat transport occurs by conduction, mantle convection, hydrothermal convection, and volcanic advection.[11] Earth's internal heat flow to the surface is thought to be 80% due to mantle convection, with the remaining heat mostly originating in the Earth's crust,[12] with about 1% due to volcanic activity, earthquakes, and mountain building.[2] Thus, about 99% of Earth's internal heat loss at the surface is by conduction through the crust, and mantle convection is the dominant control on heat transport from deep within the Earth. Most of the heat flow from the thicker continental crust is attributed to internal radiogenic sources, in contrast the thinner oceanic crust has only 2% internal radiogenic heat.[2] The remaining heat flow at the surface would be due to basal heating of the crust from mantle convection. Heat fluxes are negatively correlated with rock age,[1] with the highest heat fluxes from the youngest rock at mid-ocean ridge spreading centers (zones of mantle upwelling), as observed in the global map of Earth heat flow.[1]

The evolution of Earth's radiogenic heat flow over time.

An estimate of the present-day major heat-producing isotopes[2]
Isotope Heat release
W/kg isotope
Half-life
years
Mean mantle concentration
kg isotope/kg mantle
Heat release
W/kg mantle
238U 94.6×10−6 4.47×109 30.8×10−9 2.91×10−12
235U 569×10−6 0.704×109 0.22×10−9 0.125×10−12
232Th 26.4×10−6 14.0×109 124×10−9 3.27×10−12
40K 29.2×10−6 1.25×109 36.9×10−9 1.08×10−12

Geoneutrino detectors can detect the decay of 238U and 232Th and thus allow estimation of their contribution to the present radiogenic heat budget, while 235U and 40K is not detectable. Regardless, 40K is estimated to contribute 4 TW of heating.[17] However, due to the short half-lives the decay of 235U and 40K contributed a large fraction of radiogenic heat flux to the early Earth, which was also much hotter than at present.[10] Initial results from measuring the geoneutrino products of radioactive decay from within the Earth, a proxy for radiogenic heat, yielded a new estimate of half of the total Earth internal heat source being radiogenic,[17] and this is consistent with previous estimates.[16]

## Primordial heat

Primordial heat is the heat lost by the Earth as it continues to cool from its original formation, and this is in contrast to its still actively-produced radiogenic heat. The Earth core's heat flow—heat leaving the core and flowing into the overlying mantle—is thought to be due to primordial heat, and is estimated at 5–15 TW.[18] Estimates of mantle primordial heat loss range between 7 and 15 TW, which is calculated as the remainder of heat after removal of core heat flow and bulk-Earth radiogenic heat production from the observed surface heat flow.[9]

The early formation of the Earth's dense core could have caused superheating and rapid heat loss, and the heat loss rate would slow once the mantle solidified.[18] Heat flow from the core is necessary for maintaining the convecting outer core and the geodynamo and Earth's magnetic field, therefore primordial heat from the core enabled Earth's atmosphere and thus helped retain Earth's liquid water.[16]

## Heat flow and plate tectonics

Earth's tectonic evolution over time from a molten state at 4.5 Ga,[7] to a single-plate lithosphere,[19] to modern plate tectonics sometime between 3.2 Ga[20] and 1.0 Ga.[21]

Controversy over the exact nature of mantle convection makes the linked evolution of Earth's heat budget and the dynamics and structure of the mantle difficult to unravel.[16] There is evidence that the processes of plate tectonics were not active in the Earth before 3.2 billion years ago, and that early Earth's internal heat loss could have been dominated by advection via heat-pipe volcanism.[19] Terrestrial bodies with lower heat flows, such as the Moon and Mars, conduct their internal heat through a single lithospheric plate, and higher heat flows, such as on Jupiter's moon Io, result in advective heat transport via enhanced volcanism, while the active plate tectonics of Earth occur with an intermediate heat flow and a convecting mantle.[19]

## References

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2. Donald L. Turcotte; Gerald Schubert (25 March 2002). Geodynamics. Cambridge University Press. ISBN 978-0-521-66624-4.
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4. ^ Archer, D. (2012). Global Warming: Understanding the Forecast. ISBN 978-0-470-94341-0.
5. ^ Lowrie, W. (2007). Fundamentals of geophysics. Cambridge: CUP, 2nd ed.
6. ^ Thomson, William. (1864). On the secular cooling of the earth, read 28 April 1862. Transactions of the Royal Society of Edinburgh, 23, 157–170.
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