I believe the temperature gradient underground is as high as 30°C per kilometer of depth. Thus, it is very warm only 1 kilometer below the Earth's surface. Yet, it is commonly stated that geothermal energy is insignificant to the Earth's surface temperature. How can this be?
11$\begingroup$ 1km of rock is a damn good insulator. Very little energy reaches the surface. $\endgroup$– MichaelMar 17 at 12:44
One kilometer of rock is actually a lot to dig through to get to that very warm condition.
The key quantity here is heat flux. The crux of the matter is:
Geothermal heat flux is only a small fraction of a percent of solar heat flux.
Solar heat flux balance terms are on the order of tens to hundreds of watts per square meter source:
The earth’s surface absorbs 156 W/m² from the sun (as a global average) and emits 55 W/m² long-wave energy to the atmosphere. The atmosphere absorbs 84 W/m² and emits 185 W/m² as longwave radiation to space.
The above figures are from Barry and Chorley, 2003[¹]. The account in Kiehl and Trenberth’s 1997 paper[²] is more complicated, but it can be partially summarized by this picture:
In particular, note that they list:
342 W/m² (341 W/m²) average power hitting the Earth’s atmosphere.
198 W/m² (184 W/m²) average power hitting the Earth’s surface.
168 W/m² (161 W/m²) average power being absorbed by the Earth’s surface.
Bracketed figures are from the Trenberth et al 2009 paper[³].
In contrast, geothermal heat flux is measured in tens of milliwatts per square meter:
Heat flows constantly from its sources within Earth to the surface. Total heat loss from Earth is estimated at 44.2 TW (4.42 × 10¹³ watts).[⁴] Mean heat flow is 65 mW/m² over continental crust and 101 mW/m² over oceanic crust.[⁴] This is 0.087 watt/square metre on average (0.03 percent of solar power absorbed by Earth[⁵]), but is much more concentrated in areas where the lithosphere is thin, such as along mid-ocean ridges (where new oceanic lithosphere is created) and near mantle plumes.[⁶]
R. G. Barry and R. J. Chorley (2003), Atmosphere, Weather and Climate, Routledge, London, 2003.
J. T. Kiehl and Kevin E. Trenberth (1997), "Earth’s annual global mean energy budget", Bull. Amer. Meteor. Soc. 78, 197–208.
K. E. Trenberth, J. T. Fasullo, and J. Kiehl (2009), "Earth’s global energy budget", Bull. Amer. Meteor. Soc. 90, 311–323.
Pollack, Henry N., et.al. (1993) "Heat flow from Earth's interior: Analysis of the global data set", Reviews of Geophysics, 31, 3, p. 273. Archived 2011-08-11 at the Wayback Machine. doi:10.1029/93RG01249
"Climate and Earth's Energy Budget". NASA. 2009-01-14.
Richards, M. A.; Duncan, R. A.; Courtillot, V. E. (1989). "Flood Basalts and Hot-Spot Tracks: Plume Heads and Tails". Science 246 (4926): 103–107. Bibcode:1989Sci...246..103R. doi:10.1126/science.246.4926.103. PMID 17837768. S2CID 9147772.