# Global heat flow

In it's simplist form, the rate of heat flowing out of the Earth is calculated by $$Q = -\lambda \frac{\delta T}{\delta z}$$, where $$\lambda$$ is thermal conductivity, an intrinsic physical property of a given rock type, and $$\delta T$$ the temperature gradient over a given depth interval $$\delta z$$. In this equation $$Q$$ has units $$W m^{-2}$$, however, when referring to geothermal heat flow, it is more typical to report values in $$mW m^{-2}$$ as estimates are more clearly represented in this manner outside of active volcanic zones. The negative sign out front is by convention as heat is determined to flow in the positive direction with decreasing temperature.

For continental heat flow estimates, it is often necessary to take into account the effect of radiogenic heat production due to the presence of elements $$K$$, $$Th$$ and $$U$$ throughout the crust. Our initial heat flow equation can be supplemented to account for this and becomes  $$Q = -\lambda \frac{\delta T}{\delta z} + A$$, where $$A$$ is the contribution to heat flow from the summation of heat generating elements throughout the entire depth interval. When estimating surface heat flow, it is necessary to produce an estimate of heat generation throughout the entire crustal column, a difficult task considering the vertical distribution of heat producing elements throughout the crustal column is relatively unknown and cannot be directly measured. Heat generation can therefore be one of the largest sources of uncertainty when estimating surface heat flow.

The calculation of heat flow therefore requires the measurement of three properties, temperature, $$^\circ K$$, thermal conductivity, $$\lambda$$, and heat generation, $$A$$, which all happen to be stored in the ThermoGlobe database! Obviously there is a lot more to it and books can and have been written on the subject. For anyone interested in learning more about heat flow, we recommend the book Crustal Heat Flow : A Guide to Measurement and Modelling , by Beardsmore and Cull (2001).

## Global Distribution

While most countries around the globe feature at least a handful of measurements, there remains large swathes of the continental surface that are underrepresented in ThermoGlobe. For instance, despite its size, the African continent features only 1439 heat flow estimates (at time of writing) and data is sparse particularly through the central regions. South America is also underrepresented with only 641 estimates, most of which come from Brazil (445 estimates). Antarctica, due it's inaccesibility, is also underrepresented with only 36 estimates. On the other hand, the USA features 15,447 heat flow estimates (over 17,000 including territorial waters!), far more than any other country and almost 1/3 of total continental heat flow estimates! Obviously this has the potential to skew global statistics which is one of the reasons researchers tend to model global heat flow as a grid of weighted averages.

Oceanic heat flow is tightly coupled with the age of the sea floor. This means that heat flow estimates close to mid-ocean ridges, where new oceanic crust is being created and sea floor ages are therefore youngest, will always be higher than estimates away from ridges where crustal age is greater. This would not be a problem if the ocean floor was regularly sampled, however, this is not the case as active tectonic settings tend to attract the majority of research interest. As a result of this, *statistics relating to the largest oceans as a whole should be interpreted and used with caution.

*We are actively working on a better way to visually display heat flow variations throughout the oceans.
See Lucazeau (2019), Analysis and Mapping of an Updated Terrestrial Heat Flow Data Set , for the latest detailed analysis using gridded weighted averages.

## Continental vs Oceanic heat flow

Continental heat flow estimates produce a normalised distribution with a mean of 112 $$mW m^{-2}$$ and a median value of 59 $$mW m^{-2}$$. The elevated mean is due mostly to geothermal areas that skew results to higher values. If we select against these areas by only using heat flow values of $$< 250$$ $$mW m^{-2}$$, we can see the mean drop to a much more reasonable value of 64 $$mW m^{-2}$$. Oceanic heat flow features a far wider range of values thanks mostly to non-conductive processes near mid-ocean ridges resulting in an elevated arithmetic mean of 420 $$mW m^{-2}$$! If this value held true through all of the world's ocean's, the Earth would be losing an enormous amount of heat! The median on the other hand is only 71 $$mW m^{-2}$$ which is far more reasonable. If we go and remove the effect of hydrothermal processes near mid-ocean ridges by limiting oceanic values to $$< 250$$, the resulting median is 64 $$mW m^{-2}$$ and the mean drops to a more realistic value of 79 $$mW m^{-2}$$.

Avoiding hydrothermal effects and geothermal hotspots is a key part of global modelling because they can skew the results by so much. While limiting continental heat flow in the way we have done here is a viable method (the same value was used by Lucazeau (2019)), for continental estimates, other researchers have used ifnormation such as sea floor age, ruggedness, sediment thickness or distance to seamount to avoid the problem.

## Seas & Oceans

This plot features the top 20 sampled seas and ocean by count and sorted by median heat flow value. The Gulf of California, at the top of this list, is one of the more well sampled seas outside the major oceans. It's geological setting is dominated by the northern end of the East Pacific Rise, an extensive mid-ocean ridge that propagtes all the way to the bottom of South America. As a mid-ocean ridge, it naturally features very high heat flow values throughout. Similarly, the Red Sea owes it's origins to the Red Sea Rift which makes up the north-west arm of the Afar Triple Junction in East Africa. Others at the top of this list such as the Eastern China Sea, the Japan Sea and the Phillipine Sea are all related to the complex processes of the subducting Phillipine and Pacific tectonic plates. The general conclusion here is that statistically derived heat flow values for any given sea are largely controlled by the general tectonic environment.

Check out the full descriptive analysis of seas and oceans in tabular format here .

The lower and upper fence (min and max) values on the box plot are caluclated as |(1.5*IQR) plus or minus q1 and q3 respectively. Notchspans are a representation of the confidence interval defined by $$1.57*IQR /sqrt(N)$$ where $$N$$ is the number of measurements.

## Tectonic Environment

Following on, it makes sense then to look at heat flow values with respect to the tectonic environment in which they were measured. In confirmation of the findings above we see that rifts largely make up the higher end of median heat flow while shields and cratons, both representative of tectonically inactive terrains, feature closer to the bottom end of the scale. Of course the level of tectonic activity isn't the only predictor of heat flow. The Gawler Craton in South Australia, which has remained tectonically unaltered for around 1450 Ma, has a mean heat flow of $$87 mW m^{-2}$$, thanks largely to regions of anomalously high heat producing granites and gneisses. Of course this is based on a mere 172 measurements from (presumably) select regions over a large area, however, it highlights the point that tectonic stability (or lack thereof) is not necessarily a reliable indicator of heat flow.

Check out the full descriptive analysis of tectonic environments in tabular format here .

We are working on improving this plot to highly the point more effectively.

## Age Distributions

Age is generally a reliable proxy for oceanic heat flow where a direct relationship is easily defined between the two. On the other hand, continental crust exhibits greater compositional variability, a wider range of potential values across most physical properties and is subject to being thermally "reset" by tectonic processes. For these reasons, age relationships between continental crust and heat flow tend to show a significant dispersion in their underlying data which is why it is necessary to first aggregate the data before summarising it statistically. In the past, people have done so using various maps, in particular, the USGS (1997), Geologic province and thermo‐tectonic age maps . Of course this map is now over 20 years old and fast becoming outdated as more and more data are collected world wide, fortunately, we have access to a newly created and far more detailed map of the worlds geological provinces in that of Hasterok (2021). From this we are able to group our data into geologic timescales by eon, era and period before applying statistical analyses, the results of which are below.

We have made our own interpretations of these plots in our paper which you will be able to read when it is eventually published. We will leave our opinion out of this section though and let you come to your own conclusions. We will however point out a few things related to potentail outliers that are not readily apparent in these plots. Regarding juvenile age data from the Carboniferous, all 131 of these data points are from the West Thompson Orogen in Australia which is completely overlain by the Eromanga Basin and encompasses all of the Cooper Basin, which are some of the most prospective regions in the world for geothermal applications. For the thermotectonic ages, the Ecstasian period features 224 measurements, all of which are from a single province in the US known as the Yavapai terrane and likewise the 90 data points from the Paleozoic are all from the Sydney-Surat province in eastern Australia.

Vertical error bars represent the standard deviation of heat flow values for a given grouping while horizontal bars express the age interval over which the values were aggregated. Size of the circles relates to the count of data points in each group with larger circles representing more data points.