Abstract
Abstract. This paper uses a suite of Earth system models which simulate the distribution of He isotopes and radiocarbon to examine two paradoxes in Earth science, each of which results from an inconsistency between theoretically motivated global energy balances and direct observations. The helium–heat paradox refers to the fact that helium emissions to the deep ocean are far lower than would be expected given the rate of geothermal heating, since both are thought to be the result of radioactive decay in Earth's interior. The isopycnal mixing paradox comes from the fact that many theoretical parameterizations of the isopycnal mixing coefficient ARedi that link it to baroclinic instability project it to be small (of order a few hundred m2 s−1) in the ocean interior away from boundary currents. However, direct observations using tracers and floats (largely in the upper ocean) suggest that values of this coefficient are an order of magnitude higher. Helium isotopes equilibrate rapidly with the atmosphere and thus exhibit large gradients along isopycnals while radiocarbon equilibrates slowly and thus exhibits smaller gradients along isopycnals. Thus it might be thought that resolving the isopycnal mixing paradox in favor of the higher observational estimates of ARedi might also solve the helium paradox, by increasing the transport of mantle helium to the surface more than it would radiocarbon. In this paper we show that this is not the case. In a suite of models with different spatially constant and spatially varying values of ARedi the distribution of radiocarbon and helium isotopes is sensitive to the value of ARedi. However, away from strong helium sources in the southeastern Pacific, the relationship between the two is not sensitive, indicating that large-scale advection is the limiting process for removing helium and radiocarbon from the deep ocean. The helium isotopes, in turn, suggest a higher value of ARedi below the thermocline than is seen in theoretical parameterizations based on baroclinic growth rates. We argue that a key part of resolving the isopycnal mixing paradox is to abandon the idea that ARedi has a direct relationship to local baroclinic instability and to the so-called "thickness" mixing coefficient AGM.
Highlights
Because the ocean is highly stratified and weakly forced, tracer mixing occurs predominantly along surfaces of constant neutral density (Ledwell et al, 1998)
The coarse-resolution Earth system models do a reasonable job at reproducing the large-scale hydrography of the ocean
The values that are most consistent with the observations are comparable to what is found nearer to the surface. This suggests that the isopycnal mixing paradox is not a matter of ARedi being much larger than AGM in the surface layer and in the deep ocean
Summary
Because the ocean is highly stratified and weakly forced, tracer mixing occurs predominantly along surfaces of constant neutral density (Ledwell et al, 1998). A few models (the CMCC ESM of Fogli et al, 2009, and CNRM CM3 of Salas-Melia et al, 2005) use relatively large values of ARedi (2000 m2 s−1 in both cases) in the ocean interior We term this order of magnitude difference between the values if ARedi emerging from theory and direct observations the isopycnal mixing paradox. This paper examines two connections between the tracers and isopycnal mixing It examines whether resolving the isopycnal mixing paradox in favor of higher values of ARedi more consistent with observations could allow for a different relationship between mantle helium and radiocarbon. Insofar as isopycnal mixing brings deep water to the surface and returns it rapidly to depth, it would be expected to vent mantle helium without necessarily replenishing radiocarbon Were this a dominant transport process, it would allow for the relationship in Fig. 1c with higher mantle helium fluxes.
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