RC1: 'Comment on gchron-2021-29', William Guenthner, 23 Nov 202

Whipp and co-authors present a set of figures and accompanying code that illustrates the interaction among spherical radius, effective uranium (eU), and closure temperature for the apatite and zircon (U-Th)/He systems. This short communication will be a useful reference for illustrating how radiation damage (as proportional to eU here) influences closure temperature for a variety of grain sizes and cooling rates. This article is a nice contribution that provides several useful modeling tools and reference points for the community. I appreciate that someone has created plots of closure temperature for apatite and zircon (U-Th)/He data that are easily referenced and citable, and that go beyond the canonical closure temperature numbers that are still cited in some parts of the literature. The article could be essentially published as is given the scope of the short communication submission goals. I do have a few minor comments though:

Line 61: typo with “concentrations”

Amended

Line 91: Could you provide more details on the software here? Open-source code? What language? Basic design?

We have modified and added a few sentences to give some additional information about the software, as well as more clearly refer the reader to where to find the software if they would like to use it. The modified text now reads: “The software used comprises programs for predicting (U-Th)/He (Ketcham et al., 2018) and apatite fission-track (Ketcham et al., 2000, as implemented in Braun et al., 2012) closure temperatures and ages written by Richard Ketcham in the C and C++ programming languages, and our scripts written in the Python language for producing the cooling histories and plots (each figure has a separate script file). The software is all open source and details about licensing can be found in the software archive online (see Code availability section). Each script file has a section of user-modifiable values at the start of the script and using this software it is possible for users to reproduce and customize versions of Figures 2-5. Furthermore, in addition to the linear cooling histories presented here it is possible to define more complex thermal histories involving multi-stage cooling and reheating events, as well as export predicted AFT length distributions. Details about how to use and customize the software are available in the code description in the software archive online.”

Line 103: provide a short definition of what ESR is and why it’s a useful concept for thinking about grain size

Response: We have added the following text to the manuscript: He mobility is a thermally-controlled volume diffusion process and therefore sensitive to grain size (e.g., Reiners and Farley, 2001), which is typically quantified as equivalent spherical radius (ESR), based on the observation that isothermal outgassing of apatite well fits a spherical diffusion model (Wolf et al., 1996).

Line 115: also the annealing temperatures are higher than apatite

Response: Agree. We have added the following text to the manuscript: “Zircon annealing temperatures are higher than for apatite, and zircon is also more resistant to geological cycling than apatite.”

Line 177: this is an interesting observation, and deserving of a little more explanation and highlighting. Do you an intuitive sense for why this is? Or, more precisely, can you explain this behavior in the context of the damage-diffusivity response?

Response: This outcome surprised us also and we agree that it deserves more explanation in the context of damage-diffusivity in zircon. The observation is that the most pristine zircon (low Eu, fast cooling rate) diffuses He more efficiently than even slightly damaged zircon. Usually in thermal diffusion systems faster cooling rates result in higher effective closure temperatures. Yet, it has been shown (in a foundational contribution by the reviewer) that alpha damage in zircon decreases dramatically with increased alpha dosage for low magnitudes of alpha dosage, likely by increasing the tortuosity of the He diffusion pathways in the crystal (Guenthner et al., 2013 AJS, doi: 10.2475/03.2013.01). For a given cooling rate, crystals with low amounts of damage result in a higher effective closure temperature (and older cooling age) than crystals with no damage. What we observe here is that since the time accumulating damage is shorter under faster cooling scenarios, the decreased degree of damage in zircon for the faster cooled scenarios has a greater impact on closure T and cooling age than the faster cooling rate itself. We do not see this effect manifest in the apatite models (Fig. 3b). We have added the following text to the manuscript to discuss this: “Although this result seems potentially contrary to thermal diffusion systems in which faster cooling rates generally result in higher closure temperatures (e.g. Fig. 4b), in the case of zircon, the faster cooling scenarios also result in the most pristine crystals because of the increasingly shorter time to accumulate alpha damage (low eU, fast cooling rate). Moderate dosages of alpha damage are known to decrease diffusivity compared to pristine to low alpha damage dosage crystals (Guenthner et al., 2013). The implication is that zircon with low eU under fast cooling rates is more sensitive to the degree of alpha damage than to cooling rate.”

Figure 1: Because of the thermal history used here, the age differences in a and c are slight, and within the standard deviation that we typically see in apatite and zircon (U-Th)/He dates without any radiation damage effect. I’m wondering if a slower cooling rate and therefore longer time period might be more representative of a “typical” time-temperature path for which we’d want to investigate a date-eU correlation? Maybe all that changes with a longer time-temperature path is the absolute numbers, but the contours look relatively the same, so the basic point here remains unchanged. It just seems that a cooling history of only 25-0 Ma and 250-0 oC would not really yield a date-eU correlation in natural samples that would be interpretable.

Response: We appreciate and fully agree with this comment and suggestion. In response, we have added a new Figure 3, which reproduces the ESR and eU conditions of Fig. 2, but applying a 1 C/myr cooling rate (model run time of 250 myr). To discuss the differences between Fig. 2 and Fig. 3 we have added the following text: “While the 10 °C/Myr cooling rate applied in Figure 2 could represent active orogenic settings, slower cooling rates are also common to many geological environments. To compare the effect of an order of magnitude slower cooling on He diffusion, we have applied all the same parameters as in the 10 °C/Myr scenario to a 1 °C/Myr constant cooling rate, equating to a model run time of 250 Myr (Fig. 3). The primary difference in the behavior of He in apatite under slower cooling is that AHe ages and closure temperatures correlate much more strongly with eU concentration than with ESR, resulting in ~30 °C variability in closure temperature over the range of eU concentration considered (Fig. 3b) and variation in AHe age of up to 30 Myr (Fig. 3a). The slower cooling provides a greater period of time for accumulation of alpha decay-induced crystal damage. In an empirical study, such a cooling scenario could be expected to produce statistically-significant positive age-eU correlations. The ZHe system in this scenario continues to be insensitive to ESR, and while it is highly sensitive to eU concentration for values <500 ppm, it is quite insensitive to eU concentration for values >500 ppm (Fig. 3c,d). Thus, there is an eU concentration threshold above which zircons may not show an age-eU relationship. This threshold could be important to recognize when interpreting the significance of zircon age-eU plots.”

General comments:

Whipp et al. present explored the full range of low-temperature thermochronological closure temperatures as a function of uniform cooling rate, grain size and effective uranium. Their age predictions and derived closure temperatures are based on state-of-the-art diffusion and annealing models. They found a range of boundary conditions under which thermochronological ages overlap (e.g. apatite (U-Th)/He ages older than apatite fission track ages). Overall this short communication does present high-quality figures that can be used for teaching and making rough interpretation of multi-thermochronological data. The only substantial correction I ask the authors is a comparison of predicted ages (with their software) with those predicted by HeFTy (to make sure that they have integrated the provided annealing and diffusion models from Richard Ketcham correctly). After adding this, I am optimistic that the manuscript from Whipp et al. will be a valuable contribution for the thermochronological community.

 Technical corrections:

Line 91-95: I would add a short paragraph and report some details of the software.

We have modified and added a few sentences to give some additional information about the software, as well as more clearly refer the reader to where to find the software if they would like to use it. The modified text now reads: “The software used comprises programs for predicting (U-Th)/He (Ketcham et al., 2018) and apatite fission-track (Ketcham et al., 2000, as implemented in Braun et al., 2012) closure temperatures and ages written by Richard Ketcham in the C and C++ programming languages, and our scripts written in the Python language for producing the cooling histories and plots (each figure has a separate script file). The software is all open source and details about licensing can be found in the software archive online (see Code availability section). Each script file has a section of user-modifiable values at the start of the script and using this software it is possible for users to reproduce and customize versions of Figures 2-5. Furthermore, in addition to the linear cooling histories presented here it is possible to define more complex thermal histories involving multi-stage cooling and reheating events, as well as export predicted AFT length distributions. Details about how to use and customize the software are available in the code description in the software archive online.”

I also encourage the authors to provide information about the comparison with age predictions made in HeFTy. Simply model for the most extreme cases and some intermediate the corresponding thermochronological ages with HeFTy and your own software.

Response: We appreciate this suggestion and since HeFTy is a widely used tool, this is an important point. We have added a direct comparison between HeFTy model predictions (v. 1.9.3) and our software, in which we use identical parameters to model the four corners of Figs. 2, 3, and 4, and the fastest and slowest cooling scenarios in Fig. 5 (revised version figure numbering). We have used the same code used in HeFTy for the (U-Th)/He age prediction in our results, so the predicted ages vary by less than 1% from the values in HeFTy. The fission-track age prediction was taken from Pecube (Braun et al., 2012) using the code described in Ketcham et al. (2000). The predicted AFT ages are 3-5% older than HeFTy in our results, which does not affect the relationships we report between thermochronometers. The comparison table is available in the attached supplement, and will be added to the final software archive if the article is accepted.