<table><caption>TABLE 3. CHECKLIST OF NEEDED (OR REFERENCED) INFORMATION FOR THERMAL HISTORY MODELS</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Thermochronologic data inputs</td><td></td></tr><tr><td>☐ All data needed for modeling and for reproducing model results (either reported in the same paper or cite published reference containing the necessary data)</td><td></td></tr><tr><td>☐ Data input</td><td></td></tr><tr><td>– What data were used in the modeling and why (e.g., types of thermochronologic data, such as zircon and/or apatite (U-Th)/He and whether other data such as fission-track are included or excluded; specific analyses that are included or excluded from the modeling)</td><td></td></tr><tr><td>– How data were input (i.e., as single grains or as synthetic grains representing sample or kinetic subgroup averages)</td><td></td></tr><tr><td>– Uncertainties used in the modeling</td><td></td></tr><tr><td>Model structure, geologic constraints, and anything else used to define or limit the character of tested tT paths or solutions and why</td><td></td></tr><tr><td>☐ Rationale for overall model design and/or hypotheses to be tested with the model (e.g., continuous cooling/exhumation or multiphase heating/burial and cooling/exhumation)</td><td></td></tr><tr><td>☐ Geologic information used to impose tT constraint boxes that limit tT path trajectories to those considered geologically valid or the most geologically realistic</td><td></td></tr><tr><td>– Assumption (e.g., tT model space; tT constraint box dimensions; priors assumed for thermal history parameters for QTQt)</td><td></td></tr><tr><td>– Explanation for assumption (e.g., stratigraphic age; paleosurface constraint, such as volcanic rocks marking when samples were at the surface)</td><td></td></tr><tr><td>– References that are the source of information for the assumption</td><td></td></tr><tr><td>☐ Any other criteria or information used to define or limit tT path solutions</td><td></td></tr><tr><td>– Character of tT path segments (e.g., number of breakage points; cooling rates)</td><td></td></tr><tr><td>– Any criteria used to limit tT path solutions and justification for criteria, including path simplicity</td><td></td></tr><tr><td>System- and model-specific parameters</td><td></td></tr><tr><td>☐ Statistical fitting criteria for a tT path "fit" (e.g., what criteria used to evaluate which tT paths acceptably reproduce the observed data; statistical thresholds used)</td><td></td></tr><tr><td>☐ Kinetic model used (e.g., citation of paper(s) describing model(s) used, optional parameters, etc.)</td><td></td></tr><tr><td>☐ Modeling code: specific code used and version # if applicable</td><td></td></tr><tr><td>☐ Running and ending conditions (e.g., number of paths tried; burn-in, post-burn-in, if applicable; criteria for termination)</td><td></td></tr><tr><td>Model outputs</td><td></td></tr><tr><td>☐ Clear representation and explanation of thermal history model outputs</td><td></td></tr><tr><td>☐ Representation of how well the tT path solutions fit the observed data (e.g., goodness of fit number for HeFTy and plots of observed vs. modelled dates for QTQt)</td><td></td></tr><tr><td>☐ Explanation of how model outputs were used to reach the final geologic interpretation</td><td></td></tr></tbody></table>

statistic (e.g., mean sample date) is appropriate for samples with normally distributed dates (e.g., common in geochronologic studies), but it is not correct for samples with substantially skewed dates or kinetic variation. We recommend explaining the rationale for combining or not combining sample data using a summary statistic. If a summary statistic is used, then state how data are combined (e.g., unweighted mean, weighted mean and nature of weighting), how the uncertainty is calculated, what factors are included in the uncertainty, and the confidence interval ($1\sigma$ or $2\sigma$).

# 5. INTERPRETING DATA WITH THERMAL HISTORY MODELS

## 5.1. Overview

Thermal history modeling is an interpretive step that is commonly used to convert thermochronologic data into thermal histories from which geologic conclusions are derived (Fig. 6). This is done because (U-Th)/He dates are quantities that represent a mineral's time-integrated thermal history, and a variety of tT paths can yield the same (U-Th)/He date (see sections 2.1 and 2.5 of companion paper, Flowers et al., 2022). Much can generally be learned from (U-Th)/He data sets even without tT modeling, but it can be powerful for testing specific hypotheses and exploring particular questions with a data set. This process involves using He diffusion kinetic model(s) for the mineral(s) of interest in a tT modeling program to determine the range of thermal histories that can explain the data while honoring other geologic and geochronologic constraints on the tT path.

Thermal history modeling can be done in both a forward and an inverse sense. Forward modeling involves choosing a given tT path to predict the dates (e.g., Ketcham, 2005). Different segments of the selected tT path (e.g., heating magnitude or duration, cooling timing or rate) can be varied by the user to gain a conceptual understanding of how different parts of the tT history influence the predicted date pattern and to determine which tT path segments the data are sensitive to and actually constrain. Forward modeling is therefore a recommended preliminary step before inverse modeling, so that the latter is not a "black box." Inverse thermal history modeling involves generating a suite of forward tT paths with a defined set of characteristics from which dates are predicted, compared with the observed input data, and used to constrain the suite of viable tT histories that can account for the thermochronologic, as well as any independent geologic and geochronologic, data (e.g., Ketcham, 2005, 2012; Gallagher, 2012).

Thermal history modeling requires careful consideration of the input thermochronologic data, a solid understanding of independent geologic and tT constraints that may bear on the samples and how to reasonably and defensibly incorporate them into the models, deliberate implementation of a geologically plausible level of complexity in tT path solutions given the sample context, an understanding of the criteria used to determine solutions and how these criteria affect interpretation of model outcomes, complete representation of tT model outputs, and full explanation of all of the above aspects in published products (Table 3). Deciphering the complete, continuous thermal history of the sample is generally not feasible. More commonly, the goal

is to resolve the tT path well in the tT range of interest for the problem being addressed. Being cognizant of which portions of the thermal history the data do and do not constrain is key for reliable data interpretation.

The two most commonly used thermal history modeling programs are HeFTy (Ketcham, 2005) and QTQt (Gallagher, 2012). Both programs allow for forward and inverse modeling. The differing strategies and philosophies that these programs use for generating tT paths during inverse modeling, for statistically determining which paths predict dates that acceptably reproduce the observed data, and for depicting inversion model results were recently discussed in a paper and associated comments and replies (Vermeesch and Tian, 2014; Gallagher and Ketcham, 2018; Gallagher and Ketcham, 2020; Vermeesch and Tian, 2020; Green and Duddy, 2020). Broadly comparing software approaches, HeFTy uses frequentist statistics, testing the null hypothesis that the data could be a sample from the set of possibilities implied by the model given measurement uncertainties. A Monte Carlo scheme is used to generate tT paths, with the user assigning a degree of permitted complexity to different segments of the history to help ensure a fuller mapping of the set of geologically reasonable paths that fit the data. QTQt uses a Bayesian methodology, which allows the user to set up a series of priors concerning the thermal history and optionally include other factors such as diffusion kinetics, allowing them to vary. The Markov Chain Monte Carlo (MCMC) method is used to search the solution space by learning from earlier-attempted paths and includes a penalty for complex paths (with many nodes); thus, it seeks and highlights the simplest set of solutions that best fit the data.
<table><caption>TABLE 3. CHECKLIST OF NEEDED (OR REFERENCED) INFORMATION FOR THERMAL HISTORY MODELS</caption><thead><tr><th></th><th></th></tr></thead><tbody><tr><td>Thermochronologic data inputs</td><td></td></tr><tr><td>☐ All data needed for modeling and for reproducing model results (either reported in the same paper or cite published reference containing the necessary data)</td><td></td></tr><tr><td>☐ Data input</td><td></td></tr><tr><td>– What data were used in the modeling and why (e.g., types of thermochronologic data, such as zircon and/or apatite (U-Th)/He and whether other data such as fission-track are included or excluded; specific analyses that are included or excluded from the modeling)</td><td></td></tr><tr><td>– How data were input (i.e., as single grains or as synthetic grains representing sample or kinetic subgroup averages)</td><td></td></tr><tr><td>– Uncertainties used in the modeling</td><td></td></tr><tr><td>Model structure, geologic constraints, and anything else used to define or limit the character of tested tT paths or solutions and why</td><td></td></tr><tr><td>☐ Rationale for overall model design and/or hypotheses to be tested with the model (e.g., continuous cooling/exhumation or multiphase heating/burial and cooling/exhumation)</td><td></td></tr><tr><td>☐ Geologic information used to impose tT constraint boxes that limit tT path trajectories to those considered geologically valid or the most geologically realistic</td><td></td></tr><tr><td>– Assumption (e.g., tT model space; tT constraint box dimensions; priors assumed for thermal history parameters for QTQt)</td><td></td></tr><tr><td>– Explanation for assumption (e.g., stratigraphic age; paleosurface constraint, such as volcanic rocks marking when samples were at the surface)</td><td></td></tr><tr><td>– References that are the source of information for the assumption</td><td></td></tr><tr><td>☐ Any other criteria or information used to define or limit tT path solutions</td><td></td></tr><tr><td>– Character of tT path segments (e.g., number of breakage points; cooling rates)</td><td></td></tr><tr><td>– Any criteria used to limit tT path solutions and justification for criteria, including path simplicity</td><td></td></tr><tr><td>System- and model-specific parameters</td><td></td></tr><tr><td>☐ Statistical fitting criteria for a tT path "fit" (e.g., what criteria used to evaluate which tT paths acceptably reproduce the observed data; statistical thresholds used)</td><td></td></tr><tr><td>☐ Kinetic model used (e.g., citation of paper(s) describing model(s) used, optional parameters, etc.)</td><td></td></tr><tr><td>☐ Modeling code: specific code used and version # if applicable</td><td></td></tr><tr><td>☐ Running and ending conditions (e.g., number of paths tried; burn-in, post-burn-in, if applicable; criteria for termination)</td><td></td></tr><tr><td>Model outputs</td><td></td></tr><tr><td>☐ Clear representation and explanation of thermal history model outputs</td><td></td></tr><tr><td>☐ Representation of how well the tT path solutions fit the observed data (e.g., goodness of fit number for HeFTy and plots of observed vs. modelled dates for QTQt)</td><td></td></tr><tr><td>☐ Explanation of how model outputs were used to reach the final geologic interpretation</td><td></td></tr></tbody></table>

statistic (e.g., mean sample date) is appropriate for samples with normally distributed dates (e.g., common in geochronologic studies), but it is not correct for samples with substantially skewed dates or kinetic variation. We recommend explaining the rationale for combining or not combining sample data using a summary statistic. If a summary statistic is used, then state how data are combined (e.g., unweighted mean, weighted mean and nature of weighting), how the uncertainty is calculated, what factors are included in the uncertainty, and the confidence interval ($1\sigma$ or $2\sigma$).

# 5. INTERPRETING DATA WITH THERMAL HISTORY MODELS

## 5.1. Overview

Thermal history modeling is an interpretive step that is commonly used to convert thermochronologic data into thermal histories from which geologic conclusions are derived (Fig. 6). This is done because (U-Th)/He dates are quantities that represent a mineral's time-integrated thermal history, and a variety of tT paths can yield the same (U-Th)/He date (see sections 2.1 and 2.5 of companion paper, Flowers et al., 2022). Much can generally be learned from (U-Th)/He data sets even without tT modeling, but it can be powerful for testing specific hypotheses and exploring particular questions with a data set. This process involves using He diffusion kinetic model(s) for the mineral(s) of interest in a tT modeling program to determine the range of thermal histories that can explain the data while honoring other geologic and geochronologic constraints on the tT path.

Thermal history modeling can be done in both a forward and an inverse sense. Forward modeling involves choosing a given tT path to predict the dates (e.g., Ketcham, 2005). Different segments of the selected tT path (e.g., heating magnitude or duration, cooling timing or rate) can be varied by the user to gain a conceptual understanding of how different parts of the tT history influence the predicted date pattern and to determine which tT path segments the data are sensitive to and actually constrain. Forward modeling is therefore a recommended preliminary step before inverse modeling, so that the latter is not a "black box." Inverse thermal history modeling involves generating a suite of forward tT paths with a defined set of characteristics from which dates are predicted, compared with the observed input data, and used to constrain the suite of viable tT histories that can account for the thermochronologic, as well as any independent geologic and geochronologic, data (e.g., Ketcham, 2005, 2012; Gallagher, 2012).

Thermal history modeling requires careful consideration of the input thermochronologic data, a solid understanding of independent geologic and tT constraints that may bear on the samples and how to reasonably and defensibly incorporate them into the models, deliberate implementation of a geologically plausible level of complexity in tT path solutions given the sample context, an understanding of the criteria used to determine solutions and how these criteria affect interpretation of model outcomes, complete representation of tT model outputs, and full explanation of all of the above aspects in published products (Table 3). Deciphering the complete, continuous thermal history of the sample is generally not feasible. More commonly, the goal

is to resolve the tT path well in the tT range of interest for the problem being addressed. Being cognizant of which portions of the thermal history the data do and do not constrain is key for reliable data interpretation.

The two most commonly used thermal history modeling programs are HeFTy (Ketcham, 2005) and QTQt (Gallagher, 2012). Both programs allow for forward and inverse modeling. The differing strategies and philosophies that these programs use for generating tT paths during inverse modeling, for statistically determining which paths predict dates that acceptably reproduce the observed data, and for depicting inversion model results were recently discussed in a paper and associated comments and replies (Vermeesch and Tian, 2014; Gallagher and Ketcham, 2018; Gallagher and Ketcham, 2020; Vermeesch and Tian, 2020; Green and Duddy, 2020). Broadly comparing software approaches, HeFTy uses frequentist statistics, testing the null hypothesis that the data could be a sample from the set of possibilities implied by the model given measurement uncertainties. A Monte Carlo scheme is used to generate tT paths, with the user assigning a degree of permitted complexity to different segments of the history to help ensure a fuller mapping of the set of geologically reasonable paths that fit the data. QTQt uses a Bayesian methodology, which allows the user to set up a series of priors concerning the thermal history and optionally include other factors such as diffusion kinetics, allowing them to vary. The Markov Chain Monte Carlo (MCMC) method is used to search the solution space by learning from earlier-attempted paths and includes a penalty for complex paths (with many nodes); thus, it seeks and highlights the simplest set of solutions that best fit the data.
In both programs, constraints or priors can be
used to enforce external information concerning
the thermal history, such as depositional events
(i.e., stratigraphic ages).

To interpret the geologic significance of ther-
mal histories derived from the modeling effort,
additional assumptions, such as the geother-
mal gradient or other factors, are then required
(Fig. 6). Thermal-kinematic modeling software
such as PECUBE, which computes the spatial
and temporal variability of upper crustal tem-
peratures during topographic evolution and
faulting, can also be used to constrain which
geomorphic, structural, and geodynamic histo-
ries are most consistent with a (U-Th)/He data
set (e.g., Braun, 2003; Ehlers and Farley, 2003;
Ehlers, 2005; Braun et al., 2012).

We do not address all of these complex top-
ics here but instead focus specifically on the
practical choices and assumptions that must be
made by the user during setup of inverse thermal
history models. A critical point is that interpre-
tive decisions are unavoidable when setting up
models, including what data types and samples
to simulate, how to input these data into the mod-
els, what modeling program to use, whether to
explore and represent a wide range of feasible
histories or to favor simpler tT paths in model
outputs, what criteria are used to determine
whether the data are replicated, and what inde-
pendent geologic and geochronologic data are
relevant to the samples and should be honored.
These choices should be carefully considered
and deliberately made, but they are not always
clear cut, such that there may be multiple reason-
able paths through this decision tree. It therefore
is essential that published products articulate the
choices made and logic used along this path and
represent how well the preferred tT path solu-
tions reproduce the data (section 5.4; Table 3).
We first reiterate the critical concepts of "model
structure" and hypothesis testing that are central
to constructing inverse thermal history models
(Gallagher and Ketcham, 2018; section 5.2), de-
scribe two common strategies for inputting data
into inverse models (section 5.3), and conclude
with some recommendations for model report-
ing (section 5.4; Table 3).

5.2. Designing a Model Structure, Testing
Hypotheses, and Evaluating Model
Outputs

Thermal history modeling is carried out with-
in a deliberately designed model structure to test
and explore specific hypotheses for a data set,
such as the timing, magnitude, or rates of cool-
ing/exhumeration and/or heating/burial event(s)
across a study area (e.g., Gallagher and Ket-
cham, 2018). The model structure is informed

by the geologic and geochronologic context
of the samples, by preliminary interpretations
made from the data based on the temperature
sensitivity(s) of the dated mineral(s), and per-
haps by additional plots of sample date(s) versus
elevation or distance along a transect that may
aid in better understanding the spatial patterns
of the data (Fig. 6).

The model structure is implemented in a
number of ways. First, independent geologic
and geochronologic knowledge is incorporated
into the models by choosing whether and how
to apply tT constraint boxes through which all
tested tT paths must pass. This step is essential
for designing geologically valid model frame-
works. These constraints may be based on local
geologic observations, such as an unconformity
that requires the rocks to have been at the sur-
face at a specific time, or based on the broader
context such as knowledge that the study area is
within a larger region that was undergoing burial
within a certain interval. Characteristics of the
intervening tT path segments are also specified
(e.g., number of breakage points, cooling rates).
In some cases, for example, when using QTQt,
an additional decision is required about whether
to explore and represent a wide range of tT path
possibilities or to limit outcomes by penalizing
more complex solutions with rate-variant tra-
jectories even if they replicate the data as well
as simpler solutions. It is common to iteratively
carry out multiple models that assume different
model frameworks and that vary different model
aspects to fully understand the limits of a data set
and extract the maximum information from it.

As an example of model structure, it may be
possible that a history of continuous slow cool-
ing/exhumeration, or one of early rapid cooling/
exhumeration followed by one or more episodes
of heating/burial and cooling/re-exhumeration,
can fit a thermochronologic data set equally well
(Fig. 10A). In this case, the level of complexity
that the authors infer is most geologically realis-
tic will determine how the model is constructed
(e.g., McClure Mountain syenite example; An-
derson et al., 2017, 2018; Weisberg et al., 2018a,
2018b). Thus, in the continuous cooling inverse
model, reheating would be precluded, and the
only tT constraints imposed may be the high-
temperature crystallization age and the modern
surface temperature (Fig. 10B). In contrast, in
the heating and cooling inverse model, reheat-
ing would be allowed, and additional constraint
boxes would be defined, for example, based on
unconformable relationships inferred to be rel-
evant to the samples that constrain earlier inter-
vals when the sample was at or near the surface
(Fig. 10C). The outcomes of each model then
support or refute the hypothesis tested by the
model structure by either yielding or not yielding

tT solutions that are considered to acceptably re-
produce the data. This process assumes that the
data are reliable, appropriate uncertainties are
applied, and the kinetic models account for the
mineral diffusion characteristics sufficiently well
(e.g., Gallagher and Ketcham, 2020).

It is not possible to infer thermal histories from
the thermochronologic data alone without adopt-
ing a model framework. Models that seek, favor,
and highlight the simplest solutions embed mod-
el frameworks that test the hypothesis that rate-
and direction-invariant thermal histories with
limited inflections can explain the data (for ex-
ample, this approach is sometimes adopted when
using QTQt). The outcomes of these models do
not falsify the possibility that more complex tT
paths can statistically reproduce the data as well
or better than more simplistic paths, because
the models were designed to penalize and reject
non-monotonic tT trajectories that change in rate
and direction rather than explore them. Whether
this approach yields the most geologically likely
suite of tT paths, or yields overly simplistic and
geologically unrealistic or illogical outcomes,
depends entirely on the sample context, model
design, and study objectives. It is important to be
aware that the outcomes of models that highlight
simple solutions may imply that the data restrict
thermal histories in a temperature range that the
results are not sensitive to and therefore cannot
limit. For example, outcomes of inverse thermal
history models of apatite (U-Th)/He data sets
that penalize rate-variant paths may depict a nar-
row range of rate-invariant monotonically cool-
ing tT paths at temperatures <30 °C, although in
reality the apatite (U-Th)/He data allow any tT
trajectory at these low temperatures; this may be
key in a circumstance in which one is trying to
determine the most recent phase of cooling that
the data can constrain, such as associated with
incision of a canyon. This again underscores the
need to understand, clearly articulate, and justify
embedded assumptions in thermal history mod-
els so that it is clear what the models do and do
not test and/or resolve.

It is crucial to carefully evaluate the model
outcomes. This evaluation includes confirming
and conveying in the published product that the
preferred solutions reproduce the data, for ex-
ample via statements of the specified statistical
fitting criteria (for HeFTy; note that QTQt inver-
sion models will always yield solutions even if
the fit quality is poor) and/or graphical depictions
of observed and predicted data (Flowers et al.,
2016; Gallagher et al., 2016). This assessment
also includes inspecting the model outcomes to
ensure that they are not invalidated by incontro-
vertible geologic and chronologic information
that constrains the tT path, such as a time when
the sample was at the surface based on the age of
In both programs, constraints or priors can be
used to enforce external information concerning
the thermal history, such as depositional events
(i.e., stratigraphic ages).

To interpret the geologic significance of ther-
mal histories derived from the modeling effort,
additional assumptions, such as the geother-
mal gradient or other factors, are then required
(Fig. 6). Thermal-kinematic modeling software
such as PECUBE, which computes the spatial
and temporal variability of upper crustal tem-
peratures during topographic evolution and
faulting, can also be used to constrain which
geomorphic, structural, and geodynamic histo-
ries are most consistent with a (U-Th)/He data
set (e.g., Braun, 2003; Ehlers and Farley, 2003;
Ehlers, 2005; Braun et al., 2012).

We do not address all of these complex top-
ics here but instead focus specifically on the
practical choices and assumptions that must be
made by the user during setup of inverse thermal
history models. A critical point is that interpre-
tive decisions are unavoidable when setting up
models, including what data types and samples
to simulate, how to input these data into the mod-
els, what modeling program to use, whether to
explore and represent a wide range of feasible
histories or to favor simpler tT paths in model
outputs, what criteria are used to determine
whether the data are replicated, and what inde-
pendent geologic and geochronologic data are
relevant to the samples and should be honored.
These choices should be carefully considered
and deliberately made, but they are not always
clear cut, such that there may be multiple reason-
able paths through this decision tree. It therefore
is essential that published products articulate the
choices made and logic used along this path and
represent how well the preferred tT path solu-
tions reproduce the data (section 5.4; Table 3).
We first reiterate the critical concepts of "model
structure" and hypothesis testing that are central
to constructing inverse thermal history models
(Gallagher and Ketcham, 2018; section 5.2), de-
scribe two common strategies for inputting data
into inverse models (section 5.3), and conclude
with some recommendations for model report-
ing (section 5.4; Table 3).

5.2. Designing a Model Structure, Testing
Hypotheses, and Evaluating Model
Outputs

Thermal history modeling is carried out with-
in a deliberately designed model structure to test
and explore specific hypotheses for a data set,
such as the timing, magnitude, or rates of cool-
ing/exhumeration and/or heating/burial event(s)
across a study area (e.g., Gallagher and Ket-
cham, 2018). The model structure is informed

by the geologic and geochronologic context
of the samples, by preliminary interpretations
made from the data based on the temperature
sensitivity(s) of the dated mineral(s), and per-
haps by additional plots of sample date(s) versus
elevation or distance along a transect that may
aid in better understanding the spatial patterns
of the data (Fig. 6).

The model structure is implemented in a
number of ways. First, independent geologic
and geochronologic knowledge is incorporated
into the models by choosing whether and how
to apply tT constraint boxes through which all
tested tT paths must pass. This step is essential
for designing geologically valid model frame-
works. These constraints may be based on local
geologic observations, such as an unconformity
that requires the rocks to have been at the sur-
face at a specific time, or based on the broader
context such as knowledge that the study area is
within a larger region that was undergoing burial
within a certain interval. Characteristics of the
intervening tT path segments are also specified
(e.g., number of breakage points, cooling rates).
In some cases, for example, when using QTQt,
an additional decision is required about whether
to explore and represent a wide range of tT path
possibilities or to limit outcomes by penalizing
more complex solutions with rate-variant tra-
jectories even if they replicate the data as well
as simpler solutions. It is common to iteratively
carry out multiple models that assume different
model frameworks and that vary different model
aspects to fully understand the limits of a data set
and extract the maximum information from it.

As an example of model structure, it may be
possible that a history of continuous slow cool-
ing/exhumeration, or one of early rapid cooling/
exhumeration followed by one or more episodes
of heating/burial and cooling/re-exhumeration,
can fit a thermochronologic data set equally well
(Fig. 10A). In this case, the level of complexity
that the authors infer is most geologically realis-
tic will determine how the model is constructed
(e.g., McClure Mountain syenite example; An-
derson et al., 2017, 2018; Weisberg et al., 2018a,
2018b). Thus, in the continuous cooling inverse
model, reheating would be precluded, and the
only tT constraints imposed may be the high-
temperature crystallization age and the modern
surface temperature (Fig. 10B). In contrast, in
the heating and cooling inverse model, reheat-
ing would be allowed, and additional constraint
boxes would be defined, for example, based on
unconformable relationships inferred to be rel-
evant to the samples that constrain earlier inter-
vals when the sample was at or near the surface
(Fig. 10C). The outcomes of each model then
support or refute the hypothesis tested by the
model structure by either yielding or not yielding

tT solutions that are considered to acceptably re-
produce the data. This process assumes that the
data are reliable, appropriate uncertainties are
applied, and the kinetic models account for the
mineral diffusion characteristics sufficiently well
(e.g., Gallagher and Ketcham, 2020).

It is not possible to infer thermal histories from
the thermochronologic data alone without adopt-
ing a model framework. Models that seek, favor,
and highlight the simplest solutions embed mod-
el frameworks that test the hypothesis that rate-
and direction-invariant thermal histories with
limited inflections can explain the data (for ex-
ample, this approach is sometimes adopted when
using QTQt). The outcomes of these models do
not falsify the possibility that more complex tT
paths can statistically reproduce the data as well
or better than more simplistic paths, because
the models were designed to penalize and reject
non-monotonic tT trajectories that change in rate
and direction rather than explore them. Whether
this approach yields the most geologically likely
suite of tT paths, or yields overly simplistic and
geologically unrealistic or illogical outcomes,
depends entirely on the sample context, model
design, and study objectives. It is important to be
aware that the outcomes of models that highlight
simple solutions may imply that the data restrict
thermal histories in a temperature range that the
results are not sensitive to and therefore cannot
limit. For example, outcomes of inverse thermal
history models of apatite (U-Th)/He data sets
that penalize rate-variant paths may depict a nar-
row range of rate-invariant monotonically cool-
ing tT paths at temperatures <30 °C, although in
reality the apatite (U-Th)/He data allow any tT
trajectory at these low temperatures; this may be
key in a circumstance in which one is trying to
determine the most recent phase of cooling that
the data can constrain, such as associated with
incision of a canyon. This again underscores the
need to understand, clearly articulate, and justify
embedded assumptions in thermal history mod-
els so that it is clear what the models do and do
not test and/or resolve.

It is crucial to carefully evaluate the model
outcomes. This evaluation includes confirming
and conveying in the published product that the
preferred solutions reproduce the data, for ex-
ample via statements of the specified statistical
fitting criteria (for HeFTy; note that QTQt inver-
sion models will always yield solutions even if
the fit quality is poor) and/or graphical depictions
of observed and predicted data (Flowers et al.,
2016; Gallagher et al., 2016). This assessment
also includes inspecting the model outcomes to
ensure that they are not invalidated by incontro-
vertible geologic and chronologic information
that constrains the tT path, such as a time when
the sample was at the surface based on the age of
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

volcanic rocks directly overlying the sample or an interval of heating/burial based on a package of sedimentary rocks sitting above the sample. If such constraints are violated by the tT path solu-

Figure 10. Examples are shown of two different thermal history model frameworks that may be constructed based on the setting of a thermochronologic sample. (A) Geologic setting of a basement sample that crystallized at depth at some known time in the past based on independent geochronologic data (t₀, orange square) and is collected at the surface today (t-present, yellow square). Constraining the thermal history in the intervening time is the aim of the thermochronologic study. Unconformable relationships in the region indicate that nearby basement was at the surface by the time that overlying sedimentary rocks were deposited (t-unconformity, gray units). Whether or not the unconformity is considered relevant to the sample will dictate the structure of the thermal history model. (B) Continuous cooling/exhumation model framework assumes that the unconformity is not relevant to the sample and the sample was not buried by the sedimentary rocks in the region. In this model, the high temperature crystallization age (t-init) and present-day surface conditions (t-present) are imposed on the model, all tested tT paths are forced through these two constraints, the sample is assumed to have undergone continuous cooling and exhumation during its path to the surface, and reheating/burial is not allowed by the model. The red curve marks one possible tT path that can explain the data and assumed constraints, while the gray field encompasses the larger range of the most statistically probable tT paths within this cooling-only model framework. (C) Reheating/burial model framework assumes that the unconformity is relevant to the sample, such that the sample was exhumed to the surface by the age of the unconformity, was buried by sedimentary rocks that were later eroded, and was re-exhumed to the surface by present day. In this model, a third constraint (t-unconformity) is also imposed on the model, through which all tested tT paths must also pass. The red curve and gray field again depicts the most statistically probable tT paths within this reheating/burial model framework. The outcomes of the continuous exhumation model in panel B and of the burial model in panel C support the hypothesis tested by each model, because statistically viable thermal histories are found that can explain the data and the imposed constraints. The interpretation by the authors will depend on which geologic framework they consider to be the most geologically probable. HePRZ—He partial retention zone.

tions, the model should be discarded or reformulated to include them, because later portions of tT path solutions can be dependent on earlier segments that are in the temperature sensitivity window of the thermochronometer and vice versa (see section 2 of companion paper, Flowers et al., 2022). Sensible and reliable interpretations cannot be drawn from models that flatly contradict relevant geology.

A key point is that simply finding *statistically probable* tT paths within a given model framework does not mean that those are the most *geologically probable* thermal histories. Nor should the default be to assume that the simplest model structure and simplest possible tT path is always (or perhaps ever) the most geologically realistic, especially over longer timescales. Additional arguments are required to establish the most geologically valid model framework(s) for a given thermochronologic data set, and these should be communicated along with thermal history models (Fig. 10; section 5.4; Table 3).

### 5.3. Common Strategies for Data Input

An important consideration when deciding whether and how to include data in a modeling effort is the connection between the data and the theoretical and computational framework within which we are attempting to interpret and repro-

duce them. Current (U-Th)/He models account for a limited range of mechanisms: thermally activated volume diffusion as possibly modified by domain size and radiation damage, and long alpha stopping distances. Zoning in U-Th can also be incorporated, but it is typically not measured and requires assumptions to extrapolate to three dimensions. If dates are strongly influenced by a mechanism that is not included in the model framework (e.g., U-Th zonation, He implantation, unconstrained kinetic factors), there are no logical grounds for expecting the model to reproduce them; essentially, the only option the model has to fit the data is to distort the tT path to compensate for the physical attribute or process it is missing. If omitted factors have limited and symmetric effects on dates, as might be inferred from modest but non-skewed excess dispersion, then the data can probably be modeled safely, perhaps while including some means of accommodating the excess dispersion such as increasing the estimated uncertainty. If the omitted factors impart a strong positive skewness to the data distribution (e.g., old-date excursions that cannot be explained by eU or grain size), modeling becomes more dangerous and should be executed with extreme caution, if at all. Inverse thermal history modeling should only be undertaken for data that have been carefully evaluated, are considered reliable, and yield sensible and
<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

volcanic rocks directly overlying the sample or an interval of heating/burial based on a package of sedimentary rocks sitting above the sample. If such constraints are violated by the tT path solu-

Figure 10. Examples are shown of two different thermal history model frameworks that may be constructed based on the setting of a thermochronologic sample. (A) Geologic setting of a basement sample that crystallized at depth at some known time in the past based on independent geochronologic data (t₀, orange square) and is collected at the surface today (t-present, yellow square). Constraining the thermal history in the intervening time is the aim of the thermochronologic study. Unconformable relationships in the region indicate that nearby basement was at the surface by the time that overlying sedimentary rocks were deposited (t-unconformity, gray units). Whether or not the unconformity is considered relevant to the sample will dictate the structure of the thermal history model. (B) Continuous cooling/exhumation model framework assumes that the unconformity is not relevant to the sample and the sample was not buried by the sedimentary rocks in the region. In this model, the high temperature crystallization age (t-init) and present-day surface conditions (t-present) are imposed on the model, all tested tT paths are forced through these two constraints, the sample is assumed to have undergone continuous cooling and exhumation during its path to the surface, and reheating/burial is not allowed by the model. The red curve marks one possible tT path that can explain the data and assumed constraints, while the gray field encompasses the larger range of the most statistically probable tT paths within this cooling-only model framework. (C) Reheating/burial model framework assumes that the unconformity is relevant to the sample, such that the sample was exhumed to the surface by the age of the unconformity, was buried by sedimentary rocks that were later eroded, and was re-exhumed to the surface by present day. In this model, a third constraint (t-unconformity) is also imposed on the model, through which all tested tT paths must also pass. The red curve and gray field again depicts the most statistically probable tT paths within this reheating/burial model framework. The outcomes of the continuous exhumation model in panel B and of the burial model in panel C support the hypothesis tested by each model, because statistically viable thermal histories are found that can explain the data and the imposed constraints. The interpretation by the authors will depend on which geologic framework they consider to be the most geologically probable. HePRZ—He partial retention zone.

tions, the model should be discarded or reformulated to include them, because later portions of tT path solutions can be dependent on earlier segments that are in the temperature sensitivity window of the thermochronometer and vice versa (see section 2 of companion paper, Flowers et al., 2022). Sensible and reliable interpretations cannot be drawn from models that flatly contradict relevant geology.

A key point is that simply finding *statistically probable* tT paths within a given model framework does not mean that those are the most *geologically probable* thermal histories. Nor should the default be to assume that the simplest model structure and simplest possible tT path is always (or perhaps ever) the most geologically realistic, especially over longer timescales. Additional arguments are required to establish the most geologically valid model framework(s) for a given thermochronologic data set, and these should be communicated along with thermal history models (Fig. 10; section 5.4; Table 3).

### 5.3. Common Strategies for Data Input

An important consideration when deciding whether and how to include data in a modeling effort is the connection between the data and the theoretical and computational framework within which we are attempting to interpret and repro-

duce them. Current (U-Th)/He models account for a limited range of mechanisms: thermally activated volume diffusion as possibly modified by domain size and radiation damage, and long alpha stopping distances. Zoning in U-Th can also be incorporated, but it is typically not measured and requires assumptions to extrapolate to three dimensions. If dates are strongly influenced by a mechanism that is not included in the model framework (e.g., U-Th zonation, He implantation, unconstrained kinetic factors), there are no logical grounds for expecting the model to reproduce them; essentially, the only option the model has to fit the data is to distort the tT path to compensate for the physical attribute or process it is missing. If omitted factors have limited and symmetric effects on dates, as might be inferred from modest but non-skewed excess dispersion, then the data can probably be modeled safely, perhaps while including some means of accommodating the excess dispersion such as increasing the estimated uncertainty. If the omitted factors impart a strong positive skewness to the data distribution (e.g., old-date excursions that cannot be explained by eU or grain size), modeling becomes more dangerous and should be executed with extreme caution, if at all. Inverse thermal history modeling should only be undertaken for data that have been carefully evaluated, are considered reliable, and yield sensible and
understandable data patterns believed to be ac-
counted for by the model (section 3).

There are two principal options for data input:
(1) inputting the individual analyses and their as-
sociated uncertainties or (2) using averaging into
"synthetic" grains either for the entire sample or
within kinetic subgroups.

(1) One approach is to input the individual analyses and their associated uncertainties. This can be considered the most holistic approach, as it allows the inversion procedure to sort through possibly competing kinetic influences from size, eU, and other factors such as composition or zoning if appropriate data have been gathered. However, it has a higher computational overhead and assumes that the uncertainties are fully characterized, which is generally not the case. Most reported uncertainties do not currently include those associated with the F<sub>T</sub> correction and cannot incorporate factors that are not characterized (e.g., He implantation, eU zonation). If uncertainties are underestimated, the result can be either no fits or an overly restricted swath of tT paths. To compensate, if excess dispersion appears symmetric, individual estimated uncertainties can be increased. However, if some dates partially result from omitted factors or mechanisms leading to a highly skewed distribution, including these dates can distort any joint solution or preclude finding one. QTQt software will search for thermal histories that reproduce the input data to the maximum extent possible and may simultaneously prefer simpler solutions. QTQt also allows uncertainties in U, Th, Sm, He, and grain size to be re-evaluated as a part of the fitting process. However, because of this flexibility, results must be checked carefully against the original data to ensure that any degree of misfit is acceptable.

An additional consideration is the representa-
tion of (U-Th)/He data relative to other data be-
ing modeled simultaneously (e.g., fission track,
vitrinite). In both HeFTy and QTQt, the more in-
stances of a given type of data that are included,
the more that data type influences the solution.
Consequently, modeling, for example, five in-
dividual (U-Th)/He dates and one fission-track
date may weight the solution toward the (U-Th)/
He data in a manner not necessarily anticipated
or desired by the researcher.

(2) Another approach is to use averaging into "synthetic" grains either for the entire sample or within kinetic subgroups. This approach allows one to apply an uncertainty model that does a better job of characterizing group dispersion than the individual estimated uncertainties, and it also decreases computational load and equalizes weighting among data types. For samples for which it is reasonable to report a mean (see section 4), one could use the weighted or un-

weighted mean and uncertainty reported for
the sample, often without loss of information.
This approach is functionally analogous to the
standard procedure of combining fission-track
single-grain dates into one date and uncertainty.

For samples for which it is not reasonable to
report a mean, one can model the data within
appropriate kinetic bins, usually eU, but poten-
tially incorporating other factors such as size or
composition, if they appear to organize the data
(e.g., date-eU correlations or anticorrelations).
Uncertainties for each bin can be estimated us-
ing the methods in section 4.2.

For both data input cases, when the data show
skewed excess dispersion, the question can arise
of whether one must use all data or may attempt
to identify and omit outliers during the modeling
process. In addition to the approaches to outlier
identification discussed in section 3.1, another
procedure involves evaluating single grains of
a sample for compatibility by modeling them
individually and overlaying their solutions to
determine if one or more are inconsistent with
the rest (Sousa and Farley, 2020). This approach
provides a potentially concrete and non-biased
way of screening grains, but it is not without
weaknesses. Underestimated uncertainties on
the individual analyses or an inappropriate model
structure may yield results that suggest an analy-
sis is inconsistent with the rest of the data when
it is not, or a grain can be partially influenced by
an omitted factor in such a way that it remains
sufficiently consistent with other grains to be in-
cluded but nevertheless distorts the joint solution.
Integrating multiple approaches to outlier identi-
fication can be valuable and appropriate.

5.4. Recommendations for Reporting
Thermal History Models

Thermal history modeling of (U-Th)/He data sets is an interpretational exercise. There are multiple reasonable approaches to this process, including those outlined above, with the strategy partly dependent on the data pattern, software used, and interpreted geologic context. It is not unusual for scientists to approach modeling of a single data set in different ways. This is no different from the interpretation of any data set in the Earth sciences, where scientists may reasonably reach divergent conclusions depending on the factors most weighted in the interpretational process. As long as the published product clearly explains the rationale for why and how interpretations were developed, and transparently conveys how well the preferred solutions reproduce the observed thermochronologic and geologic data, these differences can be healthy and help focus future work to best test and refine interpretations.

For these reasons, we emphasize that publica-
tions should clearly explain the rationale for the
model setup and the path to the favored geologic
interpretation. Table 3 is a checklist of minimum
needed information to report for thermal history
models. A semi-standardized format for present-
ing this information was proposed previously
(Flowers et al., 2015). All information needed
to assess and reproduce the conclusions, and for
others to use the same data to develop alternative
models and interpretations, must be provided.
However, there is no thermal history modeling
approach that is clearly superior to all others for
all data sets, and a single modeling philosophy
should not be forced on the interpretation of (U-
Th)/He data sets.

6. OPPORTUNITIES AND LOOKING FORWARD

Numerous opportunities exist to acquire in-
formation to improve decisions about how to
interpret data, incorporate them into modeling,
and infer geologic meaning from the results.
Looking forward, we see opportunities in the
following areas:

(1) *Improved grain characterization.* In some circumstances, the acquisition of additional information regarding parent isotope zonation, radiation damage, He distribution, and other factors via LA-ICP-MS, Raman spectroscopy, in situ He analysis (Danišík et al., 2017), and other methods may assist with data interpretation. Implementing efficient lab workflows that include the acquisition of such data as a more routine aspect of (U-Th)/He dating would be an important step in this direction.

(2) *Diffusion kinetics.* Improved understanding of He diffusion kinetics, and in particular how they are impacted by radiation damage accumulation and annealing, will improve our ability to properly interpret (U-Th)/He data sets, from appropriately attributing dispersion to deriving reliable thermal histories.

(3) *Uncertainties and dispersion.* Improved quantification of individual analysis uncertainties (see companion paper, Flowers et al., 2022) would be beneficial for determining whether individual analyses vary beyond what is expected from analytical and geometric effects and thus whether they are or are not truly “dispersed.” Appropriate uncertainties on eU, crystal size, and other parameters are similarly needed to effectively interrogate data for date-eU correlations, date-size relationships, and other data patterns.

(4) *Representation and statistical characterization of dispersed data sets.* Samples with (U-Th)/He dates that differ by more than the single-grain analytical uncertainties are relatively common. This may be due either to ex-
understandable data patterns believed to be ac-
counted for by the model (section 3).

There are two principal options for data input:
(1) inputting the individual analyses and their as-
sociated uncertainties or (2) using averaging into
"synthetic" grains either for the entire sample or
within kinetic subgroups.

(1) One approach is to input the individual analyses and their associated uncertainties. This can be considered the most holistic approach, as it allows the inversion procedure to sort through possibly competing kinetic influences from size, eU, and other factors such as composition or zoning if appropriate data have been gathered. However, it has a higher computational overhead and assumes that the uncertainties are fully characterized, which is generally not the case. Most reported uncertainties do not currently include those associated with the F<sub>T</sub> correction and cannot incorporate factors that are not characterized (e.g., He implantation, eU zonation). If uncertainties are underestimated, the result can be either no fits or an overly restricted swath of tT paths. To compensate, if excess dispersion appears symmetric, individual estimated uncertainties can be increased. However, if some dates partially result from omitted factors or mechanisms leading to a highly skewed distribution, including these dates can distort any joint solution or preclude finding one. QTQt software will search for thermal histories that reproduce the input data to the maximum extent possible and may simultaneously prefer simpler solutions. QTQt also allows uncertainties in U, Th, Sm, He, and grain size to be re-evaluated as a part of the fitting process. However, because of this flexibility, results must be checked carefully against the original data to ensure that any degree of misfit is acceptable.

An additional consideration is the representa-
tion of (U-Th)/He data relative to other data be-
ing modeled simultaneously (e.g., fission track,
vitrinite). In both HeFTy and QTQt, the more in-
stances of a given type of data that are included,
the more that data type influences the solution.
Consequently, modeling, for example, five in-
dividual (U-Th)/He dates and one fission-track
date may weight the solution toward the (U-Th)/
He data in a manner not necessarily anticipated
or desired by the researcher.

(2) Another approach is to use averaging into "synthetic" grains either for the entire sample or within kinetic subgroups. This approach allows one to apply an uncertainty model that does a better job of characterizing group dispersion than the individual estimated uncertainties, and it also decreases computational load and equalizes weighting among data types. For samples for which it is reasonable to report a mean (see section 4), one could use the weighted or un-

weighted mean and uncertainty reported for
the sample, often without loss of information.
This approach is functionally analogous to the
standard procedure of combining fission-track
single-grain dates into one date and uncertainty.

For samples for which it is not reasonable to
report a mean, one can model the data within
appropriate kinetic bins, usually eU, but poten-
tially incorporating other factors such as size or
composition, if they appear to organize the data
(e.g., date-eU correlations or anticorrelations).
Uncertainties for each bin can be estimated us-
ing the methods in section 4.2.

For both data input cases, when the data show
skewed excess dispersion, the question can arise
of whether one must use all data or may attempt
to identify and omit outliers during the modeling
process. In addition to the approaches to outlier
identification discussed in section 3.1, another
procedure involves evaluating single grains of
a sample for compatibility by modeling them
individually and overlaying their solutions to
determine if one or more are inconsistent with
the rest (Sousa and Farley, 2020). This approach
provides a potentially concrete and non-biased
way of screening grains, but it is not without
weaknesses. Underestimated uncertainties on
the individual analyses or an inappropriate model
structure may yield results that suggest an analy-
sis is inconsistent with the rest of the data when
it is not, or a grain can be partially influenced by
an omitted factor in such a way that it remains
sufficiently consistent with other grains to be in-
cluded but nevertheless distorts the joint solution.
Integrating multiple approaches to outlier identi-
fication can be valuable and appropriate.

5.4. Recommendations for Reporting
Thermal History Models

Thermal history modeling of (U-Th)/He data sets is an interpretational exercise. There are multiple reasonable approaches to this process, including those outlined above, with the strategy partly dependent on the data pattern, software used, and interpreted geologic context. It is not unusual for scientists to approach modeling of a single data set in different ways. This is no different from the interpretation of any data set in the Earth sciences, where scientists may reasonably reach divergent conclusions depending on the factors most weighted in the interpretational process. As long as the published product clearly explains the rationale for why and how interpretations were developed, and transparently conveys how well the preferred solutions reproduce the observed thermochronologic and geologic data, these differences can be healthy and help focus future work to best test and refine interpretations.

For these reasons, we emphasize that publica-
tions should clearly explain the rationale for the
model setup and the path to the favored geologic
interpretation. Table 3 is a checklist of minimum
needed information to report for thermal history
models. A semi-standardized format for present-
ing this information was proposed previously
(Flowers et al., 2015). All information needed
to assess and reproduce the conclusions, and for
others to use the same data to develop alternative
models and interpretations, must be provided.
However, there is no thermal history modeling
approach that is clearly superior to all others for
all data sets, and a single modeling philosophy
should not be forced on the interpretation of (U-
Th)/He data sets.

6. OPPORTUNITIES AND LOOKING FORWARD

Numerous opportunities exist to acquire in-
formation to improve decisions about how to
interpret data, incorporate them into modeling,
and infer geologic meaning from the results.
Looking forward, we see opportunities in the
following areas:

(1) *Improved grain characterization.* In some circumstances, the acquisition of additional information regarding parent isotope zonation, radiation damage, He distribution, and other factors via LA-ICP-MS, Raman spectroscopy, in situ He analysis (Danišík et al., 2017), and other methods may assist with data interpretation. Implementing efficient lab workflows that include the acquisition of such data as a more routine aspect of (U-Th)/He dating would be an important step in this direction.

(2) *Diffusion kinetics.* Improved understanding of He diffusion kinetics, and in particular how they are impacted by radiation damage accumulation and annealing, will improve our ability to properly interpret (U-Th)/He data sets, from appropriately attributing dispersion to deriving reliable thermal histories.

(3) *Uncertainties and dispersion.* Improved quantification of individual analysis uncertainties (see companion paper, Flowers et al., 2022) would be beneficial for determining whether individual analyses vary beyond what is expected from analytical and geometric effects and thus whether they are or are not truly “dispersed.” Appropriate uncertainties on eU, crystal size, and other parameters are similarly needed to effectively interrogate data for date-eU correlations, date-size relationships, and other data patterns.

(4) *Representation and statistical characterization of dispersed data sets.* Samples with (U-Th)/He dates that differ by more than the single-grain analytical uncertainties are relatively common. This may be due either to ex-
pected date variation from variable kinetics or
to overdispersion from other causes. Additional
approaches for representing such data sets and
statistically characterizing them are needed.

(5) **Outlier identification.** The development and implementation of analytical and statistical methods for fingerprinting (U-Th)/He dates that are anomalous would increase confidence in the identification of biased analyses that should be banished from data sets. For example, continuous ramped heating methods hold promise in this arena (e.g., Idleman et al., 2018).

(6) *Generation of larger data sets via cost-effective and higher throughput methods.* Larger (U-Th)/He data sets would aid in identifying data patterns (e.g., date-eU relationships), characterizing the distribution of sample populations, and fingerprinting anomalous analyses. This would enhance data interpretation and decisions about how to statistically characterize sample data. More data are also required for detrital studies (e.g., Vermeesch, 2004), to decipher thermal histories in areas with complexly evolving thermal structures owing to topography and faulting (Gautheron and Zeitler, 2020), and to interpret orogenic-scale patterns of exhumation and relief change (e.g., Thomson et al., 2010; Ehlers et al., 2015). Developing more cost-effective methods that speed sample throughput will aid in achieving this. Laser ablation techniques (e.g., Boyce et al., 2006; Tripathy-Lang et al., 2013; Evans et al., 2015; Horne et al., 2016; Pickering et al., 2020) and more rapid dissolution methods for refractory phases like zircon are possible options.

(7) *Data management.* With the desire to increase the amount and types of analytical data associated with (U-Th)/He dates comes an associated need for effective data management tools. Efficient and fully integrated data reduction and management workflows in labs that harness the power of modern database systems would improve the traceability, recoverability, and organization of lab metadata and thereby increase the volume of high-quality data that can be produced and managed. Associated training of lab personnel in data management systems would enable these systems to be further adapted and customized in tandem with new analytical developments.

(8) *Thermal history modeling software.* Continued improvement in inverse thermal history modeling tools is needed to maximize the tT information extracted from different types of (U-Th)/He data sets. This includes optimizing their ability to efficiently simulate large and dispersed data sets, including deeper-time results for which inversion results are increasingly non unique, large portions of tT space must be searched, and assuming the simplest

monotonic cooling-only tT path framework is
less likely to be correct. Promoting user under-
standing of these modeling programs, the pros
and cons of each for different types of data
sets, and how to set up, present, and defend the
model structures used for the tT simulations,
will enhance the accuracy and clarity of thermal
history interpretations.

(9) *Thermal and kinematic modeling software.* Quantitative thermal and kinematic interpretation tools, ranging from 1-D and 2-D models of crustal thermal structures to 3-D numerical models that track the evolution of the crustal thermal field, have advanced in tandem with innovations in the (U-Th)/He technique (e.g., Braun, 2003; Ehlers and Farley, 2003; Braun et al., 2012; Mora et al., 2015). Such software enables modeling of the tT paths of rocks transiting through the crust to test geologic hypotheses for the data. It is important that these models are updated to include the most recent He diffusion kinetic models. As laboratory studies continue to constrain the factors that can contribute to a broad span of He diffusivity within single-mineral He thermochronometers, an ongoing challenge is how to honor and exploit this valuable intra-sample complexity when large multi-sample data sets are combined in thermokinematic models.

7. CONCLUSIONS

This manuscript summarizes key consider-
ations associated with evaluating, integrating,
and interpreting conventional individual aliquot
(U-Th)/He data. The methods associated with
the representation, statistical characterization,
interpretation, and modeling of different types
of (U-Th)/He data sets are under active develop-
ment. Our goals are to help guide non-experts in
the interpretational process, aid in transparent re-
porting and interpretational practices, and assist
in decisions about whether and how to assimilate
data into thermal history modeling.

(1) *Intra-sample date dispersion (section 2; Table 1).* A variety of factors can cause individual (U-Th)/He dates to vary beyond their analytical uncertainties, either due to interpretable kinetic effects (e.g., radiation damage, grain size) or other factors (e.g., U-Th zoneation, grain fragmentation and abrasion, parentless He). Many of these effects are magnified by tT paths characterized by protracted cooling through the HePRZ or reheating and partial He loss in the HePRZ. Table 1 summarizes these possible influences on the (U-Th)/He date, if they are affected by the character of the tT path, and whether they can be identified, exploited, and/or circumvented.

(2) *Evaluating (U-Th)/He thermochronologic data sets (section 3.1).* A reasonable workflow

for evaluating (U-Th)/He data sets in thermo-
chronometer studies includes: (1) evaluating
individual analysis quality, (2) constructing
date-eU and date-grain size plots, (3) assessing
the significance of data patterns, (4) consider-
ing outliers, and (5) deciding whether it is ap-
propriate to combine individual analyses from
a sample using a summary statistic such as a
mean date.

(3) *Evaluating (U-Th)/He geochronologic data sets (section 3.2).* When evaluating (U-Th)/He geochronologic data sets, assessing analysis quality and outliers before combining results is recommended. In this case, the data are expected to define a normally distributed population appropriate for reporting a mean sample date.

(4) *Additional considerations in detrital studies (section 3.3).* An important first step in detrital studies that affects the interpretational process is to establish whether detrital samples are (1) unreset, such that the (U-Th)/He dates are older than or equal to the time of deposition and record the thermal history of the source region; (2) fully reset, such that the dates are younger than the depositional age and record information about peak burial heating and subsequent cooling; or (3) partially reset, such that dates are both older and younger than deposition and record information about maximum burial temperatures. Detrital samples typically yield wide dispersion, even those that are partially or fully reset, owing not only to the factors that can affect bedrock samples, but also due to variable pre-depositional histories, variable amounts of grain abrasion, and generally lower grain quality.

(5) *Integrating individual analyses (section 4; Table 2).* Use of a summary statistic to represent sample data assumes that the underlying distribution of dates for the sample population is known (e.g., He et al., 2021). For samples with normally distributed single grain dates, reporting a central tendency statistic is appropriate, but such a statistic is inappropriate for samples characterized by substantial skew in the date distribution or by kinetic variation. The criteria for combining or not combining individual analyses into a summary statistic should be stated, although at present there is no community agreement on approach. If data are combined, then how they are combined (e.g., unweighted mean, weighted mean, nature of weighting), how the uncertainty is represented, what factors are included in the uncertainty, and the confidence interval (1σ or 2σ) should be reported.

(6) *Interpreting data with thermal history models (section 5; Table 3).* Thermal history modeling is a central tool used to convert (U-Th)/He data to thermal history interpretation and test hypotheses for the data based on the
pected date variation from variable kinetics or
to overdispersion from other causes. Additional
approaches for representing such data sets and
statistically characterizing them are needed.

(5) **Outlier identification.** The development and implementation of analytical and statistical methods for fingerprinting (U-Th)/He dates that are anomalous would increase confidence in the identification of biased analyses that should be banished from data sets. For example, continuous ramped heating methods hold promise in this arena (e.g., Idleman et al., 2018).

(6) *Generation of larger data sets via cost-effective and higher throughput methods.* Larger (U-Th)/He data sets would aid in identifying data patterns (e.g., date-eU relationships), characterizing the distribution of sample populations, and fingerprinting anomalous analyses. This would enhance data interpretation and decisions about how to statistically characterize sample data. More data are also required for detrital studies (e.g., Vermeesch, 2004), to decipher thermal histories in areas with complexly evolving thermal structures owing to topography and faulting (Gautheron and Zeitler, 2020), and to interpret orogenic-scale patterns of exhumation and relief change (e.g., Thomson et al., 2010; Ehlers et al., 2015). Developing more cost-effective methods that speed sample throughput will aid in achieving this. Laser ablation techniques (e.g., Boyce et al., 2006; Tripathy-Lang et al., 2013; Evans et al., 2015; Horne et al., 2016; Pickering et al., 2020) and more rapid dissolution methods for refractory phases like zircon are possible options.

(7) *Data management.* With the desire to increase the amount and types of analytical data associated with (U-Th)/He dates comes an associated need for effective data management tools. Efficient and fully integrated data reduction and management workflows in labs that harness the power of modern database systems would improve the traceability, recoverability, and organization of lab metadata and thereby increase the volume of high-quality data that can be produced and managed. Associated training of lab personnel in data management systems would enable these systems to be further adapted and customized in tandem with new analytical developments.

(8) *Thermal history modeling software.* Continued improvement in inverse thermal history modeling tools is needed to maximize the tT information extracted from different types of (U-Th)/He data sets. This includes optimizing their ability to efficiently simulate large and dispersed data sets, including deeper-time results for which inversion results are increasingly non unique, large portions of tT space must be searched, and assuming the simplest

monotonic cooling-only tT path framework is
less likely to be correct. Promoting user under-
standing of these modeling programs, the pros
and cons of each for different types of data
sets, and how to set up, present, and defend the
model structures used for the tT simulations,
will enhance the accuracy and clarity of thermal
history interpretations.

(9) *Thermal and kinematic modeling software.* Quantitative thermal and kinematic interpretation tools, ranging from 1-D and 2-D models of crustal thermal structures to 3-D numerical models that track the evolution of the crustal thermal field, have advanced in tandem with innovations in the (U-Th)/He technique (e.g., Braun, 2003; Ehlers and Farley, 2003; Braun et al., 2012; Mora et al., 2015). Such software enables modeling of the tT paths of rocks transiting through the crust to test geologic hypotheses for the data. It is important that these models are updated to include the most recent He diffusion kinetic models. As laboratory studies continue to constrain the factors that can contribute to a broad span of He diffusivity within single-mineral He thermochronometers, an ongoing challenge is how to honor and exploit this valuable intra-sample complexity when large multi-sample data sets are combined in thermokinematic models.

7. CONCLUSIONS

This manuscript summarizes key consider-
ations associated with evaluating, integrating,
and interpreting conventional individual aliquot
(U-Th)/He data. The methods associated with
the representation, statistical characterization,
interpretation, and modeling of different types
of (U-Th)/He data sets are under active develop-
ment. Our goals are to help guide non-experts in
the interpretational process, aid in transparent re-
porting and interpretational practices, and assist
in decisions about whether and how to assimilate
data into thermal history modeling.

(1) *Intra-sample date dispersion (section 2; Table 1).* A variety of factors can cause individual (U-Th)/He dates to vary beyond their analytical uncertainties, either due to interpretable kinetic effects (e.g., radiation damage, grain size) or other factors (e.g., U-Th zonation, grain fragmentation and abrasion, parentless He). Many of these effects are magnified by tT paths characterized by protracted cooling through the HePRZ or reheating and partial He loss in the HePRZ. Table 1 summarizes these possible influences on the (U-Th)/He date, if they are affected by the character of the tT path, and whether they can be identified, exploited, and/or circumvented.

(2) *Evaluating (U-Th)/He thermochronologic data sets (section 3.1).* A reasonable workflow

for evaluating (U-Th)/He data sets in thermo-
chronometer studies includes: (1) evaluating
individual analysis quality, (2) constructing
date-eU and date-grain size plots, (3) assessing
the significance of data patterns, (4) consider-
ing outliers, and (5) deciding whether it is ap-
propriate to combine individual analyses from
a sample using a summary statistic such as a
mean date.

(3) *Evaluating (U-Th)/He geochronologic data sets (section 3.2).* When evaluating (U-Th)/He geochronologic data sets, assessing analysis quality and outliers before combining results is recommended. In this case, the data are expected to define a normally distributed population appropriate for reporting a mean sample date.

(4) Additional considerations in detrital studies (section 3.3). An important first step in detrital studies that affects the interpretational process is to establish whether detrital samples are (1) unreset, such that the (U-Th)/He dates are older than or equal to the time of deposition and record the thermal history of the source region; (2) fully reset, such that the dates are younger than the depositional age and record information about peak burial heating and subsequent cooling; or (3) partially reset, such that dates are both older and younger than deposition and record information about maximum burial temperatures. Detrital samples typically yield wide dispersion, even those that are partially or fully reset, owing not only to the factors that can affect bedrock samples, but also due to variable pre-depositional histories, variable amounts of grain abrasion, and generally lower grain quality.

(5) *Integrating individual analyses (section 4; Table 2).* Use of a summary statistic to represent sample data assumes that the underlying distribution of dates for the sample population is known (e.g., He et al., 2021). For samples with normally distributed single grain dates, reporting a central tendency statistic is appropriate, but such a statistic is inappropriate for samples characterized by substantial skew in the date distribution or by kinetic variation. The criteria for combining or not combining individual analyses into a summary statistic should be stated, although at present there is no community agreement on approach. If data are combined, then how they are combined (e.g., unweighted mean, weighted mean, nature of weighting), how the uncertainty is represented, what factors are included in the uncertainty, and the confidence interval (1σ or 2σ) should be reported.

(6) *Interpreting data with thermal history models (section 5; Table 3).* Thermal history modeling is a central tool used to convert (U-Th)/He data to thermal history interpretation and test hypotheses for the data based on the
sample context. Which data are simulated, how
they are input into the model (section 5.3), and
what independent geologic and geochronologic
constraints are considered reliable, relevant to
the simulated samples, and therefore important
to honor (section 5.2) are all interpretive deci-
sions that must be made and should be carefully
considered during model setup. Different mod-
eling philosophies and approaches have been
developed, and it can be entirely reasonable for
divergent scientific conclusions to be reached de-
pending on the choices made and weighting of
different factors during the interpretational path.
Consequently, when thermal history models are
used to interpret data, it is imperative to clearly
explain the rationale for the model framework
and how geologic interpretations are developed
from model results so that the others can assess
the reliability of the outcomes and how they can
be further tested. Therefore, the published prod-
uct should state and explain (also see section 5.4
and checklist in Table 3): (1) the rationale for
the model structure, logic for the imposed tT
constraints, and details of the model setup; (2)
constraints on the character of tested tT paths or
solutions; (3) what data are used in the modeling
and why; (4) how data are input (i.e., as single
grains, or as synthetic sample or kinetic sub-
group averages); (5) the kinetic model(s) used;
(6) all data and information need to reproduce
thermal history model results; (7) tT modeling
program used and statistical fitting criteria; (8)
clear representation and explanation of model
outputs, including a representation of how well
the tT path results fit the observed data; and (9)
how model outputs were used to reach the final
geologic interpretation.

ACKNOWLEDGMENTS

Two anonymous reviewers and Kip Hodges provided
helpful comments that improved this contribution. We
thank Brad Singer for efficient editorial handling and
Kerry Gallagher for feedback on an earlier version of
this manuscript. U.S. National Science Foundation
grants EAR-1822119, -1844182, and -1925489 to R.M.
Flowers provided partial support for this work.

REFERENCES CITED

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Anderson, A.J., Hodges, K.V., and van Soest, M.C., 2018, Comment on ‘Distinguishing slow cooling versus multiphase cooling and heating in zircon and apatite (U-Th)/He datasets: The case of the McClure Mountain syenite standard’ by Weisberg, Metcalf, and Flowers: Chemical Geology, v. 498, p. 150–152, https://doi.org/10.1016/j.chemgeo.2018.07.006.

Ault, A.K., and Flowers, R.M., 2012, Is apatite U–Th zonation information necessary for accurate interpretation of apatite (U–Th)/He thermochronometry data?: Geochimica et Cosmochimica Acta, v. 79, p. 60–78, https://doi.org/10.1016/j.gca.2011.11.037.

Ault, A.K., Gautheron, C., and King, G.E., 2019, Innovations in (U–Th)/He, fission track, and trapped charge thermochronometry with applications to earthquakes, weathering, surface-mantle connections, and the growth and decay of mountains: Tectonics, v. 38, p. 3705–3739, https://doi.org/10.1029/2018TC005312.

Baughman, J.S., and Flowers, R.M., 2020, Mesoproterozoic burial of the Kaapvaal craton, southern Africa during Rodinia supercontinent assembly from (U-Th)/He thermochronology: Earth and Planetary Science Letters, v. 531, https://doi.org/10.1016/j.epsl.2019.115930.

Beucher, R., Brown, R.W., Roper, S., Stuart, F., and Persano, C., 2013, Natural age dispersion arising from the analysis of broken crystals: Part II. Practical application to apatite (U–Th)/He thermochronometry: Geochimica et Cosmochimica Acta, v. 120, p. 395–416, https://doi.org/10.1016/j.gca.2013.05.042.

Boyce, J.W., Hodges, K.V., Olszewski, W.J., Jercinovic, M.J., Carpenter, B.D., and Reiners, P.W., 2006, Laser microprobe (U-Th)/He geochronology: Geochimica et Cosmochimica Acta, v. 70, p. 3031–3039, https://doi.org/10.1016/j.gca.2006.03.019.

Braun, J., 2003, Pecube: A new finite-element code to solve the 3-D heat transport equation including the effects of a time-varying, finite amplitude surface topography: Computers & Geosciences, v. 29, p. 787–794, https://doi.org/10.1016/S0098-3004(03)00052-9.

Braun, J., van der Beek, P., Valla, P., Robert, X., Herman, F., Glotzbach, C., Pedersen, V., Perry, C., Simon-Labric, T., and Prigent, C., 2012, Quantifying rates of landscape evolution and tectonic processes by thermochronology and numerical modeling of crustal heat transport using PECUBE: Tectonophysics, v. 524–525, p. 1–28, https://doi.org/10.1016/j.tecto.2011.12.035.

Brown, R.W., Beucher, R., Roper, S., Persano, C., Stuart, F., and Fitzgerald, P., 2013, Natural age dispersion arising from the analysis of broken crystals. Part I: Theoretical basis and implications for the apatite (U-Th)/He thermochronometer: Geochimica et Cosmochimica Acta, v. 122, p. 478–497, https://doi.org/10.1016/j.gca.2013.05.041.

Campbell, I.H., Reiners, P.W., Allen, C.M., Nicolescu, S., and Upadhyay, R., 2005, He–Pb double dating of detrital zircons from the Ganges and Indus Rivers: Implications for quantifying sediment recycling and provenance studies: Earth and Planetary Science Letters, v. 237, p. 402–432, https://doi.org/10.1016/j.epsl.2005.06.043.

Cogné, N., Gallagher, K., Cobbold, P.R., Riccomini, C., and Gautheron, C., 2012, Post-breakup tectonics in southeast Brazil from thermochronological data and combined inverse-forward thermal history modeling: Journal of Geophysical Research: Solid Earth, v. 117, p. 1–16, https://doi.org/10.1029/2012JB009340.

Colgan, J.P., Shuster, D.L., and Reiners, P.W., 2008, Two-phase Neogene extension in the northwestern basin and range recorded in a single thermochronology sample: Geology, v. 36, p. 631–634, https://doi.org/10.1130/G24897A.1.

Cooperdock, E.H.G., and Ault, A.K., 2020, Iron oxide (U-Th)/He thermochronology: New perspectives on faults, fluids, and heat: Elements, v. 16, p. 319–324, https://doi.org/10.2138/gselements.16.5.319.

Cooperdock, E.H.G., Ketcham, R.A., and Stockli, D.F., 2019, Resolving the effects of 2-D versus 3-D grain measurements on (U-Th)/He age data and reproducibility: Geochronology, v. 1, p. 17–41, https://doi.org/10.5194/gchron-1-17-2019.

Daniškí, M., Pfaff, K., Evans, N.J., Manoloukos, C., Staude, S., McDonald, B.J., and Markl, G., 2010, Tectono-thermal history of the Schwarzwald Ore District (Germany): An apatite triple dating approach: Chemical Geology, v. 278, p. 58–69, https://doi.org/10.1016/j.chemgeo.2010.08.022.

Daniškí, M., Shane, P., Schmitt, A.K., Hogg, A., Santos, G.M., Storm, S., Evans, N.J., Fifield, L.K., and Lindsay, J.M., 2012, Re-anchoring the late Pleistocene tephrochronology of New Zealand based on concordant radiocarbon ages and combined $^{238}$U/$^{230}$Th disequilibrium and (U–Th)/He zircon ages: Earth and Planetary Science Letters, v. 349, p. 240–250, https://doi.org/10.1016/j.epsl.2012.06.041.

Daniškí, M., McInnes, B.I.A., Kirkland, C.L., McDonald, B.J., Evans, N.J., and Becker, T., 2017, Seeing is believing: Visualization of He distribution in zircon and implications for thermal history reconstruction on single crystals: Science Advances, v. 3, no. 2, https://doi.org/10.1126/sciadv.1601121.

Daniškí, M., Ponomareva, V., Portnyagin, M., Popov, S., Zastrozhnov, A., Kirkland, C.L., Evans, N.J., Konstantinov, E., Hauff, F., and Garbe-Sönberg, D., 2021, Gigantic eruption of a Carpathian volcano marks the largest Miocene transgression of Eastern Paratethys: Earth and Planetary Science Letters, v. 563, https://doi.org/10.1016/j.epsl.2021.116890.

dos Santos Albuquerque, M.F., Horbe, A.M.C., and Daniškí, M., 2020, Episodic weathering in Southwestern Amazonia based on (UTh)/He dating of Fe and Mn lateritic duricrust: Chemical Geology, v. 553, https://doi.org/10.1016/j.chemgeo.2020.119792.

Ehlers, T.A., 2005, Crustal thermal processes and the interpretation of thermochronometer data, in Reiners, P.W., and Ehlers, T.A. eds., Low-Temperature Thermochronology: Techniques, Interpretations, and Applications: Mineralogical Society of America, Reviews in Mineralogy and Geochemistry, v. 58, p. 315–350, https://doi.org/10.1515/9781501509575-014.

Ehlers, T.A., and Farley, K.A., 2003, Apatite (U-Th)/He thermochronometry: Methods and applications to problems in tectonic and surface processes: Earth and Planetary Science Letters, v. 206, p. 1–14, https://doi.org/10.1016/S0012-821X(02)01069-5.

Ehlers, T.A., Szameitá, A., Enkelmann, E., Yanites, B.J., and Woodsworth, G.J., 2015, Identifying spatial variations in glacial erosion with detrital thermochronology, Coast Mountains British Columbia: Journal of Geophysical Research: Earth Surface, v. 120, p. 1023–1039, https://doi.org/10.1002/2014JF003432.

Enkelmann, E., and Garver, J.I., 2016, On the use of low-temperature thermochronology to study ancient exhumation processes: Journal of Geodynamics, v. 93, p. 17–30, https://doi.org/10.1016/j.jog.2015.11.001.

Enkelmann, E., Zeitler, P.K., Garver, J.I., Pavlis, T.L., and Hooks, B.P., 2010, The thermochronological record of tectonic and surface process interaction at the Yakutat–North American collision zone in southeast Alaska: American Journal of Science, v. 310, p. 231–260, https://doi.org/10.2475/04.2010.01.

Enkelmann, E., Ridgway, K.D., Carignano, C., and Linnemann, U., 2014, A thermochronometric view into an ancient landscape: Tectonic setting, development, and inversion of the Paleozoic Paganzo basin, Argentina: Lithosphere, v. 6, p. 93–107, https://doi.org/10.1130/L309.1.

Enkelmann, E., Ehlers, T.A., Merli, G., and Methner, K., 2015, Thermal and exhumation history of the Eocene Chumstick Basin, Washington State, USA: Tectonics, v. 34, p. 951–969, https://doi.org/10.1002/2014TC003767.

Evans, N.J., McInnes, B.I.A., McDonald, B., Daniškí, M., Becker, T., Vermeesch, P., Shelley, M., Marillo-Sialer, E., and Patterson, D.B., 2015, An in situ technique for (U-Th-Sm)/He and U-Pb double dating: Journal of Analytical Atomic Spectrometry, v. 30, p. 1636–1645, https://doi.org/10.1039/C5JA00085H.

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Farley, K.A., 2000, Helium diffusion from apatite: General behavior as illustrated by Durango fluorapatite: Journal of Geophysical Research: Solid Earth, v. 105, p. 2903–2914, https://doi.org/10.1029/1999JB009348.

Farley, K.A., 2002, (U-Th)/He dating: Techniques, calibrations, and applications, in Porcelli, D., Ballentine, C.J., and Wieler, R., eds., Noble Gasses in Geochemistry and Cosmochemistry: Berlin, Germany, Walter de Gruyter, Reviews in Mineralogy and Geochemistry, v. 47, p. 819–846, https://doi.org/10.1515/9781501509056-020.

Farley, K.A., Rusmore, M.E., and Bogue, S.W., 2001, Post-10 Ma uplift and exhumation of the northern Coast mountains, British Columbia:
sample context. Which data are simulated, how
they are input into the model (section 5.3), and
what independent geologic and geochronologic
constraints are considered reliable, relevant to
the simulated samples, and therefore important
to honor (section 5.2) are all interpretive deci-
sions that must be made and should be carefully
considered during model setup. Different mod-
eling philosophies and approaches have been
developed, and it can be entirely reasonable for
divergent scientific conclusions to be reached de-
pending on the choices made and weighting of
different factors during the interpretational path.
Consequently, when thermal history models are
used to interpret data, it is imperative to clearly
explain the rationale for the model framework
and how geologic interpretations are developed
from model results so that the others can assess
the reliability of the outcomes and how they can
be further tested. Therefore, the published prod-
uct should state and explain (also see section 5.4
and checklist in Table 3): (1) the rationale for
the model structure, logic for the imposed tT
constraints, and details of the model setup; (2)
constraints on the character of tested tT paths or
solutions; (3) what data are used in the modeling
and why; (4) how data are input (i.e., as single
grains, or as synthetic sample or kinetic sub-
group averages); (5) the kinetic model(s) used;
(6) all data and information need to reproduce
thermal history model results; (7) tT modeling
program used and statistical fitting criteria; (8)
clear representation and explanation of model
outputs, including a representation of how well
the tT path results fit the observed data; and (9)
how model outputs were used to reach the final
geologic interpretation.

ACKNOWLEDGMENTS

Two anonymous reviewers and Kip Hodges provided
helpful comments that improved this contribution. We
thank Brad Singer for efficient editorial handling and
Kerry Gallagher for feedback on an earlier version of
this manuscript. U.S. National Science Foundation
grants EAR-1822119, -1844182, and -1925489 to R.M.
Flowers provided partial support for this work.

REFERENCES CITED

Anderson, A.J., Hodges, K.V., and van Soest, M.C., 2017, Empirical constraints on the effects of radiation damage on helium diffusion in zircon: Geochimica et Cosmochimica Acta, v. 218, p. 308–322, https://doi.org/10.1016/j.gca.2017.09.006.

Anderson, A.J., Hodges, K.V., and van Soest, M.C., 2018, Comment on 'Distinguishing slow cooling versus multiphase cooling and heating in zircon and apatite (U-Th)/He datasets: The case of the McClure Mountain syenite standard' by Weisberg, Metcalf, and Flowers: Chemical Geology, v. 498, p. 150–152, https://doi.org/10.1016/j.chemgeo.2018.07.006.

Ault, A.K., and Flowers, R.M., 2012, Is apatite U–Th zona-
tion information necessary for accurate interpretation of
apatite (U–Th)/He thermochronometry data?: Geochi-
mica et Cosmochimica Acta, v. 79, p. 60–78, https://doi
.org/10.1016/j.gca.2011.11.037.

Ault, A.K., Gautheron, C., and King, G.E., 2019, Innovations
in (U–Th)/He, fission track, and trapped charge thermo-
chronometry with applications to earthquakes, weath-
ering, surface-mantle connections, and the growth and
decay of mountains: Tectonics, v. 38, p. 3705–3739,
https://doi.org/10.1029/2018TC005312.

Baughman, J.S., and Flowers, R.M., 2020, Mesoproterozoic
burial of the Kaapvaal craton, southern Africa during
Rodinia supercontinent assembly from (U-Th)/He
thermochronology: Earth and Planetary Science Let-
ters, v. 531, https://doi.org/10.1016/j.epsl.2019.115930.

Beucher, R., Brown, R.W., Roper, S., Stuart, F., and Persano,
C., 2013, Natural age dispersion arising from the analy-
sis of broken crystals: Part II. Practical application to
apatite (U–Th)/He thermochronometry: Geochimica et
Cosmochimica Acta, v. 120, p. 395–416, https://doi.org
/10.1016/j.gca.2013.05.042.

Boyce, J.W., Hodges, K.V., Olszewski, W.J., Jercinovic,
M.J., Carpenter, B.D., and Reiners, P.W., 2006, Laser
microprobe (U-Th)/He geochronology: Geochimica et
Cosmochimica Acta, v. 70, p. 3031–3039, https://doi
.org/10.1016/j.gca.2006.03.019.

Braun, J., 2003, Pecube: A new finite-element code to solve
the 3-D heat transport equation including the effects
of a time-varying, finite amplitude surface topography:
Computers & Geosciences, v. 29, p. 787–794, https://
doi.org/10.1016/S0098-3004(03)00052-9.

Braun, J., van der Beek, P., Valla, P., Robert, X., Herman, F., Glotzbach, C., Pedersen, V., Perry, C., Simon-Labric, T., and Prigent, C., 2012, Quantifying rates of landscape evolution and tectonic processes by thermochronology and numerical modeling of crustal heat transport using PECUBE: Tectonophysics, v. 524–525, p. 1–28, https://doi.org/10.1016/j.tecto.2011.12.035.

Brown, R.W., Beucher, R., Roper, S., Persano, C., Stuart, F., and Fitzgerald, P., 2013, Natural age dispersion arising from the analysis of broken crystals. Part I: Theoretical basis and implications for the apatite (U-Th)/He thermochronometer: Geochimica et Cosmochimica Acta, v. 122, p. 478–497, https://doi.org/10.1016/j.gca.2013.05.041.

Campbell, I.H., Reiners, P.W., Allen, C.M., Nicolescu,
S., and Upadhyay, R., 2005, He–Pb double dating of
detrital zircons from the Ganges and Indus Rivers:
Implication for quantifying sediment recycling and
provenance studies: Earth and Planetary Science Let-
ters, v. 237, p. 402–432, https://doi.org/10.1016/j.epsl
.2005.06.043.

Cogné, N., Gallagher, K., Cobbold, P.R., Riccomini, C., and Gautheron, C., 2012, Post-breakup tectonics in southeast Brazil from thermochronological data and combined inverse-forward thermal history modeling: Journal of Geophysical Research: Solid Earth, v. 117, p. 1–16, https://doi.org/10.1029/2012JB009340.

Colgan, J.P., Shuster, D.L., and Reiners, P.W., 2008, Two-phase Neogene extension in the northwestern basin and range recorded in a single thermochronology sample: Geology, v. 36, p. 631–634, https://doi.org/10.1130/G24897A.1.

Cooperdock, E.H.G., and Ault, A.K., 2020, Iron oxide (U-
Th)/He thermochronology: New perspectives on faults,
fluids, and heat: Elements, v. 16, p. 319–324, https://doi
.org/10.2138/gselements.16.5.319.

Cooperdock, E.H.G., Ketcham, R.A., and Stockli, D.F., 2019, Resolving the effects of 2-D versus 3-D grain measurements on (U-Th)/He age data and reproducibility: Geochronology, v. 1, p. 17–41, https://doi.org/10.5194/gchron-1-17-2019.

Daniškí, M., Pfaff, K., Evans, N.J., Manoloukos, C., Staude,
S., McDonald, B.J., and Markl, G., 2010, Tectono-
thermal history of the Schwarzwald Ore District (Ger-
many): An apatite triple dating approach: Chemical
Geology, v. 278, p. 58–69, https://doi.org/10.1016/j
.chemgeo.2010.08.022.

Daniškí, M., Shane, P., Schmitt, A.K., Hogg, A., Santos,
G.M., Storm, S., Evans, N.J., Fifield, L.K., and Lind-
say, J.M., 2012, Re-anchoring the late Pleistocene
tephrochronology of New Zealand based on concordant
radiocarbon ages and combined <sup>238</sup>U/<sup>230</sup>Th disequilib-
rium and (U–Th)/He zircon ages: Earth and Planetary
Science Letters, v. 349, p. 240–250, https://doi.org/10
.1016/j.epsl.2012.06.041.

Daniškí, M., McInnes, B.I.A., Kirkland, C.L., McDonald,
B.J., Evans, N.J., and Becker, T., 2017, Seeing is believ-
ing: Visualization of He distribution in zircon and im-
plications for thermal history reconstruction on single
crystals: Science Advances, v. 3, no. 2, https://doi.org
/10.1126/sciadv.1601121.

Daniškí, M., Ponomareva, V., Portnyagin, M., Popov, S.,
Zastrozhnov, A., Kirkland, C.L., Evans, N.J., Konstan-
tinov, E., Hauff, F., and Garbe-Sönberg, D., 2021,
Gigantic eruption of a Carpathian volcano marks the
largest Miocene transgression of Eastern Paratethys:
Earth and Planetary Science Letters, v. 563, https://doi
.org/10.1016/j.epsl.2021.116890.

dos Santos Albuquerque, M.F., Horbe, A.M.C., and Daniškí,
M., 2020, Episodic weathering in Southwestern Ama-
zonia based on (UTh)/He dating of Fe and Mn lateritic
duricrust: Chemical Geology, v. 553, https://doi.org/10
.1016/j.chemgeo.2020.119792.

Ehlers, T.A., 2005, Crustal thermal processes and the inter-
pretation of thermochronometer data, in Reiners, P.W.,
and Ehlers, T.A. eds., Low-Temperature Thermochro-
nology: Techniques, Interpretations, and Applications:
Mineralogical Society of America, Reviews in Miner-
alogy and Geochemistry, v. 58, p. 315–350, https://doi
.org/10.1515/9781501509575-014.

Ehlers, T.A., and Farley, K.A., 2003, Apatite (U-Th)/He ther-
mochronometry: Methods and applications to problems
in tectonic and surface processes: Earth and Planetary
Science Letters, v. 206, p. 1–14, https://doi.org/10.1016
/S0012-821X(02)01069-5.

Ehlers, T.A., Szameitá, A., Enkelmann, E., Yanites, B.J., and Woodworth, G.J., 2015, Identifying spatial variations in glacial erosion with detrital thermochronology, Coast Mountains British Columbia: Journal of Geophysical Research: Earth Surface, v. 120, p. 1023–1039, https://doi.org/10.1002/2014JF003432.

Enkelmann, E., and Garver, J.I., 2016, On the use of low-
temperature thermochronology to study ancient ex-
humation processes: Journal of Geodynamics, v. 93,
p. 17–30, https://doi.org/10.1016/j.jog.2015.11.001.

Enkelmann, E., Zeitler, P.K., Garver, J.I., Pavlis, T.L., and
Hooks, B.P., 2010, The thermochronological record of
tectonic and surface process interaction at the Yaku-
tat–North American collision zone in southeast Alas-
ka: American Journal of Science, v. 310, p. 231–260,
https://doi.org/10.2475/04.2010.01.

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Farley, K.A., Shuster, D.L., and Ketcham, R.A., 2011, U and Th zonation in apatite observed by laser ablation ICPSM, and implications for the (U–Th)/He system: Geochimica et Cosmochimica Acta, v. 75, p. 4515–4530, https://doi.org/10.1016/j.gca.2011.05.202.

Fitzgerald, P.G.G., Baldwin, S.L.L., Webb, L.E.E., O'Sullivan, P., and O'Sullivan, P.B., 2006, Interpretation of (U-Th)/He single grain ages from slowly cooled crustal terranes: A case study from the Transantican Mountains of southern Victoria Land: Chemical Geology, v. 225, p. 91–120, https://doi.org/10.1016/j.chemgeo.2005.09.001.

Flowers, R.M., 2009, Exploiting radiation damage control on apatite (U–Th)/He dates in cratonic regions: Earth and Planetary Science Letters, v. 277, p. 148–155, https://doi.org/10.1016/j.epsl.2008.10.005.

Flowers, R.M., and Kelley, S.A., 2011, Interpreting data disper-
sion and "inverted" dates in apatite (U-Th)/He and fission-
track datasets: An example from the US midcontinent:
Geochimica et Cosmochimica Acta, v. 75, p. 5169–5186,
https://doi.org/10.1016/j.gca.2011.06.016.

Flowers, R.M., Shuster, D.L., Wernicke, B.P., and Farley, K.A., 2007, Radiation damage control on apatite (U-Th)/He dates from the Grand Canyon region, Colorado Plateau: Geology, v. 35, p. 447–450, https://doi.org/10.1130/G23471A.1.

Flowers, R.M., Wernicke, B.P., and Farley, K.A., 2008, Un-
roofing, incision and uplift history of the southwestern
Colorado Plateau from (U-Th)/He apatite thermochron-
ometry: Geological Society of America Bulletin,
v. 120, p. 571–587, https://doi.org/10.1130/B26231.1.

Flowers, R.M., Ketcham, R.A., Shuster, D.L., and Farley, K.A., 2009, Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model: Geochimica et Cosmochimica Acta, v. 73, p. 2347–2365, https://doi.org/10.1016/j.gca.2009.01.015.

Flowers, R.M., Farley, K.A., and Ketcham, R.A., 2015, A reporting protocol for thermochronologic modeling illustrated with data from the Grand Canyon: Earth and Planetary Science Letters, v. 432, p. 425–435, https://doi.org/10.1016/j.epsl.2015.09.053.

Flowers, R.M., Farley, K.A., and Ketcham, R.A., 2016, Re-
sponse to comment on "A reporting protocol for ther-
mochronologic modeling illustrated with data from the
Grand Canyon": Earth and Planetary Science Letters,
v. 441, p. 213, https://doi.org/10.1016/j.epsl.2016.02.024.

Flowers, R.M., Zeitler, P.K., Danišk, M., Reiners, P.W., Gautheron, C., Ketcham, R.A., Metcalf, J.R., Stockli, D.F., Enkelmann, E., and Brown, R.W., 2022, (U-Th)/He chronology: Part 1. Data, uncertainty, and reporting: Geological Society of America Bulletin, Special Volume on Reporting and Interpretation of Geochronologic Data, v. 134, https://doi.org/10.1130/B36266.1.

Fosdick, J.C., Grove, M., Graham, S.A., Hourigan, J.K., Lo-
vera, O., and Romans, B.W., 2015, Detrital thermochrо-
nologic record of burial heating and sediment recycling
in the Magallanes foreland basin, Patago ni an Andes:
Basin Research, v. 27, p. 546–572, https://doi.org/10.
1111/bre.12088.

Fox, M., Dai, J.G., and Carter, A., 2019, Badly behaved de-
tritual (U-Th)/He ages: Problems with He diffusion mod-
els or geological models?: Geochemistry, Geophysics,
Geosystems, v. 20, p. 2418–2432, https://doi.org/10.
1029/2018GC008102.

Gallagher, K., 2012, Transdimensional inverse thermal history modeling for quantitative thermochronology: Journal of Geophysical Research: Solid Earth, v. 117, no. B2, https://doi.org/10.1029/2011JB008825.

Gallagher, K., 2016, Comment on "A reporting protocol for thermochronologic modeling illustrated with data from the Grand Canyon" by Flowers, Farley and Ketcham: Earth and Planetary Science Letters, v. 441, p. 211–212, https://doi.org/10.1016/j.epsl.2016.02.021.

Gallagher, K., and Ketcham, R.A., 2018, Comment on the "Thermal history modelling: HeFTy vs. QTQt" by Vermees and Tian, Earth-Science Reviews (2014), 139, 279–290: Earth-Science Reviews, v. 176, p. 387–394, https://doi.org/10.1016/j.earscirev.2017.11.001.

Gallagher, K., and Ketcham, R.A., 2020, Comment on the reply to the Comment on "Thermal history modelling: HeFTy vs. QTQt" by Vermees and Tian, Earth-Science

Reviews (2014), 139, 279-290: Earth-Science Reviews,
v. 203, https://doi.org/10.1016/j.earscirev.2019.102878.

Gautheron, C., and Zeitler, P.K., 2020, Noble gases deliver
cool dates from hot rocks: Elements, v. 16, p. 303–309,
https://doi.org/10.2138/gselements.16.5.303.

Gautheron, C., Tassan-got, L., Barbarand, J., and Pagel, M., 2009, Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology: Chemical Geology, v. 266, p. 157–170, https://doi.org/10.1016/j.chemgeo.2009.06.001.

Gautheron, C., Tassan-Got, L., Ketcham, R.A., and Dobson, K.J., 2012, Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: 3-D modeling of diffusion, zoning, implantation, and abrasion: Geochimica et Cosmochimica Acta, v. 96, p. 44–56, https://doi.org/10.1016/j.gca.2012.08.016.

Gautheron, C., Barbarand, J., Ketcham, R.A., Tassan-Got, L., van der Beek, P., Pagel, M., Pinna-Jamme, R., Couffignal, F., and Fialin, M., 2013, Chemical influence on α-recoil damage annealing in apatite: Implications for (U-Th)/He dating: Chemical Geology, v. 351, p. 257–267, https://doi.org/10.1016/j.chemgeo.2013.05.027.

Gerin, C., Gautheron, C., Oliviero, E., Bachelet, C., Mbongo Djimi, D., Seydoux-Guillaume, A.M., Tassan-Got, L., Sarda, P., Roques, J., and Garrido, F., 2017, Influence of vacancy damage on He diffusion in apatite, investigated at atomic to mineralogical scales: Geochimica et Cosmochimica Acta, v. 197, p. 87–103, https://doi.org/10.1016/j.gca.2016.01.018.

Grabowski, D., Enkelmann, E., and Ehlers, T.A., 2013, Evaluation of the spatial extent of rapid exhumation in the St. Elias syntaxic region, SE Alaska: Journal of Geophysical Research: Earth Surface, v. 118, p. 1–18, https://doi.org/10.1002/jgrf.20136.

Green, P., and Duddy, I., 2020, Discussion: Extracting thermal history from low temperature thermochronology. A comment on recent exchanges between Vermeesch and Tian and Gallagher and Ketcham: Earth-Science Reviews, v. 2016, https://doi.org/10.1016/j.earscirev.2020.103197.

Guenther, W.R., Reiners, P.W., Ketcham, R.A., Nasdala, L., and Giester, G., 2013, Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology: American Journal of Science, v. 313, p. 145–198, https://doi.org/10.2475/03.2013.01.

Guenther, W.R., Reiners, P.W., Decelles, P.G., and Kendall, J., 2015, Sevier belt exhumation in central Utah constrained from complex zircon (U-Th)/He data sets: Radiation damage and He inheritance effects on partially reset detrital zircons: Geological Society of America Bulletin, v. 127, p. 323–348, https://doi.org/10.1130/B310321.

He, J., Thomson, S.N., Reiners, P.W., Hemming, S.R., and Licht, K.J., 2021, Rapid erosion of the central Transantarctic Mountains at the Eocene–Oligocene transition: Evidence from skewed (U-Th)/He date distributions near Beardmore Glacier: Earth and Planetary Science Letters, v. 567, https://doi.org/10.1016/j.epsl.2021.117009.

Horne, A.M., van Soest, M.C., Hodges, K.V., Tripathy-Lang, A., and Hourigan, J.K., 2016, Integrated single crystal laser ablation U/Pb and (U-Th)/He dating of detrital accessory minerals—Proof-of-concept studies of titanites and zircons from the Fish Canyon tuff: Geochimica et Cosmochimica Acta, v. 178, p. 106–123, https://doi.org/10.1016/j.gca.2015.11.044.

Hourigan, J.K., Reiners, P.W., and Brandon, M.T., 2005, U-Th zonation-dependent alpha-ejection in (U-Th)/He chronometry: Geochimica et Cosmochimica Acta, v. 69, p. 3349–3365, https://doi.org/10.1016/j.gca.2005.01.024.

Idleman, B.D., Zeitler, P.K., and McDannell, K.T., 2018, Characterization of helium release from apatite by continuous ramped heating: Chemical Geology, v. 476, p. 223–232, https://doi.org/10.1016/j.chemgeo.2017.11.019.

Janowski, M., Loget, N., Gautheron, C., Barbarand, J., Bellahsen, N., Van den Driessche, J., Babault, J., and Meyer, B., 2017, Neogene exhumation and relief evolution in the eastern Betics (SE Spain): Insights from the Sierra de Gador: Terra Nova, v. 29, p. 91–97, https://doi.org/10.1111/ter.12252.

Johnstone, S., Hourigan, J., and Gallagher, C., 2013, LA-ICP-MS depth profile analysis of apatite: Protocol and

implications for (U-Th)/He thermochronometry: Geo-
chimica et Cosmochimica Acta, v. 109, p. 143–161,
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Kelly, N.M., Flowers, R.M., Metcalf, J.R., and Mojzsis, S.J., 2018, Late accretion to the Moon recorded in zircon (U-Th)/He thermochronometry: Earth and Planetary Science Letters, v. 482, p. 222–235, https://doi.org/10.1016/j.epsl.2017.11.009.

Ketcham, R.A., 2005, Forward and inverse modeling of low temperature thermochronometry data, in Reiners, P.W., and Ehlers, T.A. eds., Thermochronology: Reviews in Mineralogy and Geochemistry, v. 58, p. 275–314, https://doi.org/10.1515/9781501509575-013.

Ketcham, R.A., 2012, Basin thermal history analysis using (U-Th)/He thermochronometry, in Harris, N.B., and Peters, K.E., Analyzing the Thermal History of Sedimentary Basins: Methods and Case Studies: Society for Sedimentary Biology (SEPM) Special Publication 103, p. 105–123, https://doi.org/10.2110/sepmsp.103.105.

Ketcham, R.A., van der Beek, P., Barbarand, J., Bernet, M., and Gautheron, C., 2018, Reproducibility of thermal history reconstruction from apatite fission-track and (U-Th)/He data: Geochemistry, Geophysics, Geosystems, v. 19, p. 2411–2436, https://doi.org/10.1029/2018GC007555.

Kirkland, C.L., Barham, M., and Danišk, M., 2020, Find a match with triple-dating: Antarctic sub-ice zircon debris on the modern shore of Western Australia: Earth and Planetary Science Letters, v. 531, https://doi.org/10.1016/j.epsl.2019.115953.

Lippolt, H.J., Leitz, M., Wernicke, R.S., and Hagedorn, B., 1994, (Uranium + thorium)/helium dating of apatite: Experience with samples from different geochemical environments: Chemical Geology, v. 112, p. 179–191, https://doi.org/10.1016/0009-2541(94)90113-9.

Mbongo Djimi, D., Gautheron, C., Roques, J., Tassan-Got, L., Gerin, C., and Simoni, E., 2015, Impact of apatite chemical composition on (U-Th)/He thermochronometry: An atomistic point of view: Geochimica et Cosmochimica Acta, v. 167, p. 162–176, https://doi.org/10.1016/j.gca.2015.06.017.

McDannell, K.T., and Flowers, R.M., 2020, Vestiges of the ancient: Deep-time noble gas thermochronology: Elements, v. 16, p. 325–330, https://doi.org/10.1238/gselements.16.5.325.

McDannell, K.T., Zeitler, P.K., Janes, D.G., Idleman, B.D., and Fayon, A.K., 2018, Screening apatites for (U-Th)/He thermochronometry via continuous ramped heating: He age components and implications for age dispersion: Geochimica et Cosmochimica Acta, v. 223, p. 90–106, https://doi.org/10.1016/j.gca.2017.11.031.

McKay, R., Enkelmann, E., Hadlari, T., Matthews, W., and Monthereau, F., 2021, Cenozoic exhumation history of the eastern margin of the Northern Canadian Cordillera: Tectonics, v. 40, p. 1–18, https://doi.org/10.1029/2020TC006582.

McKeon, R.E., Zeitler, P.K., Pazzaglia, F.J., Idleman, B.D., and Enkelmann, E., 2014, Decay of an old orogen: Inferences about Appalachian landscape evolution from low-temperature thermochronology: Bulletin of the Geological Society of America, v. 126, p. 31–46, https://doi.org/10.1130/B30808.1.

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duction–diffusion equation for finite diffusion domains
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Meesters, A.G.C.A., and Dunai, T.J., 2002b, Solving the production-diffusion equation for finite diffusion domains of various shapes part II. Application to cases with α-ejection and nonhomogeneous distribution of the source: Chemical Geology, v. 186, p. 57–73, https://doi.org/10.1016/S0009-2541(01)00423-5.

Mitchell, S.G., and Reiners, P.W., 2003, Influence of wildfires on apatite and zircon (U-Th)/He ages: Geology, v. 31, p. 1025–1028, https://doi.org/10.1130/G19758.1.

Mora, A., Casallas, W., Ketcham, R.A., Gomez, D., Parra, M., Namson, J., Stockli, D., Almendral, A., Robles, W., and Ghorbal, B., 2015, Kinematic restoration of contractional basement structures using thermokimematic models: A key tool for petroleum system modeling: American Association of Petroleum Geologists Bulletin, v. 99, p. 1575–1598, https://doi.org/10.1306/04281411108.
Geology, v. 29, p. 99–102, https://doi.org/10.1130
0091-7613(2001)029<0099:PMUAEO>2.0.CO;2

Farley, K.A., Shuster, D.L., and Ketcham, R.A., 2011, U and Th zonation in apatite observed by laser ablation ICPSM, and implications for the (U–Th)/He system: Geochimica et Cosmochimica Acta, v. 75, p. 4515–4530, https://doi.org/10.1016/j.gca.2011.05.202.

Fitzgerald, P.G.G., Baldwin, S.L.L., Webb, L.E.E., O'Sullivan, P., and O'Sullivan, P.B., 2006, Interpretation of (U-Th)/He single grain ages from slowly cooled crustal terranes: A case study from the Transantican Mountains of southern Victoria Land: Chemical Geology, v. 225, p. 91–120, https://doi.org/10.1016/j.chemgeo.2005.09.001.

Flowers, R.M., 2009, Exploiting radiation damage control on apatite (U–Th)/He dates in cratonic regions: Earth and Planetary Science Letters, v. 277, p. 148–155, https://doi.org/10.1016/j.epsl.2008.10.005.

Flowers, R.M., and Kelley, S.A., 2011, Interpreting data disper-
sion and "inverted" dates in apatite (U-Th)/He and fission-
track datasets: An example from the US midcontinent:
Geochimica et Cosmochimica Acta, v. 75, p. 5169–5186,
https://doi.org/10.1016/j.gca.2011.06.016.

Flowers, R.M., Shuster, D.L., Wernicke, B.P., and Farley, K.A., 2007, Radiation damage control on apatite (U-Th)/He dates from the Grand Canyon region, Colorado Plateau: Geology, v. 35, p. 447–450, https://doi.org/10.1130/G23471A.1.

Flowers, R.M., Wernicke, B.P., and Farley, K.A., 2008, Un-
roofing, incision and uplift history of the southwestern
Colorado Plateau from (U-Th)/He apatite thermochro-
nometry: Geological Society of America Bulletin,
v. 120, p. 571–587, https://doi.org/10.1130/B26231.1.

Flowers, R.M., Ketcham, R.A., Shuster, D.L., and Farley, K.A., 2009, Apatite (U-Th)/He thermochronometry using a radiation damage accumulation and annealing model: Geochimica et Cosmochimica Acta, v. 73, p. 2347–2365, https://doi.org/10.1016/j.gca.2009.01.015.

Flowers, R.M., Farley, K.A., and Ketcham, R.A., 2015, A reporting protocol for thermochronologic modeling illustrated with data from the Grand Canyon: Earth and Planetary Science Letters, v. 432, p. 425–435, https://doi.org/10.1016/j.epsl.2015.09.053.

Flowers, R.M., Farley, K.A., and Ketcham, R.A., 2016, Re-
sponse to comment on "A reporting protocol for ther-
mochronologic modeling illustrated with data from the
Grand Canyon": Earth and Planetary Science Letters,
v. 441, p. 213, https://doi.org/10.1016/j.epsl.2016.02.024.

Flowers, R.M., Zeitler, P.K., Danišk, M., Reiners, P.W., Gautheron, C., Ketcham, R.A., Metcalf, J.R., Stockli, D.F., Enkelmann, E., and Brown, R.W., 2022, (U-Th)/He chronology: Part 1. Data, uncertainty, and reporting: Geological Society of America Bulletin, Special Volume on Reporting and Interpretation of Geochronologic Data, v. 134, https://doi.org/10.1130/B36266.1.

Fosdick, J.C., Grove, M., Graham, S.A., Hourigan, J.K., Lo-
vera, O., and Romans, B.W., 2015, Detrital thermochro-
nologic record of burial heating and sediment recycling
in the Magallanes foreland basin, Patago ni an Andes:
Basin Research, v. 27, p. 546–572, https://doi.org/10.
1111/bre.12088.

Fox, M., Dai, J.G., and Carter, A., 2019, Badly behaved de-
tritual (U-Th)/He ages: Problems with He diffusion mod-
els or geological models?: Geochemistry, Geophysics,
Geosystems, v. 20, p. 2418–2432, https://doi.org/10.
1029/2018GC008102.

Gallagher, K., 2012, Transdimensional inverse thermal history modeling for quantitative thermochronology: Journal of Geophysical Research: Solid Earth, v. 117, no. B2, https://doi.org/10.1029/2011JB008825.

Gallagher, K., 2016, Comment on "A reporting protocol for thermochronologic modeling illustrated with data from the Grand Canyon" by Flowers, Farley and Ketcham: Earth and Planetary Science Letters, v. 441, p. 211–212, https://doi.org/10.1016/j.epsl.2016.02.021.

Gallagher, K., and Ketcham, R.A., 2018, Comment on the "Thermal history modelling: HeFTy vs. QTQt" by Vermees and Tian, Earth-Science Reviews (2014), 139, 279–290: Earth-Science Reviews, v. 176, p. 387–394, https://doi.org/10.1016/j.earscirev.2017.11.001.

Gallagher, K., and Ketcham, R.A., 2020, Comment on the reply to the Comment on "Thermal history modelling: HeFTy vs. QTQt" by Vermees and Tian, Earth-Science

Reviews (2014), 139, 279-290: Earth-Science Reviews, v. 203, https://doi.org/10.1016/j.earscirev.2019.102878.

Gautheron, C., and Zeitler, P.K., 2020, Noble gases deliver
cool dates from hot rocks: Elements, v. 16, p. 303–309,
https://doi.org/10.2138/gselements.16.5.303.

Gautheron, C., Tassan-got, L., Barbarand, J., and Pagel, M., 2009, Effect of alpha-damage annealing on apatite (U-Th)/He thermochronology: Chemical Geology, v. 266, p. 157–170, https://doi.org/10.1016/j.chemgeo.2009.06.001.

Gautheron, C., Tassan-Got, L., Ketcham, R.A., and Dobson, K.J., 2012, Accounting for long alpha-particle stopping distances in (U-Th-Sm)/He geochronology: 3-D modeling of diffusion, zoning, implantation, and abrasion: Geochimica et Cosmochimica Acta, v. 96, p. 44–56, https://doi.org/10.1016/j.gca.2012.08.016.

Gautheron, C., Barbarand, J., Ketcham, R.A., Tassan-Got, L., van der Beek, P., Pagel, M., Pinna-Jamme, R., Couffignal, F., and Fialin, M., 2013, Chemical influence on α-recoil damage annealing in apatite: Implications for (U-Th)/He dating: Chemical Geology, v. 351, p. 257–267, https://doi.org/10.1016/j.chemgeo.2013.05.027.

Gerin, C., Gautheron, C., Oliviero, E., Bachelet, C., Mbongo Djimi, D., Seydoux-Guillaume, A.M., Tassan-Got, L., Sarda, P., Roques, J., and Garrido, F., 2017, Influence of vacancy damage on He diffusion in apatite, investigated at atomic to mineralogical scales: Geochimica et Cosmochimica Acta, v. 197, p. 87–103, https://doi.org/10.1016/j.gca.2016.01.018.

Grabowski, D., Enkelmann, E., and Ehlers, T.A., 2013, Evaluation of the spatial extent of rapid exhumation in the St. Elias syntaxic region, SE Alaska: Journal of Geophysical Research: Earth Surface, v. 118, p. 1–18, https://doi.org/10.1002/jgrf.20136.

Green, P., and Duddy, I., 2020, Discussion: Extracting thermal history from low temperature thermochronology. A comment on recent exchanges between Vermeesch and Tian and Gallagher and Ketcham: Earth-Science Reviews, v. 2016, https://doi.org/10.1016/j.earscirev.2020.103197.

Guenther, W.R., Reiners, P.W., Ketcham, R.A., Nasdala, L., and Giester, G., 2013, Helium diffusion in natural zircon: Radiation damage, anisotropy, and the interpretation of zircon (U-Th)/He thermochronology: American Journal of Science, v. 313, p. 145–198, https://doi.org/10.2475/03.2013.01.

Guenther, W.R., Reiners, P.W., Decelles, P.G., and Kendall, J., 2015, Sevier belt exhumation in central Utah constrained from complex zircon (U-Th)/He data sets: Radiation damage and He inheritance effects on partially reset detrital zircons: Geological Society of America Bulletin, v. 127, p. 323–348, https://doi.org/10.1130/B310321.

He, J., Thomson, S.N., Reiners, P.W., Hemming, S.R., and Licht, K.J., 2021, Rapid erosion of the central Transantarctic Mountains at the Eocene–Oligocene transition: Evidence from skewed (U-Th)/He date distributions near Beardmore Glacier: Earth and Planetary Science Letters, v. 567, https://doi.org/10.1016/j.epsl.2021.117009.

Horne, A.M., van Soest, M.C., Hodges, K.V., Tripathy-Lang, A., and Hourigan, J.K., 2016, Integrated single crystal laser ablation U/Pb and (U-Th)/He dating of detrital accessory minerals—Proof-of-concept studies of titanites and zircons from the Fish Canyon tuff: Geochimica et Cosmochimica Acta, v. 178, p. 106–123, https://doi.org/10.1016/j.gca.2015.11.044.

Hourigan, J.K., Reiners, P.W., and Brandon, M.T., 2005, U-Th zonation-dependent alpha-ejection in (U-Th)/He chronometry: Geochimica et Cosmochimica Acta, v. 69, p. 3349–3365, https://doi.org/10.1016/j.gca.2005.01.024.

Idleman, B.D., Zeitler, P.K., and McDannell, K.T., 2018, Characterization of helium release from apatite by continuous ramped heating: Chemical Geology, v. 476, p. 223–232, https://doi.org/10.1016/j.chemgeo.2017.11.019.

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Peyton, S.L., Reiners, P.W., Carrapa, B., and Decelles, P.G., 2012, Low-temperature thermochronology of the northern Rocky Mountains, western U.S.A: American Journal of Science, v. 312, p. 145–212, https://doi.org/10.2475/02.2012.04.

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Pujols, E.J., Stockli, D.F., Constenius, K.N., and Horton, B.K., 2020, Thermochronological and geochronological constraints on Late Cretaceous unroofing and proximal sedimentation in the Sevier Orogenic Belt, Utah: Tectonics, v. 39, p. 1–32, https://doi.org/10.1029/2019TC005794.

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Reiners, P.W., and Farley, K.A., 2001, Influence of crystal size on apatite (U-Th)/He thermochronology: An example from the Bighorn Mountains, Wyoming: Earth and Planetary Science Letters, v. 188, p. 413–420, https://doi.org/10.1016/S0012-821X(01)00341-7.

Reiners, P.W., Campbell, I.H., Nicolescu, S., Allen, C.M., Hourigan, J.K., Garver, J.I., Mattinson, J.M., and Cowan, D.S., 2005, (U-Th)/(He-Pb) double dating of detrital zircons: American Journal of Science, v. 305, p. 259–311, https://doi.org/10.2475/ajs.305.4.259.

Reiners, P.W., Thomson, S.N., McPhillips, D., Donelick, R.A., and Roering, J.J., 2007, Wildfire thermochronology and the fate and transport of apatite in hillslope and fluvial environments: Journal of Geophysical Research: Earth Surface, v. 112, https://doi.org/10.1029/2007JF000759.

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Stanley, J.R., and Flowers, R.M., 2020, Mesozoic denudation history of the lower Orange River and eastward migration of erosion across the southern African Plateau: Lithosphere, v. 12, p. 74–87, https://doi.org/10.1130/L1121.1.

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Thomson, K.D., Stockli, D.F., Clark, J.D., Puigdefabregas, C., and Fildani, A., 2017, Detrital zircon (U-Th)/(He-Pb) double-dating constraints on provenance and foreland basin evolution of the Ainsa Basin, south-central Pyrenees, Spain: Tectonics, v. 36, p. 1352–1375, https://doi.org/10.1029/2017TC004504.

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Tremblay, M., Cooperdock, E.H.G., and Zeitler, P.K., eds., 2020, Noble gas thermochronology: Elements, v. 16, no. 5, https://doi.org/10.2138/gselements.16.5.331.

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SCIENCE EDITOR: BRAD S. SINGER

MANUSCRIPT RECEIVED 3 AUGUST 2021

REVISED MANUSCRIPT RECEIVED 4 DECEMBER 2021

MANUSCRIPT ACCEPTED 3 FEBRUARY 2022

Printed in the USA
Murray, K.E., Orme, D.A., and Reiners, P.W., 2014, Effects of U-Th-rich grain boundary phases on apatite helium ages: Chemical Geology, v. 390, p. 135–151, https://doi.org/10.1016/j.chemgeo.2014.09.023.

Orme, D.A., Reiners, P.W., Hourigan, J.K., and Carrapa, B., 2015, Effects of inherited cores and magmatic overgrowths on zircon (U-Th)/He ages and age-eU trends from Greater Himalayan sequence rocks, Mount Everest region, Tibet: Geochemistry, Geophysics, Geo- systems, v. 16, p. 2499–2507, https://doi.org/10.1002/2015GC005818.

Peak, B.A., Flowers, R.M., Macdonald, F.A., and Cottle, J.M., 2021, Zircon (U-Th)/He thermochronology reveals pre-Great Unconformity paleotopography in the Grand Canyon region, USA: Geology, v. 49, p. 1462–1466, https://doi.org/10.1130/G49116.1.

Peyton, S.L., Reiners, P.W., Carrapa, B., and Decelles, P.G., 2012, Low-temperature thermochronology of the northern Rocky Mountains, western U.S.A: American Journal of Science, v. 312, p. 145–212, https://doi.org/10.2475/02.2012.04.

Pickering, J., Matthews, W., Enkelmann, E., Guest, B., Sykes, C., and Koblinger, B.M., 2020, Laser ablation (U-Th-Sm)/He dating of detrital apatite: Chemical Geology, v. 548, https://doi.org/10.1016/j.chemgeo.2020.119683.

Powell, J., Schneider, D., Stockli, D., and Fallas, K., 2016, Zircon (U-Th)/He thermochronology of Neoproterozoic strata from the Mackenzie Mountains, Canada: Implications for the Phanerozoic exhumation and deformation history of the northern Canadian Cordillera: Tectonics, v. 35, p. 663–689, https://doi.org/10.1002/2015TC003989.

Pujols, E.J., Stockli, D.F., Constenius, K.N., and Horton, B.K., 2020, Thermochronological and geochronological constraints on Late Cretaceous unroofing and proximal sedimentation in the Sevier Orogenic Belt, Utah: Tectonics, v. 39, p. 1–32, https://doi.org/10.1029/2019TC005794.

Rahl, J.M., Reiners, P.W., Campbell, I.H., Nicolescu, S., and Allen, C.M., 2003, Combined single-grain (U-Th)/He and U/Pb dating of detrital zircons from the Navajo Sandstone, Utah: Geology, v. 31, p. 761–764, https://doi.org/10.1130/G19653.1.

Recanati, A., Grozavu, N., Bennani, Y., Gautheron, C., and Missenard, Y., 2021, Apatite (U-Th-Sm)/He date dispersion: First insights from machine learning algorithms: Earth and Planetary Science Letters, v. 554, https://doi.org/10.1016/j.epsl.2020.116655.

Reiners, P.W., and Farley, K.A., 2001, Influence of crystal size on apatite (U-Th)/He thermochronology: An example from the Bighorn Mountains, Wyoming: Earth and Planetary Science Letters, v. 188, p. 413–420, https://doi.org/10.1016/S0012-821X(01)00341-7.

Reiners, P.W., Campbell, I.H., Nicolescu, S., Allen, C.M., Hourigan, J.K., Garver, J.I., Mattinson, J.M., and Cowan, D.S., 2005, (U-Th)/(He-Pb) double dating of detrital zircons: American Journal of Science, v. 305, p. 259–311, https://doi.org/10.2475/ajs.305.4.259.

Reiners, P.W., Thomson, S.N., McPhillips, D., Donelick, R.A., and Roering, J.J., 2007, Wildfire thermochronology and the fate and transport of apatite in hillslope and fluvial environments: Journal of Geophysical Research: Earth Surface, v. 112, https://doi.org/10.1029/2007JF000759.

Reiners, P.W., Carlson, R.W., Renne, P.R., Cooper, K.M., Granger, D.E., McLean, N.M., and Schoene, B., 2018, The (U-Th)/He system, in Reiners, P.W., Carlson, R.W., Renne, P.R., Cooper, K.M., Granger, D.E., McLean, N.M., and Schoene, B., eds., Geochronology and Thermochronology: Hoboken, New Jersey, John Wiley & Sons Ltd., p. 291–356.

Schwartz, S., Gautheron, C., Audin, L., Dumont, T., Nomade, J., Barbarand, J., Pinna-Jamme, R., and van der Beek, P., 2017, Foreland exhumation controlled by crustal thickening in the Western Alps: Geology, v. 45, p. 139–142, https://doi.org/10.1130/G38561.1.

Shuster, D.L., Vasconcelos, P.M., Heim, J.A., and Farley, K.A., 2005, Weathering geochronology by (U-Th)/He dating of goethite: Geochimica et Cosmochimica Acta, v. 69, p. 659–673, https://doi.org/10.1016/j.gca.2004.07.028.

Shuster, D.L., Flowers, R.M., and Farley, K.A., 2006, The influence of natural radiation damage on helium diffusion kinetics in apatite: Earth and Planetary Science Letters, v. 249, p. 148–161, https://doi.org/10.1016/j.epsl.2006.07.028.

Sousa, F.J., and Farley, K.A., 2020, A framework for evaluating variation in (U-Th)/He datasets: Minerals, v. 10, p. 1–15, https://doi.org/10.3390/min10121111.

Spiegel, C., Kohn, B., Belton, D., Berner, Z., and Gleadow, A., 2009, Apatite (U-Th-Sm)/He thermochronology of rapidly cooled samples: The effect of He implantation: Earth and Planetary Science Letters, v. 285, p. 105–114, https://doi.org/10.1016/j.epsl.2009.05.045.

Stanley, J.R., and Flowers, R.M., 2020, Mesozoic denudation history of the lower Orange River and eastward migration of erosion across the southern African Plateau: Lithosphere, v. 12, p. 74–87, https://doi.org/10.1130/L11211.1.

Stock, G.M., Ehlers, T.A., and Farley, K.A., 2006, Where does sediment come from? Quantifying catchment erosion with detrital apatite (U-Th)/He thermochronometry: Geology, v. 34, p. 725–728, https://doi.org/10.1130/G22592.1.

Stockli, D.F., and Najman, Y.M.R., 2020, Earth's dynamic past revealed by detrital thermochronometry: Elements, v. 16, p. 311–317, https://doi.org/10.2138/gselements.16.5.311.

Stockli, D.F., Farley, K.A., and Dumitru, T.A., 2000, Calibration of the apatite (U-Th)/He thermochronometer on an exhumed fault flock, White Mountains: Geology, v. 28, p. 983–986, https://doi.org/10.1130/0091-7613(2000)28<983:COTAHT>2.0.CO;2.

Sturrock, C.P., Flowers, R.M., and Macdonald, F.A., 2021, The Late Great Unconformity of the Central Canadian Shield: Geochemistry, Geophysics, Geosystems, v. 22, p. 1–22, https://doi.org/10.1029/2020GC009567.

Thomson, K.D., Stockli, D.F., Clark, J.D., Puigdefabregas, C., and Fildani, A., 2017, Detrital zircon (U-Th)/(He-Pb) double-dating constraints on provenance and foreland basin evolution of the Ainsa Basin, south-central Pyrenees, Spain: Tectonics, v. 36, p. 1352–1375, https://doi.org/10.1002/2017TC004504.

Thomson, S.N., Brandon, M.T., Tomkin, J.H., Reiners, P.W., Vásquez, C., Wilson, N.J., and Vasquez, C., 2010, Glaciation as a destructive and constructive control on mountain building: Nature, v. 467, p. 313–317, https://doi.org/10.1038/nature09365.

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SCIENCE EDITOR: BRAD S. SINGER

MANUSCRIPT RECEIVED 3 AUGUST 2021

REVISED MANUSCRIPT RECEIVED 4 DECEMBER 2021

MANUSCRIPT ACCEPTED 3 FEBRUARY 2022

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