T_c1D, the modeling software used in this study, is a 1D thermal and thermochronometer age prediction software package written in Python that simulates the dynamic thermal effects of common geological processes at the scale of the full lithosphere . The software uses recorded thermal histories to calculate various thermochronometer ages for particles that reach the model surface during and at the end of simulations. The design of T_c1D is deliberately simple, allowing the user to vary a range of parameters and quickly explore their effects in (multi-)thermochronometry datasets. Thus, the goal is not to simulate all the geological details of a complex geodynamic process like lithospheric delamination or post-orogenic collapse, but rather to produce first-order dynamic “geological” heat transfer models and explore the relationships between those models, the corresponding depth and thermal histories experienced by particles reaching the model surface, and calculated low-temperature thermochronometry ages and characteristics (Fig. ). Thermochronometer systems supported in T_c1D include apatite (U–Th)/He (AHe), apatite fission-track (AFT), zircon (U–Th)/He (ZHe), and zircon fission track (ZFT). A more complete description of T_c1D, its design, and technical details can be found in .

T_c1D uses the finite-difference method to solve the transient heat transfer equation in 1D in the crust and lithospheric mantle, including the thermal effects of advection and volumetric heat production. Temperatures are fixed at the surface and base of the model, and the initial thermal field is calculated at a steady state using an optional advection velocity specified for the start of the simulation. The temperature calculation forward in time from the initial state can use either an implicit or explicit finite-difference solution with user-defined time steps. Rock thermal and physical properties are defined separately for the crust, lithospheric mantle, and asthenosphere. A variety of erosion models are built into T_c1D allowing users to explore many different burial (i.e., negative erosion) and exhumation histories (see Sect.  for details).

Thermal histories are recorded by tracking the temperature of particles that reach the model surface at the end of the simulation, and optionally at specified intervals during the simulation. The thermal histories are used to predict thermochronometer ages using the radiation damage accumulation and annealing models for AHe and ZHe , and the fission track annealing models for AFT and ZFT using the kinetics of or . The program used for AHe and ZHe age predictions is from , the AFT age prediction program is from as implemented in , and the ZFT age prediction code was ported to Python following its implementation in .

As noted above, all T_c1D models begin from an initial thermal steady state. In some of the model scenarios presented in this work, additional time at the thermal steady state (e.g., 5 Myr) is included in the design in order to highlight the onset of changes in the thermal history that result from various geological processes. For example, when processes such as the onset of faulting or heating due to removal of the mantle lithosphere are included, additional time at the start of the simulation is included in order to clearly show the timing of the changes in the recorded temperatures following the onset of such processes.

The durations of the models in this work are all ∼50 Myr to account for both times during which tectonic activity occurs and post-tectonic erosional exhumation. Although this may be a longer duration than recorded in thermochronometer data from active tectonic settings today, such as the Himalaya or Southern Alps of New Zealand, these generic models can be used as templates that can be modified to explore “younger” regions. To aid in supporting this, two examples of “younger” activity are provided in the supplementary material under Code and data availability.

Erosional exhumation in T_c1D is driven by movement of material toward the model surface point (i.e., rock uplift). The surface point has a fixed location at 0 km depth in the model, which is equivalent to the local surface elevation on Earth. Depending on the defined surface temperature, this point could be at sea level or somewhere above or below. As the surface point is fixed in space, any movement of material by the defined velocity field in the model will produce erosion (or sedimentation) at a rate equal to the velocity. In other words, we assume any surface uplift (or subsidence) is perfectly balanced by erosion (or sedimentation). Movement of material toward (or away from) the surface in T_c1D is defined in various “erosion models”. Examples include vertical motion at a constant velocity, multi-stage exhumation with step-function changes in the exhumation rate, vertical motion with an exponentially decaying rate, or convergent/extensional faulting where rates of motion vary above and below a defined fault depth. Details about each of the erosion models can be found in the online T_c1D documentation at https://tc1d.readthedocs.io/en/latest/erosion-models.html (last access: 16 April 2026) as well as in the supplementary material under Code and data availability.

All models presented here involve a significant amount of erosional exhumation because the calculated thermochronometer ages and closure temperatures in the models rely on the tracking particle reaching the surface at the end of the model run (hereafter called the final surface particle). Any scenarios involving insufficient exhumation will not capture the thermal history of the geological process under investigation. In these cases, the calculated cooling age will yield an unreset age roughly equivalent to the duration of the model, or a partially reset age. These cases are all clearly indicated as “partially/unreset” in the results. Such situations should also be clear in T_c1D thermal history plots, where ages for different chronometers are plotted on the thermal history at the time corresponding to their calculated age. A partially reset age, for example, could thus appear on a heating path. In this way, T_c1D can also be employed to explore minimum erosion magnitudes required to “capture” information about past geological processes using low-temperature thermochronology.

The complex effects of alpha damage accumulation on He retention in apatite and especially in zircon renders it impossible to accurately simulate He diffusion behavior in any models in which the final surface particle begins the simulation in a position of He and alpha damage accumulation see also. Crystal damage is thought to anneal in a similar way, and under similar temperature conditions, to fission tracks . Hence, most of the scenarios explored below involve a starting depth for which open system behavior is expected, and zircon or apatite should not have accumulated any alpha damage (∼300 °C). This is a recommended practice when using the T_c1D code.

Although we do not explore this in the presented results, it is also possible to vary the grain size and parent isotope concentrations for the AHe and ZHe systems in T_c1D. These values can be provided for single crystals in a T_c1D model by defining the relevant model parameters (e.g., ap_rad or ap_uranium for the effective spherical radius or uranium concentration in apatite). It is also possible to include multiple crystals of varying size and with variable parent isotope concentrations using an age data file, as described in the online documentation at https://tc1d.readthedocs.io/en/latest/age-data.html (last access: 16 April 2026). In addition, sensitivity to ranges of grain dimensions and parent isotope concentrations can be explored using the thermal history that is saved in the csv directory where T_c1D is run and importing that into T_cplotter .

Five common geological processes are explored with T_c1D. The first set of 12 models explores various styles of erosional exhumation (EE), followed by 6 sedimentary burial models (SB), 4 thrust faulting (TF) models, 4 extensional faulting (EF) models, and 4 lithospheric delamination models (DL) (Table , Fig. ). The scenarios presented are not intended to be exhaustive, or tailored to fit a particular natural analogue, but rather are designed to explore the sensitivity of low temperature thermochronometers to the effects of heat transfer influenced by these various processes. The different geological scenarios primarily affect movement of material within the model, resulting in heat transfer by advection and displacement of a thermal history tracking particle. Each model has a thickness of 125 km and a final Moho depth of 35 km. More detailed descriptions of each scenario are given below and other common model parameters are summarized in Table .

Twelve EE scenarios were explored, in which various magnitudes of exhumation and volumetric heat production, and different exhumation histories were applied over the 50 Myr of model run time (Fig. c; Table ).

EE1, in which 10 km of material was removed via constant exhumation at a rate of 0.2 kmMyr-1, shows FM and MM thermal histories for the final surface particle that are slightly concave upwards, reflecting the modest rate of exhumation. Tracked particles start cooling from ∼290 and ∼320 °C for the FM and MM model variants, respectively, reaching 0 °C at 0 Ma, or the model present (Fig. a). The different initial temperature at 10 km depth for the FM history versus the MM history relates to the differing initial Moho depths (35 vs. 45 km, respectively), and initial temperatures at the Moho (∼700 and ∼900 °C, respectively; see also supplementary plots under Code and data availability), which together result in different geothermal gradients and crustal temperature evolutions for the two scenarios. The Pe values also reflect the moderate rate of exhumation, with a constant value of ∼0.2 for the FM model and ∼0.9 for the MM model, indicating only a limited effect of exhumation on the crustal temperatures. The difference in Pe values results from application of the advection velocity to only the crust in the FM model, while the entire lithosphere is advected in the MM model. Both final surface particle starting temperatures are likely hot enough to produce open system/annealing behavior in all four low-temperature thermochronometers. The thermochronometer closure/annealing temperatures between the FM and MM scenarios are nearly identical, but the ages differ between the two scenarios because of the different thermal histories. The ZFT age for the MM scenario is ∼7 Myr younger than for the FM scenario (the ages differ by ∼20 %), with smaller differences in cooling age for the lower temperature thermochronometers as the two thermal histories converge towards 0 Ma at the surface.

EE2 is nearly identical to EE1, with 10 km of material being removed via constant exhumation, except the volumetric heat production of the (entire) crust is lowered to 1 µWm-3. The thermal history for the final surface particle in EE2 is similar to EE1, but with much cooler starting temperatures of ∼200 °C for the FM and MM scenarios, corresponding to an initial geothermal gradient for the upper 10 km of crust of only about 20 °Ckm-1. Due to lower initial temperatures that are within or cooler than the partial annealing temperature range for ZFT, the ZFT age is ignored here and in all subsequent models for which total exhumation is only 10 km. The thermal history trajectories for the FM and MM scenarios show less difference than in EE1. Despite contrasts in starting Moho temperature similar to the EE1 models of ∼500 and ∼700 °C, respectively, there is less difference in the FM and MM geotherms at shallow depths due to the lower radiogenic heat production. In these models, the dimensionless heat production f is ∼0.7, which is half its value in the EE1 models. However, as the thickness and rates of the exhumed layers have not changed compared to the EE1 models, the Pe values for the EE2 models are identical to those in EE1. The result is cooling ages that differ by 35 % on average between EE1 and EE2 (e.g., AFT and ZHe ages are respectively ∼7 and ∼9 Myr older in EE2), largely as a result of the cooler initial temperature of the final surface particles.

EE3 and EE4 are two-stage linear exhumation models that incorporate the same total amount of exhumation and volumetric heat production as in EE2, but either an initial 5 Myr period of rapid exhumation at 1 kmMyr-1 followed by slower exhumation at ∼0.1 kmMyr-1 over the remaining 45 Myr (EE3), or slower exhumation during the initial 45 Myr and a final 5 Myr period of rapid exhumation (EE4). These exhumation histories produce average Pe values of ∼0.2 and ∼0.9 for the FM and MM models, respectively, that are similar to the EE1 and EE2 models. However, the difference in exhumation rates over time yields maximum Pe values reach ∼0.9 for the FM variants and ∼4.5 for the MM variants, indicating efficient advective heat transfer during more rapid exhumation. In EE3, the early, rapid exhumation results in significantly older ages compared to EE2, while in EE4 the late rapid exhumation results in significantly younger low-temperature thermochronometer ages. Note that despite the common erosion rate while traversing the effective closure temperatures of the ZHe and AFT systems for these two models, the lag between the two systems is much shorter for EE3 (∼5 Myr) than for EE4 (∼10 Myr), due to the immediately preceding period of rapid erosion and cooling.

EE5 and EE6 represent fairly extreme erosional models in which 20 km of crust is removed in 50 Myr, corresponding to a long-lived constant erosion rate of 0.4 kmMyr-1. The difference in Moho depth in the MM scenario thus also differs by 20 km, resulting in an unrealistically hot starting Moho temperature of ∼1200 °C for EE5, in which the crust has a high heat production value (2 µWm-3), and >850 °C for EE6, in which the crust has an average heat production value (1 µWm-3). Though these are high Moho temperatures, the models are nevertheless instructive in accentuating the heat conduction effects observed in EE1 and EE2.

The cooling paths in EE5 and EE6 show more curvature than in EE1 and EE2, despite the constant erosion rate, as the final surface particle begins closer to the Moho and farther from the surface. The cooling rate initially is low following the onset of exhumation (and heat advection) before beginning to increase and produce a curved cooling trajectory. This curvature results from curvature in the geotherm (changes in the geothermal gradient with depth) as the result of more efficient advective heat transfer. In these models, the Pe values are ∼0.4 for the FM variants and ∼1.8 for the MM variants, double those for the EE1 and EE2 models. As the tracking particle nears the surface, the cooling path becomes more linear through the upper 10 km of exhumation, similar to EE1 and EE2. In these and all EE models, the shape of the thermal and depth histories match most closely in the uppermost crust, below ∼10 km depth and ∼250 °C and mainly show deviations at higher temperatures and deeper crustal depths. The ages for the four thermochronometers are clustered most closely in EE5, and particularly in the EE5 MM scenario, compared to any of the other scenarios explored thus far, spanning ca. 11 Myr. This reflects the high geothermal gradient from the high, sustained exhumation rate and high heat production for EE5. ZHe and AFT ages are particularly close and would be indistinguishable for typical reported errors of those methods.

Similar to EE3 and EE4, scenarios EE7 and EE8 explore two-stage linear exhumation models, but in which half of the 20 km total exhumation occurs in either the first 5 million years of run time (EE7) or the last 5 million years of run time (EE8) at a rate of 2 kmMyr-1, and erosion throughout the remainder of each model occurring at ∼0.2 kmMyr-1. In both FM and MM versions of EE7, the period of rapid exhumation at the model start shows a significant geometric deviation between the linear depth history and an S-shaped thermal history. The initial period of rapid exhumation (maximum Pe values of ∼1.8 and ∼9.0 for the FM and MM variants, respectively) advects heat upwards with limited cooling and the thermal adjustment to the slower cooling rate then lags behind the decrease in the exhumation rate. Thus, cooling ages may similarly lag behind the change in exhumation rate. However, since all thermochronometers close on the slow-exhumation segment of the depth history path, this deviation does not impact cooling ages in EE7, and the cooling age patterns in the MM and FM models are relatively similar to EE1. In EE8, there is a similar lag in the thermal history compared to the depth history during the rapid exhumation phase, here occurring in the last 5 Myr of the model, although the deviation is much smaller than in EE7 due to being closer to the model surface, with limited space to exhume without cooling. In this model, the difference in depth history for the FM and MM scenarios results in a ZFT age that is ∼11 Myr older (an increase of ∼190 %) in the FM scenario, despite its lower calculated effective closure temperature. Otherwise, rapid cooling through the upper crust shows a relatively close alignment between thermal and depth histories, and between the FM and MM scenarios.

In scenarios EE9–EE12, exponentially decaying exhumation rates are explored, with short (EE9), medium (EE10), and long (EE11) characteristic decay times of 2, 10, and 50 Myr, respectively. Each model involves erosional removal of 10 km of crust, as well as an exhumation scenario with 20 km of erosional exhumation (EE12) and a 2 Myr characteristic time. The low decay scenario, EE11, has a gently-curving, near-linear cooling path, making it quite similar to EE2. The average Pe values (∼0.2 (FM) and ∼0.9 (MM)) for this case are identical to EE2, and the maximum Pe values only reach ∼0.3 (FM) and ∼1.4 (MM). However, the medium and high exponent scenarios (EE9, EE10, EE12) show FM and MM thermal histories that quite closely follow the depth history, in contrast to most of the linear exhumation scenarios described above. In EE10, there is a brief period of limited cooling at the start of the simulation, after which the cooling histories follow the depth history as the exhumation rate decreases. In EE9, the cooling and depth histories are nearly indistinguishable. Although the exhumation rate decays over the same time in EE9 and EE12, the starting depth and rate of exhumation is twice as high in EE12, producing an initial period of limited cooling (where advection dominates conductive cooling) before tracking the shape of the depth history. This efficient advection is reflected in maximum Pe values for EE9, EE10, and EE12 of 4.4–42.6 for the MM variants, and produces a small lag between the thermal and depth histories. In all of the intermediate and rapidly decaying exponential exhumation rate models (EE9, EE10, and EE12), the thermochronometer ages would be indistinguishable between the FM and MM scenarios within typical reported errors. However, the two high-exponent scenarios (EE9, EE12) both predict an inverted relationship of ZHe ages younger than AFT ages, while the medium exponent scenario in EE10 results in ZHe ages almost equal to AFT ages, matching the pattern reported in for low eU-rapid and low eU-intermediate linear cooling rates (see their Fig. 5b).

Models SB1–SB6 explore the influence of different rates of sedimentary burial and different volumetric heat production values during burial and exhumation. SB1 and SB2 have intermediate sedimentary burial rates of 0.9 kmMyr-1 for the first 10 Myr followed by 40 Myr of exhumation at a rate of 0.25 kmMyr-1 (average Pe values: ∼1.7; maximum Pe values: ∼4.1), and crustal radiogenic heat production values of 2 and 1 µWm-3, respectively (Fig. a). The peak temperature experienced by the final surface particle in the basement beneath the added sedimentary package reaches ∼240 °C in SB1 compared to ∼160 °C in SB2. This difference is the result of dimensionless heat production values in SB2 of ∼0.7, which are half those in SB1. In both models, the basement rocks reach peak temperatures slightly later than their peak burial depths, lagging by about 4–5 Myr. Cooling ages in the cooler SB2 scenario are significantly older compared to the SB1 scenario (e.g., the ZHe ages differ by ∼46 % or ∼10 Myr older) due to the higher peak temperatures associated with higher rates of radiogenic heat production, but the effective closure temperatures are similar. The lag in age between ZHe and AHe is ∼10 Myr in SB1, compared to ∼16 Myr in SB2. As with the above EE models, the ZFT thermochronometer does not reach a temperature sufficient for annealing in any of the SB models and is ignored here.

SB3 and SB4 involve the same amount of sedimentary burial and exhumation as SB1 and SB2, except the burial rate is slower (0.45 kmMyr-1) over 20 Myr and exhumation is more rapid at a rate of ∼0.33 kmMyr-1 over the remaining 30 Myr (Fig. b). As before, SB3 is the high volumetric heat production scenario, with SB4 being the average (values of 2 and 1 µWm-3, respectively). Peak temperatures reached for the final surface particle (corresponding to basement rock originally lying 1 km beneath the eroded basin) in SB3 are ∼250 °C and in SB4 are ∼175 °C, slightly higher than for SB1 and SB2, respectively, due to the slower rate of sedimentation and less cooling from thermal advection (maximum Pe values only ∼2.0). Peak temperature conditions in both scenarios also have a shorter lag following the peak in burial depth, relative to SB1 and SB2, of only 2–3 Myr. This is due to less disturbance of the conductive geotherms from sedimentation at a slower rate. Because of the difference in peak temperature, cooling ages in SB4 are older than in SB3, for example ∼8 Myr older for the ZHe thermochronometer. The difference in age between ZHe and AHe is ∼7 Myr in SB3, and ∼13 Myr in SB4.

The final two scenarios, SB5 and SB6, represent extreme scenarios, with a very high sedimentation rate of 9 kmMyr-1 for 1 Myr followed by slow exhumation at ∼0.2 kmMyr-1 for the remaining 49 Myr (Fig. c). SB5, with high volumetric heat production (2 µWm-3), reaches a peak temperature for the final surface particle of ∼220 °C, while SB6, the average heat production scenario (1 µWm-3), reaches a peak temperature of only ∼140 °C, the lowest value among the SB model set. These models also show the longest lag of peak temperature following peak burial depth, at about 8 Myr. Here the rate lag is due to the larger perturbation of the conductive geotherm by the extremely rapid rate of sedimentary burial (maximum Pe values up to ∼40.1). Cooling ages in SB6 are ∼11 Myr older (ZHe) than in SB5, and the difference in age between ZHe and AHe is ∼12 Myr in SB5 compared to ∼19 Myr in SB6.

Models TF1–TF4 explore the effects of thrust faulting on final surface particles in the hanging wall and footwall of a thrust fault (Fig. ). The fault slip rate (5 kmMyr-1) and dip angle (30°) are the same in all models, and FM and MM variants are presented. In TF1 and TF2, fault motion is equally partitioned between FW and HW and as explained in Sect. , the initial fault depth b varies for hanging wall and footwall particle, with b=15.5 km for TF1 and b=2 km for TF2. In TF1, the HW thermal path for both MM and FM conditions shows a continuous cooling history, with accelerated cooling and exhumation during fault slip, a reduction in cooling immediately after fault motion ends, and a gradual increase in the rate of cooling as the final surface particle is exhumed. The FW thermal histories for this scenario, shown in TF2, show heating during faulting that slightly extends after faulting ceases, delaying significant cooling by around 10 Myr after fault cessation in both FM and MM results. Unfortunately, calculation of Pe numbers for this model type is not yet supported in T_c1D. Since the fault position is at a deeper structural level, most of the lower temperature thermochronometers in TF1 and TF2 show similar cooling ages that are strongly influenced by post-faulting exhumation rather than the faulting stage. For instance, the ZHe ages for the MM scenarios in TF1 and TF2 differ only by ∼4 Myr, which is the largest difference for AHe, AFT, and ZHe. However, the ZFT ages in model TF1 reflect cooling during fault activity, most clearly for the MM scenario. In this case, the ZFT age in the hanging wall is ∼7 Myr younger than the equivalent age in the footwall, which is unreset.

In scenarios TF3 (HW) and TF4 (FW), the footwall remains fixed with respect to b (Fig. c), and all slip is partitioned into hanging wall motion, doubling its rate of motion toward the surface compared to TF1. The thermal history for the HW in this scenario correspondingly shows a more rapid cooling rate during fault slip than for TF1, followed by slower cooling to reach the surface at the end of the model run time than for TF1. As the final surface particle is exhumed closer to the surface during faulting than in TF1, the post-faulting cooling history is more linear compared to the concave upward cooling history in TF1 (Fig. a and c). The footwall is held in a fixed position during faulting and then exhumes once faulting has ceased. In this instance, FW heating caused by juxtaposition of the hotter HW is negligible and has no impact on the predicted thermochronometer ages. However, in contrast to TF1, most thermochronometer ages are controlled by fault-related uplift and erosional exhumation, nicely documenting the timing of fault slip in the HW. For example, the AFT, ZHe, and ZFT ages are all ∼45–50 Ma in TF3. In contrast, the AFT, ZHe, and ZFT ages in TF4 are not reset. However, AHe ages are reset in both TF3 and TF4, reflecting post-faulting exhumation and with similar ages (∼34–39 Ma).

The extensional faulting (EF) models use the same approach as for the TF scenarios, but with a reversed slip direction. Thus, the two different extensional faulting scenarios have a slip rate of 5 kmMyr-1 during 50–45 Ma after an initial 5 Myr of steady state, producing equal end-of-slip fault depths in the upper crust for the HW and FW model variants (8.75 km for EF1 and EF2 and 2.5 km for EF3 and EF4). The final model stage comprises exhumation to the surface at the end of the model (Fig. ; Table ). The first set of models (EF1–EF2) use a partitioning factor of 0.5, while for the second set (EF3–EF4) the HW is fixed during faulting (λ=1). For both scenarios, we examined a final surface particle situated 500 m above the fault in the HW (EF1, EF3), and a final surface particle situated 500 m below the fault in the FW (EF2, EF4). As above, calculation of Pe numbers for this model type is not yet supported in T_c1D.

In EF1 and EF2, the HW is buried from 2.5 to 8.75 km during fault slip, while the FW block is continuously exhumed from 15 to 8.75 km during fault slip, and the final surface particle in both scenarios is exhumed at a slower rate to the surface by the end of the model. Here, heating of the HW due to burial and subsequent cooling during exhumation closely follows the depth history of the particle in EF2. This reflects heat from the hot uplifting footwall partially compensating cooling of the HW. Hence, the hanging wall remains closer to conductive thermal equilibrium than it would for a pure burial scenario (e.g., models SB5 and SB6; Fig. ). In contrast, the greater thickness of uplifting crust in the footwall, compared to the hanging wall, advects heat to shallower model depths during faulting, but still produces rapid cooling during fault motion. Faulting-related cooling is then followed by a short pulse of modest heating (1–2 Myr) after fault motion stops. The heating in this case reflects warming of the hanging wall after faulting, due to the onset of exhumation of the entire crust or lithosphere. Thermochronometer age patterns in EF1 and EF2 are similar to those observed earlier for TF1 and TF2. The AHe, AFT, and ZHe ages are reset during post-faulting exhumation, the ZFT ages in the exhuming footwall record fault-related cooling, and the ZFT ages in the hanging wall are unreset. Interestingly, the evolution of the Moho depth (fixed vs. moving) seems to have more impact on the thermochronometer ages than structural position relative to the fault for TF1 and TF2.

In the EF3 and EF4 scenarios, the HW remains fixed during extensional faulting while the FW is exhumed from 15 to 2.5 km depth (Fig. c). Then both the HW and FW are exhumed together to the surface. In this case, heating of the stationary hanging wall in EF3 is clearly visible during and after the period of fault activity in the footwall and followed by slow cooling. The footwall (EF4) shows rapid cooling during faulting, but no period of heating after fault motion stops, as the hanging wall has not cooled like was the case for EF2. Instead, the rate of post-faulting cooling gradually decreases as the final surface particle is exhumed to the surface. Similar to the thrust faulting models TF3 and TF4, only the AHe ages are reset for the hanging wall in EF3, while the rapid cooling during faulting leads to resetting of the AFT, ZHe, and ZFT ages in EF4 (except for ZFT in the FM model variant). As before in TF3, the AHe age in EF4 is reset during post-faulting exhumation.

In models DL1–4, delamination is simulated by removal of the underlying lithospheric mantle and juxtaposition of the asthenosphere against the base of the crust at 50 Ma, followed by 15 km of exhumation over the remainder of the 55 Myr model run time. Exhumation styles are similar to scenarios explored in the EE model set, with DL1 involving linear exhumation, and scenarios DL2–4 involving an exponentially decaying rate of erosion with short (2 Myr), medium (10 Myr), and long (50 Myr) exponential decay constants. Each DL model is run with a fixed Moho (FM) and a moving Moho (MM). As for above, the MM scenarios start with a thicker crust (50 km), such that the final Moho depth for FM and MM scenarios is the same, 35 km. For comparison, the individual DL scenarios are plotted against equivalent EE scenarios involving the same magnitude and rate of exhumation, but without lithospheric mantle removal. In this way, it is possible to isolate the influence of bottom-up heating due to the delamination during exhumation of the crust. We note here that Pe values listed below are only for the EE model equivalents to the DL models because the DL models use a high thermal conductivity in the asthenosphere to simulate the thermal effects of mantle convection (Table ), which biases the calculated Pe values to be too low.

Scenario DL1 involves delamination followed by exhumation of 15 km of crust at a constant rate of 0.3 kmMyr-1 (Pe values: ∼0.3 (FM), ∼1.4 (MM); Fig. a and b). Cooling ages for both MM (Fig. a) and FM (Fig. b) are younger than for the EE scenarios without delamination, with cooling not beginning until 5–10 Myr after delamination, despite the continuous rate of exhumation (Fig. a). In the MM DL1 scenario, the final surface particle is initially heated by ∼10 °C before beginning its cooling trajectory, resulting in low-temperature thermochronometer ages that are ∼1-5 million years (or up to ∼16 %) younger than the corresponding EE scenario. However, in the FM DL1 scenario (Fig. b), the final surface particle is heated by ∼100 °C before cooling, and so low-temperature thermochronometer ages are ∼2–18 Myr (or up to ∼36 %) younger compared to the EE scenario (e.g., ZFT age ∼28 Ma in MM DL1 compared to ∼42 Ma in the corresponding EE scenario). Clearly, delamination leads to conductive heating from the base of the crust and younger ages in both cases, but the thinner initial crustal thickness in the FM model variant shows a larger effect. This general observation of younger ages for DL scenarios relative to the equivalent EE scenario is common to DL1, DL3, and DL4, in both the FM and MM scenarios (Fig. ).

The DL2 scenarios, with exponential decay of the exhumation rate over a short period (2 Myr), show rapid cooling immediately following delamination (Fig. c and d). The final surface particle is transferred quickly into the uppermost crust, escaping delamination-related heating, despite the middle and lower crust experiencing effective temperature increases of up to 250 °C in the first 1–5 Myr of model run time, and reaching peak temperatures that are much higher than in DL1 (see supplementary plots link under Code and data availability). The rapid and significant increase in temperature in the middle and lower crust is a function of both the asthenospheric heating, and the rapid transport of deeper, hotter crust to shallower levels due to the aggressive erosion (maximum Pe values of ∼6.9 for FM and ∼32.5 for MM). As a result, there is almost no difference among the DL2 FM and MM scenarios and their equivalent EE scenarios, despite quite different, rapidly evolving geothermal gradients during the 55 Myr model run time.

The remaining DL scenarios, DL3 and DL4, with erosion occurring via medium and long exponential decay constants, respectively, show thermal histories that are intermediate between DL1 and DL2. Similar to DL1, the FM scenarios (Fig. f and h) show between 5–10 Myr of heating before reaching peak temperatures and cooling, representing the interplay of surface processes with a dynamic geothermal gradient over the course of the 55 Myr model run time.

Notably, although delamination leads to younger cooling ages in most scenarios (DL1, DL3, DL4), the ages do not record the timing of delamination. Thus it may be quite difficult to determine the timing of such an event from thermochronometer age data alone. In the supplementary results, a more recent delamination scenario is explored, with delamination occurring at 7.5 Ma. In that case, the shallower starting depth of the final surface particle (8 km) prevents full resetting of the zircon thermochronometers, cooling of the particle following delamination is slightly delayed despite active erosion, and the thermal history is largely controlled by exhumation.

Since low-temperature thermochronology studies are primarily focused on the evolution of the upper crust, the position and evolution of the Moho during the thermal history under investigation is not typically considered. However, in comparing scenarios in which the Moho depth moves down as material is added at the surface (burial), or shallows as material is removed from the surface (exhumation) with equivalent scenarios in which the Moho depth is held fixed, it is clear that the evolution of the Moho depth can influence upper crustal thermal histories. In most of the model scenarios above (with the exception of the SB scenarios), a FM run was compared against a MM run. FM scenarios are considered to be broadly representative of a syn-collisional setting and MM scenarios of a post-tectonic setting e.g.,, recognizing that this is a simplification and does not address feedback relationships between tectonics and surface processes , for example.

The primary observation from these comparisons is that for identical depth histories, the MM or “post-tectonic” models almost always produce younger cooling ages compared to the FM or “collisional” set of models. This pattern of younger MM cooling ages compared to FM cooling ages is consistent among most models run for this study and reflects the higher geothermal gradient in the MM models due to a thicker starting crustal thickness and increased contribution of radiogenic heat production. This produces a higher starting temperature and faster cooling rate during exhumation. In the EE1 case, for example, the starting geothermal gradient of the upper 10 km of crust is only subtly different in the two models at 32 °Ckm-1 (MM) vs. 29 °Ckm-1 (FM), yet the resulting ZHe and ZFT ages are 3–7 Myr (or 15 %–19 %) younger for the MM variant. As would be expected, the difference in predicted age for FM and MM scenarios decreases when samples are very rapidly exhumed, suggesting the influence of Moho position on thermal histories is less important for such settings.

It is also worth noting, however, that the presented FM model variants have a velocity below the crust that is zero, while the velocity of the mantle can also be negative as the result of subduction. This can act to partially compensate the advective heat transport resulting from crustal uplift e.g., and reduce crustal temperatures. Thus, we include some additional results in the supplementary material under Code and data availability that use a negative mantle velocity with a magnitude equal to the crustal uplift velocity. The predicted ages from these select results are ∼3 % older on average compared to the case with a zero mantle velocity.

One natural question is whether the differences in age for the MM and FM model variants would be resolvable within the typical uncertainties of apatite and zircon (U–Te)/He or fission-track thermochronometers 10 %–20 %; e.g.,. Across all of the models presented in Table , the average difference in age between the MM and FM scenarios is ∼10 %, but numerous cases feature age differences of >20 %. In particular, EE models with larger exhumation magnitudes (EE5–EE8) have predicted ages that differ by more than 20 % for most of the chronometers we modeled (often for all four) with differences as large as ∼100 % for ZFT in EE8. Despite a lower exhumation magnitude, the AFT and ZHe ages in EE4 also differ by at least 30 % due to the slow cooling prior to a phase of more rapid exhumation. Similarly, the EE model with a constant rate of 15 kilometers of exhumation (EE2, 15 km) has ZHe and ZFT ages that differ by more than 20 %. Age differences are smaller for the EF, TF, and DL scenarios either due to differences in the model kinematics or the effects of heat transfer from delamination, but there are still cases where the age difference is 15 %–20 %. Thus, we believe that these differences in age due to Moho behavior are indeed significant and should be detectable in measured ages for erosion-dominated scenarios with larger exhumation magnitudes. In addition, mantle subuction would further increase these difference in age between the FM and MM variants, making it more likely that the age differences are detectable in measured ages.

A notable exception to the trend of younger ages for the MM models is for the models of lithospheric mantle delamination (DL models), where little difference in cooling age is observed for both variants. In the DL models, this is the result of two competing factors that to affect the cooling ages. First, crustal temperatures are higher for scenarios where the crustal thickness is larger, due to a larger contribution of radiogenic heat production over the thicker layer. In contrast, however, heating of the middle and upper crust is greater for delamination models when the crustal thickness is lower, due to heat being conducted across a thinner layer. Thus, heating from delamination is greater at upper crustal levels when the crust is thin, and radiogenic heating of the crust is higher when the crust is thick. For example, the final surface particle in the MM variant of model DL1 starts at a higher temperature than its equivalent in the FM version of DL1 (∼330 versus ∼270 °C; Fig. a and b). In many of the other models presented earlier, this would result in younger ages for the MM model. However, the thermal effects of delamination have a larger impact on mid-upper crustal depths in the FM model variant, increasing temperatures by ∼100 °C during exhumation, compared to the more modest temperature increase of ∼10 °C for the MM version of DL1. The result of these competing factors is a set of predicted thermochronometer ages for the FM and MM variants that differ by less than 0.5 Myr.

In general, however, the incorporation of the full lithospheric column into thermal history models has shown that the evolution of the Moho can have a strong influence on the thermal structure of the upper crust and should be given consideration when relating rock thermal histories to geological interpretations.

Although rock cooling in the upper crust can have many causes, it is most commonly considered to be a proxy for rock exhumation e.g.,, or the approach of a rock towards the Earth's surface. This is because proximity to surface temperatures has a strong control on rock temperature in many, if not most geological settings. The models presented here track both thermal and depth histories of exhumed particles and thus clearly distinguish conditions under which there is a strong relationship between exhumation and thermal history trajectories, and conditions under which they can be decoupled.

Perhaps the most important observation to be made in understanding the relationship between thermal history and exhumation can be found by comparing models EE1 and EE2. These four scenarios (EE1 (FM), EE1 (MM), EE2 (FM) and EE2 (MM)) share an identical, simple exhumation history and final crustal thickness, but produce four different thermal histories, with cooling ages differing by up to 30 %. This outcome emphasizes the fact that even a perfectly known thermal history may be derived from multiple non-unique possible geological histories. In these and all EE models, the shape of the thermal and depth history paths match most closely at depths shallower than ∼8 km and below ∼200 °C and tend to show deviations at high temperatures and deeper crustal depths. The challenge of non-unique geological histories can be partially mitigated by strategic sampling, such as along vertical profiles and using relationships between elevation and measured age e.g.,. Vertical profile sampling to determine exhumation rates, however, can be challenging due to topographic effects on subsurface temperatures, non-vertical sampling, changes in exhumation rate after chronometer closure, and other factors e.g.,. Although data collected in vertical transects may seemingly be difficult to incorporate in 1D software such as T_c1D, it is possible to correct for the effects of surface topography e.g.,, which can provide an option for data interpretation in regions where rates of exhumation may have varied during sample exhumation, for example.

In the models exploring sedimentary burial, the lag time for heating during burial is evident, as is the relative contribution of volumetric heat production to both heating rate and peak temperature in sedimentary basin settings (Fig. ). In particular, a very fast sedimentation/burial rate could manifest in a thermal history as a slower heating event, regardless of heat production values. In contrast, slower sedimentation rates track burial trajectories more closely.

The fault models presented here show the role of heat conduction in cooling hot fault walls and heating cool ones. The examples presented here, however, likely underestimate the heat transfer produced during faulting since frictional heating is ignored.

The effect of lithospheric delamination is to add heat to the crust, which must dissipate to allow low-temperature thermochronometers to reach closure temperature conditions, moving thermochronometer dates farther from the timing of the delamination event than for an identical erosion scenario that lacks a delamination event.

Rapid exhumation scenarios (the exponential decay scenarios with a short decay time: EE12, DL2) are insensitive to bottom-up heat advection, or position of the Moho, and show the shortest lag times between individual thermochronometers within a given scenario (i.e., overlapping ZFT, ZHe, AFT, and AHe ages, at typical reported errors), and the narrowest difference in thermochronometer ages between moving Moho and fixed Moho scenarios. We infer from this outcome that closely spaced to overlapping ages from multiple thermochronometers are most likely diagnostic of an aggressive, erosional exhumation-dominated system, not a thermal event like delamination or heat transfer by thrust faulting.

While we argue that a 1D model can help understand how various geological processes are recorded in thermochronological data, it is important to recognize its inherent limitations, and the limitations of how various geological processes have been implemented. The most obvious limitation is the reduction of 3D geological processes to 1D. Subsurface temperatures in the upper crust are affected by surface topography, which can perturb isotherms to depths of roughly 10 km, depending on the exhumation rate and topographic amplitude and wavelength e.g.,. This effect is largest in mountainous regions, and although this process can be accounted for to some degree in 1D models by applying a topographic correction e.g.,, such a correction was not applied here and thus care should be used in comparing our results to data from regions characterized by significant topography. In addition, dip-slip fault motion frequently involves both vertical and horizontal motions, resulting in 2D or 3D thermal advection that perturbs the crustal thermal field in a horizontal direction. This effect would be most significant in the results of Sects.  and , where the vertical thermal components of dip-slip faulting are simulated for thrust and extensional faults. While the vertical component of motion may be most important for thermochronometer data in rapidly eroding settings e.g.,, horizontal heat transfer may be more important in regions of active faulting with lower rates of exhumation. Considering both points above, T_c1D would ideally be applied to interpret data from regions with limited topographic relief, moderate to slow rates of exhumation, and little to no active faulting. In other cases, T_c1D may be able to provide estimates of data sensitivity to various geological processes, but a detailed analysis of thermochronometer data may require more sophisticated software such as Pecube .

Our results also do not simulate dynamic erosional responses to geological processes, such as increased erosional exhumation following topographic uplift resulting from lithospheric delamination (Sect. ). It is estimated that removal of the mantle lithosphere would trigger isostatic uplift of the surface by ∼1 km due to the combination of thermal and density changes. This uplift would likely result in a period of increased erosional exhumation that could be simulated with a surface process model, for example. However, surface process models generally require at least two dimensions to simulate hillslope diffusion, and fluvial and glacial erosion processes. It may be possible to link estimated magnitudes of isostatic uplift to a surface process model using T_c1D predictions, but this was not done for the presented results. Additionally, such an exercise would require consideration of topographic effects, as mentioned in the previous paragraph.

The effects of melting and magmatic processes are also not included in the T_c1D results. Partial crustal melting from delamination or magmatic intrusions would be expected to transfer mass, advect heat in the crust, and consume and release heat during melting and crystallization e.g.,. This could be locally important in some settings e.g., and in some of the model results presented here, such as those for the delamination models or select erosional exhumation scenarios (Sect.  and ). For instance, present-day reported Moho temperatures greater than 800 °C have been correlated with <10 Ma magmatism in the overlying crust e.g.,, and temperatures 850–1000 °C in the lower crust are expected to cross the wet granite and dry granite solidi . Since T_c1D does not simulate melting and melt transport, the EE5 MM scenario deviates from geological reality. In cases where crustal melting is a concern, it is possible to plot crustal solidi for various rock compositions in T_c1D to estimate the magnitude of the effects of melting and crystallization.

Finally, we note a few additional limitations that may affect the model predictions for different scenarios. The fixed Moho models are presented as analogs to tectonic scenarios where crustal thickening is balanced by erosion in a syn-tectonic erosional scenario. While this is a reasonable approximation for situations where uplift and erosion are close to in balance, this may not apply for early stages of orogenesis where crustal surface uplift may outpace erosion and thicken the crust e.g.,. Additionally, sediment compaction is not modeled for the sedimentary burial and erosional exhumation models (Sect. ). In essence, this means that deposited sediments do not compact, though most sediments can compact by more than 40 %, depending on composition e.g.,. The result is that deposited sediment thicknesses are likely overestimated for the erosional exhumation that follows deposition in the T_c1D models. And finally, the concentration of heat-producing elements in the T_c1D models presented here is constant with depth, rather than decaying. The option for exponential decay of the concentration of heat-producing elements is available in T_c1D, but was not used for the presented results. As a result, lower crustal temperatures may be higher than expected for some scenarios.