The role of plume-lithosphere interaction in Hawaii-Emperor chain formation

Domain: earth_science
Published: 2024-08-03
Editorial outcome: minor_revision

Abstract
Paleolatitudes of volcanic rocks reveal that prominent changes in volcanic trend of the Hawaii-Emperor hotspot chain represent meridional migration of the magma source. However, models assuming latitudinal plume migration fail to explain the observed age distribution, rock composition, and erratic paleolatitude changes of the oldest Emperor seamounts. Here we use data-assimilation models to better reproduce the Hawaii-Emperor hotspot track by systematically considering plate reconstruction, plume-lithosphere interaction, and simplified melt generation and migration. Our results show that plate drag and plume-ridge interaction are both important in explaining the observed seamount ages. These shallow dynamic processes could account for 50% of the observed paleolatitude’s secular reduction and erratic variations over time, where the necessary southward migration of the Hawaiian plume root is significantly less than previously thought. We conclude that plume-lithosphere interaction represents a common mechanism in affecting hotspot track, and has important implications in understanding mantle dynamics and plate reference frames.

Introduction
The Hawaii-Emperor volcanic chain lies in the middle of the North Pacific Ocean, with age-progressive seamounts ranging from ~85 Ma on the northern end to 0 Ma at Hawaii (Fig. 1). Since Wilson1 first suggested that the Hawaii chain could be explained by Pacific Plate motion over a fixed spot of melting, the Hawaii-Emperor volcanic chain has become a canonical example of the hotspot hypothesis. The chain has a prominent 60° direction change at the 47 Ma Hawaii-Emperor Bend (HEB) and a subtle change at ~80 Ma (Fig. 1). There have been numerous models trying to explain the formation of this hotspot chain, especially the HEB, including a southward drifting Hawaii plume2–4, a direction change of Pacific Plate movement from northwest to west at ~47 Ma5, and the Hawaii plume attracted by a mid-ocean ridge6.

Paleolatitude measurements3,7,8 reveal that the underlying hotspot (source of melt) drifted southward from ~80 Ma to ~47 Ma during the formation of the Emperor chain. The 78 Ma Detroit Seamount displays the highest paleolatitude of ~35°N, while all younger seamounts demonstrate a southward migration trend until 47 Ma with an early constant moving speed of about 0.4°/Myr6. Based on the drift rates and direction from geodynamic models, Torsvik et al.5 showed that the directional change at HEB (~47 Ma) cannot be solely due to southward plume motion, which, in the absence of a directional change of the Pacific Plate motion at 47 Ma, requires an unrealistically large migration speed of the Hawaiian plume. Accordingly, they suggest a plate motion history highlighting the 60° Pacific Plate deflection at ~47 Ma.

In addition, the southward moving plume model is challenged by the observed paleolatitude of the 86-Ma Meiji Seamount7 (19°N), whose implied latitude location is near that of present-day Hawaii. This data, if reliable, means that the hotspot should have gone rapidly northward at ~80 Ma and then moved back to the south. Instead of neglecting this data point as many early studies did, Sun et al.6 proposed a plume-ridge interaction model where the plume head was temporally captured by the northward-moving Izanagi-Pacific mid-ocean ridge. This model is further supported by trace element analysis9, where basalts from the oldest seamounts, such as Meiji and Detroit, are more MORB(mid-ocean ridge basalt)-like, indicating melting at a spreading center, while basalts from the younger seamounts are more OIB(ocean island basalt)-like, consistent with a plume origin. However, this plume-ridge interaction model is qualitative, with multiple aspects of observation untested, such as the effect of the realistic plate motion history, the amount of plume deflection by the ridge, as well as the resulting shape and age distribution of the simulated Hawaii-Emperor chain.

A recent numerical simulation aiming at quantifying the effect of realistic subduction history on the evolution of the Hawaiian plume10 has been conducted. This study, by showing an LLSVP (large low shear velocity province)-rooted southward migrating plume source and projecting the plume conduit at 350 km directly onto the surface, showed that a systematically older-than-observed hotspot track with all seamounts older than ~70 Ma on the Emperor chain should have already been subducted by now. This is inconsistent with the observed age distribution along the hotspot chain, where seamounts as old as 85 Ma are still yet to subduct. Therefore, the mechanism inferred from this numerical study is not satisfactory, and other mechanisms must have been in operation to reproduce the correct seamount age distribution.

Here, we design 3-D data assimilation models to further investigate shallow dynamic processes, especially at asthenospheric depths. These dynamic processes are pertinent to the interaction of the Hawaiian plume and the overlying lithosphere, which may affect melt generation and evolution. Furthermore, by considering both different plate reconstructions11–13 and plume migration histories, we attempt to better understand the formation of the Hawaii-Emperor chain through reproducing multiple key geological records, including the shape of the hotspot chain, the age distribution of seamounts, as well as the observed erratic paleolatitude variations.

Results
Our numerical models are implemented using the code CitcomS14–16 based on data assimilation17,18 that simulates both subduction and plume-lithosphere interaction. The model domain is large enough to capture the subduction processes within the western and northern Pacific Oceans since the Early Cretaceous, and to locate the Hawaiian plume far from the model boundaries. The geographic coordinates of all model inputs are rotated to low latitudes to avoid the polar problem of meshing in a regional model (Supplementary Fig. 1).

Besides solving thermochemical convection, we further consider melting and melt advection19,20, so that the model could capture more shallow dynamic effects than recent studies of its kind. The surface hotspot track is defined through two different approaches, with track #A recording the vertical projection of the plume source (at ~600 km depth) onto the moving surface, and track #B recording the temporally changing location of simulated melt eruption, where # denotes the model number. More details of the model setup can be found in Methods.

We first test the fixed plume hypothesis (Model 1) based on the plate reconstruction of Müller et al. 11. The plume source is implemented at its present location, which is seismically imaged at ~600 km depth slightly northwest of Hawaii island at 157°W, 20°N21,22 (Supplementary Table 1). We adopt a 1° radius of the plume source as imaged21. For most models, we assume a pure thermal (unless otherwise noted) plume whose excess temperature at the asthenospheric depth is 200°C, consistent with recent estimates22,23. In this case, the location difference between track 1A (1 denoting model number) and track 1B (Fig. 2) shows the effect of shallow processes due to plume-lithosphere interaction and melt advection. Among them, track 1B provides a closer fit to observation than track 1A, both in their spatial proximity to the observed hotspot chain and the predicted seamount ages (Fig. 2). Relative to the recent modeling study10 where the >70 Ma portion of the hotspot track has been subducted by now, our predicted hotspot tracks (1A & 1B) locate all seamounts younger than 90 Ma within the present Pacific Plate, as observed.

As the tracks in Model 1 still deviate from the observed hotspot chain, we further consider a moving plume source at ~600 km depth to introduce the effect of plume migration in Model 2. The key reason track 2B differs from 2A can also be attributed to the effect of plume-lithosphere interaction and lateral melt advection. More specifically, their difference arises from the capture of the rising plume by the northward-moving Izanagi-Pacific ridge during the early part of the Emperor chain. When this ridge is far south of the Hawaiian plume, the plume conduit is clearly bent northward toward shallow depth due to the drag of the fast-moving Izanagi Plate (Fig. 3a). When the ridge approaches the plume from the south, the plume conduit becomes nearly vertical (Fig. 3b). This indicates that the northward drag of the Izanagi plate is compensated by the southward attraction from the ridge. During this period, when the ridge axis overrides the plume (Fig. 3c), the eruption volume notably increases due to enhanced melting by the thinning oceanic lithosphere. The eruption then becomes temporally disrupted when the plume gets captured and advected northward by the ridge (Fig. 3d), characterized by a sudden northward displacement of the top of the plume and the melting region (i.e., hotspot). During the subsequent northward passage of the ridge axis, the southern flank of the ridge arrives above the plume, meaning that the overriding plate switches to the Pacific Plate (Fig. 3d). As the ridge system moves farther away to the north, the ridge attraction effect gradually diminishes to the level of pure Pacific drag, whose influence lasts to as late as 40 Ma when the northward plate motion finally diminishes (Figs. 3e, f and 4a). Therefore, this plume-ridge interaction first decreases the paleolatitude of the melting region due to southward ridge attraction (Fig. 3a–c), then suddenly increases its paleolatitude due to northward ridge advection (Fig. 3c–e), and eventually reduces it again due to the weaker drag of the Pacific plate (Fig. 3e, f). This prediction is reminiscent of the observed erratic paleolatitude variations from Meiji to Detroit and then to Suiko-Koko seamounts (Fig. 1b).

To further investigate the effect of ridge location on seamount evolution, we ran several additional models with various ridge locations. In the model (Model 2C) that is identical to Model 2B but without a ridge (thus no ridge attraction and advection), the track deviates from Model 2B significantly before ~70–65 Ma (Supplementary Fig. 10). This is because in Model 2C, as there is no ridge between the Izanagi plate and Pacific plate, both plates move at the same Pacific plate velocity, which delay the arrival of the Pacific plate at the plume compared with Model 2B (Fig. 3d). At the same time, as the Izanagi plate changes its motion to the NW direction instead of the nearly northward direction as in Model 2B (Fig. 3e), the northwestward deflection of the track develops. The ridge effect diminishes after ~70–65 Ma because the ridge is far away from the plume (Supplementary Fig. 10 and Fig. 3f). In other models that are modified from Model 2B by varying the initial ridge location, the predicted tracks during 0–55 Ma are similar to those in Model 2B, but clearly drift off before Detroit formation (~75–90 Ma), especially at Detroit (Supplementary Fig. 11). Since during this period of these models, the plume moves southward while the ridge moves northward, shifting the ridge further south will delay the timing of plume-ridge interaction, and vice versa, resulting in the plume either meeting the ridge too early (blue, purple) or too late (red). In addition, except for the track in the model with a much southern ridge (Supplementary Fig. 11, model a, −10°), others deviate from the reference model (2B) toward the northwest side (Supplementary Fig. 11), which may result from the drift change of the Pacific plate motion from NW to nearly northward during ~75–90 Ma (Fig. 3d, e). It is worth noting that all tracks are more (purple track) or less (yellow track) shifted eastwards compared to the observed seamounts during ~75–55 Ma. However, the mechanism is quite different from the previous one, as during this period, the Pacific plate movement was relatively stable. Based on the result of Model 2B, we propose that it may be the plume-plate boundary interaction that influences the tracks. As shown in Model 2B (Fig. 3d, e), during ~75–55 Ma, the plate boundary between the Pacific plate and the Izanagi plate sits very close to the plume. While the velocities of the adjacent plates are quite different, there should be a pressure difference, which may lead to a Couette flow beneath that could affect the drag on the plume and result in a track deviation at the surface. In conclusion, the ridge location determines the timing of plume-ridge interaction, plume-plate boundary interaction, as well as the relative motion between plates, thus shaping the geometry and age distribution of the seamount chain.

On the basis of this result, we further analyze the paleolatitude of modeled hotspot tracks (Fig. 4). The calculated paleolatitudes based on the reconstruction of Müller et al. 11 (red line in Fig. 4) are lower for Detroit and higher for Meiji than their respective observational counterparts. But the result that Meiji’s paleolatitude is lower than that of Detroit matches observation. The calculated paleolatitudes in models (Models 3 & 5) based on other plate reconstructions are shown in Supplementary Fig. 2. In the reference case (Model 1, Supplementary Fig. 12), the predicted paleolatitude offset (north of the present Hawaii island) increases from the initial 0.8° at 105 Ma, when the ridge first encounters the plume, to 4.1° at 97 Ma, and to the highest value of 5.8° at 82 Ma, after which the value gradually diminishes. This predicted maximum offset (5.8°) at 82 Ma accounts for half of the total offset by further including plume migration (green line in Fig. 4), and its timing is slightly earlier than that observed (~78 Ma).

Another major shallow process that affects the hotspot track is plate drag. This process is long-lasting and beyond the duration of the plume-lithosphere interaction. According to the model results, as the plate moves, it excites a Couette flow (the amplitude of horizontal velocity decreases with increasing depth) in the underlying asthenosphere, which will drag the plume in the same direction. For example, the fast-moving Izanagi Plate bends the plume northward (Fig. 3a and Supplementary Fig. 12a), but this effect is almost entirely balanced by the southward attraction of the ridge when it approaches the plume (Fig. 3b and Supplementary Fig. 12b). Similarly, the slower-moving Pacific plate entrains the plume as well, although with reduced strength. Furthermore, the varying speed of the Pacific Plate explains the two local maxima of calculated paleolatitudes (Model 1) at 82 and 97 Ma during plume-ridge interaction: The drop in predicted paleolatitude at 97 Ma is in response to the temporary southward Pacific movement; the calculated paleolatitude rises again when the Pacific switches to moving northward after 95 Ma (Fig. 4a). On the basis of these observations, we can estimate the maximum amount of the calculated paleolatitude offset caused by direct ridge attraction to be about 3.3° (from 0.8° at 105 Ma to 4.1° at 97 Ma when the Pacific motion is small) and that by Pacific drag in response to the ~10 cm/yr northward Pacific velocity increase to be about 2.7° (95–80 Ma) (Fig. 4a). Note that these two effects occur at slightly different times, their combined effect could start at ~109 Ma when the ridge is close enough to attract the plume from the south and end at ~80 Ma when the ridge is far away, resulting in a maximum of 5.8° offset (Supplementary Fig. 12 and Fig. 4a).

Plume buoyancy can also potentially influence the model results. Studies suggest that the Hawaii plume may include some eclogites20,24, which may represent recycled oceanic crust. Therefore, we evaluate the effect of eclogite density in our models, by testing how variations in net plume buoyancy can influence the predicted paleolatitudes. We collect test results when the plume with reduced buoyancy (Models 10, 11, 12, 13) can rise to the surface and form a continuous volcanic track as in Model 1. As shown in Supplementary Fig. 3, reducing plume buoyancy has little effect on the extent of plate drag during plume-ridge interaction, thus, the resulting paleolatitude predictions. Among these tests, the maximum modeled paleolatitude offset always occurs around 85 Ma by no more than 6°.

We also test the effect of asthenospheric viscosity by increasing and reducing its value by a factor of 2 (Model 13, 14). The choice of this value range is based on multiple of our previous studies with data assimilation that matches both past subduction history and the present mantle structures17,18. As shown in Supplementary Fig. 9, the resulting paleolatitude offsets are not sensitive to the tested asthenospheric viscosity. This is likely due to the tradeoff between the vertical and lateral motions of the plume: while reducing asthenospheric viscosity allows the plume to rise faster, the plume also migrates faster laterally due to pressure-driven flow with reduced viscous resistance, thus resulting in a similar eruption site and hotspot location.

Contribution of plume migration
In order to further improve the model to fit with the observation, we also consider the movement of the plume source. We treat this exercise as an inverse problem where we explore different trajectories of simple plume motion (assuming a two-stage linear movement history unless otherwise noted, Fig. 4b) by minimizing model mismatches with multiple aspects (shape, location, age, and paleolatitude) of the observed Hawaii chain (Figs. 1, 2, 4a). In practice, we focus on varying the two-stage plume source trajectory only to fit the locations of the two kinks (at HEB and Detroit) within the hotspot track. The optimal Model 2 (with track 2B), compared to Model 1 (track 1B) that assumes a fixed plume source, not only significantly improves the overall shape of the observed hotspot track, but also reproduces all seamount ages within a 5-Myr error range (Fig. 2) and paleolatitudes of nearly all seamounts (green line in Fig. 4a). This result is more reasonable than that in Hassan et al. 10, whose predicted seamounts older than 70 Myr are all north of the Bering trench. Importantly, the predicted paleolatitudes with the moving plume source closely match the observed values of all seamounts, with Meiji being the only exception (Fig. 4a).

In our best-fit model (Model 2B, Fig. 2), the required amount of meridional migration of the plume during the Emperor chain formation (86–47 Ma) is much smaller than recent inferences3,4,10. Our optimal plume source model has a constant southward speed of 0.13°/Myr, or a total of 4.4° southward migration between 80 and 47 Ma (Fig. 4), about one-third of that implied by paleolatitude measurements (Fig. 1b). Constraining the longitudinal motion of the plume source from paleomagnetic records remains a major challenge. Our exercise, by forcing the modeled hotspot track to match observation, provides a means to infer this motion. Although the result depends on the adopted plate motion history, models based on all three plate reconstructions (Models 2, 4, 6, Supplementary Table 1) considered here produce a consistent SSW-directed motion of the plume source prior to 47 Ma, after which the plume turns to ESE (Fig. 4b and Supplementary Figs. 2, 4). We interpret this E-W flipping motion at 47 Ma as reflecting a return-flow response of the lower mantle to the increased westward motion of the Pacific around this time.

Another unexpected improvement in the moving plume models (Models 2, 4, 6) is in the timing of the Meiji-Detroit bend (Figs. 1a, 2) and associated paleolatitude change (Figs. 1b, 4a and Supplementary Fig. 4). In model 2, because the Hawaiian plume source is about 6.4° more north around 80 Ma than in the fixed-plume model (Model 1), it encounters the Izanagi-Pacific ridge much later. Consequently, the timing of the simulated peak paleolatitude offset is delayed to around the formation of Detroit (green line in Fig. 4a), more consistent with observation than in Model 1 (red line in Fig. 4a). In addition, the maximum simulated paleolatitude offset in Model 2 is increased to 11.4° around the time of the Detroit formation. This amount nearly equals the combined offsets due to plume source migration (~6°) and to the plume-lithosphere interaction (~5.8°), thus verifying the respective contributions from the deep and shallow mantle processes.

We note that the simulated paleolatitude offset of Meiji is always higher than observed, with the misfit being 5−10° from models based on all three reconstructions (Fig. 4 and Supplementary Figs. 2, 4). The reason may lie in the inaccuracies of (1) the paleolatitude measurements at Meiji, (2) the adopted plate reconstruction model, or (3) the assumed plume migration history. Examination of the first possibility is beyond our capability. Regarding the second one, we first choose a plate reconstruction model11, combined with the observed positions and ages of the present Hawaii-Emperor chain, reversing the chain back to the time when it was generated, and then obtaining the Meiji paleolatitude. However, the resulted paleolatitude offset of Meiji is still much higher than that observed (purple dots in Fig. 4, Supplementary Fig. 4 for other reconstruction models). This means that plate motion history cannot account for the abnormally low Meiji paleolatitude. As the plume’s precise moving history is unknown, here we perform another model (Model 7) to test the third possibility and obtain a three-stage plume movement history (Supplementary Fig. 5). It differs from Model 2 only in that the plume source moves northward at 90 Ma from the current location of Hawaii to the 80-Ma location in Model 2. In this case, the paleolatitude of Meiji is indeed improved (Supplementary Fig. 5b), but its present location is far more south, thus still violating certain observations (Supplementary Fig. 5c). Accordingly, the above presumed three-stage plume movement is not a reasonable scenario.

On the basis of these additional tests regarding Meiji’s abnormally low paleolatitude, we propose one way to reconcile this dilemma is to suggest that the Pacific plate rotated clockwise during the formation of Meiji but stopped before Detroit formed. Chandler et al. 25 find that the Ontong Java Plateau, which was formed at ~123 Ma and is now located in the southwest Pacific, may have experienced ~40° of clockwise rotation. If this plateau was part of the Pacific Plate back then, the region where Meiji formed should have also rotated by a similar amount. This scenario could naturally account for the difference between the simulated and observed Meiji-Detroit chain orientations, which also differ by ~40° (Supplementary Fig. 5c).

Implications on deep mantle dynamics and hotspot track formation
In this study, we quantitatively evaluate the effects of shallow dynamic processes on the formation of the Hawaii-Emperor chain, using several recent plate reconstruction models11–13. On the base of this result, we further infer the necessary latitudinal migration of the plume source by best reproducing the observed hotspot chain properties. This workflow is motivated by the fact that our knowledge of surface plate kinematics is better than that of the deepest mantle. Indeed, current models of the Hawaii-Emperor chain formation, even by acknowledging the observed paleolatitude offsets26, involved drastically different views on lower mantle dynamics, including a stationary plume6, a moving plume toward a stationary LLSVP27, and a migrating plume originated from the retreating edge of LLSVP10.

To circumvent the uncertain lower mantle dynamics, we attempt to infer the effective plume motion by correcting the contribution from the better-constrained shallow mantle processes through quantitative numerical calculations. In practice, we place the present-day plume source at ~600 km depth where seismic tomography detects the plume conduit21. Our result agrees with that from recent convection studies10,28 in that the plume source moves southward during most of the time when the Emperor seamounts formed. But our inferred amount of southward plume motion is only half of that from these recent results, with the shallow processes accounting for the other half. This conclusion is based on the above presented systematic study through which the preferred model could match more data (track shape, seamount age, and paleolatitude) than all previous models. Therefore, the lower mantle flow that dislocates the plume and/or the LLSVP should be less vigorous than previously thought. Our result also quantifies the contribution of shallow processes as being equally important in forming the Hawaii-Emperor chain. So, future research concerning mantle evolution and plate reconstruction should take such shallow effects into account.

Our preferred model with two-stage plume movement (Model 2) predicts 11.4° of maximum paleolatitude offset around the Detroit seamount, which is within the uncertainty range (8–18°) of the observed mean offset (12°). Although allowing more southward plume migration may slightly increase the maximum offset10, such exercise fails to reproduce seamount ages with a large portion of the observed Emperor chain being subducted by now (Fig. 2 and Supplementary Fig. 6). Therefore, the 11.4° offset should represent a realistic value, which implies that some very large offsets (>20°) near Detroit may represent inaccurate records of the true paleolatitudes resulting from limited sampling data and analytical error29, possibly due to post-eruption deformation by the underlying plume-lithosphere interaction. Similar reasoning can be applied to the very low paleolatitude offset (~0°) of Meiji28 if future research rules out the scenario of rapid clockwise rotation of the Pacific plate prior to 80 Ma as implied in our three-stage plume motion model (Supplementary Fig. 5).

An even broader implication is that this identified plume-lithosphere interaction with an nearby ridge could have affected other hotspot tracks as well. Paleolatitude data computed from GMHRF-3 (global moving hotspot reference frame)30 shows that, besides Hawaii, New England, Reunion, and Tristan all experienced prominent paleolatitude shifts by different amounts (5° to 10°) (Supplementary Fig. 7 and Movie 1). The paleolatitude of the New England hotspot decreased rapidly starting at 120 Ma, as could reflect a similar mechanism to that for Hawaii: the northward velocity (thus drag) of the North American plate that the hotspot interacted with prior to 70 Ma suddenly decreased after 120 Ma, followed by ridge attraction of the approaching North America-Africa ridge from the south. When the ridge passes over the plume, the ridge attraction is simply compensated by the plate drag, resulting in no change in the paleolatitude trend of the volcanoes. Eventually, the plate drag is further reduced as the plume migrates below the slow-moving African plate (Supplementary Fig. 7a and Movie 1). Similarly, the sudden increase of Reunion’s paleolatitude around 70~60 Ma is consistent with it traversing the northward moving Indian-Africa ridge, and the subsequent rapid paleolatitude decrease reflects reduced plate drag (due to slower plate velocity) south of this ridge, a mechanism that has also been suggested by Bredow et al. 31,32. (Supplementary Fig. 7b and Movie 1). It is worth noting that during ~53–39 Ma, plate motion increases while paleolatitude decreases, which indicates that the fading ridge effect may still play an important role during this stage. Tristan’s paleolatitude gradually decreases after ~120 Ma, which could also be related to both the diminishing northeastward plate drag and the long-lasting attraction from the Africa-South America ridge, where the hotspot has been hovering around since the Late Cretaceous (Supplementary Fig. 7c and Movie 1).

In conclusion, we demonstrate that the plume-ridge interaction can temporally modulate the long-lasting plume-lithosphere interaction, leading to significant hotspot track deviations and paleolatitude offsets in multiple hotspot chains. Consequently, the observed abnormal hotspot motions require much less contribution from the deep plume source than previously thought. For the Hawaii chain, plume-lithosphere interaction could account for around 50% of paleolatitude change, and lower mantle dynamics or plume source motion may account for the other 50%. These inferences should enlighten further research in both mantle dynamics and plate reconstruction.

Methods
Model setup
In order to reproduce the history of the Hawaii-Emperor hotspot chain while considering possible dynamic effects from all nearby plate boundaries, our regional models manage to include the subduction of the Izanagi, Kula, and Northern Pacific plates since the middle Mesozoic. Because these features are too close to the North Pole, the default mesh of a regional model defined by latitudes and longitudes in CitcomS will not work. Therefore, we conducted a coordinate transformation, and the transformed computation domain is shown in Supplementary Fig. 1. Similarly, all the boundary data from the adopted plate reconstruction models are transformed as well.

We model the mantle as an incompressible viscous fluid under the Boussinesq approximation. Besides, we use a data assimilation method17,18 to reproduce past subduction and mantle flow. In our model, all model boundaries, except the surface, are free to slip. The model’s surface assimilates kinematic boundary conditions from the plate reconstruction models, which also provide information about seafloor age and plate boundary geometries at a 1-Myr time interval. The input seafloor age and plate motion are smoothly interpolated between the two adjacent snapshots. To get robust results, we test three different reconstruction models from Müller et al. 11, Müller et al. 12, and Torsvik et al. 13.

In our model, we prescribe a thoroughly weakened vertical zone along all side walls to minimize the artificial flow due to the impermeable vertical boundaries17,18. In addition, the study region is near the center of the model domain, and the plume does not move much laterally. Hence, the model’s side boundaries are always far from the plume, and the plume evolution is not affected by the side boundaries.

We solve for thermochemical convection, where compositional tracers at 20 per element are used to track key tectonic features, including the crust, the mantle, and the plume. Tracers with different physical properties (density and viscosity) are used to facilitate realistic subduction17,18. Additional model components, like eclogite inside the plume and simplified melt migration, are also realized through tracers.

The main difference between our model and previous studies10 is that, instead of simply projecting the location of the plume conduit from its source to the surface, we further consider the lateral advection of the plume within the asthenosphere due to interaction with the moving plate at the surface. In addition, we also incorporate a simplified melting function into the evolution of the thermal plume, such that the melt could accumulate over time and advect with the ambient mantle flow. The plume conduit could then be bent by plate drag and mid-ocean ridge attraction, while the melt region could move laterally within the plume head, as shown in Fig. 3.

Simulating partial melting
In order to track the formation of the Hawaii-Emperor chain, we consider the melting process of the mantle. In this study, we only consider the melt of peridotite and adopt a linear melting function for the volumetric degree of melting (before considering extraction and depletion) φ0 19:

φ = min(1, max(0, (T - Tsolidus) / (Tliquidus - Tsolidus))) (1)

where Tsolidus and Tliquidus are pressure-dependent solidus and liquidus constrained by experiments on dry peridotite33,34:

Tsolidus = 1080 + 134.2P - 6.581P^2 + 0.1054P^3 (2)

Tliquidus = 1762 + 57.46P - 3.487P^2 + 0.077P^3 (3)

where P is pressure in GPa, and T is temperature in °C. The pressure is calculated using a 1D reference density model35.

We assume melt materials would erupt at a rate of 10%/Myr when the local melt percentage reaches a threshold of Mmax = 4%19. When an eruption happens, the erupted melt is put on the surface instantaneously. This simplified modeling may result in that the depth at which the melt reaches the eruption threshold is very shallow, usually right below the LAB. This means melt percolation happens mostly within the high-viscosity lithosphere, where the mantle wind is absent. Thus, such simplification would not cause a notable mismatch at the surface eruption site. Melt depletion φextracted is also calculated to record the amount of erupted melt. The in situ melt fraction is φ = φ0 - φextracted.

Model rheology
Our models adopt a depth-, temperature-, and composition-dependent viscosity law for the whole model domain before considering melting effects:

ηnomelt = N0(r) * C * exp(E0(r) / (T + T0(r)) - E0(r) / (Tm + T0(r))) (4)

where ηnomelt is the effective viscosity before considering melting effects, N0(r) is the depth-dependent background viscosity, C is the viscosity multiplier due to compositional effects, E0(r) is the activation energy, T0(r) is the temperature offset, and r is the radial distance from the earth’s core. T is the temperature and Tm is the background temperature. These parameters and their values are listed in Supplementary Table 2. Most parameters have been used and tested in other studies17,18,36.

The background mantle includes a four-layer viscosity profile: 0–44, 44–410, 410–660, and 660–2867 km. The background viscosity in each depth range is 10^20 Pa·s, 10^20 Pa·s, 10^21 Pa·s and 10^23 Pa·s, respectively. The temperature dependence leads to four orders of magnitude in lateral viscosity variation. This viscosity structure is largely consistent with our previous inferences based on data assimilation models for simulating past subduction and mantle flow17,18,36, which provide a tight range on the values of viscosity at each mantle depth. Besides, a viscosity cut-off (10^19–10^23 Pa·s) was employed in our models to avoid too large variation due to compositional and melting effects. These model parameters have been extensively tested in recent studies, as shown to be appropriate for simulating subduction and mantle flow dynamics17,18,36.

We consider two kinds of melt weakening mechanisms to account for melt effects on viscosity. The first concerns melt extraction, during which the viscosity of the whole rock column between the melt source and the surface would be weakened37:

η = ζ1 * ηnomelt (5)

where ζ1 is the melt weakening pre-factor. This mimics the process of melt eruption. The whole eruption channel from the node where melt is extracted to the surface would get weakened, following a recent study37.

Another weakening mechanism arises from the fact that rheologically weak melt can be retained inside the mantle20. We assume the effective viscosity depends on the in situ melt fraction following:

η = ηnomelt * exp(-ζ2 * φ) (6)

Where ηnomelt and η are the effective viscosity before and after considering melting effects, respectively. ζ2 is another melt weakening pre-factor20, and φ is the in situ melt fraction. Since the maximum in situ melt fraction in our model is limited to 4%, this weakening mechanism leads to a maximum viscosity reduction of one order of magnitude.

Volcano tracking
We develop surface hotspot tracks through two different approaches. Track A records the vertical projection of the plume source at 600 km depth onto the moving surface, and track B records the temporally changing location of the simulated melt eruption.

For track A, because the location of the plume source is known a priori, we simply advect the corresponding tracers at the Earth’s surface following plate motions from the reconstruction models.

For track B, after the erupted melt is moved to the surface instantly, this erupted material would be attached to an existing tracer near the surface, representing the volcano. Thus, it could move with the plates and even subduct under another plate. Since this melt has been moved to the surface and solidified, it has no effect on viscosity anymore. In practice, this volcano material is removed from the model when it subducts to a depth greater than 1000 km.

Then, we use a post processing script to collect volcanic materials to generate a 2D map of the hotspot track. We first choose several control points, and then use a moving rectangle window to get the weighted mean location and age of volcanoes inside the window. By moving the window from one control point to another, we can obtain a modeled hotspot track (Supplementary Fig. 8). Simulated paleolatitude offsets are calculated using the latitude difference of the seamounts at the same age in the two tracks between the predicted track #A and track #B.

Robust plume source migration results
To test the robustness of our results, we further tested the reconstruction models of Müller et al. 12 and Torsvik et al. 13 in addition to the model of Müller et al. 11, as shown in the main text. We tested both the fixed and moving plume source trajectories for each reconstruction. All the results are shown in Supplementary Fig. 2.

For models with a moving plume source (Supplementary Fig. 2c), all three models share the same north-south motion. However, different east-west plume movements are required for different reconstructions to match the locations of the HEB and Meiji-Detroit bends. Based on these reconstructions, all three models produce a consistent SSW-directed motion of the plume source prior to 47 Ma, after which the plume turns to ESE. The results of the robustness tests on the motion of the Hawaii hotspot are shown in Supplementary Fig. 4. The paleolatitudes inferred from these additional tests are similar to those based on Müller et al. 11. Specifically, the paleolatitude of Detroit is always larger than that of Meiji.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This paper is an extension of the work by Sun et al. [2021] where the inter- action of plumes and ridges are studied by a simple numerical model of mantle convection in a two-dimensional Cartesian box. In this study, the authors developedaregionalthree-dimensionalsphericalshellmodelneartheHawaii-Emperor seamount chain, with special emphasis on the possible influences of plume-ridge interactionontheformationofseveraldiscontinuouschangesinthetrackbetween theMeijiandDetroitseamounts. TheauthorsconfirmedtheearlierfindingsbySun et al. [2021] that the ascent of plume in the shallow mantle is greatly influenced bythecombinedeffectsof(i)thedragfromthemotionofoverlyingplatesand(ii) the presence of thinner lithosphere beneath the spreading ridges. The highlight of the present numerical experiments lies in the temporal changes in the relative importancebetween(i)and(ii)dependingontherelativepositioningbetweenthe plumesandridges,whichmayfurtherimplythatthediscontinuouschangesbe- tweentheMeijicanbecausedbythepassageoftheridgebetweentheIzanagiand Pacific plates over the Hawaiian hotspot. In addition, the authors showed that, by takingtheabovemechanismintoaccount,theobservedsecularreductioninpaleo- latitudeanditserratictemporalvariationscanbesufficientlyexplainedevenifthe southwardmigrationoftheHawaiianplumerootisverysmall.\nI feel that the authors’ numerical results are generally correct and their findingsareinessenceveryimportantintheunderstandingofthedynamicsofEarth’s lithosphere and mantle through the hotspot tracks. Unfortunately, however, I am notfullyconvincedoftheauthors’claimthatthediscontinuouschangebetweenthe Meiji and Detroit is caused by the plume-lithosphere interaction, solely from the discussion in the presented manuscript. I therefore would like to offer the authors the following revisions, most of which are intended to improve the persuasion of themanuscript.\n1-1. I think that in Figure 3 the authors should show the results for Case 2A or 2B, not for Case 1A. This is partly because, in my understanding, Case 1A istheleastreliableamongthefourcasespresentedinFigure2,considering therelevanceoftheassumptionsusedtodrawthehypotheticaltracks.\nAnother reason is that in this case the timings of the events induced by the plume-ridge interaction are inconsistent with those of the events actu- ally observed in the Hawaii-Emperor seamount chain. Indeed, the event which “first decreases the paleolatitude of the melting region due to south- wardridgeattraction(Figs.3a-c)”occursaround105Ma,whichlargelyde- viates from the timing of the discontinuity between the Meiji and Detroit seamounts (around 80 Ma), even though a highly reliable model of plate reconstruction [Müller et al., 2016] is employed. I therefore would like to make sure if the cases other than 1A can yield the events corresponding to theMeiji-Detroitdiscontinuityatthetimingconsistentwiththeobservation.\n1-2. I do not think that the influence of asthenospheric viscosity is sufficiently investigatedontheplume-lithosphereinteraction.\nThisispartlybecausetheemployedvariationinasthenosphericviscosityis too small in this study. In the present manuscript the authors conducted the calculationsofModels13and14wheretheviscosityintheasthenosphereis increasedanddecreasedonlybyafactorof2,respectively. Consideringthat the viscosity of mantle materials can significantly vary depending on sev- eralfactorssuchasthewatercontent,theauthorsshouldconductadditional calculationsbyvaryingtheviscositymorestrongly.\nAnother, and more critical, reason is that the assumption of the ascent of generated magma employed in this study is in essence not very good at in- vestigating the plume-lithosphere interaction. As was stated in “Method” section,theauthorsassumedthat“Wheneruptionhappens,theeruptedmelt would be put on the surface instantly (instantaneously?)”. This assumption means that the migration of generated magma takes place without feeling the “mantlewind”inthebackgroundasthenosphere,whichmayfurtherim- plythattheeffectofthedragfromthemotionofoverlyingplatesisnotfully taken into account. I therefore ask the authors to add some discussion on thislimitationintherevisedmanuscript.\nInaddition,Ithinkthatthe“Method”sectionneedsintensiverevisions.\n2-1. I do not think that the coordinate transformation should be discussed in de- tail. Thisisquiteobvious.\n2-2. The authors should instead add some statements on the boundary condi- tions employed in this study. Considering the motion of surface plates over about 100 million years (several thousand kilometers), I do not think that theemployednumericaldomain(120◦inlatitude,210◦inlongitude)iswide enoughtothoroughlyexcludetheinfluencesfromtheverticalsidewallsde- spitetheauthors’conjecture(orexpectation).\n2-3. Ifeltquiteoddwiththenomenclatureorthenamesofseveralsymbols.\n• T (r)“activationtemperature”?\n0\n• φ“meltingrate”?\nThisphrasewouldliterallymeantheamountofgeneratedmeltperunit\ntime. Itshouldinsteadbecalled“meltfraction”.\n• “meltretentionrate”?\nFromthisphraseonewouldimaginethatthesolidmatrixactivelypre-\nventsthemigrationofmelt. Isitwhattheauthorstrulymean?\n• η\nwithoutmelt\nIsitdifferentfromη forsure?\nnomelt\n2-4. The subsection “Model rheology” needs careful revisions in order to de- scribetheemployedviscositylawmorecorrectlyandthoroughly.\n• IdidnotfoundanywhereinthetexttheemployedvaluesofT andE .\n0 0\n• ThevalueandmeaningofC shouldbeclearlyindicated.\n• The authors should clearly state that a “cut-off” of viscosity has been\nemployedinordertoavoidtoolargevariation.\n• Istronglyasktheauthorstomakesurethemagnitudeofthereduction\ninviscosityduetothepresenceofmeltinthepresentnumericalexper- iments. Thevalueofexp(ζ ) ≈ 105impliesthattheviscositydropsby\n2\natmostfiveordersofmagnitude. Ilearnedthat,ontheotherhand,the\nemployedcut-offofviscosityallowsthevariationsinviscosityonlyby\nfourordersofmagnitude.\nIthinkthattheequationshouldinsteadbewrittenas,\nη = η ×max[exp(−ζ ),somelowerbound]\nnomelt 2\n2-5. Intheequationsdefiningthesolidusandliquidustemperatures,theunitsof\ntemperatureandpressureshouldclearlyindicated.\nSeveralother(mostlyminor)comments/suggestionsfollow.\n3-1. I felt quite odd with the statement beginning in line 72 “Therefore, other\nmechanismsmusthavebeeninoperationtoreproducethecorrectseamount\nagedistribution”.\nI do not understand why the conjecture on “a systematically older-than-observed hotspot track with all seamounts older than ∼ 70 Ma on the Em- peror chain being already subducted by now” needs other mechanisms to reproduce the correct (or, do the authors imply “thorough”?) seamount age distribution.\n3-2. InFigure3,Iwouldliketoseetheisosurfacesofmeltfractioninwhiteand\nthose of hot anomaly in red. Although I believe that the distributions of\nmeltshouldbeofmoreinterestthanthoseoftemperature,myeyeshadbeen\nstronglycaughtbythewhiteisosurfacesoftemperature.\nIn addition, it could be nice if the authors indicate the position at the top\nsurfacejustabovethemagmasourceinthefigure.\n3-3. In the reference list, #21 [Ye et al., 2022] and #35 [Afonso et al., 2016]\nare wrongly indicated. In addition, #22 [Herzberg, 2006] had been quoted\nnowhereinthemanuscript.", "reviewer_2": "The paper presents a numerical model that aims to reproduce observations (paleolatitude derived from paleomagnetism, geochemistry and seamount ages and location) of the Hawaiian-Emperor seamount chain in the Pacific Ocean, and in particular to address the unresolved discrepancy of the oldest seamount of this chain. The authors aim to test the importance and effect on the seamount track of geodynamic processes overlooked in previous studies, in particular shallow processes like the plume -ridge interactions. I note that this subject was recently discussed in a paper published by Sun et al (2021) who used geochemical data and 2D modelling to show that plume-ridge interaction can indeed explain the age progression, geochemistry and paleomagnetism of the seamounts which are offset from the linear track of the seamount track.\nThe innovative aspect of this study is the use of a 3D model to assess several shallow processes, it takes into account plate reconstructions, it explores the plume-ridge interaction also considering melting and melt advection. It is interesting to see that by correcting the contribution from the better-constrained shallow mantle processes through quantitative numerical calculations they derive a better understanding of deep mantle and their conclusion refute published models by advocating that plume-lithosphere interaction could account for 50% of paleolatitude change, and lower mantle dynamics or plume source motion may account only for the other 50%.\nThis approach and conclusion has broader implications for other hotspot tracks, whose evolution and proceses involved require revisiting.\nI consider the paper provocative and innovative and recommend publishing it after minor revisions. In particular, the authors should specify how their modelling method and approach are different from Hassan et al paper, besides implementing the shallow mantle processes.\nSome detailed suggestions and comments:\nFor Model 1 -what is the methodological difference between your model and the Hassan et al?\nModel 6B in Fig2b suppl seems to fit the observations better (at least the track location and shape, as I can distinguish very well the predicted ages due to the complex colour scale) that Model 2B in Fig.2\nlines 209-201 what exactly means “lateral” – is this longitudinal?\nThe movement of the plume source at CMB or in the astenosphere?\nFigure 1 needs a scalebar and a reference to background image\nFigure 2 – colour scale – I wonder if this scale can have an easier to follow colour scheme -for example like the ocean agegrid published by Mueller et al (various publications) or other uniform color palette\nPlease add ref to Plate Boundaries\n“Track A shows the trace of vertical projection of the plume source onto the surface” according to your model?\nFig3. Again, difficult to distinguish colours as the melt fraction contours have the same dark red colour as the asthenosphere", "reviewer_3": "The manuscript “The role of plume-lithosphere interaction in Hawaii-Emperor chain formation” by Xie et al. investigates how the plate tectonic history of the Pacific ocean may have shaped the Hawaii-Emperor chain through plume lithosphere interaction. More specifically, the authors suggest that a mid-oceanic ridge passing over the Hawaiian plume at around 105 Ma could be responsible for half of the latitudinal drift inferred from seamount paleomagnetic data along the Emperor chain by temporarily deflecting the upper part of the plume stem. This result would have important implications on estimates of plume drift, plate reconstructions and associated lower mantle dynamics.\nAlthough there have been a lot of studies focusing on the formation of the Hawaii-Emperor chain, there are still certain aspects that have not been explained yet. Previous work has shown that the bend at about 47 Ma is likely caused by a change in the motion direction of the Pacific plate, with a potential influence of southward drift of the Hawaiian plume. However, drift rates of the plume, as well as details in plate motion, remain poorly constrained, and most models fail to reproduce both ages and paleolatitudes of the samples taken along the Emperor seamount chain. As a consequence, a model that could explain both data would be very valuable, and could have significant implications within the Earth Sciences.\nWhile I think the results presented here are very interesting, I do have a few questions and comments that would require moderate revisions. Particularly, I have some concerns regarding how much the ridge can influence the plume at the given time, and how much the results depend on accuracy and errors from paleomagnetic data and plate reconstructions. I have to admit though that I am not an expert on paleomagnetism, so maybe some of my questions and comments are less relevant than I think.\nMain comments:\n1) While it is plausible to me that a plume interacting with a ridge will be deflected in the upper mantle towards the ridge, I have some doubts about some of your interpretations. You claim that the ridge still affects the plume even if it is >10° (~1100 km) away from the plume stem. This seems like a very big distance, probably too big to have any significant influence (see also comment #9). To really show how much the ridge matters, you would have to run a model without the ridge and compare the results. For example in Sun et al. (2021), the plume is only affected as long as the ridge is <800 km away from the plume stem, Bredow et al. (2017, G3) mention a length scale of ~1000 km. You need to prove that the ridge actually matters for Meiji, Detroit and other seamounts, and that the change in plate speed of the Pacific plate alone is not enough to produce the observations.\n2) Related to this: How much do your results depend on the position of the Izanagi ridge, and the timing and paleolatitude of the seamounts? Both timing and latitude measurements of erupted magmas have errors and uncertainties, and the location of the ridge may not be well constrained after all. So what happened if the ridge was a few degree further north or south, or had a slightly different orientation? Plate reconstructions of ridges that are subducted are difficult, and the Pacific Ocean floor is complicated (see Sager (2022), and my comment #14).\n3) What would be the effect of True Polar Wander? If you deal with paleomagnetic data, you have to correct for TPW in order to compare to current latitudes. In Torsvik et al. (2017), the show that this may result in paleolatitudes of most Emperor seamounts similar to that of Hawaii today, and only Detroit may be further north. It seems to me that TPW was not included in the data you used? This would also play a role when comparing absolute and relative plate reconstruction reference frames. Would this also explain some of the very abrupt jumps of velocity magnitude and direction seen in Figure 4, Extended Data Figure 7, and the Movie 1?\n4) I was able to understand the text, but sometimes the grammar or the chosen expressions distracted me from the actual content of the sentence. I will only list some of those sentences under minor comments, but I will not provide detailed suggestions on how to correct them (this is up to the authors). However, I would strongly recommend to check the language carefully and make sure that the grammar and the chosen words are appropriate for the way they are used. One word that irritated me throughout the text is “plate entrainment”. Maybe it is better say “plate drag”? “entrainment” would imply for me that parts of the plate are entrained in the plume, as this is typically used when referring to small portions of chemically distinct material brought up from the core-mantle boundary by the plume.\n5) Abstract, line 18: you mention that you use melt migration, but the melt in your models is not really migrating. You use tracer particles that are advected with the flow, but do not move independently. Real melt migration would consider a 2-phase flow according to Darcy’s law, or even a more complex and realistic behavior of the melt. Your approach does neglect some local dynamics associated with melt migration, but I think the models are fine for the purpose. Still, I would suggest to rephrase “melt migration” here (and elsewhere?), maybe to something like “simplified melt migration” or “passive melt migration”.\n6) Lines 39-45: I think Torsvik et al. don’t really use the paleolatitude that much in their argument why a change in Pacific plate direction is necessary to explain the Hawaiian-Emperor Bend at 47 Ma. They base this mostly on the drift rates and direction from geodynamic models. In fact, I am not sure if their models can explain the paleolatitudes of the Emperor seamounts.\n7) Figure 2: for which model 2 is the green background derived, model 2A or 2B? I guess 2B, but you should specify this.\n8) Related to Figure 2 (and other figures that are alike): did you try to compare your suggested melt volumes and locations to observations? One thing that I notice is that there is quite a difference between the models, including a significant portion of melting away from the plume track. How realistic are your estimates and locations, apart from the hotspot track that you predict?\n9) Figure 3, and related to the respective paragraph in the text: The panels in the figure are very confusing and do not really show what you discuss. First of all, the plume tilt at any time is almost invisible (too small, perspective is not ideal), secondly the North direction is towards the right (and not towards the top as one would expect, especially since this is not clearly indicated by an arrow or mentioned in the text). In addition, the viscosity scale would better be labeled “log Δvisc”. And finally, I don’t see any plume stem tilt at 88 Ma, and the ridge is already about 18° away (meaning ~2000 km). I am not sure if the ridge still has an influence at this time, the distance seems too large. You would need to provide a more detailed figure to demonstrate this, and maybe a model without the ridge as mentioned in comment #1.\n10) Lines 169-177: I am surprised that the pacific plate changed its direction so much in such a short time, but I guess this is from the plate reconstructions models (is that consistent between all models?). However, the combined effect of ridge attraction and plate motion would just be 5° (from 0.8° to 5.8°), and I don’t think the split you mention is accurate. In fact, the northwards drag of the ridge starts as soon as the ridge is north of the plume, thus at 105 Ma, and then decreases over time as the ridge moves away. On the other hand, the Pacific plate sped up over the course of about 13 Myr between 95 Ma and 82 Ma, according to your Figure 4, so the plate drag will increase over that period of time. Therefore, I think the impact of the plate drag is much larger than what you indicate, potentially even accounting for all 5° at around 80 Ma. To really quantify this, you would need to run the same simulations, but disable the ridge (comment #1).\n11) Lines 189-191: I don’t think this is the correct reason, and I honestly don’t see why this should be connected at all. First of all, you don’t actually model independent melt motion, neither vertical nor lateral, so your models cannot show this. In addition, the Couette component of the flow (i.e. plate drag) does not change with lower asthenosphere viscosity, only the Poiseuille component (pressure-driven component of the asthenosphere flow due to plume injection) could change, but the reason for the latitude offset is not the pressure-driven component, which is constant for constant plume flux (unless changed by subduction zones).\n12) Line 254 and Figure 4: I am not sure how you obtain the purple dots. Can you please explain this, for example in the Methods section?\n13) Line 257 and Extended Data Figure 5: the proposed plume drift between 90 Ma and 80 Ma seems unrealistically high, so I don’t think this is a plausible explanation.\n14) Line 302: I am not sure if Sager (2022) is the correct citation for this, Sager had a more general criticism of the data than just for Detroit seamount. And what about the other criticism that he mentioned with respect to the study of Sun et al. (2021)? Don’t your models suffer from similar shortcomings of paleomagnetic data, plate reconstructions, age constraints, and the distance from the ridge that I mentioned in comment #9?\n15) Lines 317-320: Did you have a look at the paper by Bredow et al. (2017, G3)? This would be good to cite here, as it also looks at plume-ridge interactions and how this affects melting and the volcanic chain.\n16) Lines 311-324 and Extended Data Figure 7: At the time the ridge passes over the New England Hotspot at around 85 Ma, there seems to be no change in the paleolatitude trend of the volcanoes. Does that mean that the ridge attraction is simply compensated by the plate drag? And for Reunion, the increase in paleolatitude could be related to the fast motion of the Indian plate, partly compensated by the ridge attraction towards the south. After passing the ridge, the plume is underneath a plate with significantly lower northward velocity, reducing paleolatitude. If this is true, ridge attraction may play a much smaller role than suggested in this paper, and only matter while the plume is in (close) vicinity of the ridge (maybe <1000 km as suggested by Bredow et al. (2017, G3); note, however, that melting would probably require a thin area rather close to a ridge, which may not be applicable to Detroit seamount?).\nMinor comments:\n- line 47: What is NS location? North-South? Why not call it latitude?\n- line 67: The sentence seems incomplete to me, and is “devoted” the best word here?\n- Line 73-76: the sentence is complicated, can you rewrite this?\n- Lines 119-120: This sentence is unclear to me. The plate is thinnest close to the ridge, and thicker further away. So if the ridge is south of the plume, the plate gets thicker towards the north. I guess what you mean is that the plume stem is tilted towards the north in the upper mantle, but this is not clear.\n- Lines 122-124: another confusing sentence. Please clarify what you mean here.\n- Lines 128-134: Please clarify these sentences, I have problems following you here. Also please check if you use the correct terms here.\n- Line 182: typo, it should be buoyancy\n- Line 298: the citation should just be a number\n- Methods, second paragraph after the first equation: The sentence “The surface assimilates … two adjacent snaphshots.” is very long and complicated. Please rephrase and clarify this.\n- Methods, last sentence before subsection “Robust Plume Source Migration Results”: which two track are you talking about?\n- Appendix, Extended Data Figure 7: maybe it would be best to replace the hotspot age by a perceptually uniform color palette, the green area is very difficult to distinguish (especially for Reunion hotspot motion). Furthermore, there are no blue lines to mark plate boundaries, at least I don’t see them.\n- Appendix, Extended Data Figure 8: I don’t see any red or blue rectangles here.", "reviewer_4": "Inthisversionofthemanuscript,theauthorsmadesignificantrevisionoftheir original manuscript in response to the comments raised by the reviewers (includ- ing me). I feel that most of comments and/or suggestions by reviewers had been adequately considered in the revised manuscript. In particular, I very much appreciate the authors’ addition of detailed descriptions on their numerical models, althoughIdonotlikesomeoftheemployedassumptionsorformulations.\nFollowingsareseveral(minor)commentsandsuggestions.\n1. Idonotliketheparagraphstartingatline109oftherevisedmanuscript.\nThestatementsinthisparagraphread(atleasttome)thattheemphasislies\nin the comparison between Model 1 and Model 2 rather than that between\nthetracks#Aand#B.Inotherwords,thediscussionmadeherewouldimply\nthat the “plume migration” is more important than the “plume-lithosphere\ninteraction”, which is inconsistent with the title of this section (and that of\nthismanuscript).\nI therefore suggest that the authors could restore the relevant statements in\nthe original version, where the comparison had been made simply between\nModels1Aand1Bwithouttheeffectsof“plumemigration”.\n2. ThelegendofFigure3needsrevisions.\nIn the revised figure the authors had added “the temperature contour (black\ncontour)andmeltarea(outlinedbyredline)oftheplume”“onthetopright\ncorner of each snapshot”, which I like very much. However, the authors\nshouldmakeclearONWHICHPLANEthecontourmapsaredrawn.\n3. Misspellings\n(a) Lines71–72;“…showedthatsuggesteda…”\n(b) Line146;“Th isbecause…”", "reviewer_5": "The revised version of this manuscript is considerably improved and the authors satisfactorily addressed the comments. The paper needs a final revision of the language. I have three minor comments:\n1. Throughout the text around line 190 the authors discuss paleolatitudes \"drop\" or \"increase\". I feel that they should refer to paleolatitude \"(measured or modelled) values\".\n2. line 279 what means a “proper” plate reconstruction model? Do you mean alternatives are “improper”? Please clarify\n3.line 280 maybe say “observed and calculated” positions and ages", "reviewer_6": "I appreciate how the authors responded to my previous comments, and I am mostly satisfied with the changes and the additional models. There are only 2 (related) major and a few minor comments left to address from my side. Line numbers refer to the updated manuscript (with only the added text highlighted in red). The major comments and the first minor comment still refer to how long the ridge affects the hotspot track, which I think could be shown and discussed better. The remaining comments are very minor.\nMajor comments:\n1) Maybe it is just me, but I am still a bit confused with the timings, so maybe you can help me get this right. The ridge crosses the plume at around 105 Ma in Model 1 or 95 Ma in model 2 (the difference arising from the fact that the plume in model 2 moves southwards). In the test without ridge based on model 1 you ran (model 1C), the hotspot track starts to differ for seamounts older than ~70 Ma (Supplementary Figure 10), but at that time the ridge seems to be far away (Supplementary Figure 12) and I would not expect it to have any influence. Surprisingly, Supplementary Figure 10 also shows basically no track for model 1C between 75 Ma and 95 Ma, thus leaving a gap of 20 Myr in which the plume did not move relative to the plate(?). Why is that? How did you prescribe the surface velocity boundary condition for model 1C? I would have tried to prescribe the same time-dependent plate velocities above the plume itself as in 1B, but without having a ridge that separates the two plates (maybe you did that?). I know that messes up the plate models (and it is tricky to avoid that this has unwanted side effects on the general convection pattern, which in turn can affect the plume and the hotspot track), but the current model 1C may give a false impression on the duration of the ridge effect.\n2) Related to that: it would have been more educating to do the model without ridge (model C) for model 2 instead of model 1 to get a better assessment on the influence of the ridge on Detroit and Meiji. Based on the tests you ran (both Supplementary Figure 10 and 11), I would not expect that the ridge has any influence on seamounts younger than ~75-80 Ma, and the effect on Detroit can be considered debatable if the effect of the ridge disappears by 82 Ma. You say it yourself that the tracks in Supplementary Figure 11 with shifted ridges are basically identical for anything younger than 75 Ma. However, not all the changes in the tracks have an obvious explanation, since both the plume-ridge interaction timing and the plate velocities above the plume changed between the cases. In fact, the yellow curve (ridge 10° or ~1000 km further south) is not that far off from reality either, while red (ridge 5° or ~500 km further south) is totally wrong. Blue and purple are similar, but both tilted too early. So how far away does the ridge actually influence the seamounts, and how much is simply attributed to the plate drag which differs between these models as well? That is an interesting question, and I think only a model 2C can actually answer that. It would be great and improve the impact of the study to know this better, and make the paper consistent regarding the timing throughout the text. I think Supplementary Figure 11 (which I really appreciate) is actually more educating than model 1C, but a model 2C would be very helpful or even necessary to clearly show the importance of the ridge for your best-fitting model. And I am aware that this might be difficult within the limits of Nature, but an extended discussion of Supplementary Figure 11 and how the tracks differ because of the timing of plume-ridge interaction could be interesting.\nMinor comments:\n- Line 143-146: As mentioned above, I think it may have been better to use model 2 as a reference, since model 1 does not reproduce the track well even with the ridge. For model 2, the deviation will likely be at a different location than Nintoku (which model 1 predicts to be much older than it actually is). If you leave model 1C, I would suggest to rephrase the sentence a bit to make clear that the deviation of the track is not starting at the time of Nintoku. Later (in Line 198) you actually state that the ridge probably does not play a major role for the track younger than 82 Ma, which is around or shortly after Detroit. So the ridge is mostly relevant for Meiji and partly for Detroit, but not the rest. In fact, 82 Ma is even before Detroit, so maybe the end of the ridge effect is later (maybe ~78 Ma?), although the distance between ridge and plume seems large at 78 Ma in Figure 3e. So I think a model 2C and a more detailed look at the models in Supplementary Figure 11 can help to identify if the ridge matters for Detroit or not. Based on a simple estimate from Figure 4 (using the plate velocity above the plume and ignoring any possible plume drift southwards, which would increase distances), Meiji at 85 Ma might be about 450 km away (5 Myr plate drift with 3 cm/yr and 5 Myr with 6cm/yr) from the ridge at the time of eruption, but Detroit at 79 Ma is at least 890 km away (another 2 Myr with 6cm/yr and 4 Myr with 8cm/yr). So Detroit may or may not be influenced by the ridge, depending on exact locations, drift rates, etc. Only a detailed comparison of models 2B, 2C and the ones in Supplementary Figure 11 can tell that (which might be beyond the possibilities here, but would nonetheless be interesting and important).\n- Line 153: I think you only need to refer to Supplementary Figure 11, not 12\n- Line 218: “eruption site”\n- Line 350-356: I would say the rapid increase in paleolatitude for Reunion (simply due to plate drag of the increase in plate velocity of the Indian plate) is between 70-60 Ma, not 60-50 Ma. I agree with the rest of the statement about Reunion, but I think it is the “fading ridge effect” that is responsible for the paleolatitude decrease between after 55 Ma despite a slowly increasing plate velocity. After all, the distance between the ridge and the plume is increasing, meaning that the plume tilt will be reduced to what is caused by the plate drag. So maybe add a “fading” to the sentence, if you agree with me.\n- Line 377: The cited paper of Bredow and Steinberger is also related, but not the one on Reunion that I meant. I was thinking about the study of Bredow et al. (2017), https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017GC006875\n- Supplementary Figure 7: Thanks for adding the crosses, that helps. However, for future work, maybe you should consider using color palettes that are better suitable for colorblind people than the rainbow palette. There are by now a lot of perceptually uniform color palettes available in all formats.\n- Supplementary Figure 8: I think you forgot yo update the Figure in the Supplementary. In the response to my previous comment, the blue and red rectangles are shown, but not in the actual supplementary figure.\n- Supplementary Figure 11: I think there is a typo in the caption, the reference model is 2B, not 1B, right?\n- Figures 3 and Supp. Figure 12: I prefer the new figures compared to the old ones, especially the inlay showing the plume tilt is very helpful. Would it be possible though to make plate boundaries a little bit more obvious?", "reviewer_7": "I am satisfied the the changes the authors made, and the explanations given in the Response to Reviewers. I have only two very minor suggestions that can but don't have to be included:\n1) Line 150: I would say that the biggest deviation between tracks 2B and 2C starts around 70 Ma (or maybe 68 Ma), but this is a personal interpretation. I do see some smaller deviations already at ~65 Ma. So if you agree, maybe just say \"... ~70-65 Ma\", bot here and in Line 156? I leave this up to you to decide which you think is more appropriate.\n2) Line 167: Maybe rephrase this sentence a bit to something like \".... that all tracks are more (purple track) or less (yellow track) shifted eastwards compared to the observed seamounts during ~75-55 Ma\". At first when I read the sentence, I was looking for an east-west direction of the plume track, not the general shift that can be seen in Figure S11."}, "author_response": "Responses to comments on Nature Communications manuscript\nWe appreciate the editor for handling this work, and the constructive comments from\nthe reviewers which greatly enhanced the quality of this work. Below, we have listed\nthe original comments in black and our response in blue. We have carefully considered\nall the reviewers’ questions and suggestions. We hope that we have properly addressed\nall the concerns.\nReviewer #1 :\nThis paper is an extension of the work by Sun et al. [2021] where the interaction\nof plumes and ridges are studied by a simple numerical model of mantle convection in\na two-dimensional Cartesian box. In this study, the authors developed a regional three-\ndimensional spherical shell model near the Hawaii-Emperor seamount chain, with\nspecial emphasis on the possible influences of plume-ridge interaction on the formation\nof several discontinuous changes in the track between the Meiji and Detroit seamounts.\nThe authors confirmed the earlier findings by Sun et al. [2021] that the ascent of plume\nin the shallow mantle is greatly influenced by the combined effects of (i) the drag from\nthe motion of overlying plates and (ii) the presence of thinner lithosphere beneath the\nspreading ridges. The highlight of the present numerical experiments lies in the\ntemporal changes in the relative importance between (i) and (ii) depending on the\nrelative positioning between the plumes and ridges, which may further imply that the\ndiscontinuous changes between the Meiji can be caused by the passage of the ridge\nbetween the Izanagi and Pacific plates over the Hawaiian hotspot. In addition, the\nauthors showed that, by taking the above mechanism into account, the observed secular\nreduction in paleolatitude and its erratic temporal variations can be sufficiently\nexplained even if the southward migration of the Hawaiian plume root is very small.\nI feel that the authors’ numerical results are generally correct and their findings are\nin essence very important in the understanding of the dynamics of Earth’s lithosphere\nand mantle through the hotspot tracks. Unfortunately, however, I am not fully\nconvinced of the authors’ claim that the discontinuous change between the Meiji and\nDetroit is caused by the plume-lithosphere interaction, solely from the discussion in the\npresented manuscript. I therefore would like to offer the authors the following revisions,\nmost of which are intended to improve the persuasion of the manuscript.\nQ1-1. I think that in Figure 3 the authors should show the results for Case 2A or\n2B, not for Case 1A. This is partly because, in my understanding, Case 1A is the least\nreliable among the four cases presented in Figure 2, considering the relevance of the\nassumptions used to draw the hypothetical tracks. Another reason is that in this case\nthe timings of the events induced by the plume-ridge interaction are inconsistent with\nthose of the events actually observed in the Hawaii-Emperor seamount chain. Indeed,\nthe event which “first decreases the paleolatitude of the melting region due to\nsouthward ridge attraction (Figs. 3a-c)” occurs around 105 Ma, which largely deviates\nfrom the timing of the discontinuity between the Meiji and Detroit seamounts (around\nis employed. I therefore would like to make sure if the cases other than 1A can yield the\nevents corresponding to the Meiji-Detroit discontinuity at the timing consistent with the\nobservation.\nR1-1: Thanks for raising this point. We agree with your comments that Model 2B is\nbetter than Model 1, we’ve changed Figure 3 to the snapshots of Model 2B. As is shown\nin the new Figure 3, the timings of the events induced by the plume-ridge interaction\nare inconsistent with those of the events actually observed in the Hawaii-Emperor\nseamount chain. For example, the predicted first paleolatitude’s decrease of the melting\nregion at ~ 95-90 Ma agrees better to the observed paleolatitude variations from Meiji\nto Detroit (~85-80 Ma) than Model 1 does. See lines 109 - 141, 171 - 180 and Figure 3\nin the main text (also see the figure below).\nFigure 3. Snapshots of the Hawaiian plume model (Model 2B). The 3D contour\nrepresenting the +100°C temperature anomaly is shown in red. The 3D contour of 1% melt\nfraction is shown in white. The core-mantle boundary is shown in light blue. Plate boundaries\nare shown as green lines. Plate velocities are shown as black arrows. The length of the arrows\nqualitatively shows the magnitude of the plate velocity. The background shows the log-\nnormalized (relative to 1021 Pa s) mantle viscosity profile. The snapshots of before (a-b), during\n(c), and after (d-f) the ridge arrival are shown. Both the ridges and the Hawaiian plume produce\nmelt. On the top right corner of each snapshot shows the temperature contour (black contour)\nand melt area (outlined by red line) of the plume.\nQ1-2. I do not think that the influence of asthenospheric viscosity is sufficiently\ninvestigated on the plume-lithosphere interaction.\nThis is partly because the employed variation in asthenospheric viscosity is too small\nin this study. In the present manuscript the authors conducted the calculations of\nModels 13 and 14 where the viscosity in the asthenosphere is increased and decreased\nonly by a factor of 2, respectively. Considering that the viscosity of mantle materials\ncan significantly vary depending on several factors such as the water content, the\nauthors should conduct additional calculations by varying the viscosity more strongly.\nAnother, and more critical, reason is that the assumption of the ascent of generated\nmagma employed in this study is in essence not very good at investigating the plume-\nlithosphere interaction. As was stated in “Method” section, the authors assumed that\n“When eruption happens, the erupted melt would be put on the surface instantly\n(instantaneously?)”. This assumption means that the migration of generated magma\ntakes place without feeling the “mantle wind” in the background asthenosphere, which\nmay further imply that the effect of the drag from the motion of overlying plates is not\nfully taken into account. I therefore ask the authors to add some discussion on this\nlimitation in the revised manuscript.\nR1-2: Thanks for the suggestions.\nWe agree that mantle viscosity can be strongly influenced by factors like water\ncontent. However, the asthenosphere is generally thought to be dry, as inferred from\nthe MORB composition. Some researchers do suggest the uppermost mantle may\nindeed hold more water, but whether the water is ponded at the oceanic LAB (affecting\nasthenospheric flow) or within the lithosphere (not affect asthenospheric flow) is still\ndebated. Deep-rooted mantle plumes are generally considered quite dry, plus melting\nat the base of the lithosphere could remove pre-existing water as well. Even assuming\nthere is some water near the LAB, its localized distribution is unlikely to fully decouple\nthe lithosphere and the underlying asthenosphere, as this flow regime is controlled by\nthe large-scale rheological structure rather than local features.\nThat said, we emphasize that the asthenospheric viscosity we employed is already\nquite small compared to other studies. The reference value is based on multiple of our\nprevious studies with data assimilation that match both past subduction history and the\npresent mantle structures (e.g., Liu & Stegman, 2011; Hu et al., 2016). The presented\nviscosity tests are designed to examine whether the background viscosity in the\nasthenosphere changes could make notable differences. In this case, a factor of 4 in\nvariation is already quite generous, because this difference would result in very clear\nmismatches in the mantle structures (Liu & Stegman, 2011). Therefore, we prefer to\nkeep the current range of viscosity variation. See lines 211 - 213. We also added a\nreasoning for this viscosity choice in the rheology part of Method, see lines 544 - 550.\nRegarding whether the melt treatment misses an effect of the mantle wind, in our\nmodel, although the simulation of melt eruption is a little over-simplified, the depth\nwhere the melt reaches the eruption threshold is very shallow, usually right below the\nLAB (see the figure below). This means melt percolation happens mostly within the\nhigh-viscosity lithosphere, where the mantle wind is absent. So, this process would not\ncause notable mismatch in the surface eruption site. We’ve added some discussions in\nlines 523 – 530.\nSnapshot of Model 4 at 40 Ma. The red surface is +100 degree anomaly which\npresented the plume. 1% Melt is shown using the color of depth. For mid-ocean related\nmelt, it is around 50 km depth. For plume, the melt depth is relative shallow (~ 100 km,\nat lithospheric depth), which means the magma have already felt the mantle wind and\narrived at the bottom of lithosphere.\nIn addition, I think that the “Method” section needs intensive revisions.\nQ2-1. I do not think that the coordinate transformation should be discussed in detail.\nThis is quite obvious.\nR2-1: We agree with your comment. We’ve deleted the detailed demonstration of\ncoordinate transformation, see line 482.\nQ2-2. The authors should instead add some statements on the boundary conditions\nemployed in this study. Considering the motion of surface plates over about 100 million\nyears (several thousand kilometers), I do not think that. the employed numerical domain\n(120◦ in latitude, 210◦ in longitude) is wide enough to thoroughly exclude the influences\nfrom the vertical side walls despite the authors’ conjecture (or expectation).\nR2-2: Thanks for the suggestion. We have provided more details about the boundary\nconditions in lines 485 - 497. To reiterate, although the simulation time is quite long,\nthe nature of data-assimilation methods suggests that flow in the upper mantle is mostly\naffected by the surface plate motion within the above region. The reviewer is correct\nthat the plate moves a long distance over 100 million years. However, our study region\nis near the center and the plume does not move much laterally, so the model’s side\nboundaries are always far enough from the plume. In addition, another important\nrheological feature is a thoroughly weakened vertical zone along all side walls, so that\nartificial flow due to the impermeable boundaries are minimized further.\nQ2-3. I felt quite odd with the nomenclature or the names of several symbols.\nQ(1): T (r) “activation temperature”?\nthe values we used in Supplementary Table 2.\nQ(2): 𝜙 “melting rate”?\nThis phrase would literally mean the amount of generated melt per unit time. It\nshould instead be called “melt fraction”.\nR(2): Thanks for pointing this out. We use 𝜙 to mean the in-situ melt fraction that has\nnot erupted, and we have revised this in lines 563 - 565 and added its definition in line\n551.\nQ(3): “melt retention rate”?\nFrom this phrase one would imagine that the solid matrix actively prevents the\nmigration of melt. Is it what the authors truly mean?\nR(3): Here, we meant to say the melt fraction retained in the solid matrix or non-\nextractable melt amount as defined in Gerya and Meilick (2011). In the revised\n“Method” section, we have changed its name to the in-situ melt fraction, see lines 563\n- 565.\nQ(4): 𝜂\n𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑚𝑒𝑙𝑡\nIs it different from 𝜂 for sure?\n𝑛𝑜 𝑚𝑒𝑙𝑡\nR(4): We sincerely apologize for the confusion. Both of them mean the effective\nviscosity before considering the melt. In the revised “Method” section, we use η\nno melt\nto indicate the effective viscosity without considering melt for consistency, see lines\n561 - 565.\nQ2-4. The subsection “Model rheology” needs careful revisions in order to describe\nthe employed viscosity law more correctly and thoroughly.\nR2-4: Thanks for the suggestions. We’ve modified this section carefully and thoroughly,\nsee lines 531 - 565.\nQ(1): I did not found anywhere in the text the employed values of T and E .\n0 0\nR(1): Thanks for the reminder. T (r) isthe temperature offset, E (r) is the activation\n0 0\nenergy, r is the radial distance from the earth’s core, we have included the employed\nvalues of T (r) and E (r) in the revised Supplementary Table 2. See lines 537 - 538 in\n0 0\nthe main text.\nQ(2): The value and meaning of C should be clearly indicated.\nR(2): C is the viscosity multiplier due to compositional effects, please see lines 536 -\n537, and its value is listed in the revised Supplementary Table 2.\nQ(3): The authors should clearly state that a “cut-off” of viscosity has been employed\nin order to avoid too large variation.\nR(3): Thanks for the suggestion, we’ve added clearly state of the cut-off of viscosity,\nplease see lines 547 - 548.\nQ(4): I strongly ask the authors to make sure the magnitude of the reduction in viscosity\ndue to the presence of melt in the present numerical experiments. The value of exp(ζ2)\n≈ 105 implies that the viscosity drops by at most five orders of magnitude. I learned that,\non the other hand, the employed cut-off of viscosity allows the variations in viscosity\nonly by four orders of magnitude.\nI think that the equation should instead be written as,\n𝜂 = 𝜂 ×max[exp(−𝜁 ),𝑠𝑜𝑚𝑒 𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑]\n𝑛𝑜 𝑚𝑒𝑙𝑡 2\nR(4): Thanks for the suggestions. Indeed, we applied a cutoff value to the minimum\nviscosity to permit relatively fast convergence of the model, as is why the total viscosity\nvariation is four orders of magnitude. In addition, because we only allow the melt\nfraction retained in the mantle not to exceed 4%, the weakening effect is indeed around\none magnitude at most. We have specified this point in lines 558 - 565.\nQ2-5. In the equations defining the solidus and liquidus temperatures, the units of\ntemperature and pressure should clearly indicated.\nR2-5: Thanks for the suggestions. In the equations defining the solidus and liquidus\ntemperatures, the unit of temperature is ˚C, and the unit of pressure is GPa. We’ve\nadded the units to line 521.\nSeveral other (mostly minor) comments/suggestions follow.\nQ3-1: I felt quite odd with the statement beginning in line 72 “Therefore, other\nmechanisms must have been in operation to reproduce the correct seamount age\ndistribution”.\nI do not understand why the conjecture on “a systematically older-than observed\nhotspot track with all seamounts older than ∼ 70 Ma on the Emperor chain being\nalready subducted by now” needs other mechanisms to reproduce the correct (or, do\nthe authors imply “thorough”?) seamount age distribution.\nR3-1: Thanks for the question. To clarify, the statement “a systematically older-than\nobserved hotspot track with all seamounts older than ∼ 70 Ma on the Emperor chain\nbeing already subducted by now” is not a conjecture but an observation, as Hasson et\nal.’s published result clearly shows this. According to this model, the seamounts that\nare older than 70 Ma would not be found on Earth now as they have already subducted.\nIn addition, all seamounts on the Emperor chain were predicted older than the observed\nages, and this is not a subtle difference. We suggest that this major discrepancy between\ntheir model result and observation implies that the mechanism inferred from this\nnumerical model is not reasonable, i.e., other mechanisms are needed. See lines 71-77.\nQ3-2. In Figure 3, I would like to see the isosurfaces of melt fraction in white and those\nof hot anomaly in red. Although I believe that the distributions of melt should be of\nmore interest than those of temperature, my eyes had been strongly caught by the white\nisosurfaces of temperature.\nIn addition, it could be nice if the authors indicate the position at the top surface\njust above the magma source in the figure.\nR3-2: Thanks for the suggestions, and we’ve modified Figure 3 to the snapshots of\nModel 2B as it is the best-fit model. In addition, as you suggested, we’ve 1) changed\nthe isosurfaces of melt fraction to white and those of hot anomaly in red; 2) changed\nthe color of viscosity field to cold color; 3) denoted the melt area with a red line on the\nsurface. See Figure 3 (or see the figure below), lines 171 - 180 in the main text, also\nsee response R1-1 to your comment Q1-1 above.\nFigure 3. Snapshots of the Hawaiian plume model (Model 2B). The 3D contour\nrepresenting the +100°C temperature anomaly is shown in red. The 3D contour of 1% melt\nfraction is shown in white. The core-mantle boundary is shown in light blue. Plate boundaries\nare shown as green lines. Plate velocities are shown as black arrows. The length of the arrows\nqualitatively shows the magnitude of the plate velocity. The background shows the log-\nnormalized (relative to 1021 Pa s) mantle viscosity profile. The snapshots of before (a-b), during\n(c), and after (d-f) the ridge arrival are shown. Both the ridges and the Hawaiian plume produce\nmelt. On the top right corner of each snapshot shows the temperature contour (black contour)\nand melt area (outlined by red line) of the plume.\nQ3-3. In the reference list, #21 [Ye et al., 2022] and #35 [Afonso et al., 2016] are\nwrongly indicated. In addition, #22 [Herzberg, 2006] had been quoted nowhere in the\nmanuscript.\nR3-3: Thanks for the reminder, we’ve modified the citations, see lines 427 - 428, 465 -\n466, 116.\nReviewer #2:\nThe paper presents a numerical model that aims to reproduce observations\n(paleolatitude derived from paleomagnetism, geochemistry and seamount ages and\nlocation) of the Hawaiian-Emperor seamount chain in the Pacific Ocean, and in\nparticular to address the unresolved discrepancy of the oldest seamount of this chain.\nThe authors aim to test the importance and effect on the seamount track of geodynamic\nprocesses overlooked in previous studies, in particular shallow processes like the plume\n-ridge interactions. I note that this subject was recently discussed in a paper published\nby Sun et al (2021) who used geochemical data and 2D modelling to show that plume-\nridge interaction can indeed explain the age progression, geochemistry and\npaleomagnetism of the seamounts which are offset from the linear track of the seamount\ntrack.\nThe innovative aspect of this study is the use of a 3D model to assess several\nshallow processes, it takes into account plate reconstructions, it explores the plume-\nridge interaction also considering melting and melt advection. It is interesting to see\nthat by correcting the contribution from the better-constrained shallow mantle processes\nthrough quantitative numerical calculations they derive a better understanding of deep\nmantle and their conclusion refute published models by advocating that plume-\nlithosphere interaction could account for 50% of paleolatitude change, and lower\nmantle dynamics or plume source motion may account only for the other 50%.\nThis approach and conclusion has broader implications for other hotspot tracks,\nwhose evolution and proceses involved require revisiting.\nI consider the paper provocative and innovative and recommend publishing it after\nminor revisions. In particular, the authors should specify how their modelling method\nand approach are different from Hassan et al paper, besides implementing the shallow\nmantle processes.\nSome detailed suggestions and comments:\nQ1: For Model 1 -what is the methodological difference between your model and the\nHassan et al?\nR1: Thanks for the question. In Hassan’s paper, they used a purely thermal plume, and\nthe method used were inherited from the related previous article. They decided the\nvolcanos’ location by simply projecting the location of plume conduit from 350 km\ndepth to the surface without considering how upper mantle, especially Asthenosphere,\ndynamics influences the upwelling.\nOur method differs from Hassan’s in two ways. First, in our model, we traced the\nlocation of the plume at the base of the lithosphere instead of at 350 km depth, so that\nour plume can be advected by the asthenospheric wind laterally and reach a much\nfurther distance downwind from the location of the deep plume conduit. Second, we\nincorporated the function of melting within the thermal plume. The melt fraction also\ninfluenced the effective viscosity and the final eruption location. In summary, eruption\nin our model happened at the top of the Asthenosphere, after the plume experienced\nlateral bent and entrained by upper mantle flow, including both plate drag and mid-\nocean ridge attraction. See lines 503 - 510, 77 - 80.\nQ2: Model 6B in Fig2b suppl seems to fit the observations better (at least the track\nlocation and shape, as I can distinguish very well the predicted ages due to the complex\ncolour scale) that Model 2B in Fig.2\nR2: In Model 6B (Supplementary Figure 2), it seems that the track location and the\nshape of the seamount chain fit the observations better, while some of the seamounts’\n(Suiko, Nintoku, and Detroit) are not in the zone where melt erupted. Besides, the\npredicted seamounts ages in Model 6B are worse than those in Model 2B, especially in\nMeiji where the predicted age is between 90-95 Ma; while in Model 2B (Figure 2), the\npredicted one is more accurate (80-85 Ma), which is closer to the observed age of Meiji\n(~ 85 Ma). Thus, we consider Model 2B as the best model.\nBesides, we prefer the reconstruction model used in Model 2B. Model 2B is based\non the reconstruction of Muller et al. (2016), as we can see from Figure 4a (purple dots),\npaleolatitudes of seamounts inversed from Muller et al. (2016) are within the error\nbound of observed paleolatitudes. However, Model 6B is based on the reconstruction\nof Torsvik et al. (2019), as shown in Supplementary Figure 4b. Paleolatitude of\nseamounts from this reconstruction is not agree well with the observed paleolatitudes.\nThus, we prefer Model 2B as a better model.\nQ3: lines 209-201 what exactly means “lateral” – is this longitudinal? The movement\nof the plume source at CMB or in the astenosphere?\nR3: Thanks for the reminder. As we put the plume source at 600 km depth, the “lateral\nmovement” here means the plume source moves in the plane of 600 km depth, that is,\nin either longitude or latitude direction. We’ve modified the sentence here, see lines 236\n- 237.\nQ4: Figure 1 needs a scalebar and a reference to background image.\nR4: Thanks for the reminder. We’ve modified Figure 1, see line 61. The background\nimage is drawn with GMT software package by us, not from the previous studies.\nQ5-1: Figure 2 – colour scale – I wonder if this scale can have an easier to follow\ncolour scheme -for example like the ocean agegrid published by Mueller et al (various\npublications) or other uniform color palette\nR5-1: Thanks for the suggestion. The increment of color scale we used here is only 5\nMa, which is reasonable to capture the age difference between seamounts. If we use a\nmore continuous color scheme (see the figure below), it would be hard to distinguish\nthe exact seamounts ages.\nFigure S1. Results of Model 1A, 1B, 2A, and 2B with a uniform color palette for\nseamounts ages. Colored lines are the tracks from our numerical models. Blue thin\nlines with red and white circles are the results of Hassan et al. (2016). Modified from\nFig. 2 in the main text.\nQ5-2: Please add ref to Plate Boundaries\nR5-2: We’ve added the reference to plate boundaries, see line 102.\nQ5-3: “Track A shows the trace of vertical projection of the plume source onto the\nsurface” according to your model?\nR5-3: Yes, Track A shows the results of our models, see line 103.\nQ6: Fig3. Again, difficult to distinguish colours as the melt fraction contours have the\nsame dark red colour as the asthenosphere.\nR6: Thanks for the reminder, we’ve modified Figure 3 to the snapshots of Model 2B as\n2B is the best-fit model. In addition, as you suggested, we’ve: 1) changed the\nisosurfaces of melt fraction to white and those of hot anomaly in red; 2) changed the\ncolor of viscosity field to cold color; 3) denoted the melt area with a red line on the\nsurface. See the new Figure 3 (or see the figure below), lines 171 - 180 in the main text.\nFigure 3. Snapshots of the Hawaiian plume model (Model 2B). The 3D contour representing\nthe +100°C temperature anomaly is shown in red. The 3D contour of 1% melt fraction is shown\nin white. The core-mantle boundary is shown in light blue. Plate boundaries are shown as green\nlines. Plate velocities are shown as black arrows. The length of the arrows qualitatively shows\nthe magnitude of the plate velocity. The background shows the log-normalized (relative to 1021\nPa s) mantle viscosity profile. The snapshots of before (a-b), during (c), and after (d-f) the ridge\narrival are shown. Both the ridges and the Hawaiian plume produce melt. On the top right\ncorner of each snapshot shows the temperature contour (black contour) and melt area (outlined\nby red line) of the plume.\nReviewer #3:\nThe manuscript “The role of plume-lithosphere interaction in Hawaii-Emperor\nchain formation” by Xie et al. investigates how the plate tectonic history of the Pacific\nocean may have shaped the Hawaii-Emperor chain through plume lithosphere\ninteraction. More specifically, the authors suggest that a mid-oceanic ridge passing over\nthe Hawaiian plume at around 105 Ma could be responsible for half of the latitudinal\ndrift inferred from seamount paleomagnetic data along the Emperor chain by\ntemporarily deflecting the upper part of the plume stem. This result would have\nimportant implications on estimates of plume drift, plate reconstructions and associated\nlower mantle dynamics.\nAlthough there have been a lot of studies focusing on the formation of the Hawaii-\nEmperor chain, there are still certain aspects that have not been explained yet. Previous\nwork has shown that the bend at about 47 Ma is likely caused by a change in the motion\ndirection of the Pacific plate, with a potential influence of southward drift of the\nHawaiian plume. However, drift rates of the plume, as well as details in plate motion,\nremain poorly constrained, and most models fail to reproduce both ages and\npaleolatitudes of the samples taken along the Emperor seamount chain. As a\nconsequence, a model that could explain both data would be very valuable, and could\nhave significant implications within the Earth Sciences.\nWhile I think the results presented here are very interesting, I do have a few\nquestions and comments that would require moderate revisions. Particularly, I have\nsome concerns regarding how much the ridge can influence the plume at the given time,\nand how much the results depend on accuracy and errors from paleomagnetic data and\nplate reconstructions. I have to admit though that I am not an expert on paleomagnetism,\nso maybe some of my questions and comments are less relevant than I think.\nR: Thanks for your constructive comments and suggestions. To really show how much\nthe ridge matters, we’ve conducted several additional models with various ridge\nlocations (see Supplementary Fig. 10, 11). According to the model results, we inferred\nthat ridge locations are closely related to the time when plume and ridge meet with each\nother, and they mainly significantly affect the period when plume-ridge interaction\ndominates during the formation of seamounts chain. Detailed illustrations can be found\nbelow in responses R1 and R2 to your questions Q1 and Q2. Besides, we’ve tested the\neffects of different plate reconstructions (see section “Robust Plume Source Migration\nResults”). Based on these reconstructions, all three models produce a consistent SSW-\ndirected motion of the plume source prior to 47 Ma, after which the plume turns to ESE.\nThe paleolatitudes inferred from these tests are also similar (Supplementary Fig. 4).\nMain comments:\nQ1. While it is plausible to me that a plume interacting with a ridge will be deflected in\nthe upper mantle towards the ridge, I have some doubts about some of your\ninterpretations. You claim that the ridge still affects the plume even if it is >10° (~1100\nkm) away from the plume stem. This seems like a very big distance, probably too big to\nhave any significant influence (see also comment #9). To really show how much the\nridge matters, you would have to run a model without the ridge and compare the results.\nFor example in Sun et al. (2021), the plume is only affected as long as the ridge is <800\nkm away from the plume stem, Bredow et al. (2017, G3) mention a length scale of ~1000\nkm. You need to prove that the ridge actually matters for Meiji, Detroit and other\nseamounts, and that the change in plate speed of the Pacific plate alone is not enough\nto produce the observations.\nR1: Thanks for the questions. In our paper, we show that both plume-ridge interaction\nand plate drag are important, as shown in the Section “Effects of plume-lithosphere\ninteraction”, we’ve analyzed when the two mechanisms happen. We agree that plume-\nridge interaction cannot influence the plume which is 10° away; when the plume is far\naway, it is the plate drag effect that is dominant. When the plume is 10° away, the\nPacific ridge moves rather fast northward.\nAs you suggested, to really show how much the ridge matters, we’ve run an\nadditional model (Model 1C, based on Model 1B) without ridge effect. The results of\nModel 1C show that ridge does matter for the evolution of seamount chain. In this\nmodel, both the track and seamounts ages between Nintoku and Hawaii are similar to\nthose in the Model 1B (Supplementary Fig. 10, can also see the figure below). The\nreason behind is that during this period, plate drag dominates as the ridge is far away\nfrom the plume (Supplementary Figs. 10 & 12, Fig. 4a). Whereas, the trace of\nseamounts between Nintoku and Meiji exhibits distinct deviation from it in Model 1B\n(Supplementary Fig. 10). Since during this stage ridge capture is the main force causing\nthe plume to move laterally, the new test suggests that the ridge is necessary for better\nmatching the data. Please see lines 142 - 150.\nSupplementary Figure 10. Simulated hotspot tracks of models with (1A and 1B)\nand without ridge (1C) effects.\nQ2. Related to this: How much do your results depend on the position of the Izanagi\nridge, and the timing and paleolatitude of the seamounts? Both timing and latitude\nmeasurements of erupted magmas have errors and uncertainties, and the location of\nthe ridge may not be well constrained after all. So what happened if the ridge was a\nfew degree further north or south, or had a slightly different orientation? Plate\nreconstructions of ridges that are subducted are difficult, and the Pacific Ocean floor\nis complicated (see Sager (2022), and my comment #14).\nR2: Thanks for the questions. We agree with the reviewer about these uncertainties,\nand that’s why we tested different reconstructions. Practically speaking, it is the routine\nway in geodynamic modeling to explore published reconstructions and draw the\nconclusion that way. Speculating far beyond the existing reconstructions is neither\nrealistic nor fair for modelers who do not create plate reconstructions. That said, we’ve\nrun several models (based on Model 1B) by varying the ridge position with -10˚, -5˚,\n+5˚, +10˚ (+ for north, - for south) from that in Model 1B (Supplementary Fig. 11),\nwith the caveat that these ridge adjustments may not entirely follow tectonic rules.\nAll the models produce a similar track during 75~0 Ma. During this period, plate\ndrag is the most important driving force, and plume-ridge interaction has little effect.\nBut the tracks are different at 90~75 Ma, especially at Detroit. Among them, the\nreference model, Model 2B, is the best, thus confirming our conclusion. For this model,\nthe ridge is close to the plume during 90~75 Ma. Since the plume moves southward\nwhile the ridge moves northward during this period, shifting the ridge further south will\ndelay the timing of plume-ridge interaction, and vise versa. Therefore, for other models,\nthe plume either met the plume too early (blue, purple) or too late (red). See lines 142\n- 158.\nSupplementary Figure 11. Simulated hotspot tracks of models with different ridge\nposition. Solid lines with different colors of outline denote different ridge positions.\nModel 2B is the reference model. In model a, b, c and d, (yellow, red, purple, blue\nrespectively) the ridge deviated from it in 1B for -10˚, -5˚, +5˚, +10˚ (+ for north, - for\nsouth).\nQ3. What would be the effect of True Polar Wander? If you deal with paleomagnetic\ndata, you have to correct for TPW in order to compare to current latitudes. In Torsvik et al. (2017), the show that this may result in paleolatitudes of most Emperor seamounts\nsimilar to that of Hawaii today, and only Detroit may be further north. It seems to me\nthat TPW was not included in the data you used? This would also play a role when\ncomparing absolute and relative plate reconstruction reference frames. Would this also\nexplain some of the very abrupt jumps of velocity magnitude and direction seen in\nFigure 4, Extended Data Figure 7, and the Movie 1?\nR3: Thanks for the questions. TPW may certainly affect paleolatitudes, as long as the\nrotation pole is not on the north/south pole. On the other hand, this effect on\npaleolatitude should not show up if TPW was already considered in the utilized plate\nreconstruction model. In fact, one the plate reconstructions we tested, i.e., Torsvik et\nal., 2019, does incorporate their inferred TPW in its reference frame: A major difference\nof this reconstruction from the other ones we used (e.g., Muller et al., 2016) is the\namount of TPW considered. From the rather similar modeling results based on these\nreconstructions, we may conclude that the “known” TPW events do not cause\nsignificant differences.\nOn the other hand, we do echo the reviewer’s concern here regarding the rapid\npaleolatitude variation, especially during the late Cretaceous period (Fig. 4). In fact, we\npropose that “one way to reconcile this dilemma is to suggest that the Pacific plate\nrotated clockwise during the formation of Meiji but stopped before Detroit formed.”\nThis proposal is similar to what Chandler et al. (2013, ref 26) found for the large\nrotation of the Ontong Java Plateau around this time. We further state that “If this\nplateau was part of the Pacific Plate back then, the region where Meiji formed should\nhave also rotated by a similar amount. This scenario could naturally account for the\ndifference between the simulated and observed Meiji-Detroit chain orientations, which\nalso differ by ~40° (Supplementary Fig. 5c).”. However, we cannot decide at the\nmoment that this should be a TPW event, and would like to leave for further research.\nQ4. I was able to understand the text, but sometimes the grammar or the chosen\nexpressions distracted me from the actual content of the sentence. I will only list some\nof those sentences under minor comments, but I will not provide detailed suggestions\non how to correct them (this is up to the authors). However, I would strongly\nrecommend to check the language carefully and make sure that the grammar and the\nchosen words are appropriate for the way they are used. One word that irritated me\nthroughout the text is “plate entrainment”. Maybe it is better say “plate drag”?\n“entrainment” would imply for me that parts of the plate are entrained in the plume,\nas this is typically used when referring to small portions of chemically distinct material\nbrought up from the core-mantle boundary by the plume.\nR4: Thanks for the suggestions. Although the term plate entrainment was also used is\nsome other geodynamics literature with a similar meaning to ours, we appreciate the\nreviewer’s concern and have changed the word “entrainment” to “drag”. See this\nchange in lines 19, 124, 126, 135, 139, 146, 148, 181, 195, 207, 344, 347, 348, 352,\n357, 508. We also carefully checked and modified the grammar and expressions of the\nwhole text.\nQ5. Abstract, line 18: you mention that you use melt migration, but the melt in your\nmodels is not really migrating. You use tracer particles that are advected with the flow,\nbut do not move independently. Real melt migration would consider a 2-phase flow\naccording to Darcy’s law, or even a more complex and realistic behavior of the melt.\nYour approach does neglect some local dynamics associated with melt migration, but\nI think the models are fine for the purpose. Still, I would suggest to rephrase “melt\nmigration” here (and elsewhere?), maybe to something like “simplified melt migration”\nor “passive melt migration”.\nR5: We agree with your comments and suggestions. Follow your suggestions, we’ve\nmodified “melt migration” to “simplified melt migration” in the paper, see lines 18,\n501, 506.\nQ6. Lines 39-45: I think Torsvik et al. don’t really use the paleolatitude that much in\ntheir argument why a change in Pacific plate direction is necessary to explain the\nHawaiian-Emperor Bend at 47 Ma. They base this mostly on the drift rates and direction\nfrom geodynamic models. In fact, I am not sure if their models can explain the\npaleolatitudes of the Emperor seamounts.\nR6: Thanks for raising this point. We agree with you that Torsvik et al. (2017) don’t\nreally use the paleolatitude that much in explaining the Hawaiian-Emperor Bend (HEB)\nat 47 Ma. What we really what to state is that based on their geodynamic models, they\nsuggested that solely hotspot drift is insufficient to produce such long Emperor Chain,\nand the directional change of Pacific Plate motion is required to account for the\nformation of HEB. We’ve modified the sentences, see lines 41 - 42.\nActually, we did calculate the paleolatitudes of the seamounts based on plate\nreconstruction results of Torsvik et al. and the current observed seamounts’ locations.\nAs shown in Supplementary Fig. 4 (can also see the figure below), the purple points\nrepresent the paleolatitudes of seamounts we calculated.\nSupplementary Figure 4. Paleolatitude predictions using additional\nreconstructions. b) Model 5, 6 based on Torsvik et al.13. All the notations are the\nsame as Fig. 4 in main text.\nQ7. Figure 2: for which model 2 is the green background derived, model 2A or 2B?\nI guess 2B, but you should specify this.\nR7: Thanks for the reminder. In Figure 2, the green background is derived from Model\n2B, we’ve specified it in line 102.\nQ8. Related to Figure 2 (and other figures that are alike): did you try to compare your\nsuggested melt volumes and locations to observations? One thing that I notice is that\nthere is quite a difference between the models, including a significant portion of melting\naway from the plume track. How realistic are your estimates and locations, apart from\nthe hotspot track that you predict?\nR8: Thanks for the questions. We’ve compared the chain’s geometry, the seamounts\nages and locations with observations, but did not consider the predicted melt volumes.\nThe latter would also beg more model variables such as plume flux over time, which is\nunknown a prior, so we assumed a largely constant plume flux history. Because the\nmelt here originates from different dynamic processes, including eruption from the\nplume and melt from the middle ocean ridge, it’s quite difficult to distinguish which\npart is generated from the plume. The erupted melt sites in green shades in Fig. 2 is the\nresults from the best-fit Model 2B (see lines 101 - 102, we’ve pointed this out). That’s\nwhy the erupted melt sites agree well with Model 2B’s track, but are away from the\ntracks of Model 1A, 1B and 2A. In fact, as we can see from Fig. 2, the erupted melt\nsites are consistent with the predicted seamounts chain’s track, subduction zones and\nsubduction history of Model 2B, which could validate that our estimates and the\nlocations are reasonable. Please see lines 109 - 141.\nQ9. Figure 3, and related to the respective paragraph in the text: The panels in the\nfigure are very confusing and do not really show what you discuss. First of all, the\nplume tilt at any time is almost invisible (too small, perspective is not ideal), secondly\nthe North direction is towards the right (and not towards the top as one would expect,\nespecially since this is not clearly indicated by an arrow or mentioned in the text).\nIn addition, the viscosity scale would better be labeled “log Δvisc”. And finally, I don’t\nsee any plume stem tilt at 88 Ma, and the ridge is already about 18° away (meaning\n~2000 km). I am not sure if the ridge still has an influence at this time, the distance\nseems too large. You would need to provide a more detailed figure to demonstrate this,\nand maybe a model without the ridge as mentioned in comment #1.\nR9: Thanks for the suggestions. We’ve modified Fig. 3 (see the figure below)\naccording to your suggestions: (1) On the top right corner of each snapshot, we added a\ntemperature contour to show the geometry of the plume. (2) We’ve added the North\ndirection pointing to the right direction to the lower right corner of Fig. 3. (3) The\nviscosity scale was modified to “log Δvisc”. (4) We’ve changed Fig. 3 to the results of\nModel 2B, the best fitted model, the plume stem tilted northward obviously at ~90 Ma\n(Fig. 3d); At this time, the ridge is still close to the plume and could have an influence.\n(Fig. 3, see lines 119 - 141 in the main text). The results of Model 1 are then shown in\nSupplementary Fig. 12. We’ve changed the color palette and added the plume’s cross\nsection to the top right conner of each snapshot. The figure shows that the plume stem\ntilts northward at ~88 Ma mainly due to the Pacific plate drag. Furthermore, we’ve run\nan additional model without the ridge (see lines 142 - 158, Supplementary Fig. 10),\nmore details about the illustrations, please see the response #1 (R1) to your comment\n#1 (Q1) in the preceding part of this response letter.\nFigure 3. Snapshots of the simulated Hawaiian plume model (Model 2B). The 3D\ncontour of +100°C temperature anomaly is shown in red. The 3D contour of 1% melt\nfraction is shown in white. The core-mantle boundary is shown in light blue. Plate\nboundaries are shown as green lines. Plate velocities are shown as black arrows. The\nlength of the arrows qualitatively shows the magnitude of the plate velocity. The\nbackground shows the log-normalized (relative to 1021 Pa s) mantle viscosity profile.\nThe snapshots of before (a-b), during (c), and after (d-f) the ridge arrival are shown.\nBoth the ridges and the Hawaiian plume produce melt. On the top right corner of each\nsnapshot shows the temperature contour (black contour) and melt area (outlined by red\nline) of the plume.\nSupplementary Figure 12. Snapshots of the simulated fixed Hawaiian plume\nmodel (Model 1). The 3D contour of +100°C temperature anomaly is shown in red.\nThe 3D contour of 1% melt fraction is shown in white. The core-mantle boundary\nis shown in light blue. Plate boundaries are shown as green lines. Plate velocities are\nshown as black arrows. The length of the arrows qualitatively shows the magnitude of\nthe plate velocity. The background shows the log-normalized (relative to 1021 Pa s)\nmantle viscosity profile. The snapshots of before (a-b), during (c), and after (d-f) the\nridge arrival are shown. Both the ridges and the Hawaiian plume produce melt. On the\ntop right corner of each snapshot shows the temperature contour (black contour) and\nmelt area (outlined by red line) of the plume.\nQ10. Lines 169-177: I am surprised that the pacific plate changed its direction so much\nin such a short time, but I guess this is from the plate reconstructions models (is that\nconsistent between all models?). However, the combined effect of ridge attraction and\nplate motion would just be 5° (from 0.8° to 5.8°), and I don’t think the split you mention\nis accurate. In fact, the northwards drag of the ridge starts as soon as the ridge is north\nof the plume, thus at 105 Ma, and then decreases over time as the ridge moves away.\nOn the other hand, the Pacific plate sped up over the course of about 13 Myr between\nperiod of time. Therefore, I think the impact of the plate drag is much larger than what\nyou indicate, potentially even accounting for all 5° at around 80 Ma. To really quantify\nthis, you would need to run the same simulations, but disable the ridge (comment #1).\nR10: Thanks for your questions and suggestions. The motion of Pacific Plate is from\nplate reconstructions models (Muller et al., 2016). According to Muller er al. (2016),\nthe Pacific Plate first moved southward during ~105-95 Ma, then changed to drift\nnorthward after ~95 Ma. Other plate reconstructions (say Muller et al., 2019; Torsvik\net al., 2019) we tested show similar kinetic characters of the Pacific Plate motion\n(Supplementary Fig. 4, Fig. S1 below).\nFigure S1. Snapshots of plate reconstructions from (a, b) Muller er al. (2016),\n(c, d) Muller et al. (2019), and (e, f) Torsvik et al. (2019).\nAs shown in the snapshots of Model 1 (Supplementary Fig. 12), the ridge axis is\nexactly on the top of plume at ~105 Ma. At this time, the interaction between ridge and\nplume is strong. However, before the ridge axis' arrival, the plume has already been\nattracted by the ridge (~ 109 Ma). At this time, the plate drag is almost compensated by\nthe ridge attraction, which results in a nearly vertical plume stem (0˚ paleolatitude\noffset). Thus, we suggest that when we estimate the combined effect of ridge attraction\nand plate motion, we should consider the start time at ~ 109 Ma (0˚ paleolatitude offset),\nnot 105 Ma (0.8˚ paleolatitude offset), the latitude offset should be 5.8˚ then. See lines\n197 - 200.\nTo quantify the ridge effects, we’ve run an additional model (Model 1C,\nSupplementary Fig. 10) without a ridge as you suggested (see R1 to Q1 above). In\nModel 1C, both the trace and age of seamounts between Nintoku (~56Ma) and Hawaii\n(0Ma) are similar to them in Model 1B, because during this time, the ridge is quite far\naway from the plume. However, the trace of the seamount chain deviated significantly\nfrom Model 1B before Nintoku generated, which means that the ridge effects cannot be\nneglected before seamount Nintoku formed. See lines 142 - 150. Therefore, our\nestimation that the contribution of 3.3˚ from ridge attraction and 2.7˚ from Pacific Plate\nmotion to the paleolatitude offset is reliable.\nQ11. Lines 189-191: I don’t think this is the correct reason, and I honestly don’t see\nwhy this should be connected at all. First of all, you don’t actually model independent\nmelt motion, neither vertical nor lateral, so your models cannot show this. In addition,\nthe Couette component of the flow (i.e. plate drag) does not change with lower\nasthenosphere viscosity, only the Poiseuille component (pressure-driven component of\nthe asthenosphere flow due to plume injection) could change, but the reason for the\nlatitude offset is not the pressure-driven component, which is constant for constant\nplume flux (unless changed by subduction zones).\nR11: Thanks for your questions. We apologize for not making our point clear enough.\nThis sentence has been changed to “This is likely due to the tradeoff between the\nvertical and lateral motions of the plume: while reducing asthenospheric viscosity\nallows the plume to rise faster, the plume also migrates faster laterally due to pressure-\ndriven flow with reduced viscous resistance, thus resulting in a similar erupt site and\nhotspot location.” See lines 214 - 218.\nQ12. Line 254 and Figure 4: I am not sure how you obtain the purple dots. Can you\nplease explain this, for example in the Methods section?\nR12: We first choose a proper plate reconstruction model (Muller et al., 2016),\ncombined with the positions and ages of the present Hawaii-Emperor chain, reversing\nthe chain back to the time when it generated. The resulted seamounts latitudes are the\nestimated paleolatitudes shown in purple dots. We’ve added a brief demonstration in\nlines 279 - 283.\nQ13. Line 257 and Extended Data Figure 5: the proposed plume drift between 90 Ma\nand 80 Ma seems unrealistically high, so I don’t think this is a plausible explanation.\nR13: We treat the tests on plumes’ locations as an inverse problem where we explore\ndifferent trajectories of simple plume motion. As the plume’s precise moving history is\nunknown, we tested several conceptual models to see the results of which one fit the\nobservations best. Supplementary Fig. 5 (Model 7) is one of our tests that cannot\nprovide a perfect paleolatitudes result, we did propose that the corresponding three-\nstage plume motion seems unreasonable, accordingly. See lines 284 - 291.\nQ14. Line 302: I am not sure if Sager (2022) is the correct citation for this, Sager had\na more general criticism of the data than just for Detroit seamount. And what about the\nother criticism that he mentioned with respect to the study of Sun et al. (2021)? Don’t\nyour models suffer from similar shortcomings of paleomagnetic data, plate\nreconstructions, age constraints, and the distance from the ridge that I mentioned in\ncomment #9?\nR14: Thanks for your questions. We agree that Sager (2022) is not an ideal citation\nhere, and we’ve modified the sentence in line 332 - 333. In addition to uncertainty for\nradiometric dates, Sager (2022) also mentioned that in the study of Sun et al. (2021),\nthere are uncertainties in the tectonic model for ancient spreading ridge/plate boundary\nlocations, Hawaii hotspot plume motion, and modeling plume response to upper mantle.\nOur model suffers from similar shortcomings of data as Sun et al. does, while the\nimprovement of data quality is beyond the scope of this paper. To partly remedy this\nproblem, we’ve improved our models in many other aspects: 1) test different plate\nreconstructions (Fig. 4, Supplementary Fig. 4); 2) run additional models with various\nridge locations (see R1 to Q1, R2 to Q2 above); 3) incorporate plume-lithosphere\ninteraction and melt during modeling (Fig. 2); 4) test different plume motion history\n(Fig. 4, Supplementary Fig. 2). Thus, compared with Sun et al. (2021), our results\nshould be more comprehensive and our conclusion more objective. The fact that we\nachieved a model that best satisfies the seamounts’ ages and paleolatitudes,\npublished\nplume motion history, and evolution/shape of the Hawaii-Emperor chain (while no\nprevious models did) should render our conclusion more plausible than previous studies\n(see lines 403 - 510).\nQ15. Lines 317-320: Did you have a look at the paper by Bredow et al. (2017, G3)?\nThis would be good to cite here, as it also looks at plume-ridge interactions and how\nthis affects melting and the volcanic chain.\nR15: Thanks for your suggestions. We’ve read the paper by Bredow et al. (2017, G3),\nthey proposed the plume can be captured by the ridge resulting in the increasing of melt.\nIn addition, it is the combined effect of plume-ridge interactions, plate motion and\nmantle flow that controls the melt generation and eruption, as well as the hotspots tracks.\nThese conclusions are consistent with ours. Therefore, we considered Bredow et al.\n(2017, G3) as a proper citation here, and added the citation to lines 352 - 353.\nQ16. Lines 311-324 and Extended Data Figure 7: At the time the ridge passes over the\nNew England Hotspot at around 85 Ma, there seems to be no change in the\npaleolatitude trend of the volcanoes. Does that mean that the ridge attraction is simply\ncompensated by the plate drag? And for Reunion, the increase in paleolatitude could\nbe related to the fast motion of the Indian plate, partly compensated by the ridge\nattraction towards the south. After passing the ridge, the plume is underneath a plate\nwith significantly lower northward velocity, reducing paleolatitude. If this is true,\nridge attraction may play a much smaller role than suggested in this paper, and only\nmatter while the plume is in (close) vicinity of the ridge (maybe <1000 km as suggested by\nBredow et al. (2017, G3); note, however, that melting would probably require a thin\narea rather close to a ridge, which may not be applicable to Detroit seamount?).\nR16: Thanks for the questions. For New England Hotspot at around 85 Ma, no change\nin the paleolatitude trend of the volcanoes means that the ridge attraction is simply\ncompensated by the plate drag, as the reviewer properly explained (see lines 346 - 348).\nFor Reunion plume, the increase in paleolatitude (70 - 60 Ma) could be mainly related\nto the fast motion of the Indian plate (Supplementary Figure 7). After passing the ridge,\nthe plate overriding the plume changed to African Plate with a much slower motion,\nthe paleolatitude decreases then. However, during ~ 53 - 39 Ma, plate motion increases\nwhile paleolatitude decreases. This indicates plate motion is not the dominant factor,\nridge effect still plays an important role during this stage (see lines 350 - 356).\nWe agree with the idea that ridge attraction matters in a certain distance, just as\nindicated by our model results (Fig. 3) and Bredow et al. (2017, G3), but this effect\nshould also depend on the amplitude of plate motion and the underlying plume\nmigration rate, a detailed study of which is beyond the scope here. Combined with the\nadditional models with different ridge locations (Supplementary Fig. 11, see lines 150\n- 158), we suggested that both plume-ridge interaction and plate drag are important for\nHawaii, a hotspot within a fast-moving plate. Furthermore, we believe that their\ncontributions are similar. As a result, plume source motion may account for 50% of the\nobserved abnormal hotspot motions, plume-lithosphere interaction (includes plume-\nridge interaction and plate drag) could contribute to the other 50%.\nMinor comments:\nQ17. Line 47: What is NS location? North-South? Why not call it latitude?\nR17: Thanks for raising this point. NS location means latitude here, we’ve modified\n“NS” to “latitude”, see line 48.\nQ18. Line 67: The sentence seems incomplete to me, and is “devoted” the best word\nhere?\nR18: Thanks for the question, we’ve changed “devoted” to “aiming at” and modified\nthis sentence, see lines 68 - 69.\nQ19. Line 73-76: the sentence is complicated, can you rewrite this?\nR19: Thanks for the suggestion, we’ve rewritten the sentence, see lines 77 - 80.\nQ20. Lines 119-120: This sentence is unclear to me. The plate is thinnest close to the\nridge, and thicker further away. So if the ridge is south of the plume, the plate gets\nthicker towards the north. I guess what you mean is that the plume stem is tilted towards\nthe north in the upper mantle, but this is not clear.\nR20: Thanks for the suggestion, it means that when the ridge is far from the plume,\nthe plume stem geometry is mainly affected by plate drag. We’ve modified the sentence to\nmake it clear, see lines 122 - 124.\nQ21. Lines 122-124: another confusing sentence. Please clarify what you mean here.\nR21: Thanks for your suggestion. The sentence means that the northward drag of the\nIzanagi plate is compensated by the southward attraction from the ridge, and result in a\nnearly vertical plume. The reason behind the southward attraction of the ridge is that:\nthe lithospheric thickness gets thinner and the pressure decreases as approaching to the\nridge axis, mantle material then flows from the high-pressure zone (the plume) towards\nthe low-pressure zone (the ridge axis). We’ve modified the sentence, see lines 125 -\n127.\nQ22. Lines 128-134: Please clarify these sentences, I have problems following you here.\nAlso please check if you use the correct terms here.\nR22: Thanks for the suggestion. What we want to state here is that: After the ridge axis\npasses over the plume and moves northward continuously, its south flank arrives. As\nthe ridge is not that far away from the plume, it can still attract the plume, together with\nthe norward plate drag, the greatest amount of northward translation of the melt source\nhappens. We’ve modified the sentences, see lines 131 - 136.\nQ23. Line 182: typo, it should be buoyancy\nR23: Thanks for the reminder, we’ve modified “buoyance” to “buoyancy”, see line 205.\nQ24. Line 298: the citation should just be a number\nR24: Thanks for pointing this out, we’ve modified it, see line 328.\nQ25. Methods, second paragraph after the first equation: The sentence “The surface\nassimilates … two adjacent snaphshots.” is very long and complicated. Please rephrase\nand clarify this.\nR25: Thanks for the suggestion, we’ve rephrased the sentence. It means that: The\nsurface assimilate kinematic boundary conditions are from the plate reconstruction\nmodels, these models can also provide information about seafloor age, and plate\nboundary geometries at a 1-Myr time interval. We use seafloor age and plate motion as\ninputs to the dynamic model and smoothly interpolate between the two adjacent\nsnapshots. See lines 485 - 491.\nQ26. Methods, last sentence before subsection “Robust Plume Source Migration\nResults”: which two track are you talking about?\nR26: Thanks for the question, the two tracks are the predicted track #A and track #B\nfrom our numerical models, respectively. See lines 584 - 585.\nQ27. Appendix, Extended Data Figure 7: maybe it would be best to replace the hotspot\nage by a perceptually uniform color palette, the green area is very difficult to\ndistinguish (especially for Reunion hotspot motion). Furthermore, there are no blue\nlines to mark plate boundaries, at least I don’t see them.\nR27: Thanks for the suggestions. Though the color palette of hotspot age is difficult to\ndistinguish, we’ve added marks of “Black Crosses” with 10 Ma increments to help\ndistinguish the age. In addition, we’ve deleted the sentence “Blue lines are plate\nboundaries. Black lines represent coastlines”.\nQ28. Appendix, Extended Data Figure 8: I don’t see any red or blue rectangles here.\nR28: Thanks for the reminder, we’ve modified the figure as shown below.\nSupplementary Figure 8. The moving rectangular window for calculating the\nHawaii chain as a curve. The red and blue rectangles show two moving windows. The\nlocation and age of a point on the hotspot chain are the weighted means for all erupted\nmelts inside the window. The width of the window is set wide enough to capture all\nerupted melt on both sides of the central line. The yellow points are control points along\nthe line. Tests show that the result is independent of the choice of yellow points.\nReview of the revised version of Xie et al.,\n“The role of plume-lithosphere interaction in\nHawaii-Emperor chain formation”\nReviewer #1 (Remarks to the Author):\nInthisversionofthemanuscript,theauthorsmadesignificantrevisionoftheir\noriginal manuscript in response to the comments raised by the reviewers (includ-\ning me). I feel that most of comments and/or suggestions by reviewers had been\nadequately considered in the revised manuscript. In particular, I very much appreciate\nthe authors’ addition of detailed descriptions on their numerical models, althoughIdonotlikesomeoftheemployedassumptionsorformulations.\nFollowingsareseveral(minor)commentsandsuggestions.\n1. Idonotliketheparagraphstartingatline109oftherevisedmanuscript.\nThestatementsinthisparagraphread(atleasttome)thattheemphasislies\nin the comparison between Model 1 and Model 2 rather than that between\nthetracks#Aand#B.Inotherwords,thediscussionmadeherewouldimply\nthat the “plume migration” is more important than the “plume-lithosphere\ninteraction”, which is inconsistent with the title of this section (and that of\nthismanuscript).\nI therefore suggest that the authors could restore the relevant statements in\nthe original version, where the comparison had been made simply between\nModels1Aand1Bwithouttheeffectsof“plumemigration”.\n2. ThelegendofFigure3needsrevisions.\nIn the revised figure the authors had added “the temperature contour (black\ncontour)andmeltarea(outlinedbyredline)oftheplume”“onthetopright\ncorner of each snapshot”, which I like very much. However, the authors\nshouldmakeclearONWHICHPLANEthecontourmapsaredrawn.\n3. Misspellings\n(a) Lines71–72;“…showedthatsuggesteda…”\n(b) Line146;“Th isbecause…”\n(cid:4)\nThe revised version of this manuscript is considerably improved and the authors satisfactorily\naddressed the comments. The paper needs a final revision of the language. I have three minor\ncomments:\n1. Throughout the text around line 190 the authors discuss paleolatitudes \"drop\" or \"increase\". I feel\nthat they should refer to paleolatitude \"(measured or modelled) values\".\n2. line 279 what means a “proper” plate reconstruction model? Do you mean alternatives are\n“improper”? Please clarify\n3.line 280 maybe say “observed and calculated” positions and ages\nReviewer #3 (Remarks to the Author):\nI appreciate how the authors responded to my previous comments, and I am mostly satisfied with\nthe changes and the additional models. There are only 2 (related) major and a few minor comments\nleft to address from my side. Line numbers refer to the updated manuscript (with only the added\ntext highlighted in red). The major comments and the first minor comment still refer to how long the\nridge affects the hotspot track, which I think could be shown and discussed better. The remaining\ncomments are very minor.\nMajor comments:\n1) Maybe it is just me, but I am still a bit confused with the timings, so maybe you can help me get\nthis right. The ridge crosses the plume at around 105 Ma in Model 1 or 95 Ma in model 2 (the\ndifference arising from the fact that the plume in model 2 moves southwards). In the test without\nridge based on model 1 you ran (model 1C), the hotspot track starts to differ for seamounts older\nthan ~70 Ma (Supplementary Figure 10), but at that time the ridge seems to be far away\n(Supplementary Figure 12) and I would not expect it to have any influence. Surprisingly,\nSupplementary Figure 10 also shows basically no track for model 1C between 75 Ma and 95 Ma,\nthus leaving a gap of 20 Myr in which the plume did not move relative to the plate(?). Why is that?\nHow did you prescribe the surface velocity boundary condition for model 1C? I would have tried to\nprescribe the same time-dependent plate velocities above the plume itself as in 1B, but without\nhaving a ridge that separates the two plates (maybe you did that?). I know that messes up the plate\nmodels (and it is tricky to avoid that this has unwanted side effects on the general convection\npattern, which in turn can affect the plume and the hotspot track), but the current model 1C may\ngive a false impression on the duration of the ridge effect.\n2) Related to that: it would have been more educating to do the model without ridge (model C) for\nmodel 2 instead of model 1 to get a better assessment on the influence of the ridge on Detroit and\nMeiji. Based on the tests you ran (both Supplementary Figure 10 and 11), I would not expect that the\nridge has any influence on seamounts younger than ~75-80 Ma, and the effect on Detroit can be\nconsidered debatable if the effect of the ridge disappears by 82 Ma. You say it yourself that the\ntracks in Supplementary Figure 11 with shifted ridges are basically identical for anything younger\nthan 75 Ma. However, not all the changes in the tracks have an obvious explanation, since both the\nplume-ridge interaction timing and the plate velocities above the plume changed between the\ncases. In fact, the yellow curve (ridge 10° or ~1000 km further south) is not that far off from reality\neither, while red (ridge 5° or ~500 km further south) is totally wrong. Blue and purple are similar, but\nboth tilted too early. So how far away does the ridge actually influence the seamounts, and how\nmuch is simply attributed to the plate drag which differs between these models as well? That is an\ninteresting question, and I think only a model 2C can actually answer that. It would be great and\nimprove the impact of the study to know this better, and make the paper consistent regarding the\ntiming throughout the text. I think Supplementary Figure 11 (which I really appreciate) is actually\nmore educating than model 1C, but a model 2C would be very helpful or even necessary to clearly\nshow the importance of the ridge for your best-fitting model. And I am aware that this might be\ndifficult within the limits of Nature, but an extended discussion of Supplementary Figure 11 and\nhow the tracks differ because of the timing of plume-ridge interaction could be interesting.\nMinor comments:\n- Line 143-146: As mentioned above, I think it may have been better to use model 2 as a reference,\nsince model 1 does not reproduce the track well even with the ridge. For model 2, the deviation will\nlikely be at a different location than Nintoku (which model 1 predicts to be much older than it\nactually is). If you leave model 1C, I would suggest to rephrase the sentence a bit to make clear that\nthe deviation of the track is not starting at the time of Nintoku. Later (in Line 198) you actually state\nthat the ridge probably does not play a major role for the track younger than 82 Ma, which is around\nor shortly after Detroit. So the ridge is mostly relevant for Meiji and partly for Detroit, but not the\nrest. In fact, 82 Ma is even before Detroit, so maybe the end of the ridge effect is later (maybe ~78\nMa?), although the distance between ridge and plume seems large at 78 Ma in Figure 3e. So I think a\nmodel 2C and a more detailed look at the models in Supplementary Figure 11 can help to identify if\nthe ridge matters for Detroit or not. Based on a simple estimate from Figure 4 (using the plate\nvelocity above the plume and ignoring any possible plume drift southwards, which would increase\ndistances), Meiji at 85 Ma might be about 450 km away (5 Myr plate drift with 3 cm/yr and 5 Myr with\n6cm/yr) from the ridge at the time of eruption, but Detroit at 79 Ma is at least 890 km away (another\ndepending on exact locations, drift rates, etc. Only a detailed comparison of models 2B, 2C and the\nones in Supplementary Figure 11 can tell that (which might be beyond the possibilities here, but\nwould nonetheless be interesting and important).\n- Line 153: I think you only need to refer to Supplementary Figure 11, not 12\n- Line 218: “eruption site”\n- Line 350-356: I would say the rapid increase in paleolatitude for Reunion (simply due to plate drag\nof the increase in plate velocity of the Indian plate) is between 70-60 Ma, not 60-50 Ma. I agree with\nthe rest of the statement about Reunion, but I think it is the “fading ridge effect” that is responsible\nfor the paleolatitude decrease between after 55 Ma despite a slowly increasing plate velocity.\nAfter all, the distance between the ridge and the plume is increasing, meaning that the plume tilt will\nbe reduced to what is caused by the plate drag. So maybe add a “fading” to the sentence, if you agree\nwith me.\n- Line 377: The cited paper of Bredow and Steinberger is also related, but not the one on Reunion\nthat I meant. I was thinking about the study of Bredow et al. (2017),\nhttps://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017GC006875\n- Supplementary Figure 7: Thanks for adding the crosses, that helps. However, for future work,\nmaybe you should consider using color palettes that are better suitable for colorblind people than\nthe rainbow palette. There are by now a lot of perceptually uniform color palettes available in all\nformats.\n- Supplementary Figure 8: I think you forgot yo update the Figure in the Supplementary. In the\nresponse to my previous comment, the blue and red rectangles are shown, but not in the actual\nsupplementary figure.\n- Supplementary Figure 11: I think there is a typo in the caption, the reference model is 2B, not 1B,\nright?\n- Figures 3 and Supp. Figure 12: I prefer the new figures compared to the old ones, especially the\ninlay showing the plume tilt is very helpful. Would it be possible though to make plate boundaries a\nlittle bit more obvious?\nResponses to comments on Nature Communications manuscript\nWe appreciate the editor for handling this work, and the constructive comments from\nthe reviewers which greatly enhanced the quality of this work. Below, we have listed\nthe original comments in black (italic) and our response in blue. We have carefully\nconsidered all the reviewers’ questions and suggestions. We hope that we have properly\naddressed all the concerns. Line numbers refer to the updated manuscript.\nReviewer #1 :\nIn this version of the manuscript, the authors made significant revision of their\noriginal manuscript in response to the comments raised by the reviewers (including\nme).\nI feel that most of comments and/or suggestions by reviewers had been adequately\nconsidered in the revised manuscript. In particular, I very much appreciate the authors’\naddition of detailed descriptions on their numerical models, although I do not like some\nof the employed assumptions or formulations.\nFollowings are several (minor) comments and suggestions.\nQ1. I do not like the paragraph starting at line 109 of the revised manuscript.\nThe statements in this paragraph read (at least to me) that the emphasis lies in the\ncomparison between Model 1 and Model 2 rather than that between the tracks #A and\n#B. In other words, the discussion made here would imply that the “plume migration”\nis more important than the “plume-lithosphere interaction”, which is inconsistent with\nthe title of this section (and that of this manuscript).\nI therefore suggest that the authors could restore the relevant statements in the original\nversion, where the comparison had been made simply between Models 1A and 1B\nwithout the effects of “plume migration”.\nR1: Thanks for the suggestions. We agree with your comments, and we’ve restored the\nrelevant statements in the original version as you suggested, please see lines 109 – 121\nin the new revised version.\nQ2. The legend of Figure 3 needs revisions.\nIn the revised figure the authors had added “the temperature contour (black contour)\nand melt area (outlined by red line) of the plume” “on the top right corner of each\nsnapshot”, which I like very much. However, the authors should make clear ON\nWHICH PLANE the contour maps are drawn.\nR2: Thanks for the reminder. We’ve modified the legend as you suggested, and also\nadded the position of the profile of each snapshot in Figure 3, please see lines 190, 192,\n199, 200.\nFigure 3. Snapshots of the simulated Hawaiian plume evolution (Model 2B). The 3D\ncontour representing the +100°C temperature anomaly is shown in red. The 3D contour\nof the 1% melt fraction is shown in white. The core-mantle boundary is shown in light\nblue. Plate boundaries are shown as green lines. Plate velocities are shown as black\narrow. The length of the arrows qualitatively shows the magnitude of the plate velocity.\nThe background shows the log-normalized (relative to 1021 Pa s) mantle viscosity\nprofile. The snapshots of before (a-b), during (c), and after (d-f) the ridge arrival are\nshown. Both the ridges and the Hawaiian plume produce melt. On the top right corner\nof each snapshot shows the temperature contour (black contour) and melt area (outlined\nby the red line) of the plume, the profile of the temperature contour in each snapshot is\ndenoted by black dotted line on the top of the plume.\nQ3. Misspellings\n(a) Lines 71–72; “…showed that suggested a …”\nR3a: Thanks for the reminder. We’ve modified this sentence, see line 71.\n(b) Line 146; “Th_is because …”\nR3b: Thanks for the reminder. We’ve modified this paragraph in line 149-157.\nReviewer #2:\nThe revised version of this manuscript is considerably improved and the authors\nsatisfactorily addressed the comments. The paper needs a final revision of the language.\nR: Thanks for the suggestions. We’ve carefully and thoroughly revised the language of\nthis paper. Please see the red lines in the new revised version.\nI have three minor comments:\nQ1: Throughout the text around line 190 the authors discuss paleolatitudes \"drop\"\nor \"increase\". I feel that they should refer to paleolatitude \"(measured or modelled)\nvalues\".\nR1: Thanks for the suggestions. We’ve modified this section and the related parts,\nplease see lines 182, 210, 211, 212, 214, 224, 229, 286, 289, 298.\nQ2: Line 279 what means a “proper” plate reconstruction model? Do you mean\nalternatives are “improper”? Please clarify\nR2: Thanks for your questions. In this paper, we’ve tested the effects of different\nreconstruction models on the evolution of the plume, as shown in Figure 4 and\nSupplementary Figure 4. Altering the reconstruction model would not lead to\nsignificant difference of the model results, and all three plate reconstruction models can\nresult in reasonable model predictions. As our reference model is based on Muller et al.\n(2016), we then tested other models using it too, but this does not mean that the other\ntwo are improper. Therefore, “proper” may not be a precise word here, to avoid\nmisleading, we’ve deleted this word, please see line 298.\nQ3: lines 208 maybe say “observed and calculated” positions and ages\nR3: Thanks for the reminder. We did not find the state of “positions and ages” in line\n208, while it appears in line 280, and we’ve modified this sentence, please see line 298\nin the new revised version.\nReviewer #3:\nI appreciate how the authors responded to my previous comments, and I am mostly\nsatisfied with the changes and the additional models. There are only 2 (related) major\nand a few minor comments left to address from my side. Line numbers refer to the\nupdated manuscript (with only the added text highlighted in red). The major comments\nand the first minor comment still refer to how long the ridge affects the hotspot track,\nwhich I think could be shown and discussed better. The remaining comments are very\nminor.\nMajor comments:\nQ1. Maybe it is just me, but I am still a bit confused with the timings, so maybe you can\nhelp me get this right. The ridge crosses the plume at around 105 Ma in Model 1 or 95\nMa in model 2 (the difference arising from the fact that the plume in model 2 moves\nsouthwards). In the test without ridge based on model 1 you ran (model 1C), the hotspot\ntrack starts to differ for seamounts older than ~70 Ma (Supplementary Figure 10), but\nat that time the ridge seems to be far away (Supplementary Figure 12) and I would not\nexpect it to have any influence. Surprisingly, Supplementary Figure 10 also shows\nbasically no track for model 1C between 75 Ma and 95 Ma, thus leaving a gap of 20\nMyr in which the plume did not move relative to the plate(?). Why is that? How did you\nprescribe the surface velocity boundary condition for model 1C? I would have tried to\nprescribe the same time-dependent plate velocities above the plume itself as in 1B, but\nwithout having a ridge that separates the two plates (maybe you did that?). I know that\nmesses up the plate models (and it is tricky to avoid that this has unwanted side effects\non the general convection pattern, which in turn can affect the plume and the hotspot\ntrack), but the current model 1C may give a false impression on the duration of the\nridge effect.\nR1: Thanks for the questions. As you understand, in Model 1C, the hotspot track starts\nto differ for seamounts older than ~70 Ma (Figure S1 below). Although the ridge seems\nto be far away as shown in Supplementary Figure 12 in Model 1, according to our recent\nmodels, we are unable to confirm the exact distance that the ridge effect matters, as the\nevolution of hotspot chain is influenced by the combined effect of multiple factors (such\nas mantle convection, plate drag, ridge effect, etc.). What the recent model results can\ntell us about the ridge effect is that as the ridge leaves the plume, its influence fades.\nThus, to quantify the precise distance of how far the ridge influences the plume, more\nmodels (or even different configures of the model) are needed, which are beyond the\nscope of this paper. In Model 1C, what we want to emphasize is that the model’s only\ndifference from 1B is that it does not incorporate the ridge, thus during the entire\nevolution of the model (not only after 70 Ma), the ridge effect is not present. Therefore,\nas shown in Figure S1 below, by comparing Model 1C with 1B, we can infer that\nintroducing a ridge into the model or not would significantly influence the modeled\nhotspot track at least before ~ 70 Ma.\nFigure S1. Simulated hotspot tracks of models with (1A and 1B) and without ridge\n(1C) effects.\nThe reason why Supplementary Figure 10 (Figure S1 above) shows no track for\nmodel 1C between 75 Ma and 95 Ma is that: In Model 1C, at ~ 90 -100 Ma, the ridge\nmoves quite close to the plume, which generates much melt both from the ridge and the\nplume (Figure S2a). The abundant melt of ~ 90 -100 Ma then mixes with the melt\ngenerates after 90 Ma and makes up a large part of the mixture (Figure S2b, 2c). As the\nway we calculate the seamounts age (tracks in Figure S1 above) is based on a method\nof weighted average, therefore, when the melt generates after 90 Ma mixes with the\nolder one (melt of ~ 90-100 Ma), as it makes up only little part of the mixed melt, the\nseamounts build on it may also be defined as 90-100 Ma. After that, the ridge\ncontinuous leaves the plume, the melt generation thus turns to a normal level after ~ 70\nMa (Figure S2d), which is similar to the one in Model 1B, thus allowing for a clearer\nhotspot track.\nFigure S2. Snapshots of Model 1C at (a) 100 Ma, (b) 90 Ma, (c) 80Ma, (d) 70 Ma.\nThe green shades are the predicted erupted melt sites. The black solid lines are plate\nboundaries, the red point with black outline denotes the position of the plume.\nRegarding our implementation of the boundary conditions, to rule out the ridge\neffect, we assume that there is no initial upward flow beneath the Izanagi ridge, but the\nposition of ridge is consistent with that in Model 1B. Specifically, we prescribe a 0\ncm/yr spreading velocity of the ridge in model 1C, under the condition of which the\nIzanagi plate moves in the same velocity and direction as the Pacific plate (less than the\nIzanagi plate’s movement in 1B). As the predicted track in Model 1B deviates from\nobservation, and considering your suggestions in Q2 below, we replaced Model 1C by\n2C and modified the Supplementary Figure 10 to the results of Model 2. Please see\nlines 147 – 157.\nQ2. Related to that: it would have been more educating to do the model without ridge\n(model C) for model 2 instead of model 1 to get a better assessment on the influence of\nthe ridge on Detroit and Meiji. Based on the tests you ran (both Supplementary Figure\n10 and 11), I would not expect that the ridge has any influence on seamounts younger\nthan ~75-80 Ma, and the effect on Detroit can be considered debatable if the effect of\nthe ridge disappears by 82 Ma. You say it yourself that the tracks in Supplementary\nFigure 11 with shifted ridges are basically identical for anything younger than 75 Ma.\nHowever, not all the changes in the tracks have an obvious explanation, since both the\nplume-ridge interaction timing and the plate velocities above the plume changed between\nthe cases. In fact, the yellow curve (ridge 10° or ~1000 km further south) is not that far off from reality\neither, while red (ridge 5° or ~500 km further south) is totally wrong. Blue and purple are similar, but\nboth tilted too early. So how far away does the ridge actually influence the seamounts, and how\nmuch is simply attributed to the plate drag which differs between these models as well?\nThat is an interesting question, and I think only a model 2C can actually answer that.\nIt would be great and improve the impact of the study to know this better, and make the\npaper consistent regarding the timing throughout the text. I think Supplementary Figure\n11 (which I really appreciate) is actually more educating than model 1C, but a model 2C\nwould be very helpful or even necessary to clearly show the importance of the ridge for\nyour best-fitting model. And I am aware that this might be difficult within the limits of Nature,\nbut an extended discussion of Supplementary Figure 11 and how the tracks differ\nbecause of the timing of plume-ridge interaction could be interesting.\nR2: Thanks for the questions and suggestions. First, we apologize for the misleading\nlegend of Supplementary Figure 11, the models with different ridge positions are based\non Model 2B. We’ve modified the legend accordingly, see lines 93 - 94 in the\nSupplementary Material. Comparing Model 1C with 1B, it seems the ridge effect has\nlittle influence on seamounts younger than ~ 70 Ma (Figure S1, see R1 to Q1 above).\nHowever, these two models did not consider the influence of plume motion, and the\npredicted tracks deviate from the observation a lot. Thus, we agree that Model 2C based\non Model 2B is more proper here to help illustrate the ridge effect and we’ve run 2C\n(see the Figure below, also see Supplementary Figure 10). As we can see from the\nFigure 3c (Model 2B), the ridge is almost on top of the plume at ~ 95 Ma, after which\nthe plume is beneath the Pacific plate. We can estimate the average velocity of the\nPacific plate between 95 - 80 Ma as ~ 5.5 cm/yr based on the plate reconstruction, the\ndistance between the plume and the ridge during this 15 Ma thus can be calculated as\n~ 825 km (< 1000 km), which is not so far away between the plume and the ridge\naccording to the previous study. It indicates that before 80 Ma, ridge effect matters and\nit may influence the development of seamount Detroit. Besides, when we compare\nModel 2B (with ridge) and 2C (without ridge), the tracks differ from each other prior\nto the formation of seamount Suiko (61 Ma), so we suppose that the ridge effect matters\nto the formation of seamount Detroit.\nSupplementary Figure 10. Simulated hotspot tracks of models with (2A and 2B)\nand without ridge (2C) effects.\nIn Supplementary Figure 11, the models with different ridge positions refer to\nModel 2B. Our previous statement that “the tracks in Supplementary Figure 11 with\nshifted ridges are basically identical for anything younger than 75 Ma” is not precise.\nActually, according to Supplementary Figure 11, the tracks with different initial ridge\npositions differ from each other prior to seamount Ojin (55 Ma). Between 75 - 55 Ma,\nthe tracks mainly deviate from the reference model (2B) in an east-west direction.\nBetween ~ 75 - 65 Ma, all the tracks deviate from Model 2B in an eastward direction.\nThis may come from the relative location of the plate boundary between the Pacific and\nthe Kula plate: (1) during ~ 75 - 65 Ma, the plate boundary is quite close to the plume\n(Figure 3e), the different plate motion of the adjacent plates (both in velocity direction\nand magnitude) could result in a pressure difference underneath, which may drive a\nmantle flow and attract the plume. (2) After that, the plate boundary leaves the plume,\nand its influence fades (Figure 3f).\nIn comparison, before ~ 75 Ma, the deviation of tracks has its own characters\n(Supplementary Figure 11): (1) Though the track in model a (-10˚, yellow) is similar to\nModel 2B before ~75 Ma, the age distribution differs a lot. (2) In model b (-5˚, red),\nbefore ~ 75 Ma, the Pacific plate changed its motion from NNW to nearly N; While\nduring 75-60 Ma, the plate movement changed again to NW (Figures S3a-c). Thus, the\ntrack in model b deviates northwestward from 2B (Supplementary Figure 11). (3) When\nthe ridge is in the north (model c, +5˚, purple; d, +10˚, blue) compared with it in Model\n2B, the predicted track is much more westward than it in Model 2B, which may also\nresult from the change of the Pacific plate motion from NNW to nearly N, then back to\nNNW (Figures S3d-f). (4) In addition, as the ridge in model a (-10˚) or b (-5˚) is much\nmore southern, which delays the time of the encounter between the ridge and the plume,\nso the track on the Pacific plate starts much later than it does in Model 2B. Vice versa,\nthe track in model c (+10˚) or d (+5˚) begins at an earlier time. As you suggested, we’ve\nadded some detailed discussions on the results of these models with various ridge\npositions, please see lines 157 – 177.\nFigure S3. Plate reconstruction of model b (ridge deviates from 2B for - 5˚) and\nmodel d (ridge deviates from 2B for + 10˚).\nMinor comments:\nQ3. Line 143-146: As mentioned above, I think it may have been better to use model 2\nas a reference, since model 1 does not reproduce the track well even with the ridge.\nFor model 2, the deviation will likely be at a different location than Nintoku (which\nmodel 1 predicts to be much older than it actually is). If you leave model 1C, I would\nsuggest to rephrase the sentence a bit to make clear that the deviation of the track is\nnot starting at the time of Nintoku. Later (in Line 198) you actually state that the ridge\nprobably does not play a major role for the track younger than 82 Ma, which is around\nor shortly after Detroit. So the ridge is mostly relevant for Meiji and partly for Detroit,\nbut not the rest. In fact, 82 Ma is even before Detroit, so maybe the end of the ridge\neffect is later (maybe ~78 Ma?), although the distance between ridge and plume seems\nlarge at 78 Ma in Figure 3e. So I think a model2C and a more detailed look at the\nmodels in Supplementary Figure 11 can help to identify if the ridge matters for Detroit\nor not. Based on a simple estimate from Figure 4 (using the plate velocity above the\nplume and ignoring any possible plume drift southwards, which would increase\ndistances), Meiji at 85Ma might be about 450 km away (5 Myr plate drift with 3 cm/yr\nand 5 Myr with 6cm/yr) from the ridge at the time of eruption, but Detroit at 79 Ma is\nat least 890 km away (another 2 Myr with 6cm/yr and 4Myr with 8cm/yr). So Detroit\nmay or may not be influenced by the ridge, depending on exact locations, drift rates,\netc. Only a detailed comparison of models 2B, 2C and the ones in Supplementary\nFigure 11 can tell that (which might be beyond the possibilities here, but would\nnonetheless be interesting and important).\nR3: Thanks for the questions. We agree that using Model 2 as a reference model is\nmore proper, and we’ve run Model 2C (see R1 to Q1 above, Supplementary Figure 10,\nsee lines 147 - 157). As is shown in the new Supplementary Figure 10, for model 2B\nand 2C, the tracks’ deviation is at Suiko (61 Ma). We do state that the ridge probably\ndoes not play a major role for the track younger than 82 Ma (in line 198), however, this\ninference originates from Model 1B without considering the movement of the plume\nsource, the simulated track of which deviates from the observation. Besides, what we\nreally want to emphasize is that the maximum amount of paleolatitude offset caused by\nthe combined effect of direct ridge attraction and plate drag is 5.8˚. As we estimate in\nR2, the ridge effect matters for the formation of Detroit. How the ridge influences the\nevolution of hotspot chain is also discussed in R2 to Q2 above. We’ve modified the\nrelated paragraph in lines 147 - 177.\nQ4. Line 153: I think you only need to refer to Supplementary Figure 11, not 12\nR4: Thanks for the suggestion. We’ve modified this sentence, see lines 159-160.\nQ5. Line 218: “eruption site”\nR5: Thanks for pointing this out. We’ve modified “erupt site” to “eruption site” as you\nsuggested, see line 238.\nQ6. Line 350-356: I would say the rapid increase in paleolatitude for Reunion (simply\ndue to plate drag of the increase in plate velocity of the Indian plate) is between 70-60\nMa, not 60-50 Ma. I agree with the rest of the statement about Reunion, but I think it is\nthe “fading ridge effect” that is responsible for the paleolatitude decrease between\nafter 55 Ma despite a slowly increasing plate velocity. After all, the distance between\nthe ridge and the plume is increasing, meaning that the plume tilt will be reduced to\nwhat is caused by the plate drag. So maybe add a “fading” to the sentence, if you agree\nwith me.\nR6: Thanks for raising this point. We agree that the rapid increase in paleolatitude for\nReunion is between 70 – 60 Ma, and we’ve modified this sentence, see line 370. After\nthe ridge meets the plume, it moves away and the ridge effect decreases, so we agree\nthat it is the “fading ridge effect” that is responsible for the paleolatitude decrease after\nsentence as you suggested, see line 375.\nQ7. Line 377: The cited paper of Bredow and Steinberger is also related, but not the\none on Reunion that I meant. I was thinking about the study of Bredow et al. (2017),\nhttps://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2017GC006875\nR7: Thanks for the suggestion. We’ve added the paper of Bredow et al. (2017) you\nrecommended to the reference, see lines 373, 493 – 495.\nQ8. Supplementary Figure 7: Thanks for adding the crosses, that helps. However, for\nfuture work, maybe you should consider using color palettes that are better suitable for\ncolorblind people than the rainbow palette. There are by now a lot of perceptually\nuniform color palettes available in all formats.\nR8: Thanks for the suggestions. We will consider using much uniform color palettes\nthat are suitable for colorblind people in our future work. We’ve modified\nSupplementary Figure 7d into a suitable case for colorblind people. See Supplementary\nMaterial, line 56.\nSupplementary Figure 7. Past plate configurations relevant to observed\npaleolatitude shifts in three other hotspots. a) New England hotspot. b) Reunion\nhotspot. c) Tristan hotspot. The observed paleolatitudes of these hotspot tracks are\nshown in the inset box, with data from GMHRF-3. The current location of each hotspot\nis shown as a red dot. Blue lines are plate boundaries. Black lines represent coastlines.\nThe surface traces of each hot spot are shown as rainbow-colored swaths, color-coded\naccording to their age. Black crosses are shown at 10 Ma increments.\nQ9. Supplementary Figure 8: I think you forgot to update the Figure in the\nSupplementary. In the response to my previous comment, the blue and red rectangles\nare shown, but not in the actual supplementary figure.\nR9: Thanks for the reminder. We’ve updated the Supplementary Figure 8. See line 65\nin the Supplementary Material.\nQ10. Supplementary Figure 11: I think there is a typo in the caption, the reference\nmodel is 2B, not 1B, right?\nR10: Thanks for the reminder. The reference model is Model 2B. We’ve modified this\ncaption, see lines 87-88 in the Supplementary Material.\nQ11. Figures 3 and Supp. Figure 12: I prefer the new figures compared to the old ones,\nespecially the inlay showing the plume tilt is very helpful. Would it be possible though\nto make plate boundaries a little bit more obvious?\nR11: Thanks for your suggestions. We’ve modified the plate boundaries, see Figure 3\nin the main text (line 190) and Supplementary Figure 12 in the Supplementary Material\n(line 96).\nREVIEWERS' COMMENTS\nReviewer #3 (Remarks to the Author):\nI am satisfied the the changes the authors made, and the explanations given in the\nResponse to Reviewers. I have only two very minor suggestions that can but don't have\nto be included:\n1) Line 150: I would say that the biggest deviation between tracks 2B and 2C starts\naround 70 Ma (or maybe 68 Ma), but this is a personal interpretation. I do see some\nsmaller deviations already at ~65 Ma. So if you agree, maybe just say \"... ~70-65 Ma\",\nbot here and in Line 156? I leave this up to you to decide which you think is more\nappropriate.\n2) Line 167: Maybe rephrase this sentence a bit to something like \".... that all tracks are more\n(purple track) or less (yellow track) shifted eastwards compared to the\nobserved seamounts during ~75-55 Ma\". At first when I read the sentence, I was looking\nfor an east-west direction of the plume track, not the general shift that can be seen in\nFigure S11.\nResponses to comments on Nature Communications manuscript\nWe appreciate the editor for handling this work, and the constructive comments from\nthe reviewers which greatly enhanced the quality of this work. Below, we have listed\nthe original comments in black (italic) and our response in blue. We hope that we have\nproperly addressed all the concerns. Line numbers refer to the updated manuscript.\nReviewer #3:\nI am satisfied the changes the authors made, and the explanations given in the\nResponse to Reviewers. I have only two very minor suggestions that can but don't have\nto be included:\nMinor comments:\nQ1. Line 150: I would say that the biggest deviation between tracks 2B and 2C starts\naround 70 Ma (or maybe 68 Ma), but this is a personal interpretation. I do see some\nsmaller deviations already at ~65 Ma. So if you agree, maybe just say \"... ~70-65 Ma\",\nboth here and in Line 156? I leave this up to you to decide which you think is more\nappropriate.\nR1: Thanks for the suggestions. We agree with that the deviation between 2B and 2C\nbegins at ~70-65Ma, we’ve modified the illustration, please see lines 146, 152.\nQ2. Line 167: Maybe rephrase this sentence a bit to something like \".... that all tracks\nare more (purple track) or less (yellow track) shifted eastwards compared to the\nobserved seamounts during ~75-55 Ma\". At first when I read the sentence, I was looking\nfor an east-west direction of the plume track, not the general shift that can be seen in\nFigure S11.\nR2: Thanks for the suggestions. We’ve modified this sentence, please see lines 163-\n164."}]

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