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Evolving topography in glaciated regions not only complicates interpretations of past climates but also exerts a fundamental influence on past ice-sheet dynamics and creates the framework for present ice-sheet behaviour1,2,3,4,5. Today, the Antarctic Peninsula (AP) is rapidly warming and contributing to sea-level rise as its glaciers retreat from grounding lines located in deeply incised fjords6. These fjords dissect a gently undulating topographic plateau that constitutes the spine of the AP (Fig. 1c)7. We can leverage this topography to create an estimate of the pre-glacial topography, facilitating more-realistic assessment of the climatic conditions required to initiate ice-sheet growth on the AP.

Fig. 1: Topographic change along the AP.
figure 1

a, The topography of the AP today shows a low-relief, high-elevation spine dissected by glacial valleys. The elevation of the spine is slightly higher in the north than in the south. The greatest ridge-to-valley relief is approximately 3,000 m where the spine is high, and the valleys are deeply incised. b, The pre-glacial, fluvial landscape as predicted from our inversion. Elevations along the length of the AP are lower, and the greatest relief is approximately 1,000 m. The over-deepened glacial valleys have been filled with graded river profiles following Flint’s Law17. The position of the base level is held constant; however, there is sufficient flexibility in the model to account for errors introduced by changes in the position of the base level. c, Low-relief, high-elevation surface of the AP looking towards the northwest. The location and direction of the view are indicated in panel a by the blue star and arrow. Panorama in c made from trimetrogon aerial photography collected by the US Navy on 27 December 1968, flightline 2152, frames 364R to 368R.

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Alpine glaciation was initiated on the AP by 37–34 Ma (ref. 2), and the extent of glaciation has been closely linked to Cenozoic climate change. The start of AP glaciation occurred when global temperatures were 4 °C higher than today8,9,10 and might have been a response to the development of the Antarctic Circumpolar Current during the tectonic opening of the Drake Passage11,12 or a decline in \(p_{{\mathrm{CO}}_2}\) (ref. 8). Progressive cooling potentially caused expansion of ice and a permanent, polythermal ice sheet was established by 9 million years ago (Ma) (refs. 2,9).

The early Antarctic ice sheets, in general, were thinner and more dynamic than those of today, and they fluctuated on Milankovitch frequencies13. It has been assumed that >2 km high topography of the AP may have acted as a focus for ice-sheet nucleation in response to orographically forced precipitation in climates that were warmer and wetter than at present14. Antarctic topography, however, has been reconstructed only at a continental scale15,16 not at the detail or physical basis required for catchment-scale glacial modelling across the AP.

In this Article, we exploit remnants of the low-relief fluvial networks of the northern part of the AP to reconstruct a fluvial landscape that obeys geomorphic scaling laws (Methods)17,18. This is in contrast to previous approaches for topographic reconstruction, which generate smooth topography by interpolating a surface through topographic highs and ultimately lack the clear nucleation sites and topographic hypsometry necessary for mountain glaciation15,16,19. As a result, our topographic reconstruction provides a physically plausible topographic boundary condition. The requirement that the topography is realistic also provides independent constraints on tectonic uplift and landscape evolution. Ice-sheet simulations on a realistic palaeotopography illustrate quantitatively how topography affects glacial extent even with invariant climatic conditions.

Topographic data and fluvial reconstruction

The topographic data we used for this analysis are from the 100-m-resolution digital elevation model (DEM) of ref. 20, which captures the current topography of the AP under the ice. This model has been constructed only where there is ice, and we use the BEDMAP 2 bedrock model21 for areas not covered by the 100 m DEM (Fig. 1a). The AP includes low-slope topographic surfaces at high elevations along its length. This surface appears to be dissected by deep glacial valleys and glacial cirques (Fig. 1c). The alternative explanation, that low-relief surfaces formed in response to glacial bevelling of previous high-relief topography, is negated by the available thermochronometry, which indicates relatively recent (<15 Ma) development of the deep glacial valleys and slow erosion rates across the low-slope surfaces22. Ridge-to-sea-level relief along the length of the peninsula is relatively uniform at approximately 2 km (Fig. 1a). In general, the western side of the AP is steeper with a greater degree of glacial dissection than the eastern side. Before we reconstructed the topography, we first calculated flexural rebound associated with removal of the ice using an effective elastic thickness of 35 km, Poisson’s ratio of 0.25, a crustal density of 2,700 kg m–3, mantle density of 3,200 kg m–3, ice density of 920 kg m–3 and a Young’s modulus of 7.0 × 1010 N m–2. This rebounded topography provided the data points for our inverse scheme, outlined in the following.

We extracted the drainage network using the Terraflow function in GRASS (Geographic Resources Analysis Support System)23, where all depressions are filled to account for overdeepenings and errors in the DEM. However, this is simply to calculate the flow routing: the topographic reconstructions interpolated over the overdeepenings with sloping river profiles. Once the drainage network was obtained, we calculated values of normalized response time, or χ, for all points in the landscape with an upstream drainage area greater than 0.5 km2; χ is the time that information takes to propagate upstream from the base level normalized to a uniform erodibility24,25. If knickpoints arrive at the drainage divide at different times, erosion rates will differ and the divide will migrate. For our purposes, we used the analytical stream power model, which relates χ to elevation. To down-sample the data, once χ had been calculated using the high-resolution DEM, we randomly selected 15% of the dataset. Reducing the size of the dataset is important for the following inversion. This random process ensures that high χ values are probably found close to low χ values, improving resolution, and prevents selection biases.

Our inversion approach is based on the steady-state stream power model18,26. This states that the elevation of a node within the low-relief surface is equal to the integral of normalized rock uplift rate, u*, along the profile of the river from the base level to the χ value (Methods),

$$z\left(x\right)=\mathop{\int}\limits_{0}^{{\rm{\chi }}\left({\rm{x}}\right)}{\left(\frac{u\left({\chi }^{{\prime} }\right)}{K{A}_{0}^{m}}\right)}^{\frac{1}{n}}{\rm{d}}{{\rm{\chi }}}^{{\prime} }$$
(1)

and \(u^{*}=(u/{KA_{0}^{m}})^{1/n}\) (ref. 24), where u is the rock uplift rate (with respect to base level) and K, A0, n and m are constants within the stream power incision model (Methods). In this way, u* represents a scaled rock uplift rate. If the rock uplift rate increases, knickpoints will propagate upstream, but the landscape above the knickpoints will preserve the previous uplift rate conditions. Similarly, if glacial erosion has been minimal across the low-relief landscape of the AP but intense within glacial valleys, the low-relief landscape can be used to infer the previous normalized rock uplift conditions. These conditions can then be extrapolated across the incised, rebounded topography and used to reconstruct a fluvial landscape. To do this, we state that the elevation is a combination of steady-state palaeotopography plus an additional component of surface uplift (measured with respect to base level). This surface uplift (s.u.) varies spatially but, based on the topography, must be a long-wavelength function. We discretize space into pixels of constant u* and s.u. values. The resulting discrete equations of elevation as a function of along-channel normalized rock uplift and local s.u. are arranged in matrix–vector form and solved with smoothness constraints27 (Methods). This linear inverse method is preferable to approaches to build fluvial landscapes that require known rock uplift functions28 or nonlinear methods3 because it solves for unknown rock uplift and surface uplift functions.

It is important to note that low-relief, high-elevation topography can be developed in fluvial landscapes through changes in rock uplift rate or drainage capture29. In turn, a low-relief, high-elevation landscape with deeply incised fluvial canyons may have existed before glaciation. This is unlikely because detrital thermochronometry reveals that valley incision occurred at about 15 Ma, after the initiation of glaciation in the region22, and generally coincided with the arrival times of the spreading ridge at different latitudes. Therefore, the palaeotopography we resolve probably existed before 15 Ma and was later uplifted and dissected.

We selected an inversion result that represents a compromise between fit to the data and model smoothness to reconstruct the topography (Fig. 2). The model shows short-wavelength variations in u* that lead to the steeper western side of the AP and long-wavelength variations in s.u. that are consistent with the relatively uniform elevation of the low-relief landscape. The variability in u* probably reflects local variations in lithology, which are unknown below the ice, and potentially geomorphic noise (artefacts in the DEM and flow-routing algorithms, drainage divide migration or modifications of the low-relief topography by glacial erosion). The long-wavelength uplift s.u. contains two components: (1) the primary tectonic uplift; (2) the secondary isostatic response to glacial incision. Therefore, we subtracted the rebounded topography from the predicted and uplifted palaeotopography to calculate the change in topographic volume. Note this topographic volume is not equivalent to total sediment production of the AP (for a full discussion, see the Supplementary Information Section 3). The topographic volume was converted to a mass, which was used to calculate the flexural response to this mass change using an effective elastic thickness of 35 km and a Poisson’s ratio of 0.25. Removing this secondary isostatic component of s.u., which can reach values of 500 m, provides the primary uplift. The overall pattern of primary uplift is approximately radial, displaying key similarities to the estimated dynamic topography inferred from a global tectonic model (Fig. 3c)30, with maximum values of 1.4 km close to 65o S that decay to the north (Fig. 3b). We note that dynamic topography is difficult to constrain and alternative models exist; however, the comparison is encouraging. Therefore, the high elevations of the AP can be explained as a combination of isostatic response to erosion and dynamic topography. Here dynamic topography may be the result of opening of a slab window behind subducting oceanic ridge lithosphere31. This would also lead to a general younging of surface uplift towards the north32,33.

Fig. 2: The elevations of the remnant surfaces are a function of parameters controlling the relief on the fluvial pre-glacial landscape and the more recent surface uplift.
figure 2

These parameters can be obtained through linear inversion of the stream power model using the remnant elevations as data points (black crosses). a, The normalized rock uplift rate (dz/dχ, or u*) describes the steepness of a river accounting for changes in upstream drainage area. This information is preserved by local variations in elevation and the branching river network. b, The surface uplift describes the additional amount of elevation difference between the modern topography and the elevations obtained by integrating slopes along the river profiles. Our inversion minimizes elevation misfit and the spatial smoothness of the u* (\(\alpha {W}_{u}\,{u}^{* }\,\)) and s.u. (\(\lambda {W}_{{{\mathrm{s.u.}}}}{{\mathrm{s.u.}}}\)) parameter maps. The contribution of the smoothness constraints to the total misfit is weighted by α = 102 and λ = 101. See Methods for information on the parameters.

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Fig. 3: Surface uplift of the spine of the Antarctic Peninsula is a combination of primary tectonic uplift and isostatic response.
figure 3

a, The isostatic response is calculated by subtracting the modern ice-free, rebounded topography from the uplifted pre-glacial topography to calculate the amount of incision. This incision is a negative load, and the deflection of an elastic plate due to this load is calculated assuming an elastic plate of 35 km. b, The surface uplift, extracted from the spine of the AP, minus the valley incision rebound provides the primary tectonic uplift. Highest values are approximately 1,400 m around Anvers Island. Tectonic uplift decreases towards the north and south and is lowest close to Adelaide Island at around 700 m. An area of high uplift is observed on the east side of the AP. This is called Jason Peninsula, and we expect that this area of flat topography is actually uplifted continental shelf and does not represent part of a palaeo-surface. c, Independently constrained dynamic topography across the AP shows a very similar pattern to the tectonic uplift, with highest values close to Anvers Island, decreasing towards the north and south. The similarity in the magnitude and pattern of our inferred tectonic uplift and the dynamic topography indicates that dynamic topography is responsible for the uplift of the AP.

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Ice-sheet reconstructions

To reveal the sensitivity of the ice sheets across the Antarctic Peninsula, we used a simplified ice-sheet model34 based on the shallow-ice approximation (SIA). This simplified model is sufficient to illustrate how changes in topography strongly influence ice-sheet extents. In this model, the accumulation rate is set to 2 m yr–1 (ref. 35), the equilibrium line altitude (ELA) is set to 500 m and the mass-balance gradient is set to 0.04 m–1. This is higher than the estimated ELA (up to 400 m (ref. 36)) because with a lower ELA, our glaciers extend out into the surrounding ocean and the SIA is not suited for buoyant glaciers. Other parameters used in the ice model are given in ref. 34. These parameters result in an ice sheet that is roughly consistent with the modern ice-sheet extents using the modern topography (Fig. 4a). If we use the same climatic parameters for the pre-glacial topography, we see that the ice sheet is thicker but the extent of the ice sheet is much smaller (Fig. 4b). In fact, the volume of ice north of 70° S that is predicted on the pre-glacial topography is 4.4 × 104 km3, but on the modern topography it is 4.0 × 104 km3. However, considering northern and southern regions separately, divided at 66° S, the changes in ice volume are important and differ by region: the volume of ice increases in the north from 1.3 × 104 km3 in the pre-glacial landscape to 1.8 × 104 km3 in the modern topography but decreases in the south from 3.1 × 104 km3 to 2.2 × 104 km3. The uplift and dissection of the AP has enhanced ice-sheet growth in the north while inhibiting it in the south.

Fig. 4: Ice-sheet simulations on the two topographies highlights topographic control on glaciation.
figure 4

a, A simple SIA model reproduces the general pattern of modern glaciation on the modern topography. b, The same model parameters produce a very different pattern of glaciation on the pre-glacial topography. Importantly, it appears that the pre-glacial landscape can support more ice south of approximately 66° S but less ice to the north of this location, for a simplified modern climate. This highlights how uplift and erosion control the amount of ice topography can support. The SHALDRIL site is just to the northeast of our study area.

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Our findings have some important implications for the onset and advance of glaciation on the AP as interpreted from the SHALDRIL cores10. The onset of mountain glaciation on the AP is inferred as early as 35.9 Ma, but the provenance of glacial dropstones is proposed to be either from the James Ross Island, proximal to the SHALDRIL sites, or from further south on the AP10. Our findings provide evidence that the latter is more likely. Furthermore, the timeline for advance of glaciation on the AP, although admittedly limited by the depositional ages of sampled sedimentary core, matches our timeline for relief production on the AP and the inferred advance of ice sheets to their present extent. An increase from minor glacial influence in offshore sediment north of the AP at ~24 Ma to the advance of an ice sheet in the northern part of the AP by ~12 Ma (ref. 10) had previously been suggested to be caused by climate change in the middle Miocene. However, relief production from 15 Ma (ref. 22) and the uplift of the pre-glacial topography to the modern topography could also explain glacial advance in the vicinity of the SHALDRIL site on the same timescale.

Implications for glaciation on evolving topography

It is essential to account for topographic evolution when interpreting ice-sheet extent in terms of climate change, and few have accounted for this with realistic topography37,38. The iconic topography of the Antarctic Peninsula, with its low-relief, high-elevation spine, provides a unique record of transience that can be exploited to resolve surface uplift and normalized rock uplift rate. In this Article, we show that high elevations are the result of primary tectonic uplift and isostatic response to large-scale dissection. The primary tectonic uplift can be explained in terms of dynamic topography. Under a modern (or interglacial) climate, the restored pre-glacial topography can support a similar volume of ice, but the spatial pattern of glaciation is very different from the modern pattern. This highlights the influence of dynamic topography on glaciation, as has been shown across the East Antarctic Ice Sheet over the past 3 million years for the case of ice-sheet retreat and stability39. Transition between the pre-glacial topography and the uplifted and dissected landscape explains the apparent advance of ice sheets across the north of the peninsula, without invoking climatic changes. Glacial erosion has dissected the landscape, and the associated isostatic uplift increases surface slopes and forms deep valleys with elevations below the ELA. Ultimately, glacial erosion reduces the amount of ice the landscape can support. Similar impacts of topographic changes are likely across other glaciated landscapes and should be evaluated when estimating past climatic conditions from glacial deposits.

Methods

To process the information constraining landscape evolution, we use the normalized analytical, steady-state stream power model,

$${{z}}\left({{x}}\right)={{z}}\left({{{x}}}_{{\rm{b}}}\right)+\left(\frac{{{U}}}{{{K}}{{{A}}}_{0}^{{{m}}}}\right){}^{\frac{1}{{{n}}}}{{\chi }}$$
(2)

where z is the elevation, x is the along-stream distance from base level, xb is the base level, U is the rock uplift rate, K is the erodibility, and m and n are the area and slope exponents of the detachment-limited stream power model18; \((U/{A_{0}^{m}}K)^{1/n}\) is the normalized rock uplift rate, which is termed u*. Equation 2 relies on the χ transformation24, a transformation of the horizontal coordinate of the river network, achieved by setting

$${{\chi }}=\mathop{\int}_{{{\rm{x}}}_{{\rm{b}}}}^{{\rm{x}}}\,\left(\frac{{{\rm{A}}}_{0}}{{\rm{A}}\left({{\rm{x}}}^{{\prime} }\right)}\right){}^{m}{{\rm{dx}}}^{{\prime} }.$$
(3)

Here, A is the upstream drainage area and A0 is a reference drainage area used to keep the units of χ in metres. The value of A0 is set to a value of 1 m2 so that the values of u* are comparable to previous studies40. We also use a value of 0.45 for m, appropriate for tectonically active regions41. Note that if n is not equal to one, the relationship between z and χ is still linear, and linear inverse methods can be used to infer the model parameters. In this way, u* could be converted to rock uplift rate, provided K and n are known, without changing our ability to reconstruct topography. Therefore, we do not specify a value of n or K to reproduce palaeotopography. If u* varies in space, we can write a discrete version of equation (2) for pixels in a DEM along a channel,

$${z}_{i}={z}_{j}+\left({\chi }_{i}-{\chi }_{j}\right){u}^{* }$$
(4)

where the ith pixel is upstream of the jth pixel, and the lowest pixel has an elevation of zero. In the case of the Antarctic Peninsula, the modern topography is expected to be a function of any initial fluvial relief and a component of additional rock uplift. Across the relict part of the landscape, this additional rock uplift corresponds to s.u. Therefore, any point on the relict part of the landscape can be written as:

$${z}_{i}={z}_{j}+\left({\chi }_{i}-{\chi }_{j}\right){u}^{* }+{{{\mathrm{s.u.}}}}_{i}$$
(5)

The branching network of river channels and the expectation that u* varies smoothly in space provides redundant information that enables maps of u* to be inferred from limited elevation pixels.

Equation 5 shows that similar topographies can be predicted by changing u* or s.u. However, by forcing the values of u* or s.u. to vary smoothly across many branches of the river network, the response to changes in these parameters is distinct. For example, the same increase in u* will lead to a small increase in elevation between nodes that have small differences in χ along the trunk stream, but at confluences, where the change χ is much larger due to the change in upstream drainage area, a larger change in elevation is predicted. By contrast, changes in s.u. will lead to identical increases in elevation regardless of the change in χ. Therefore, linearized inverse schemes enable maps of u* and s.u. (or maps of surface uplift) to be determined by simplifying the drainage network to reduce the number of nodes, by discretizing space into blocks of constant u* and s.u. values and by introducing smoothness constraints on u* and s.u. Therefore, the aim of the inversion is to find a topography that represents the predissected landscape, and this requires finding the model parameters (u* and s.u. values) that minimize the misfit between predicted and observed elevations of low-relief surfaces.

The expressions for all relict pixels in the dataset can be combined in matrix form as

$$\left( {\begin{array}{c} G \\ {\begin{array}{cc} \alpha {W}_{u} & .\\ . & \lambda {W}_{{{\mathrm{s.u.}}}}\end{array}} \end{array}} \right)\left(\begin{array}{c}{u}^{* }\\ {{\mathrm{s.u.}}}\end{array}\right)=\left(\begin{array}{c}z\\ 0\\ 0\end{array}\right)$$

where G is the 2npixel × nnodes containing χ values and entries of one to satisfy equation (5), αWu (npixel × npixel) is the weighting matrix for the normalized uplift rate parameters and λWs.u. (npixel × npixel) is the weighting matrix for the cumulative surface uplift rate. Importantly, α can control the roughness of both u* and s.u. and λ can similarly control the roughness of u* and s.u. (see refs. 27,40 for further details).

With a large value of α, the inversion attempts to minimize the misfit associated with the smoothness constraints (that the Laplacian of the u* values should be close to zero), resulting in a smooth model. With small values of α, the inversion finds results that fit the data well but are more sensitive to anomalous topography and geomorphic noise, and therefore, results may be meaningless. The same is true for λ and its control on the smoothness of s.u. maps. Within this context, geomorphic noise encapsulates artefacts in the DEM, landslides blocking rivers and over-steepening rivers and small-scale variations in erodibility.