Consequences of permafrost degradation for Arctic infrastructure-bridging the model gap between regional and engineering scales

Infrastructure built on perennially frozen ice-rich ground relies heavily on thermally stable subsurface conditions. Climate warming-induced deepening of ground thaw puts such infrastructure at risk of failure. For better assessing the risk of large-scale future damage to Arctic infrastructure, improved strategies for model-based approaches are urgently needed. We used the laterally-coupled one-dimensional heat conduction model CryoGrid3 to simulate permafrost degradation 20 affected by linear infrastructure. We present a case study of a gravel road built on continuous permafrost (Dalton highway, Alaska) and forced our model under historical and strong future warming conditions (following the RCP8.5 scenario). As expected, the presence of a gravel road in the model leads to higher net heat flux entering the ground compared to a reference run without infrastructure, and thus a higher rate of thaw. Further, our results suggest that road failure is likely a consequence of lateral destabilization due to talik formation in the ground beside the road, rather than a direct consequence 25 of a top-down thawing and deepening of the active layer below the road centre. In line with previous studies, we identify enhanced snow accumulation and ponding (both a consequence of infrastructure presence) as key factors for increased soil temperatures and road degradation. Using differing horizontal model resolutions we show that it is possible to capture these key factors and their impact on thawing dynamics with a low number of lateral model units, underlining the potential of our model approach for use in pan-arctic risk assessments. 30 Our results suggest a general two-phase behaviour of permafrost degradation: an initial phase of slow and gradual thaw, followed by a strong increase in thawing rates after exceedance of a critical ground warming. The timing of this transition and the magnitude of thaw rate acceleration differ strongly between undisturbed tundra and infrastructure-affected https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c © Author(s) 2020. CC BY 4.0 License.


Introduction
Land surface temperatures in the Arctic are reported to have warmed by more than 0.5 °C per decade since 1981 (Comiso 45 and Hall, 2014). This exceeds the average global warming by a factor between two to three and already is leading to pronounced observable cryospheric changes ranging from sea-ice decline, Greenland ice sheet melt and reduction in spring snow cover, to a wide range of permafrost degradation processes (Rowland et al., 2010). Rapid changes of permafrost landscapes are in particular triggered and accelerated by melting of excess ground ice, resulting in land surface subsidence (Kokelj and Jorgenson, 2013). The potential damage to ecosystems and infrastructure caused by permafrost thaw is linked to 50 diverse ecological, social, and financial risks. The economic development of the Arctic requires highly resilient infrastructure such as supply roads, pipelines, fuel storages, airports, and other buildings to be constructed on highly sensitive frozen ground (Larsen and Fondahl, 2015). Even offshore activities and shipping in the Arctic depend on reliable onshore facilities in permafrost-dominated regions such as ports and local transportation networks. Functional and safe infrastructure is important for the livelihood of the local population, and is directly dependent on the thermal stability of the 55 underlying and surrounding permafrost .
Field investigations have demonstrated that the degradation of permafrost landscapes is not limited to top-down soil warming and thawing, but is often accompanied by thermokarst and a variety of erosional and mass wasting processes that operate on different spatial and temporal scales (Fortier et al., 2007;Liljedahl et al., 2016). Landslides, thermokarst features, 60 and thermo-erosion gullies are prominent geomorphological features that reflect the active dynamics of destabilized permafrost landscapes, which directly threaten man made infrastructure (Nelson et al., 2001). Infrastructure itself can also cause thermokarst and other processes resulting from thawing ground ice. Significant efforts are made during road planning to quantify ground ice (Trochim et al., 2016). Ground ice distribution is one important factor towards understanding and predicting thermokarst processes that affect infrastructure. Additionally, these thermokarst processes in turn affect local heat, water, erosion and carbon and nutrient exchange processes, so that a variety of feedback mechanisms such as additional greenhouse gas emissions may well be associated with permafrost erosion (Chapin et al., 2005;Schuur et al., 2015;Schneider von Deimling et al., 2015;Walter Anthony et al., 2018). Climate, terrain and local processes are critical additions to generate holistic understanding of infrastructure response to permafrost (Stephani et al., 2014). Reliable and prompt assessments of risks of possible damages to both the ecology and infrastructure are therefore critically important. 70 Recent studies indicate that many areas are already experiencing issues, including Alaska where this study is focused. 18% (34 out of 187) of rural communities evaluated there were designated as high risk with over half located in continuous permafrost (Kanevskiy et al., 2019). In the oilfield region of Prudhoe Bay on the North Slope of Alaska, permafrost degradation has been documented over 62 years with acceleration after 1990 in the rates of thermokarst related to a rise in 75 summer air and permafrost temperatures (Raynolds et al., 2014). Considering projected climate change under the RCP8.5 scenario, Streletskiy et al. (2019) and Suter et al. (2019) show that infrastructure built on permafrost will be negatively affected by decreases in bearing capacity and ground subsidence by mid-century, resulting in large infrastructure lifecycle replacement costs. The risk of disasters caused by damage to sensitive infrastructure such as pipelines, fuel storages, and plants have yet to be estimated. Passive cooling techniques can be effective at reducing climate effects but mitigation and 80 adaptation can be more expensive than conventional construction (Doré et al., 2016). Globally, the emission of additional greenhouse gases from thawing permafrost is increasing the risk for extra costs of overall climate change (Hope and Schaefer, 2016;Melvin et al., 2017).
Given the lack of high-resolution circum-Arctic model projections of permafrost thaw and subsidence, recent risk assessment studies of infrastructure failure have used statistical approaches and suggested that fundamental engineering structures in the 85 Arctic are at risk by mid-century (Hjort et al., 2018;Karjalainen et al., 2019). Such statistical approaches allow accounting for various sources of local-scale information such as ground ice content, sediment type, or slope gradient at comparatively low computational costs. They have their strength in providing high resolution geospatial maps for evaluating the potential of future infrastructure failure in specific regions. But these statistical approaches cannot capture transient changes in permafrost well enough and they particularly fail to predict dynamical and non-linear features of permafrost degradation 90 (such as thermokarst). Therefore these approaches can miss key factors that determine the timing of future infrastructure damage, which likely lead to an underestimation of the timing when infrastructure is at risk in the future. Daanen et al. (2011) have suggested a risk assessment approach that can benefit frozen ground engineering applications. Their approach accounts for dynamical permafrost modelling, driven by regional climate change predictions, to estimate a Permafrost Thaw Potential which includes the effects of climate warming and infrastructure elements on future thawing depths but does not 95 account for lateral interactions between infrastructure and adjacent permafrost ground. Different approaches used in previous studies have their strengths and weaknesses, outlined below. https: //doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.

1.1
State-of-the-art global modelling of permafrost degradation The current global land surface models (LSMs) have undergone extensive improvements within the last decade to include 100 key processes related to permafrost changes and degradation. The focus of these model developments is on a better description of physical thaw processes and of biogeochemical cycles of soil carbon release, but the impact of infrastructure has not yet been included.
Widespread thawing of permafrost is expected in a warmer future climate and LSM-based model studies suggest large-scale degradation of near-surface permafrost at the end of the 21st century (Lawrence et al., 2008;Lawrence et al., 2011). 105 However, current modelling approaches used to simulate permafrost degradation under a warming climate are highly simplistic since they only consider one-dimensional (top-down) thawing and ignore important lateral processes such as snow redistribution, soil erosion and mass wasting -common processes in many regions that accelerate thaw. This limits the ability to understand the magnitude of impacts under permafrost thaw. Thus, current model assessments are most likely far too conservative in their estimates of permafrost thaw impacts, which is underlined by observational evidence of strong 110 permafrost degradation even under present day climate conditions not being captured by models (Farquharson et al., 2019;Nitzbon et al., 2020).

Modelling climate change impacts on infrastructure built on permafrost -an issue of scales
Under the current projections of climate warming in the Arctic, there is an increasing need to incorporate these permafrost 115 thaw scenarios into understanding the fate of infrastructures in the Arctic region. Given the pace of permafrost degradation, Arctic infrastructure may well be seriously affected within 30 years, a common service lifespan for many infrastructure types. It is important to note that infrastructure constructed on permafrost is not only being impacted by climate change, but it is itself affecting ground thermal and hydrological conditions, thus leading to infrastructure-related impacts on permafrost stability. Infrastructure embankments strongly change ground thermal properties and surface albedo. They result in an 120 increased winter insulation where additional snow accumulates (e.g. at the embankment shoulder and toe, (Fortier et al., 2011;O'Neill and Burn, 2017). In contrast, snow clearance at the road surface leads to strong subsurface winter cooling.
Infrastructure embankments can also act as a dam that alters natural drainage networks, causing water to accumulate next to the road (Andersland and Ladanyi, 1994;de Grandpre et al., 2012;O'Neill and Burn, 2017). An elevated permafrost table in the embankment also hampers drainage, which may result in ponding at the embankment toe and increase the potential for 125 thaw subsidence there. Further, dust deposition from the road on the adjacent tundra is favoured and can alter snow-related thermal insulation (Raynolds et al., 2014). These examples underline the need for capturing fine-scale components (meter scale) when modelling infrastructure elements.
Comparable to the challenge of modelling microtopographic landscape features such as for polygonal tundra dynamics Nitzbon et al., 2020), a key limitation of modelling infrastructure in current LSMs is in their coarse 130 https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License. spatial grid, given typical horizontal model resolutions of ~100 km. Therefore, to the best of our knowledge, no studies using LSMs have analysed consequences of permafrost degradation on Arctic infrastructure so far. Other model-based studies of Arctic infrastructure failure are rare and are usually limited to geotechnical site-specific studies (Fortier et al., 2011;Flynn et al., 2016;O'Neill and Burn, 2017).

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The following sections give a short overview of differing modelling strategies of simulating infrastructure state and permafrost degradation, underlining their strengths and limitations.

Geotechnical models (GTMs)
With a focus on fine scales and the aim to describe site-specific conditions and complex processes and interactions, 140 Geotechnical models (in the following referred to as GTMs) are specifically designed for engineering problems. The temporal focus of the modelling is on the construction phase (months to a couple of years), but does not usually account for longer time horizons. Boundary conditions are often prescribed as stationary present day temperature and soil moisture state.
Prescribing representative boundary conditions for the local site is essential for producing accurate model results (Darrow, 2011). However, model initialization by 2D or 3D temperature and soil moisture fields is usually hampered given the 145 scarcity of measurements, and the computational burden of these models does not allow for long spin-up runs to ensure the model domain is in equilibrium with realistic boundary conditions. Thermal insulation by snow is a key component of permafrost modelling, but is often not accounted for in GTM studies.
More complex Thermo-Hydro-Mechanical (THMs) models (e.g. Plaxis, GeoStudio) allow for a coupled model description of thermal, hydrological, and mechanical components, but their high computational costs limit their applicability for long-term 150 climate-warming model runs, the model scales are typically limited to a few tens of meters. A strength of GTMs lies in the possibility to couple mechanical processes, and providing specific model diagnostics in the form of stability and deformation measures, failure modes and quantification of the time to failure, which allow inferring direct measures for ground stability and road safety.

Land surface models (LSMs) 155
Representing the land surface components of Earth System Models (ESMs), LSMs describe exchange processes of water and energy fluxes at the land surface-to-atmosphere interface and ultimately enable the feedback from land to the climate system. Yet, the representation of permafrost within state-of-the-art LSMs contained in the last IPCC assessment was less than satisfactory (Ciais et al., 2013;Koven et al., 2013), and the latest model simulations submitted for the forthcoming IPCC assessment have not substantially improved on this (Burke et al., 2020). However, most of the latest IPCC ESM's can at 160 least realistically account for the insulating effects of snow, and soil water phase changes (Burke et al., 2020). The greatest shortcoming in the majority of the models is that they lack a sufficiently high vertical resolution in the soil column and a https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.
representation of heat flux in deep soil layers (Burke et al., 2020). The standalone versions of LSM's are generally more advanced than the ESM versions, due to the additional technical work required for coupling to the atmosphere. In offline mode, more LSM's account for these key processes, and other major factors such as the impact of organic matter on soil 165 thermal and hydraulic properties (Lawrence et al., 2012;Chadburn et al., 2015;Kleinen and Brovkin, 2018;Qiu et al., 2019).
In addition, the current development of improved schemes for capturing of water flow dynamics will help in accounting for additional processes of importance to infrastructure stability, such as ice lens formation or frost heave .
Despite these efforts, LSMs still miss representing key processes for modelling rapid permafrost degradation, and scaleissues remain a challenge as the processes involved in abrupt permafrost degradation are very localized. 170 Virtual tiling has recently been used in LSMs to take into account sub-grid variability in surface characteristics combined with representing excess ground ice, but such tiling schemes are not spatially explicit and more or less static with only limited possibilities of taking into account changes in land surface cover (Lee et al., 2014;Aas et al., 2019;Ekici et al., 2019;Cai et al., 2020). Nonetheless, the combination of these developments enable a first order quantification of land surface subsidence associated with permafrost thaw and subsequent land surface transformation such as wetland and thermokarst 175 lake formation. The benefit of these developments will be realised in the capacity to understand and quantify permafrost thaw-associated feedbacks to the climate system in a comprehensive and fully coupled manner that no other models can represent.

Process-based Tiling Models (PTMs) 180
Modelling the interactions between climate warming, permafrost degradation, and infrastructure requires combining the high level of detail of GTMs with the large-scale and long-term capabilities of LSMs. This challenge of bridging the gap in scales can be met by the use of computationally-efficient Process-based Tiling Models (PTMs) through reducing complexity while still resolving key processes for capturing infrastructure-affected permafrost thaw. A reduced order representation allows much faster time integration compared to GTMs and therefore allows for adequate model spin-up, long-term simulations 185 over many decades, and uncertainty quantification through ensemble simulations. Capturing key dynamic processes despite reduced model complexity is enabled by making use of the flexibility of PTMs in terms of scalability to a specific problem.
For this purpose a case-specific tiling concept is needed to segregate infrastructure and tundra into individual structural units adapted to the scales of the modelling task. Examples of using a PTM (CryoGrid) in a tiling setting for describing diverse permafrost landscape dynamics can be found in Nitzbon et al. (2019Nitzbon et al. ( , 2020, where the authors capture micro-topography 190 features to model dynamics of polygonal tundra degradation, and in (Langer et al., 2016), where accelerated thaw through talik formation induced by thermokarst lakes is simulated.
In this study, we used a laterally-coupled version of the 1D heat conduction PTM CryoGrid3 for modelling impacts from permafrost degradation caused by climate change on Arctic infrastructure. To demonstrate how permafrost-affected https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.
infrastructure failure though climate change can be captured in a modelling context, we present a case study focusing on 195 gravel roads built over ice-rich permafrost, particularly the area around the Prudhoe Bay (Dalton highway, Alaska). In section 2, we give details about our simulation set-up. In section 3, we show model results of permafrost degradation affected by linear infrastructure for historical, present day and future warming climate conditions. In section 4 we discuss how our modelling approach can be applied pan-arctic wide where we suggest a strategy for modelling impacts of permafrost degradation on Arctic infrastructure by bridging the gap between small and large scales. Conclusions are drawn 200 in section 5. Details of model set-up and model evaluation are given in the appendix.

Model description and simulation setting
We aimed to simulate the temperature regime under a typical gravel road built on continuous permafrost and its thermal evolution under climate warming. Given the abundance of infrastructure in the Prudhoe Bay Area (Alaska, coastal plain), we chose this region as our target region for modelling (Fig. 2). 205 We used a (laterally-coupled) one-dimensional heat conduction model (CryoGrid3) which is able to simulate dynamic surface and subsurface processes in permafrost landscapes (Langer et al., 2016;Westermann et al., 2016). The CryoGrid3 model includes a dynamic snow cover representation and an explicit surface energy balance scheme for simulating heat and water exchange with the atmosphere. Our model version also accounted for lateral heat and water fluxes in the ground 210 between adjacent tiles . Vertical water flow is described by an instantaneous infiltration scheme, while the calculation of lateral water fluxes is based on Darcy's law, assuming a constant lateral hydraulic conductivity. The model has been extensively evaluated with respect to its performance in representing key physical processes in tundra landscapes, namely surface energy balance, thermal state of ground, soil hydrology, and snow cover dynamics (Westermann et al., 2011;Langer et al., 2013;Westermann et al., 2016), 215 including subsurface water exchange Nitzbon et al., 2020). Further, the model has been evaluated under different climate conditions and for different permafrost landscape types such as peat plateaus and palsas . The source code of the model version used in this study can be downloaded from Github (https://github.com/CryoGrid/CryoGrid3/tree/xice_mpi_IS).

Model limitations 220
We do not model heat advection by lateral water flow which can strongly accelerate road failure (de Grandpre et al., 2012;Chen et al., 2019). Our model represents the thermal impact of the snow cover on the ground by a simple bulk snow density approach neglecting any temporal changes in snow cover properties resulting from snow metamorphism (i.e., depth hoar) or wind compaction (i.e., ice crusts). The snow scheme emulates lateral redistribution of snow, but without explicitly https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License. calculating wind drift. Besides infrastructure failure due to thawing of ice-rich soils, frost heave in frost-susceptible ground 225 below the embankment can also lead to severe infrastructure damage -a process which is not captured in our model.
In this study we assess the timing when infrastructure failure might occur in the future due to melting of ground ice and subsequent subsidence. The exact timing of failure will depend on road design and local climate conditions which can of course deviate from the case that we are discussing here (especially if road protecting cooling devices are installed such as thermosiphons, ducts, insulating layers, or snow sheds). Rather than trying to simulate a specific infrastructure element at a 230 given location and inferring specific estimates of infrastructure failure, we want to demonstrate the broader applicability of our modelling approach for capturing critical processes of key importance to the stability of infrastructure on ice-rich permafrost grounds which are not represented in other modelling frameworks.

Model set-up 235
Down-scaled climate data (SNAP, (Lader et al., 2017) was used to force our model under historical, present day and projected climate change. We bias-corrected climate forcings to ensure that our simulated present day soil temperature conditions were close to observations (see appendix). For describing future climate evolution we used the RCP8.5 scenario, which leads to mean annual surface air temperature warming of about 5° C above year 2020 levels at Deadhorse at mid-

century. 240
We set up our model to represent a transect from the road centreline to the adjacent tundra up to a distance of 100 m. The tundra and infrastructure elements were accounted for by prescribing different ground stratigraphies (Tab. 1 and Fig. 3), and by adapting surface-and below-ground specific parameters (Tab. 2). We investigated a 'conservative' and a 'vulnerable' case for our model simulations. In the latter case we consider pond formation next to the road and increased solar incoming 245 radiation on the road shoulder by assuming southerly facing conditions. Further we assumed snow-free conditions on the road surface and additional snow accumulation on the road shoulder and toe (Fig. 3). In the appendix we give detailed information about model spin-up, ground stratigraphy choices, and gravel road design choices. Table 2 lists key model parameters which affect surface and subsurface heat fluxes. Further standard model parameter choices can be found in Westermann et al. (2016) and Nitzbon et al. (2019). 250

Simulation setting
The model domain was subdivided into structural units (SUs) of differing surface and subsurface characteristics (e.g., with respect to albedo, snow accumulation, excess ice presence and ground composition, see Fig. 3). All SUs were laterally connected to allow for below-ground lateral exchange of heat and water between the gravel road and the adjacent tundra. 255 https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License. The sensitivity of model to horizontal model resolution was investigated using three set-ups to capture the gravel road and tundra up to a distance of 100 m from the road centre with increasing horizontal resolution (Tab. 3 and appendix).

3
Results and discussion 3.1 Present day conditions 260 Figure 4 illustrates how a replacement of the tundra surface by a gravel embankment is affecting subsurface temperatures: the removal of the protective peat layer and the clearance of snow on the road centre increases the coupling of surface air and ground temperatures. Warm summer air temperatures penetrate much deeper into the ground under the road surface as compared to the tundra (Fig. 4, right panels). Snow accumulation at the toe and road shoulder results in strong winter ground warming (Fig. 4, left panels). 265 Our simulation results describe a gravel road which is stable under year 2000 climate conditions as simulated thaw depths only reach levels well above the embankment base (Fig. 4). Warming from the beginning of the century until today (year 2020) has increased overall ground temperatures, which leads to a pronounced active layer deepening under the toe (SU3). In University. https://www2.gwu.edu/~calm/data/data-links.html.). The formation of a zone of temperatures approaching zero degrees at the end of the winter season (light bluish areas in Fig. 4, March 2020) indicates vulnerable conditions where additional future warming will have a strong effect on thaw depths. The general characteristic of strongly increased heat penetration below the road centre as compared to the tundra and the increased soil warming under the toe caused by snow accumulation was also inferred in other modelling approaches (Fortier et al., 2011;Flynn et al., 2016). For a vegetated 280 hillslope side, Jafarov et al. (2018) inferred a pronounced effect on soil warming from preferential snow accumulation.
For investigating the impact of infrastructure on permafrost degradation we have additionally run a reference run (single tile) with identical parameter choices, but without including infrastructure. It can be seen that the outer tundra tiles from the laterally coupled setting reach soil temperatures very close to the reference run (separate right soil temperature columns), therefore justifying our assumption of a zero boundary flux at the outer model domain. 285 https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.

Development under future climate change
Under the 21st century future climate change scenario, the simulated ground thermal regime shows strong increases in maximum thaw depths. The prescribed additional mean annual surface air warming of about 5°C above 2020 levels (7° above 2000 levels) until the mid-century for the Prudhoe Bay region (following RCP8.5) leads to the formation of an open 290 talik below the pond (toe tile). This warming signal further spreads into the embankment, subgrade and adjacent tundra (Fig.   4, see also the animated temperature evolution in the supplementary material). The thermal buffering of the lower shoulder is not sufficient anymore to prevent strong thawing in the embankment subgrade. In the case of the thaw front reaching thawunstable ice-rich layers, subsequent ground subsidence would result in failure of the embankment shoulder. In contrast, the road centreline is stable by 2050 as winter heat extraction is still strong enough to prevent active layer deepening below the 295 embankment base. Nonetheless, further warming and lateral growth of the talik into the embankment core and subgrade will strongly destabilize the road foundation and lead to subsequent total road failure if the road was built on ice-rich ground ( Fig. 4 lowest panels).
Our results under the 21st century climate change scenario reveal pronounced differences in the dynamics of simulated thaw depths among the different structural units (Fig. 5; road centre, shoulder, toe, tundra). Thawing rates can be split into two 300 periods: a period of slow and gradual increase in maximum thaw depths, followed by a sharp increase in thawing rates once a critical warming of the ground has been reached. As a consequence of snow accumulation and subsequent ground warming, the toe structural unit is the first location where an increase in thawing rates is seen. In the 'vulnerable' setting with ponding at the toe, this increase is very pronounced and starts already around 2015 after pond formation (Fig. 5b), reaching thawing rates of 20 cm yr -1 . The shoulder tile reveals a lagged thaw rate increase, reaching thaw penetration below 305 the embankment base around 2040 (around 2055 if no pond is assumed). Further warming will ultimately lead to road destabilization if the ground below the embankment base is ice-rich. In contrast, the road centre is much more stable with a thaw rate increase many decades later. The outer road edge is destabilized by around the year 2060 (2075 without ponding).
By contrast, the adjacent tundra reveals a gradual active layer deepening without showing accelerated thaw in the 21 st century. The occurrence of individual cold winters can result in a strong winter refreeze in a particular year, causing large 310 year-to-year changes in the maximum thaw depths (Fig. 5).
Our inferred dynamics of thaw rate acceleration resemble the thawing behaviour seen in a model study of a gravel road on discontinuous permafrost (Fortier et al., 2011). Figure 5 underlines that model studies that do not explicitly incorporate infrastructure in their model design are likely to strongly underestimate the timing of infrastructure damage following permafrost thaw, as infrastructure presence can promote enhanced ground warming. 315 https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.

Sensitivity to number of structural units
A key question of interest to modelling concerns the amount of detail necessary to satisfactorily capture the road thermal state and its adjacent environment. We investigated this aspect by running our model with low lateral resolution (1 road tile, 1 tundra tile), with medium resolution resolving all structural units (road, shoulder, toe, tundra) and with high resolution. In 320 the latter case we further subdivided structural units into multiple tiles (total of 30 tiles, Tab. 1). When describing our model-setup by only two tiles, our results suggest that permafrost degradation under the road centre is underestimated, resulting in less pronounced thaw The medium and high resolution settings show consistent results, with slight differences when focusing on the outer edge of the road (Fig. 6a). In contrast, modelled maximum thaw depths for the adjacent tundra show no sensitivity to horizontal model resolution (Fig. 6b). The toe and shoulder tiles (Fig. 6c, d) are not 325 resolved in the low resolution setting and reveal much stronger permafrost degradation, underlining the importance of accounting for these elements in the model design. While the difference in simulated thaw trajectories between medium and high resolution runs is rather small for the shoulder tile (Fig. 6c), larger deviations are seen for the toe tile (Fig. 6d). Yet both experiments reveal very similar thaw dynamics and reveal differences in the timing of thaw below the embankment base of only a few years. 330

Perspective on future modelling of Arctic infrastructure failure
Our results clearly exhibit that there are combined effects from climate warming, permafrost degradation, and the presence of infrastructure. This highlights that future model-based risk-assessment of Arctic infrastructure should take into account all three components in understanding and quantifying the consequences of permafrost degradation on Arctic infrastructure. For such a purpose the use of numerical modelling appears the most appropriate tool to account for the full spectrum of 335 dynamical permafrost changes expected in a warmer future.
We suggest that a collaborative development of models from decimetre to meter scale used in geotechnical models (GTM) to typically a hundred kilometres used in land surface models (LSMs), could help in capturing processes operating across scales and therefore enabling an accounting for process interactions between infrastructure and permafrost affect land areas.

340
Despite the large difference in scales between (GTMs) and (LSMs), we see a potential for bridging this gap by the use of physically-based tiling models (PTMs). These models are computationally more efficient than GTMs, structurally more flexible in terms of describing processes of relevance to permafrost degradation, and adaptable to differing scales. They can be run for climate change scenarios and be used to explore the minimum number of structural units needed to satisfactorily simulate the thermal state of specific infrastructure elements. This information could then be used by LSMs to define a 345 tiling-based model-setup for describing infrastructure in a reduced but manageable manner (Cai et al., 2020). The result of these tiling-based LSM simulations can produce a pan-Arctic map showing key regions where infrastructure failure through https://doi. org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License. melting of excess ice and subsequent ground subsidence is likely for a given infrastructure design under a given scenario of future climate change.
Additional information of importance for a risk assessment could then come from further PTM simulations with a focus on 350 identified key risk regions. These PTM simulations could be conducted in an ensemble setting to account for parameter and structural uncertainty in the model set-up, thus allowing probabilities to be linked to infrastructure failure estimates. To better capture regional weather scales, these simulations could also be driven by downscaled climate forcings, or they could be run for an ensemble of climate input data inferred from different ESM simulations. In a final step, a GTM-based case study could be performed with boundary conditions taken from the PTM modelling (i.e. using simulated soil temperature 355 and soil moisture fields). The GTM application would allow a more case-specific model setup for a given location, therefore allowing it to better capture design-specific aspects of certain infrastructure elements. This approach could also provide additional diagnostics of importance to road stability determination.

Conclusions
In our study we show the applicability of a laterally-coupled one-dimensional heat conduction model for simulating 360 permafrost-affected infrastructure failure, demonstrated for the case of a gravel road built on continuous permafrost. Our simulation results allow an improved process understanding of how the ground below infrastructure can degrade under a scenario of intensive future climate change, and underline the potential for use of such models in pan-arctic risk assessments.
Our model simulations show a transition from slow and gradual thaw to fast, and likely irreversible permafrost degradation, and point to a threshold-like behaviour where (without extensive active ground cooling measures) road failure is inevitable 365 once a critical level of ground warming has been reached. Rather than a simple top-down thawing and deepening of the active layer below the road centre, we identify lateral destabilization of the embankment and subgrade caused by talik formation under the toe, a key process which results in accelerating thaw rates and results in subsequent road failure.
The comparison of modelled thawing depths under the road and tundra underlines that infrastructure can exert a strong impact on ground temperatures as a consequence of increased net heat input in the subsurface. Therefore it is crucial that 370 model-based estimates of the timing of Arctic infrastructure failure account for the amplification of permafrost degradation through the presence of Arctic infrastructure itself.
Based on our modelling results with differing lateral model resolutions we conclude that the minimum number of model tiles should be chosen such that important structural units are captured, such that small-scale processes which exert a key impact on the ground thermal regime are accounted for. In our example of a gravel road we have identified snow accumulation and 375 ponding at the shoulder and toe such key processes. For our linear infrastructure example we suggest a minimum number of four structural units to represent the road surface, the shoulder, the toe, and the tundra. For other types of infrastructure, https://doi. org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.
structural units have to be adapted accordingly. If more spatial detail is needed (such as the information about the thermal state of the embankment at the road edge), structural units can be further subdivided into individual tiles of finer lateral resolution. Our simulations demonstrate that a low number of structural units can be sufficient to resolve processes operating 380 on engineering scales. Our use of a laterally-coupled one-dimensional model allows us to infer results in line with more complex 2D-and 3D-models but our model's computational efficiency enables us to calculate long-term climate change impacts on infrastructure from permafrost degradation. Further, our simulation results show the potential for reducing model complexity and therefore underline the capability of use in computationally extensive pan-arctic analyses.
Our results underline that it is crucial to consider climate change effects when planning and constructing infrastructure on 385 permafrost as a transition from a stable to a highly unstable state can well occur within the infrastructure's service lifetime (about 30 years). With our focus on the Dalton highway at Deadhorse (Prudhoe Bay, Alaska), we illustrate that such a transition can even occur in the coming decade for infrastructure built on continuous permafrost that displays cold and relatively stable conditions today.

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Appendix A: Details of model set-up

A1 Climate Forcing
We used down-scaled climate data (for air temperature, humidity, pressure, wind speed, rain and snow precipitation, and incoming long-wave and short-wave radiation) provided by the SNAP database (SNAP, (Lader et al., 2017) to force our model under historical, present day and projected future climate change conditions. We follow the approach by Westermann 395 et al. (2016) of using monthly climate anomaly fields in combination with high-frequency reference climate data to generate bias-corrected climate forcings. The monthly anomalies are calculated based on a downscaled GFDL model run under the RCP8.5 scenario. The reference climate data cover the period 2005 to 2015 and are taken from the downscaled SNAP ERA data.
The RCP8.5 forcing describes a scenario of extensive future climate change resulting in a radiative forcing of 8.5 W m -2 by 400 2100. For the Prudhoe Bay area (Deadhorse) this forcing leads to mean annual air temperatures about 5° C above mean year 2020 levels by the year 2050 (about 8° C by 2075).

A2 Initialization and boundary conditions
We initiate soil temperatures based on borehole data at 10 m and 20 m depth  and start our 405 simulations in the year 1975, using the first 25 years for spinning-up our model domain under historical climate conditions. https://doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.
For capturing observed high soil moisture conditions, we prescribe an external water flux of 2 mm day -1 for the period of unfrozen soil surface conditions. Based on borehole data (Raynolds et al., 2014), we prescribe the tundra soil stratigraphy by assuming a 30 cm peat layer on 410 top of a two meter thick silty mineral soil layer. Below, a sandy mineral soil layer is assumed extending to the bedrock boundary at 10 m depth (see Fig. 3). In our model setting with ponding ('vulnerable' setting), we assume a layer of high excess ice between 1 m and 2 m, mimicking a case of a buried ice wedge next to the road. The maximum model depth is constrained to 1000 m with a lower boundary flux condition given by a geothermal heat flow of 0.05 W m -2 (Lachenbruch et al., 1982). Ground stratigraphies for tundra and infrastructure conditions are given in Tab. 1. 415 In our model setup we consider a transect from the road centreline to the adjacent tundra up to a distance of 60 m (low and medium resolution) or 100 m (high resolution), assuming symmetry along the centreline for computational efficiency. At the outer model boundaries we assume zero lateral flux conditions given our symmetry assumption with regard to the road centreline and negligible lateral gradients at the outer tundra model boundary. 420

A3 Model resolution and subdivision into structural units
We have run CryoGrid3 in three different set-ups in which we have captured the gravel road and tundra up to a distance of 100 m from the road centre with increasing horizontal resolution. In a low resolution setting (LowRes) we have only used two tiles (i.e. simulating two connected soil columns) to describe the gravel road centre by one SU coupled to a tundra SU. 425 In contrast, in the medium resolution (MidRes) and high resolution (HighRes) settings we use four SUs which allow us to resolve our model domain in greater spatial detail, e.g. by accounting for small-scale effects of snow accumulation and ponding in the vicinity of the road (see Fig. 3). In these settings we additionally consider one structural unit for the embankment shoulder (SU2) and one structural unit for the toe (SU3). Further, we resolve the outer edge of the road surface separately by one additional tile (MidRes). In the HighRes setting we describe the tundra with finer horizontal resolution 430 close to the road, and increasingly coarser resolution towards the outer boundary at 100 m distance from the road (Tab. 2).
The vertical model grid node spacing is 2 cm in the upper 4 m, 10 cm between 4 m to 10 m, 20 cm in the depth range 10 m to 20 m, followed by 10 more layers of increasing thickness down to the lower model domain boundary at 1000 m.

A4
Road embankment and toe 435 We assume that the road surface is 2.5 m above ground with a total embankment thickness of four meters (i.e. we imply an excavation of the uppermost 1.5 m of ground during construction). The material in the top 10 cm of the road surface is finegrained gravel, all other parts of the embankment are assumed to consist of coarse-grained gravel. We assume that the road https: //doi.org/10.5194/tc-2020-192 Preprint. Discussion started: 16 September 2020 c Author(s) 2020. CC BY 4.0 License.
centre is permanently snow free as a consequence of snow plowing. We capture this effect in the model by removing snowfall from the road centre. 440 We constrain landscape-scale maximum snow height on the adjacent tundra to 40 cm to simulate snow heights in the range of observations . As we do not simulate snow redistribution (through plowing and wind drift), we realize additional snow accumulation at the toe and shoulder by scaling snowfall by a factor of four. We constrain total snow heights depending on the distance to the surface road edge and describe a linear profile which results in largest snow heights at the toe (see Fig. 3, light blue shading). In our LowRes setting we cannot resolve ponding or snow accumulation along the 445 shoulder and toe, as we only include one road tile and one larger-scale tundra tile with uniform snow height.
The embankment has an assumed slope of 1:2 (1 m vertical vs. 2 m horizontal) and determines the maximum height of snow accumulation at the shoulder and toe (Fig. 3). In our conservative setting, we assume a general orientation of the Dalton highway in North-South direction. In our vulnerable setting we assume a southerly facing road shoulder and account for increased incident solar radiation. We acknowledge that a specific gravel road can deviate strongly from our assumed setting 450 here (e.g. (Andersland and Ladanyi, 1994).

Video supplement
The supplement to this article (https://doi.org/10.5446/47699) contains an animated video showing the results of the simulations described in section 3.

Author contributions
TSvD and ML designed the study. TSvD extended the model code for including infrastructure, carried out the simulations and wrote the paper. SJ generated model forcing data sets. All authors interpreted the results and contributed to the paper.

Competing interests. 485
All authors declare that they have no conflict of interest.       Table 1: Ground stratigraphies with volumetric fractions of the ground constituents. Negative depths correspond to layers elevated relative to the tundra surface at 0 m. The setting for the road shoulder is identical to the road centre, besides lacking a fine grained surface layer and starting from elevations between the road surface and the tundra (see Fig. 3). The road embankment base is assumed at 1.5 m depth. In the case of ponding at the toe ('vulnerable' setting), we assume high excess ice in the ground between 1 m and 2 m depth. albedo snow free surface gravel road 0.3 (Andersland and Ladanyi, 1994) albedo fresh snow 0.85 (Grenfell and Maykut, 1977) albedo old snow 0.5 (Grenfell and Maykut, 1977) density snow cover 250 kg m -3 (Sturm et al., 2010) thermal conductivity mineral soil and gravel fraction 3.0 W m -1 K -1 (Langer et al., 2013), (Farouki et al., 1982) thermal conductivity organic soil fraction 0.25 W m -1 K -1 (Farouki et al., 1982) volumetric heat capacity mineral soil and gravel fraction 2.0*10 6 J K -1 m -3 Farouki (1982) volumetric heat capacity organic soil fraction 2.5*10 6 J K -1 m -3 Farouki (1982) geothermal heat flux lower model boundary 0.05 W m -2 (Lachenbruch et al., 1982)