The thermal response of permafrost to coastal floodplain flooding

Flooding of low-lying Arctic regions has the potential to warm and thaw permafrost by changing the surface reflectance of solar insolation, increasing subsurface soil moisture, and increasing soil thermal conductivity. However, the impact of flooding on permafrost in the continuous permafrost environment remains poorly understood. To address this knowledge gap, we used a combination of available flooding data on the Ikpikpuk delta and a numerical model to simulate the hydro-thermal processes under coastal floodplain flooding. We first constructed the three most common flood events based on water level data on the Ikpikpuk: snowmelt floods in the late spring and early summer, middle and late summer floods, and floods throughout the whole spring and summer. Then the impact of these flooding events on the permafrost was simulated for one-dimensional permafrost columns using the Advanced Terrestrial Simulator (ATSv1.0), a fully coupled permafrost-hydrology and thermal dynamic model. Our results show that coastal floods have an important impact on coastal permafrost dynamics with a cooling effect on the surficial soil and a warming effect on the deeper soil. Cumulative flooding events over several years can cause continuous warming of the deep subsurface but cool down the surficial layer. Flood timing is a primary control of the vertical extent of the permafrost thaw and the active layer deepening.


Introduction
Arctic coastal flooding is observed and expected to increase in frequency and duration, which places unprecedented stress on Arctic coastal systems (Arp et al 2010, Sultan et al 2010, Irrgang et al 2022. Increased flooding could accelerate coastal erosion, seawater inundation, and permafrost degradation (Barnes 1990, Irrgang et al 2022. Coastal infrastructure, including cultural and archaeological sites, will become more vulnerable to flooding (Radosavljevic et al 2016, Yumashev et al 2019. A recent estimate of the cost of flood mitigation to protect coastal roads of Hooper Bay in Alaska was in the hundreds of millions of dollars (Miller and Ravens 2022). Thus, understanding the impact of increasing coastal flooding on coastal landscapes is vital for Arctic coastal protection.
Flooding in the Arctic coastal regions is driven by snowmelt, summer rain storms, ocean storm surge, land subsidence, coastal erosion, and river ice breakup and jamming (Barnes 1990, Arp et al 2010, Kondo et al 2021, Irrgang et al 2022, Provan et al 2022. Permafrost thaw in response to rising temperatures accelerates the rate of coastal erosion and land subsidence, which may cause extensive seawater-induced inundation (Tape et al 2013). With warmer air and seawater, retreating sea ice leads to an increase in the magnitude and frequency of storm surges (Irrgang et al 2022). Intensified magnitude and frequency of summer storms also results in increased coastal flooding (Arp et al 2010). River ice break-up impacts water levels causing local flooding (Prowse et al 2011). Snow dam outburst floods from drained thermokarst lakes as a result of spring meltwater and snow failures generate flooding downstream. Winters with more snow are projected to cause larger dam snow outbursts (Arp et al 2020). Spring snowmelt in Arctic watersheds leads to floods due to limited or no storage available in permafrost-affected soils (Kane et al 2008).
The early studies that documented the effect of flooding on Arctic coasts focused more on storm surge-induced coastal flooding, where significant thermo-erosion and coastal shoreline retreat were reported (Reimnitz andMaurer 1979, Kowalik 1984). Most of the focus was on the land surface change, where the morphologic and surface hydrologic changes were easily detected (Marsh and Schmidt 1993, Lantz et al 2020, Kim et al 2021. However, due to the lack of observational data, the impact of coastal flooding on subsurface hydro-thermal conditions, especially permafrost thaw, is poorly understood. To date, very few studies have investigated the flooding effect on coastal permafrost thaw. For example, Zheng et al (2019) developed a heat exchange model to study river flow changes and their impact on the river bed and bank permafrost in the Kuparuk River in Alaska. They found that permafrost warms faster when inundated, which makes a deeper active layer thickness (ALT) in the channel belt. An earlier spring freshet and inundation condition can significantly increase permafrost temperature. They suggested that spring flooding taking place earlier and lasting longer is affecting permafrost more than higher air temperatures along. However, they focused more on the permafrost in riverine systems. The impact of coastal flooding on extended low-lying coastal regions remains largely unexplored.
In this study, we address this gap by using a wellestablished hydrothermal numerical model to simulate permafrost hydrothermal dynamics under different flooding events, including spring and early summer snowmelt-induced floods, middle and late summer storm-induced floods, and all floods through the spring and summer.

Model description
In this study, we used the Advanced Terrestrial Simulator (ATS)  with its Arctic thermalhydrologic configuration. This configuration couples groundwater flow and heat transport representing the soil physics needed to capture permafrost dynamics, including ice, air, and liquid saturation, the flow of unfrozen water in the presence of phase change, and non-homogeneous soil layering . Specifically, the surface energy balance module simulates surface mass and energy balance with incoming and outgoing radiation, latent and sensible heat, and input of rainfall and snow (Atchley et al 2015). The surface module is coupled with the variably saturated subsurface domain. The conservation equations of mass and energy of the subsurface partitions ice and liquid phases in the subsurface zone, which allows the coexistence of liquid water with ice when the temperature is below 0 • C (Painter 2011, Painter andKarra 2014). Bulk thermal conductivity is defined as a function of porosity and the saturation of liquid, ice, and gas. The subsurface flow is represented by a modified variably saturated three-dimensional (3D) Richards equation (Richards 1931) coupled with an energy transport equation to model subsurface water dynamics with phase change. A detailed description of the model equations is provided by Painter (2011), Painter andKarra (2014), and Atchley et al (2015).

Experimental design
The experiment design was inspired by the observed coastal flooding events in 2012 on the Ikpikpuk delta in the North Slope Borough of Alaska (figure 1), which includes flooding events due to snowmelt in the spring and storm surges in the summer. The delta is of low-relief, is underlain by moderately icerich to ice-rich permafrost deposits, with a ubiquitous cover of ice wedge polygonal terrain, thermokarst ponds and lakes, drained lake basins, and meandering stream channels (Jorgenson et al 2014). The Ikpikpuk lies in a zone of continuous permafrost (Fuchs et al 2018).
To examine the flooding effect, we focused on the effects of inundation of freshwaters on low-lying areas and do not include salinity impacts. Based on our forcing dataset, we do not have estimates of the salinity of the flood waters or whether late summer storm driven flooding results in direct seawater inundation or freshwater flooding due to back water effects on the delta channels. The effects of salinity are potentially important and will be explored in future studies.
We designed a synthetic one-dimensional (1D) permafrost column (1.00 m × 1.00 m × 45.00 m) with three standard soil layers: peat (0.15 m), mineral (2.00 m), and deep soil (42.85 m) (figure 2(a)). We focused on examining the effect on soil temperature and moisture in the vertical direction and neglected lateral flow during flooding events as previous studies showed that the vertical heat and water transport due to surface inundation dominated over lateral flow (Magnússon et al 2022).

Meteorological forcing and flooding scenarios
Based on the observed floods at the Ikpikpuk delta, we generated three flooding scenarios, including (a) all floods in 2012, (b) the late spring and early summer portion of the all floods (hereinafter referred to as early floods), and (c) the middle and late summer portion of the all floods (hereinafter referred to as mid-to-late floods) (see figure 2(b)). These three scenarios represent a different combination of flood timing, magnitude, and climate seasonality. The early    (2020) van Genuchten ν (-) 0.19 0.248 0.52 Jan et al (2020) floods started on the 135th day each year (mid of May) with the highest water level of 0.72 m primarily due to spring snow melt, and the mid-to-late floods started on the 183rd day (early July) with the relatively uniformly distributed floods (averaged water level of 0.12 m) due to summer rainfall storms and storm surges.
The meteorological forcing is derived from a National Oceanic and Atmospheric Administration's weather station (Station Utquigvik: www.ndbc.noaa. gov/) close to the Ikpikpuk delta. The mean annual temperature is −8.15 • C, and the mean annual precipitation is 315 mm. The meteorological data includes air temperature, snow, rainfall, long-and short-wave radiation, wind speed, and humidity (an example of one-year forcing is shown in figure 2(b)). We used the simplified meteorological data with its seasonal trends allowing us to focus on the flooding effect and limit the effect of meteorological oscillation/variability on subsurface temperature and moisture. Likewise, we used the seasonally averaged rainfall and snow as the precipitation in the warm and cold seasons, respectively.

Model settings
We decomposed the subsurface domain into 50 mesh layers with a resolution gradually coarsening with depth. The thinnest layers are located at the upper peat and mineral layers with a thickness of 0.02 m to capture the details of water and heat fluxes and the thickest layer are around ∼10 m to reduce computational cost. The settings of peat, mineral, and deep soil followed the geological core samples at the Ikpikpuk delta (Gryc 1988). The parameters representing the thermal and hydraulic properties at each layer are set according to their features as peat, mineral, or deep soil (see the summary of parameterization in table 1).
The surface water level is prescribed by the time series of observed inundated water depth (see the time series of floods in figure 2(b)). Therefore, our simulations do not explicitly simulate how the inundated water routes off the domain. The prescribed water ponding level captures the rising and draining of water at the ground surface. The initial flooding water temperature is the same as the air temperature, then changes based on the energy balance, including the radiation inputs, heat exchange, and the heat loss due to evaporation, etc.
To examine the flooding effect, we compared the flooding simulations with a reference simulation without flooding. Firstly, we ran spin-up simulations with the repeated meteorological forcing each year (presented in figure 2(b)) until the thermal and hydraulic equilibrium conditions are reached, including the dynamic equilibrium of subsurface temperature, subsurface soil moisture, and surface water. After this, we used the spin-up simulation results as the initial condition and conducted simulations with the same meteorological forcing each year for ten years. Meanwhile, the flooding events each year were added to the flooding simulations and repeated for ten years.

Soil moisture change due to flooding
We first looked at the impact of flooding on permafrost by comparing the subsurface liquid water saturation level in the top 6 m in the first flooding year (figure 3). Figure 3(a) shows the soil moisture variation without flooding events. The largest variation is located in the top 2 m of the soil zone (the 0.25 saturation contour line), and the largest increase occurs in the spring and summertime. Soil saturation levels can increase up to 0.6 m in the summer. Later in the season, the liquid water saturation level decreases due to evaporation and soil re-freezing processes.
In contrast, in the simulations with floods (figures 3(b)-(d)), there are significant increases in soil moisture in the top 1 m soil in response to surface flooding (indicated by the bright-yellow color). The temporal variation depends on the timing of the flooding events. The flooding effect on soil moisture is minor beyond the top 1 m soil zone. This is mainly because the lower part is still frozen or partially frozen (see details of the subsurface temperature profile in section 3.3).

The changes in subsurface hydro-thermal properties
Floods also drive changes to other subsurface hydrothermal properties, including ice saturation and thermal conductivity, especially for the top 2 m soil, where the largest variation of the properties occurred. We focused on temporal changes in the first two years because the system reached a dynamic equilibrium after the first two years of flooding.
The temporal variation of the depth-averaged liquid saturation level in figure 4(a) is consistent with the variations shown in figure 3 above, where the soil saturation level increases with the flooding events during the spring and summertime. In particular, the cases with the mid-to-late floods (the purple lines in figure 4(a)) and all floods (blue lines in figure 4(a)) had the largest increase in subsurface liquid water content. The liquid saturation dropped to zero during the winter re-freezing.
For the ice saturation ( figure 4(b)), the difference among the cases became pronounced when the soil re-froze in the first winter. The cases with more spring and summer flooding water input and less water loss due to evaporation end up with a higher ice saturation in the winter. The ice saturation is the highest with the mid-to-late floods because of its highest liquid saturation level. In the second year, there is a slight difference in ice saturation among the cases in the summertime because most of the ice in the top 2 m of soil melts. After the flooding events in the second year, the ice saturation shows a similar difference as in the first year during the re-freezing process in the winter.
For thermal conductivity, the increased ice and liquid water contents under floods can facilitate heat transport. Therefore, we see higher thermal conductivities in the flooding scenarios with the largest increase with the mid-to-late floods and the least increase with the early floods (figure 4(c)).

Subsurface temperature change
We also looked at the differences in subsurface temperature between the reference simulation and the flooding simulations in the top 2 m soils (figure 5) and the deeper soils below the top 2 m (figure 6). As shown in figure 5, the flooding simulations shows differences relative to the reference simulation when the first flooding event occurs. In the first spring and summer, all flooding scenarios show a lower temperature near the top 0.3-0.5 m soil layer (the negative value and cool color) and higher temperature in the deeper soil (the positive value and warm color), compared with the reference case. The lower temperature is caused by the increased soil moisture that slows down the soil warming and increases the latent heat flux needed to thaw the frozen subsurface and evaporate soil water. This is evidenced by the latent heat flux in each scenario in figure 7. The increase of heat capacity for the wetter soil may also contribute to the lower temperature as the soil needs more heat to warm it up to the same temperature, compared with a dryer soil.
Although the surficial soil zone is cooler under floods, the increased thermal conductivity (see figure 4(c)) facilitates heat penetration to deeper soil during and after the flooding events. Therefore, we observe an increase in soil temperature below the top 0.3-0.5 m soil zone, compared with the reference case.
In the re-freezing stage in the first fall and winter seasons, the cases with floods show remarkably higher temperatures (+1.2 to +4.8 K) because of a higher heat capacity and higher latent heat for refreeze. In particular, the soil temperature is the highest with the mid-to-late floods (the red color in figure 5(b)) because of the highest soil temperature before the floods and the most downward heat transport.
In the second year, the high ice saturation due to the floods in the first year causes high soil moisture in the second spring, which continues to cool the surficial soil before the floods in the second year occur (e.g. the case with the mid-to-late floods in figure 5(b)). The cooling effect is observed to be more significant in the second year as the lower temperature extends deeper (the blue regions are darker). We only show the surficial soil temperature change in the first two years because the surficial soil temperature reaches  In contrast, the temperature variation in the deeper soil (figure 6) is different from the topsoil. The warming effect of floods is dominant. With the repeated flooding events each year, we see the extent of subsurface warming continuously deepens over time because the increased thermal conductivity in the top 2 m soil zone facilitates heat penetration to the deeper soil zone. In particular, the mid-to-late flood scenario shows the fastest warming as the most heat is transported to the deeper soil layer ( figure 6(b)).

ALT dynamics
Subsurface warming due to floods drives the dynamics of ALT, the thickness of seasonally unfrozen soil. Figure 8 shows the variation of the ALT in the first two flooding years. In this study, the maximum ALT can reach 0.7-0.8 m below the ground surface during the summertime. The mid-to-late flooding scenario in the first year causes the deepest ALT (the purple line) due to the highest heat penetration. Although the other two flooding scenarios show increased subsurface temperature (e.g. figures 5 and 6), the warming effect does not cause a phase change of water from ice to liquid. Therefore, we do not observe a deepening of the ALT (the yellow and blue lines) compared with the reference case (the red line). The ALT profile in the wintertime shows a delayed re-freezing process with the flood impact due to the need of extra latent heat to freeze the mostly saturated soil. However, in the second year, the flooding scenarios show shallower ALTs compared with the reference case due to the cumulative cooling effect of the floods. The cases with the mid-to-late floods and all floods present the largest retreat of ALT profiles in the second year. After the second flooding year, the ALT profile is very similar because the system reaches a dynamic equilibrium.

Impact of flooding on permafrost dynamics
Our model-based study provides the first investigation of the impact of floods on low-lying coastal permafrost hydro-thermal dynamics. Our modeling results show that coastal flooding can significantly increase soil saturation level, which leads to changes in subsurface hydro-thermal properties that affect heat transport, energy balance, and water balance. However, floods affect subsurface thermal dynamics differently with depth and time. The cooling effect of floods is stronger in the near-surface soil layers (e.g. the top 0.5 m soil in figure 5), where the hydrothermal dynamics are highly affected by the freezethaw and evaporation at the surface. This is consistent with some previous studies showing a shallower active layer or cooler surface layer with wetter soil (Clayton et al 2021, Magnússon et al 2022. In addition, we found that the warming effect of floods dominates the temperature change of deeper soils where heat can transport through the more conductive wet soil (below the 0.5 m soil zone in figures 5 and 6).
The flooding events occurring early in the year are more likely to have a smaller impact on permafrost thaw due to a cooler air and soil temperature and a higher water and energy loss due to evaporation. Whereas the mid-to-late summer floods are more likely to have a stronger influence on the hydrothermal dynamics of permafrost because a higher air and soil temperature in the middle or late summer provides more heat input to the soil zone, and the flooding water can offset soil water loss from evaporation in the summer season.
We found that the cumulative effect of floods over the years is important. On the one hand, the cooling effect of floods is stronger in the second year due to the carry-over cooling effect of the floods in the first year (e.g. the blue color in the second year is darker in figure 5). On the other hand, the repeated flooding over the years can result in continuous warming of the deeper soil (e.g. figure 6).
We also analyzed the observed subsurface temperature change at the 15 cm and 100 cm soil depths with its corresponding surface ponded water level at the Ikpikpuk delta site from 15 May to 5 November 2012 (figure 9). We see a clear decline of subsurface temperature at the 15 cm soil depth when floods occurred. This decline in temperature likely reflects the cooling effect of floods on the topsoil of the permafrost, which is consistent with our model simulations showing a cooling effect of floods concentrates on the top 0.5 m soil zone. The thermal response of the deeper soil zone (100 cm) to the floods is not detectable from this observational dataset. It is possible that some factors, such as a low thermal conductivity, surface vegetation coverage, lateral water fluxes, and high latent heat in topsoil, would limit the flooding effect on deeper soils. Thus, more information from the field observation is still needed to further confirm this flooding effect, such as the local climate condition/variability, surface-subsurface hydro-thermal properties, and energy fluxes.

Hydrological and biogeochemical implications
The permafrost dynamics due to floods have important hydrological and biogeochemical implications. The warmer subsurface due to floods may open new water flow paths, through which the connectivity between land and ocean/river is increased. For example, the increased ALT in the first year would provide more room for seawater intrusion, which may intensify permafrost thaw due to changes in water density, thermal conductivity, and heat capacity in salty soil water (Guimond et al 2021). With the decreased ALT in the second year due to the carry-over cooling effect of floods, we argue that the intruded seawater is more likely to be locked into the frozen soil, which would increase saltwater residence time and increase its impact on coastal vegetation and geochemical reactions.
Additionally, with the enhanced hydrologic connectivity, ancient microorganisms, chemical materials, and seawater may be re-introduced into the current environment (Miner et al 2021). In our simulation, although the soil zone below the active layer remains frozen, the temperature of the frozen soil continues to rise under floods, which would create a favorable condition for some ancient bacteria to become active (Niederberger et al 2010). The enhanced activities of these microorganisms would change the current permafrost environment by affecting the carbon and nitrogen cycles.

Limitation and future work
We used a physically-based model to simulate the hydro-thermal dynamics of permafrost under coastal flooding. This synthetic case reflects the response of permafrost to flooding in a real-world system, especially its water and heat transport in the vertical direction. Though previous studies showed that hydrothermal variations in the vertical direction should be more dominant in permafrost dynamics under flooding events (Magnússon et al 2022), a 3D modeling of the hydro-thermal interactions among hillslope, river, and coastal ocean processes will better capture water and heat fluxes from all sources. We used a smoothed climate forcing to exclude the impact of climate variabilities on the subsurface thermal dynamics and to focus more on the flooding effect. In the next step, we will include a more realistic climate forcing. For example, the temporal variations of snow, rain, and temperature are important in modulating permafrost temperature and soil moisture (Jafarov et al 2018). Late snowfall will provide more favorable conditions for further permafrost cooling, while early snow will lead to more subsurface heat storage. These will be explored in future studies. Different vegetation coverage (e.g. shrub or tundra) and organic matter may also have an important control on the energy balance as explored by Atchley et al (2015). These buffer layer effect should be included in future study to better predict the flooding effect on permafrost thaw. We will explore the salinity effect in our next step to understand how saltwater intrusion would affect permafrost thaw.

Conclusion
In this study, we investigated how coastal freshwater flooding would affect the hydro-thermal processes of permafrost by using a physically-based hydrothermal dynamic model, ATS. We simulated the changes in subsurface temperature, soil moisture, and ice content of a synthetic coastal permafrost landscape under three flooding scenarios, including the late spring and early summer floods, mid to late summer floods, and all floods throughout the spring and summer. We found that floods have an important impact on coastal permafrost dynamics. Flooding leads to cooler surficial soil due to the increase of latent heat of thawing and evaporation of the wetter soil. Conversely, floods facilitate heat penetration to the deeper soil zone with increased thermal conductivity in the wetter soil. The cooling effect of floods may be intensified in the second year because the increased ice content and soil moisture in the first year can continue affecting the subsurface temperature in the second year. Although the cooling effect may reduce the heat input and weaken the warming effect, the subsurface warming continues with repeated floods year after year. The timing of floods is a key factor controlling the flooding effect. The floods occurring in the middle or late summer are more likely to cause warmer permafrost and a deeper thaw depth, compared with the floods from the late spring and early summer. This model-based exploration of the flooding effect on permafrost landscapes helped improve our understanding of the coastal permafrost thaw mechanism, which will improve our assessment of the flooding risk to coastal landscapes.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https:// data.ess-dive.lbl.gov/datasets/doi:10.15485/1916476 (Jones 2023). This dataset includes the observed subsurface temperature and surface inundation level at Ikpikpuk delta.