Increasing non‐linearity of the storage‐discharge relationship in sub‐Arctic catchments

The Arctic is warming at an unprecedented rate. We hypothesis that as seasonally frozen soils thaw and recede in extent as a response to this warming, flow path diversity and thus hydrologic connectivity increases. This enhanced hydrologic connectivity then increases the non‐linearity of the storage‐discharge relationship in a catchment. The objective of this study is to test this hypothesis by quantifying trends and spatio‐temporal differences in the degree of linearity in the storage‐discharge relationships for 16 catchments within Northern Sweden from 1950 to 2018. We demonstrate a clear increase in non‐linearity of the storage‐discharge relationship over time for all catchments with 75% showing a statistically significant increase in non‐linearity. Spring has significantly more linear storage‐discharge relationships than summer for most catchments (75%) supporting the idea that seasonally frozen soils with a low degree of hydrological connectivity have a linear storage‐discharge relationship. For the period considered, spring also showed greater change in storage‐discharge relationship trends than summer signifying that changes in recessions are primarily occurring during the thawing period. Separate storage‐discharge analyses combined with preceding winter conditions demonstrated that especially cold winters with little snow yielded springs and summers with more linear storage‐discharge relationships. We show that streamflow recession analysis reflects ongoing hydrological change of an arctic landscape as well as offering new metrics for tracking change across arctic and sub‐arctic landscapes.

ity then increases the non-linearity of the storage-discharge relationship in a catchment. The objective of this study is to test this hypothesis by quantifying trends and spatio-temporal differences in the degree of linearity in the storage-discharge relationships for 16 catchments within Northern Sweden from 1950 to 2018. We demonstrate a clear increase in non-linearity of the storage-discharge relationship over time for all catchments with 75% showing a statistically significant increase in non-linearity. Spring has significantly more linear storage-discharge relationships than summer for most catchments (75%) supporting the idea that seasonally frozen soils with a low degree of hydrological connectivity have a linear storage-discharge relationship. For the period considered, spring also showed greater change in storagedischarge relationship trends than summer signifying that changes in recessions are primarily occurring during the thawing period. Separate storage-discharge analyses combined with preceding winter conditions demonstrated that especially cold winters with little snow yielded springs and summers with more linear storage-discharge relationships. We show that streamflow recession analysis reflects ongoing hydrological change of an arctic landscape as well as offering new metrics for tracking change across arctic and sub-arctic landscapes.

K E Y W O R D S
arctic hydrology, recession analysis, seasonally frozen soil, storage-discharge, thaw 1 | INTRODUCTION Arctic environments are warming at a faster rate than any other region on earth. This warming is causing concentrated, rapid hydrological changes such as increased freshwater discharge, earlier spring peak flows, increased precipitation and thawing permafrost (Walvoord & Kurylyk, 2016). Climate change influences almost every characteristic of an Arctic catchment: snow and rainfall precipitation distributions, vegetation coverage, groundwater storage, permafrost and thawing depth Hinzman, Yoshikawa, & Kane, 2005). Permafrost and seasonally frozen soils are of specific concern as sentinels of longterm change in the Arctic (Jorgenson et al., 2010). Permafrost is defined as soil, rock or other natural material that has been frozen for two or more consecutive years (van Everdingen & Association, 1998). This definition means that permafrost differs from soils that are frozen for less than 2 years or that thaw every summer, which are considered seasonally frozen soils. Permafrost has been reported to redirect the flow of groundwater (Hinzman, Johnson, Kane, Farris, & Light, 2000). In this context, the role of permafrost connecting and disconnecting groundwater flow and river flow is especially vulnerable to climate change.
Apart from permafrost, seasonally frozen soils will likely impact these connections as well. Understanding the effects of seasonally thawing soils on river discharge could provide valuable insights into long-term changes across transitions from permafrost to non-permafrost regions.
Moreover, as 55-60% of the land surface in the northern hemisphere is currently frozen during winter (Niu & Yang, 2006), with 23.9% of the exposed land area underlain with permafrost (Zhang, Barry, Knowles, Heginbottom, & Brown, 2008), understanding how seasonally frozen soils in permafrost affect the flow of water is crucial to predict hydrological responses to a changed climate.
Based on a synthesis of multiple arctic terrestrial studies examining arctic freshwater processes across different hydrophysiographical regions, Bring et al. (2016) concluded that warming-induced increases in the active layer thickness will likely lead to changes in the storage capacity of groundwater thereby altering river flow dynamics. Walvoord and Kurylyk (2016) reviewed multiple arctic water flow models and showed that while groundwater exchange and subsurface connectivity are predicted to increase locally, model results are inconclusive on how surface connectivity and river flow dynamics will change across spatial scales. Hinzman, Yoshikawa, and Kane (2005) suggest that evapotranspiration in the Arctic will increase as temperatures increase, leading to dryer soils and lower river flows. Prowse et al. (2015) put forward that the ecological transition from tundra to boreal is strongly hydrologically mediated. All of these studies show there is no single dominant permafrost thaw effect on the hydrologic cycle, but rather several interacting changes that exacerbate other changes to create complex responses that differ by region and are typically hard to predict. Predicting such complex and interacting changes in the Arctic is one of the key challenges in hydrology (Peel & Blöschl, 2011;Tetzlaff, Carey, McNamara, Laudon, & Soulsby, 2017). Therefore, observation-based approaches are crucial to reveal the ongoing change trajectories, help identify dominant processes, and support building reliable models that can project change trajectories into the future. Although still considered sparse, river discharge is the most commonly available hydrologic observation throughout the Arctic (Laudon & Sponseller, 2018) and contains integrated signals of catchment processes affected by Arctic warming (Bring et al., 2016). In this study, we aim to quantify long-term trends in how catchments release water (i.e., trends in catchment storage-discharge relationships) throughout Northern Sweden and evaluate if these trends can be attributed to changes in the spatial extent and timing of frozen soils.
Several studies have previously investigated long-term trends in storage-discharge relationships in the Arctic (Bogaart, Van Der Velde, Lyon, & Dekker, 2016;Brutsaert, 2008;Lyon et al., 2009;Lyon & Destouni, 2010;Sjöberg, Frampton, & Lyon, 2013;Watson, Kooi, & Bense, 2013). Typically, these studies assumed linear storagedischarge relationships during winter baseflow conditions and found that groundwater flows more easily (i.e., resistance to flow reduces) into rivers with more pronounced Arctic warming. Lyon et al. (2009) related such changes to an increased active aquifer depth of between 0.7 and 1.3 cm/year in Northern Sweden. Still, under non-base flow conditions (i.e., following a rainfall or snowmelt event) the relationship between river discharge and water storage is typically nonlinear (Brutsaert & Nieber, 1977;Kirchner, 2009;Wittenberg & Sivapalan, 1999), and cannot easily be related to active flow depths (Bense, Ferguson, & Kooi, 2009). However, under wetter conditions even more pronounced effects of frozen soils on river discharge are expected as seasonal frost hampers infiltration of melt and rainwater into the deeper groundwater, and impacts groundwater outflow into rivers (Ploum, Lyon, Teuling, Laudon, & van der Velde, 2019;Walvoord & Kurylyk, 2016). Frozen soils are found to seasonally alter the hydrological connectivity within catchments by redirecting water through shallow (above the frozen layer) and deep (below the frozen layer) flow paths towards rivers (Ploum et al., 2019). A change in hydrological connectivity typically alters the functional form of the storage-discharge relationship (i.e., degree of non-linearity) (Lyon & Destouni, 2010).
How is the hydrologic response of Arctic and sub-Arctic catchments impacted as the climate warms and the extent of frozen soils decreases? Following up on the study of Ploum et al. (2019), we anticipate that under thawed conditions deep groundwater, shallow groundwater and overland flow paths all contribute to discharge.
Contrarily, under frozen topsoil conditions, shallow flow paths dominate although deep groundwater can still contribute to a lesser extent. This increase in flow path diversity is assumed to occur under a warming climate over both the long-term (i.e., as permafrost thaws and summer active layer increases) and on a seasonal timescale (i.e., as seasonally frozen soil thaw starts earlier in the spring occurs).
Previous studies have shown that when catchments become wet and the diversity of flow paths increases, increasingly non-linear relationships between storage and discharge are observed (Brutsaert & Nieber, 1977).
Based on previous studies, our hypothesis is that as seasonally frozen soils thaw and recede in extent, flow path diversity and therefore hydrologic connectivity increases, which in turn increases the nonlinearity of the storage-discharge relationship. In this current study, our objective is to test this hypothesis by quantifying trends and spatio-temporal differences in storage-discharge relationships for 16 catchments within Northern Sweden from 1950 to 2018. Northern Sweden has had strong temperatures increases from the start of the 1800s to present day of almost 0.1 C/decade, with a cooling period occurring between 1940s and 1970s (Klingbjer & Moberg, 2003). Multiple proxies for seasonal and intra-annual differences in extent and depth of frozen soils are used to test whether the observed trends and patterns in storage-discharge relationships can be related to thawing soils.

| Recession analysis
Recession analysis is a well-established hydrologic method to examine storage-discharge relationships of catchments and offers the advantage of being relatively insensitive to meteorological forcing (Tallaksen, 1995).
Recession analysis relates the rate of decline of river discharge to the absolute river discharge. Under the assumptions of a unique relationship between storage and discharge and a closed water balance, recession curves quantify the storage-discharge relationship (Brutsaert, 2008;Kirchner, 2009).
Recession curves are determined by fitting a non-linear storagedischarge relationship to falling limbs of hydrographs during periods without precipitation and evapotranspiration. These are periods when changes in discharge reflect changes in catchment water storage (Brutsaert & Nieber, 1977;Kirchner, 2009;Ploum et al., 2019). Traditionally, the rate of discharge decline during the recession, namely where to changes in storage (Kirchner, 2009 The recession curve analysis technique has been applied to many regions to help improve understanding the relationship between groundwater and river discharge (Brauer, Teuling, Torfs, & Uijlenhoet, 2013;Dralle, Karst, Charalampous, Veenstra, & Thompson, 2017;Lyon et al., 2015) and as such can also be used to better understand the response of the storage-discharge relationship to climate change (Ploum et al., 2019;Shaw & Riha, 2012;Wrona et al., 2016).
Here, we extend Equation (1) to alleviate the constrains of no-rain and no-evapotranspiration conditions, which allows us to include and account for periods with small amounts of precipitation and evapotranspiration relative to discharge at the cost of a higher data requirement: where P is precipitation [mm/d] and E is evapotranspiration [mm/d].

| Conceptualizing storage-discharge relationships
Recession curve slopes can be conceptually interpreted as a measure of hydrologic connectivity as illustrated by a series of sand-filled buckets ( Figure 1). A catchment with one dominant flow path where discharge increases exponentially with storage behaves similar to a bucket with a single spigot representing a linear reservoir (β ≈ 1) ( Figure 1). Observed examples of such linear reservoirs are catchments with a deeply incised rivers flowing during baseflow conditions, a confined aquifer below permafrost, or shallow water flow above a frozen soil (Brutsaert & Hiyama, 2012;Lyon & Destouni, 2010;Ploum et al., 2019). In an unconfined aquifer, both the pressure as well as the saturated thickness control flow (Troch et al., 2013), which can be represented by a bucket with multiple evenly distributed and equally sized spigots (analogous to flow paths). Here, flow not only depends on the pressure exerted by storage on the spigots but also by the number of spigots. Such a sand-filled bucket behaves as a non-linear reservoir (specifically with β = 1.5). Finally, we can consider the case of a bucket with increasing density of spigots or increasing size of spigots towards the surface. Such a system will have β > 1.5 as has been seen in many natural systems (e.g., Kirchner (2009) 2013)). In these systems, as catchments become wetter, lower order streams are activated and start to contribute to the catchment's discharge. Thusly, each spigot from the bottom upward could be interpreted as a lower stream order with a larger area starting to contribute. A special case is when the resistance of the spigots decreases exponentially towards the surface yielding an exponential reservoir (β = 2) as is frequently observed in relatively flat catchments (e.g., Bogaart et al. (2016) and Brauer et al. (2013)). Reservoirs where the resistance declines hyperbolically towards the surface yield β > 2 (Brutsaert & Nieber, 1977;Kirchner, 2009;Troch et al., 2013).
With the understanding that potential flow paths are disrupted by frozen soils, we use recession curve analyses to understand how declining permafrost extent and shifts in extent of seasonally frozen soils may have affected river flow and specifically the non-linearity of the storage-discharge relationship (e.g., recession curve slope). Therefore, we set out to identify temporal and seasonal changes in recession curve slopes (β) which we compare to expected changes in recession curve slopes caused by a declining extent of frozen soils based on the conceptualizations in Figure 1.

| Study sites
Our study sites are situated in Northern Sweden. The 16 catchments were chosen because they (a) have presumed permafrost presence in the past and present Brown et al., 1997;Gisnås et al., 2017;Zhang et al., 1999), (b) have widespread occurrence of seasonally frozen soils and (c) have no current or past known obstructions of the waterways by human intervention (Sjöberg et al., 2013). Land cover in Northern Sweden is mainly forests, which are used for logging. Since 1903 there has been strict forest management across Northern Sweden to insure restoration of the forests (Anderberg, 1991), indicating no dramatic change in land cover over the past century.

| Discharge, rainfall, temperature and snow depth data
Observed discharge and meteorological data were obtained from the Swedish Meteorological and Hydrological Institute (SMHI), (SHMI, 2018) for the stations listed in the supplementary information (Table S1). These data are derived from public domain online repositories and range from 67 to 32 years in length with an average of 46 years. Gauträsk has a dataset gap of 6 years and Kaalasjärvi has two dataset gaps of 10 and 3 years. For metrological data, daily measurements of precipitation, maximum and minimum temperatures and snow depth were used. Maximum and minimum temperatures were used to roughly estimate daily potential evapotranspiration with the Priestley-Taylor approach (Priestley & Taylor, 1972). For catchments where discharge data are collected separately from meteorological data, the geographically closest meteorological station was used (see the supplementary (Table S1) for the names of stations used for each catchment). The distance between meteorological and discharge stations was on average 14 km and the maximum did not exceed 45 km. No correction was done for elevation differences between meteorological stations and discharge stations.
) was irregularly documented in the catchments by SMHI. For periods when direct observations were not available or were very sparse, the snow depth was roughly approximated by using the recorded data in combination with sums of winter precipitation during freezing conditions (i.e., 0 C and below).

| Recession curve slope (β)
To determine the degree of non-linearity of the storage-discharge relationship (β), we selected hydrograph recession observations when Q was larger than 0.5 mm/d in order (1) to focus on the wetter periods when we expect a larger effect of frozen soil layers and (2) to exclude low flows with typically a large effect of evaporation and a large measurement uncertainty. We also added a condition that hydrograph observations would only be included when both precipitation and evapotranspiration were less than half of Q. Data were excluded during the first 3 days after a precipitation event to avoid errors in monitoring the timing and extent of precipitation that could influence the catchment response. β is determined as the slope of a linear line fitted directly to the selected data points in a plot in which the x-axis corresponds to log(Q) and the y-axis to the full left side of Equation (2).

| Season definitions
We analysed spring and summer recessions separately. The onset of spring was defined based on a degree day methodology approach proposed by Ploum et al. (2019). Mean daily temperatures were summed with cumulative sums below zero reset to zero. The first day the cumulative summed temperature exceeded 15 degree days was

| Analyses approach
To identify and quantify the potential effects warming and a subsequent decline in frozen soil extent may have had on recessions, we performed the following four analyses that connect to four hypotheses/expectations: because it is relatively insensitive to outliers and gives a magnitude of the trend (Figure 3b).
During spring periods, we expect that the hydrologic effects of frozen ground is stronger than during summer periods. Therefore, we expect that spring periods have a lower recession curve slope (more linear storage-discharge relationship) than summer periods.
Recessions were grouped into spring and summer recessions for each catchment. The two-sample z-test (Cohen, Cohen, West, & Aiken, 2003) was used to test whether the recession curve slopes were significantly different between both groups.
3. Temporal trends in spring and summer recession curve slopes. The aim was to identify which season contributed most to the observed yearly trends (i.e., Analysis 1 above). If a declining extent of frozen soils is the dominant driver for a change in recession curve slopes, we expect spring to show a greater change than summer.
This analysis followed the same method as for the trend over time analysis described in Analysis 1 (above) but was applied separately for spring and summer periods (Figure 3b).
4. Frozen soil influence on recession curve slopes. We expect recessions following winters with deeply frozen soil to have a more linear recession curve slope than those following shallow frozen soil winters.
The depth of seasonal freezing depends on winter air temperatures and the thickness of the insulating snow cover (Zhang, 2005). As such, we considered three proxies for frozen soil depth: average winter temperature, winter snow depth and a combination of both. The soil potentially freezes deeper during cold winter. Therefore, it potentially takes longer for frozen soil to thaw during spring after a cold winter compared to springs after warmer winters (Lawrence & Slater, 2010).
Hence, recession curve slopes during springs following cold winters are expected to be more linear compared to the warm winters. We split winters into two equally sized groups: cold winters and warm winters, based on the average winter temperatures (Figure 3a). We then used the two-sample z-test to test for significant differences in recession curve slope between both groups. We performed the same analysis for snow depth. Winters with shallow snow are expected to have more soil frost and therefore we expect that springs following shallow snow winters have a more linear recession curve slope. Winters were split into two equally sized groups based on the maximum winter snow depth and again the two-sample z-test was used to test for significant differences between both groups. As a last proxy for frozen soils we combined winter temperature and snow depth recognizing that soils freeze during periods when both snow depth and temperatures are low. We expect that recession curve slopes after such winters are more linear. The insulation effect of snow was found to peak at about 40 cm (Zhang, 2005). To isolate this insulating effect, we calculated the cumulative winter temperature for the days with a snow depth below 20 cm, which can be considered a shallow snow pack. The years are divided into two groups to create "shallow snow: cold winter" years and "shallow-snow: warm winter" years ( Figure 3a). We again used the two-sample z-test to test for significant differences in recession curve slope between both groups (Figure 3d).

| Spatial visualization
To visualize the spatial pattern of changing recession curve slopes we plotted the trend magnitude of change in summer, spring and year-round recession curve slopes as an arrow at the catchment outlet (example in Figure 3c). Upward arrows indicate an increase in non-linearity with time and downward arrows a decrease in nonlinearity with time. Similarly, we plotted the differences in recession curve slopes between warm and cold winter groups, thick and shallow snow depth groups, and "cold-winter-during-shallow-snow" and "warm-winter-during-shallow-snow" groups as an arrow (example in Figure 3e)   Note: For overall and seasonal trends, if the trend is significant (p < .05) for Theil Sen, it will be denoted by an " ‡," if it is significant (p < .05) for Mann Kendall, then it will be denoted as " †." The greatest change of trend between spring and summer is bolded, only if both trends are significant. For the z-test comparing spring to summer, the more non-linear recession curve slope is bolded, only when the difference is significant. The catchments are ordered from north to south.

| Spring and summer difference
Our second hypothesis (Analysis #2) that spring recessions are more linear than summer recessions was also substantiated. Twelve out of sixteen catchments had more linear spring storage-discharge relationships and more non-linear summer storage-discharge relationships ( Table 2). The catchments with significant results are indicated with thick purple arrows in Figure 5b. Mertajärvi, Junosuando, Stenudden and Tängvattnet were the catchments without a significant difference between summer and spring periods.
The Mann Kendall test yielded six catchments with a significant trend in the recession curve slope for the summer (Analysis #3): Mertajärvi, Kaalasjärvi, Stenudden, Killingi, Niavve and Tängvattnet (

| Attribution to winter conditions
Twelve of sixteen catchments had recession curve slopes closer to linearity for colder winters than for warmer winters as shown in Table 3. Ten of those twelve catchments had a significant difference between cold and warm winters. None showed significant higher non-linearity in cold winters compared to warm winters. These results follow our hypothesis (Analysis #4) that years following warm winters exhibit more non-linear storage-discharge relationships. Our results were inconclusive, however in regards to differences in recession curve slopes between thick and shallow snow cover: six catchments had a significant higher recession curve slope during shallow snow cover, while five catchments had a significant lower recession curve slope during shallow snow cover. Five catchments had no significant difference that could be related to snow cover. There was geographical clustering of the significant catchments ( Because many of the warmer winters occurred within recent years, it is possible that our results are due to a general increase in temperatures rather than winter temperature differences between individual years. Therefore, we wanted to test if winter temperature also impacted the recession curve slopes for the period leading up to 1990, when there was no clear trend in recessions-curve slope for most catchments (Figure 4). In that period, for the four catchments with the longest observational records, (Mertajärvi, Karats, Niavve and Tängvattnet), we found no significant difference for any of the analyses for any catchment. We should mention that there are less data if we limit the analyses to pre-1990, which increases uncertainty and decreases the probability of significant differences.  (Figure 4). We find recession curve slopes as low as 0.7 and as high as 2.6 enveloping the entire range of slopes found by theoretical consideration (Troch et al., 2013). Previous studies have indicated that catchments analysed with different regression methods will result in different recession curve slope values (Brauer et al., 2013;Karlsen et al., 2019;Kirchner, 2009;Ploum et al., 2019;Sjöberg et al., 2013;Troch et al., 2013;Van Der Velde, Lyon, & Destouni, 2013). However, the direction of differences between catchments and between periods of the same catchment using the same method are expected to be comparable (Shaw & Riha, 2012).
Within our datasets, there has been no known physiographic changes, such as topography changes (Silfverstrand, 2019), and SHMI continually checks for errors in discharge data to insure accurate observations. Therefore, the observed changes in recession curve slopes come from other aspects, such as land cover change, or thawing permafrost. If soil frost thaw is truly causing a change in recession curve slope, it is mainly by the increasing thickness of the active layer as the soil thaws. This increasing active layer thickness causes a larger diversity in flow paths contributing to stream discharge during a hydrograph recession as the landscape moves from wet to dry conditions.
In addition to significant differences in seasonal recessions found by Groundwater flow through thawing soils is a complex process.
Arctic catchments have been documented to be changing over a long period of time, with streamflow and precipitation increasing, land cover shifts, changes in soils, decline in permafrost and seasonally frozen soil depth and changes in the snow cover extent and timing (Bring et al., 2016;Hirota et al., 2006;Prowse et al., 2015;Wrona et al., 2016). We provide corroborating evidence that recession curve slopes are increasing in Northern Sweden. This means that storagedischarge relationships are becoming increasingly non-linear. Under low to intermediate wetness conditions, water is stored more effectively within the catchments while under wet conditions water is released faster. In times when the water flow paths are filled, usually during snowmelt or periods of continued precipitation when the landscape is by-and-large saturated, overland flow will contribute to discharge along with the usual groundwater flow, creating potentially even higher discharge peaks then under periods with extensive permafrost spatial extents. More non-linear storage-discharge relationships likely also make river peak flows more unpredictable as uncertainties in precipitation and/or snowmelt inputs propagate more strongly into discharge under such conditions. It is clear from these results that hydrological models which aim to predict changes in artic river discharges caused by climate change cannot rely on constant storage-discharge relationships, but need to account for climate warming effects on the physical catchment properties that underlie storage-discharge relationships. Krycklan. With 15 more catchments, we also find storage-discharge relationships with consistently higher recession curve slopes (higher non-linearity) in summer than in spring (Table 2). We interpret this robust finding in terms of flow paths and storage. The subsurface volume available for water storage within a catchment increases from spring to summer due to thawing soils. The more non-linear storagedischarge relationship in summer compared to spring implies that when conditions are wet and storages full, a more immediate and strong response of discharge to additional rainfall is expected in summer compared to spring. However, due to the large snowmelt volume discharges in spring tend to be higher. In line with findings of Karlsen et al. (2019), it is apparent that spring and summer recession are different.

| Trends in spring and summer recession curve slope
Spring recession curve slopes had stronger trends compared to summer. However, our results for spring and summer trends are not completely straightforward. Although trend analysis with year-round data shows clear increases in non-linearity of the storage-discharge relationship, separate trend analyses for spring and summer recessions do not clearly yield one dominant period that controls the observed yearly trend in recessions. For 12 catchments, summer has the higher recession curve slope (i.e., more non-linear) (Analysis #2), but over time (Analysis #3), we see that spring is undergoing a greater change than summer (Table 2). Of the six catchments with significant differences, five have higher trends in spring. Frampton, Painter, Lyon, and Destouni (2011) suggested that thawing soils lead to increasing flow path diversity, which in turn will decrease seasonal variability in water flow. This can explain why the summer recessions observed in this study do not have strong trends as seasonally frozen soils have already thawed in spring and are no longer affect discharge during summer. However, when permafrost is omnipresent within the catchment and permafrost is slowly disappearing, summer recessions may be affected more strongly than spring recession when soils are still primarily underlain with a frozen layer.

| Attribution to winter conditions
For the region in this study, there has been increasing winter temperatures since the start of 1900 (Luterbacher, Dietrich, Xoplaki, Grosjean, & Wanner, 2004). With no exceptions, all 10 catchments with significant differences between cold and warm winters have a higher recession curve slope following warm winters than cold winters. Therefore, it can be concluded that there is a significant increase in non-linearity of recession curve slopes for warmer winters relative to colder winters for these sub-arctic catchments (Figure 5b). Our hypothesis was that this pattern is because warmer winters have a shallower frozen soil layer, which thaws quicker than after colder winters with a deeper frozen soil layer. However, we could not confirm this when examining data before 1990 for the four catchments with the longest records. St. Jacques and Sauchyn (2009) also found evidence of winter air temperatures affecting streamflow. They suggested that this effect is caused by thawing soils that increase infiltration and subsequent subsurface flow of water to the stream. Payn, Gooseff, McGlynn, Bencala, and Wondzell (2012) found that the correlation between subsurface flow paths and surface attributes decreased during recession because subsurface structures gain more influence on the subsurface flow paths during low flows. Subsurface structures can be many things, including permafrost, the geologic features of the catchment, and seasonally frozen soil. Moreover, these subsurface structures can be dynamic and indirectly related to surface features. Snow, for example, is an important and variable surface feature for impacting the dynamics of frost depth as it insulates the ground from heat loss (Hirota et al., 2006). Catchment-scale seasonal soil freezing is a complex process that cannot easily be captured by just a simple snow depth assumption. Eleven of the catchments investigated here showed significantly different recession curve slopes between thick and shallow winter snow packs, but there was no clear pattern. Out of 11 catchments with significant differences in thick and shallow snow packs six catchments show the expected higher recession curve slope during thick snow depths.
Shallow snow depth (here, depths below 20 cm) periods and winter air temperatures were combined to identify years with higher than average (and lower than average) frozen soil depth. Research shows soils to freeze deeper when cold temperatures occur during periods with little snow (Hardy et al., 2001;Osterkamp, 2007). Ten catchments had significant differences, with nine catchments having higher recession curve slopes for shallow snow warm winters (Table 2). This result confirms our expectation that frozen ground decreases recession curve slopes. Using snow depth in combination with winter air temperatures to group years based on frozen soil depth yielded much clearer results than grouping based on snow depth only. Kohler, Brandt, Johansson, and Callaghan (2006)

modelled snow depth in
Abisko and concluded increasing snow depth averages over the last century. Åkerman and Johansson (2008) also found that five of their nine catchments close to Abisko also had increasing snow depths.
In fact, for much of the Arctic, a thicker snow pack is becoming more common while winter temperatures are increasing (Lind & Kjellström, 2008). Our results suggest that this direction of climate change likely causes more non-linear storage discharge relationship throughout the arctic.
We provide evidence that recession curve slopes depend on preceding winter conditions. These winter conditions control when flow paths start to flow and the amount of flow paths available. As recent winters globally have been some of the hottest on record (LeComte, 2020), we wanted to determine if similar significant results can be found in the first half of our datasets, when recession curve slopes were not yet clearly increasing. The four pre-1990 catchments showed no significant difference for any analysis. If these pre-1990 analyses had been significant we could suggest that our soil frost related proxies directly control between year variability in recession curve slope. However, we did not find such direct controls on variability, but we did find clear long-term controls. Therefore, it becomes more likely that the observed changes in recession curves slopes are a result of the catchments slowly adapting to climatic changes during the last decades. The limited amount of data pre-1990 may also be an important reason for no significant difference during that period.

| Effects of frozen soil and permafrost on recessions: A conceptual model
Based on our results and results of previous studies we summarized our finding into a conceptual model ( Figure 6). We found approximately linear storage-discharge relationships during spring for all catchments. Moving into summer, these storage-discharge relationships become more non-linear. A similar transition was found with the storage-discharge relationship trend over time. When permafrost thaws or the extent and depth of seasonally frozen soils reduces both the spring and summer storage-discharge relationship become more non-linear. Based on our results, spring recessions change more than summer recessions. Although conceptually straightforward, it remains a challenge to confirm this conceptual model with a physically based model. First steps have been made in this direction by (Frampton et al., 2011;Sjöberg et al., 2016;Walvoord, Voss, & Wellman, 2012). Seasonally frozen soils along with decreasing amounts of permafrost influence groundwater flow in Arctic catchments ( Figure 6).
Storage-discharge relationships in the catchments considered in this current study are becoming increasingly non-linear, though the degree of change likely depends on the specific catchment's topography, differences in bedrock and surficial geology and current continuity of permafrost presence. We hypothesized that recession curve slopes are partly controlled by frozen ground and in turn react to thawing ground. Our results support this hypothesis, but we cannot exclude that other changes within the catchments could have similar effects on recessions. This study did not examine, for example, the potential effect of soil moisture on the recession curve slope. Other studies are suggesting Arctic catchments are becoming wetter, which may also change the storage-discharge relationship, and consecutively, the recession curve slope (Raynolds & Walker, 2016;Rowland et al., 2010). Changes in the recession curve slope could also be caused by land cover change. As vegetation migrates further north into the Arctic, new flora and soil biota will have different water requirements and effects on soil structure, which influence water flowing to the rivers (Costa, Botta, & Cardille, 2003).
While we set out to answer how permafrost and seasonally frozen soil thaw affect recession curve slopes, we must acknowledge that the extent of permafrost in Sweden is mostly discontinuous or sporadic. Although continuous permafrost has been present in Sweden, the extent and timing appears uncertain as permafrost detection methods have been limited in the past. (Gisnås et al., 2017;Kullman, 1989;Lagerbäck & Rodhe, 1985;Sjöberg et al., 2013). The remaining permafrost in Sweden is in mountainous regions at high elevation. Gruber and Haeberli (2009) state that for mountainous regions, permafrost is impacted by slope of a catchment, topography, elevation and strong winds dictating snow cover conditions. Follow up research would benefit from looking similar increases in the non-linearity of the storage discharge relationships in flatter permafrost regions where permafrost is still more continuous.

| CONCLUSION
We show that catchments in Northern Sweden have been undergoing a significant change in their discharge reaction to rainfall and snowmelt events since 1950 and especially since 1990. The storage-discharge relationships of thirteen out of sixteen investigated catchments has become more non-linear (i.e., mostly linear recessions (β = 0.8-1.3) in the period 1950-1970 increasing more non-linear recessions (β = 1.3-2.2) during the period 2010-2018) with a greater change in spring than summer. This means these catchments are better able to store their water under low to medium wetness conditions but release their water more quickly under wet conditions, making peak river discharge in the Arctic likely more unpredictable. In addition, we show that frozen soil depth, approximated by snow depth and air temperatures, affects storage-discharge relationships, with nine of the sixteen catchments exhibiting more non-linear relationships during years with shallow frozen soil depth. We hypothesized that these changes are primarily caused by disappearing permafrost and a reduced thickness of seasonal soil frost. Although our data-analysis tests confirm parts of this hypothesis, without solid knowledge of the extent of permafrost, F I G U R E 6 A diagram showing how the change in seasonally frozen soil can potentially affect the flow paths/conductivity of the soil and influence the recession curve. The light green represents spring and shows spring recession while the dark green represents summer. The active layer (light blue) increases as the frozen soils thaw in spring. An accumulation of the organic layer (brown) includes an increasing amount of ecology. The white arrows are representative of the increasing number of flow paths depth of winter frozen soils and summer active layer depth, this link remains speculative. It is likely that other landscape changes such as vegetation change, soil organic matter and soil biota changes also strongly affect water flow paths thusly contributing to the observed changes in storage-discharge relationships ( Figure 6). Our results clearly demonstrate that predicting arctic river discharges in a warming climate cannot rely on models that assume fixed storage-discharge relationships, but requires models that describe how warming affects the physical properties of catchments that underlie the storagedischarge relationships.
The main contribution of this study is that we established hydrological change trajectories of the storage-discharge relationships for terrestrial Northern Sweden. Because of the complexity of the changing Artic in which climate, vegetation, soils, ice, and landscape form (e.g., river systems) interact, the future of the Artic is very difficult to predict. Understanding and predicting the effect of further Arctic warming starts with establishing such ongoing change trajectories and use process-based models to reproduce and extrapolate these trajectories into the future.

ACKNOWLEDGEMENTS
This work is part of the research programme Netherlands Polar Programme with project number ALWPP.2016.014, which is financed by the Dutch Research Council (NWO). We thank Claudia Brauer and an anonymous reviewer for their valuable comments which improved our manuscript.

DATA AVAILABILITY STATEMENT
The discharge data that supports the findings of this study were obtained from the Swedish Meteorological and Hydrological Institute (SMHI), at Vattenwebb. URL: (https://vattenwebb.smhi.se/station/#), the list of catchment used can be found in the supplement. Meteorological data were taken from (SMHI), from the URL: (https:// opendata-download-metobs.smhi.se/explore/?parameter=0#). These data were derived from resources available in the public domain.