The LRET phenomenon was widely documented in other cold regions (Fig. 4), including, but not limited to, the headwater of Yellow River (Yang et al., 2019) and a small headwater catchment at the Cape Bounty Arctic Watershed Observatory, Melville Island, Nunavut, Canada (Lafrenière and Lamoureux, 2019). For example, at the headwater of Yellow River on 8–9 July 2014, there was a 21.9 mm rainfall event, with a temperature of 6.5 ∘C but little 1.5 m3 s-1 runoff. On 21–23 July 2014, there was a 27.4 mm rainfall event with temperature of 7.2 ∘C, but only 5.1 m3 s-1 runoff. Lafrenière and Lamoureux (2019) found that the undisturbed frozen soil at the Cape Bounty Arctic Watershed Observatory had little runoff generation in the early thawing season. But after the frozen soil was disturbed, the runoff response to rainfall event was much larger. Hence, this paired catchment study illustrated that frozen soil played a key role in causing the LRET phenomenon.

In Fig. 5, we plot the groundwater recession on semi-logarithmic scale. In the beginning of freezing season, baseflow presented a clear linear recession and was able to be fitted by setting the recession coefficient (Ks) as 80 d. However, interestingly, simultaneously with the LRET phenomenon, we observed a clear discontinuous baseflow recession in the Hulu catchment (Fig. 5). The baseflow bent down, and Ks became 60 d at the end of the recession period. This DBR phenomenon informed us that the groundwater system was disturbed. We also noted the spikes during the thawing in Fig. 5, which means that groundwater was suddenly released. To our best knowledge, these discontinuous baseflow recession (DBR) phenomena are a new observation for mountainous frozen soil hydrology.

We also plot the variation in groundwater depth of four wells at the WW01 site from 2016 to 2019 (Figs. 1, 11). The wells of 5, 10, and 15 m only had liquid water in thawing seasons and gradually went dry in recession periods. The water level of the 25 m well was decreasing in the entire frozen seasons but in a discontinuous way. From the observed groundwater depth, the groundwater level decreases faster at beginning. And after the groundwater level dropped below around 17 m, the decrease in the groundwater level became slower. The turning point from Ks=80 d to Ks=60 d occurred simultaneously, while the groundwater level went down to 17 m (Figs. 5, 11). The bending down discontinuous baseflow recession and slower decrease of groundwater level indicated that there was a disturbance that reduced the groundwater discharge and lead to a slower decrease in the groundwater level.

Frozen soil process is able to disturb the groundwater system by freezing the liquid groundwater to reduce groundwater storage and leading to the DBR. But the DBR could also be caused by many other reasons, for instance soil evaporation, root tapping, capillary rise, impermeable layer, and heterogenous hydraulic conductivities in different landscapes (riparian area and hillslope). Since the DBR phenomenon started from the middle of the freezing period and lasted until the end of frozen season, in which time the evaporation, root tapping, and capillary rise were very inactive even totally stopped, this allowed us to exclude these impacts. The impermeable layer and heterogenous hydraulic conductivities are both able to result in discontinuous recession at the small scale.

To further understand the DBR phenomenon, we collected larger-scale runoff data in this region, including the Zhamashike (5526 km2) and Qilian (2924 km2), which are also the subbasins of the upper Heihe. The permafrost and seasonal frozen soil map of the upper Heihe River basin shows that the Zhamashike subbasin has 74 % permafrost and 26 % seasonal frozen soil, which is similar to the Hulu catchment while the Qilian subbasin has much less permafrost area (38 %) and is mostly covered by seasonal frozen soil (62 %; Fig. 1).

Interestingly, when plotting the hydrographs of these two subbasins on a logarithmic scale, we can clearly see that, in the permafrost-dominated Zhamashike subbasin, discontinuous recessions occurred, with Ks=60 d in the beginning and Ks=20 d at the end of the recession period. This DBR phenomenon is the same as found in the Hulu catchment, although the Zhamashike and Hulu catchment have quite different scales (5526 vs. 23.1 km2; Chen et al., 2018; Gao et al., 2014). Discontinuous baseflow recession happened almost every year at the Zhamashike station, and we only highlight the hydrograph in 1974 to demonstrate this phenomenon in Fig. 6. On the other hand, while being of similar size as the Zhamashike, the Qilian subbasin (2924 km2), which is mostly covered by seasonal frozen soil, only has one continuous recession, with Ks=60 d. The results from these two paired catchments provided good reasons to interpret the DBR phenomenon in the Hulu catchment as the result of frozen soil.

The FLEX-Topo model classified the entire Hulu catchment into four landscapes, i.e., glaciers, alpine desert, vegetation hillslope, and riparian zone. The Hulu catchment (from 2960 to 4820 m) was classified into 37 elevation bands, with 50 m intervals (Fig. 2). Combining the four landscapes and 37 elevation bands, we had 37 × 4 = 148 hydrological response units (HRUs). The structure of FLEX-Topo model consisted of four parallel components representing the distinct hydrological function of different landscape elements (Savenije, 2010; Gao et al., 2014; Gharari et al., 2014; Gao et al., 2016). And the corresponding discharge of all elements was subsequently aggregated to obtain the simulated runoff.

We interpolated the precipitation (P) and temperature (T) based on elevation bands from in situ observation (2980 m) to each elevation band. The precipitation increasing rate was set as 4.2 %/100 m and the temperature lapse rate as -0.68 ∘C/100 m, based on field measurements (Han et al., 2013). Snowfall (Ps) or rainfall (Pl) was separated by air temperature, with the threshold temperature as 0 ∘C (Gao et al., 2020).

FLEX-Topo is a semi-distributed conceptual bucket model (Savenije, 2010; Gao et al., 2014), with three modules, i.e., the snow and glacier module, the rainfall–runoff module, and the groundwater module. The water balance and constitutive equations can be found in Table 1. The model parameters and their prior ranges for calibration are listed in Table 2.

The temperature index method was employed to simulate snow and glacier melting (Gao et al., 2017, 2020; He et al., 2021). We used a snow reservoir (Sw) to account for the snow accumulating, melting (Mw), and water balance (Eq. 4). The snow degree day factor (Fdd) needs to be calibrated. For glaciers, we assumed its area was constant in our simulation (from 2011 to 2014). Glacier melting (Mg) was also calculated by the temperature index method (Eq. 7) but with a different degree day factor. With the same air temperature, the glacier has less albedo than snow cover, thus with a larger amount of melting. The glacier degree factor was obtained by multiplying the snow degree day factor (Fdd) with a correct factor Cg (Eq. 8; Gao et al., 2020).

There are two reservoirs to simulate rainfall–runoff process, including the root zone reservoir (Su; Eq. 10) and fast response reservoir (Sf; Eq. 17). To account for the different rainfall–runoff processes in different landscapes and simultaneously avoid over-parameterization, we kept the same model structure for vegetation hillslope, riparian zone, and alpine desert (Eqs. 11, 12) but gave different root zone storage capacity (Sumax) values, i.e., Sumax_R for riparian zone, Sumax_D for cold desert, and Sumax_V for hillslope vegetation. For vegetation hillslope, a larger prior range was constrained for the root zone storage capacity (Sumax_V), which means more water is required to fill in its storage capacity to meet its water deficit, which is evidenced by previous studies in this region (Gao et al., 2014). For alpine desert, due to its sparse vegetation cover, we constrained a shallower root zone storage capacity (Sumax_D). For the riparian area, due to the location where is prone to be saturated, we also constrained a shallower root zone storage capacity (Sumax_R). The initial states (beginning of 2011) of the reservoirs were obtained from the end values (end of 2014) of the simulation, which is a normal procedure in modeling practice.

Other parameters in the rainfall–runoff module (Eqs. 11–18; Table 1) include the threshold value controlling evaporation (Ce), the shape parameter of the root zone reservoir (β), the splitter (D) separating the generated runoff (Ru) from the root zone reservoir (Su) to the fast response reservoir, the recession parameter of faster reservoir (Kf), and the lag time from rainfall event to peak flow (TlagF). We set D as 0.2 from the isotope study (Ma et al., 2021) and other parameters were calibrated, with prior ranges (Table 2) based on previous studies (Gao et al., 2014, 2020).

The baseflow (Qs) is generated from groundwater recession. The groundwater was simulated by a linear reservoir (Ss), described in Sect. 3.2 and Eq. (19). We set the prior range for s recession coefficient of the baseflow reservoir (Ks) as 10–100 d. To estimate the impacts of frozen groundwater on hydrological processes, we set the groundwater in different landscapes as parallel. But we analyzed the groundwater level as an integrated system because the groundwater system is connected, and this affects the groundwater level. Since the subpermafrost groundwater is even deeper than 20 m in the Hulu catchment and almost disconnected to streamflow, we only model the supra-permafrost groundwater. 4Qs=Ss/Ks.

The FLEX-Topo-FS model employed the Stefan equation (Eq. 20) to provide an approximate solution to estimate freeze/thaw depth (Fig. 9). The Stefan equation is a temperature-index-based freeze–thaw algorithm which assumes the sensible heat is negligible in soil freeze–thaw simulation (Xie and Gough, 2013). The form of Stefan equation is written as follows: 5ε=2⋅86400⋅k⋅FQL0.5=2⋅86400⋅k⋅FL⋅ω⋅ρ0.5, where ε is the freeze/thaw depth, k is the thermal conductivity (W (m K)-1) of the soil, and F is the surface freeze–thaw index. The freeze index (∘ of degree days) is the accumulated negative ground temperature while freezing, and the thaw index (∘ of degree days) is the accumulated positive ground temperature while thawing. QL (J m-3) is the volumetric latent heat of soil. QL=L⋅ω⋅ρ, where L is the latent heat of the fusion of ice (3.35×105 J kg-1). ω is the water content, as a decimal fraction of the dry soil weight, and ρ is the bulk density of the soil (kg m-3).

We set the thermal conductivity as k=2 W (m K)-1, the water content as a decimal fraction of the dry soil weight ω=0.12, and the bulk density of the soil as ρ=1000 kg m-3. Since the Stefan equation requires ground surface temperature, which is difficult to measure and often lacks data, we used a multiplier to translate the air temperature to ground temperature. The multiplier during freezing was set as 0.6, and during thawing, we assumed the ground surface temperature was the same as the air temperature (Gisnås et al., 2016).

In this model, we did not consider the impacts of snow cover on soil freeze–thaw because the snow effects were complicated in the Hulu catchment. First, this is because precipitation in the Hulu catchment mostly happens in summer as rainfall, and snow depth in the Hulu catchment was less than 10 mm in most areas most of the time. Second, the snow cover has contrary effects on ground temperature. Snow cover as an isolation layer increased ground temperature in winter. But, simultaneously, snow cover also increased albedo, which decreased the net radiation and decreased ground temperature. To avoid over-parameterization, we did not consider snow effect in the Stefan equation.

In this study, the Stefan equation was driven by distributed air temperature, which allowed us to simulate the distributed soil freeze–thaw processes. With the distributed soil freeze index and thaw index, we can also estimate the lower limit of permafrost at which elevation the freeze index equals the thaw index in mountainous regions. Field surveys on the lower limit of permafrost (Wang et al., 2016) can provide another strong confirmation of our simulated soil freeze–thaw process, except for the spot-scale freeze/thaw depth.

The distributed freeze–thaw status calculated by the FLEX-Topo-FS model allowed us to simulate the impacts of frozen soil on soil and groundwater systems, their connectivity, and, eventually, catchment runoff.

In freezing and frozen seasons, precipitation was in the phase of snowfall, and topsoil was frozen, thus without surface runoff. During this period, runoff is only contributed from the groundwater discharge of the supra-permafrost layer (Qs). There is no runoff generation (Ru) from the root zone reservoir to the response routine (Ss and Sf) in this period. In the conceptual model, we set Ru=0 (Eq. 11). In freezing season, when frozen depth was less than 3 m (the depth of active layer in this region), the entire groundwater volume in the supra-permafrost layer was still connected and could be simulated by linear groundwater reservoir (Ss). Once the frozen depth of certain elevation zone is larger than 3 m, the groundwater in that elevation zone was frozen (Fs). In the FLEX-Topo-FS model, we reduced the groundwater storage (Ss) to 10 % of its total storage to simulate its frozen status (Eqs. 21, 22). This amount of frozen water (Fs, 90 % of groundwater storage when frozen and marked as Ss(t̃)) was held in the groundwater system as frozen soil (Eq. 22) but did not disappear. We set 90 % as frozen, rather than 100 %, because there is still unfrozen liquid water in frozen soil (Romanovsky and Osterkamp, 2000). Groundwater discharge was controlled by the frozen status, which was frozen from high elevations to lower elevations. This process is progressively stopping the function of a series of cascade groundwater buckets, resulting in the discontinuous recession. Simultaneously, the decrease in discharge (Qs) slowed down the decrease in the groundwater level (Ss). This conceptual model allowed us to simulate the bending down of baseflow recession and slower decrease in groundwater level. 6dSsdt=Rs-Qs-Fs7Fs=0.9⋅Ss(t̃);once freeze depth≥3 m-0.9⋅Ss(t̃);once thaw depth reach to yearly max or thaw  depth≥freeze  depth. In thawing seasons, the freeze–thaw condition in the lowest elevation zone plays a key role, controlling the hydraulic connectivity between soil and groundwater systems. In the conceptual model, if the freeze depth calculated by the Stefan equation is larger than the thaw depth, then this means that the frozen layer still exists, which obstructs the soil and groundwater connection. In the conceptual model, we kept Ru=0 (Eq. 11) as the runoff generation. Since there is no percolation from soil to groundwater, root zone soil moisture (Su) is accumulating and even ponding in some local depressions (Fig. 7). The only outflow of the root zone is evaporation in this period. This conceptual model allowed us to reproduce the LRET observation. For groundwater reservoir, once the thaw depth goes to its yearly maximum (in permafrost area) or thaw depth > freeze depth (in seasonal frozen soil area), the frozen water (90 % of groundwater storage when frozen; Ss(t̃)) was released to the groundwater again (Eq. 22). The sudden release of frozen groundwater causes the spikes in hydrograph, which could happen in either thawing seasons or complete thaw seasons, depending on its elevation. But either way, the water balance calculation is 100 % closed.

Complete thaw in the lowest elevation marked the end of thawing season and the start of complete thaw season. In the complete thaw season, soil water and groundwater are connected, and runoff generation (Ru) returns to normal circumstances, which can be simulated by the FLEX-Topo model without frozen soil.

Figure 9 demonstrates that the Stefan equation was capable to reproduce the freeze–thaw process. This verified the success of the freeze–thaw parameterization and the parameter sets. Also, the simulated lower limit of permafrost is 3716 m, which is largely close to the field survey in the upper Heihe River basin, at around 3650–3700 m (Wang et al., 2016), and the expert-based estimation of 3650 m of the Hulu catchment. Both the well reproduced freeze–thaw variation in the spot scale and the lower limit of permafrost in the catchment scale gave us strong confidence in the simulation of soil freeze–thaw processes.

While considering the impacts of frozen soil, the FLEX-Topo-FS model, compared with FLEX-Topo, dramatically improved the model performance. Figure 10 shows the simulated hydrograph by FLEX-Topo-FS on both normal and log scales. Both the LRET and the DBR observations were almost perfectly reproduced by the FLEX-Topo-FS model. The KGE of FLEX-Topo-FS in calibration was 0.78, which was the same as FLEX-Topo. But in validation, the performance was significantly improved; the KGE improved from 0.58 to 0.66, KGL from 0.36 to 0.72, NSE from 0.41 to 0.60, R2 from 0.82 to 0.83, and RMSE reduced from 0.95 to 0.79 mm d-1. All the model evaluation criteria were improved. The most significant improvement was the baseflow simulation, and KGL was increased from 0.36 to 0.72. We also noted that the FLEX-Topo-FS model reproduced the spikes during the thawing in Fig. 10. This further confirms our conceptual model of a sequence of thawing breakthroughs, which triggers the sudden release of groundwater starting at lower elevations and progressing to higher landscape elements.

To further verify the FLEX-Topo-FS model, we averaged the simulated groundwater storage (Ss) of all HRUs and compared this with the observed groundwater depth on the log scale (Fig. 11). We included the frozen groundwater in the total groundwater storage (Ss) because the liquid groundwater is in connection with the frozen groundwater, and this affects the groundwater level variation. Figure 11 clearly demonstrates that the simulated groundwater storage decreased slower, and the timescale of the recession increased. The trends of simulated groundwater storage and observed groundwater level, which are not the same but have a similar physical meaning describing the groundwater dynamic, correspond surprisingly well. This is particularly encouraging, given that the periods of simulation (2011–2014) and observation (2016–2019) were not overlaid, and a point observation may not be straightforwardly representative for the entire basin.

The success in reproducing groundwater level trends is another strong confirmation for the FLEX-Topo-FS model. All the successes of the FLEX-Topo-FS model in reproducing spot-scale freeze/thaw depth variations lower the limit of permafrost, LRET and DBR events, and groundwater level trends, giving us strong confidence in the realism of our qualitative perceptual model and quantitative conceptual model.

Frozen soil happens underneath the ground, with frustrating spatiotemporal heterogeneities, and is difficulty to measure. Although there are spot and hillslope measurements, its impact on catchment hydrology is still hard to explore. Hydrography, easily and widely observed and globally accessible, can be regarded as the by-product of the entire catchment hydrological system (Gao, 2015). Hydrography as an integrated signal provides us with a vital source of information, reflecting how the complex hydrological system works, i.e., transforming precipitation into runoff. Hence, hydrography itself is a valuable source of data for understanding catchment frozen soil hydrology. Especially the baseflow embodies the influence of basin characteristics, including the geology, soils, morphology, vegetation, and frozen soil (Blume et al., 2007; Ye et al., 2009). Hence, a quantitative description of baseflow is a valuable tool for understanding how the groundwater system behaves (McNamara et al., 1998). Baseflow recession was used to identify the impacts of climate change on permafrost hydrology. In previous studies, Slaughter and Kane (1979) found that basins with permafrost have higher peak flows and lower baseflows. The baseflow, representing groundwater recession, provides important information about the storage capacity and recession characteristics of the active layer in permafrost regions (Brutsaert and Hiyama, 2012).

Moreover, the hydrological system has tremendous influencing factors. The hydrograph of paired catchments provides a good reference, as a controlled experiment, to isolate one influencing factor from the others. Nested catchments help us to acknowledge the importance of region-specific knowledge, which is often the key to interpreting the unexplained variability in large sample studies (Fenicia and McDonnell, 2022). In this study, the pair catchment method helped us to confirm the impacts of frozen soil on LRET and DBR observations.

Additionally, by analyzing the nested subbasins of the Lena river in Siberia, Ye et al. (2008) used the peak flow/baseflow ratio to quantify the impact of permafrost coverage on hydrograph regime in the Lena river basin and found that frozen soil only affects the discharge regime over high permafrost regions (greater than 60 %) and has no significant affect over the low permafrost (less than 40 %) regions. In this study, we reconfirmed this statement. The permafrost area proportions of the Hulu catchment and Zhamashike subbasin are 64 % and 74 %, with significant effects on discharge, while 38 % of the Qilian subbasin is covered by permafrost, with no significant effects on discharge regime.

By using the paired catchments comparison, interestingly, the Ks in Zhamashike and Qilian in the early recession period are both 60 d, which is exactly within the standard value of 45 ± 15 d derived in earlier studies for basins ranging in size between 1000 and 100 000 km2 (Brutsaert and Sugita, 2008; Brutsaert and Hiyama, 2012), which was likely the results of catchment self-similarity and co-evolution. But we also noticed that the Ks in the small Hulu catchment (Ks=80 and 60 d) is quite a bit larger than the Zhamashike (Ks=60 and 20 d) and Qilian (Ks=60 d). This could be rooted in different scale and drainage density (Brutsaert and Hiyama, 2012). The Hulu catchment is located in the headwater with less drainage density; hence, there is less contact area between the hillslope and river channel, a slower baseflow recession, and a larger Ks value. We argue that, even without the impacts from frozen soil, it is difficult to give accurate Ks estimation in small catchments (less than 1000 km2) in moderate climates. It is more substantially difficult to estimate the discontinuous Ks in different periods in frozen soil catchments without calibration. Thus, estimating the value of recession coefficient (Ks) in different catchments and periods, especially for small catchments and in cold regions, is still an intriguing scientific question for hydrologists.

Observation is still a bottleneck in complex mountainous cold regions. Traditionally, fragmented observations are only for specific variables, like puzzles. In this study, we collected multi-source data, including soil moisture, groundwater level, topography, geology survey, isotope, soil temperature, freeze/thaw depth, permafrost and seasonal frozen soil maps, and hydrographs in paired catchments. Multi-source data analysis provides a multi-dimensional perspective to investigate frozen soil hydrology. We argue that, on the one hand, multi-source observations helped us to deliver the perceptual and conceptual models. And on the other hand, perceptual and conceptual models bridge the gap between experimentalists and modelers (Seibert and McDonnell, 2002), allowing us put fragmented observations together and understand the hydrological system in an integrated and qualitative way.

The data gap is a common issue in mountainous hydrology studies. For example, in this study, runoff data have a gap period at the end of the thawing season in 2013 due to flooding and equipment malfunction. Soil moisture and groundwater level data had large gap, which cannot be used for continuous modeling. Luckily, the meteorological data, which are important forcing data for running the models, were continuous and without any gap. With sufficient meteorological forcing data, we successfully run the hydrological models from 2011 to 2014. The runoff data gap at the end of thawing season in 2013 merely influenced model validation. While evaluating the models, we did not involve the data gap period. Hence, the data gap does not have any impact on the consolidation of the conclusions.

Although soil moisture had large gap, there were, fortunately, some observations during the LRET periods, which were sufficient to distinguish the impacts of frozen soil on soil moisture profile. Additionally, although the groundwater level observation (2016–2019) was not overlaid with other hydrometeorological measurements (2011–2014), its repeating seasonal pattern allowed us to qualitatively understand how groundwater system behaves. Groundwater fluctuation in natural catchments has strong periodicity, which can be observed in Fig. 11. Groundwater variation does not show significant difference among different years, which is especially true for the 25 m well. Due to the extreme difficulty of continuous observation in this region, there was no groundwater measurement in 2011–2014. But, due to the strong repeated temporal variation in the groundwater level, we have good reason to believe the trends in 2016–2019 also happened in 2011–2014. Moreover, this is a qualitative comparison rather than a quantitative one, which we do not think has any impact on our conclusions.

In general, we argue that data gap always exists. In another words, we can never have sufficient data. The only thing we can do is use the accessible data to understand processes. Although perfect data do not exist, the more multi-source and the better the data quality, the more accurate understanding we can achieve. This needs close collaboration among multi-disciplinary researchers, including, but not limited to, hydrologists, meteorologists, ecologists, geocryologists, geologists, and engineers.

By a simple water balance inspection, we found that the total annual runoff of the Hulu catchment was 499 mm a-1, which is even larger than the observed annual precipitation of 433 mm a-1. This means that, without considering the distributed meteorological forcing, the runoff coefficient is larger than 1, and the water balance cannot be closed. This result is also in line with previous studies, showing that precipitation in mountainous areas is largely underestimated (Immerzeel et al., 2015; Chen et al., 2018).

Although the semi-distributed FLEX-Topo has considered tremendous processes, including rainfall–runoff processes, distributed forcing, landscape heterogeneity, topography, and snow and glacier melting, there was still model discrepancy in reproducing the LRET and DBR observations. This means that there must be some processes that were missed in the model. After our expert-driven data analysis, we attributed the model discrepancy to soil freeze–thaw processes.

Model fitness is the goal which all modelers are pursuing. But we argue that, in many cases, the model discrepancy can tell us more interesting things than a perfect fit can. In this study, we used the FLEX-Topo model, without frozen soil, as a diagnostic tool to understand the possible impacts of frozen soil on the complex mountainous hydrology. Using tailor-made hydrological model and integrated observations as diagnostic tools is a promising approach to understanding the complex mountainous hydrology in a stepwise manner understand.