Changes of Nonlinearity and Stability of Streamflow Recession Characteristics under Climate Warming in a Large Glaciated Basin of the Tibetan Plateau

. The accelerated climate warming in the Tibetan Plateau after 1997 has strong consequences in hydrology, 10 geography, and social wellbeing. In hydrology, the change of streamflow as a result of changes of dynamic water storage originating from glacier melt and permafrost thawing in the warming climate directly affects the available water resources for societies of the most populated nations in the world. In this study, annual streamflow recession characteristics are analyzed using daily climate and hydrological data during 1980–2015 in the Yarlung-Zangpo River basin (YRB) of south Tibetan Plateau. The recession characteristics are examined in terms of d Q /d t = - aQ b and the response/sensitivity of streamflow to 15 changes of groundwater storage. Major results show that climate warming significantly increased the nonlinearity of the response ( b ) and decreased streamflow stability [log( a )] in most sub-basins of YRB. These changes of recession characteristics are attributed to opposite effects of increases of available water storage and recession timescale on the recession. Climate warming increased sub-basin water storage considerably by more recharge from accelerated glacier melting and permafrost thawing after 1997. Meanwhile, the enlarged storage lengthens recession timescales and thereby decreases the sensitivity of 20 discharge to storage. In the recession period when the recharge diminished, increased evaporation under warmer temperatures acts as a competing process to reduce water storage and streamflow. While reservoir regulations in some basins helped reduce and even reverse some of these climate warming effects, this short-term remedy could only function before the solid water storage is exhausted when the climate warming continues. of streamflow is higher in YBJ and LS and in upstream of NGS. CV decreases towards the wetter downstream of YRB, partially because of strengthening watershed regulation as the sub-basin areas increase and the dams are included in the area of the analysis.

. These effects on the recession rate can result in strong nonlinear behavior of streamflow in time and space.
During periods with little or no precipitation, the baseflow recession (or relationship of dQ/dt vs. Q, where Q is discharge) is 60 typically quantified by a power law differential equation (Brutsaert and Nieber, 1977;Tallaksen, 1995), i.e., dQ/dt = -aQ b . The depletion of baseflow in relation to the parameters a and b contains valuable information concerning storage properties and aquifer characteristics of basins (Tallaksen, 1995). The recession scale parameter a is a function of the hydraulic and geometric properties of the aquifer in a basin and can be used as a proxy for effective depth to permafrost in frozen areas (Lyon and Destouni, 2010). The parameter b as reflected in the concavity of the hydrograph or the nonlinearity of recession (Dralle et al., 65 2017) is a function of boundary conditions to describe the equivalent water depth profile of an aquifer (Brutsaert and Nieber, 1977;Tashie et al., 2020). So, b can be interpreted as a measure of the diversity of water transport timescales throughout various parts of a catchment (Harman et al., 2009). Therefore, the variations of a and b in time and space can describe recession characteristics distribution of a basin (e.g., Brutsaert and Nieber, 1977;Kirchner, 2009).
Changes of the recession characteristics in time reflect their vulnerability to climatic and anthropogenic factors (Berghuijs et 70 al., 2016;Brooks et al., 2015;Buttle, 2018). Streamflow stability, log(a), has a significant seasonal cycle for over 99% of basins examined in the Continental United States (Tashie et al., 2020). Moistening climate in catchments could increase the diversity of flow paths and the nonlinear relationships between storage/recharge and discharge (Brutsaert and Nieber, 1977;Hinzman et al., 2020). In cold climate regions, reduced glacier size can lead to considerable amplification of seasonality of streamflow (Juen et al., 2007;Vuille et al., 2008). Hinzman et al. (2020) report a widespread increase in nonlinearity of 75 recessions in Northern Sweden due to climate warming. In addition, they find that this nonlinearity is significantly higher in warm winters than in cold winters.
In the southern TP, the Yarlung-Zangpo River basin (YRB) with decades of observations offers an opportunity to estimate variations of the recession characteristics of streamflow as YRB is a typical large river that drains in the high and cold area of TP (Fig. 1a). Recent studies have shown that the climate in the YRB has become warmer and wetter from 1980-2015 (Wang 80 et al., 2021). Climate warming has reduced the buffering effect of glacial and permafrost on streamflow, leading to catchment property change with shorter streamflow response time to precipitation in YRB . These changes must have affected streamflow recession characteristics.
The objective of this study is to investigate temporal and spatial variations of streamflow recession characteristics driven by climate and landscape changes in YRB. The changes of these characteristics are examined using comparisons and contrasts of 85 streamflow recessions in different sub-basins and time periods. In order to describe temporal variability of the recession characteristics under climate warming, the recession parameters of a and b are fitted by individual recessions from 1980 to 2015 and then regressed with mean temperature in recession period for each sub-basin of YRB. Sensitivity analysis shows the effect of climate warming on the recession parameters, the recession rates, and the storage/recharge-discharge relations in different sub-basins. They show the extent of the nonlinearity in the variation of the streamflow recessions in this glaciated 90 basin of TP.

Study region and data
The YRB (28.2°-31.2°N; 82.0°-94.9°E) is the largest river basin in TP (Fig. 1). The main stem of YRB is formed by major suture zones in southern TP, resulted from the collision between the Indian plate and the Eurasian plate. The modern YRB flows along the suture from the west to the east before bending to the south at the eastern Himalayan syntaxes with an average 95 gradient about 2.63 ‰ (Fig. 1a)  . In this study, we selected the upstream of the Great Gorge of YRB (main stem about 1100 km with an area of 2.0 ×10 5 km 2 ). The elevation of the study area drops drastically from 6234 m in the west to 2030 m in the east (You et al. 2007. Climate in YRB is heavily influenced by the Indian monsoon in summer and the westerlies in winter (Ren et al., 2018;Tian et al., 2020). From the west to the east of the basin, mean annual temperature varies from -9.3 to 22.0 °C, and the mean annual 100 precipitation varies from 300 to 1050 mm. Nearly 90% of annual precipitation falls during June to September. As a result, the mean annual total streamflow of the entire basin, 289.7 mm, is highly unevenly distributed in seasons. The summer streamflow is derived from monsoon rainfall and glacier meltwater. Groundwater accounts for about 54% of the annual streamflow.
There are four hydrological stations along the main stem of YRB: LZ, NGS, YC, and NX shown in Fig. 1a. Two additional hydrological stations, YBJ and LS, are located in the major tributaries of the Lhasa River which originates from the 105 Nyainqêntanglha Mountains north of YRB (Fig. 1a). Daily streamflow data from 1980 to 2015 are available at these hydrological stations, except LZ. Accordingly, we divide YRB into five sub-basins, with three nested sub-basins of NGS, YC, and NX in the main stem of YRB, and two sub-basins of YBJ and LS in the tributary of the Lhasa River.
There are four main dams/reservoirs (marked by the purple squares in Fig. 1a) in YRB above the NX hydrological station. The reservoirs, ML, ZK, PD, and ZM, were built in 1999. The reservoirs of ML, PD, and ZM 110 are operated daily while the reservoir of ZK is operated seasonally. The impact of reservoir regulations on streamflow is minor for the sub-basins of NGS, YC, and NX in the main stem of YRB because the reservoirs are daily operated and affect less than 10% of the areas in the tributaries. In the tributary of the Lhasa River, the sub-basin YBJ has no reservoirs while the sub-basin LS has two reservoirs, PD and ZK, which have impacts on streamflow.
Daily gridded data (0.1°0.1° spatial resolution) of precipitation (P), and mean surface air temperature (T) during 1980-2015 115 were provided by the National Tibetan Plateau Data Center (Yang and He, 2019;He et al., 2020;http://data.tpdc.ac.cn). The sub-basin averaged P and T are calculated by the geometric mean of the gridded data.  The glacier area, permafrost area, and the normalized difference vegetation index (NDVI) were collected from National Tibetan Plateau Data Center (Table 1, http://data.tpdc.ac.cn). Glacier areas are located at altitudes from 3370 to 6460 m above the sea 125 level (Yao et al., 2010, Fig. 1a). The glacier and permafrost area before 2000 accounts for 1.88% and 41.8% of the YRB area, respectively. These coverage percentages have reduced prominently since 2000 ( Table 2). The annual mean NDVI was calculated by the maximum value synthesis method from the Global GIMMS NDVI3g v1 dataset with a 15-day temporal resolution and 1/12° spatial resolution. The vegetation types are mainly alpine meadow, alpine steppe in the upstream (LZ), alpine shrubs, grasslands in the middle region (LZ-NGS), and alpine grassland and forest in the lower YRB (NGS-NX) (Liu 130 et al., 2014).
The annual depth of glacial melt data (G) during 1980-2015 are available from estimations using the degree-day model (Su et al., 2015;Liu and Zhang, 2018). The details of the calculation procedures are provided in Wang et al. (2021). The annual ALT is estimated using a linear statistical function of air freezing index (FIair) described in Xu et al. (2017), in which FIair is calculated according to the cumulative value of the daily mean temperature below 0 ℃ in a year. 135 https://doi.org/10.5194/hess-2022-25 Preprint. Discussion started: 24 January 2022 c Author(s) 2022. CC BY 4.0 License.
After the end of warm season (June-September), there is little precipitation (Hayashi, 2020) in YRB, and the melting of snow and glacier is minor due to cold temperatures (<-5 °C, Fig. 3). Subsequently, the flow discharge recedes from September to February of the following year. In this study, we use the daily discharge (Qt) in the recession period, which is defined from 1 October to 15 February of the following year, in our analysis of the recession process.  1983-1996 (1988), 1997, 2003, 2012, 2017 Mean

Detection of changes in annual climate and hydrological series
The Mann-Kendall (MK) method (Mann, 1945;Kendall, 1975) combines trend-free pre-whitening treatment (TFPW-MK) (Yue & Wang, 2002) with Sen-slope (Sen 1968). The TFPW-MK is used in this study to test the temporal trend of annual sequence for the meteorological and hydrological variables at the specified significance level of α=0.05. 145 The Pettitt method is applied to detect the change point (year) of annual hydrological and meteorological variables. Pettitt method is nonparametric and has been widely used in mutation point detection (Pettitt, 1979;Mallakpour et al., 2016;Wang et al., 2021).

Streamflow recession analysis
Based on analytical solutions to the Boussinesq equation, the relationship of streamflow (Q) and streamflow change (-dQ/dt) 150 in the recession period is expressed by the power-law equation (Brutsaert and Nieber, 1977): where Q is streamflow (mm·d −1 ), dQ/dt is streamflow recession (mm·d −2 ), t is time (day), and a (mm 1-b ·d b-2 ) and b (dimensionless) are the recession coefficients (Brutsaert and Nieber, 1977;Tashie et al., 2020).
Based on (1), the relationship between dynamic groundwater storage (S) and streamflow (Q) can be derived: 155 The recession timescale (τ) is estimated to measure the recession rates of individual recessions (Kirchner, 2009), and defined as = = 1 −1 ( 3) 160 From (1)-(3), the storage sensitivity of discharge (λS) for the recession curve (Berghuijs et al., 2016) is where λS (mm −1 ) is a measure of the sensitivity of instantaneous discharge values to water storage changes, and indicates the fractional increase in discharge for each unit of increase in storage. The larger (or smaller) the values of a (or b) the more sensitive the discharge to water storage. 165 Both the relationships of -dQ/dt -Q and S-Q are linear if b=1 and nonlinear if b≠1. When b≠1, the discharge recession is where Q0 and Qt are initial discharge and discharge at time t. For any specific initial discharge Q0, the larger the b is the faster the hydrograph recession is for high discharge and the more stable the recession is for low discharge (Tashie et al., 2020).
The recession parameters a and b can be determined by fitting the daily observation data points of (ΔQ/Δt) -Q in log-log 170 space using linear least-squares regression. The fitted parameter values of a and b are used to estimate -dQ/dt and Qt using (1) and (5). The accuracy of the estimated -dQ/dt values is evaluated by the root-mean-square logarithmic error (RMSLE) (Bekele and Nicklow, 2007): Where Qobs.i and Qest.i are the observed and estimated discharges, respectively. dQest(i)/dt and dQobs(i)/dt are derivatives of (1). 175 In practice, ΔQ/Δt is determined from the observed recession segments ΔQ in time interval Δt. N in (6) is the number of data points of -dQ/dt in individual recessions.
For each recession hydrograph, the fitting should ensure that the estimated volume of recession discharge approaches to that of the observed recession during the study period (Dralle et al., 2017), or by minimizing their differences where EMAP is the absolute relative error between Qobs.i and Qest.i over the recession period.

Changes of recession characteristics under climate warming
Recession coefficients a and b are functions of catchment properties, such as the hydraulic conductivity, the drainage density of the basin, and drainable porosity. In cold regions, recession coefficients are closely related to the thickness of the active layer in the soil profile above permafrost layer (Bense et al., 2012;Brutsaert and Hiyama, 2012). Changes of these catchment 185 properties depend on daily, seasonal, and annual temperature variability in the refreezing areas. For example, the transition from unfrozen to frozen ground for temperature varying between 0 and -0.5°C coincides with a reduction in hydraulic conductivity of several orders of magnitude for saturated porous media (Burt and Williams, 1976;McCauley et al., 2002). On the other hand, when temperature rises, the thawing front in the active soil layer moves progressively downward as summer proceeds, leading to increasing water storage in the active layer. If the frozen soil beneath the thawing front is ice-saturated 190 (thus relatively impermeable), the active soil layer can function as a very shallow perched aquifer that controls streamflow response to snowmelt and summer precipitation (Carey and Woo, 2005;Yamazaki et al., 2006;Wright et al., 2009;Koch et al., 2014).
Accordingly, the variability of the parameters a and b can be expressed as a function of temperature (T), i.e., a(T) and b(T). In this study, we use 195 where α and α1 are coefficients for a(T), β and β1 are coefficients for b(T), and T is the mean surface air temperature in the recession period (Tre). These coefficients can be obtained by fitting the recession parameters of individual recession events with known Tre in each sub-basin.
Because the recession parameters a and b are functions of T in (8), S is a function of T and Q. The change of S (ΔS) can therefore be expressed as where λT is the sensitivity coefficient of ΔS to T. λT can be derived as

Spatial variations
According to the mean values of the observed climate and hydrological variables during 1980-2015 in different sub-basins, climate has become warmer and wetter ( Fig. 2a-2c and Table 2) along the main stem of YRB. The wet trend is largest in YBJ, as well as LS sub-basins, whereas the mean temperature of YBJ is lowest because most of its area is at high altitudes. The 220 percentage of glacier area is 1.63%, 1.52%, and 1.92% in NGS, YC, and NX sub-basin, respectively, and 9.91% and 0.75% for YBJ and LS, respectively. The percentage of permafrost area (PPA) ranges from 41.8%-47.7% in the five sub-basins.  a reference value in the sub-period before 1997, and the mean of Aice in 2001,2009, and 2013 is used as a reference value in the sub-period after 1997. The subscript "1", and "2" represent 1980-1996, and 1997-2015, respectively.  for Qre. In contrast, annual Qre in LS decreased insignificantly (Fig. 2d), possibly because of initial water storage when the ZK reservoir (Fig. 1a)  identified by the dramatic changes of surface conditions, i.e., the reversed NDVI trend before and after 1997 (Fig. 2g), increased ALT after 1997 (Fig. 2h), and accelerated thawing of permafrost after 1997 (Fig. 2i). Accordingly, in this study, the study period of 1980-2015 is separated into two periods: the early period from 1980 to 1996, and the recent period from 1997 260 to 2015.

Annual variations of climate and hydrological variables during 1980-2015
Compared with P and T in the two periods, climate in the recent period changes to be markedly warmer and wetter. The mean annual P after 1997 increased by 27-46 mm or 7.9-10.7 % more than that in the early period for the five sub-basins. The mean annual T in the recent period is 0.75-1.52℃ warmer than that in the early period, and a larger rise of 1.40-1.78℃ was found for the mean Tre after 1997. These changes concurred with 8.6-55.9 mm or 23.8-81.1% increase of glacier meltwater after 265 1997 in the five sub-basins. As a result, mean annual streamflow increased by 29.6-50.2 mm or 12.7-31.5% in the recent period compared to that before 1997. This increase in Q and Qre after 1997 is much larger in the upstream sub-basins such as NGS and YC.

Annual recession characteristics
As shown in Fig. 3, the annual hydrographs in the five sub-basins are consistent, delineating a single peak response to 270 maximum precipitation and temperature in July-August. The statistic values of daily discharge series in the two periods show that the mean value in the recent period exceeds that in the early period in all sub-basins. Meanwhile, daily discharge variability in the recession of the annual hydrograph in the recent period is also greater than that of the early period, shown by larger coefficients of variation (CV) after 1997 for most sub-basins, except the glacierized sub-basin YBJ ( Table 2).
The recessions in the sub-basins are faster in the recent periods when the climate is warmer and wetter. As shown in Figs. 4a-275 4e, the fitted line of the -dQ/dt vs. Q after 1997 has a steeper slope. According to the non-overlapping moving averages of the 5-day series of the recession discharge, the estimated average recession rate after 1997 [(ΔQ/Δt)2] is larger than that before

Estimation of the recession parameters
Targeting the observed hydrograph in each year, its recession was fitted to obtain the recession parameters a and b. The results 285 are summarized in Table 3. The mean annual value of parameter a during 1980-2015 ranges from 0.022 to 0.042 mm 1-b · d b-2 , and the mean annual value of b ranges from 1.36 to 1.85 for the five sub-basins. The mean values of a and b decrease from upstream to downstream along the main stem of YRB (Table 3). Figure 5 shows the errors of the estimated recession (RMLSE and EMAP) for the recession curve of each sub-basin. Mean annual RMLSE is less than 0.15 in all sub-basins. The mean annual EMAP is lower than 10%, except in the sub-basins YBJ and LS where EMAP is 0.15 and 0.14, respectively. 290  For the multiyear mean values of parameters a and b in the two periods (Table 3), the mean value of a in the recent period ranges between 0.021-0.039 mm 1-b ·d b-2 , smaller than that in the early period when they range between 0.022-0.046 mm 1-b ·d b-305 2 in the sub-basins, except LS. Oppositely, the mean value of b in the recent period ranges between 1.47-1.89, larger than that in the early period (1.25-1.81) for all sub-basins. These results indicate that warming and wetting climate increases the nonlinearity of the recession (b) and reduces streamflow stability [log(a)] for most sub-basins in YRB.

Change of storage-discharge relationship under climate warming
The strong sensitivity of the recession parameters of a and b to the near surface air temperature means that climate warming 310 can change the nonlinear relationship between the water storage (S) and discharge/streamflow (Q) (Eq. (2)). This change is demonstrated by the increase of the recession coefficient K in the recent period (11.5-73.2 mm b-1 ·d 2-b for K in Table 3) and decrease of m (=2-b) in Eq. (2) because b increases with the temperature (Table 3 and Fig. 6). The increase of K and decrease of m mean a lower discharge for a specific storage in the recent warmer period. As an example, we show in Fig. 7 the relationship of S with Q for different K and/or m between the two periods in sub-basin YC. Q decreases significantly with 315 increase of K or decrease of m for any specific storage S (Figs. 7a and 7b). The combination of increase of K and decrease of m leads to marked decrease of Q for any specific storage S (Fig. 7c). Correspondingly, the recession timescale (τ=dS/dQ) https://doi.org/10.5194/hess-2022-25 Preprint. Discussion started: 24 January 2022 c Author(s) 2022. CC BY 4.0 License. increases by 5.2-20.7 days in the recent warmer period in all sub-basins (Table 3)   The lower discharge for a specific storage or higher storage for any specific discharge can be further illustrated by the results of the storage sensitivity of discharge (λS in Eq. (4)) in Table 4. The mean value of λS during 1980-2015 ranges between 0.036 -0.059 mm -1 for the five sub-basins. These values mean that 1 mm decrease in storage results in 3.6-5.9% decrease in discharge.
In terms of Eq. (4), the increase of the recession timescale (τ) and discharge (Q) should result in the decrease of λS, supported 325 by the smaller λS values in the recent warmer period (see the negative values of λS in Table 4). Meanwhile, for the sub-basins in the main stem of YRB (NGS, YC and NX), the mean annual value of λS during 1980-2015 decreases towards the warmer and wetter downstream (from NGS to NX, see Table 4). This change suggests that climate warming weakens λS, meaning that a unit decrease in storage releases less water to discharge in the recession period. This is especially so in glaciated basins, e.g., YBJ, where the decrease of λS (λS in Table 4) is largest in the recent period, corresponding to the largest increase of τ. We 330 note that the decrease of λS (λS) in LS is relatively small in the recent period primarily because of regulation of reservoirs on discharge.

Sensitivity of recession parameters to storage change under climate warming
Change of the sensitivity of discharge to storage (λS) should affect the recession processes, which is described by the sensitivity of the recession parameters to storage change ΔS (λa and λb for a and b, respectively). As listed in Table 4, λb shows positive while λa has negative value in all five sub-basins. The larger negative λa and positive λb could be found in the recent period after 1997, particularly in the glaciated sub-basin YBJ (Δλa and Δλb in Table 4). Therefore, increase in storage due to climate 345 warming will enhance the nonlinearity of recession (b) and weaken streamflow stability [log(a)] in YRB. This sensitivity can be dampened however by anthropogenic effect (reservoir regulations) as suggested by the less sensitive result of the recession parameters of a and b to ΔS in LS sub-basin.  Table 4 show an increase in the recent period in all sub-basins, especially in YBJ and YC. Thus, the enlarged storage is largely attributed to climate 355 warming. As expected, λT is smaller in the warm and wet NX sub-basin and the sub-basin LS with reservoir regulation. The values of λQ in Table 4 also become bigger in the recent period in all sub-basins. These changes indicate that the climate warming increases storage and discharge.
However, the increase of discharge ΔQ in response to the increase in storage ΔS can be quite different in response to different rate of change of temperature ΔT in the five sub-basins. In terms of Eq. (14), the relationship between ΔS and ΔQ for different 360 ΔT in the five sub-basins is shown in Fig. 8. As temperature rises, ΔS becomes greater while the greater increase of storage volume (in thawing soil layers) allows smaller amount of water to be released as baseflow. For example, as temperature rises https://doi.org/10.5194/hess-2022-25 Preprint. Discussion started: 24 January 2022 c Author(s) 2022. CC BY 4.0 License.
to be 1.2℃ higher than mean annual temperature (i.e., ΔT = 1.2℃), an increase of discharge (e.g., ΔQ = 0.2 mm· d -1 ) corresponds to a storage increase of about 92 mm in NGS, 160 mm in YC, 63 mm in NX, 42 mm in LS and huge increase of 478 mm in YBJ (see the value of the ΔS vs. ΔQ point in Fig 8). These results suggest that a larger increase of water storage 365 caused a smaller increase of baseflow in the glaciated sub-basins, reflecting a buffering effect of freezing on streamflow dynamics. When the mean surface air temperature (Tre) increased from the early to the recent period, i.e.,   of storage but small increase of discharge. As an example, the YBJ sub-basin has 97.3% of the total increase in storage vs. 380 only 2.7% of the total increase in discharge. Again, this relationship is distorted in basins with human regulatory actions in water management. In the sub-basin LS with strong reservoir regulations, changes in both the storage and discharge are small (e.g., 0.1% in the total increase of storage).

Discussions
Observations have shown that climate warming has accelerated glacier melting and permafrost thawing in cold climate and 385 high-altitude regions. Subsequent changes are found in vegetation growth and thickening of talik and active soil layer thickness.
These changes have altered land surface conditions and unconsolidated soil profiles and subsurface permafrost and redefined surface and groundwater exchange and balance in those regions (Fig. 9). Our case study of YRB in southern TP shows that accelerated glacier melting and permafrost thawing in YRB during 1980-2015 have substantially increased its dynamic groundwater storage, defined as ( ) − 0 = − ∫ ( ) 0 . These results with the decrease of terrestrial water storage (TWS) 390 in south TP, including YRB  in recent decades, indicate that a transform of water storage from the solid form (glacier and permafrost) to the liquid volume (soil moisture, surface water in rivers/lakes, and groundwater) (Fig. 9b).
According to water balance in a catchment, i.e., dS/dt= (Pr E Q), where E is evapotranspiration, S is regarded as the "liquid volume" (here, change of S is equal to the sum of changes in soil moisture and groundwater) and Pr is the recharge from glacier melting, permafrost thawing and precipitation, the increase of S infers that Pr is larger than the sum of E and Q in a study 395 region. Because cold regions tend to have a greater coverage percentage of glacier and permafrost, glacier melting and permafrost thawing could substantially increase water storage under climate warming. Higher water storage could extend the recession period and sustain healthy annual streamflow.
Our study also shows that the increase of water storage and its effect on the annual recession of streamflow weakened towards the warmer downstream areas of YRB (with diminishing glacier melting and permafrost thawing effect). Accordingly, if the 400 climate warming continues, the shrinking of glacier and permafrost volume could eventually reach a point when there is not enough melting to recharge the liquid volume of water in YRB. From that point onward, steady streamflow in YRB would be in danger.
While the processes initiated by the accelerated glacier melting and permafrost thawing lengthen subsurface flow paths (Hinzman et al., 2020) and the streamflow recession time (τ), the increase of surface temperature and E can also increase 405 surface water loss. According to the discharge relation -dQ/dt = -= (Pr +E +Q)/τ (Kirchner, 2009), where Pr can be neglected in the recession period, a faster recession (-dQ/dt) could occur under climate warming from faster decrease of storage (dS/dt) due to increasing of E. Meanwhile, the decreased sensitivity of discharge to the storage (dQ/dS =1/τ) as the storage expands in the warming climate would slow down the streamflow recession (-dQ/dt). These competing effects from the warming climate on dS/dt and dQ/dS would increase the nonlinearity of the recession (b) and reduce streamflow stability [log(a)] in cold climate regions such as YRB. In comparison, in the warm climate area, the effect of storage decrease (dS/dt) on recession (-dQ/dt) strengthens and the effect of the recession timescale (1/τ or dQ/dS) on the recession weakens. As shown in Fig. 8, when temperature is higher (e.g., large positive ΔT), hydrograph recession (negative ΔQ) is faster along with the faster decline of storage (ΔS).
415 Figure 9. A schematic illustration of climate warming effect on surface conditions and subsurface profile as well as hydrological variables. The larger sizes of the arrows indicate a large increase of the hydrological variables, e.g., glacier melting, precipitation, discharge, and evaporation.
Additionally, deep circulating groundwater through macro structures, such as north-south oriented active tensile faults (Fig.   1b) could also affect baseflow and its recharge and discharge . According to studies using multi-tracer data 420 (e.g., 2 H, 3 H, 18 O, and Sr), modern meltwater is found to primarily maintain the rapid recharge of phreatic groundwater in alpine regions through faults and fissures . In the middle of YRB (i.e., NGS-YC), changes of storage sensitivity to temperature (λT in Table 4) and recession timescale (τ) are greater than those in the upstream and downstream areas (NGS and NX, respectively). Rising temperature can greatly increase storage (Fig. 8b).
Finally, anthropogenic effect such as reservoir regulation can reduce the climate warming effect on these storage-discharge 425 responses in YRB. For example, in the sub-basin of LS, operations of two reservoirs, PD and ZK, significantly reduced the sensitivity of the recession parameters a and b to climate warming, and increased streamflow stability [log(a)]. It remains questionable however as how this human effort in water management in YRB would be practical/beneficial after the point https://doi.org/10.5194/hess-2022-25 Preprint. Discussion started: 24 January 2022 c Author(s) 2022. CC BY 4.0 License.
when the increase of water storage from glacier and permafrost melt has exhausted the solid volume of water resources in the basin following the climate warming. 430

Concluding remarks
Climate warming accelerated after 1997 in YRB of south Tibetan Plateau, especially in its cold and high-altitude upstream areas. Since 1997, the mean annual temperature has risen by 0.75-1.52 ℃, and the mean temperature in the annual recession period (1 October -15 February of the following year) has risen by 1.40-1.78 ℃ in the five sub-basins of YRB. The larger rise of temperature occurred in the drier and colder sub-basins in the upstream YRB. The recent strong warming has accelerated 435 glacier melting and permafrost thawing, and thereby increased annual streamflow (12.7-31.5% larger than the mean value in the early period before 1997) and streamflow in the recession period (20.9-25.8% larger than before 1997) for the five subbasins, except LS where reservoir operations are active. These processes initiated by climate warming have changed the hydrological properties of sub-basins considerably and altered the recession characteristics and the storage-discharge relationships. 440 It has been found that the recession parameter a that characterizes the stability of streamflow has decreased exponentially in the sub-basins, except LS. Meanwhile, the other parameter b that describes the nonlinearity of the recession to discharge increases exponentially in all the sub-basins. These results indicate that climate warming increases the nonlinearity of the recessions and reduces streamflow stability in most of the sub-basins in YRB. Our sensitivity analysis further shows the decrease of the sensitivity of discharge/streamflow to storage under the warming climate. Currently, the accelerated glacier 445 melting and permafrost thawing have recharged the system, thickening the active subsurface zone and increasing groundwater storage. Only a small fraction of the enlarged storage is released in surface streams because the increase of active water layer lengthens subsurface flow paths. These changes have also increased the recession timescale particularly in high altitude cold climate areas. In the warm climate areas downstream of YRB, effect of these changes is minor.
As the liquid water storage has increased greatly from melting glaciers and thawing permafrost in YRB in the recent warming 450 climate, the fast erosion of the solid water storage has weakened its buffering effect of the streamflow which is becoming less stable and more vulnerable to individual intense precipitation events. There are two potential consequences from these changes: one is the increase of flush flooding in the trend of rising precipitation in the high-altitude sub-basins where more land is exposed after the retreat of glaciers, and the other would be the extreme scenario of exhaustion of the water resources in the upstream of YRB after the buffering effect of glacier and permafrost is lost following the continued warming of the climate. 455 While human interference with these processes, via reservoirs and regulations, can reduce and curb these impacts of climate warming on storage-discharge relationships, recession characteristics, and streamflow in short term, as shown in the sub-basin LS, long-term strategies need to be developed to not only cope with the short-term needs but also the sustainability of water resources in the Tibetan Plateau under the threat of the continued warming that could change the entire hydrological system in this critical source region of water for the world most populated nations.