Potential role of permafrost thaw on increasing Siberian river discharge

Streamflow commonly originates from surface water (e.g. precipitation, snow/glacial melting, and etc) and groundwater discharge (e.g. lateral flow, permafrost thawing, and etc.). Therefore, we divide the streamflow ($Q$) into two components, surface-water-fed flow (${Q_{\text{s}}}$) and groundwater-fed flow (${Q_{\text{g}}}$). Different from ${Q_{\text{s}}}$, ${{Q_{\text{g}}}}$ as a portion of relatively stable streamflow changes slightly in-season throughout a year (Tan et al 2020). However, ${{Q_{\text{g}}}}$ may increase slowly over years throughout the northern Eurasia (Evans et al 2020) due to enhanced groundwater discharge and (or) increased shallow groundwater diffusive recharge caused by permafrost thawing (Walvoord and Kurylyk 2016, Biskaborn et al 2019). As shown in figure 2(a), when the permafrost warms up, the active layer and talik thicken (O'Donnell et al 2017). As a result, the upper boundary of permafrost starts to decline from State 1 to State 2. With subsequent increase in groundwater storage and groundwater flow (Lamontagne-Halle et al 2018), ${{Q_{\text{g}}}}$ gradually increases from State 1 to State 2, correspondingly, as shown in figure 2(b).

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In cold regions, surface runoff during winter is negligible due to freezing conditions. Thus, winter streamflow is presumably from groundwater (St. Jacques and Sauchyn 2009). Assuming that winter streamflow is the minimum continuous stable flow throughout a year for cold regions (Paznekas and Hayashi 2016), the yearly ${{Q_{\text{g}}}}$ described in figure 2(b) can be estimated by the observed winter streamflow. Whilst the influence of climate warming on streamflow varies (Tan et al 2020), long-term changes in ${{Q_{\text{g}}}}$ can be perceived as an indicator of climate change. In this study, the winter period (ice-covered period) in Siberia is from November to April (Wild et al 2019).

Following the Budyko framework (Budyko 1948), the basin-scale evapotranspiration (E) and streamflow (Q) can be calculated as a function of precipitation (P), potential evapotranspiration (E₀) and a parameter that describes basin properties (n) (Roderick and Farquhar 2011). Budyko equation, derived rigorously from a single mathematical assumption concerning the Budyko hypothesis, is widely applied to estimate the climate elasticity of streamflow (Sposito 2017). The generalized form of Budyko equation can be expressed as (Choudhury 1999, Roderick and Farquhar 2011):

$$\begin{equation}E = \frac{{P{E_0}}}{{{{\left( {{P^n} + {E_0}^n} \right)}^{1/n}}}}.\end{equation} \tag{ 1 }$$

Assuming a steady state water balance for basins larger than 10 000 km², an analytical expression using first order approximation can be derived from equation (1) to quantify the sensitivity coefficients of streamflow to climate (P, E₀) and basin properties (n) (Roderick and Farquhar 2011):

$$\begin{align}\frac{{{\text{d}}Q}}{Q} & = \left[ {\frac{P}{Q}\left( {1 - \frac{{\partial E}}{{\partial P}}} \right)} \right]\frac{{{\text{d}}P}}{P} - \left[ {\frac{{{E_0}}}{Q}\frac{{\partial E}}{{\partial {E_0}}}} \right]\frac{{{\text{d}}{E_0}}}{{{E_0}}}\nonumber\\ & \quad - \left[ {\frac{n}{Q}\frac{{\partial E}}{{\partial n}}} \right]\frac{{{\text{d}}n}}{n} = {\varepsilon _P}\frac{{{\text{d}}P}}{P} - {\varepsilon _{{E_0}}}\frac{{{\text{d}}{E_0}}}{{{E_0}}} - {\varepsilon _n}\frac{{{\text{d}}n}}{n},\end{align} \tag{ 2 }$$

where $_P$, ${\varepsilon _{{E_0}}}$, and _n are the sensitivity coefficients of P, E₀, and n to Q, respectively.

For cold regions, climate warming induced permafrost thawing can increase winter streamflow (St. Jacques and Sauchyn 2009), which eventually contribute to the streamflow. We assume that the winter streamflow is completely contributed by groundwater and it remains constant throughout a year. With this assumption, we calculate the annual groundwater-fed baseflow (${{Q_{\text{g}}}}$) in figure 2 from the measured winter streamflow. As mentioned earlier, changes in ${{Q_{\text{g}}}}$ is expected to be a result of variation in temperature, which is confirmed for the three great Siberian rivers (section 3.3). Therefore, the relationship between changes in ${{Q_{\text{g}}}}$ and T can be described as:

$$\begin{equation}{\text{d}}{Q_{\text{g}}} = {\alpha _{\text{T}}} \times {\text{d}}T \times {Q_{\text{g}}},\end{equation} \tag{ 3 }$$

where ${\text{d}}{Q_{\text{g}}} = {Q_{\text{g}}} - \overline {{Q_{\text{g}}}}$ is the groundwater-fed baseflow departure, mm; ${\text{d}}T = T - {\overline T}$ is the temperature departure, °C; ${\alpha _{\text{T}}}$ is the change rate of ${\text{d}}{Q_{\text{g}}}/{Q_{\text{g}}}$ as a function of ${\text{d}}T$, °C⁻¹; $\overline {{Q_{\text{g}}}}$ and ${\overline T}$ are long-term mean annual groundwater-fed baseflow and temperature, respectively. Next, the changes in streamflow induced by temperature can be written as:

$$\begin{equation}\frac{{{\text{d}}{Q_{\text{g}}}}}{Q} = {\alpha _{\text{T}}}*{\text{d}}T*\left( {{Q_{\text{g}}}/Q} \right).\end{equation} \tag{ 4 }$$

For a large basin, ${Q_{\text{g}}}/Q$ in equation (4) represents the percentage of groundwater-fed streamflow of the total streamflow, and it is highly dependent on the surface-water-fed streamflow (${Q_{\text{s}}}$) (see figure 2(b)). ${Q_{\text{s}}}$ is a partial product of $P\,$ and ${E_0}$. Assuming other hydrological and hydrogeological conditions remain constant, ${Q_{\text{s}}}$ increases when $P\,$ increases and ${E_0}$ decreases. Therefore, we propose an empirical dependence of ${Q_{\text{g}}}/Q$ on the ($P - {E_0}$) as follows (see example of figure S5 in supplementary files (available online at stacks.iop.org/ERL/16/034046/mmedia)):

$$\begin{equation}\frac{{{Q_{\text{g}}}}}{Q} = \beta - \gamma \left( {P - {E_0}} \right),\end{equation} \tag{ 5 }$$

where $\beta$ and$\,\gamma$ are the empirical parameters.

The Ob, Yenisei and Lena river basins differ greatly in temperature with multiyear mean (1936–2019) basin-averaged values of −0.07 °C, −5.91 °C and −10.09 °C, respectively (figure 3(a), table S1). These values are consistent with their areal extent of the permafrost (figure 1). For the Ob river basin, continuous permafrost constitutes merely 1% of the total basin area. By contrast, for the Yenisei and Lena river basins, continuous permafrost accounts for 30% and 73% of the total basin area, respectively (Brown et al 2002). Nevertheless, the warming rates of these three basins in the past 84 years are relatively consistent with approximately 0.25 °C/decade (p< 0.001) (table S1). Meanwhile, the Ob, Yenisei and Lena river basins experienced notable warming during winter (November to April according to Wild et al (2019)) with 0.36 °C/decade, 0.35 °C/decade and 0.36 °C/decade (all p < 0.001), respectively, which are all greater than the trends in the annual mean temperature.

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The multiyear mean (1936–2019) annual precipitation (P) of the Ob, Yenisei and Lena river basins were 423 mm, 418 mm, and 348 mm, respectively (figure 3(b), table S1). During the past 84 years, precipitation had positive trends in these three basins, i.e. 9.18 mm/decade, 5.30 mm/decade and 7.67 mm/decade (all p< 0.001), respectively. Increased precipitation in this region could be related to enhanced regional evapotranspiration (McClelland et al 2004) and atmospheric moisture transport (Bintanja 2018), and also the Arctic Oscillation (Frey and Smith 2003) under climate warming.

The mean annual potential evaporation (E₀) in the Ob River basin (620 mm) is much larger than that in the Yenisei (472 mm) and Lena (433 mm) river basins (figure 3(c)). The E₀ slightly trended upward across the Ob, Yenisei and Lena river basins with 5.23 mm/decade, 3.38 mm/decade and 2.51 mm/decade (all p< 0.001), respectively. In the period 1936–2019, the P–Q (i.e. difference between P and Q) of the Ob, Yenisei and Lena river basins were about 41%, 38% and 29% of E₀, respectively. Similar to the multi-year trend of E₀ from west to east, the P–Q in these three basins increased with 7.7 mm/decade, 3.2 mm/decade, 2.3 mm/decade, respectively.

Yenisei is the largest river in Siberia with the mean annual streamflow (Q) of 242 mm yr⁻¹, followed by the Lena (Q = 223 mm yr⁻¹) and Ob (Q = 168 mm yr⁻¹) rivers (figure 3(d)). In the period 1936–2019, streamflow of the Lena River increased significantly with a positive trend of 5.26 mm/decade (p < 0.001). While no significant trends in annual streamflow were detected for the Ob and Yenisei rivers over the same period (table S2). Analysis of 'naturalized' daily discharge (Shiklomanov 2010) showed that winter streamflow of the Ob (1950–2007, p < 0.001), Yenisei (1960–2004, p < 0.001) and Lena (1959–2007, p < 0.01) rivers significantly increased by 1.57 mm/decade, 4.17 mm/decade, and 0.90 mm/decade, respectively.

Overall, among these three basins, the Ob River Basin is relatively warm, has ample precipitation and the highest potential evaporation, while the Lena River Basin is characterized by the coldest climate, less precipitation and the lowest potential evaporation (figure 3(e)).

Following the methods of Risbey and Entekhabi (1996) and Fu et al (2007), we calculate the annual percentage departures for streamflow ($\Delta Q = \frac{{Q - {\overline Q}}}{{{\overline Q}}} \times 100\%$), surface-water-fed streamflow ($\Delta {Q_{\text{s}}} = \frac{{{Q_{\text{s}}} - \overline {{Q_{\text{s}}}} }}{{\overline {{Q_{\text{s}}}} }} \times 100\%$), groundwater-fed baseflow ($\Delta {Q_{\text{g}}} = \frac{{{Q_{\text{g}}} - \overline {{Q_{\text{g}}}} }}{{\overline {{Q_{\text{g}}}} }} \times 100\%$), precipitation ($\Delta P = \frac{{P - \bar P}}{{\bar P}} \times 100\%$), and temperature (${\text{d}}T = T - {\overline T}$) for a specific basin and plot the results on a precipitation-temperature plane (figure 4). To better compare streamflow–precipitation–temperature relationship among different basins, we divide the precipitation and temperature departures by their corresponding standard deviations.

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As shown in figure 4, it is clear that changes in Q are highly sensitive to changes in P but they are less sensitive to changes in T for the Ob and Lena river basins, which is consistent with a previous study (Xu et al 2020). By contrast, changes in Q are sensitive to both changes in P and changes in T for the Yenisei river basin. As a major component of streamflow, ${Q_{\text{s}}}$ is even more sensitive to P for all three river basins, which is likely due to direct influence of P on ${Q_{\text{s}}}$ (Ficklin et al 2016). To differ from Q and ${Q_{\text{s}}}$, changes in Q_g are positive response to changes in T, probably due to the enhanced groundwater discharge induced by permafrost thawing under a warming climate (Liu et al 2003). Additionally, Q_g also appears sensitive to P for Ob and Lena river basins. This is because Q_g reacts slowly to other delayed sources (such as P), although Q_g usually comes from groundwater storage (Hall 1968, Eckhardt 2008). Specifically, the response of changes in Q and Q_g to changes in climate variables in the Yenisei river basin is quite different from that in the other two river basins. This is probably because of reservoir regulations (Yang et al 2004, Stuefer et al 2011) and a lack of continuous discharge data for the Yenisei River during 1963–1979.

Similar to Roderick and Farquhar (2011), we assume that changes in river basin storage are less relative to the magnitude of fluxes (P, E, Q) over the pre-breakpoint (1936–1987) and post-breakpoint (1988–2019) periods of temperature, i.e. dQ= dP− dE. Typically, values of n in equation (1) range between 0.6 and 3.6, and lower values of n denote a lower estimate of E for a given P and E₀ (Roderick and Farquhar 2011). As shown in table S3, for the Ob basin, the parameter n changes slightly from 0.99 to 1.08 from one state (pre-breakpoint) to another state (post-breakpoint). For the other two basins, the parameter n does not change between two states (n= 0.75 for the Yenisei basin, and n= 0.61 for the Lena basin), indicating the basin properties generally remain unchanged over the past 84 years (figure S3). The decreasing values of n from the Ob, Yenisei to Lena river basins suggest that relative value of E for given P and E₀ is getting smaller from the west to east Siberian basins, which consistent with the air temperature gradient across the Siberian. Previous studies (Li et al 2013, Shi et al 2019) estimated the values of n as between 1.1 and 1.2 for all three basins, which are higher than our calculated values (especially for the Yenisei and Lena river basins). These differences could be due to the different reanalysis data of P and E₀ used in analysis.

On this basis, theoretical result of Budyko framework (table S3) quantitatively predicts a positive response of streamflow to precipitation, and a 10% increase in P would result in increases in Q by approximately 16.2%, 13.5% and 12.6% for the Ob, Yenisei and Lena rivers, respectively. However, a 10% increase in E₀ would reduce Q by approximately 6.2%, 3.5% and 2.6% for the Ob, Yenisei and Lena rivers, respectively. These results indicate that the relative impact of P on the Q is much larger than E₀ for all three basins. Besides, the response of Q to climatic factors P and E₀ decreases from West to East Siberian, indicating that streamflow in colder regions with developed permafrost is less sensitive to P and E₀.

As mentioned earlier, changes in Q_g reflects the influence of temperature changes on streamflow. Analysis of the 'naturalized' daily discharge data by removing the dam/reservoir impact shows that Q_g of the Ob (1950–2007), Yenisei (1960–2004) and Lena (1959–2007) river basins changed notably with increasing trends of 1.57 mm, 4.17 mm and 0.90 mm per decade (p < 0.05), respectively. Analysis of relationship between annual mean temperature departure ($T - {\overline T}$) and changes in Q_g (${\text{d}}{Q_{\text{g}}}/\overline {{Q_{\text{g}}}}$) indicates that an increase of 1 °C annual mean temperature would increase Q_g of the Ob, Yenisei and Lena river basins by approximately 6.1%, 10.5% and 7.8% (all p< 0.05), respectively. Equivalently, 1 °C warming would increase the annual streamflow of the Ob, Yenisei and Lena river basins by approximately 2.2%, 2.7%, and 1.0%, respectively. This suggests that a warmer climate would cause the baseflow to rise, which could lead to an increase in total streamflow in cold regions. Nonetheless, the influence of rising temperature on the streamflow is rather complex (Tan et al 2020).

By neglecting the changes in basin properties (n), we apply equations (2), (4) and (5) and consider the effect of T, P and E₀ on streamflow to predict the streamflow of the three great Siberian Rivers (listed in table S4). Figure 5 shows the relationship between observed and simulated dQ/Q during the period 1936–2019. In general, the simulated dQ/Q is in good agreement with the observed, especially for the Lena River. The correlation between simulated and observed dQ/Q is quite low for the Yenisei River, probably related to the intense reservoir operations which altered natural changes and variations in river regime (Yang et al 2004, Stuefer et al 2011). Additionally, the lack of continuous daily streamflow data during the period 1963–1979 for the Yenisei River weakens the reliability and accuracy in streamflow simulation.

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Relative to the period 1980–2000, the annual mean air temperature in Siberia is likely to increase by ∼3 °C–5 °C by the end of the 21st century (Groisman et al 2013). An increase in temperature would be accompanied by increasing precipitation, intense and frequent extreme precipitation events (Burt et al 2016). To understand the further changes in Q that corresponds to climate changes, we adopt the modeling results for the highest emission scenario RCP 8.5 by the Institute of Numerical Mathematics Climate Model Version 4 (INMCM4). Comparing 2081–2100 (RCP8.5) with 1981–2000, the annual average temperatures of the Ob, Yenisei, and Lena river basins would increase by 4.54 °C, 4.64 °C, and 4.71 °C, respectively; and their annual precipitations would increase by 17%, 21%, and 24%, respectively (Martynova and Krupchatnikov 2018). We use the equations described in table S4 to estimate streamflow in 2081–2100. We correlate changes in E₀ with change T (by using the correlation between annual E₀ and annual average temperature during the period 1936–2019), assuming the changes in E₀ only depend on the T changes (figure S4).

As shown in table S5, by comparing 2000–2019 with 1981–2000, the mean annual temperatures of the Ob, Yenisei and Lena river basins have increased by 0.53 °C, 0.62 °C, and 0.71 °C, respectively. This confirms that climate warming rate increased from west to east Siberia. This is similar to the predicting scenario trend in 2081–2100 and also shows that warming effect in colder regions is much greater than the warmer regions. Observations demonstrate that over the past 20 years, streamflows of the Ob, Yenisei, and Lena rivers have increased by 5%, 2% and 9%, respectively. It is expected that the intensified climate warming to the end of 21st century would significantly increase the annual streamflow of the Lena (∼28%) and Yenisei (∼20%) rivers, and some increase in the streamflow of the Ob River (∼9%) (table S5). Our predictions are in agreement with the previous estimates, which suggested that an increase of annual mean streamflow would be up to 15% for the Ob River, 20% for the Yenisei River, and 25% for the Lena River by 2081–2100 (Groisman et al 2013). This suggests that in the colder region (such as Lena River), where most of the basin area is covered by continuous permafrost, streamflow is more sensitive and responsive to a warmer climate (Liu et al 2003, Zhao et al 2020).

Considering an empirical relationship between Q_g/Q and P–E₀ (figure S5), we further estimated the changes in Q_g under a warming climate for Lena River, a drainage basin with larger extent of continuous permafrost (table S1). From 1981–2000 to 2000–2019, a 0.71 °C warming resulted in an increase in Q_g of approximately 2 mm, accounting for 10% of the total increase in Q (∼20 mm). When the temperature increases by 4.71 °C by the end of 21st century, a percentage of the increase in Q_g (∼12 mm) to the total increase in Q (∼62 mm) is expected to hit 19% (table S5). This suggests that the contribution of groundwater discharge to annual streamflow due to permafrost thawing in permafrost-dominated basins would continue to increase under global warming.