Original vegetation condition and precipitation growth rate bifurcate sediment flux trend on the Qinghai-Tibet Plateau

Abstract

Riverine sediment flux on the Qinghai-Tibet Plateau follows separate trends in different headwater basins because of complicated pathways under global warming. Here we successfully reconstructed historical sediment fluxes from seven pathways at 25 hydrological stations during 1982 ~ 2022 using a conceptual Multivariate Climate Elasticity Model based on Taylor expansion and revealed the bifurcation in sediment flux trend. Significantly increasing trends occurred at five stations, caused either by elevated runoff from increased precipitation (contributing -10 ~ 50%) or by temperature modifying the underlying surface (-12 ~ 100%). Significantly decreasing trends were found at six stations, primarily owing to vegetation expansion (11 ~ 100%). Combinations of original vegetation condition and increasing rate of precipitation are pivotal for bifurcating the sediment flux trend. In the future, slowly increasing precipitation with greatly increasing temperature or poor original vegetation condition followed by rapid vegetation expansion may decelerate sediment yield, whereas rapidly increasing precipitation may overwhelm the marginal conservation effect of plentiful vegetation.

Introduction

Climate change has caused sediment pathways on the Qinghai-Tibet Plateau to alter substantially^1,2,3, with repercussions for the local environment and affecting certain key engineering projects in the lower plateau^4,5. Although temperature and precipitation have both experienced rising trends in the Qinghai-Tibet Plateau during the past 60 years^2,6,7, recorded sediment fluxes have exhibited somewhat ambiguous behavior, with opposing change trends. For example, the headwaters of the Brahmaputra River (Yarlung Tsangpo River) experienced a significantly increasing trend in sediment flux³, whereas drainage areas of the Tangnaihai station in the source region of the Yellow River⁸ and of the Aral station in Tarim River basin⁹ experienced decreasing trends. The primary reason for the distinctly different change patterns in the Qinghai-Tibet Plateau may lie in the complicated pathways that drive sediment flux change through climate change. Generally speaking, heavier precipitation increases sediment load either directly by eroding the land or indirectly through the runoff yield process. Higher land surface temperature accelerates sediment yield by melting permafrost and expanding the active erodible layer^{10,11,12,13,14,15,16,17} (Fig. 1a). Conversely, as vegetation cover spreads, it protects the land from erosion; this process is enhanced by warming and wetting, and is fertilized by elevated CO₂ concentration in the atmosphere³. Moreover, the observed shift in monthly precipitation peak from June-July to July-August in the period from 1986 to 2014 may have also buffered rainfall erosivity on the Qinghai-Tibet Plateau¹ (Fig. 1a). The balance of power between increasing and decreasing pathways within a drainage area determines the change patterns of sediment fluxes at the outlet of the basin.

Fig. 1: Sediment flux trend and the overall contributions of major pathways on sediment yield at each hydrological station.

a Locations of hydrological stations (black acronyms, see explanations in Supplementary Table 1) at each studied rivers (gray words) with significant increase trend (red triangles), decrease trend (blue triangles) and no significant trend (green triangles), overall contributions of precipitation (blue pie charts), temperature (orange pie charts) and vegetation (green pie charts) to sediment yield, and major pathways for the effects of climatic factors on sediment yield. Thereinto, Pathway I represents the rainfall erosivity of soil; Pathway II represents sediment yield by river discharge; Pathways III and IV represent the sediment flux affected by the erodibility of the underlying soil and by vegetation cover, respectively; Pathways V and VI represent the runoff yield from precipitation and melting, respectively; Pathways VII and VIII represent the runoff yield affected by vegetation cover or by the underlying soil surface; Pathway IX represents the modification of the active layer by temperature; Pathways X and XI represent vegetation growth affected by precipitation and temperature, respectively. b Major pathways for stations with significantly increasing sediment flux. c Major pathways for stations with significantly decreasing sediment flux. The map in (a) was created by the authors using ArcMap software (version 10.7). The raw data is presented in Data availability.

To explore the bifurcation point at which sediment flux can either increase or decrease in response to warming and wetting, it is essential to trace the main pathways that drive change in sediment flux and estimate their specific individual contributions. Several previous studies have focused on sediment change processes on the Qinghai-Tibet Plateau, notably responses to variations in precipitation and temperature^{1,18,19,20,21,22,23}. Such studies either employed process-based models such as Water Erosion Prediction Project (WEPP)²⁴, Soil and Water Assessment Tool (SWAT)²⁵, and Integrated Nitrogen Catchment model (INCA)²⁶, or relied on statistical models such as Revised Universal Soil Loss Equation (RUSLE)²⁷, Dynamic Revised Universal Soil Loss Equation (D-RUSLE)²⁸, multiple double mass curves²⁰, Climate Elasticity Model (CEM)², and Partial Least Squares Path Modeling (PLS-PM)³. The data requirement for running a process-based model is usually very high, given that many parameters need to be calibrated, thus either confining the study area or introducing large uncertainty²⁹. Conversely, statistical models are often implemented in large areas. However, expressed in rather simple forms, these statistical relationships are usually unable to trace the sediment change induced through complicated pathways (as shown in Fig. 1a). Zhang et al.¹ proposed a statistical method called Partial Least Squares Structural Equation Modeling (PLS-SEM) which is sufficiently powerful to incorporate a series of factors in a large headwater basin. When driven by the historical covariance between pairs of all key factors, the PLS-SEM method is used in practice to test correlations between sediment load and different driving factors, rather than to estimate flux variations quantitatively. Shi et al.³ tried to quantify the contributions from precipitation and runoff yield in a large area of the Qinghai-Tibet Plateau based on an improved Sediment Identity Method which employed a chain of ratios between different climatic/hydrological variables, rather than estimating the separate contributions by each variable. To the authors’ knowledge, no proper method is available for retracing the quantitative sediment yield affected by the major interacting factors over a large area. Here we set up a physically sound framework analogous to Maxwell’s thermodynamic relations³⁰ which combines the advantages of current methods (see Methods), and then quantify sediment changes driven through the main physical pathways by data that are relatively straightforward to obtain at large scale (i.e., covering two-fifths of the land area of the Qinghai-Tibet Plateau). Moreover, the bifurcation point beyond which sediment flux either increases or decreases is unknown to date. Therefore, circumstances that lead either to increasing or decreasing sediment flux are also explored to assess the implications for future sediment change driven by various levels of climate change.

Results

Historical trends in sediment flux

Historical sediment flux series, with a maximum time span from 1982 to 2022, were collected at 25 gauging stations from multiple sources (see Supplementary Table 1) covering a total drainage area of 1,544,263 km² (two-fifths of the total Qinghai-Tibet Plateau, see Supplementary Table 1). The M-K trend tests showed that different patterns occurred. Only five gauging stations were found to have significant increase trends in sediment flux, namely Tuotuo (TT in Fig. 1a) in the Yangtze River basin, Changmapu and Panjiazhuang (CMP and PJZ in Fig. 1a) in the Shule River basin, Daojieba (DJB in Fig. 1a) in the Nujiang River basin, and Partab Bridge (PB in Fig. 1a) in the Indus River basin. By contrast, six other gauging stations exhibited significant decrease trends in sediment flux, i.e., Maqu (MQ in Fig. 1a) in the Yellow River basin, Xinzhai and Panzhihua (XZ and PZH in Fig. 1a) in the Yangtze River basin, Yanqi and Aral (YQ and ARL in Fig. 1a) in the Tarim River basin, and Dainyor Bridge (DB in Fig. 1a) in the Indus River basin. Sediment flux changes were insignificant at the remaining 14 gauging stations (Supplementary Table 1). Our results were supported by previous studies that confirmed increasing trends in sediment flux at the Tuotuo, Changmapu, Panjiazhuang, Daojieba, and Partab Bridge stations^2,31,32,33, and found decreasing trends at the Xinzhai, Tangnaihai, Yanqi, Aral, and Dainyor Bridge stations^8,34,35,36.

Driving pathways for different sub-areas

To analyse the complicated pathways that influence sediment yield in the studied area (Fig. 1a) and interpret the major pathways in detail, we set up a Multi-order Multivariate Climate Elasticity Model based on Taylor expansion (see Methods), which properly reconstructed the historical sediment flux series (Supplementary Fig. 1 and Supplementary Table 2). The pathways were divided by factors into four groups, namely: discharge-related (Pathway II), precipitation-related (Pathway I and Pathway V), temperature-related (Pathway VI, Pathway IX ~ VIII and Pathway IX ~ III) and vegetation-related (Pathway VII and Pathway IV) pathways (Supplementary Table 3). The sequence of pathway numbers corresponds to the sequence within the pathway chain. For instance, in the case of Pathway IX ~ VIII, temperature influences the underlying surface (IX), which in turn affects the discharge (VIII). The complex contributions by each pathway are shown in the corresponding partial elasticity coefficients of multiple orders (see Methods).

The lowest-order term of the partial elasticity coefficient of the discharge-related pathway (see Methods), Pathway II, which reflects the sediment transport capacity of runoff, is invariably positive for each gauging station. Given that the lowest-order term usually acts as the major component, this indicates that larger river discharge usually carries more sediment in the rivers of the Qinghai-Tibet Plateau.

Of the precipitation-related pathways, Pathway I reflects precipitation erosivity, and Pathway V represents runoff generated from precipitation. The partial elasticity coefficients of both these pathways are usually positive in the lowest order term, indicating positive contributions to changes in both sediment and discharge as precipitation increases.

The effects of the temperature-related pathways are more complicated in different sub-basins. Pathway VI and Pathway IX ~ VIII together reflect the total influence of temperature on runoff; in such cases, the total partial elasticity coefficient can be either positive (i.e., increasing temperature accelerates runoff yield) or negative (i.e., increasing temperature corresponds to less snow/glacial melt runoff in the long term^37,38,39 and enhanced evaporation). Pathway VI, which reflects the influence of temperature on snowmelt-induced runoff, is often characterized by a negative partial elasticity coefficient, which implies that an increase in temperature usually leads to a decrease in snowmelt runoff³⁹. The partial elasticity coefficient of Pathway IX ~ VIII is derived by subtracting the partial elasticity coefficient of Pathway VI from the total effect of temperature on runoff and represents the indirect influence of temperature on runoff through modification of the underlying soil surface; the partial elasticity coefficient of Pathway IX ~ VIII is usually positive. We do not separately consider glacial-melt runoff which is expected to rise at first and fall later in the future^{12,40,41,42,43} because of the lack of a sufficiently long continuous data series for the entire Qinghai-Tibet Plateau. Pathways IX ~ III, reflecting the indirect influence of temperature on sediment flux through modification of the underlying soil surface, can possess either positive or negative values of partial elasticity coefficient at different stations, most likely due to different soil types in the permafrost layer. For instance, coarser, cohesionless soil released from melting permafrost may increase sediment flux⁴⁴, whereas cohesive soil may reduce sediment flux because erosion resistance increases with cohesion^45,46.

As for the vegetation-related pathways, the partial elasticity coefficient of Pathway IV is usually negative, indicating that vegetation growth decreases sediment flux^47,48,49 perhaps through the interception of raindrops, provision of additional surface roughness, and addition of organic substances to soil within the basin^50,51. However, the partial elasticity coefficient of Pathway VII, which reflects the impact of vegetation on runoff, is usually positive. This counterintuitive phenomenon may be induced by the co-linearity of vegetation growth and precipitation/temperature. When taking into consideration the effects of precipitation and temperature on vegetation (i.e., Pathway X and Pathway XI indicated by the dotted lines in Fig. 1a), the partial elasticity coefficients are re-calculated. It is found that Pathway XI is significant at almost all the stations, while Pathway X is significant at about half of the stations (Supplementary Table 2). Therefore, it is highly probable that the effects of Pathway X and Pathway XI have not been separated from Pathway VII.

Of all the pathways mentioned above, we focus on those starting from natural factors and finally linking to sediment change, which we call a pathway chain. Three types of pathway chains are identified (Supplementary Table 2): precipitation pathway chains (Pathway I and Pathway V ~ II), temperature pathway chains (Pathway VI ~ II, Pathway IX ~ VIII ~ II, and Pathway IX ~ III), and vegetation pathway chains (Pathway IV and Pathway VII ~ II). Note that the discharge-related pathway (Pathway II) does not constitute a whole pathway chain alone, but forms a single link in other different pathway chains.

To analyze the major pathway chains driving the increasing trend in sediment flux in the five sub-areas (i.e., the stations marked by red triangles in Fig. 1a), we find that two pathway chains are usually significant (Fig. 1b). One enhances sediment yield by increasing erodibility of the underlying soil surface through melting permafrost (Pathway IX ~ III), as occurs at Changmapu and Panjiazhuang stations (CMP and PJZ in Fig. 1a) in the Shule River basin and at Partab Bridge station (PB in Fig. 1a) in the Indus River basin. The other major pathway chains boost sediment load through enhanced runoff from increased precipitation (Pathways V ~ II), as evidenced by the sediment fluxes at Tuotuo station (TT in Fig. 1a) in the Yangtze River basin and Daojieba station (DJB in Fig. 1a) in the Nujiang River basin. Strengthened erosivity driven by rising precipitation also makes a significant contribution to the increasing sediment load at Tuotuo station in the Yangtze River basin.

Sub-areas with decreasing trends in sediment load also encounter two major pathway chains (Fig. 1c). One retains sediment by vegetation, as evident at the Yanqi and Aral stations (YQ and ARL in Fig. 1a) in the Tarim River basin, and the Dainyor Bridge station (DB in Fig. 1a) in the Indus River basin (Pathway IV). The other decreases sediment yield through the impact of rising temperature on the underlying surface (Pathway IX ~ III), as observed at Xinzhai station (XZ in Fig. 1a) in the Yangtze River basin and Tangnaihai station (TNH in Fig. 1a) in the Yellow River basin. Note that Pathway IX ~ III is also one of the major pathway chains identified in the sub-area with increasing trend. The different role of Pathway IX ~ III in sub-areas with decreasing trend could be due to modification of the land surface by vegetation growth under a warming climate.

Quantitative contribution by the major pathways to sediment flux change

The change in sediment flux due to it taking a given pathway chain over any one year during the historical period can be quantitatively calculated by comparing the sediment yield from the pathway chain in that year to that in all previous years (Fig. 2a). Analogous to the M-K method which successfully detects the trend signals of a time series, the mean percentage contribution of that pathway chain over the whole historical period can be estimated by averaging over all years and all pathway chains (see Methods). The contribution from the precipitation pathway chain (Pathway I and Pathway V ~ II) is usually positive (20% averaged over the drainage area), whereas the contributions from the temperature pathway chain (Pathway VI ~ II and Pathway IX ~ VIII ~ II and Pathway IX ~ III) and the vegetation pathway chain (Pathway IV and Pathway VII ~ II) are most likely to be negative (-8% and −23% averaged over the drainage area, respectively). Competition between negative and positive contributions to the change in sediment flux leads to the final trend of increasing or decreasing sediment flux (Fig. 2b, c and d).

Fig. 2: Percentage contributions to sediment flux change and contributions to sediment flux anomaly.

a Percentage contributions to sediment flux change from each pathway chain, and the dominant control factor at each gauging station. b–d Each pathway chain and its overall contribution to mean historical annual sediment flux at a representative precipitation-dominated station, Shigu station in the Yangtze River basin (b), a representative temperature-dominated station, Changmapu station in the Shule River basin (c), and a representative vegetation-dominated station, Yanqi station in the Tarim River basin (d). The bold lines in (b–d) represent the controlling pathway chains.

Our quantitative contribution analysis also highlights dominant pathway chains. Here, 16%, 36%, and 48% of the stations are precipitation-dominated, temperature-dominated, and vegetation-dominated (Fig. 2a). Stations dominated by precipitation all exhibit an increasing trend in historical sediment flux, due to increasing precipitation. From the southeast to the northwest, the influence of temperature gradually grows as the temperature itself increases, whereas the influence of precipitation gradually weakens as the precipitation decreases; there is an increasing influence of vegetation cover from upstream to downstream as the vegetation becomes denser^52,53,54 (Fig. 1a). In some areas, the contribution of a single factor can even exceed 75%, with that factor almost entirely determining the change of sediment flux, examples being temperature at Panjiazhuang station (PJZ in Fig. 1a) in the Shule River, precipitation at Nuxia station (NX in Fig. 1a) in the Yarlung Tsangpo River, and vegetation cover at Dainyor Bridge station (DB in Fig. 1a) in the Indus River.

Previous studies have basically supported our quantitative estimation methodology. For example, we found that the effect of precipitation dominates (more than 60% on average) the change in sediment flux in the Yarlung Tsangpo River basin, similar to observations by Shi et al.³. For the Tuotuo River basin, Zhang et al.¹ found that the increase in suspended sediment concentration is mainly due to increased precipitation, again similar to our research findings. However, the rainfall erosivity pathway is not as significant in the present study as in the investigations by Shi et al.³ and Zhang et al.¹, with the discrepancies most likely due to the selection of hydrological gauging stations.

Circumstances that cause the increasing/decreasing trends in sediment flux to bifurcate

Using the spectral clustering method, the 25 gauging stations are grouped into 6 clusters (Supplementary Fig. 2 and Supplementary Table 4–5). Except for the temperature change rate which exhibits an increasing trend across all groups, all other factors experience varying trends among the clusters. Thus, mean temperature, mean precipitation and precipitation change rate, mean vegetation coverage, and the growth rate of vegetation fraction are employed to illustrate the circumstances that may lead to a bifurcation in sediment trend.

Comparing the characteristics of each of the above factors among the different clusters, we find that a decrease in precipitation is likely to result in a decrease in sediment flux, probably due to the decrease in runoff by rainfall and rainfall erosivity (Cluster 1 in Fig. 3a). When precipitation increases at a relatively slow rate, sediment flux tends to decrease due to accelerated evaporation with warming (Cluster 2 and 3 in Fig. 3a). When precipitation increases at a relatively rapid rate, the original vegetation conditions tend to determine the trend in sediment flux: extremely poor vegetation cover at the start point is linked to sediment reduction, probably due to relatively fast growth in vegetation coverage (Cluster 4 in Fig. 3a); relatively good vegetation condition may lead to sediment increase, most likely due to the diminished marginal conservation effect of vegetation (Cluster 5 in Fig. 3a). Relatively cool, dry areas where the rates of increase in temperature and precipitation are high compared to the original condition may also exhibit increases in sediment flux due to the more active thermal and hydrological processes related to sediment yield (Cluster 6 in Fig. 3a). It should be noted that the foregoing clustering analysis provides only an overall indication of the circumstances in which a bifurcation in sediment flux is most likely to appear. An exception is found in the case of Partab Bridge station (PB in Fig. 1a) which exhibits a significant increase in sediment flux but is classified within a decreasing cluster.

Fig. 3: Bifurcation diagram and change trends in sediment flux and three driving factors.

a Bifurcation diagram for sediment flux change. b–d Increasing (red shading) and decreasing (blue shading) trends in sediment flux in history and in the future due to vegetation, temperature, and precipitation conditions, as shown at: Panjiazhuang station which experiences an accelerating trend of increase under SSP585 (b); Shigu station where the sediment flux alters from an increasing to a decreasing trend under SSP126 (c); and Aral station where the sediment flux gradually shifts from a decreasing to an increasing trend under SSP126 (d). The bold lines in (b–d) represent the controlling factor, and the dashed lines in (b–d) represent the trend line of each controlling factor.

Discussion

Future riverine sediment flux in the Qinghai-Tibet Plateau may either maintain its current trend or switch onto another track, depending on whether conditions in the sub-area have crossed the bifurcation point. In the catchment areas of stations that are controlled by temperature pathway chains (Pathways VI ~ II, IX ~ VIII ~ II and IX ~ III), the sediment yield tends to maintain its current trend, especially for high-emission scenarios (SSP370 and SSP585 prescribed by CMIP6 models, see Supplementary Table 6). In the drainage areas of Changmapu and Pangjiazhuang stations (Fig. 3b, locations of CMP and PJZ in Fig. 1a) in the Shule River basin, the growth rate of sediment flux may even accelerate due to the extremely fast ongoing increase in temperature (0.65°C/10 yr under SSP585).

By contrast, when the sediment yield is controlled by precipitation or vegetation pathway chains, the current trend in sediment flux may break or even be reversed, leading to bifurcation (Supplementary Table 6). Regarding sub-areas controlled by precipitation pathway chains, a decrease/increase in the precipitation change rate of over 0.5 mm/yr is probably the critical condition for sediment flux bifurcation. Examples are provided by Shigu station (SG in Fig. 1a) in the Yangtze River basin (Fig. 3c) and Lhasa station (LS in Fig. 1a) in the Yarlung Tsangpo River basin, which presently exhibit increasing trends in sediment flux, and may switch onto a decreasing or insignificant trend track under SSP126 because of an obvious decrease in precipitation growth rate. On the other hand, in catchment areas where sediment yield is controlled by vegetation pathway chains (Pathways VII ~ II and IV), the change rates of sediment load may slow down under SSPs 370/585 or even be reversed under SSPs 126/245, due to the slower increasing trends or even decreasing trends in vegetation coverage in the future (Fig. 3d and Supplementary Table 6). Although it is difficult to give a value range beyond which bifurcation in sediment flux trend may occur, our results show in Cluster 5 that the marginal effect of vegetation conservation would decrease gradually when vegetation cover fraction exceeds 0.2 (or 20%).

It should be emphasized that critical conditions in terms of precipitation and vegetation may vary with time or regions. Moreover, the dominant pathway chain of each sub-area may change, leaving the future sediment flux trend even more obscure. For instance, when the capacity of vegetation for sediment retention becomes saturated, the precipitation or temperature pathway chains are likely to dominate over the vegetation pathway chains; such change patterns have yet to be explored.

Bifurcation of the sediment flux trend due to complicated pathways may also appear in other cryospheric areas and flood plains. Taking the Andes as an example of the cryospheric area, where historical vegetation degradation has driven an increase in sediment flux⁵⁵, trend bifurcation is likely to occur if vegetation cover is restored in the future. For floodplains where vegetation is typically dense, it is possible that the impact of vegetation cover has reached a tipping point where the marginal benefits are diminishing. Consequently, a divergence in precipitation trend may result in a corresponding divergence in sediment flux.

Expansion or shrinkage of the river channel is bound to radical changes in sediment flux, together with discharge and vegetation^56,57. An increase in sediment flux and water discharge could potentially enhance the erosion capability of the river flow, causing the channel to expand. Conversely, decreasing sediment flux and water discharge can mitigate riverbed erosion. When the riverbed is stabilized by increased vegetation along its banks, the riverine sediment flux is consequently reduced. Thus, while sediment flux helps to shape river morphology, river channel evolution potentially influences sediment flux trends.

Our study has certain limitations. Owing to a lack of observed data, we did not explicitly consider the effect of ice melt which could cause glacial till collapse, landslides, and debris flows, dramatically altering sediment flux in rivers^2,58,59. Herein, the effect of ice melt was implicitly included in the pathway whereby temperature modifies the underlying soil surface. In addition, anthropogenic impacts were neglected because the river basins on the Qinghai-Tibet Plateau are supposed to be hardly affected by human activities. However, with the exploitation of water resources on the Qinghai-Tibet Plateau, the anthropogenic impacts will continue to increase, and it is recommended that future studies incorporate the contribution by human activities to sediment flux.

Our research quantified historical trends in riverine sediment flux which were either decreasing or increasing in different catchments of the Qinghai-Tibet Plateau. Noting that sediment flux is affected by complex mechanisms driven by climate change, we identified significant pathway chains and quantified their contributions at 25 gauging stations on the Qinghai-Tibet Plateau. We found that increasing sediment flux pathway chains are usually related to hydrological and thermal sediment yield processes, whereas decreasing sediment flux pathway chains mostly reflected sediment retention by vegetation. The balance of power between increasing and decreasing pathway chains finally determines the variation trend in sediment flux. Consequently, the bifurcation point is likely to be sensitive to the precipitation growth rate and the original vegetation conditions. Rapidly increasing precipitation in relatively cold and dry areas may accelerate sediment yield. However, a slow increase in precipitation, combined with a rapid rise in temperature, may lead to a decrease in sediment yield. Even in the face of rapidly escalating precipitation, poor original vegetation cover followed by swift expansion may also contribute to sediment reduction. Therefore, the future sediment change trend may change or even reverse when precipitation growth rate and vegetation cover fraction cross the bifurcation point under different SSPs of CMIP6 models. The present study provides insights that are transferable to other high-mountain or high-latitude areas undergoing complex sediment yield processes due to global warming.

Methods

M-K trend test method

The Mann-Kendall (M-K) trend test⁶⁰, which is two-sided, is a nonparametric method widely used to quantify trends in non-normal data such as precipitation, temperature, and discharge. The M-K method assumes that the time series of elements may be expressed,

$${{\rm{X}}}=({{x}}_{1}{,{{x}}}_{2}{,{{\ldots }},{{x}}}_{{{n}}})$$

(1)

where n is the number of sample sequences. The detection statistic S is given by:

$${{S}}=\mathop{\sum}\limits_{i=1}^{n-1}\mathop{\sum}\limits_{j=i+1}^{n}{{\rm{sgn}}}({{x}}_{j}{-{{x}}}_{i})$$

(2)

Where

$${{\rm{sgn}}}({{x}}_{j}{-{{x}}}_{i})=\left\{\begin{array}{c}+1,({{x}}_{j}{-{{x}}}_{i}) > 0 \\ 0,({{x}}_{j}{-{{x}}}_{i})=0\\ -1,({{x}}_{j}{-{{x}}}_{i}) < 0 \end{array}\right.$$

(3)

The standardized statistic Z is:

$$Z=\left\{\begin{array}{c}\frac{S-1}{\sqrt{{{\rm{Var}}}(S)}},S > 0\\ 0,S=0\\ \frac{{{S}}+1}{\sqrt{{{\rm{Var}}}(S)}},S < 0\end{array}\right.$$

(4)

where Var(S) is the variance of S which is calculated as:

$${{\rm{Var}}}(S)=\frac{1}{18}n(n-1)(2n+5)$$

(5)

For a given significance level α, if |Z | ≥ Z_(1-α/2), there is an obvious upward (Z > 0) or downward (Z < 0) trend in the time series data X. Specifically, if |Z | ≥ 1.96 or |Z | ≥ 2.58, the significance test was passed at a level of 0.05 or 0.01, respectively.

Multi-order Multivariate Climate Elasticity Model

First, let us examine the Climate Elasticity Model (CEM) previously used to analyze the sensitivity of sediment load to a single climate factor² (i.e., precipitation or temperature). At the core of CEM is the elasticity coefficient, defined as:

$${{{\varepsilon }}}_{Y-X}=\frac{{{\rm{d}}}Y/Y}{{{\rm{d}}}X/X}=\frac{{{\rm{d}}}Y}{{{\rm{d}}}X}\cdot \frac{X}{Y}$$

(6)

where X is the independent time series and Y is the dependent time series, i.e., Y = f(X). Therefore, the relationship between dY and dX is:

$${{\rm{d}}}Y=\left({{{\varepsilon }}}_{Y-Y}\cdot \frac{Y}{X}\right){{\rm{d}}}X$$

(7)

By definition, the elasticity coefficient is the derivative of X with respect to Y divided by $\frac{X}{Y}$:

$${\varepsilon }_{Y-X}=f\mbox{'}(X)\cdot \frac{X}{Y}$$

(8)

Previous studies based on double mass curves or regression have shown that the growth rate of sediment load (holding all other variables constant) roughly obeys linear relationships with the growth rates of precipitation and temperature². An alternative form of Eq. (7) under the linear assumption is²:

$${{\Delta }}Y=\left({\varepsilon }_{Y-X}\cdot \frac{\overline{Y}}{\overline{X}}\right){{\Delta }}X$$

(9)

where ∆X and ∆Y are the anomalies, and $\bar{X}$ and $\bar{Y}$ are the mean values of the respective time series. Thus, the elasticity coefficient can then be determined by performing a linear regression at each step of the time series.

However, when the non-linear components of f(X) play an important role, Eq. (9) is no longer a good approximation to Eq. (7) because ∆X is far beyond the neighbourhood of X. Therefore, high-order terms should be included based on a Taylor expansion, and corresponding high-order elasticity coefficients should be defined. Assuming that X lies within the radius of convergence of the Taylor series, we have:

$$\begin{array}{c}{{\Delta }}Y=f\mbox{'}(X)\cdot {{\Delta }}X+\frac{f\mbox{''}(X)}{2!}\cdot {{\Delta }}{X}^{2}+\cdots +\frac{{f}^{k}(X)}{{{k}}!}\cdot {{\Delta }}{X}^{k}+\\ \cdots +\frac{{f}^{N}(X)}{N!}\cdot {{\Delta }}{X}^{N}+{R}_{N}(X)\end{array}$$

(10)

where f ^k(X) is the k-th order derivative of f(X), N is the total number of orders that are included to approximate ΔY, and R_N(X) is the remainder of the series. By analogy to Eq. (8), the k-th order elasticity coefficient is:

$${\varepsilon }_{Y-X}^{k}=\frac{{f}^{k}(X)}{k!}\cdot \frac{{\overline{X}}^{k}}{\overline{Y}}$$

(11)

Equation (10) can then be rewritten as:

$$\frac{{{\Delta }}Y}{\overline{Y}}=\mathop{\sum}\limits_{k=1}^{N}{\varepsilon }_{Y-X}^{k}\cdot {\left(\frac{{{\Delta }}X}{\bar{X}}\right)}^{k}+\frac{1}{\overline{Y}}\cdot {R}_{N}(X)$$

(12)

from which the k-th order elasticity coefficients can be obtained by performing multivariate linear regression between $\frac{{{\Delta }}Y}{\bar{Y}}$ and ${(\frac{{{\Delta }}X}{\bar{X}})}^{k}$.

In fact, the sediment yield process can hardly be described by a univariate function. Therefore, a Multi-order Multivariate Elasticity Model is required, based on the multivariate Taylor expansion. For a multivariate function Y = f(X₁, X₂,…, X_n), the Taylor expansion within the radii of convergence of all the variables is:

$${{\Delta }}Y=\mathop{\sum}\limits_{i=1}^{n}{{\Delta }}{X}_{i}\frac{\partial f}{\partial {X}_{i}}+\mathop{\sum}\limits_{k=2}^{N}\frac{1}{k!}\mathop{\sum}\limits_{{m}_{1}\cdots {m}_{{{k}}}=1}^{n}{{\Delta }}{X}_{{m}_{1}}\cdots {{\Delta }}{X}_{{m}_{k}}\frac{{\partial }^{k}f}{\partial {X}_{{m}_{1}}\cdots \partial {X}_{{m}_{k}}}+{R}_{N}({X}_{1},\cdots {X}_{n})$$

(13)

Here X_i stands for the i-th factor that could affect sediment load. Noting that the elasticity coefficient reflects the sensitivity of Y to a single variable, we only choose the k-th order partial derivative with respect to a single variable [i.e. m₁= … = m_k in Eq. (13)] to construct the k-th order partial elasticity coefficient by analogy to Eq. (11):

$${\varepsilon }_{Y-{X}_{i}}^{k}=\frac{1}{k!}\cdot \frac{{\partial }^{k}f}{\partial {X}_{i}^{k}}\cdot \frac{{{{\overline{X}}_{i}}}^{k}}{\overline{Y}},k=1,\cdots ,N$$

(14)

where $\frac{{\partial }^{k}f}{\partial {X}_{i}^{k}}$ is the k-th order partial derivative of f(X₁,…, X_n) with respect to X_i, N is the total number of orders that are included to approximate ΔY, and R_N(X₁,…, X_N) is the remainder for the series. Similarly, the k-th order partial elasticity coefficients can also be obtained by performing linear regression between $\frac{{{\Delta }}Y}{\bar{Y}}$ and ${(\frac{{{\Delta }}{X}_{i}}{\bar{X}})}^{k}$ in Eq. (15):

$$\frac{{{\Delta }}Y}{\overline{Y}}=\mathop{\sum}\limits_{i=1}^{{{n}}}\mathop{\sum}\limits_{k=1}^{N}{\varepsilon }_{Y-{X}_{i}}^{k}{\left(\frac{{{\Delta }}{X}_{i}}{{\overline{{X}}_{i}}}\right)}^{k}+\frac{1}{\overline{Y}}\cdot R^{\prime}_{N}({X}_{1},\cdots ,{X}_{{{n}}})$$

(15)

where R’_N(X₁,…, X_n) is the remainder including R_N(X₁,…, X_n) and the terms containing derivatives with respect to multiple variables.

In practice, the linear term in the Taylor expansion is often the most important component of a function in the neighbourhood of x₀, unless f’(x₀) approximates 0. Hence, when a factor drives sediment change, it is likely to affect sediment yield linearly. If the linear correlation is not significant for a factor, we can further test the second-order term, third-order term, and so on in the Taylor formula.

To describe Pathways I, II, III and IV in Fig. 1, we set up a multivariate function:

$${Q}_{S}={f}_{1}(P,Q,L,V)$$

(16)

where Q_S is sediment flux, P is precipitation, Q is runoff discharge, L represents the characteristics of the underlying soil surface, and V is vegetation cover. Similarly, Pathways V, VI, VII and VIII are summarized as

$$Q={f}_{2}(P,T,L,V)$$

(17)

where T is temperature. More specifically, assuming that the snowmelt-induced discharge depends on temperature, Pathway VI is described as:

$${{{Q}}}_{{\rm{SNOW}}}={f}_{3}(T)$$

(18)

Pathway (IX) is

$$L={f}_{4}(T)$$

(19)

Note that long-term observations of precipitation and temperature are usually available from meteorological stations whereas runoff and sediment load series data are acquired at hydrological stations. V can be represented by the vegetation cover fraction which is derived from the Leaf Area Index (LAI)⁶¹:

$$V{=1-{{\rm{e}}}}^{-\frac{{{\rm{LAI}}}}{2}}$$

(20)

However, L in Fig. 1 stands for the comprehensive effect of land, i.e., either acting as the underlying soil surface for runoff yield or expressing the characteristics of the active layer and erodibility of soil, and so there is no single measurable index for L. Therefore, it is useful to eliminate L from the foregoing equations. To achieve this, we start with the total differential form of Eqs. (16) and (17):

$${{\rm{d}}}{Q}_{{{\rm{S}}}}=\frac{\partial {f}_{1}}{\partial P}\cdot {{\rm{d}}}{P}+\frac{\partial {f}_{1}}{\partial Q}\cdot {{\rm{d}}}{Q}+\frac{\partial {f}_{1}}{\partial L}\cdot {{{\rm{f}}}^{\prime}_{\!4}}\cdot {{\rm{d}}}{T}+\frac{\partial {f}_{1}}{\partial V}\cdot {{\rm{d}}}{V}$$

(21)

or

$${{\rm{d}}}Q=\frac{\partial {f}_{2}}{\partial P} \cdot {{\rm{d}}}{P}+\left(\frac{\partial {f}_{2}}{\partial T}+\frac{\partial {f}_{2}}{\partial L} \cdot {{\rm{f}}}^{\prime}_{\!4}\right) \cdot {{\rm{d}}}T+\frac{\partial {f}_{2}}{\partial V}\cdot {{\rm{d}}}V$$

(22)

By defining f₄ in Eq. (18), $\frac{\partial {f}_{2}}{\partial T}$ in Eq. (22) can be approximated by the derivative of f₄ with respect to T.

Next, we consider the multivariate Taylor Expansion. To ensure all the variables lie within the radii of convergence of the different Taylor series, we normalize the changes in Q_S, P, T, Q, V and Q_SNOW to produce time series varying within (−1, 1). Taking the normalized change in Q_S given by ΔQ_Sn for example, we have:

$${{\Delta }}{Q}_{S{{\rm{n}}}}=\frac{{Q}_{{{\rm{S}}}}-{\bar{Q}}_{{{\rm{S}}}}}{{Q}_{{{{\rm{S}}}}_{{\max }}}-{Q}_{{{{\rm{S}}}}_{{\min }}}}$$

(23)

where ${\overline{Q}}_{{\mbox{S}}}$, Q_Smax and Q_Smin are mean, maximum and minimum values for Q_S, respectively. The normalized changes in P, T, Q, V and Q_SNOW (i.e., ΔP_n, ΔT_n, ΔQ_n, ΔV_n and ΔQ_SNOWn) are defined likewise. Referring to Eq. (15), the changes in Q_S, Q and Q_SNOW can be interpreted by the partial elasticity coefficients and multiple orders of the changes in P, T, Q and V (five orders are included here):

$${{\Delta }}{Q}_{{\rm{Sn}}}=\mathop{\sum}\limits_{k=1}^{5}[{\varepsilon }_{{{\rm{PW}}}-{{\rm{I}}}}^{k}{({{\Delta }}{P}_{{\rm{n}}})}^{k}{+{{\epsilon }}}_{{{\rm{PW}}}-{{\rm{II}}}}^{k}{({{\Delta }}{Q}_{{\rm{n}}})}^{k}+{\varepsilon }_{{{\rm{PW}}}-{{\rm{XI}}}-{{\rm{III}}}}^{k}{({{\Delta }}{T}_{{\rm{n}}})}^{k}+{\varepsilon }_{{{\rm{PW}}}-{{\rm{IV}}}}^{k}{({{\Delta }}{V}_{{\rm{n}}})}^{k}]$$

(24)

$${{\Delta }}{Q}_{{\rm{n}}}=\mathop{\sum}\limits_{k=1}^{5}[{\varepsilon }_{{{\rm{PW}}}-{{\rm{V}}}}^{k}{({{\Delta }}{P}_{{\rm{n}}})}^{k}+({\varepsilon }_{{{\rm{PW}}}-{{\rm{VI}}}}^{k}+{\varepsilon }_{{{\rm{PW}}}-{{\rm{IX}}}-{{\rm{VIII}}}}^{k}){({{\Delta }}{T}_{{\rm{n}}})}^{k}+{\varepsilon }_{{{\rm{PW}}}-{{\rm{VII}}}}^{k}{({{\Delta }}{V}_{{\rm{n}}})}^{k}]$$

(25)

$${{\Delta }}{Q}_{{{\rm{SNOWn}}}}=\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{VI}}}}^{k}{({{\Delta }}{T}_{{\rm{n}}})}^{k}$$

(26)

where ε^k_PW-α represents the k-th order partial elasticity coefficient of the α-th Pathway. Here we consider the first five orders in the Taylor expansion of the relative change in each variable because the regressions including the first five orders show higher precision with acceptable computational overhead. Moreover, the 2^nd- to 5^th-order terms of the normalized factor can represent the effect of extreme events. When extreme events occur, the relative change in one or more variables approaches −1 or 1, making the growth rate of the 2^nd to 5^th order terms become large, leading finally to the variable(s) contributing substantially. For example, the Tuotuo Station is a vegetation-controlled station where the vegetation cover fraction experiences extreme low and high values (identified by the 10th and 90th percentile thresholds, respectively) and sediment flux in extreme years is well simulated (Supplementary Fig. 3). We have also tested the cross-terms in the multivariate Taylor expansion and found that their impacts on the final results were very small (see Supplementary Fig. 4). Therefore, the cross-terms are not included in our method for simplicity.

By performing multivariate regressions at each gauging station, we obtain every ε^k_PW-α and choose the most significant to identify the key pathway chains at each station. Thus, the quantitative contribution of each significant pathway chain can also be calculated based on the partial elasticity coefficients because the contributions of pathway chains to the sediment flux change trend depend not only on the trends in contributory factors but also on the multivariate partial elasticity coefficient (representing the sensitivity of pathway contribution to the factors).

Quantification of the contribution of pathway chains to sediment flux change

Contribution to sediment yield and contribution to sediment flux change are not the same thing. Here we make an analogy from the statistic of S in M-K trend test which contains the trend information of the whole series to calculate the percentage contribution of a single pathway chain (selected from all the major pathway chains) to sediment flux change during the historical period of interest. The average sediment flux change due to the α-th pathway chain (C_PW-α) can be calculated from:

$${C}_{{{\rm{PW}}}-\alpha }=\frac{{\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^{n}{C}_{{\alpha }_{j}}-{C}_{{\alpha }_{i}}}{n(n-1)/2}$$

(27)

where n is the number of historical years considered; C_αi and C_αj are the sediment yields via the α-th pathway chain in years i and j. For each pathway chain in year j:

$${C}_{{{\rm{PW}}-{I}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }}) \mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{I}}}}^{k}{(\Delta {P}_{{{\rm{n}}}_{j}})}^{k}$$

(28)

$${C}_{{{{\rm{PW}}}-{{\rm{V}}}-{{\rm{II}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{K=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{II}}}}^{K}{\left[\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{V}}}}^{k}{(\Delta {P}_{{{\rm{n}}}_{j}})}^{k}\right]}^{K}$$

(29)

$${C}_{{{{\rm{PW}}}-{{\rm{VI}}}-{{\rm{II}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{K=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{II}}}}^{K}{\left[\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{VI}}}}^{k}{(\Delta {T}_{{{\rm{n}}}_{j}})}^{k}\right]}^{K}$$

(30)

$${C}_{{{{\rm{PW}}}-{{\rm{IX}}}-{{\rm{VIII}}}-{{\rm{II}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{K=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{II}}}}^{K}{\left[\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{IX}}}-{{\rm{VIII}}}}^{k}{(\Delta {T}_{{{\rm{n}}}_{j}})}^{k}\right]}^{K}$$

(31)

$${C}_{{{{\rm{PW}}}-{{\rm{IX}}}-{{\rm{III}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{IX}}}-{{\rm{III}}}}^{k}{(\Delta {T}_{{{\rm{n}}}_{j}})}^{k}$$

(32)

$${C}_{{{{\rm{PW}}}-{{\rm{VII}}}-{{\rm{II}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{K=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{II}}}}^{K}{\left[\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{VII}}}}^{k}{(\Delta {V}_{{{\rm{n}}}_{j}})}^{k}\right]}^{K}$$

(33)

$${C}_{{{{\rm{PW}}}-{{\rm{IV}}}}_{j}}=({Q}_{{{\rm{S}}}_{\max }}-{Q}_{{{\rm{S}}}_{\min }})\mathop{\sum}\limits_{k=1}^{5}{\varepsilon }_{{{\rm{PW}}}-{{\rm{IV}}}}^{k}{(\Delta {V}_{{{\rm{n}}}_{j}})}^{k}$$

(34)

Hence, the average contribution of the α-th pathway chain POR_PW-α may be determined as:

$${{{\rm{POR}}}}_{{{\rm{PW}}}-\alpha }=\frac{{\sum }_{i=1}^{n-1}{\sum }_{j=i+1}^{n}\frac{{C}_{{\alpha }_{j}}-{C}_{{\alpha }_{i}}}{{\sum }_{\alpha =1}^{7}\left|{C}_{{\alpha }_{j}}-{C}_{{\alpha }_{i}}\right|}}{n(n-1)/2}$$

(35)

The percentage uniformized contribution of the α-th pathway chain is:

$${{{\rm{PER}}}}_{{{\rm{PW}}}-\alpha }=\frac{{{{\rm{POR}}}}_{{{\rm{PW}}}-\alpha }}{{\sum }_{\alpha =1}^{7}|{{{\rm{POR}}}}_{{{\rm{PW}}}-{{\rm{\alpha }}}}|}$$

(36)

Note that a negative/positive percentage contribution of a pathway chain corresponds to a reduction/increase in sediment flux by that pathway chain regardless of its relative role in the general sediment flux change trend. This is because absolute values are employed as denominators in Eqs. (35) and (36) to indicate absolute sediment change.

Spectral Clustering

Spectral Clustering⁶² is a clustering algorithm based on graph theory; the basic idea is to treat data samples as nodes in a graph and cluster according to the characteristics of the graph. The advantage of spectral clustering is that non-convex and non-linear data structures can be found, and it is robust at handling noise and outliers. Spectral clustering only requires knowledge of the similarity matrix between the data, and so is effective for clustering sparse data (which is difficult to achieve with traditional clustering algorithms such as K-Means). The detailed procedure follows.

Each sample in dataset X = (x₁, x₂,…, x_n) is treated as a node in the graph where the vertexes V = (v₁, v₂,…, v_n) represent data points and the edges (which are directionless) represent connections between data points. These define a local neighborhood using the nearest neighbor method. Pairwise distances Di_i,j are then determined for all points v_i and v_j in the neighborhood using the standardized Euclidean distance. For any two vertexes in the graph, there is either an edge connection (Di_i,j > 0) or no edge connection (Di_i,j = 0). The edge between the two nodes is weighted by the pairwise similarity S_i,j:

$${{{S}}}_{i,j}=\exp \left(-{\left(\frac{D{i}_{i,j}}{\sigma }\right)}^{2}\right)$$

(37)

where σ is the scale factor for the kernel, here σ = 1. The resulting matrix S is the similarity matrix, also called an adjacency matrix. We obtain the following n-by-n diagonal degree matrix Dg by summing the rows of the similar matrix S:

$${{\rm{Dg}}}=\left(\begin{array}{ccc}\mathop{\sum}\limits _{j=1}^{n}{{{S}}}_{1,j} & \cdots & \cdots \\ \vdots & \ddots & \vdots \\ \cdots & \cdots & \mathop{\sum}\limits _{j=1}^{n} {{{S}}}_{i,j}\end{array}\right)$$

(38)

The Laplacian matrix L is calculated from:

$${{\rm{L}}}={{\rm{Dg}}}-{{\rm{S}}}$$

(39)

and the normalized Laplacian matrix Ln from:

$$\begin{array}{c}{{\mathrm{Ln}}={{\rm{Dg}}}}^{-1}{{\rm{L}}}\end{array}$$

(40)

Next, the normalized n-by-k matrix F, composed of eigenvectors f corresponding to the smallest k eigenvalues of Ln, is calculated, where k is the number of clusters. Each row in F is treated as a k-dimensional sample. Hence, n new samples are clustered by the K-Means clustering method, resulting in k clusters corresponding to the original dataset X.