Dynamic assessment of water scarcity utilising blue and green water can enhance water resource management. The traditional water scarcity assessment mainly considers blue water, ignoring green water, for static evaluation. The improvement objective of this study is dynamically quantifying water scarcity, integrated blue and green water. This study proposed a framework to present an overview of water scarcity within multiple indicators and pinpoint water-stressed areas within an ever-changing process. The framework is based on the theorem of mutual change of quality and quantity to assess the spatiotemporal variability of blue and green water availability and to quantify water scarcity in watersheds. A case study was carried out in Taoer River Basin, a semiarid region of China, to demonstrate the use of the framework. The anthropogenic elements (such as water demand) and natural conditions were combined to quantify water scarcity, as measured by blue and green water scarcity indices. This study also analysed the variation of water scarcity on different spatiotemporal scales. The findings demonstrate that severe water scarcity has been occurring downstream with a tendency towards upstream of the watershed. Collectively, this study provides a useful tool for dynamic water scarcity assessment, helping develop policies to promote sustainable development.

  • Proposed a coupled framework for quantifying water scarcity dynamically.

  • Integrated multiple indicators to assess the status of water scarcity efficiently.

  • Identified hot spots of water scarcity based on varied spatiotemporal analysis.

BW

Blue water

GW

Green water

BWS

Blue water scarcity

GWS

Green water scarcity

SWAT

Soil and Water Assessment Tool

TMCQQ

Theorem of mutual change of quality and quantity

TRB

Taoer River Basin

HRU

Hydrologic response unit

Water scarcity assessment is a basis to alleviate the current situation of water scarcity. The accuracy of assessment is crucial for designing and managing water resource systems (Adnan et al. 2023). Nevertheless, water scarcity assessments prioritised blue water (BW), while potential green water (GW) supplies in water cycle corridors were frequently neglected (Pan et al. 2023). This approach impeded the overall understanding of the real state of natural water resources (Falkenmark & Rockström 2010), as both BW and GW arise from precipitation, and GW accounts for some 64% of the annual global water resources flow (Yan et al. 2022). The method of blue water scarcity (BWS) assessment included water footprints (Zhuo et al. 2016), defined new indicators (Damkjaer & Taylor 2017), integrated factors (Brunner et al. 2020), and so on. Among them, more than 150 water scarcity indicators had been established (Hussain et al. 2022), and the majority were the indicators of BWS (Hussain et al. 2022), such as the Falkenmark indicator. It was the most widely used indicator of water resources assessment, which evaluated the availability of BW by assessing yearly per capita water demand (Zhong et al. 2023). Młyński analysed the impact of both the standardised precipitation index (SPI) and the normal precipitation index as indicators of the status of e-flows and water scarcity in mountain catchments (Młyński et al. 2021). Green water scarcity (GWS) assessment (Quinteiro et al. 2019) had begun to be conducted to GW management for the development and popularisation of the GW concept (Liu et al. 2017). According to previous studies, the reason for the restricted development of GW research was that it was difficult to accurately assess GW, since the measurement of evapotranspiration could not account for the transport of water vapour from non-croplands to the atmosphere (Hussain et al. 2022).

Thus, an integrated water scarcity assessment has emerged which combines BW and GW (Veettil & Mishra 2016) for its joint management (Falkenmark & Rockström 2010). In terms of research methodology, the development of hydrological models has made it possible for the simulation and quantitative assessment of spatiotemporal variations in BW and GW (Jeyrani et al. 2021). The Soil and Water Assessment Tool (SWAT), for example, has an advantage in the quantitative estimation of BW and GW since it can output the spatiotemporal distribution of each hydrological element in the hydrological cycle, i.e., the components of BW and GW (Xie et al. 2020). It accounts for the important factors influencing BW and GW, as well as variables such as different climatic conditions, soil and land use types and water resource management patterns (Liang et al. 2020). Therefore, the SWAT model has been extensively applied. However, BW and GW were appraised individually without being integrated in a meaningful way to reflect the entire condition of regional water scarcity (Xie et al. 2020). Furthermore, it had not considered the ambiguity of the term ‘water scarcity’ (Rijsberman 2006). Additionally, the long-term dynamics of water scarcity had not been assessed as a process, which made it difficult to test its variability (Hussain et al. 2022).

A gap in the current studies is summarised as detailed and systematic studies on the dynamic assessment of water scarcity within multiple indicators. The process of change involves qualitative change and quantitative change (Li et al. 2022). Of these, qualitative change entails the fundamental alteration of properties, while quantitative change emphasises changes in quantity, with the fundamental nature remaining relatively unchanged (Xie et al. 2020). A comprehensive consideration of both qualitative change and quantitative change contributes to a more holistic understanding of the nature and characteristics of change. This perspective holds particular significance in studying the dynamic processes of water scarcity, aiding a deeper comprehension of whether there has been a notable change in water scarcity status. The theorem of mutual change of quality and quantity (TMCQQ), an effective approach to evaluate the long-term dynamic assessment process of fuzzy concepts, is capable of considering the comprehensive influence of multiple indicators (Chen & Yu 2006). It is an enhancement of classical static fuzzy set theory, since it can capture the dynamic variability of fuzzy phenomena and fuzzy notions (), utilising relative difference degree () as a mathematical language and quantitative tool (Cui et al. 2023). In particular, it determines the process of quantitative and qualitative change based on the relationship of with zero, where represents the relative difference degree of transformation C of u. This theorem puts forward the idea of the qualitative change boundary, while also simultaneously considering numerous indicators, which achieves more comprehensive results (Chen 2010). The majority of previous studies, however, were on the variation diagnosis of hydrological sequences, such as runoff (Li et al. 2013), water quality (Li et al. 2009), and flood risk (Chen & Yu 2006), but there was no relevant study on the assessment of water scarcity. Therefore, this represents a new attempt to introduce TMCQQ to dynamically assess water scarcity.

The primary objective of this study is to propose a framework for efficient dynamic assessment of water scarcity between BW and GW. Therefore, the framework comprises hydrological modelling, multiple indicator construction, and coupled assessment of water scarcity within spatiotemporal dynamics. Specifically, the multiple indicators of water scarcity assessment are characterised by BWS and GWS indices derived from hydrological modelling. Furthermore, the coupled assessment of multiple indicators is characterised by the D value of TMCQQ, which represents water scarcity by coupling the magnitude of BW and GW in both quantity and distribution. Additionally, this study assumed that both BW and GW have an equal impact on water scarcity. As an empirical case to illustrate the applicability of the framework and promote its application on a wider scale, the Taoer River Basin (TRB) in a semiarid region of China is selected since it has a strained supply/demand situation and there are no studies investigating water scarcity (Li et al. 2023).

The proposed water scarcity assessment framework is highly adaptable to objects with exceptional temporal and spatial dynamics. Additionally, the BW and GW coupling-based framework enables the possibility of gaining insight into the internal relation of water scarcity and the interdependent characteristics between zones. Thus, it is crucial to water scarcity assessment and rationalises the allocation of water resources for policymakers considering climate change.

Framework

The framework proposed for dynamic water scarcity assessment mainly includes hydrological modelling, multi-variable construction, and coupling-based water scarcity analysis. This framework uses varied spatiotemporal scales to quantify water scarcity associated with BW and GW quantity and distribution patterns. The proposed dynamic water scarcity assessment framework consists of three steps. Step 1 is the hydrological model, which is able to recognise hydrological fluxes from the SWAT model within a specific time duration. Step 2 is assessment of BWS/GWS, which can construct multiple indicators within varied spatiotemporal quantities. Step 3 is TMCQQ, which can conduct multi-variable coupled modelling and water scarcity assessment. The proposed framework provides a comprehensive approach for dynamic water scarcity assessment and can be used to inform policy decisions regarding water resource management and water safety. Figure 1 demonstrates the three steps.
Figure 1

Framework for dynamic water scarcity assessment integrating BW and GW.

Figure 1

Framework for dynamic water scarcity assessment integrating BW and GW.

Close modal

Step 1: Hydrological modelling

The SWAT model was applied to simulate BW and GW in this step. It is a semi-physical and semi-distributed basin-scale model (Chen et al., 2023), which has been implemented to quantify BW and GW indicators globally (Du et al. 2018). The hydrological cycle simulated by SWAT is based on the water balance equation (Equation (1)):
(1)
where is the final soil water content (mm), is the initial soil water content on day i (mm), and t is the time (days). , , , , and are the precipitation (mm), runoff (mm), evapotranspiration (mm), seepage (mm), and return flow (mm), respectively.

During the modelling process, SWAT creates subbasins and hydrologic response units (HRUs) by overlaying DEM, land use, soil, and slope (Schuol et al. 2008). In terms of parameter calibration, the framework utilised SWAT CUP to adjust parameters and determine parameter sensitivities (Arnold et al. 2012). In terms of calibration and validation, the SUFI2 algorithm was applied to the observed monthly streamflow of the hydrological stations, Suolun and Charlson. The values of R2 and Nash–Sutcliffe (NS) served as metrics to assess the accuracy of the SWAT model. Typically, when the values satisfy the criteria of R2 > 0.6 and NS > 0.50, the results of the simulation are considered satisfactory (Jeyrani et al. 2021).

Step 2: Assessment of BWS/GWS

The BW consists of the storage of groundwater (, mm) and the water yield (, mm) (Equation (2)). This study assessed BWS in TRB using the Falkenmark indicator (Equation (3)). The assessment of BWS is categorised as follows: extreme stress (<500 m3/capita/year); high stress (500–1,000 m3/capita/year); moderate stress (1,000–1,700 m3/capita/year); just adequate (1,700–4,000 m3/capita/year); and, no stress (>4,000 m3/capita/year) (Rijsberman 2006). A value of the Falkenmark indicator less than 1,000 m3/capita/year is defined as severe BWS in this study:
(2)
(3)
where is the water entering the aquifer (mm), is the water entering the main channel from the aquifer (mm), is the Falkenmark indicator, W is the amount of rainfall (m3), and P is the population of the study area.
The GW is composed of the GW flow (ET, mm) and the green water storage (SW) (Equation (4)). The GWS in this study is derived from Equation (5), and each variable in the equation can be obtained from the HRUs output of the SWAT model (Liang et al. 2020). The assessment of GWS in this study is categorised as follows and represents the classification criteria for semiarid areas (Xie et al. 2020): low stress (<0.5); moderate stress (0.5–1); high stress (1–1.5); and, extreme stress (>1.5). A GWS value greater than 1 is defined as severe GWS in this study:
(4)
(5)
where is the actual evapotranspiration (mm), and is the soil moisture content available for crop growth and evapotranspiration (mm).

This study focused on the assessment characteristics of BWS/GWS in the TRB from two distinct perspectives, time and space. In terms of time, a thorough analysis was conducted on the proportion of different BWS/GWS for each year, with further consideration of the varied patterns in different typical reference years. From the perspective of space, a comprehensive spatial analysis was carried out on the evolution of severe BWS/GWS and gravity centre migration at the HRU scale, taking into account the viewpoints of both surface and point scales. Additionally, the migration of gravity centre was assessed using a standard deviation ellipse, which reached significant spatial characteristics including central tendency, divergence, and directional trend (Lefever 1926). All of these were derived from ArcGIS.

Step 3: TMCQQ

TMCQQ is used to determine the quantitative and qualitative process of time series through the synthetic relative difference degree of the research object and corresponding discriminant method. The synthetic relative difference degree is obtained from Equation (6). The discriminant method of quantitative and qualitative process is shown in Equations (7)–(10):
(6)
where is the relative difference degree of any element u in the domain U, and and are the relative membership degrees of the opposite fuzzy attribute, with + = 1, , .
  • 1.
    Gradual qualitative change:
    (7)
  • 2.
    Sudden qualitative change:
    (8)
  • 3.
    A state of dynamic equilibrium:
    (9)
  • 4.
    Quantitative changes:
    (10)
    where is the relative difference degree of any element u in the domain U, A is the opposing fuzzy concept (thing, phenomenon) of any element u in the domain U, is the opposing fundamental fuzzy attribute of any element u in the domain U. The parameters, and , are the relative membership degree of opposing fuzzy attribute, with + = 1,

In terms of indicator selection, this study selected two assessment indicators including the Falkenmark indicator (m3/capita/year) and GWS (dimensionless). The degree of water scarcity was divided into five levels: I (good); II (better); III (fair); IV (poor); and, V (poor). The degree of water scarcity in the TRB was assessed by the matrix of indicator standard values , which was determined by the known multiple levels, and multiple indicators, . Table 1 lists the assessment indicators and the standard values of each level.

Table 1

Relationship between water scarcity and indicator values

Assessment indicatorsLevel
Excellent (Ⅰ)Satisfactory (II)Moderate (Ⅲ)Subpar (Ⅳ)Unsatisfactory (Ⅴ)
x1/m3/capita/year 4,000 1,700 1,000 500 
x2 0.5 1.5 
Assessment indicatorsLevel
Excellent (Ⅰ)Satisfactory (II)Moderate (Ⅲ)Subpar (Ⅳ)Unsatisfactory (Ⅴ)
x1/m3/capita/year 4,000 1,700 1,000 500 
x2 0.5 1.5 

In terms of sample selection, this study selected objects from both time and space perspectives for application analysis, considering not only the characteristics of the TRB but also the applicability of TMCQQ in water scarcity assessment. Among them, the time scale samples, taking into account both the hydrological characteristics of the TRB and the factors of temporal change, were chosen from the period between the 1980s and the 2010s: for wet years (1984, 1994, 2005, 2015); normal years (1981, 1992, 2002, 2014); and, dry years (1989, 1997, 2006, 2016). This study applied three methods to categorise the references period to avoid the error of one single index, namely anomalous percentage of precipitation (M) (Zang 2017), SPI (Fooladi et al. 2021), and Person Type Ⅲ curve (P-Ⅲ) (Serago & Vogel 2018). The assessment criteria of these three methods are shown in Tables 2 and 3, and the results of flood/drought grade in each year are presented in Table S1 in the Appendix. In this study, both extremely wet years and relatively wet years are categorised as ‘wet year’, while both extremely dry years and relatively dry years are categorised as ‘dry year’. Considering the topographical characteristics of the TRB, this study separated it into three distinct hydrological subregions in the spatial scale, namely upstream, midstream, and downstream, which were further characterised spatially by applying TMCQQ to the selected indicators of different hydrological subregions based on the time scale samples.

Table 2

Grades of flood/drought based on standardised precipitation index (SPI) and anomalous percentage of precipitation (M)

SPIM (%)Level
<− 1.96 <− 75 Extreme drought 
−1.96 to −1.48 −75 to −50 Severe drought 
−1.48 to −1.0 −50 to −25 Moderate drought 
−1.0 to 1.0 −25 to 25 Normal 
1.0 to 1.48 25 to 50 Moderate wet 
1.48 to 1.96 50 to 75 Severe wet 
>1.96 >75 Extreme wet 
SPIM (%)Level
<− 1.96 <− 75 Extreme drought 
−1.96 to −1.48 −75 to −50 Severe drought 
−1.48 to −1.0 −50 to −25 Moderate drought 
−1.0 to 1.0 −25 to 25 Normal 
1.0 to 1.48 25 to 50 Moderate wet 
1.48 to 1.96 50 to 75 Severe wet 
>1.96 >75 Extreme wet 
Table 3

Grades of flood/drought based on the Person Type Ⅲ curve (P-Ⅲ)

LevelP-Ⅲ (%)
Extreme wet <12.5 
Relative wet 12.5–37.5 
Normal 37.5–62.5 
Relative drought 62.5–87.5 
Extreme drought >87.5 
LevelP-Ⅲ (%)
Extreme wet <12.5 
Relative wet 12.5–37.5 
Normal 37.5–62.5 
Relative drought 62.5–87.5 
Extreme drought >87.5 

The individual values of the eigenvalue matrix to all samples for TMCQQ were obtained from the Step 1 and Step 2 in Section 2.1, and the calculation procedures of integrated water scarcity assessment based on TMCQQ are as follows.

  • 1.

    Determining the relative membership degree matrix of water scarcity indicator i to level h in the TRB.

In calculating the relative membership degree of indicator i to level h, it predicts the position where the indicator eigenvalue falls into the standard matrix firstly, and then calculates according to Equation (11):
(11)
  • 2.
    Determining the comprehensive relative membership degree vector of water scarcity assessment object u to level h in TRB:
    (12)
    where is the indicator weight. The weight vector for indicators in this study was determined as .
  • 3.
    Calculating the level eigenvalue of water scarcity assessment object u in TRB, and determining the comprehensive relative membership degree further. The parameters and are calculated according to the following equations:
    (13)
    (14)
    where is the normalised vector of the comprehensive relative membership degree vector .
  • 4.

    Determining the value of the TRB according to Equation (6), and further applying TMCQQ to assess water scarcity according to Equations (7)–(10).

Study area

The TRB (45°40′N to 47°20′N, 119°40′E to 124°10′E), a semiarid zone with an area of about 30,800 m2 and a temperate continental climate with a mean temperature of 4.8°C, is located in Northeast China (Figure 2). The precipitation is characterised by an extremely uneven spatiotemporal distribution, drawing from recorded precipitation data spanning 1958–2018. Summarising, the mean precipitation is 434 mm/year and as much as 83% of the total rainfall occurs between June and September. Spatially, it exhibits a decreasing tendency as it moves from upstream to downstream, with downstream receiving only 42.3% of the precipitation observed upstream.
Figure 2

Geographic location and reservoir distribution in the TRB.

Figure 2

Geographic location and reservoir distribution in the TRB.

Close modal

In terms of elevation, the TRB spans an altitude range of 130–1,500 m, with a distinctive pattern of decreasing elevations from northwest to southeast. According to statistical analysis (2020 land use grid data), it was observed that the TRB is primarily covered by grassland (36.27%), cropland (30.01%), and forest (23.20%). The upstream mountainous areas prominently feature grassland and forest, whereas cropland is mainly distributed in the middle and downstream areas. This cropland plays a vital role as one of the key agricultural areas in China. Figure 2 shows the geographical location and reservoir distribution in the TRB.

Since the policy of Reform and Opening Up was introduced in 1978, there have been significant expansions, intensifying the water supply and demand imbalance in the TRB. In addition to the construction of hydraulic projects, channelising the river reduced the water sources of the marsh and wetland downstream, resulting in serious disconnection of the downstream river. Notably, it is crucial to thoroughly assess the water resources situation in the TRB.

Datasets

Inputs to the SWAT model consist of terrain, soil, land use, and weather data. Furthermore, DEM, which is used for depicting the study area and estimating the topographical features, was obtained for use in this study from the Geospatial Data Cloud with 30 m resolution. It was used to create HRUs in the SWAT model along with land use and soil data. Moreover, the monthly streamflow observed from 1991 to 2010 at the Suolun and Charlson hydrometric stations was evaluated for the validity of SWAT modelling in this study. Table 4 lists the applications and sources of these data.

Table 4

Data sources

DataSourceApplication
DEM Geospatial Data Cloud Analysis of HRU 
LUCC Resource and Environment Science and Data Center Analysis of HRU 
Population Calculation of Falkenmark indicator 
Soil Harmonized World Soil Database Analysis of HRU 
Weather Cmads Construction of databases 
Hydrological station Water Affairs Bureau of Baicheng and Hinggan League Calibration of the model 
DataSourceApplication
DEM Geospatial Data Cloud Analysis of HRU 
LUCC Resource and Environment Science and Data Center Analysis of HRU 
Population Calculation of Falkenmark indicator 
Soil Harmonized World Soil Database Analysis of HRU 
Weather Cmads Construction of databases 
Hydrological station Water Affairs Bureau of Baicheng and Hinggan League Calibration of the model 

Calibration and validation of the SWAT model

In this study, in total, 422 HRUs were distributed in 25 subbasins, which were created by two types of slopes (0–10% and above 10%) and three types of thresholds (5% land use, 5% soil and 5% slope). The simulation process of the SWAT model in the TRB included the pre-heating period from 1987 to 1990, the calibration period from 1991 to 2000, and the validation period from 2001 to 2010.

The SUFI-2 algorithm in SWAT CUP was used to analyse the sensitivity of 20 parameters for the TRB. Table 5 lists the results of selected SWAT parameters and sensitivity analysis. It can be seen that the parameters CN2, SMTMP, and ESCO were more sensitive than other parameters in the TRB. Figure 3 demonstrates the simulation and observation of monthly streamflow at Suolun and Charlson. Table 6 lists the performance indices of different stations in the TRB. It can be seen from Figure 3 and Table 6 that the simulation results (R2 > 0.8 and NS > 0.7) for Suolun and Charlson hydrometric stations were satisfactory, meeting the required criteria of R2 > 0.6 and NS > 0.5 for both calibration and validation, which meant the SWAT model was well established for TRB and could be applied to further analysis (Jeyrani et al. 2021).
Table 5

Results of selected SWAT parameters and sensitivity analysis

Sensitivity sortingSWAT parametersInitial rangeFinal valuet-StartP-value
CN2 −0.5 ∼ 0.5 0.287 −13.6143 
SMTMP −20 ∼ 20 3.606 11.0754 
ESCO 0 ∼ 1 0.895 −7.9201 
GW_DELAY 0 ∼ 500 10.228 7.0989 
SOL_K(2) −0.8 ∼ 0.8 −0.267 −4.7419 
SOL_K(1) −0.8 ∼ 0.8 −0.472 −3.2265 0.0013 
SFTMP −20 ∼ 20 −2.962 2.9373 0.0034 
ALPHA_BNK 0 ∼ 1 0.730 −2.3510 0.0191 
TIMP 0.01 ∼ 1 0.183 −2.2708 0.0236 
10 GW_REVAP 0.02 ∼ 0.2 0.161 −1.7601 0.0790 
11 SOL_AWC(1) 0 ∼ 1 0.806 −1.2295 0.2195 
12 SURLAG 0.05 ∼ 24 15.603 1.0383 0.2996 
13 CH_K2 −0.01 ∼ 500 446.643 −0.9549 0.3400 
14 GWQMN 0 ∼ 5,000 616.304 −0.8574 0.3916 
15 SMFMN 0 ∼ 20 10.716 −0.7482 0.4547 
16 SOL_AWC(2) 0 ∼ 1 0.904 0.6732 0.5011 
17 ALPHA_BF 0 ∼ 1 0.863 0.6687 0.5039 
18 SMFMX 0 ∼ 20 13.064 0.2707 0.7867 
19 SOL_BD(1) 0.9 ∼ 2.5 1.581 −0.0560 0.9553 
20 CH_N2 −0.01 ∼ 0.3 0.212 −0.0533 0.9575 
Sensitivity sortingSWAT parametersInitial rangeFinal valuet-StartP-value
CN2 −0.5 ∼ 0.5 0.287 −13.6143 
SMTMP −20 ∼ 20 3.606 11.0754 
ESCO 0 ∼ 1 0.895 −7.9201 
GW_DELAY 0 ∼ 500 10.228 7.0989 
SOL_K(2) −0.8 ∼ 0.8 −0.267 −4.7419 
SOL_K(1) −0.8 ∼ 0.8 −0.472 −3.2265 0.0013 
SFTMP −20 ∼ 20 −2.962 2.9373 0.0034 
ALPHA_BNK 0 ∼ 1 0.730 −2.3510 0.0191 
TIMP 0.01 ∼ 1 0.183 −2.2708 0.0236 
10 GW_REVAP 0.02 ∼ 0.2 0.161 −1.7601 0.0790 
11 SOL_AWC(1) 0 ∼ 1 0.806 −1.2295 0.2195 
12 SURLAG 0.05 ∼ 24 15.603 1.0383 0.2996 
13 CH_K2 −0.01 ∼ 500 446.643 −0.9549 0.3400 
14 GWQMN 0 ∼ 5,000 616.304 −0.8574 0.3916 
15 SMFMN 0 ∼ 20 10.716 −0.7482 0.4547 
16 SOL_AWC(2) 0 ∼ 1 0.904 0.6732 0.5011 
17 ALPHA_BF 0 ∼ 1 0.863 0.6687 0.5039 
18 SMFMX 0 ∼ 20 13.064 0.2707 0.7867 
19 SOL_BD(1) 0.9 ∼ 2.5 1.581 −0.0560 0.9553 
20 CH_N2 −0.01 ∼ 0.3 0.212 −0.0533 0.9575 
Table 6

Performance indices of different stations in the TRB

PeriodIndexSuolunCharlson
Calibration (1991–2000) R2 0.88 0.91 
NS 0.71 0.86 
Validation (2001–2010) R2 0.81 0.85 
NS 0.79 0.84 
PeriodIndexSuolunCharlson
Calibration (1991–2000) R2 0.88 0.91 
NS 0.71 0.86 
Validation (2001–2010) R2 0.81 0.85 
NS 0.79 0.84 
Figure 3

Simulation and observation of monthly streamflow at Solun and Charlson.

Figure 3

Simulation and observation of monthly streamflow at Solun and Charlson.

Close modal

Spatiotemporal assessment of BWS and GWS

The characteristics of temporal variation are initially described. Figure 4 shows the annual variation of BW and GW in the TRB from 1979 to 2018. It can be seen that GW is dominant in the TRB, consistent with results in other semiarid regions (Zang & Liu 2013). Figure 5(a) illustrates the area ratio variation of different levels of BWS in the TRB for annual, wet, normal, and dry years between 1979 and 2018. Considering the annual scale changes, there was an increasing pattern in the area ratio of different levels of BWS, particularly after 2000. The peak ratio of 84.8% was observed in 2017, coinciding with the highest recorded area of extreme BWS. This observation aligned with the overall trend in precipitation shown in Figure 4. Considering the variation of wet, normal, and dry years, over the period from dry year to wet year, the area ratio of extreme BWS exhibited an inverse trend compared that where there was no BWS. When comparing the area ratio of BWS in different typical reference years horizontally, it was evident that wet years exhibited the largest magnitude of fluctuation in no BWS.
Figure 4

The annual variation of BW and GW in the TRB from 1979 to 2018.

Figure 4

The annual variation of BW and GW in the TRB from 1979 to 2018.

Close modal
Figure 5

Area ratio variation of different levels of BWS/GWS in TRB from 1979 to 2018. (a) BWS (Falkenmark indicator). (b) GWS. Note: Results are plotted from left to right for annual, wet, normal and dry years, respectively, in both Figure 5(a) and 5(b).

Figure 5

Area ratio variation of different levels of BWS/GWS in TRB from 1979 to 2018. (a) BWS (Falkenmark indicator). (b) GWS. Note: Results are plotted from left to right for annual, wet, normal and dry years, respectively, in both Figure 5(a) and 5(b).

Close modal

Figure 5(b) demonstrates the area ratio variation of different levels of GWS in the TRB for annual, wet, normal, and dry years between 1979 and 2018. Regarding the dynamics of annual scale, except for low GWS, the area ratios of other levels for GWS showed an upward trend. The occurrence of the maximum and minimum area ratios for low GWS closely corresponded to the extremum of precipitation shown in Figure 4. When examining the variation of wet, normal, and dry years, it became apparent that the area ratios of extreme GWS in typical reference years displayed an upward trend, while the ratio of low GWS demonstrated a downward trend.

Furthermore, this study analyses the characteristics of spatial distribution. Figure 6 presents the patterns of severe BWS in different typical reference years during the periods of the 1980s, 1990s, 2000s and 2010s. Upon analysing the changes from wet year to dry year, a distinct reduction in the range of severe BWS was observed, particularly upstream. Comparing the lateral variations across different typical reference years over four decades, it became apparent that significant fluctuations occurred in the extent of severe BWS even under the same class of typical reference year. For instance, in wet years (Figure 6(a)), a small area of severe BWS occurred upstream in both the 2000s and 2010s, while it did not occur in the 1980s and 1990s.
Figure 6

Evolutionary pattern of severe BWS in TRB in different typical reference years from 1980 to 2018. (a) Wet year. (b) Normal year. (c) Dry year.

Figure 6

Evolutionary pattern of severe BWS in TRB in different typical reference years from 1980 to 2018. (a) Wet year. (b) Normal year. (c) Dry year.

Close modal
Figure 7 presents the patterns of severe GWS in different typical reference years during the periods of the 1980s, 1990s, 2000s, and 2010s. What can be clearly seen in Figure 7 is the small extent to which it occurred in the whole basin – affecting only a few areas downstream. Moreover, the variability of severe GWS in different typical reference years was not significant, with just a small reduction in areas of severe GWS seen between dry and wet years. This was due to the fact that the sensitivity of GW to precipitation was influenced by the precipitation threshold, which was consistent with the results shown in Figure 5(b). Figure S1 and Figure S2 depict the spatial distribution of severe BWS/GWS in the TRB from 1979 to 2018, and the analysis is described in Text S1 of the Appendix.
Figure 7

Evolutionary pattern of severe GWS in TRB in different typical reference years from 1980 to 2018. (a) Wet year. (b) Normal year. (c) Dry year.

Figure 7

Evolutionary pattern of severe GWS in TRB in different typical reference years from 1980 to 2018. (a) Wet year. (b) Normal year. (c) Dry year.

Close modal

The dynamic assessment of water scarcity

The dynamic assessment of water scarcity in this study was derived by using TMCQQ to predict BWS and GWS. This study determined the standard eigenvalue matrix Y according to the standardised value interval of graded evaluation indicators in Table 1, which can be written as follows:

In addition, it determined eigenvalue grade and synthetic relative membership degree by applying Equations (13) and (14) to normalised synthetic relative membership degree vector of all sample years (refer to Appendix), and subsequently obtained the value using Equation (6). Table 7 lists the results for each year. It can be seen as follows (Section 3.3) by applying Equations (6) and (13) of TMCQQ in Appendix to Table 7.

Table 7

Results of synthetic relative difference degree for each subregion in the TRB

DegreeYearUpstreamMidstreamDownstreamTRB
Wet year 1984 0.811 0.026 −0.295 0.418 
1994 0.815 0.069 −0.037 0.472 
2005 0.723 −0.286 −0.243 0.116 
2015 0.738 −0.302 −0.343 0.294 
Normal year 1981 0.723 −0.299 −0.281 0.107 
1992 0.31 −0.152 −0.193 0.011 
2002 0.387 −0.398 −0.406 −0.097 
2014 0.67 −0.294 −0.361 0.065 
Dry year 1989 0.712 −0.159 −0.202 0.069 
1997 0.471 −0.386 −0.439 −0.015 
2006 0.576 −0.311 −0.316 0.014 
2016 0.37 −0.22 −0.283 −0.010 
DegreeYearUpstreamMidstreamDownstreamTRB
Wet year 1984 0.811 0.026 −0.295 0.418 
1994 0.815 0.069 −0.037 0.472 
2005 0.723 −0.286 −0.243 0.116 
2015 0.738 −0.302 −0.343 0.294 
Normal year 1981 0.723 −0.299 −0.281 0.107 
1992 0.31 −0.152 −0.193 0.011 
2002 0.387 −0.398 −0.406 −0.097 
2014 0.67 −0.294 −0.361 0.065 
Dry year 1989 0.712 −0.159 −0.202 0.069 
1997 0.471 −0.386 −0.439 −0.015 
2006 0.576 −0.311 −0.316 0.014 
2016 0.37 −0.22 −0.283 −0.010 

The temporal variation of water scarcity was examined in the whole basin scale between the four eras for different typical reference years. On the whole basin scale of the TRB (Table 7), spanning the period from the 1980s to the 2010s, it can be seen that there was a quantitative change in water scarcity between each successive typical wet reference year. For the typical normal reference years, the 1990s served as a pivotal era, since a quantitative change was observed compared to the 1980s and gradual qualitative changes manifested in all eras studied from this period onwards. In contrast, for typical dry reference years, gradual qualitative changes were evident between all eras since the 1980s. It was evident that the attainment of water scarcity tipping points varied between different typical reference years – the drier the TRB, the earlier the water scarcity tipping point appeared.

The spatial distribution of water scarcity was considered in the subregion scale between the four eras for different typical reference years. On the subregion scale of the TRB (Table 7), from the 1980s to 2010s, it was found that quantitative changes in water scarcity occurred both upstream and downstream across different typical reference years. With the result of and in all typical reference years, it was clear that there was no water scarcity upstream since the 1980s – while downstream had been in a state of water scarcity – which indicated that reasonable water allocation is needed downstream to satisfy the water demand of the population and ecosystems. As far as midstream was concerned, all typical reference years showed quantitative changes except for the wet year in the period of the 1990s–2000s. Furthermore, only the wet years in the 1980s and 1990s showed , while all the other typical reference years showed . Namely, ever since the wet year in 1990s, the midstream had been in a state of water scarcity, yet the onset of normal and dry years was 1980s. Therefore, the indication, which meant the drier the basin, the earlier the water scarcity tipping point appeared, corresponded to the pattern of the water scarcity tipping point across the whole TRB in different typical reference years (Table 7).

The relationship between quantitative and qualitative changes

It follows from the proposed framework that quantitative changes usually accumulated into qualitative changes, but an occasional quantitative change could not lead to a qualitative change. This phenomenon was reflected in the following three points:

  • (1)

    The qualitative change in GW depended on continuous precipitation, i.e., the continuous quantitative change process of precipitation, compared to precipitation on the same time scale. Figure 4 illustrates the comparative process of multiple indicators in the framework. As depicted, it is evident that the occurrence of the precipitation peak in 1998 did not align with the peak of GW. Additionally, GW consistently maintained a peak state during the period 1983–1994. This remarkable phenomenon could be attributed to the sustained high levels of precipitation throughout this period, which ensured a continually high soil water content. Vegetation growth and evapotranspiration were, thus, facilitated since the root systems absorbed water from the soil sufficiently and released it to the atmosphere through the stomata of the leaves, leading to an elevated amount of GW – consistent with the Yellow River basin (Xie et al. 2020). Conversely, when the precipitation peak occurred in consecutive dry years, a BW peak occurred rather than a GW peak (1998). This was due to the fact that part of the precipitation had been lost as surface runoff without penetrating deeper into the soil, and the evapotranspiration of vegetation had not fully recovered.

Figure 8 demonstrates the correlation between BW/GW and the precipitation/2-year precipitation moving average. In Figure 8(b), the R2 value of the 2-year precipitation moving average between GW reached 0.91, which verified that the qualitative change was dependent on continuous precipitation, i.e., the continuous quantitative change process of precipitation. In terms of the different levels of GWS, it was manifested as a sensitivity of GW to precipitation and dependent on whether it met a precipitation threshold or not (Figure 5(b)). Specifically, only if the precipitation exceeded the corresponding threshold range, a dramatic change was evident in the area ratios of extreme GWS and low GWS. Moreover, the sensitivity of extreme GWS to precipitation was less than low GWS.
Figure 8

Correlation between BW/GW and precipitation/2-year precipitation moving average. (a) Correlation between BW/GW and precipitation. (b) Correlation between BW/GW and 2-year precipitation moving average.

Figure 8

Correlation between BW/GW and precipitation/2-year precipitation moving average. (a) Correlation between BW/GW and precipitation. (b) Correlation between BW/GW and 2-year precipitation moving average.

Close modal

On the contrary, BW was more significantly influenced by precipitation. As shown in Figure 8(a), the R2 values of precipitation between BW and GW within the same time scale were 0.77 and 0.51, respectively. The results indicate a closer correlation between precipitation and BW in the same time scale than with GW, which is globally consistent (Althoff & Destouni 2023). This observation was due to the fact that precipitation was the main source of BW (Zang & Liu 2013), which meant that it played a crucial role in the change process of BW. This work proved the significance of precipitation for BW proposed by Veettil et al. (2022), while the yearly change on area ratio of BWS for each degree in Figure 5(a) also reflected this.

  • (2)

    A significant variation also occurred within the same typical reference year in the spatial distribution of BWS and GWS, related to the moisture condition of the basin before the corresponding typical year, i.e., the accumulated level of precipitation quantitatively changed in the previous period. Figures 6 and 7 demonstrate the spatiotemporal dynamics of multi-variable in the framework. These reveal different degrees of variation of BWS and GWS in the spatial distribution for the same typical reference year. For example, there were small areas of severe BWS in upstream occurring in the 2000s and the 2010s during the wet years (Figure 6(a)), while a certain range of severe GWS areas appeared in the midstream and downstream (Figure 7(a)), compared to none in the 1980s and the 1990s. Actually, the phenomenon was related to the moisture condition in the TRB on the eve of that typical reference year. Specifically, 2004 and 2014 were dry and normal years, respectively, while 1983 and 1993 were both extremely wet years. This implies that the typical years of the 1980s and the 1990s were characterised by a higher degree of quantitative precipitation accumulation (Figure S4(a)), i.e., a higher amount of antecedent precipitation than in the 2000s and the 2010s, leading to easier generation of runoff and stronger growth of vegetation. Hence, there was a greater abundance of both BW and GW (Xie et al. 2020). The spatial distribution of precipitation, and its 2-year precipitation moving average, in typical years are presented in Figure S3 and Figure S4.

  • (3)

    The drier the basin, the easier it reaches the qualitative point of water scarcity between wet and dry years. The results of the water-coupled framework provide a detailed insight into the variability between time series. According to the results of the synthetic relative difference degree in Table 7, it can be seen that there was only quantitative change in water scarcity between the four eras for the wet years among the whole basin, while both normal and dry years experienced qualitative change after the 1990s and 1980s, respectively. One reason is that there was a supply shortage of BW due to the poorer precipitation during dry years, making it difficult for water resources to be adequately replenished (Veettil & Mishra 2016). Another reason is that less GW was available because of reduced soil moisture reserves and restricted vegetation growth activities (Liang et al. 2020). Consequently, there were insufficient total water resources, and an increased double-cumulative effect of water scarcity scope as well as degree, i.e., the increased accumulation of quantitative changes in water scarcity led to an earlier time of qualitative change on water scarcity.

Evolutionary characteristics of BWS and GWS

This study investigated the migration of the gravity centre. Figure 9 depicts the interannual migrations of the gravity centre between 1979 and 2018 in the TRB. The results of the standard deviation ellipse are described in Text S2 (refer to Appendix). Figure 9(a) reveals a distinctive belt-shaped distribution of the severe BWS gravity centre in the mid-to-lower stream, stretching diagonally northwest to southeast in the TRB. Additionally, the migration of the gravity centre exhibited a strong correlation with the class of typical reference year, the gravity centre shifting to the northwest as the year gets drier. By contrast, as shown in Figure 9(b), the gravity centres of severe GWS exhibited a concentrated distribution between 1979 and 2018, sharing a similar movement pattern with the migration of severe BWS gravity centre, albeit with lower sensitivity to the class of typical reference year. Consequently, it can be inferred that the impact of precipitation on BW is more pronounced, which aligns with the consistent findings presented in Figures 5 and 8.
Figure 9

Migration of the severe BWS/GWS gravity centre in the TRB from 1979 to 2018. (a) Severe BWS gravity centre. (b) Severe BWS/GWS gravity centre.

Figure 9

Migration of the severe BWS/GWS gravity centre in the TRB from 1979 to 2018. (a) Severe BWS gravity centre. (b) Severe BWS/GWS gravity centre.

Close modal

It was apparent that severe BWS demonstrated a stronger sense of direction than severe GWS, evidenced by its higher value of ellipse oblateness. In contrast to severe GWS, the standard deviation ellipse of severe BWS exhibited an increased length in the major axis, and a corresponding decrease in the minor axis, thereby validating the findings of ellipse oblateness. Compared with the results of severe GWS, these were all indicative of severe BWS with a stronger directionality and centripetal force. Additionally, upon examination of the rotation angle, it became evident that the severe BWS surpassed the severe GWS both in terms of magnitude and in its tendency towards the northwest, emphasising the greater spatial variations and the propensity for more extensive upstream expansion.

Instead of restricting consideration to BW and surface scale as in the previous research, this framework expanded water scarcity assessment to BW and GW as well as the surface/point scale in long-term dynamic spatial evolution of BWS and GWS. From the perspective view of the surface, the BWS and GWS were centralised midstream and downstream, which aligned with other studies in the TRB (Liang et al. 2010). As can be seen from Figure S1 and Figure S2, the status of BWS in TRB was more severe than GWS, clarifying that the water scarcity in the TRB mainly resulted from BWS. Furthermore, the point scale results showed that the gravity centre of severe BWS was distributed in a northwest–southeast band, and that the drier the basin on the eve of the assessment year, the more upstream the gravity centre of severe BWS was. In contrast, severe GWS had a more centralised distribution of gravity centres, which again demonstrated the intense sensitivity of BW to precipitation compared to GW (Veettil & Mishra 2016).

Evolutionary characteristics of water scarcity

From the limited study period applied to the framework (Table 7), upstream showed quantitative change without water scarcity in all typical reference years, while downstream, in contrast, was quantitative with water scarcity. The midstream was more complex, changing between different typical reference years. Except for the midstream of wet years, which witnessed a degree of water scarcity from initial nonexistence, quantitative change occurred in the rest of the eras. In terms of the wet year, the gradual qualitative change of water scarcity in the midstream occurred between the 1990s and 2000s. Yet, both the normal and dry years experienced quantitative changes in the midstream between the four eras, which were all in a state of water scarcity.

These results of applying the framework were related to factors such as precipitation characteristics of the TRB (decreasing from upstream to downstream), population distribution (increasing from upstream to downstream), and vegetation distribution (forest, grassland, and cropland, in order, from upstream to downstream) (Liang et al. 2020). Among these, the reason why more GW was found in forests is that it has a dense vegetation cover, and a more stable vegetation layer, which can help to absorb water effectively from the soil and release it to the atmosphere through evapotranspiration. In the case of grassland, with relatively less dense vegetation and weaker evapotranspiration, it has a moderate level of GW. Instead, cropland is often under irrigation and drainage treatments during agricultural production, which not only increases the supply of water in the soil, but also increases evapotranspiration and its utilisation.

It is worth noting that the qualitative change point of water scarcity also occurred in wet years. Several factors could explain this observation. Firstly, the precipitation in the TRB was unevenly distributed, with a decreasing pattern from upstream to downstream (Liang et al. 2010). Secondly, the imbalance between water supply and demand often occurred downstream, where denser populations were located. Finally, with greater evapotranspiration potential in semiarid areas, there was often a situation where this process exceeded precipitation. In summary, even in wet years, there appeared to be water scarcity problems due to high evapotranspiration, reducing the amount of available water as well as the supply of BW/GW. With the accumulation of quantitative changes in water scarcity year by year, the qualitative change point in water scarcity eventually occurred. It is clear that the TRB is facing serious challenges in terms of water resources management and agricultural production. Appropriate management and strategies are, therefore, needed to cope with the current situation of drought and supply/demand imbalance.

The characteristics of TMCQQ

The current assessment of water scarcity conditions is accounted for BW only (Bo et al. 2021), while the proposed framework can incorporate the effects of changes in the amount of both BW and GW and can provide an insight into the real natural water resource conditions within the watershed. Thus, in terms of indicators, the proposed framework is more comprehensive. Furthermore, the use of a typical annual analysis in different eras helps to reveal spatiotemporal patterns and hydrological responses. Additionally, the proposed framework is computationally simpler and yields more detailed results. Although there are numerous other methods for hydrological data trend detection, such as the Mann–Kendall trend test (Wang et al. 2020) and the Pettitt test (Yacoub & Tayfur 2019), trend detection can be only performed for a single indicator and is a deterministic avenue of study. For example, Zang & Liu (2013) used Mann–Kendall (MK) for trend detection in both BW and GW, which indicated the variability in some regional hydrological processes caused by different rainfall patterns.

This study used the MK trend test (Zang & Liu 2013) to analyse the trends of the gravity centre of severe BWS/GWS in terms of longitude, latitude, and migration distance. Meanwhile, the Theil–Sen estimator (Du et al. 2018) was applied to calculate the degree of trend. Considering the instability of the initial soil water content in the TRB at the beginning of the simulation, this study treated the GW obtained from 1979 as an outlier (Figure 9(b)), which was not taken into account in the trend test consequently. Table 8 lists the trend analysis results in migration of the severe BWS/GWS gravity centre, and Figures 10 and 11 demonstrate the migration trend of the severe BWS/GWS gravity centre in the TRB from 1979 to 2018.
Table 8

Trend analysis in migration of the severe BWS/GWS gravity centre

TypeMK (|z|)TS
Severe BWS Longitude −3.5303 −0.0104 
Latitude 2.9943 0.0045 
Migration distance −2.1532 −0.4331 
Severe GWS Longitude −1.2467 −0.0021 
Latitude 1.503 0.0009 
Migration distance −0.31452 −0.0363 
TypeMK (|z|)TS
Severe BWS Longitude −3.5303 −0.0104 
Latitude 2.9943 0.0045 
Migration distance −2.1532 −0.4331 
Severe GWS Longitude −1.2467 −0.0021 
Latitude 1.503 0.0009 
Migration distance −0.31452 −0.0363 
Figure 10

Trends in migration of the severe BWS gravity centre in the TRB from 1979 to 2018: (a) longitude; (b) latitude; (c) migration distance.

Figure 10

Trends in migration of the severe BWS gravity centre in the TRB from 1979 to 2018: (a) longitude; (b) latitude; (c) migration distance.

Close modal
Figure 11

Trends in migration of the severe GWS gravity centre in the TRB from 1979 to 2018: (a) longitude; (b) latitude; (c) migration distance.

Figure 11

Trends in migration of the severe GWS gravity centre in the TRB from 1979 to 2018: (a) longitude; (b) latitude; (c) migration distance.

Close modal

It is obvious from Table 8, Figures 10 and 11 that the MK and TS methods can only detect the migration trend in migration of the severe BWS/GWS gravity centre individually, lacking the ability to provide a comprehensive assessment for water scarcity that takes both into account. To accomplish this objective, the formulation of a new and suitable indicator is necessary. Conversely, the framework bypasses these complex steps and directly yields the desired results. Therefore, this study signifies an improved understanding of local water resource realities for industries, nations, and regions. It aids policymakers in scientifically and rationally managing water resources to address the water crises arising from climate change.

The limitation of this study is that the effectiveness of results is dependent on the time intervals set by the samples. This limitation will affect the precision of the results. The denser the time interval, the more precise the results obtained. Only if the time interval is small enough, the specific time of qualitative changes and the quantitative thresholds for qualitative changes in water scarcity can be obtained. This work is mainly to present the idea of being able to determine the qualitative and quantitative change points of water scarcity. Therefore, it considers the characteristics of hydrological evolution and the study area, and selects 10 years as the time interval of these samples as well in this study. In future studies, it is necessary to select smaller time intervals to further determine the quantitative thresholds for qualitative changes in water scarcity and introduce human activities into the model. In addition, the modelling was validated up to 2010 due to information limitations. As monitoring data are subsequently refined, further calibration and validation could be carried out to improve the modelling accuracy.

This study developed a general modelling framework based on TMCQQ for assessing the spatiotemporal variability of BW/GW availability and quantifying the water scarcity. The proposed framework incorporates multiple indicators and hydrological modelling considering both anthropogenic (such as water demand) and climatic factors to quantify water scarcity, which is based on the assumption that the indicators are identical. It can be applied to assess and alleviate water scarcity caused by climate change for other watersheds in various regions of the world. To illustrate this, the framework was applied to the TRB. Overall, the proposed modelling framework was found to be efficient to quantify water scarcity within multiple indicators and to identify hot spots within the ever-changing process, facilitating water resource management strategies for policymakers. The following conclusions were reached:

  • (1)

    Climatic factors control spatiotemporal distribution of BW/GW. For example, BW and GW in the upstream of the TRB are comparatively high, which may be associated with the higher amount of precipitation in this area, and it decreases towards the lower stream of the TRB. During the assessment period, the R2 values for annual BW/GW and annual precipitation were 0.77 and 0.51, respectively, and the R2 value for annual BW/GW and 2-year precipitation moving average were 0.42 and 0.91, respectively. This is due to the fact that BW is instantly affected by precipitation, while GW is more dependent on the continuous quantitative change process of precipitation.

  • (2)

    BWS/GWS mainly showed gradual severity from upstream to downstream, and the drier the basin was, the more the extent of BWS/GWS moved upstream. Yet, due to the stronger directionality and centripetal force of the standard deviation ellipse of severe BWS gravity centre, the spatiotemporal evaluation of the BWS is more sensitive to the class of typical reference year relative to the GWS. Compared to GWS, therefore, BWS displays higher interannual variability and is more susceptible to upstream propagation during dry periods.

  • (3)

    The characteristics of water scarcity vary across time and space. The current investigation based on TMCQQ found that water scarcity in the TRB changed qualitatively in normal and dry years, and the drier the basin, the earlier the qualitative change point appeared. From the perspective of basin zoning, there was a progressively severe status of water scarcity from upstream to downstream. Hence, intervention is needed to alleviate the critical situation in water scarce areas, especially downstream, via rational water resources management measures.

  • (4)

    The distributed hydrological model established in this study met the error requirements, which reflected the process of runoff yield and concentration. The result of GW in the TRB was more abundant than BW, accounting for greater than 90% of the total water resources, thus the TRB was more suitable for the development of agricultural production and managers need to plan wisely according to this result.

Since the water resource distribution in time and space has been altered by human activities midstream and downstream, and the time interval of the sample is not dense enough, it is only possible to identify qualitative changes in the samples. Therefore, there is a need for shorter sample time intervals, and for future BW/GW modelling to include human activities to identify the quantitative thresholds that cause qualitative changes – this can enrich the results of the dynamic assessment and, additionally, provide more reference for policy development.

This work was supported by the National Nature Science Foundation of China (Grant No. 42077348) and Open Fund of National Engineering Research Center for Geographic Information System, University of Geosciences, Wuhan 430074, China (Grant No. 2022KFJJ03).

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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