# Contribution Analysis of the Streamflow Changes in Selected Catchments on the Loess Plateau, China, Using Multiple Budyko-Based Approaches

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## Abstract

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## 1. Introduction

_{0}) the value of which, unlike other parameters, can be obtained from gauging stations; the E

_{0}being used here is often estimated using radiation-based methods, such as the Penman–Monteith (P–M for short) method recommended by Food and Agriculture Organization of the United Nations (FAO). Different estimations of E

_{0}can lead to uncertainties in results but there is a lack of studies focusing on the comparison contribution analyses using different Budyko-based methods and varying inputs of E

_{0}.

_{0}, to analyze the contributions of climate change and human activities to the streamflow changes in 12 catchments on LP during the period 1961–2018. The objectives are to (1) have more insights into the variabilities of LP streamflow; (2) capture the characteristics of the interactions between climate, human activity, and streamflow change within the study area; (3) discuss the uncertainties in the contribution analysis results that associated with different methods and parameter values.

## 2. Materials and Methods

#### 2.1. Study Area and Data

^{2}(approximately 6.6% of the entire land area of China). The plateau is dominated by arid and semiarid climates with relatively higher evaporation rates, while it is affected by both East and South Asian monsoons that mostly bring rainfall during the period from June to September. The high-intensity rainstorms, along with the coverage of highly erodible loess, accelerate the soil erosion process, especially for the regions with slopes that exceed 10° [21,39,40]. This study will investigate the hydrology in 12 catchments (Figure 1) across the regions with varying precipitation, land cover types, and land surface gradients [13,23].

#### 2.2. Trend Test and Streamflow Change Measurements

#### 2.2.1. Mann–Kendall Test

_{i}and x

_{j}are observations, n is the sample size, and sgn is the sign function. When n is larger than 8, S can be approximated as the normal distribution with a mean value of zero [47]. The variance of S can be calculated as:

_{i}is the number of ties of extent i. Then, the standard test statistic Z can be calculated:

#### 2.2.2. Indicators of Hydrological Alteration (IHA) and Range of Variability Approach (RVA)

_{o,i}is the number of years when the stream flow is within the range, the subscript i denotes the corresponding IHA statistics, and the Ne is the expected number of years when the stream flow is within the range, the value of which is typically half the total number of years.

#### 2.3. Contribution Analysis on the Impacts of Climate Change and Human Activities on the Streamflow Variability

#### 2.3.1. Budyko Hypothesis

_{0}/P). Various equations, known as Budyko-type equations, have been proposed along the years as the solution to the Budyko hypothesis. Wu et all (2017) tabulated a total of 8 mathematical functions that represent the Budyko hypothesis, respectively (Table 2) [13]. Some of these equations are non-parametric, while others include parameters that are connected with catchment characteristics, such as soil type, topography, and vegetation.

#### 2.3.2. Budyko-Based Climate Elasticity Methods

_{0}, P, and human activities are independent throughout the catchment of interest [50,51]. In this manner, the streamflow changes induced by climate change (Q

_{c}) can be expressed as:

_{0}elasticity of Q, ε

_{E}

_{0}, can be given as:

#### 2.3.3. Decomposition Method

_{c}) and human activities (C

_{h}) can be given, in percentage, as:

#### 2.3.4. E_{0} Estimation Methods

_{0}) is an important process in both water balance and energy balance. The assessment of a climate’s influence on water resources could be associated with E

_{0}estimation. However, E

_{0}is controlled by many factors, including humidity, wind, and radiation fluxes, which may lead to uncertainties in the results of estimation models. While there are several estimation methods available, most of them were developed focusing on different regions or climate types and were based on specific assumptions [52,53,54,55,56,57,58,59]. Therefore, it is necessary to compare the estimation efficiency in various circumstances to determine the feasibility of individual methods. In this study, we would like to examine the sensitivity of contribution analysis to the choice of E

_{0}estimation method. More details about the methods involved in this study can be found in Table 3.

## 3. Results and Discussion

#### 3.1. Changes in Hydrometeorological Variables

_{0}) for the 12 catchments at both interannual and intra-annual scales. Specifically, the intra-annual analysis includes trends for high-flow (June to September) and low-flow seasons (October to May), respectively. As shown in Table 4, no significant trend can be captured for P over the study area; in all the catchments, E

_{0}increased significantly in the low-flow seasons at rates ranging from 2.1 mm/yr (Kuye) to 2.5 mm/yr (Beiluo), while only the E

_{0}in Xinshui shows a significant upward trend in high-flow season. In terms of annual E

_{0}, again, not all catchments exhibit significant upward trends. On the other hand, streamflow shows downward trends in both high-flow and low-flow seasons in most catchments, except that no such trend was captured for Dali and Qingjian. Furthermore, Dali turned out to be the only catchment without a significant downward trend found at the interannual scale.

#### 3.2. Contribution Analysis of Streamflow Changes

_{0}). This research applied eight different Budyko-based methods and 13 different estimation methods for E

_{0}(except for the FAO method, all other methods have corresponding versions that have been tuned by adjusting specific parameters involved). In other words, there are a total of 104 pairs of values for the contribution of climate change and human activity to stream change in each of the 12 catchments being investigated in this research (quantitative attribution of stream flow change for each catchment is not shown here). Figure 2a,b separately illustrate the variability of climate and human contributions at the catchment scale by boxplot.

_{0}estimation methods involved will be averaged (i.e., there is only one pair of human and climate contributions left) when comparing various Budyko-based methods, and similarly, the results derived by different Budyko-based methods will also be averaged when comparing various E

_{0}estimation methods.

#### 3.2.1. Quantitative Attribution Using Various Budyko-Based Methods

_{0}. Note that the sum of human and climate contributions equals 100% by design. A red–white–blue color ramp was applied to the results of human contribution, and the same color ramp was reversed for the results of climate contribution. Consequently, in both upper and lower panel, the color that is closer to the red side of the color ramp indicates that human activity contributes more to streamflow change compared to climate change. From Figure 3, we can tell that, for catchments such as Tuwei, Gushan, and Kuye, the results of streamflow change attribution are quite consistent. In fact, except for the Budyko-based methods denoted by Fu, Wang, and Yang, all other methods have shown a predominant role of human activity in the decline of streamflow in those catchments studied. More specifically, most methods revealed that the contribution of human activity to streamflow decline ranges from 71 to 79% with the corresponding contribution of climate ranging from 29 to 21%. By applying ER measures, there has been a greening trend across LP, especially in the last 20 years, and the slope gradient has been altered due to the water-conservation constructions [60,61]. The tradeoffs between conservation objectives and the negative impacts of ER measures on the streamflow remain to be addressed in the future works. Even though some methods (e.g., Fu, Wang, and Yang) are showing higher climate contributions compared to other methods (~50%), human activities still outweigh climate change in most catchment in terms of their impacts on streamflow, the results of which are consistent with previous contribution analyses in the same region [13,23]. The three methods (i.e., FU, Wang, and Yang), with which higher climate contributions would be derived, can be termed as parametric methods (Table 2). They will typically put extra weights on factors such as topography, soil and vegetation conditions, and hydrological features at the catchment scale. However, considering more parameters may sometimes add more uncertainties, let alone geographical factors (e.g., location) and large-scale events, which can also affect the streamflow change. To draw conclusions on the sensitivity of various methods to parameters, elaborate research on a much larger sample size of catchments and corresponding hydrometeorological data is needed, but that is out of the research scope of this study. When comparing the performance of different Budyko-based methods at the catchment scale, the eight methods agreed to the largest degree in Jialu catchment with a standard deviation of 0.81%. On the other hand, the standard deviation of results derived by different methods in the Beiluo catchment reached 11.24%, which also indicates that further investigation is needed to determine the most suitable method to use when assessing human or climate contribution to streamflow change.

_{0}estimation (Figure A4), which corresponds to consistent low standard deviations across the catchments. Moreover, the results calculated by methods using the index-adjusted version of Hargreaves (HARGi) estimation show the highest standard deviations in the six austral catchments. More detailed discussions about the variability due to different E

_{0}estimations will be given in later sections.

#### 3.2.2. Discrepancies Raised by Various E_{0} Estimations

_{0}estimation methods, results were averaged over calculations using different Budyko-based methods. The same scenario of using color ramp to illustrate human and climate contributions to streamflow changes was applied as Figure 3 (i.e., the cells marked by dark red indicates that human factors predominantly contribute to streamflow change and the human contribution decreases as the cells become bluish). Figure 5 has confirmed the findings in Figure 3, that human activities are the primary driver for the streamflow decline in all the catchments studied in this research, although the magnitude of human contribution might vary due to the method applied and catchment characteristics. For the quantitative attributions using E

_{0}estimation methods, such as MAK, PT, and their coefficient-adjusted versions, the difference identified by the catchment location showed that boreal catchments (e.g., Kuye and Gushan) have higher human contributions to streamflow decline (~81%) than do austral catchments (e.g., Dali) (~74%). By calculating the standard deviation of contribution results at the catchment scale, different E

_{0}estimations tend to cause the highest variability in Xinshui, while it is the catchment Beiluo that has the highest variability of quantitative contribution in the case of comparing various Budyko-based methods (Section 3.2.1). Again, Jialu has witnessed the lowest variability in contribution results; the catchment Jialu may not be sensitive to either different Budyko-based methods or different E

_{0}estimations involved in this calculation.

_{0}, estimated by methods including FAO, JENSEN, and JENSENi, typically show reduced human contributions to the streamflow decline, while the contributions are still maintained at a level of 69%. The impacts of adjusting coefficients vary with different E

_{0}estimation methods; they either increase or decrease the final contributions calculated. However, for any particular coefficient adjustments, the sign of change (i.e., positive or negative) in the magnitude of contribution is always consistent in all catchments. For example, after adjusting the coefficient for the E

_{0}estimation method, ABTEW, the adjusted version (i.e., ABTEWi) leads to a decrease in human contribution to streamflow decline for all catchments. In other words, coefficient adjustments are independent from catchment characteristics such as geographical location. The bar plots of standard deviation in Figure 4 confirm the relatively lower sensitivity of the catchment Jialu to the method and E

_{0}estimation used in decomposing human and climate contributions. At least for austral catchments (e.g., Xinshui and Beiluo), the variabilities of contributions calculated by methods such as FU, WANG, and YANG are remarkably higher than those calculated by the other methods (Figure A5). For catchments such as Xinshui, the standard deviation of quantitative contributions derived with different E

_{0}can be over 14% when using FU and WANG methods for calculation. At the catchment scale, the level of sensitivity of Budyko-based method to E

_{0}estimation also varies.

_{0}has played a key role in calculating the sensitivity and contributions of climate change (which can also be partitioned into the contributions of P and E

_{0}separately) and human activities on streamflow variability with Budyko-based methods [1,13,21,23]. In the real world, the robustness of E

_{0}estimations by a particular method typically depends on the research domain (wet or dry climate) over which the method is applied. There is no doubt that a precise E

_{0}estimation would help to increase the accuracy of contribution analysis. Although identifying the optimal method to calculate E

_{0}for catchments on LP is not the focus of this study, the finding that, when using some estimation methods, the standard deviation is relatively lower for the contributions to the streamflow declines could provide implications for making further hypotheses regarding which method works the best on the selected catchments.

#### 3.2.3. Uncertainties in the Quantitative Attribution

_{0}. In terms of E

_{0}estimation, FAO has widely been used, while other methods could also be helpful when climate data does not feed the FAO’s appetite. When examining the discrepancy shown by Figure 5, the HARG method formed the celling of human contribution of seven catchments, and after adjusting the coefficient, HARGi formed the floor of human contribution in the same seven catchments. Moreover, in the catchments Tuwei and Gushan, the situation reversed (i.e., HARG estimation led to the lowest human contribution, and HARGi estimation led to the highest estimation). Those results indicate that the different E

_{0}estimations that were involved in this research extended the uncertainty interval of quantitative contribution, which could be attributed to the deviation between the actual value and the estimation of E

_{0}. This study indicates that the uncertainty induced by E

_{0}estimation could weight a great share in total uncertainties. It is worth launching further sensitivity analyses upon the uncertainties in subprocesses of E

_{0}estimation, such as pre-process raw data (in situ ore remotely sensed data), equations for calculating E

_{0}, and interpolating point/station data, if necessary.

_{2}concentration and land use and land cover (LULC), that directly or indirectly influence streamflow via biogeophysical and biogeochemical mechanisms. As discussed in Section 3.2.1, different Budyko-based methods greatly vary over the six catchments located at the austral part of LP, which may indicate that catchments with wet and warm climates are more easily subject to bias in contribution analysis of streamflow changes. However, a similar spatial pattern of contribution variability is not obvious for different E

_{0}estimations. This can also be demonstrated by mapping the standard deviation of quantitative contributions derived by a selected method (Budyko) and various E

_{0}estimation (Figure 6a) and the standard deviation of quantitative contributions derived by a selected E

_{0}estimation (FAO) with various calculation methods (Figure 6b). To address those uncertainties, LULC variables, such as normalized difference vegetation index (NDVI) and leaf area index (LAI), as well as meteorological variables, including temperature and precipitation anomalies, need to be investigated carefully.

## 4. Conclusions

_{0}), and precipitation were first investigated for 12 catchments within Loess Plateau (LP) during the period of 1961–2018. With analysis methods such as the Mann–Kendall (M–K) test and the Range of Variability Approach (RVA), significant declining trends were found for streamflow in most catchments: low-flow seasons for the catchments studied were characterized by a decrease in E

_{0}; and no significant trend was found for the change of precipitation in the study area on LP. Then, eight Budyko-based climate elasticity methods with 13 E

_{0}estimations were used to calculate the quantitative contributions of climate change and human activity to the decline of streamflow happening in those 12 catchments. With the whole period divided into baseline (the first 10 years) and evaluation (the remaining 48 years) periods, the results showed that human activity was the major contributor to the streamflow decline from baseline period to evaluation period for all 12 catchments, while the ratio of climate contribution to human contribution varied among catchments.

_{0}estimations applied were also examined. In conclusion, the sensitivity of a specific catchment to attribution methods or the key parameters in applied calculations vary and may be affected by geographical locations, landscape characteristics, and local climates. We argue that it would be difficult to find a combination of climate elasticity and E

_{0}estimation that is suitable for every case of contribution analysis, although it might be possible for catchments with similar climate types and catchment characteristics by more detailed sensitivity assessments. However, comparing common features and differences between methods as well as parameter values involved helps to capture the uncertainty in contribution analysis and could have implications for improving methods.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A3.**Time series of evapotranspiration change for 12 catchments at intra- and inter-annual scales.

**Figure A4.**Standard deviation of quantitative contribution to streamflow change calculated by fixed E

_{0}estimations and varied Budyko-based methods.

**Figure A5.**Standard deviation of quantitative contribution to streamflow change calculated by fixed Budyko-based methods and varied E

_{0}estimations.

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**Figure 1.**Study Area: the locations of Loess Plateau (red line), catchments (blue line, with catchment names identified), and Yellow River (green line, only the parts within Loess Plateau are shown here) are plotted on a topography basemap, sourced from Esri, USGS, and NOAA.

**Figure 2.**Boxplots made by all contribution data: (

**a**) the variability of climatic contribution to streamflow change; (

**b**) the variability of human contribution to streamflow change.

**Figure 3.**Quantitative contribution to streamflow change by climate change (%) and human activities (%): for each type of eight Budyko-based methods, contribution values are averaged over results calculated with 13 E

_{0}estimations; at the catchment scale, the variability (line plot) and standard deviation (bar plot) of contribution values derived by different methods are also shown here.

**Figure 4.**Map of the standard deviation (Std) of different Budyko-based methods for quantifying human and climate contributions to streamflow.

**Figure 5.**Quantitative contribution to streamflow change by climate change (%) and human activities (%): for each type of 13 E

_{0}estimations, contribution values are averaged over results calculated with eight Budyko-based methods; at the catchment scale, the variability (line plot) and standard deviation (bar plot) of contribution values derived by different methods are also shown here.

**Figure 6.**Map of the standard deviation (Std) of quantitative contributions calculated by (

**a**) various methods with FAO E

_{0}estimation and (

**b**) method Budyko with various E

_{0}estimations.

IHA Statistics | Hydrological Parameters | |
---|---|---|

Group 1 | Mean flow in January | Mean flow in February |

Mean flow in March | Mean flow in April | |

Mean flow in May | Mean flow in June | |

Mean flow in July | Mean flow in August | |

Mean flow in September | Mean flow in October | |

Mean flow in November | Mean flow in December |

Function Identifier | $\mathit{f}\left(\varnothing \right)$ | Parameters |
---|---|---|

Budyko | ${(\varnothing \mathrm{tanh}(1/\varnothing )\left(1-{e}^{-\varnothing}\right))}^{1/2}$ | - |

Budyko–Fu (FU) | $1+\varnothing -{\left(1+{\varnothing}^{m}\right)}^{1/m}$ | m, catchment characteristics |

Budyko–Ol’dekop (OLDEKOP) | $\varnothing \mathrm{tanh}(1/\varnothing )$ | - |

Bukyko–Pike (PIKE) | $1/\sqrt{1+{\varnothing}^{-2}}$ | - |

Budyko–Schreiber (SCHREIBER) | $1-{e}^{-\varnothing}$ | - |

Budyko–Wang (WANG) | $\frac{1+\varnothing -\sqrt{{\left(1+\varnothing \right)}^{\partial}-4\partial \left(2-\partial \right)\varnothing}}{2\partial \left(2-\partial \right)}$ | $\partial $, vegetation-related catchment characteristics |

Budyko–Yang (YANG) | $1/({\left(\frac{1}{\varnothing}{)}^{n}+1\right)}^{1/n}$ | n, climate seasonality and catchment characteristics |

Budyko–Zhang (ZHANG) | $\left(1+\omega \varnothing \right)/\left(1+\omega \varnothing +\frac{1}{\varnothing}\right)$ | $\omega $, plant-available water coefficient |

Method | Function (E_{0}) | Parameter | |
---|---|---|---|

Penman–Monteith (FAO) | $\frac{0.408\mathsf{\Delta}\left({R}_{n}-G\right)+\gamma \frac{900}{{T}_{a}+273}{U}_{2}\left({e}_{s}-{e}_{a}\right)}{\mathsf{\Delta}+\gamma \left(1+0.34\right){U}_{2}}$ | - | |

Priestley–Taylor (PT) | $f\frac{\Delta}{\Delta +\gamma}\xb7\frac{\left({R}_{n}-G\right)}{\lambda}$ | $f$ | 1.26 |

1.1623 * | |||

Makkink (MAK) | $g\frac{\Delta}{\Delta +\gamma}\xb7\frac{{R}_{s}}{\lambda}$ | $g$ | 0.61 |

0.7314 * | |||

Abtew (ABTEW) | $K\frac{{R}_{s}}{\lambda}$ | $K$ | 0.53 |

0.4352 * | |||

Hargreaves (HARG) | $n\left(T+17.8\right)\frac{{R}_{s}}{\lambda}$ | $n$ | 0.0023 |

0.0105 * | |||

Doorenbos–Pruitt (DOOR) | $\alpha \left(\frac{\Delta}{\Delta +\gamma}{R}_{s}\right)+\beta $ | $\beta $ | −0.3 |

−0.4517 * | |||

Jensen–Haise (JENSEN) | ${C}_{t}\left(T-{T}_{x}\right)\frac{{R}_{s}}{\lambda}$ | ${C}_{t}$ | 0.025 |

0.0163 * |

_{n}is net radiation flux at surface (${\mathrm{kw}/\mathrm{m}}^{2}$), G is water heat flux (${\mathrm{kw}/\mathrm{m}}^{2}$), $\gamma $ is psychrometric constant ($\mathrm{kPa}/\mathbb{C}$), T

_{a}is daily average temperature at 2 m height ($\mathbb{C}$), U

_{2}is wind speed at 2 m height (m/s), $\left({e}_{s}-{e}_{a}\right)$ is vapor pressure deficit (kPa), $\lambda $ is latent heat of water vaporization of water ($\mathrm{MJ}/\mathrm{kg}$), R

_{s}is solar radiation ($\mathrm{MJ}/{\mathrm{m}}^{2}/\mathrm{d}$), $\alpha =1.066-0.0013RH+0.045{U}_{d}-0.2\times {10}^{-3}RH\xb7{U}_{d}-0.135\times {10}^{-4}R{H}^{2}-0.0011{U}_{d}^{2}$ (RH is mean relative humidity, %; U

_{d}is mean daytime wind speed at 2 m height, m/s), T

_{x}is temperature constant (${T}_{x}=-3\mathbb{C}$); all methods listed below, except FAO (Penman–Monteith), include specific parameters, and this table lists their original values and adjusted values, denoted by *.

P | E_{0} | Q | RVA-Q | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

High | Low | Total | High | Low | Total | High | Low | Total | High | Low | Total | |

Beiluo | - | - | - | - | ↑ *** | - | ↓ *** | ↓ *** | ↓ *** | M | L | L |

Dali | - | - | - | - | ↑ *** | - | - | ↓ *** | - | M | M | M |

Fenhe | - | - | - | - | ↑ ** | - | ↓ *** | ↓ *** | ↓ *** | M | H | H |

Gushan | - | - | - | - | ↑ *** | - | ↓ *** | ↓ *** | ↓ *** | H | M | M |

Jialu | - | - | - | - | ↑ *** | ↑* | ↓ *** | ↓ *** | ↓ *** | M | H | H |

Jinghe | - | - | - | - | ↑ *** | - | ↓ *** | ↓ *** | ↓ *** | M | L | L |

Kuye | - | - | - | - | ↑** | ↑* | ↓ *** | ↓ *** | ↓ *** | M | L | M |

Qingjian | - | - | - | - | ↑ *** | - | - | ↓ ** | ↓ * | M | M | M |

Tuwei | - | - | - | - | ↑ *** | ↑* | ↓ *** | ↓ *** | ↓ *** | M | M | M |

Wuding | - | - | - | - | ↑ ** | - | ↓ *** | ↓ *** | ↓ *** | H | M | M |

Xinshui | - | - | - | ↑ * | ↑ *** | ↑ *** | ↓ *** | ↓ *** | ↓ *** | M | M | M |

Yanhe | - | - | - | - | ↑ *** | ↑ * | ↓ ** | ↓ ** | ↓ ** | H | M | M |

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## Share and Cite

**MDPI and ACS Style**

Yang, Z.; Song, J.; Jiang, C.; Wang, K.; Zhao, L.; Hao, R. Contribution Analysis of the Streamflow Changes in Selected Catchments on the Loess Plateau, China, Using Multiple Budyko-Based Approaches. *Water* **2021**, *13*, 2534.
https://doi.org/10.3390/w13182534

**AMA Style**

Yang Z, Song J, Jiang C, Wang K, Zhao L, Hao R. Contribution Analysis of the Streamflow Changes in Selected Catchments on the Loess Plateau, China, Using Multiple Budyko-Based Approaches. *Water*. 2021; 13(18):2534.
https://doi.org/10.3390/w13182534

**Chicago/Turabian Style**

Yang, Zhiyuan, Jian Song, Chong Jiang, Kao Wang, Lingling Zhao, and Runmei Hao. 2021. "Contribution Analysis of the Streamflow Changes in Selected Catchments on the Loess Plateau, China, Using Multiple Budyko-Based Approaches" *Water* 13, no. 18: 2534.
https://doi.org/10.3390/w13182534