# Using Budyko-Type Equations for Separating the Impacts of Climate and Vegetation Change on Runoff in the Source Area of the Yellow River

^{1}

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## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{4}km

^{2}, accounting for about 17% of the total area of the whole Yellow River Basin. The reach is the main water production area and water conservation area of the whole basin. The annual average runoff of the study area is 232 × 10

^{8}m

^{3}and provides more than 42% of the total water resources in the Yellow River basin [6]. The study area is in the central Qinghai-Tibet Plateau. The daily temperature range is large, while the annual range is narrow. The annual average temperature ranges from −3.3 to 2.5 °C and the annual precipitation is between 332.4 and 743.2 mm. The geographic location of the source area of the Yellow River and the spatial distribution of meteorological stations are shown in Figure 1.

#### 2.2. Data Sources

## 3. Research Methods

#### 3.1. Trend Analysis (Slope)

_{i}represents the value of the observation data at i year.

#### 3.2. Mutation Analysis

_{1}= 0, E(s

_{k}) and Var(S

_{k}) represent the mean and variance of S

_{k}, respectively. Their calculation formulas are as follows:

_{k}= UF

_{k}(k = n, n − 1, …, 1), UB

_{1}= 0 to obtain the UB statistical curve. If the UF curve intersects with the UB curve and the intersection point is in the range of the 0.05 significance level, it can be considered that the year represented by the intersection point is the abrupt change year.

_{t}and the time t is the mutation year.

#### 3.3. Budyko Hypothesis

_{0}represents the annual average potential evaporation (mm) and ω is the underlying surface characteristic parameters. ET

_{0}can be calculated using the Penman-Monteith equation.

^{−1}), R

_{n}is the net radiation flux density at the surface (MJ/m

^{2}·d), G is the sensible heat flux density from the surface to the soil (MJ/m

^{2}·d), γ is the psychrometric constant (kPa·°C

^{−1}), U

_{2}is the wind speed at 2 m (m/s), T is the average temperature (°C), e

_{a}is the saturation vapor pressure at air temperature (kPa), and e

_{d}is the actual vapor pressure of the air (kPa).

_{1}) and the change period (T

_{2}) based on the abrupt year of runoff at Tangnaihai hydrological Station in the Yellow River Basin. The annual average precipitation in the base period (T

_{1}) is P

_{1}. The average annual precipitation in the changing period (T

_{2}) is P

_{2}. The change in annual precipitation can be expressed as:

_{1}period to the T

_{2}period using formulas (17) and (18):

_{1}period to the T

_{2}period, $\mathsf{\Delta}{R}_{E{T}_{0}}$ is the runoff variation value caused by annual average potential evaporation change from the T

_{1}period to the T

_{2}period, and $\mathsf{\Delta}{R}_{\omega}$ is the runoff variation value caused by underlying surface characteristic parameter change from the T

_{1}period to the T

_{2}period.

_{1}) and the change period (T

_{2}). Next, the average NDVI change in the two periods can be calculated as:

_{1}) can be estimated as follow:

_{2}period can be calculated as follows:

_{2}period. ${\eta}_{NDV{I}_{H}}$ and ${\eta}_{NDV{I}_{C}}$ are the contribution rates of human activities and climate change to vegetation changes, respectively.

## 4. Results and Discussion

#### 4.1. Trends of Runoff, NDVI, and Climate Change

^{8}m

^{3}per year. The values of NDVI show a slight increasing trend in the source area of the Yellow River basin from 1981 to 2015. The monthly average increase of NDVI in the source area of the Yellow River basin from 1981 to 2015 is 3 × 10

^{−5}.

#### 4.2. Abrupt Changes of Runoff

#### 4.3. Assessment of the Contribution Rates of Climate Change and Human Activities to Runoff Change

_{0}), and the underlying surface characteristic parameters (ω) to estimate the elastic coefficient of climate and land cover to runoff change. The underlying surface characteristic parameter (ω) depends on soil type, topographic factors, and vegetation coverage, assuming that the soil types and topographical factors in the source area of the Yellow River basin have not changed since 1961, and used vegetation change instead of land cover change. Previous studies often attributed LUCC (land use/cover change) to human activities. However, LUCC, particularly vegetation change, are impacted by both climate change and human activities. Therefore, previous studies are likely to underestimate the effect of climate change on runoff [11,15]. To accurately assess the contribution rates of climate change and LUCC to runoff change in the source area of the Yellow River basin, it is necessary to distinguish the impact of natural and human factors on LUCC.

_{1}period (1961–1989) and the T

_{2}period (1990–2015). Several previous studies found that NDVI is closely related to precipitation and potential evaporation and can be an indicator to assess the impact of natural and human factors on LUCC [41,42,43]. The specific steps are as follows:

- (1)
- There were NDVI remote sensing image data from June 1981 to December 1989 in T
_{1}period (1961–1989), so we established the multiple linear regression relationship between NDVI and climatic factors (precipitation and potential evaporation) from July 1981 to December 1989. - (2)
- Due to a lack of NDVI values in the period from January 1961 to June 1981, we further assumed that the multiple linear regression relationship in the period from June 1981 to December 1989 was the same as the period from January 1961 to June 1981. NDVI values for the period from January 1961 to June 1981 were calculated based on precipitation and potential evaporation in the corresponding periods.
- (3)
- We calculated the mean value of measured NDVI ($\overline{NDV{I}_{{T}_{1}}}$) in T
_{1}period (1961–1989), the mean value of measured NDVI ($\overline{NDV{I}_{{T}_{2}}}$) in T_{2}period (1990–2015), and the mean value of NDVI under climate change ($\overline{NDV{I}_{{T}_{2},S}}$) in the T_{2}period (1990–2015) according to the multiple linear regression function. - (4)
- We calculated the contribution rates of climate change and human activities to NDVI changes using formula (26)–(29) (Table 1).

_{1}and T

_{2}. Next, we calculated the differences in annual average precipitation, potential evaporation, and the underlying surface characteristic parameters between the two different periods. Then, the runoff variation value of Tangnaihai station caused by precipitation, potential evaporation, and LUCC were calculated by formula (19)–(21). Runoff variation caused by LUCC can be separated into two parts: natural and human factors; their contribution ratios can be obtained from Table 1. Based on the above method, the relative contribution rates of climate change (including precipitation, potential evaporation, and subsequent vegetation changes) and vegetation changes caused by human activities to runoff at Tangnaihai station were calculated (Table 3).

#### 4.4. Discussions

- (1)
- Uncertainties of meteorological station observation data

- (2)
- Uncertainties in the division of base period and change period

- (3)
- Uncertainties caused by using NDVI to characterize land type change

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The location of hydrological and meteorological stations in the source area of the Yellow River Basin.

**Figure 2.**Change trend of annual average runoff from 1961 to 2015 (

**a**) and NDVI (

**b**) from 1981 to 2015 in the source area of the Yellow River basin.

**Figure 3.**Changing trend of annual average precipitation (

**a**) and potential evaporation (

**b**) from 1961 to 2015 in the source area of the Yellow River basin.

**Figure 4.**Result of the Mann-Kendall mutation test of the source area of the Yellow River from 1961 to 2015.

**Figure 5.**Result of the accumulative runoff anomaly of the source area of the Yellow River from 1961 to 2015.

T_{1} | T_{2} | Fitting Equation | $\Delta \overline{\mathit{N}\mathit{D}\mathit{V}\mathit{I}}$ | $\overline{\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{{\mathit{T}}_{1}}}$ | $\overline{\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{{\mathit{T}}_{2},\mathit{S}}}$ | $\overline{\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{{\mathit{T}}_{2}}}$ | ${\mathit{\eta}}_{\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{\mathit{C}}}(\%)$ | ${\mathit{\eta}}_{\mathit{N}\mathit{D}\mathit{V}{\mathit{I}}_{\mathit{H}}}(\%)$ |
---|---|---|---|---|---|---|---|---|

1961–1989 | 1990–2015 | NDVI = 3.069 × 10^{−3} P + 8.875× 10^{−4} ET_{0} + 0.1588 (R^{2} = 0.79) | 0.0282 | 0.3289 | 0.3466 | 0.3571 | 62.79 | 37.21 |

Hydrological Station | Period | ET_{0}/mm | R/mm | P/mm | $\mathit{\omega}$ | R/P | ET_{0}/P |
---|---|---|---|---|---|---|---|

Tangnaihai | T_{1} | 796.54 | 180.39 | 518.92 | 1.13 | 0.35 | 1.54 |

T_{2} | 805.38 | 148.85 | 502.66 | 1.26 | 0.30 | 1.60 |

ε_{P} | ε_{ET0} | ε_{ω} | $\Delta \mathit{R}$ | $\Delta \mathit{P}$ | $\Delta \mathit{E}{\mathit{T}}_{0}$ | $\Delta \mathit{\omega}$ | $\Delta {\mathit{R}}_{\mathit{P}}$ | $\Delta {\mathit{R}}_{\mathit{E}{\mathit{T}}_{0}}$ | $\Delta {\mathit{R}}_{\mathit{L}\mathit{C}}$ | $\Delta {\mathit{R}}_{\mathit{L}\mathit{H}}$ | ${\mathit{\eta}}_{{\mathit{R}}_{\mathit{C}}}\text{}(\%)$ | ${\mathit{\eta}}_{{\mathit{R}}_{\mathit{H}}}\text{}(\%)$ |
---|---|---|---|---|---|---|---|---|---|---|---|---|

1.77 | −0.77 | −1.16 | −31.54 | −16.26 | 8.84 | 0.13 | −9.36 | −1.41 | −13.32 | −7.89 | 75.33 | 24.67 |

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**MDPI and ACS Style**

Yan, D.; Lai, Z.; Ji, G.
Using Budyko-Type Equations for Separating the Impacts of Climate and Vegetation Change on Runoff in the Source Area of the Yellow River. *Water* **2020**, *12*, 3418.
https://doi.org/10.3390/w12123418

**AMA Style**

Yan D, Lai Z, Ji G.
Using Budyko-Type Equations for Separating the Impacts of Climate and Vegetation Change on Runoff in the Source Area of the Yellow River. *Water*. 2020; 12(12):3418.
https://doi.org/10.3390/w12123418

**Chicago/Turabian Style**

Yan, Dan, Zhizhu Lai, and Guangxing Ji.
2020. "Using Budyko-Type Equations for Separating the Impacts of Climate and Vegetation Change on Runoff in the Source Area of the Yellow River" *Water* 12, no. 12: 3418.
https://doi.org/10.3390/w12123418