# Spatial Variations in Terrestrial Water Storage with Variable Forces across the Yellow River Basin

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}) of 0.83 and a mean absolute error (MAE) of 1.2 mm. The results showed that precipitation, minimum temperature, runoff, base flow, water withdrawal for electricity, and NDVI were the main drivers of the spatiotemporal variations in the TWS, of which minimum temperature and runoff played a considerable role in TWS variations through the interplay with other variables. The critical values of the trend for interactive variables, which could alter the acting direction of the synergy on the TWS, were also estimated. In view of the connotation of interactive variables, we suggested that spatiotemporal variations in TWS resulted from the coupling of the hydrological energy system, hydrological ecosystem, and hydrological system in the YRB, of which the hydrological system plays the most significant role, followed by the hydrological ecosystem.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}(including Erdos internally drained area). The topography of the YRB is complex, spanning four geomorphic units: the Qinghai Tibet Plateau, Inner Mongolia Plateau, Loess Plateau, and Huang Huai Hai Plain. The average altitude decreases successively from northwest to southeast (Figure 1). This study focused on the upper and middle reaches of the Yellow River Basin (hereafter referred to as UMYRC), which is the area above Huayuankou station.

^{3}, and the runoff above Lanzhou station accounts for 60% of the total basin runoff. There are 13 primary tributaries with a drainage area of more than 10,000 km

^{2}in the UMYRC (Figure 1).

#### 2.2. Data

#### 2.3. Method

#### 2.3.1. Mann–Kendall and Sen’s Slope

#### 2.3.2. Pearson’s Correlation Analysis

#### 2.3.3. Multiple Adaptive Regression Splines (MARS)

- (1)
- Constant term, i.e., intercept, which represents the possible intercept of other basic equations.
- (2)
- Hinge function in the form of max (0, x-knot), or max (0, knot-x), where MARS automatically selects the variable x and its corresponding node value (knot), where the knot point is a constant splitting the variable x into two sections in each of which MARS has a linear or non-linear form and joins at the node.
- (3)
- A product of two or more hinge functions indicating the interaction between two or more variables. In a two-variable case, the product represents the interaction between the variables.

**x**= {${x}_{1}$,…,$\text{}{x}_{k}$}, ${t}_{ij}$ is the node of the basic equation, and ${K}_{j}$ is the number of interactive variables in the basic equation.

#### 2.3.4. Measures of Performance Assessment

^{2}) and mean absolute error (MAE), which are defined as follows:

## 3. Results

#### 3.1. Spatial Variations in TWS Trend and Its Uncertainty

#### 3.2. Spatial Trend Variations of Influencing Factors

#### 3.3. Correlation between Variables

#### 3.4. Variables and Their Interactions Identified by MARS

#### 3.5. Assessment of MARS Model’s Performance

^{2}) of 0.83 and a mean absolute error (MAE) of 1.18 mm. Figure 10b shows the spatial distribution of trend slopes for TWS assessed by the MARS model, which resembled the spatial distribution pattern of TWS shown in Figure 3a. Therefore, the MARS model can explain the spatiotemporal variations in TWS well, and it is credible to use the MARS model to identify the main driving factors and their interactions on the variations in TWS across the UMYRC.

^{2}), mean absolute error (MAE), and Akachi information criterion (AIC). In addition, there are two interactive variables for all the models, and the maximum number of basic equations for the forward phase was set as mentioned earlier. The evaluation indexes of the regression model based on the input variables of the four groups for the MARS model are listed in Table 3. The evaluation indexes (R

^{2}and MAE) of models for input variables of categories one to three were all lower than the total variable model. In addition, the AIC values of the models for categories one to three were all higher than the total variable model. Therefore, the total variable model (category four) can better explain the spatiotemporal variations in TWS than other categories.

## 4. Discussion

#### 4.1. Main Influencing Factors of TWS Spatiotemporal Variations

#### 4.2. Impact of Factors’ Interaction on Spatiotemporal Variations in TWS

#### 4.3. Uncertainty and Limitations

## 5. Conclusions

^{2}) of 0.83 and a root mean square error (MAE) of 1.2 mm. Moreover, the spatial distributions of trends derived from the MARS model and GRACE data were similar. The MARS model identified that Rs, ElecW, NDVI, Rsb, P, and Tmin were statistically significant factors that dominated the variation in the TWS trend across the UMYRC. Among the determinants, the contribution of Rsb was the largest and Tmin was the smallest. Apart from the effect of a single factor, there were five pairs of interactive variables driving the variations in TWS, which were ElecW with Tmin and Rs, NDVI and Rs, P with Rs and Rsb. Among the interactive variables, the synergistic effect of P and Rsb contributed the most to the spatial variations in the TWS trend, followed by Rs and NDVI.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**The location and elevation as well as the distribution of the main tributaries and irrigation areas of the study area. The green triangles represent the location of hydrological sites. LYX is Langyagnxia station; LZ is Lanzhou station; TDG is Toudaogui station; HJ is Hejin station; SMX is Sanmenxia station; HYK is Huayuankou station; HID is Hetao Irrigation District; and YID is Yinchuan Irrigation District.

**Figure 2.**(

**a**) Inter-annual TWSA across UMYRC and (

**b**) empirical cumulative distribution functions for grid trend slope of TWS. TWS

_{T}is for the slope of TWS.

**Figure 3.**Distribution maps for the Sen’s slope of (

**a**) TWS change trend during 2003–2015 and (

**b**) their standard deviations, respectively. LYX is Langyagnxia station; LZ is Lanzhou station; TDG is Toudaogui station; HJ is Hejin station; SMX is Sanmenxia station; HYK is Huayuankou station.

**Figure 4.**(

**a–g**) Distribution maps for the trend slope of hydro-climatic variables and (

**h**) NDVI during 2003–2015. LYX is Langyagnxia station; LZ is Lanzhou station; TDG is Toudaogui station; HJ is Hejin station; SMX is Sanmenxia station; and HYK is Huayuankou station.

**Figure 5.**Distribution maps for the trend slope of water withdrawal for (

**a**) domesticity, (

**b**) electricity, (

**c**) irrigation, (

**d**) livestock, (

**e**), mining, and (

**f**) manufacturing during 2003–2015. LYX is Langyagnxia station; LZ is Lanzhou station; TDG is Toudaogui station; HJ is Hejin station; SMX is Sanmenxia station; and HYK is Huayuankou station.

**Figure 6.**The diagram of correlation coefficient matrix between variables, the upper triangle number is the value of correlation coefficient, red indicates negative correlation, and blue indicates positive correlation.

**Figure 7.**Influence of single variable (

**a**) ElecW, (

**b**) P, (

**c**) Rsb, and (

**d**) NDVI. identified by MARS model on the TWS trend. Scatter plot is the relationship for the single variable trend and TWS trend calculated by GRACE. The T subscript refers to the slope of variables.

**Figure 8.**Influence of interactive variables (

**a**) P and Rs, (

**b**) P and Rsb, (

**c**) is NDVI and Rs, (

**d**) is ElecW and P, and (

**e**) ElecW and Tmin identified by MARS on the TWS trend. Scatter plot is the relationship for the trend of interactive variables and TWS trend calculated by GRACE. The T subscript refers to the slope of variables.

**Figure 10.**(

**a**) Scatter plot for simulated TWS trend (TWS

_{T}) and estimated ones by GRACE and (

**b**) spatial distribution of TWS trend estimated by MARS model.

Category | Variables | Resolution | Data Source |
---|---|---|---|

Climate | Precipitation | Daily, point-scale | China Meteorological Administration |

Maximum temperature | |||

Minimum temperature | |||

Hydrology | Net radiation | Monthly, 0.25° | Rodell et al. (2004) |

Evaporation | |||

Runoff | |||

Base runoff | |||

Water withdrawal | Domestic | Monthly, 0.5° | Huang et al. (2018) |

Electricity | |||

Irrigation | |||

Livestock | |||

Manufacturing | |||

Mining | |||

GRACE terrestrial water storage | TWSA | Monthly, 0.5° | CSR Mascon JPL Mascon |

Vegetation | NDVI | 15 Day, 1/12° | GIMMS NDVI3g.v1 |

**Table 2.**A list of the variables retained by MARS and their corresponding basic equations with coefficient and node value.

Basis | Coefficient | P | Rs | Rsb | NDVI | ElecW | Tmin |
---|---|---|---|---|---|---|---|

Function | |||||||

1 | −0.35 | 1(0) | |||||

2 | −0.48 | −1(0) | |||||

3 | −0.90 | −1(−1.47) | |||||

4 | 4.70 | 1(−2.32) | |||||

5 | 2.90 | −1(−2.32) | |||||

6 | −835.68 | 1(−0.000755) | |||||

7 | 0.51 | 1(1.95) | −1(0) | ||||

8 | 0.06 | −1(1.95) | −1(0) | ||||

9 | −770.94 | 1(−0.27) | 1(−0.000755) | ||||

10 | 243.01 | −1(−0.27) | 1(−0.000755) | ||||

11 | 0.32 | 1(−1.47) | 1(−1.89) | ||||

12 | −0.26 | 1(−7.30) | 1(−2.32) | ||||

13 | −0.58 | −1(−7.30) | 1(−2.32) | ||||

14 | −13.56 | −1(0) | 1(0.0145) | ||||

15 | −48.13 | −1(0) | −1(0.0145) |

_{+}(i.e, x > t), −1 indicates the form (t − x)

_{+}(i.e., x < t).

Category | Input Variables | R^{2} | MAE | AIC |
---|---|---|---|---|

1 | P, ET, Rs, Rsb | 0.65 | 1.84 | 2381.94 |

2 | DomW, ElecW, MinW, LivW, IrrW, MfgW | 0.66 | 1.70 | 2371.30 |

3 | NDVI, Tmin, Tmax, NetRad | 0.56 | 1.88 | 2631.62 |

4 | All factors | 0.83 | 1.18 | 1702.66 |

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## Share and Cite

**MDPI and ACS Style**

Zhou, M.; Wang, X.; Sun, L.; Luo, Y.
Spatial Variations in Terrestrial Water Storage with Variable Forces across the Yellow River Basin. *Remote Sens.* **2021**, *13*, 3416.
https://doi.org/10.3390/rs13173416

**AMA Style**

Zhou M, Wang X, Sun L, Luo Y.
Spatial Variations in Terrestrial Water Storage with Variable Forces across the Yellow River Basin. *Remote Sensing*. 2021; 13(17):3416.
https://doi.org/10.3390/rs13173416

**Chicago/Turabian Style**

Zhou, Meilin, Xiaolei Wang, Lin Sun, and Yi Luo.
2021. "Spatial Variations in Terrestrial Water Storage with Variable Forces across the Yellow River Basin" *Remote Sensing* 13, no. 17: 3416.
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