# Attribution Analysis of Dry Season Runoff in the Lhasa River Using an Extended Hydrological Sensitivity Method and a Hydrological Model

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methods

#### 2.1. Preliminary Data Analysis

#### 2.2. Statistical Methods

#### 2.2.1. Trend Analysis Method

_{t}are the observations at time t, with t = 1, 2, …, n. Vector x

_{t}of length m contains the unobserved states if the system that are assumed to evolve in time according to linear system operator G

_{t}(a m × m matrix). We observe a linear combination of the states with noise and matrix F

_{t}(m × p) is the observation operator that transforms the model states into observations. Both observation and equations can have additive Gaussian errors with covariance V

_{t}and W

_{t}.

_{t}with two hidden states ${x}_{t}=\left[{\mu}_{t}{\alpha}_{t}\right]$, where ${\mu}_{t}$ is the mean level and ${\alpha}_{t}$ is the change in the level from time t − 1 to time t. then Equation (1) can be rewritten as

#### 2.2.2. Abrupt Change Analysis

_{t}is the raw time series, r

_{1}is the lag 1 serial correlation coefficient of sample data, which can be estimated from sample data by an autocorrelation function as given in the work of Salas et al. [44].

_{1}, x

_{2}, …, x

_{n}. m

_{i}is computed as the number of x

_{i}in the series whose values exceeded x

_{j}($1\le j\le i$)). The test statistic is calculated as

#### 2.3. Coupled Water–Energy Balance Equation at an Arbitrary Time Scale

_{0}is potential evapotranspiration, P is precipitation, I is the external water supply for a basin, S is soil moisture at the beginning of the month, w is a parameter representing basin characteristics, and C is a constant for a particular basin.

#### 2.4. Extended Hydrological Sensitivity Method

_{0}, DS, and w

_{0}between the altered and baseline periods, respectively. Then $\mathsf{\Delta}{R}^{h}$ can be solved by combining Equations (6) and (7).

_{0}, DS and w, respectively. $\left\{{x}_{i}^{bp}\right\},i=1,2,3,4$ are the average respective values of P, E

_{0}, DS, and w during the baseline period. $\left\{{x}_{i}^{ap}\right\},i=1,2,3,4$ are the average respective values of P, E

_{0}, DS, and w during the altered period.

#### 2.5. An Improved ABCD Model with a Snow Melt Module

_{1}and a

_{2}, the snowmelt module was able to describe the processes of snowfall, snow cover, and snowmelt. Figure 1 is a structural diagram of the ABCD model with the snowmelt module. Detailed information on the ABCD model and snowmelt module can be found in the relevant literature [50,54] and is not covered in this article.

#### 2.6. Genetic Algorithm Mehtod

_{1}, and a

_{2}) were optimized using a genetic algorithm (GA) in MATLAB. Model calibration was achieved by maximizing the Nash–Sutcliffe Efficiency (NSE) of monthly runoff, which can be expressed as

_{1}, and a

_{2}). The flow chart in Figure 2 represents the procedure in the applied algorithm.

## 3. Study Area and Data Sources

#### 3.1. Study Area Description

^{2}and an average annual streamflow of 107.1 billion m

^{3}. Water resources in this area are abundant but also spatially and temporally heterogeneous. Precipitation is primarily concentrated from June to September and the low water period is typically from November to April. The minimum, maximum, and average runoff and precipitation for each month at the Lhasa Hydrological Station and the Lhasa Meteorological Station are given in Table 2. It is indicated from Table 2 that the river flow in May to October accounting for 87.7% of the total amount of the annual runoff, and the precipitation in June to September accounting for 89.1% of the total amount of the annual precipitation.

^{2}. It accounts for 79.8% of the total area of the LRB. There are three meteorological stations (Lhasa, Maizhokunggar, and Damxung) in the basin. Maizhokunggar meteorological station has a shorter observation time series and the data are not suitable for use. Damxung and Lhasa meteorological stations are distributed uniformly in the basin in the upper and lower parts of the Lhasa River, respectively. In addition, their observation conditions have not changed in recent decades. Therefore, Damxung and Lhasa meteorological stations were selected to provide the meteorological data. The geographical positions of hydrological and meteorological stations are shown in Figure 3.

#### 3.2. Data

_{20}pan (an evaporimeter with a diameter of 20 cm) or E-601B pan (an evaporimeter with a diameter of 61.8 cm) depending on the external environment. In Tibet, average E

_{20}pan and E-601B pan coefficients are 0.585 and 0.9, respectively [58]. Therefore, the potential evapotranspiration data used in this study were derived using the E

_{20}pan or E-601B pan observations multiplied by the corresponding coefficient.

## 4. Results and Discussion

#### 4.1. Preliminary Data Analysis

#### 4.2. Trends for Runoff, Precipitation, and Potential Evapotranspiration during the Dry Season

_{dry}) and potential evapotranspiration (E

_{0,dry}). P

_{dry}and E

_{0,dry}values using the Spearman’s test were −0.45 and −0.14, respectively, while their corresponding statistics using the MK test were 3.54 and 0.89. This showed that there was a significant increasing trend for P

_{dry}during the dry season and a non-significant decreasing trend for E

_{0,dry}over the same period. Some research [4] has confirmed increasing precipitation and almost no trend in evapotranspiration during the winter. The trend analysis results in this paper were consistent with these prior conclusions.

_{t}and W

_{t}and the autocorrelation coefficient ρ used in the DLM are estimated using he MCMC simulation algorithm. The prior mean and prior standard of ${\sigma}_{trend}^{2}$ are 0.0005 and 200%, respectively, while the prior distribution of ρ is uniform (0, 1). Figure 5 shows the measurement series and the modeled mean background flow, μ

_{t}. Overall, it is easy to see that the fits usually follow the data points very accurately. A continuous decay of flow is evident in annual minimum 1-, 3-, 7-, and 30-day flow series. The change is most visible at shorter durations. The mean value in annual minimum 90-day and dry season flow has risen from the 1956–2016. These results agree well with those obtained by MK test and Spearman’s test.

#### 4.3. Change Point Identification of Hydro-Climatic Variables

#### 4.4. Modeling Dry Season Water Storage Change

_{dry}, was evaluated by adding the monthly DS values in the dry season. Total dry season precipitation P

_{dry}and runoff R

_{dry}was used to calculate total actual evapotranspiration E

_{dry}using the water balance equation. Table 6 summarizes the differences between P

_{dry}, R

_{dry}, DS

_{dry}, and E

_{dry}before and after 1986. It can be observed that the absolute value of DS

_{dry}was about twice that of P

_{dry}during both the baseline and altered periods, indicating that change in total stored water could be a significant recharge source for runoff. It was clear that neither water storage nor deep groundwater losses can be neglected during either period.

#### 4.5. Quantitative Assessment of the Impacts of Climate Change and Anthropogenic Activities on Streamflow

_{0}, water storage variability DS, and underlying surface w on runoff variability were quantified using the sum of corresponding linear and non-linear terms. Similarly, their interacting impacts were quantified by the sum of the coupled terms. The value of each partial derivative is summarized in Table 8. The results showed that a 10% increase in precipitation would result in a 2.30% increase in runoff, while a 10% increase in potential evapotranspiration would lead to a 13.2% decrease in runoff. For basin characteristics, a 10% increase in DS would cause a 3.2% decrease in runoff, while a 10% increase in parameter w would lead to a 6.34% decrease in runoff.

#### 4.6. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 4.**Model diagnostic on the (

**a**) original minimum one-day flow and (

**b**) pre-whitened minimum 1-day flow by an estimated autocorrelation function (ACF).

**Figure 5.**DLM fit for (

**a**) annual minimum 1-day flow runoff, (

**b**) annual minimum 3-day flow runoff, (

**c**) annual minimum 7-day flow runoff, (

**d**) annual minimum 30-day flow runoff, (

**e**) annual minimum 90-day flow runoff and (

**f**) dry season runoff at Lhasa station. The dots are the observations used in the analysis, the solid line following the observations is the DLM fit obtained by a Kalman filter. The smooth solid line is the background level component of the model with 95% probability envelope.

**Figure 6.**Mutation analysis using MK testing: (

**a**) precipitation, (

**b**) potential evapotranspiration, (

**c**) annual minimum 1-day flow runoff, (

**d**) annual minimum 3-day flow runoff, (

**e**) annual minimum 7-day flow runoff, (

**f**) annual minimum 30-day flow runoff, (

**g**) annual minimum 90-day flow runoff, and (

**h**) dry season runoff at Lhasa station in the dry season. UF and UB were calculated using the MK test in the forward and backward directions, respectively. Horizontal dashed lines are ±95% confidence intervals.

**Figure 7.**Mutation analysis using Yamamoto’s method: (

**a**) Lhasa station runoff and (

**b**) dry season precipitation. Horizontal red lines are ±95% confidence intervals.

**Figure 8.**Monthly runoff simulation results using the improved ABCD model at Lhasa Hydrological Station from 1962–2016. The unit of the runoff is transferred from millimeter into cubic per second (m

^{3}/s) by multiplying by the watershed area for the convenience of comparing with observed runoff.

**Figure 9.**Simulated results for monthly change in groundwater and soil water storage in the basin from 1962–2016.

**Figure 10.**Contributions of the impacts of climate change and anthropogenic activities on runoff in the Lhasa River during the dry season.

Linear Terms | Coupled Terms | Nonlinear Terms |
---|---|---|

$\frac{\partial f}{\partial P}=1-\frac{{\varphi}^{w+1}}{{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+1}}$ | $\frac{{\partial}^{2}f}{\partial P\partial {E}_{0}}=-\frac{{\partial}^{2}f}{\partial DS\partial {E}_{0}}=-\frac{\left(w+1\right){\varphi}^{w+1}}{{E}_{0}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ | $\frac{{\partial}^{2}f}{\partial {P}^{2}}=\frac{\left(w+1\right){\varphi}^{w+1}}{{E}_{0}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ |

$\frac{\partial f}{\partial {E}_{0}}=\frac{-1}{{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+1}}$ | $\frac{{\partial}^{2}f}{\partial P\partial w}=-\frac{{\partial}^{2}f}{\partial DS\partial w}=-\frac{{\varphi}^{w}\left[K+{w}^{2}ln\varphi \right]}{{w}^{2}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ | $\frac{{\partial}^{2}f}{\partial D{S}^{2}}=\frac{\left(w+1\right){\varphi}^{w+1}}{{E}_{0}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ |

$\frac{\partial f}{\partial DS}=\frac{{\varphi}^{w+1}}{{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+1}}-1$ | $\frac{{\partial}^{2}f}{\partial P\partial DS}=-\frac{\left(w+1\right){\varphi}^{w+2}}{{E}_{0}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ | $\frac{{\partial}^{2}f}{\partial {E}_{0}{}^{2}}=\frac{\left(w+1\right){\varphi}^{w}}{{E}_{0}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ |

$\frac{\partial f}{\partial w}=-\frac{{E}_{0}K}{{w}^{2}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+1}}$ | $\frac{{\partial}^{2}f}{\partial {E}_{0}\partial w}=-\frac{K+{w}^{2}{\varphi}^{w}ln{\varphi}^{-1}}{{w}^{2}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ | $\frac{{\partial}^{2}f}{\partial {w}^{2}}=-\frac{{E}_{0}\left[{K}^{2}-2w\left({\varphi}^{w}+1\right)K+{\varphi}^{w}ln\varphi ln\frac{1+{\varphi}^{-m}}{1+{\varphi}^{m}}\right]}{{w}^{4}{\left(1+{\varphi}^{w}\right)}^{\frac{1}{w}+2}}$ |

**Table 2.**Runoff and precipitation for each month at the Lhasa Hydrological Station and the Lhasa Meteorological Station.

Months | Jan. | Feb. | Mar. | Apr. | May | Jun. | Jul. | Aug. | Sept. | Oct. | Nov. | Dec. | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Runoff (m^{3}/s) | Maximum | 85.5 | 74.3 | 78.9 | 172 | 385 | 1020 | 1370 | 1800 | 1310 | 439 | 191 | 109 |

Minimum | 33.6 | 26 | 31.4 | 36.3 | 38.8 | 121 | 309 | 203 | 141 | 87.3 | 59.5 | 41.1 | |

Average | 57.5 | 51.1 | 50.2 | 62.1 | 124.6 | 398.0 | 749.0 | 849.9 | 630.0 | 265.8 | 125.1 | 77.9 | |

Precipitation (mm) | Maximum | 5.5 | 18.9 | 19.3 | 26.2 | 78.3 | 192.5 | 258.9 | 283.2 | 147.2 | 38.4 | 22.4 | 12.7 |

Minimum | 0 | 0 | 0 | 0 | 0.2 | 5.9 | 35.3 | 29 | 11 | 0 | 0 | 0 | |

Average | 0.6 | 1.2 | 2.5 | 6.9 | 27.2 | 76.8 | 126.8 | 130.3 | 62.0 | 8.1 | 1.2 | 0.6 |

**Table 3.**Trends for different flow components in the LRB using the Spearman’s and Mann–Kendall tests.

Series | Number of Years | Spearman’s Test | Mann–Kendall Test | ||||
---|---|---|---|---|---|---|---|

r | Threshold | Tendency | z | Threshold | Tendency | ||

Annual minimum 1-day flow | 61 | −0.28 * | 0.25 | −2.24 * | 1.96 | ||

Annual minimum 3-day flow | 61 | −0.23 | 0.25 | −1.80 | 1.96 | ||

Annual minimum 7-day flow | 61 | −0.20 | 0.25 | −1.49 | 1.96 | ||

Annual minimum 30-day flow | 61 | −0.14 | 0.25 | −0.89 | 1.96 | ||

Annual minimum 90-day flow | 61 | 0.07 | 0.25 | 0.68 | 1.96 | ||

Annual dry-seasonal flow* | 61 | 0.06 | 0.25 | 0.55 | 1.96 |

Model | Calibration Method | Spin-Up Period | Baseline Period | Altered Period | ||
---|---|---|---|---|---|---|

Calibration Periods | Validation Periods | Calibration Periods | Validation Periods | |||

Improved ABCD model | Genetic algorithm | 1956.5–1962.4 | 1962.5–1970.4 | 1970.5–1986.4 | 1986.5–1996.4 | 1996.5–2017.4 |

Nash-Sutcliffe Efficiency | a | b | c | d | a_{1} | a_{2} | ||
---|---|---|---|---|---|---|---|---|

Range | / | 0~1 | 0~200 | 0~1 | 0~20 | 0~30 | −20~20 | |

Baseline period | Calibration periods | 0.86 | 0.64 | 199.97 | 0.16 | 0.08 | 18.4 | 9.2 |

Validation periods | 0.84 | |||||||

Altered period | Calibration periods | 0.83 | 0.65 | 199.98 | 0.11 | 0.07 | 14.5 | 9.5 |

Validation periods | 0.81 |

**Table 6.**Change in hydro-climatic variables (mm) in the dry season between the baseline and altered periods.

Period | P_{dry} | R_{dry} | DS_{dry} | E_{dry} |
---|---|---|---|---|

Baseline period (1962–1985) | 454.3 | 799.8 | −1026.7 | 681.1 |

Altered period (1986–2016) | 753.9 | 1100.7 | −1057.0 | 710.3 |

Total period (1962–2016) | 1208.2 | 1900.5 | −2083.7 | 1391.4 |

**Table 7.**Change in mean monthly hydro-climatic variables due to climate change and anthropogenic activities.

Variables | Baseline Period | Altered Period | Variability |
---|---|---|---|

${\overline{R}}_{dry}$ (mm/month) | 33.33 | 35.51 | 2.18 |

${\overline{P}}_{dry}$ (mm/month) | 18.93 | 24.32 | 5.39 |

${\overline{{E}_{0,}}}_{dry}$ (mm/month) | 489.24 | 465.04 | −24.20 |

${\overline{DS}}_{dry}$ (mm/month) | −42.78 | −34.10 | 8.68 |

${\overline{m}}_{dry}$ | 0.44 | 0.39 | −0.05 |

$\frac{\partial f}{\partial P}\Delta P$ | $\frac{\partial f}{\partial {E}_{0}}\Delta {E}_{0}$ | $\frac{\partial f}{\partial DS}(\Delta DS)$ | $\frac{\partial f}{\partial m}\Delta m$ | $\frac{{\partial}^{2}f}{\partial {P}^{2}}{(\Delta P)}^{2}$ | $\frac{{\partial}^{2}f}{\partial {E}_{0}{}^{2}}{(\Delta {E}_{0})}^{2}$ | $\frac{{\partial}^{2}f}{\partial D{S}^{2}}{(\Delta DS)}^{2}$ |

3.63 | 0.40 | −5.84 | 4.02 | 0.03 | 0.01 | 0.08 |

$\frac{{\partial}^{2}f}{\partial {m}^{2}}{(\Delta m)}^{2}$ | $\frac{{\partial}^{2}f}{\partial P\partial {E}_{0}}(\Delta P\Delta {E}_{0})$ | $\frac{{\partial}^{2}f}{\partial P\partial DS}(\Delta P\Delta DS)$ | $\frac{{\partial}^{2}f}{\partial P\partial m}(\Delta P\Delta m)$ | $\frac{{\partial}^{2}f}{\partial {E}_{0}\partial DS}(\Delta {E}_{0}\Delta DS)$ | $\frac{{\partial}^{2}f}{\partial {E}_{0}\partial m}(\Delta {E}_{0}\Delta m)$ | $\frac{{\partial}^{2}f}{\partial DS\partial m}(\Delta DS\Delta m)$ |

0.19 | 0.04 | −0.11 | 0.298 | −0.06 | −0.03 | −0.48 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, Z.; Mei, Y.; Chen, J.; Hu, T.; Xiao, W.
Attribution Analysis of Dry Season Runoff in the Lhasa River Using an Extended Hydrological Sensitivity Method and a Hydrological Model. *Water* **2019**, *11*, 1187.
https://doi.org/10.3390/w11061187

**AMA Style**

Wu Z, Mei Y, Chen J, Hu T, Xiao W.
Attribution Analysis of Dry Season Runoff in the Lhasa River Using an Extended Hydrological Sensitivity Method and a Hydrological Model. *Water*. 2019; 11(6):1187.
https://doi.org/10.3390/w11061187

**Chicago/Turabian Style**

Wu, Zhenhui, Yadong Mei, Junhong Chen, Tiesong Hu, and Weihua Xiao.
2019. "Attribution Analysis of Dry Season Runoff in the Lhasa River Using an Extended Hydrological Sensitivity Method and a Hydrological Model" *Water* 11, no. 6: 1187.
https://doi.org/10.3390/w11061187