# Application of Soil Moisture Data Assimilation in Flood Forecasting of Xun River in Hanjiang River Basin

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area and Data

#### 2.1. Study Area

^{2}. Abundant rainfall causes frequent floods in this area, which is characterized by a large peak volume (2690 m

^{3}/s). Therefore, accurate flood projection is necessary to maintain the safety of downstream power stations and people’s lives.

_{0}, due to the lack of actual measurement data, this study assumed 0.1 mm uniformly with reference to the adjacent watershed.

#### 2.2. Data

#### 2.2.1. Precipitation and Discharge Data

#### 2.2.2. Soil Moisture Data

^{3}/cm

^{3}), and their characteristic values corresponding to the eight floods that will be assimilated are shown in Table 2. Since the subsequent state variables to be assimilated include WU of the Xinanjiang model, these data should be converted into watershed surface water depth ${\mathrm{D}}_{\mathrm{w}}$ (mm) in advance when used, as shown in Equation (1). In addition, the soil moisture data observed by SMAP, which had a temporal resolution of 3 h, was interpolated into a 1-hour form in this study to correspond to the rainfall–runoff data.

## 3. Methodology

#### 3.1. Xinanjiang Rainfall–Runoff Model

#### 3.2. SCE-UA Method

- (1)
- SCE-UA algorithm parametersThe first step in SCE-UA is to determine the number of complex forms, p. Zhang and Jiang [35] studied the influence of different p values on model parameter calibration when data are ideal. The results showed that, when the value of p is 1 or 2, the parameter truth value basically cannot be searched. When the value of p is increased (4 and 10 examples), the true values of most parameters can be searched. In general, when the data are in good condition, p ≥ 4 can basically meet the needs of optimization parameters. The more complex the shapes, the better the applicability to higher-order nonlinear scenarios. The parameter settings of SCE-UA in this study are shown in Table 3.In this table, n is the number of parameters; m is the number of complex vertices; q is the number of subcomplex vertices; p is the number of complex forms; s is the population size; α is the number of children generated by the parent; β is the number of generations generated by the parent; k is the number of cycles to stop the iteration; and P is the critical precision to stop the iteration.
- (2)
- Objective functionIn this paper, NSE was chosen as the objective function. When NSE is closer to 1, it indicates the better simulation effect of the Xinanjiang model. The NSE calculation formula is as follows:$$NSE=1-\frac{{\sum}_{t=1}^{T}{\left({Q}_{o}^{t}-{Q}_{m}^{t}\right)}^{2}}{{\sum}_{t=1}^{T}({Q}_{o}^{t}-{\overline{{Q}_{o})}}^{2}}$$
- (3)
- Parameter calibration resultsThe SCE-UA was used to optimize the parameters of the Xinanjiang model in the Xun River watershed above Chaiping, where the first 19 floods (1999–2013) were used for parameter calibration and the last 8 floods (2017–2021) were used for parameter validation and data assimilation. The parameter calibration ranges and final values are shown in Table 4.
- (3)
- Evaluation Indicators

#### 3.3. Ensemble Kalman Filter

- (1)
- Initialize background: given the background ensemble of EnKF ${X}_{0}=({X}_{0,1}^{a},{X}_{0,2}^{a},\dots {X}_{0,n}^{a}$), the set number is n, and the state variable ${X}_{0,i}^{a}$ obeys the Gaussian distribution with mean ${X}_{0}^{a}$ and covariance ${P}_{0}^{a}$;
- (2)
- Add the state variable ensemble at time t to the prediction model, and calculate the next moment state variables ${X}_{t+1,i}^{f}$ and the prediction error covariance ${P}_{t+1}^{f}$.$${X}_{t+1,i}^{f}=M\left({X}_{t,i}^{a},{\alpha}_{t+1},{\beta}_{t+1}\right)+{W}_{i}$$$${P}_{t+1}^{f}=\frac{1}{n-1}{\displaystyle \sum}_{i=1}^{n}\left({X}_{t+1,i}^{f}-\overline{{X}_{t+1}^{f}}\right){\left({X}_{t+1,i}^{f}-\overline{{X}_{t+1}^{f}}\right)}^{T}$$
- (3)
- Calculate the gain matrix ${K}_{t+1}$ at t + 1.$${K}_{t+1}={P}_{t+1}^{f}{H}^{T}{\left(H{P}_{t+1}^{f}{H}^{T}+R\right)}^{-1}$$$${P}_{t+1}^{f}{H}^{T}=\frac{1}{n-1}{\displaystyle \sum}_{i=1}^{n}\left({X}_{t+1,i}^{f}-\overline{{X}_{t+1}^{f}}\right)[H({X}_{t+1,i}^{f}-H{\left(\overline{{X}_{t+1}^{f}}\right)]}^{T}$$$$H{P}_{t+1}^{f}{H}^{T}=\frac{1}{n-1}{\displaystyle \sum}_{i=1}^{n}\left[H\left({X}_{t+1,i}^{f}\right)-H\left(\overline{{X}_{t+1)}^{f}}\right)\right]{\left[H\left({X}_{t+1,i}^{f}\right)-H\left(\overline{{X}_{t+1)}^{f}}\right)\right]}^{T}$$
- (4)
- Combine the predicted ensemble and observation at t + 1, and calculate the analysis ensemble ${X}_{t+1,i}^{a}$ and the analysis error covariance ${P}_{t+1}^{a}$ at this moment.$${X}_{t+1}^{a},i={X}_{t+1,i}^{f}+{K}_{t+1}\left({Z}_{t+1}-H\left({X}_{t+1,i}^{f}\right)+{u}_{i}\right)$$$${P}_{t+1}^{a}=\frac{1}{n-1}{\displaystyle \sum}_{i=1}^{n}\left({X}_{t+1,i}^{a}-\overline{{X}_{t+1}^{a}}\right){\left({X}_{t+1,i}^{a}-\overline{{X}_{t+1}^{a}}\right)}^{T}$$
- (5)
- After the prediction update step, the cycle moves to the next moment.

#### 3.4. Augmented Ensemble Kalman Filter

#### 3.5. Dual Ensemble Kalman Filter

## 4. Results

#### 4.1. Simulation of Xinanjiang Model

#### 4.2. Assimilation Scheme of WU

#### 4.3. Simultaneous Assimilation of Parameters and WU

#### 4.4. Comparison of Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Chou, J.M.; Xian, T.; Dong, W.J.; Xu, Y. Regional Temporal and Spatial Trends in Drought and Flood Disasters in China and Assessment of Economic Losses in Recent Years. Sustainability
**2019**, 11, 55. [Google Scholar] [CrossRef] [Green Version] - Huang, C.C.; Pang, J.L.; Zha, X.C.; Su, H.X.; Jia, Y.F.; Zhu, Y.Z. Impact of monsoonal climatic change on Holocene overbank flooding along Sushui River, middle reach of the Yellow River, China. Quat. Sci. Rev.
**2007**, 26, 2247–2264. [Google Scholar] [CrossRef] - Yin, J.F.; Gu, H.D.; Liang, X.D.; Yu, M.; Sun, J.S.; Xie, Y.X.; Li, F.; Wu, C. A Possible Dynamic Mechanism for Rapid Production of the Extreme Hourly Rainfall in Zhengzhou City on 20 July 2021. J. Meteorol. Res.
**2022**, 36, 6–25. [Google Scholar] [CrossRef] - Han, S.S.; Coulibaly, P. Bayesian flood forecasting methods: A review. J. Hydrol.
**2017**, 551, 340–351. [Google Scholar] [CrossRef] - Devi, G.K.; Ganasri, B.P.; Dwarakish, G.S. A Review on Hydrological Models. In Proceedings of the International Conference on Water Resources, Coastal and Ocean Engineering (ICWRCOE), Mangalore, India, 11–14 March 2015; pp. 1001–1007. [Google Scholar]
- Crawford, N.H.; Burges, S.J. History of the Stanford watershed model. Water Resour. Impact
**2004**, 6, 3–6. [Google Scholar] - Fedora, M.A.; Beschta, R.L. Storm runoff simulation using an antecedent precipitation index (API) model. J. Hydrol.
**1989**, 112, 121–133. [Google Scholar] [CrossRef] - Ren-Jun, Z. The Xinanjiang model applied in China. J. Hydrol.
**1992**, 135, 371–381. [Google Scholar] [CrossRef] - Vrugt, J.A.; Diks, C.G.; Gupta, H.V.; Bouten, W.; Verstraten, J.M. Improved treatment of uncertainty in hydrologic modeling: Combining the strengths of global optimization and data assimilation. Water Resour. Res.
**2005**, 41. [Google Scholar] [CrossRef] - Gupta, H.V.; Sorooshian, S.; Yapo, P.O. Status of automatic calibration for hydrologic models: Comparison with multilevel expert calibration. J. Hydrol. Eng.
**1999**, 4, 135–143. [Google Scholar] [CrossRef] - Yi, S.L.; Zorzi, M. Robust Kalman Filtering Under Model Uncertainty: The Case of Degenerate Densities. IEEE Trans. Autom. Control.
**2022**, 67, 3458–3471. [Google Scholar] [CrossRef] - Chao, Z.; Hua-sheng, H.; Wei-min, B.; Luo-ping, Z. Robust recursive estimation of auto-regressive updating model parameters for real-time flood forecasting. J. Hydrol.
**2008**, 349, 376–382. [Google Scholar] [CrossRef] - Guo, S.; Xu, G.; Zhang, H.; Li, C. A Real-Time Flood Updating Model Based on the Bayesian Method; IAHS Press: Wallingford, UK, 2007; pp. 210–215. [Google Scholar]
- Liu, Z.; Guo, S.; Zhang, H.; Liu, D.; Yang, G. Comparative study of three updating procedures for real-time flood forecasting. Water Resour. Manag.
**2016**, 30, 2111–2126. [Google Scholar] [CrossRef] - Ricci, S.; Piacentini, A.; Thual, O.; Le Pape, E.; Jonville, G. Correction of upstream flow and hydraulic state with data assimilation in the context of flood forecasting. Hydrol. Earth Syst. Sci.
**2011**, 15, 3555–3575. [Google Scholar] [CrossRef] [Green Version] - Wu, X.-L.; Xiang, X.-H.; Wang, C.-H.; Chen, X.; Xu, C.-Y.; Yu, Z. Coupled hydraulic and Kalman filter model for real-time correction of flood forecast in the three gorges interzone of Yangtze river, China. J. Hydrol. Eng.
**2013**, 18, 1416–1425. [Google Scholar] [CrossRef] - Si, W.; Bao, W.; Gupta, H.V. Updating real-time flood forecasts via the dynamic system response curve method. Water Resour. Res.
**2015**, 51, 5128–5144. [Google Scholar] [CrossRef] - Muñoz, D.F.; Abbaszadeh, P.; Moftakhari, H.; Moradkhani, H. Accounting for uncertainties in compound flood hazard assessment: The value of data assimilation. Coast. Eng.
**2022**, 171, 104057. [Google Scholar] [CrossRef] - Walker, J.P.; Houser, P.R. Hydrologic data assimilation. In Advances in Water Science Methodologies; CRC Press: Boca Raton, FL, USA, 2005; pp. 25–48. [Google Scholar]
- Welch, G.; Bishop, G. An Introduction to the Kalman Filter; University of North Carolina at Chapel Hill: Chapel Hill, NC, USA, 1995. [Google Scholar]
- Li, Q.; Li, R.; Ji, K.; Dai, W. Kalman filter and its application. In Proceedings of the 2015 8th International Conference on Intelligent Networks and Intelligent Systems (ICINIS), Tianjin, China, 1–3 November 2015; pp. 74–77. [Google Scholar]
- Evensen, G. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. Ocean.
**1994**, 99, 10143–10162. [Google Scholar] [CrossRef] - Reichle, R.H.; McLaughlin, D.B.; Entekhabi, D. Hydrologic data assimilation with the ensemble Kalman filter. Mon. Weather. Rev.
**2002**, 130, 103–114. [Google Scholar] [CrossRef] - Reichle, R.H.; Walker, J.P.; Koster, R.D.; Houser, P.R. Extended versus ensemble Kalman filtering for land data assimilation. J. Hydrometeorol.
**2002**, 3, 728–740. [Google Scholar] [CrossRef] - Zhang, S.; Li, H.; Zhang, W.; Qiu, C.; LI, X. Estimating the soil moisture profile by assimilating near-surface observations with the ensemble Kaiman filter (EnKF). Adv. Atmos. Sci.
**2005**, 22, 936–945. [Google Scholar] - Shen, Y.; Li, H.; Li, T.; Li, W. Groundwater level forecast: Overview of application of the Ensemble Kalman filter(EnKF). Hydrogeol. Eng. Geol.
**2014**, 41, 21–24. [Google Scholar] - Li, X.-L.; Lü, H.; Horton, R.; An, T.; Yu, Z. Real-time flood forecast using the coupling support vector machine and data assimilation method. J. Hydroinform.
**2014**, 16, 973–988. [Google Scholar] [CrossRef] [Green Version] - Wang, Z.; Lu, W.; Chang, Z.; Wang, H. Simultaneous identification of groundwater contaminant source and simulation model parameters based on an ensemble Kalman filter—Adaptive step length ant colony optimization algorithm. J. Hydrol.
**2022**, 605, 127352. [Google Scholar] [CrossRef] - Tavakol, A.; McDonough, K.R.; Rahmani, V.; Hutchinson, S.L.; Hutchinson, J.S. The soil moisture data bank: The ground-based, model-based, and satellite-based soil moisture data. Remote Sens. Appl. Soc. Environ.
**2021**, 24, 100649. [Google Scholar] [CrossRef] - Chan, S.K.; Bindlish, R.; Neill, P.E.O.; Njoku, E.; Jackson, T.; Colliander, A.; Chen, F.; Burgin, M.; Dunbar, S.; Piepmeier, J.; et al. Assessment of the SMAP Passive Soil Moisture Product. IEEE Trans. Geosci. Remote Sens.
**2016**, 54, 4994–5007. [Google Scholar] [CrossRef] - Kerr, Y.H.; Waldteufel, P.; Richaume, P.; Wigneron, J.P.; Ferrazzoli, P.; Mahmoodi, A.; Al Bitar, A.; Cabot, F.; Gruhier, C.; Juglea, S.E. The SMOS soil moisture retrieval algorithm. IEEE Trans. Geosci. Remote Sens.
**2012**, 50, 1384–1403. [Google Scholar] [CrossRef] - Zhao, R.; Liu, X. Computer models of watershed hydrology. In The Xinanjiang Model; Water Resources Publications: Littleton, CO, USA, 1995; pp. 215–232. [Google Scholar]
- Jayawardena, A.; Zhou, M. A modified spatial soil moisture storage capacity distribution curve for the Xinanjiang model. J. Hydrol.
**2000**, 227, 93–113. [Google Scholar] [CrossRef] - Duan, Q.; Sorooshian, S.; Gupta, V. Effective and efficient global optimization for conceptual rainfall-runoff models. Water Resour. Res.
**1992**, 28, 1015–1031. [Google Scholar] [CrossRef] - Zhang, C.; Jiang, J. Research on the application of SCE-UA algorithm for automatic parameters optimization of Xin’anjiang model. J. China Three Gorges Univ.
**2020**, 42, 18–23. [Google Scholar] - Evensen, G. Data Assimilation: The Ensemble Kalman Filter; Springer: New York, NY, USA, 2009; Volume 2. [Google Scholar]
- Monsivais-Huertero, A.; Graham, W.D.; Judge, J.; Agrawal, D. Effect of simultaneous state–parameter estimation and forcing uncertainties on root-zone soil moisture for dynamic vegetation using EnKF. Adv. Water Resour.
**2010**, 33, 468–484. [Google Scholar] [CrossRef] - Xie, X.; Zhang, D. Data assimilation for distributed hydrological catchment modeling via ensemble Kalman filter. Adv. Water Resour.
**2010**, 33, 678–690. [Google Scholar] [CrossRef] - Moradkhani, H.; Sorooshian, S.; Gupta, H.V.; Houser, P.R. Dual state–parameter estimation of hydrological models using ensemble Kalman filter. Adv. Water Resour.
**2005**, 28, 135–147. [Google Scholar] [CrossRef] [Green Version] - Lü, H.; Hou, T.; Horton, R.; Zhu, Y.; Chen, X.; Jia, Y.; Wang, W.; Fu, X. The streamflow estimation using the Xinanjiang rainfall runoff model and dual state-parameter estimation method. J. Hydrol.
**2013**, 480, 102–114. [Google Scholar] [CrossRef]

Rainfall Stations | Gangtie Station | Dongjiangkou Station | Dongchuan Station | Chaiping Station |
---|---|---|---|---|

Location (east longitude/°) | 108.42 | 108.64 | 108.84 | 108.94 |

Location (northern latitude/°) | 33.60 | 33.65 | 33.54 | 33.33 |

Weights | 0.0865 | 0.3889 | 0.3903 | 0.1343 |

**Table 2.**Characteristic values of water content (cm

^{3}/cm

^{3}) corresponding to floods for assimilation.

Volumetric Water Content | Maximum Value | Minimum Value | Average Value | |
---|---|---|---|---|

Flood Number | ||||

1 (No. 20170927) | 0.272 | 0.392 | 0.309 | |

2 (No. 20171004) | 0.304 | 0.361 | 0.322 | |

3 (No. 20180704) | 0.223 | 0.349 | 0.266 | |

4 (No. 20190628) | 0.149 | 0.329 | 0.196 | |

5 (No. 20190807) | 0.151 | 0.329 | 0.222 | |

6 (No. 20190915) | 0.210 | 0.357 | 0.297 | |

7 (No. 20200819) | 0.229 | 0.352 | 0.291 | |

8 (No. 20210424) | 0.213 | 0.372 | 0.272 |

Parameter | n | m | q | p | s | α | β | k | P |
---|---|---|---|---|---|---|---|---|---|

Value | 15 | 31 | 16 | 4 | 124 | 1 | 31 | 5 | 0.01% |

Parameter | K | UM | LM | DM | C | IM | B | SM |
---|---|---|---|---|---|---|---|---|

Upper limit | 1.1 | 30 | 100 | 50 | 0.2 | 0.05 | 0.6 | 100 |

Lower limit | 0.1 | 10 | 50 | 20 | 0.1 | 0.01 | 0.1 | 30 |

Value | 0.38 | 20 | 73.30 | 48.61 | 0.18 | 0.04 | 0.5 | 70.6 |

Parameter | EX | KI | KG | CS | CI | CG | L | |

Upper limit | 1.5 | 0.6 | 0.6 | 0.99 | 0.99 | 1 | 10 | |

Lower limit | 1 | 0.1 | 0.1 | 0.70 | 0.70 | 0.98 | 0.1 | |

Value | 1.24 | 0.25 | 0.5 | 0.92 | 0.90 | 0.998 | 4.92 |

Flood Number | Flood Peak Relative Error | Peak Time Difference (h) | NSE |
---|---|---|---|

No. 19990705 | 0.31 | 0 | 0.860 |

No. 20000628 | 0.00 | 0 | 0.823 |

No. 20000713 | 0.36 | 1 | 0.815 |

No. 20000808 | 0.23 | 4 | 0.873 |

No. 20030716 | 0.17 | 0 | 0.898 |

No. 20030920 | 0.31 | 3 | 0.854 |

No. 20040930 | 0.16 | 3 | 0.882 |

No. 20050817 | 0.31 | 4 | 0.840 |

No. 20060927 | 0.01 | 4 | 0.943 |

No. 20070705 | 0.04 | 10 | 0.731 |

No. 20070720 | 0.14 | 0 | 0.835 |

No. 20090803 | 0.03 | 5 | 0.912 |

No. 20090819 | 0.14 | 1 | 0.703 |

No. 20090829 | 0.11 | 3 | 0.815 |

No. 20100608 | 0.01 | 7 | 0.872 |

No. 20109010 | 0.15 | 8 | 0.804 |

No. 20110622 | 0.28 | 4 | 0.851 |

No. 20110805 | 0.05 | 2 | 0.775 |

No. 20130719 | 0.08 | 5 | 0.853 |

Average | 0.15 | 3.37 | 0.839 |

Flood Number | Flood Peak Relative Error | Peak Time Difference (h) | NSE |
---|---|---|---|

1 (No. 20170927) | 0.23 | 0 | 0.846 |

2 (No. 20171004) | 0.39 | 4 | 0.580 |

3 (No. 20180704) | 0.31 | 2 | 0.622 |

4 (No. 20190628) | 0.54 | 2 | 0.661 |

5 (No. 20190807) | 0.06 | 0 | 0.805 |

6 (No. 20190915) | 0.36 | 3 | 0.779 |

7 (No. 20200819) | 0.39 | 1 | 0.604 |

8 (No. 20210424) | 0.25 | 6 | 0.910 |

Average | 0.32 | 2.25 | 0.725 |

Flood Number | Flood Peak Relative Error | Peak Time Difference (h) | NSE |
---|---|---|---|

1 (No. 20170927) | 0.22 | 0 | 0.845 |

2 (No. 20171004) | 0.36 | 3 | 0.655 |

3 (No. 20180704) | 0.31 | 2 | 0.662 |

4 (No. 20190628) | 0.53 | 2 | 0.668 |

5 (No. 20190807) | 0.06 | 0 | 0.873 |

6 (No. 20190915) | 0.36 | 3 | 0.781 |

7 (No. 20200819) | 0.36 | 1 | 0.656 |

8 (No. 20210424) | 0.22 | 5 | 0.924 |

Average | 0.30 | 2 | 0.758 |

Flood Number | Flood Peak Relative Error | Peak Time Difference (h) | NSE |
---|---|---|---|

1 (No. 20170927) | 0.21 | 0 | 0.825 |

2 (No. 20171004) | 0.32 | 3 | 0.709 |

3 (No. 20180704) | 0.39 | 3 | 0.763 |

4 (No. 20190628) | 0.45 | 1 | 0.674 |

5 (No. 20190807) | 0.07 | 1 | 0.872 |

6 (No. 20190915) | 0.30 | 2 | 0.827 |

7 (No. 20200819) | 0.29 | 1 | 0.655 |

8 (No. 20210424) | 0.21 | 5 | 0.926 |

Average | 0.28 | 2 | 0.781 |

Flood Number | Flood Peak Relative Error | Peak Time Difference (h) | NSE |
---|---|---|---|

1 (No. 20170927) | 0.21 | 0 | 0.822 |

2 (No. 20171004) | 0.29 | 3 | 0.655 |

3 (No. 20180704) | 0.42 | 3 | 0.772 |

4 (No. 20190628) | 0.41 | 1 | 0.695 |

5 (No. 20190807) | 0.09 | 1 | 0.874 |

6 (No. 20190915) | 0.32 | 2 | 0.804 |

7 (No. 20200819) | 0.31 | 1 | 0.692 |

8 (No. 20210424) | 0.16 | 6 | 0.925 |

Average | 0.27 | 2.125 | 0.779 |

Flood Peak Error | Unassimilated | WU Assimilation | AEnKF | DEnKF | |
---|---|---|---|---|---|

Flood Number | |||||

1 (No. 20170927) | 0.23 | 0.22 | 0.21 | 0.21 | |

2 (No. 20171004) | 0.39 | 0.36 | 0.32 | 0.29 | |

3 (No. 20180704) | 0.31 | 0.31 | 0.39 | 0.42 | |

4 (No. 20190628) | 0.54 | 0.53 | 0.45 | 0.41 | |

5 (No. 20190807) | 0.06 | 0.06 | 0.07 | 0.09 | |

6 (No. 20190915) | 0.36 | 0.36 | 0.30 | 0.32 | |

7 (No. 20200819) | 0.39 | 0.36 | 0.29 | 0.31 | |

8 (No. 20210424) | 0.25 | 0.22 | 0.21 | 0.16 | |

Average | 0.32 | 0.30 | 0.28 | 0.27 |

Peak Time Difference (h) | Unassimilated | WU Assimilation | AEnKF | DEnKF | |
---|---|---|---|---|---|

Flood Number | |||||

1 (No. 20170927) | 0 | 0 | 0 | 0 | |

2 (No. 20171004) | 4 | 3 | 3 | 3 | |

3 (No. 20180704) | 2 | 2 | 3 | 3 | |

4 (No. 20190628) | 2 | 2 | 1 | 1 | |

5 (No. 20190807) | 0 | 0 | 1 | 1 | |

6 (No. 20190915) | 3 | 3 | 2 | 2 | |

7 (No. 20200819) | 1 | 1 | 1 | 1 | |

8 (No. 20210424) | 6 | 5 | 5 | 6 |

NSE | Unassimilated | WU Assimilation | AEnKF | DEnKF | |
---|---|---|---|---|---|

Flood Number | |||||

1 (No. 20170927) | 0.846 | 0.845 | 0.825 | 0.822 | |

2 (No. 20171004) | 0.580 | 0.655 | 0.709 | 0.655 | |

3 (No. 20180704) | 0.622 | 0.662 | 0.763 | 0.772 | |

4 (No. 20190628) | 0.661 | 0.668 | 0.674 | 0.695 | |

5 (No. 20190807) | 0.805 | 0.873 | 0.872 | 0.874 | |

6 (No. 20190915) | 0.779 | 0.781 | 0.827 | 0.804 | |

7 (No. 20200819) | 0.604 | 0.656 | 0.655 | 0.692 | |

8 (No. 20210424) | 0.910 | 0.924 | 0.926 | 0.925 | |

Average | 0.725 | 0.758 | 0.781 | 0.779 |

RMSE | Unassimilated | WU Assimilation | AEnKF | DEnKF | |
---|---|---|---|---|---|

Flood Number | |||||

1 (No. 20170927) | 30.033 | 30.100 | 31.991 | 32.279 | |

2 (No. 20171004) | 79.529 | 72.073 | 66.196 | 72.111 | |

3 (No. 20180704) | 68.184 | 64.442 | 53.311 | 52.966 | |

4 (No. 20190628) | 53.793 | 53.216 | 53.069 | 51.032 | |

5 (No. 20190807) | 22.188 | 17.888 | 17.938 | 17.787 | |

6 (No. 20190915) | 89.175 | 88.673 | 78.769 | 83.995 | |

7 (No. 20200819) | 44.267 | 41.245 | 41.315 | 39.048 | |

8 (No. 20210424) | 33.213 | 30.685 | 29.884 | 30.376 | |

Average | 52.548 | 49.790 | 46.559 | 47.449 |

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**MDPI and ACS Style**

Bai, J.; Mu, R.; Yan, B.; Guo, J.
Application of Soil Moisture Data Assimilation in Flood Forecasting of Xun River in Hanjiang River Basin. *Water* **2022**, *14*, 4061.
https://doi.org/10.3390/w14244061

**AMA Style**

Bai J, Mu R, Yan B, Guo J.
Application of Soil Moisture Data Assimilation in Flood Forecasting of Xun River in Hanjiang River Basin. *Water*. 2022; 14(24):4061.
https://doi.org/10.3390/w14244061

**Chicago/Turabian Style**

Bai, Jueying, Ran Mu, Baowei Yan, and Jing Guo.
2022. "Application of Soil Moisture Data Assimilation in Flood Forecasting of Xun River in Hanjiang River Basin" *Water* 14, no. 24: 4061.
https://doi.org/10.3390/w14244061