# Flood Forecasting via the Ensemble Kalman Filter Method Using Merged Satellite and Measured Soil Moisture Data

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The annual average runoff is 200 million m

^{3}. The Chaohe River Basin is mainly mountainous and hilly, with a warm, temperate, monsoon, continental, semi-humid, and semi-arid climate, and rainfall is mainly concentrated from June to September. The annual average temperature ranges from 9 to 10 °C. The annual average precipitation is 502 mm and the annual runoff distribution is uneven. Rainfall is abundant in summer and autumn, whereas less rainfall occurs in spring and winter. The flood season is June–October, accounting for 66% of the year [27]. The Chaohe River Basin contains three hydrological and 15 precipitation stations. From upstream to downstream, the hydrological stations are the Dage, Gubeikou, and Xiahui stations. The control areas of the Dage, Gubeikou, and Xiahui stations are 1898, 4484, and 5128 km

^{2}, respectively.

#### 2.2. Data

#### 2.2.1. Precipitation and Runoff Data

#### 2.2.2. Soil Moisture Data

#### 2.3. Improved Xin’anjiang Model

## 3. Methods

#### 3.1. Data Merging

_{CCI}(x) and f

_{mea}(x

_{1}) represent the cumulative distribution function of the CCI SM and site SM, respectively, and X is the SM of unadjusted CCI products.

#### 3.2. Ensemble Kalman Filter (EnKF)

- Observation data update

#### 3.3. Data Assimilation Setup

^{3}/s), which change with time, and the SM data W0 (1) (upper SM data, mm) were used as multi-source data. When only the runoff is assimilated, the expression of the state variable is

**X**= (S, Q, SM, B)

^{T}and the observational operator is

**H**= (0, 1, 0, 0)

^{T}. After adding the SM data W0 (1) of multi-source data, the state variable can be expressed as

**X**= (S, Q, W0(1), SM, B)

^{T}and the observational operator is

**H**= (0, 1, 1, 0, 0)

^{T}. The distribution of the variables and parameters satisfies the Gaussian distribution. In addition, this assimilation experiment considered the uncertainty of the model itself and that of observation data. Both the model and observation errors obey a Gaussian distribution, and Gaussian white noise was used as the mean value of zero. The standard deviation, expressed as the scaling factor [38], was set to N (0, 0.1

^{2}) and N (0, 0.1

^{2}). The initial number of data assimilation sets was 200.

## 4. Results and Discussion

#### 4.1. Data Merging

#### 4.2. Data Assimilation

#### 4.2.1. Small Flood

#### 4.2.2. Medium Flood

#### 4.2.3. Large Flood

^{2}), B~N (0.2, 0.1

^{2}), and S~N (5, 2

^{2}).

^{2}, 8

^{2}, 10

^{2}, and 20

^{2}. The AE variation of the assimilation under different variance values is shown in Figure 14. With the increase in the variance, the AEs of the corresponding assimilated runoff and measured runoff values decreased first and then increased. The error value was the lowest when the variance was 10

^{2}, and the AE with a variance of 10

^{2}was 7.6% lower than the average AE with a variance of 5

^{2}. The AE with a variance of 10

^{2}was 7.7% lower than the average AE with a variance of 20

^{2}. Therefore, if the variance of the assimilation parameters increased, the assimilation effect became better, because a larger variance reflects an enlarged extraction range, the true value could be easily covered, and the assimilation efficiency was improved. However, a larger variance setting results in a too wide range. In addition, the convergence time of the assimilation parameters will also increase, which is not conducive to the assimilation effect. Therefore, choosing an appropriate variance will improve the accuracy of the assimilation.

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

NA | non-assimilation |

AF | assimilation of runoff data |

AFWR | assimilation of runoff and satellite-based soil moisture data |

AFWM | assimilation of runoff and merged soil moisture data |

RE | relative error |

SM | soil moisture |

KF | Kalman filter |

EKF | extended Kalman filter |

EnKF | ensemble Kalman filter |

DEM | digital elevation model |

ESA | European Space Agency |

CCI | Climate Change Initiative |

CDF | cumulative distribution function |

NSE | Nash–Sutcliffe efficiency coefficient |

AE | absolute error |

RMSE | root-mean-square error |

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**Figure 1.**Map of the Chaohe River Basin including the digital elevation model (DEM), basin boundary, and locations of hydrological and precipitation stations.

**Figure 3.**CDF curve for the (

**a**) measured soil moisture; (

**b**) satellite soil moisture; (

**c**) piecewise linear regression; and (

**d**) comparison before and after CDF adjustment.

**Figure 5.**Variation in the flood runoff for small floods for the measurement and four assimilation settings for the three stations: (

**a**) Dage; (

**b**) Gubeikou; (

**c**) Xiahui.

**Figure 6.**The RE values under the four assimilation settings for small floods for the three stations: (

**a**) Dage; (

**b**) Gubeikou; (

**c**) Xiahui.

**Figure 7.**Variation in the flood runoff for medium floods for the measurement and four assimilation settings for the three stations: (

**a**) Dage; (

**b**) Gubeikou; (

**c**) Xiahui.

**Figure 8.**RE values under the four assimilation settings for medium floods for the three stations: (

**a**) Dage; (

**b**) Gubeikou; (

**c**) Xiahui.

**Figure 9.**Variation in the flood runoff of large floods for the measurement and four assimilation settings for two stations: (

**a**) Gubeikou; (

**b**) Xiahui.

**Figure 10.**RE values under the four assimilation settings for medium floods for the two stations: (

**a**) Gubeikou; (

**b**) Xiahui.

**Figure 11.**RE of four assimilation settings at different hydrological stations: (

**a**) Dage; (

**b**) Gubeikou; and (

**c**) Xiahui.

**Figure 12.**RE of the four assimilation settings for different flood levels: (

**a**) large flood; (

**b**) medium flood; and (

**c**) small flood.

Number | Parameter | Meaning | Lowe | Bound |
---|---|---|---|---|

1 | C | Ratio of potential evapotranspiration | 0 | 0.3 |

2 | IMP | Ratio of the impervious area to the total area | 0.02 | 0.7 |

3 | WUM | Tension water capacity of the upper layer | 5 | 100 |

4 | WLM | Tension water capacity of the lower layer | 40 | 200 |

5 | WDM | Tension water capacity of the deeper layer | 5 | 100 |

6 | B | Exponent of the distribution of the tension water capacity | 0.1 | 0.3 |

7 | SM | Free water capacity | 5 | 100 |

8 | EX | Exponent of distribution of free water capacity | 0.5 | 2 |

9 | KG | Outflow coefficient of free water storage to groundwater | 0.05 | 0.65 |

10 | KSS | Outflow coefficient of free water storage to interflow | 0.65 | 0.8 |

11 | KKSS | Recession constant of interflow storage | 0.05 | 0.95 |

12 | KKGF | Recession constant of fast groundwater | 0 | 1 |

13 | KKGS | Recession constant of slow groundwater | 0 | 1 |

14 | KD | Division value of groundwater | 0 | 1 |

15 | K | Ratio of pan evaporation | 0 | 1 |

16 | UH(1) | First coefficient of unit graph | 0 | 1 |

17 | UH(2) | Second coefficient of unit graph | 0 | 1 |

18 | UH(3) | Third coefficient of unit graph | 0 | 1 |

19 | Fm | Maximum infiltration rate | 0 | 10 |

20 | N1 | Empirical coefficient of infiltration curve | 0 | 1 |

21 | FC | Stable infiltration rate | 0 | 1 |

**Table 2.**Average values of the absolute error (AE), relative error (RE), and root-mean-square error (RMSE) before and after CDF adjustment.

AE | RE | RMSE | |
---|---|---|---|

Before adjustment | −0.0186 | –0.0793 | 0.0391 |

After adjustment | −0.0031 | 0.0126 | 0.0350 |

Station | Average Error | NA | AF | AFWR | AFWM |
---|---|---|---|---|---|

Dage | AE | −0.524 | −0.018 | −0.193 | −0.145 |

RE | −0.292 | 0.143 | −0.021 | 0.011 | |

Gubeikou | AE | −2.438 | −0.47 | −0.417 | −0.43 |

RE | −0.449 | 0.165 | −0.09 | 0.032 | |

Xiahui | AE | −0.483 | −0.202 | −0.312 | −0.273 |

RE | 0.317 | 0.249 | 0.119 | 0.136 |

Station | Average Error | NA | AF | AFWR | AFWM |
---|---|---|---|---|---|

Dage | AE | −1.213 | 0.486 | −0.42 | −0.385 |

RE | −0.559 | 0.186 | −0.17 | −0.163 | |

Gubeikou | AE | 0.347 | –1.043 | −1.359 | −1.254 |

RE | 0.172 | −0.129 | −0.17 | −0.154 | |

Xiahui | AE | −3.313 | −2.145 | −3.752 | −3.679 |

RE | −0.201 | −0.113 | −0.298 | −0.298 |

Station | Average Error | NA | AF | AFWR | AFWM |
---|---|---|---|---|---|

Gubeikou | AE | −4.928 | 0.51 | −0.912 | −0.731 |

RE | −0.254 | 0.07 | −0.232 | −0.226 | |

Xiahui | AE | −8.551 | −3.817 | −4.116 | −4.547 |

RE | −0.453 | −0.168 | −0.203 | −0.227 |

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## Share and Cite

**MDPI and ACS Style**

Zhang, C.; Cai, S.; Tong, J.; Liao, W.; Zhang, P.
Flood Forecasting via the Ensemble Kalman Filter Method Using Merged Satellite and Measured Soil Moisture Data. *Water* **2022**, *14*, 1555.
https://doi.org/10.3390/w14101555

**AMA Style**

Zhang C, Cai S, Tong J, Liao W, Zhang P.
Flood Forecasting via the Ensemble Kalman Filter Method Using Merged Satellite and Measured Soil Moisture Data. *Water*. 2022; 14(10):1555.
https://doi.org/10.3390/w14101555

**Chicago/Turabian Style**

Zhang, Chen, Siyu Cai, Juxiu Tong, Weihong Liao, and Pingping Zhang.
2022. "Flood Forecasting via the Ensemble Kalman Filter Method Using Merged Satellite and Measured Soil Moisture Data" *Water* 14, no. 10: 1555.
https://doi.org/10.3390/w14101555