## Abstract

The temporal and spatial resolutions of rainfall data directly affect the accuracy of hydrological simulation. Weather radar has been used in business in China, but the uncertainty of data is large. At present, research on radar data and fusion in small and medium-sized basins in China is very weak. In this paper, taking the Duanzhuang watershed as an example, based on station data, Shijiazhuang's radar data are preprocessed, optimized and fused. Eleven rainfall events are selected for fusion by three methods and quality evaluation, and three flood simulations are used to test their effect. The results show that preprocessing and initial optimization have poor effects on radar data improvement. The rainfall proportional coefficient fusion method performs best in rainfall spatial estimation, where the *R*^{2} values of the three inspection stations are increased to 0.51, 0.78 and 0.82. Three fusion datasets in the peak flow and flood volume of flood simulation perform better than station data. For example, in the No.20210721 flood, the NSE of the three fusion data increased by 39, 30 and 48%. This shows that the fusion method can effectively improve the data accuracy of radar and can obtain high temporal and spatial resolution rainfall data.

## HIGHLIGHTS

Preprocessing and initially optimizing Shijiazhuang's S-band weather radar.

Using three fusion methods to optimize radar rainfall data and station data.

Evaluating and comparing fusion data on the different scales and by the HEC-HMS model simulation.

## INTRODUCTION

Rainfall is the most active element in the process of the hydrological cycle and the main driving factor of land surface hydrological processes. Due to the influence of watershed topography, geographical location, atmospheric movement and other factors, rainfall has spatiotemporal variability (Yu *et al.* 2007; Zhao & Xu 2016). The single-source rainfall observation data have great uncertainty due to the restrictions of the technology and external conditions, so it is difficult to meet the needs of high precision and high resolution of rainfall data in hydrology, agriculture, ecology and other fields (Semadeni *et al.* 2008; Wu *et al.* 2018). Therefore, refined rainfall spatial estimation has been a research hotspot in various fields.

Rainfall data are important inputs for different hydrological models (at local, regional and global levels) in water resource management, flood forecasting, warning services and drought monitoring. In the last few decades, the acquisition of rainfall data has been restricted by ground-based observations using rain gauges. These surface-based observations can accurately measure rainfall at the point scale, but at the basin scale, they are greatly affected by the density of rain gauges, which leads to great uncertainty and low precision in hydrological simulations (Mei *et al.* 2014; Zhao *et al.* 2020). Weather radar has been used to detect precipitation echoes via snapshots of electromagnetic backscatter from raindrops in a cloud band, which has the advantages of high spatial and temporal resolution and wide coverage. Thus, it has great application potential in hydrological simulation. For example, Abro *et al.* (2019) analyzed multisource rainfall data such as S-band radar and satellite products for hydrological estimation in the Qinhuai River Basin. The results show that the actual flow has the highest correlation coefficient with the S-band radar rainfall data and the performance of S-band radar in rainfall detection and flood simulation is relatively good.

With the operational use of Doppler weather radar and the increasing density of ground stations in China, the temporal and spatial resolution of precipitation monitoring has been greatly improved. However, there are some limitations leading to large initial deviations in radar rainfall data, such as season, region, precipitation nature, ground clutter, anomalous propagation, vertical reflectivity profile, Z–R relationship and sampling, which contribute to errors in rainfall estimation (Su *et al.* 2018). Various techniques have been used to overcome these limitations (Takeuchi *et al.* 1999; Rico-Ramirez *et al.* 2007; Dong & lv 2012; Zou *et al.* 2014; Arulraj & Barros 2019), among which the Z–R relation method has more physical significance as a theoretical basis and is widely used (Yin *et al.* 2020). The advantage of the Z–R relationship method is that it does not require station rainfall data, which is of great significance for rainfall observations in low-density watersheds. However, Battan (1973) summarized 69 Z–R relationships corresponding to different rain types, climate zones and radar wavelengths and the coefficient range varied greatly. Therefore, for different basins, different rainfall types, different weather conditions and other conditions, the promotion of Z–R relationship expression needs further research and testing.

Rainfall spatial estimation technology has developed into a multisource rainfall data fusion stage since the 1990s. Using the fusion algorithm to combine ground station and radar data can further improve the accuracy of rainfall spatiotemporal resolution (Li *et al.* 2014; Han *et al.* 2019). In recent years, the commonly used fusion methods have been divided into objective analysis methods, geostatistics methods, optimal interpolation (OI) methods, scale recursive estimation methods and Bayesian model averaging methods. Each method contains affiliated methods based on similar principles. Many studies based on fusion methods have been performed on radar data, ground station data, satellite data and climate model output data at home and abroad (Mahfouf *et al.* 2007; Tian *et al.* 2010; Pan *et al.* 2012; Jin *et al.* 2016; Shi *et al.* 2019). The results show that the fusion method can integrate the advantages of multiple rainfall datasets and reduce the uncertainty of the original single source, which is of great significance for further optimizing radar rainfall data using station data.

At present, there are some difficulties and challenges in rainfall observations and flood simulations in small and medium-sized basins with large topographic changes in China. The ‘Technical Guidelines for Hydrological Station Network Planning’ stipulates that the control basin area of the rainfall station should not exceed 60 km^{2}, and the mountainous area of the basin should not exceed 30 km^{2}. China has a vast territory, with few rainfall stations and uneven distribution, and most watersheds have difficulty meeting this requirement. Moreover, radar is limited by terrain factors and the technology itself, which leads to great uncertainty in its rainfall data. Two-source rainfall data fusion based on radar and station and its application in hydrological models are not common in China. Therefore, the initial optimization of watershed radar data and the two-source fusion and hydrological application verification based on radar and station rainfall data are important research contents of this paper, which is also conducive to reference for subsequent research.

The Taihang Mountain Basin is an important recharge and migration area of groundwater in the North China Plain. The terrain of the Taihang Mountain Piedmont Basin is changeable and the layout of ground stations is very limited, and the Shijiazhuang S-band radar can cover the area. Therefore, the use of rainfall fusion data to strengthen the simulation and monitoring of rainstorms and floods in the basin and reduce the uncertainty caused by rainfall input in hydrological simulation in the basin is not only conducive to the optimal use of meteorological radar rainfall data in the Taihang Mountain Piedmont Basin but also conducive to the comprehensive development and utilization of water resources in the basin and the improvement of flood control and drought resistance in the basin.

In this paper, taking the Duanzhuang watershed at the eastern foot of the Taihang Mountains as an example, the initial radar data are preprocessed, and three Z–R relation methods are used to calculate the radar rainfall. Then, the three commonly used fusion methods, the rainfall proportion coefficient method, geographically weighted regression method and OI method, are used to fuse the ground station and radar rainfall data. Then the rainfall spatial estimation of the fused data and its application potential in hydrological models are evaluated.

The objectives of this study are: (1) to proceed with the integral optimization and piecewise optimization of existing radar data and their evaluation, (2) to use three fusion methods to fuse the data of 11 rainfall events and compare the rainfall data quality, (3) to test the fusion rainfall data's hydrological application potential in the Hydrologic Engineering Center's Hydrologic Modeling System (HEC-HMS) hydrological model.

## STUDY AREA

^{2}. The basin inclines from west to east, including mountains, hills and plains, with greatly undulating terrain and complex geomorphology. Figure 1 shows the location of the river basin and the distribution of ground stations.

There are four distinct seasons in the basin. The differences in temperature between the cold and hot seasons are great. Precipitation varies over the years and is distributed unevenly throughout the year. The basin is greatly influenced by topographic relief and large- and medium-sized weather systems, which lead to frequent rainstorm disasters in this area. Complex natural geological and geomorphological conditions, expanding human activities and abundant rainfall lead to frequent geological disasters, such as debris flows, landslides and collapses. Therefore, a more accurate spatial estimation of rainfall is of great significance for disaster warning in the Duanzhuang watershed.

## MATERIALS AND METHODS

### Data and radar preprocessing

The data used in the study are the hourly rainfall data of 18 ground stations in the basin and the new-generation weather radar product in Shijiazhuang. The initial spatial-temporal resolution of the radar product is 6 min × 0.1°.

Radar rainfall data with high spatial-temporal resolution can describe more detailed rainfall processes, but radar rainfall observations are affected by various types of errors in practical applications. It is difficult to guarantee the accuracy of rainfall by simply transforming the radar reflectivity factor according to the empirical Z–R formula or the optimized Z–R relationship based on historical rainfall (Yu *et al.* 2006; Xiao & Xiao 2007; Gu *et al.* 2018). In this paper, the original radar data are preprocessed first, including reflectivity data extraction, coordinate transformation, beam shielding analysis, rainfall type identification and rainfall conversion. Then the Z–R relationship parameters of radar are further optimized by using the optimization method.

*et al.*(2001) and the radar meteorological beam propagation formula are combined to analyze beam shielding. Combining the calculation results with the principle of the lowest elevation angle, the elevation angle of the grid is selected by the occlusion effect of the grid center point. In this way, the corresponding elevation angle value of quantitative rainfall estimation based on Shijiazhuang radar in the eastern foot of the Taihang Mountains is obtained. The radar elevation value of each grid point in the basin is shown in Figure 3.

This paper uses the optimization principle method to determine parameters *a* and *b*. Radar data during the May–September flood season of 2018–2021 and four historical rainfall events are used for optimization. Since there is less radar data available and more mixed rainfall in the basin, all rainfall events are optimized using the same parameter.

*et al.*2001), and its expression is as follows:where

*i*represents the rainfall time,

*j*represents the ground station label,

*n*represents the total rainfall period and

*m*represents the total number of ground stations. represents the radar estimated rainfall of a specific ground station at a certain time, and represents the measured rainfall data of the same ground station at the same time. The reflectivity threshold was set as 15 and 35 dBz, and the optimization parameters are shown in Table 1.

. | Original parameter . | Integral optimization parameter (IO) . | Subsection optimization parameter (SO) . | ||
---|---|---|---|---|---|

< 15 dBz . | > 15 dBZ, <35 dBz . | > 35 dBz . | |||

a | 200/300 | 335 | 65 | 200 | 495 |

b | 1.4/1.6 | 2.8 | 4.8 | 3.0 | 2.8 |

. | Original parameter . | Integral optimization parameter (IO) . | Subsection optimization parameter (SO) . | ||
---|---|---|---|---|---|

< 15 dBz . | > 15 dBZ, <35 dBz . | > 35 dBz . | |||

a | 200/300 | 335 | 65 | 200 | 495 |

b | 1.4/1.6 | 2.8 | 4.8 | 3.0 | 2.8 |

### Rainfall fusion method

Radar products can describe more detailed rainfall processes, but in practical applications, radar observation rainfall will be affected by various types of errors. The radar rainfall obtained by a simple empirical Z–R formula or optimized Z–R relationship based on historical rainfall is more uncertain. In different basins, scholars have proposed different methods to fuse rainfall data from radar and rainfall stations. The geographical statistics method is based on the obvious spatial trend of rainfall distribution and establishes the quantitative relationship between meteorological elements and geographical elements. Based on the radar inversion results of the segmentation optimization, this chapter selects two geo-statistical methods, the rainfall proportional coefficient fusion method and mixed geographically weighted regression Gaussian function fusion method and OI method for radar and station data two-source fusion.

#### Rainfall proportion coefficient method

*et al.*2011; Shao

*et al.*2014). In this paper, the method is used to calculate the quantitative estimation of precipitation in the Duanzhuang basin. The rainfall ratio coefficient of hourly ground-gauged rainfall and radar rainfall is defined as :

In the formula, *λ* is a constant, in mm, and the empirical value is 10 mm; is the hourly measured rainfall of the ground station corresponding to the *k*th grid in mm; and is the hourly radar-retrieved cumulative rainfall corresponding to the *k*th grid, in mm.

*n*rainfall ratio coefficients corresponding to the rainfall period into the whole study basin, and a rainfall ratio coefficient with spatiotemporal distribution can be calculated for each grid. Based on this, the formula for estimating the integrated rainfall in the basin is obtained:where is the hourly fusion rainfall corresponding to the (

*i, j*)th grid, in mm/h ; is the hourly radar-retrieved cumulative rainfall corresponding to the (

*i, j*)th grid, in mm/h.

The fusion method proposed by Sokol is simple and has a small amount of calculation. If the current grid contains ground stations, the precipitation of the grid is expressed by the observation data of the ground station. Otherwise, the precipitation of the grid is the precipitation data that combine the radar inversion with the observation of the ground station nearby.

#### Mixed geographically weighted regression Gaussian function (MGWR-GAU) fusion

The mixed geographically weighted regression (MGWR) model adds a spatial stationary term to the GWR model (Brunsdon *et al.* 1996; Lu *et al.* 2020). Its independent variables include both global variables and local variables. By exploring the spatial stability of variables to prevent the limitations of fixed effects, global factors are identified to reduce the error of the local model. Wind speed is determined as a global variable by spatial autocorrelation analysis, and digital elevation model (DEM) slope, aspect, surface roughness and distance to coastline are determined as local variables.

*i*th grid; represents the regression coefficient of the

*k*th local variable corresponding to the

*i*th grid; denotes the

*k*th local variable corresponding to the

*i*th grid; represents the number of local variables, five in this paper, namely, DEM, slope, aspect, surface roughness and distance to the coastline; is the regression coefficient of the first global variable corresponding to the

*i*th grid; denotes the

*k*th global variable corresponding to the

*i*th grid; represents the number of global variables, one in this paper, which is wind speed; and represents random error, which is a constant term.

The core of the MGWR equation is the calculation of the regression coefficient (, ). The regression coefficient is calculated by the spatial weight matrix (*i, j*). The weight matrix is essentially a monotonically decreasing function that gradually decreases as the spatial distance increases (Mcquarrie & Tsai 1989). In this paper, the Gaussian function (GAU) is used to calculate the spatial weight, where bandwidth is determined by the AICc (Akaike Information Criterion corrected) rule (Akaike 1974; Hurvich *et al.* 1990; Burnham & Anderson 2002; Fotheringham *et al.* 2017).

#### Optimal interpolation method

*i*is the grid in the basin; is the fusion rainfall of the

*i*th grid;

*k*is the effective grid in the basin;

*n*is the number of effective grids, that is, the number of grids with ground stations; is the weight function, which represents the weight factor of the observed value on the

*k*th effective grid and the rainfall bias value of the initial estimate; is the gauge observation rainfall of the

*k*th effective grid; and is the radar observation rainfall of the

*k*th effective grid.

*i*th and

*j*th grid, and represents the relative mean square error of the observation of the

*i*th station, which is zero in the actual calculation.

*i*th and

*j*th grid; represents the distance between the center point of the

*i*th and

*j*th grid; and

*d*is the maximum influence radius, representing the distance value when the correlation function approaches 0, and its value is related to the actual gauge distribution.

In Formula (8), Formula (a) is suitable for sparse rainfall stations, and Formula (b) is suitable for dense stations. The distribution of stations in the Duanzhuang basin is uneven. Based on the above two formulas and assumptions, the calculation of the spatial weight matrix still has the disadvantage of complicated derivation. The adaptive correlation function method can dynamically calculate the optimal weight factor and improve the complex calculation of the OI method. Therefore, this method is selected for weight calculation. Given the initial radius of 3 km, the number of rain gauge stations is searched within this range and the number of stations is not less than 2. If the conditions are met, the correlation function is directly calculated by Formula (b). Otherwise, the search range will be enlarged step by step by 3 km until the condition is satisfied. If the search radius is smaller than the critical value (30 km), the correlation function will be calculated by Formula (b).

## RESULTS

### Rainfall fusion data quality evaluation

Eleven rainfall events in the basin were selected for fusion, and the fusion results were evaluated. Eighteen stations in the basin are divided into 15 interpolation stations and three test stations (Jiangjunmu station, Dukou station and Shibanfang station). In the rainfall proportional coefficient fusion method, the rainfall of the three test stations is obtained by interpolating the data of the 15 interpolation stations. Because the stations in the basin have a low density, the removal of the three-station data has a great influence on the MGWR-GAU method and OI method which are both based on geostatistics theory. Therefore, 18 stations are used in the last two fusion methods, but the analysis at the point scale still uses these three stations. The selection principle of the inspection station is as follows: Jiangjunmu station is the area where the rainfall station is densely distributed, Dukou station is the area where the station is sparsely distributed, and Shibanfang station is in the western mountainous area where the station is densely distributed on one side. To compare the accuracy and distribution of the rainfall fusion data of different station densities under the three fusion methods, the point scale, surface scale and spatial distribution of the rainfall fusion data are analyzed and compared below.

#### Point-scale quality evaluation

The root mean square error (RMSE), Nash efficiency coefficient () and correlation coefficient (*R*) are selected as quality assessment indicators. Based on the selected 11 rainfall events, the quality assessment indicators calculated for the three test stations are shown in Table 2.

Rainfall event . | Station . | RMSE/mm . | . | R. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

. | MGWR-GAU . | OI . | Radar . | . | MGWR-GAU . | OI . | Radar . | . | MGWR-GAU . | OI . | ||

20090509 | Jiangjunmu | 0.01 | 4.76 | 0.27 | 3.51 | 1.00 | −4.85 | 0.95 | −1.76 | 1.00 | −0.15 | 0.98 |

Dukou | 0.01 | 8.18 | 1.09 | 5.37 | 1.00 | −0.94 | 0.97 | 0.16 | 1.00 | −0.36 | 0.99 | |

Shibanfang | 0.03 | 2.99 | 0.84 | 4.45 | 1.00 | −1.57 | 0.77 | −0.52 | 1.00 | −0.05 | 0.92 | |

20110815 | Jiangjunmu | 0.03 | 4.64 | 0.72 | 0.15 | 1.00 | −2.75 | 0.84 | 0.2 | 1.00 | −0.31 | 0.95 |

Dukou | 0.02 | 7.18 | 3.91 | 9.37 | 1.00 | −21.25 | −5.47 | −0.31 | 1.00 | 0.67 | 0.92 | |

Shibanfang | 0.03 | 9.74 | 2.21 | 2.91 | 1.00 | −0.41 | 0.93 | −0.08 | 1.00 | 0.62 | 0.99 | |

20150721 | Jiangjunmu | 1.40 | 0.58 | 1.95 | 4.55 | 0.53 | 0.98 | 0.74 | −0.43 | 0.79 | 0.99 | 0.87 |

Dukou | 4.43 | 4.34 | 3.22 | 6.97 | 0.46 | −20.54 | −13.39 | −0.32 | 0.80 | 0.75 | 0.61 | |

Shibanfang | 0.01 | 5.11 | 7.69 | 1.58 | 1.00 | −0.81 | −2.27 | −0.29 | 1.00 | −0.15 | 0.98 | |

20150802 | Jiangjunmu | 0.26 | 7.22 | 2.77 | 7.30 | 0.77 | −0.42 | 0.83 | −1.87 | 0.93 | −0.23 | 0.97 |

Dukou | 0.27 | 6.35 | 2.21 | 12.00 | 0 | −19.82 | −1.02 | N | 0.74 | −0.27 | 0.98 | |

Shibanfang | 0.01 | 7.06 | 5.03 | 7.87 | 1.00 | −2.6 | −99.45 | −0.18 | 1.00 | −0.04 | 0.64 | |

20180625 | Jiangjunmu | 0.01 | 8.77 | 2.09 | 3.33 | 1.00 | −0.47 | 0.92 | −174.92 | 1.00 | −0.52 | 0.93 |

Dukou | 0.01 | 3.06 | 0.22 | 8.80 | 1.00 | −40.82 | 0.79 | −5.34 | N | N | N | |

Shibanfang | 0.01 | 9.65 | 4.77 | 0.32 | 1.00 | −3.87 | −0.19 | −6.96 | 1.00 | −0.1 | 1.00 | |

20180712 | Jiangjunmu | 0.45 | 6.69 | 2.62 | 3.40 | 0.67 | −189.81 | −35.51 | −18.17 | 0.90 | −0.22 | 0.62 |

Dukou | 2.27 | 4.01 | 0.13 | 6.30 | 0.84 | −22.07 | 0.71 | −0.25 | 0.92 | −0.06 | 0.91 | |

Shibanfang | 0.01 | 4.67 | 1.92 | 0.26 | 1.00 | 0.84 | 0.70 | −0.55 | 1.00 | −0.04 | 0.95 | |

20180716 | Jiangjunmu | 5.00 | 3.42 | 0.11 | 8.28 | 0.27 | −79.19 | 0.14 | −2.47 | 0.68 | 0.23 | 0.74 |

Dukou | 8.20 | 3.37 | 0.55 | 54.15 | 0.58 | −12.71 | 0.66 | −17.3 | 0.98 | 0.24 | 0.89 | |

Shibanfang | 0.02 | 2.58 | 0.44 | 9.21 | 1.00 | 0.67 | 0.68 | −0.21 | 1.00 | 0.43 | −0.15 | |

20180730 | Jiangjunmu | 4.95 | 6.49 | 1.27 | 9.16 | 0.28 | 0.98 | 0.97 | −1.46 | 0.75 | −0.24 | −0.22 |

Dukou | 2.92 | 2.70 | 0.09 | 7.65 | 0.76 | −3.17 | 0.85 | −0.67 | 0.88 | 0.27 | 0.25 | |

Shibanfang | 0.01 | 3.47 | 1.19 | 4.73 | 1.00 | 0.56 | 0.17 | −0.11 | 1.00 | 0.15 | −0.04 | |

20180805 | Jiangjunmu | 3.58 | 3.77 | 4.05 | 4.47 | 0.39 | 0.28 | 0.17 | −0.91 | 0.51 | 0.76 | 0.72 |

Dukou | 1.93 | 13.75 | 4.58 | 3.10 | 0.26 | −0.18 | 0.87 | −1.34 | 0.54 | −0.23 | 1.00 | |

Shibanfang | 2.38 | 10.36 | 2.66 | 5.00 | 0.46 | −0.53 | 0.90 | −0.34 | 0.89 | −0.12 | 1.00 | |

20180813 | Jiangjunmu | 1.50 | 8.14 | 7.18 | 0.38 | 0.94 | −5.13 | −5.22 | −0.06 | 0.60 | 0.14 | 0.48 |

Dukou | 3.85 | 8.11 | 4.40 | 2.82 | −0.9 | −0.73 | 1.00 | −0.02 | 0.38 | −0.06 | 0.41 | |

Shibanfang | 0.01 | 6.65 | 19.11 | 1.15 | 1.00 | 0.12 | −13.07 | −0.07 | 1.00 | −0.12 | 0.42 | |

20180818 | Jiangjunmu | 1.54 | 6.43 | 3.41 | 2.69 | 0.42 | −0.98 | 0.99 | −0.78 | 0.66 | 0.13 | 0.82 |

Dukou | 2.17 | 6.33 | 7.90 | 3.83 | 0.56 | −0.75 | 0.16 | −0.37 | 0.77 | 0.12 | 0.56 | |

Shibanfang | 0.01 | 6.08 | 3.34 | 1.62 | 1.00 | −1.40 | 0.28 | −0.23 | 1.00 | 0.01 | 0.39 |

Rainfall event . | Station . | RMSE/mm . | . | R. | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

. | MGWR-GAU . | OI . | Radar . | . | MGWR-GAU . | OI . | Radar . | . | MGWR-GAU . | OI . | ||

20090509 | Jiangjunmu | 0.01 | 4.76 | 0.27 | 3.51 | 1.00 | −4.85 | 0.95 | −1.76 | 1.00 | −0.15 | 0.98 |

Dukou | 0.01 | 8.18 | 1.09 | 5.37 | 1.00 | −0.94 | 0.97 | 0.16 | 1.00 | −0.36 | 0.99 | |

Shibanfang | 0.03 | 2.99 | 0.84 | 4.45 | 1.00 | −1.57 | 0.77 | −0.52 | 1.00 | −0.05 | 0.92 | |

20110815 | Jiangjunmu | 0.03 | 4.64 | 0.72 | 0.15 | 1.00 | −2.75 | 0.84 | 0.2 | 1.00 | −0.31 | 0.95 |

Dukou | 0.02 | 7.18 | 3.91 | 9.37 | 1.00 | −21.25 | −5.47 | −0.31 | 1.00 | 0.67 | 0.92 | |

Shibanfang | 0.03 | 9.74 | 2.21 | 2.91 | 1.00 | −0.41 | 0.93 | −0.08 | 1.00 | 0.62 | 0.99 | |

20150721 | Jiangjunmu | 1.40 | 0.58 | 1.95 | 4.55 | 0.53 | 0.98 | 0.74 | −0.43 | 0.79 | 0.99 | 0.87 |

Dukou | 4.43 | 4.34 | 3.22 | 6.97 | 0.46 | −20.54 | −13.39 | −0.32 | 0.80 | 0.75 | 0.61 | |

Shibanfang | 0.01 | 5.11 | 7.69 | 1.58 | 1.00 | −0.81 | −2.27 | −0.29 | 1.00 | −0.15 | 0.98 | |

20150802 | Jiangjunmu | 0.26 | 7.22 | 2.77 | 7.30 | 0.77 | −0.42 | 0.83 | −1.87 | 0.93 | −0.23 | 0.97 |

Dukou | 0.27 | 6.35 | 2.21 | 12.00 | 0 | −19.82 | −1.02 | N | 0.74 | −0.27 | 0.98 | |

Shibanfang | 0.01 | 7.06 | 5.03 | 7.87 | 1.00 | −2.6 | −99.45 | −0.18 | 1.00 | −0.04 | 0.64 | |

20180625 | Jiangjunmu | 0.01 | 8.77 | 2.09 | 3.33 | 1.00 | −0.47 | 0.92 | −174.92 | 1.00 | −0.52 | 0.93 |

Dukou | 0.01 | 3.06 | 0.22 | 8.80 | 1.00 | −40.82 | 0.79 | −5.34 | N | N | N | |

Shibanfang | 0.01 | 9.65 | 4.77 | 0.32 | 1.00 | −3.87 | −0.19 | −6.96 | 1.00 | −0.1 | 1.00 | |

20180712 | Jiangjunmu | 0.45 | 6.69 | 2.62 | 3.40 | 0.67 | −189.81 | −35.51 | −18.17 | 0.90 | −0.22 | 0.62 |

Dukou | 2.27 | 4.01 | 0.13 | 6.30 | 0.84 | −22.07 | 0.71 | −0.25 | 0.92 | −0.06 | 0.91 | |

Shibanfang | 0.01 | 4.67 | 1.92 | 0.26 | 1.00 | 0.84 | 0.70 | −0.55 | 1.00 | −0.04 | 0.95 | |

20180716 | Jiangjunmu | 5.00 | 3.42 | 0.11 | 8.28 | 0.27 | −79.19 | 0.14 | −2.47 | 0.68 | 0.23 | 0.74 |

Dukou | 8.20 | 3.37 | 0.55 | 54.15 | 0.58 | −12.71 | 0.66 | −17.3 | 0.98 | 0.24 | 0.89 | |

Shibanfang | 0.02 | 2.58 | 0.44 | 9.21 | 1.00 | 0.67 | 0.68 | −0.21 | 1.00 | 0.43 | −0.15 | |

20180730 | Jiangjunmu | 4.95 | 6.49 | 1.27 | 9.16 | 0.28 | 0.98 | 0.97 | −1.46 | 0.75 | −0.24 | −0.22 |

Dukou | 2.92 | 2.70 | 0.09 | 7.65 | 0.76 | −3.17 | 0.85 | −0.67 | 0.88 | 0.27 | 0.25 | |

Shibanfang | 0.01 | 3.47 | 1.19 | 4.73 | 1.00 | 0.56 | 0.17 | −0.11 | 1.00 | 0.15 | −0.04 | |

20180805 | Jiangjunmu | 3.58 | 3.77 | 4.05 | 4.47 | 0.39 | 0.28 | 0.17 | −0.91 | 0.51 | 0.76 | 0.72 |

Dukou | 1.93 | 13.75 | 4.58 | 3.10 | 0.26 | −0.18 | 0.87 | −1.34 | 0.54 | −0.23 | 1.00 | |

Shibanfang | 2.38 | 10.36 | 2.66 | 5.00 | 0.46 | −0.53 | 0.90 | −0.34 | 0.89 | −0.12 | 1.00 | |

20180813 | Jiangjunmu | 1.50 | 8.14 | 7.18 | 0.38 | 0.94 | −5.13 | −5.22 | −0.06 | 0.60 | 0.14 | 0.48 |

Dukou | 3.85 | 8.11 | 4.40 | 2.82 | −0.9 | −0.73 | 1.00 | −0.02 | 0.38 | −0.06 | 0.41 | |

Shibanfang | 0.01 | 6.65 | 19.11 | 1.15 | 1.00 | 0.12 | −13.07 | −0.07 | 1.00 | −0.12 | 0.42 | |

20180818 | Jiangjunmu | 1.54 | 6.43 | 3.41 | 2.69 | 0.42 | −0.98 | 0.99 | −0.78 | 0.66 | 0.13 | 0.82 |

Dukou | 2.17 | 6.33 | 7.90 | 3.83 | 0.56 | −0.75 | 0.16 | −0.37 | 0.77 | 0.12 | 0.56 | |

Shibanfang | 0.01 | 6.08 | 3.34 | 1.62 | 1.00 | −1.40 | 0.28 | −0.23 | 1.00 | 0.01 | 0.39 |

It can be seen from the table that when comparing the RMSE values of the rainfall fusion data with the subsection-optimized radar data, all three methods have different degrees of reduction. Compared with the dispersion of radar data and ground stations on the point scale, the method is the best, the OI method is the second best and the MGWR-GAU method is the worst. Regarding the Nash efficiency coefficient, except for the Dukou station of 20180813, the remaining of the method is greater than 0, indicating that the radar data fused by the method have good consistency with the station data. Compared with the subsection optimized radar data, the optimization effect of of the MGWR-GAU method and OI method is better. The number of cases with values greater than 0 increases (the MGWR-GAU method increases by 6, and the OI method increases by 23). This indicates that the three fusion methods have improved the consistency of radar data and ground station data. According to the correlation coefficient, among the rainfall events with *R* values greater than 0.60 at the three test stations, there are nine rainfall events by the method, zero rainfall events by the MGWR-GAU method and seven rainfall events by the OI method. In general, the optimization effect of the MGWR-GAU method is the worst, with most of the *R* values less than 0.60 and many less than 0. The OI method has a medium optimization effect, but there are also cases with *R* values less than 0 (such as 20180716 and 20180730). The method is the best, with an *R* value between 0.38 and 1.00.

Therefore, from the perspective of the correlation between the fusion data and ground stations, the method is the best, the OI method is the second best and the MGWR-GAU method is the worst. The reason may be due to the calculation method of rainfall deviation. The method uses the Kriging interpolation method to interpolate the rainfall proportion coefficient in the whole basin, fully considering the influence of terrain. In the OI method, it is assumed that there is no correlation among the observation errors, or between the observation error and the deviation field error, when calculating the rainfall deviation by the optimal weight function formula. Additionally, the initial radius of the adaptive function model is artificially given, which may lead to some errors. When the MGWR-GAU method is used to calculate the rainfall bias function, theoretically each grid should have local and global variables of the specified scale, but in fact, the data resolution is limited (such as 1 km × 1 km hourly wind speed data using the interpolation of 0.1° × 0.1° ERA5 reanalysis data). Therefore, although this method can consider the spatial variability of rainfall bias, due to data limitations, the optimization effect may not be at the point scale.

*y*=

*x*. The RMSE value after the fusion of the method is higher than that before the fusion. Overall, the three fusion methods have a better improvement on the high-value underestimation of radar data. At Dukou station, the

*R*and RMSE of the method fusion data are obviously improved, and the

*R*value is increased from 0.10 to 0.78 with a good correlation degree. Comparatively speaking, the optimization effect of the other two methods is poor. This may be due to the sparse stations near Dukou station. The OI method is greatly affected by the adaptive correlation function model in the process of obtaining the optimal weight function, and the poor results of the MGWR-GAU method are due to the insufficient global variable resolution. The fusion effect of the method and OI method at Shibanfang station is better. The correlation coefficient

*R*increases from 0.11 to 0.82 and 0.66 and the RMSE value decreases. This indicates that the error of the method and OI method is relatively small in the station where there are dense stations on the right and sparse stations on the left (hereinafter referred to as inclined density). On the point scale, the method has the best fusion effect, followed by the OI method, and the MGWR-GAU method has the worst.

#### Rainfall spatial distribution quality evaluation

### Evaluation for potential hydrological application

Flood no. . | Rainfall input type . | Rev (%) . | Rep (%) . | Ret (h) . | NSE . |
---|---|---|---|---|---|

20180813 | Runoff measured value | – | – | – | – |

Station data | 14.38 | −5.66 | −5 | 0.79 | |

fusion data | 4.88 | 0.59 | −5 | 0.85 | |

MGWR-GAU fusion data | 16.49 | 0.78 | −5 | 0.74 | |

OI fusion data | −5.28 | 3.91 | −4 | 0.80 | |

20210721 | Runoff measured value | – | – | – | – |

Station data | 13.39 | −5.61 | 8 | 0.46 | |

fusion data | −3.29 | −9.24 | 1 | 0.64 | |

MGWR-GAU fusion data | 30.23 | −2.63 | 2 | 0.60 | |

OI fusion data | 17.72 | −1.95 | 12 | 0.68 | |

20210726 | Runoff measured value | – | – | – | – |

station data | −4.18 | 0.31 | 5 | 0.62 | |

fusion data | 3.63 | −0.06 | 5 | 0.70 | |

MGWR-GAU fusion data | 1.10 | −1.69 | 5 | 0.66 | |

OI fusion data | 3.72 | 2.71 | 5 | 0.70 |

Flood no. . | Rainfall input type . | Rev (%) . | Rep (%) . | Ret (h) . | NSE . |
---|---|---|---|---|---|

20180813 | Runoff measured value | – | – | – | – |

Station data | 14.38 | −5.66 | −5 | 0.79 | |

fusion data | 4.88 | 0.59 | −5 | 0.85 | |

MGWR-GAU fusion data | 16.49 | 0.78 | −5 | 0.74 | |

OI fusion data | −5.28 | 3.91 | −4 | 0.80 | |

20210721 | Runoff measured value | – | – | – | – |

Station data | 13.39 | −5.61 | 8 | 0.46 | |

fusion data | −3.29 | −9.24 | 1 | 0.64 | |

MGWR-GAU fusion data | 30.23 | −2.63 | 2 | 0.60 | |

OI fusion data | 17.72 | −1.95 | 12 | 0.68 | |

20210726 | Runoff measured value | – | – | – | – |

station data | −4.18 | 0.31 | 5 | 0.62 | |

fusion data | 3.63 | −0.06 | 5 | 0.70 | |

MGWR-GAU fusion data | 1.10 | −1.69 | 5 | 0.66 | |

OI fusion data | 3.72 | 2.71 | 5 | 0.70 |

In the No.20180813 flood, the simulated flood peaks of the four input data were significantly advanced, and the relative errors were within 20%. The station data and the MGWR-GAU method fusion data both overestimate the flood peak flow by more than 10%. The simulated flood peak flow of the method fusion data and the OI method fusion data is closer to the measured flow, indicating that these two methods have an improvement effect on flood peak simulation. Although the MGWR-GAU method simulates the flood process closer to the site simulation effect, there is an abnormal increase in the flow during the measured flood decline process, which may be due to the existence of abnormal points when the MGWR-GAU method fuses the rainfall data. The simulation effect of the three fusion datasets on flood volume is better than that of the station simulation value. The measured flood volume simulated by the method fusion data is the closest to the measured value. The runoff depth simulated by the OI fusion data is overestimated by 3.91%. The simulation error of the four rainfall inputs on flood volume is within 5%. The NSEs of the four rainfall inputs are all qualified, and the NSEs of the fusion data of the method and the OI method are higher. The four flood hydrographs are relatively smooth, which indicates that they can be used as rainfall input in the Duanzhuang watershed, and the performance of the method fusion data and OI method fusion data is better than that of the station data.

In No.20210721, the simulation error of the MGWR-GAU method fusion data on the peak flow at the outlet of the basin is more than 15%, indicating that the two rainfall inputs and station data will cause the peak flow to be overestimated. The peak flow simulated by the method is the closest to the measured value. The simulated flood volumes of the four rainfall inputs were underestimated, but the relative errors were within 10%. The peak time difference of the station data is large, which is 8 h later than the measured peak time, and the NSE is low, indicating that the station data cannot be used as the rainfall data input of the flood. The method fusion data and the MGWR-GAU fusion data have a better effect on the improvement of the peak time. After the fusion, the flood peak lag time is reduced to 1 and 2 h, respectively, but the MGWR-GAU method fusion data simulate the flood peak flow. The NSE in the flood simulation corresponding to the three fusion datasets increases. On the whole, the method has the best performance in this flood. The flood hydrographs corresponding to the four rainfall inputs are smooth, and the method has the best optimization effect.

In No.20210726, the difference between the simulated peak flow and flood volume of the four rainfall input data and the measured value is small, and the relative error is less than 5%, which indicates that the hydrological application effect of the four rainfall datasets is good. Among them, the flood peak flow and flood volume of the method fusion data are significantly improved compared with the station data, the NSE is also increased to 0.70 and the simulation effect is the best. The simulation effect of the station data, the OI method fusion data and the MGWR-GAU method fusion data is weakened in turn. The flood process line simulated by the station data fluctuates greatly, which is quite different from the measured flood process, and there are two peaks. This shows that there is a large uncertainty in the flood process simulated by the station data in this flood. The reason may be that the regional precipitation does not cover the station, resulting in the lack of representativeness of the station rainfall data in the control area, which leads to a decrease in the flow at 16:00 on 26 July. The outlet flood hydrographs simulated by the method fusion data, OI fusion data and MGWR-GAU fusion data are relatively stable, and the NSE corresponding to the three fusion datasets is better than that of the station data simulation. It shows that these three fusion datasets are more suitable for the flood rainfall input than the single-source station data.

In summary, the application effect of method fusion data in the HEC-HMS distributed hydrological model of Duanzhuang Basin is better than that of site data, and it has the best hydrological application potential among the three fusion methods. Both the MGWR-GAU method and the OI method have certain optimization effects. The flood hydrographs simulated by these two fusion data are smoother than that simulated by the station data and closer to the measured flood hydrographs. Therefore, the three fusion datasets are better than the single-source radar data and the station data. The simulation results show better hydrological application potential than station data.

## DISCUSSION

Radar data have the advantages of high spatial and temporal resolutions, a wide measurement range, strong timeliness and convenient management and maintenance, but the data accuracy is often not high due to ground occlusion and other reasons. To promote the use of radar data in the Duanzhuang basin at the eastern foot of the Taihang Mountains, this paper first used the Z–R relationship optimization method, including empirical formula method, IO method and SO method, to optimize the radar data and obtain hourly rainfall. Then, the radar data and ground gauged data were fused and optimized by three methods: the method, MGWR-GAU method and OI method. The point scale rainfall value and rainfall spatial distribution of the three fusion data were evaluated. Finally, three fusion datasets were used to drive the HEC-HMS hydrological model, and the simulated values of the three fusion datasets, the simulated values of the rainfall station and the measured values were compared and analyzed. The following conclusions have been drawn.

- (1)
Based on the base data of Shijiazhuang S-band weather radar from 2018 to 2020 and three historical rainstorm datasets, the radar is initially processed and optimized. The radar base data are processed by the radar quantitative estimation rainfall step, and the results show that when the first elevation angle (0.5°) is used for observation, most of the western mountainous areas are occluded. As the elevation angle increases, the occlusion situation continues to weaken until it increases to the fourth elevation angle (3.4°). The optimization method is used to optimize the radar Z–R relationship as a whole and in sections, and a quality evaluation is carried out. The optimized data improve the shortcomings of high underestimation, low overestimation and discontinuous spatial variation of the radar original rainfall observation data to a certain extent, but the optimization effect is still limited in terms of point rainfall.

- (2)
Three fusion methods are used to fuse the two-source rainfall data of radar and rainfall stations. The rainfall scale coefficient fusion method, the mixed geographically weighted regression Gaussian function fusion method, and the OI method are used for fusion processing. The results show that the three fusion methods can better optimize the original radar data in point rainfall and spatial distribution. According to various quality evaluation index values, the method has the best fusion effect, the consistency between the fusion data and the rainfall station is the best, the OI method is the second best and the MGWR-GAU method is the worst due to the low resolution of wind speed data.

- (3)
The fusion data of the No.20180813, 20210721 and 20210726 floods in the corresponding period are used as rainfall input data of the HEC-HMS model. The results show that the three fusion data have better flood simulation effects than the measured data. This shows that the radar data after fusion processing can perform better than the rainfall station data as the rainfall input of the HEC-HMS model in the study basin and has the application potential to describe the rainfall information of the basin.

## CONCLUSIONS

In this paper, the fusion of 11 rainfall events in the Duanzhuang basin at the eastern foot of the Taihang Mountains was selected for preliminary discussion. Compared with the original radar rainfall data, the fusion data have a better consistency with ground station data, which shows that fusion methods have very important significance and potential with respect to radar application in basins with sparse rainfall stations. The rainfall fusion data show better hydrological application potential than station data in the HEC-HMS hydrological model. This provides an idea for radar data accuracy and radar popularization and application. More data and research for further discussion are needed to show the applicability of various fusion methods.

However, the deficiencies in the research are as follows: (1) there are few historical radar data, and the obtained Z–R optimization relationship may not be universal; (2) the selection of inspection sites is subjective; and (3) only using the HEC-HMS semi-distributed hydrological model to test the hydrological potential of fusion data may not be universal. Therefore, in future research, the Z–R relationship can be optimized based on a large amount of historical radar data, the simulation effect can be tested in multiple hydrological models and the appropriate test stations and multiple fusion methods can be selected for rainfall evaluation.

## ACKNOWLEDGEMENTS

This work was supported by the National Natural Science Foundation of China (No. 52279022, 52079086).

## DATA AVAILABILITY STATEMENT

All relevant data are included in the paper or its Supplementary Information.

## CONFLICT OF INTEREST

The authors declare there is no conflict.

Radar Observation of the Atmosphere. University of Chicago Press, Chicago