**5. Conclusions**

In this paper, radar-rain gauge merging categories were conducted. Eight different storm events were chosen from two catchments in semi-humid and semi-arid areas of Northern China to test six different radar-rain gauge-merging methods that belong to three categories using a LOOCV and a rainfall-runoff model (Hybrid-Hebei model). We generated six merged radar-rain gauge rainfall products and compared their performances at gauged location estimations to further their effectiveness as inputs to a semi-distributed rainfall-runoff model of the two study catchments, the Zijingguan and the Fuping catchments in the Northern China. Their relative performances were assessed based on the LOOCV and compared. Two main conclusions can be drawn:

(1) The merging methods have significant potential to improve the quality of rainfall estimates. The integration category performed best in most cases. The bias adjustment category always performed significantly worse. The interpolation category ranked between the aforementioned. The degree of improvement can be a function of merging method that is affected by the quality of both the data and the ability to capture small-scale rainfall features and methodological factors. The total bias of the merging products is because of components of merging methods or other uncertainties. This means that the use of merging methods, without considering the small-scale rainfall features, can be misleading. The quality and representativeness of the radar and rain gauge data should be carefully considered with refinements to mathematical techniques.

(2) In this study, we assumed that a higher quality of the merging products would be indicated from agreements between the simulated and observed runoff using the merging products as the input of the rainfall-runoff model. As expected, the results revealed that a higher quality of merging products indicated a better agreemen<sup>t</sup> between the observed and simulated runoff. However, the precipitation estimation random errors will be averaged out to a lower extent when the correlation length of random errors is close to the catchment's response time. Thus, it is hard to know if the streamflow simulation errors were due to precipitation estimation random errors or the rainfall-runoff model's structural errors.

It should be noted that the computational requirements and runtimes are a significant challenge in the merging process. In general, the bias adjustment methods are the least complex and are easy to compute. The interpolation methods are computed relying on the solution of the kriging system, which increases the computational complexity by adding the variables. The integration methods are the most complex and will continuously increase with radar QPE of higher spatial resolution.

In conclusion, this synthetic study demonstrated the potential benefit of the radar-rain gauge-merged rainfall precipitation at a high spatial resolution. The performance in gauged locations evaluation and hydrological application based on the different merging methods was also demonstrated. It is should be noted that the quality of radar QPE will be improved in the future with the increasing available of dual-polarization radars [61]. As discussed in Section 4.1, the quality of QPE plays a

critical role on the performance of di fferent merging methods, in which the spatial information of QPE is employed in di fferent merging techniques. It is recommended that the three merging categories are tested in combination with the higher quality QPEs, and it is critical to study how the quality of QPE affects the performance of these merging methods [44]. Furthermore, with the increasing of monitoring stations, a further work should be implemented to study the a ffection of di fferent density of rain gauges on the merging performance in the future. Notably, the conditions and assumptions of this study, including the hydrology parameters chosen and the Gaussian assumptions in the kriging, are merely simplifications of reality. The di fference between the theoretical study and simulated data in this study is that the rainfall observations from radar or rain gauge in reality are even more complicated due to dynamic spatial changes.

**Author Contributions:** Conceptualization, Q.Q. and J.L.; methodology, Q.Q.; software, Q.Q.; validation, Q.Q., C.L. and Y.J.; formal analysis, J.L. and J.T.; investigation, W.W.; resources, C.L.; data curation, F.Y.; writing—original draft preparation, Q.Q. and J.L.; writing—review and editing, Q.Q. and J.T.; visualization, Q.Q.; supervision, Q.Q. and Y.J.; project administration, F.Y.; funding acquisition, C.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (51822906), the National Key Research and Development Project (2017YFC1502405), the Major Science and Technology Program for Water Pollution Control and Treatment (2018ZX07110001), and the IWHR Research & Development Support Program (WR0145B732017).

**Acknowledgments:** Thanks to Alexandre Wadoux for help on KED computation; thanks to Xinyi Li for help on scatter figure.

**Conflicts of Interest:** The authors declare no conflict of interest.
