Basin-scale runoff forecasting requires controlling absolute relative errors within 0.2 for accurate predictions. This study examines the sensitivity of simulated flood deviations in frequently flooded humid regions to discrepancies in precipitation driving the Weather Research and Forecasting (WRF)-Hydro model. Key parameters of various WRF-Hydro modules are calibrated from 23 flood events between 2003 and 2017. Two experiments were designed with minimized uncertainty in both model and parameterization to explore the sensitivity of streamflow changes to precipitation misestimations, both in total and graded precipitation. The sensitivity of runoff relative errors is more pronounced than that of precipitation relative errors, influenced by the magnitude, variability, and duration of rainfall. During processes involving heavy rainstorm, precipitation absolute relative errors increased by 50%, while runoff absolute relative errors increased by more than 60%. This sensitivity trend is linked to variations in components generated by misestimated precipitation. Runoff relative errors are higher when precipitation is misestimated at high rainfall levels compared to the same misestimation at low rainfall levels. For effective flood simulation and prediction, it is crucial to emphasize the accuracy of precipitation, especially during high rainfall events. Future research will incorporate more realistic precipitation forcing mechanisms and additional metrics for evaluating precipitation forecast.

  • We systematically calibrated the main parameters of each module in the Weather Research and Forecasting (WRF)-Hydro model.

  • This study reveals that the sensitivity of runoff relative errors is more pronounced than that of precipitation relative errors in extreme flood events.

  • The sensitivity of forecast errors at different rainfall levels to flood simulation is discussed under the WRF-Hydro modeling forced by the idealized precipitation.

Precipitation, a fundamental component of the global water cycle, holds a central position in shaping environmental systems, exerting substantial impacts on hydrology, geomorphology, and regional economies (IPCC 2013). Notably, extreme precipitation events and rainstorms have been identified as triggers for flooding, leading to considerable property damage and casualties (Arduino et al. 2005; Tabari 2020). Despite advancements in technology and modeling, numerical precipitation forecasts, while improving, remain susceptible to errors and uncertainties, particularly in dynamic and rapidly changing weather conditions.

In a specific geographic context, the interplay between available energy and precipitation governs rates of evapotranspiration, runoff, and soil moisture variations (Arora 2002). L'vovich (1979) has highlighted the well-established phenomenon of varying catchment sensitivities across diverse climates. Sensitivity analyses consistently reveal that alterations in precipitation result in corresponding variations in runoff, with a more pronounced amplification of runoff in arid catchments (Chiew et al. 1995). Building upon the Budyko concept, Roderick & Farquhar (2011) introduced a sensitivity framework directly assessing runoff sensitivity. In addition, Donohue et al. (2011) presented findings suggesting that a yearly increment of 10 mm in precipitation anticipates an annual increase of 7 mm in runoff within specific high-yield catchments in Australia. This intricate interplay underscores the nuanced relationship between precipitation dynamics and catchment responses, shedding light on the complex nature of hydrological processes.

The evaluation of flood modeling efficacy hinges significantly on the relative error (RE), a key metric in this assessment. Standardized metrics, a fundamental criterion in Chinese hydraulic engineering outlined by MWR (2008), serve as benchmarks for proficient flood prediction. These established standards delineate the requirements for accurate flood forecasting, specifying that the absolute RE for total runoff or peak flow rate should not exceed 0.2, representing the permissible threshold for authorization error. An additional measure to assess the adequacy of a hydrological model is the ensemble pass rate (EPR), which quantifies the proportion of accurately predicted flood events within a given sequence. If the EPR exceeds 60%, the ensemble flood prediction is considered a benchmark forecast. For publication as an ensemble forecast, the model must achieve an EPR exceeding 70%. An exceptional representation is acknowledged when the EPR surpasses 85%, marking the hydrological model as outstanding in its predictive capabilities. These standardized metrics and thresholds offer a comprehensive framework for evaluating the accuracy and reliability of flood modeling outputs.

Hydrological models constitute a primary approach for capturing the intricate dynamics of the water cycle within specific catchments. Among these models, the Weather Research and Forecasting (WRF)-Hydro model emerges as a coupled land surface and hydrologic modeling system, employing mathematical algorithms and physically based representations to simulate water, energy, and momentum exchanges among the atmosphere, land surface, and subsurface (Gochis et al. 2020). Operating on a fixed grid system, the WRF-Hydro model utilizes meteorological data inputs to replicate and analyze intricate land–atmosphere exchange processes, showcasing exceptional adaptability for coupling with numerical weather and climate models and flexible scale conversion. Widespread application extends to modeling large-scale spatial and temporal hydrological processes (Arnault et al. 2021), as well as simulating flash flood events within small catchment areas (Camera et al. 2020; Shuvo et al. 2021).

The calibration of parameters represents a crucial preparatory phase preceding the practical implementation of the WRF-Hydro model. This calibration is essential due to the unique characteristics of climatic conditions, channel attributes, soil texture, land use, and other basin-specific factors significantly impacting runoff and drainage simulations. The adaptation of flood modeling to watersheds often requires specific parameter adjustments. Yucel et al. (2015) proposed a stepwise approach for the WRF-Hydro model, aiming to minimize model runs and reduce computational time. Notably, four parameters – surface runoff parameter (REFKDT), surface retention depth scaling parameter (RETDEPRT), overland flow roughness scaling parameter (OVROUGHRT) from the high-resolution terrain grid, and the channel Manning roughness coefficient (MANN) – outlined by Yucel et al. (2015), have been widely calibrated in subsequent studies (Kerandi et al. 2018; Rummler et al. 2019).

Further investigations, such as Liu et al. (2021), have explored the sensitivities of these parameters in the WRF-Hydro model across semi-humid and semi-arid catchments in Northern China. Building on the stepwise approach, Yang et al. (2018) emphasized the calibration of soil hydraulic parameters and soil bottom drainage partition (SLOPE) as equally crucial alongside REFKDT. Sun et al. (2020) extended parameter calibration to the concept-based flow module, including GWEXP, in their study. These calibration efforts collectively enhance the precision and reliability of the WRF-Hydro model in capturing diverse hydrological processes and responding effectively to the unique attributes of various watersheds.

The primary objective of this study is to investigate the sensitivity of flood runoff to precipitation in the flood-prone region of Eastern China, specifically focusing on the Xixian watershed (XXW) within the Upper Huaihe River basin (HRB). Employing the WRF-Hydro model, our research endeavors to establish relationships between precipitation and other water cycle elements, using related or absolute errors (AEs) as a metric for sensitivity evaluation. To achieve this objective, a systematic calibration of parameters across all WRF-Hydro modules was initially conducted, and the model's applicability within the study area was thoroughly examined. Subsequently, two idealized experiments were designed to explore the impact of the precipitation errors on the total streamflow errors. In Experiment 1, precipitation was scaled hourly, allowing for an analysis of how changes in the RE of precipitation influenced the RE of total streamflow. In Experiment 2, we introduced an error in total precipitation from Experiment 1, perturbing it to a specific rainfall level with a new scaled factor while maintaining precipitation constant at other rainfall levels. This facilitated an exploration of the impact of precipitation forecasting errors at different rainfall levels on streamflow forecasting. Both idealized experiments employed the calibrated WRF-Hydro model. By establishing relationships between the error in changing total scaled precipitation or specific rainfall level scaled precipitation and the error in the WRF-Hydro total streamflow, our study aims to offer theoretical support for disaster prevention and mitigation measures. These measures include the design of floods, construction of dams, and scheduling of reservoir operations, contributing to the advancement of strategies for managing and mitigating flood-related risks based on flash and extreme rainfall processes in the studied region.

Study area

This research centers on the XXW, a pivotal source within the upper reaches of the HRB. The HRB, situated in Eastern China between the Yellow River and the Yangtze River, is characterized by frequent occurrences of extreme precipitation owing to its location in the climatic transition zone between the northern and southern regions of China. As depicted in Figure 1, the XXW's geographical location, river distribution, land types, and soil textures provide a comprehensive overview. Encompassing an area of approximately 10,404 km2, the rivers of the XXW originate from mountainous regions in the southern and western sectors, featuring elevations ranging from 30 to 1,118 m.
Figure 1

Geographic location of the XXW, three-layer nested downscaling regions (D01, D02, D03) in the WRF model, location of meteorological and hydrological stations within the watershed, and spatial distribution of land use and soil texture.

Figure 1

Geographic location of the XXW, three-layer nested downscaling regions (D01, D02, D03) in the WRF model, location of meteorological and hydrological stations within the watershed, and spatial distribution of land use and soil texture.

Close modal

The central and eastern watershed areas exhibit a predominantly flat terrain, with an annual precipitation range of 800–1,400 mm, subject to significant variations due to topographical influences. Notably, around 60% of the total rainfall occurs during the flood season, spanning from June to September, leading to an uneven distribution of water resources. This region functions prominently as a significant agricultural zone, characterized by subsurface soil compositions predominantly comprised of clay and loam. These distinctive combinations of geographical and environmental attributes underscore the significance of the XXW within the broader context of the HRB.

Datasets

The forcing data, encompassing incoming shortwave and longwave radiation, specific humidity, air temperature, surface pressure, as well as near-surface wind components in both the u and v dimensions, were retrieved from the NASA Global Land Data Assimilation System Version 2 (GLDAS-2) product (https://disc.gsfc.nasa.gov/). Initially, the temporal resolution of this dataset was 3 h, which was subsequently linearly interpolated to 1 h. In addition, the spatial resolution underwent regridding to 3 km utilizing the bilinear method within the Earth System Modeling Framework (ESMF) Regridding Script (https://ral.ucar.edu/dataset/earth-system-modeling-framework-esmf-regridding-scripts).

The WRF model was propelled by the ERA5 Reanalysis dataset, representing the fifth iteration of the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis for climate and weather spanning the last four to seven decades. This dataset furnishes variables at both single levels (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-pressure-levels) and pressure levels (https://cds.climate.copernicus.eu/cdsapp#!/dataset/reanalysis-era5-single-levels), boasting a temporal resolution of 1 h and a spatial resolution of 0.25° (Hersbach et al. 2018a, 2018b). To provide more accurate initial conditions for both the atmosphere and land surface in simulating flood processes at a 3 km resolution in the XXW using the WRF-Hydro model, a three-level domain nesting approach in the WRF model was employed around the XXW for three downscaling iterations, as illustrated in Figure 1. During the downscaling process, both accuracy and computational speed were considered. The downscaling ratio for accuracy should not be too large, and the three nested layers were presented at resolutions of 27, 9, and 3 km, respectively. To enhance computational speed, the area covered by each of the three nested layers gradually decreases around the study area. Domain 1 encompasses the majority of China, while Domain 2 covers several provinces in Eastern China. Domain 3 predominantly encompasses the study area with a spatial resolution of 3 km. The initial field was generated through the WRF Preprocessing System and real-time WRF modeling, utilizing the ERA5 reanalysis dataset for forcing and the three-level domain nesting configuration.

The temporal interpolation of observed flow rate data obtained from the Xixian hydrological station was accomplished through the utilization of the linear method. Concurrently, hourly precipitation data from several rain gauge stations were subjected to spatial interpolation via the inverse distance weighting method. The geographical distribution of these rain gauge stations and hydrological stations is elucidated in Figure 1. Elevation and stream network maps were derived from the digital elevation model accessible at http://glovis.usgs.gov/.

To adapt the flood characteristics and the geographical features of the XXW, a spatial resolution of 3 km was designated for the initial field, forcing data, and output dataset. Correspondingly, the temporal resolution for observed flow rate data, forcing data, and the output dataset was standardized to 1 h. This meticulous adjustment in spatial and temporal resolutions aims to enhance the fidelity of flood simulation and the representation of the study area in the analysis.

Methods

In the present investigation, our focus is directed toward the analysis of 23 flood events spanning the period from 2003 to 2017, as delineated in Table 1 through the extraction of observed flow rate data. Within the realm of flood modeling, the calibration process is fundamental, and two primary methodologies are employed: auto-calibration and manual calibration. Senatore et al. (2015) employed the Model-Independent Parameter Estimation (PEST) auto-calibration method for modeling flood processes in southern Italy. In our study, we opted for the manual calibration method, guided by the Manual Stepwise Approach proposed by Yucel et al. (2015). The calibration process involved the categorization of parameters into two distinct groups: one governing total streamflow and the other influencing the shape of the hydrograph. The sequence of calibration entailed prioritizing parameters in the total streamflow-controlled group, followed by calibration of parameters in the group influencing the hydrograph's shape. The WRF-Hydro model underwent calibration using data from 18 of the aforementioned flood events occurring between 2003 and 2015, with subsequent validation based on the remaining 5 events spanning between 2016 and 2017. To mitigate uncertainties associated with initial soil conditions, a spin-up period of at least 1 month was applied to the WRF-Hydro model. This meticulous approach aims to enhance the reliability of our findings by minimizing uncertainties in the calibration process and providing a robust foundation for simulating flood events within the WRF-Hydro model. Subsequently, 4 specific flood events were selected from the pool of 23 events to conduct idealized precipitation experiments.

Table 1

Characteristics of 23 flood events in the XXW

YearFlood IDLast hours (h)Peak flow (m3/s)
2003 030630 211 3,780 
030721 110 3,960 
2005 050721 165 1,350 
050820 215 1,720 
050829 124 4,410 
050903 97 1,650 
2007 070628 211 2,240 
070707 111 3,830 
070714 133 4,250 
070724 93 1,340 
2008 080813 237 3,220 
080829 107 1,880 
2009 090828 201 2,070 
2010 100716 417 3,570 
2014 140829 305 1,070 
140911 109 872 
140928 178 1,960 
2015 150625 353 1,810 
2016 160701 137 1,810 
160719 217 3,430 
2017 170709 171 2,040 
170910 129 910 
171002 201 2,260 
YearFlood IDLast hours (h)Peak flow (m3/s)
2003 030630 211 3,780 
030721 110 3,960 
2005 050721 165 1,350 
050820 215 1,720 
050829 124 4,410 
050903 97 1,650 
2007 070628 211 2,240 
070707 111 3,830 
070714 133 4,250 
070724 93 1,340 
2008 080813 237 3,220 
080829 107 1,880 
2009 090828 201 2,070 
2010 100716 417 3,570 
2014 140829 305 1,070 
140911 109 872 
140928 178 1,960 
2015 150625 353 1,810 
2016 160701 137 1,810 
160719 217 3,430 
2017 170709 171 2,040 
170910 129 910 
171002 201 2,260 

Our study incorporates two meticulously designed idealized precipitation experiments to further our understanding of the sensitivity of flood runoff to precipitation. In Experiment 1, we systematically altered the total precipitation by applying a scale factor, incrementally varied by 0.1. The range for the maximum and minimum ideal total precipitation was set at 1.5 and 0.5 times the observed total precipitation, respectively. It is crucial to note that the selection of scale factors considered the authenticity of precipitation forecasts, excluding excessively high or low factors corresponding to extreme errors between forecasted and actual precipitation, as they are not addressed in this paper. The calibrated WRF-Hydro model was then forced with the total scaled precipitation obtained from Experiment 1. Experiment 2 involved the rescaling of hourly mean areal precipitation to 12-h accumulated mean areal precipitation. CMA (2017) indicated that mean areal precipitation was categorized into various levels based on a 12-h accumulated scale, as delineated in Table 2. Subsequently, we posited that all errors in total scaled precipitation from Experiment 1 occurred at specific rainfall levels, rather than across the entire rainfall process. Keeping the precipitation values at other rainfall levels constant, a new scaling factor at the th rainfall level can be defined as follows:
formula
(1)
where represents the scale factor employed in Experiment 1, denotes the total observed mean areal precipitation, and signifies the observed mean areal precipitation at the th rainfall level. The newly scaled precipitation values at various rainfall levels were then utilized to drive the calibrated WRF-Hydro model.
Table 2

Precipitation levels classified by using 12 h accumulated mean areal precipitation (CMA 2017)

Precipitation levelRange of 12 h accumulated mean areal precipitation (mm)
No rain <0.1 
Light rain 0.1–2.9 
Moderate rain 3–9.9 
Heavy rain 10–19.9 
Rainstorm 20–39.9 
Heavy rainstorm 40–79.9 
Torrential rainstorm ≥80 
Precipitation levelRange of 12 h accumulated mean areal precipitation (mm)
No rain <0.1 
Light rain 0.1–2.9 
Moderate rain 3–9.9 
Heavy rain 10–19.9 
Rainstorm 20–39.9 
Heavy rainstorm 40–79.9 
Torrential rainstorm ≥80 
The concepts of AE and RE are two fundamental mathematical and statistical concepts widely used in various scientific and engineering fields. They are used to measure the difference between a measured value and the true value, as well as the proportion of this difference relative to the true value (JCGM 100 2008). The formulations are delineated as follows:
formula
(2)
formula
(3)
where and represent the simulated and real values for meteorological and hydrological variables in our study, respectively. The positive (or negative) sign of the RE or AE serves as an indicator that the simulation results exceed (or fall short of) the real values. A diminished absolute RE or AE conveys an improved model simulation performance.
During the calibration and validation phases, Sim and Real represent the simulated and observed hydrological variations at the Xixian hydrological station. For a singular simulation, the RE of total streamflow () and peak flow rate () can be delineated as follows:
formula
(4)
formula
(5)
where and denote the simulated total streamflow and peak flow rate, while and represent the observed total streamflow and peak flow rate at the Xixian hydrological station.
Another pivotal statistical metric employed in the calibration and validation of the WRF-Hydro model is the Nash–Sutcliffe efficiency (NSE) coefficient, which assesses the conformity of the hydrograph output (Nash & Sutcliffe 1970). For a singular simulation, the NSE can be computed as follows:
formula
(6)
where T represents the duration of a flood process, t signifies 1 h within the duration T, is the observed flow rate at time t, and denotes the total average of the observed flow rate. The NSE value spans from negative infinity to 1, and a proximity to 1 suggests a high-quality model with substantial credibility.
Two comprehensive objective functions, with respect to and NSE at the Xixian hydrological station, were adopted in view of the Compromise Programming Method (Bardossy et al. 2016) as follows:
formula
(7)
formula
(8)
where n represents the number of flood events, i denotes the ith flood event, and and signify the objective functions for and NSE, respectively. These functions are employed to identify optimal parameter values in the first-order group using and for parameters in the second-order group using . The optimal parameter values are characterized by the lowest and the highest .
For the assessment of flood simulation performance in the WRF-Hydro model, the EPR is defined by the following expression:
formula
(9)
where A represents the total number of flood events and denotes the number of flood events accurately simulated by the WRF-Hydro model. In accordance with the standard proposed in MWR (2008), an absolute (or ) lower than 0.2 indicates that the model successfully passes the accuracy test in a single flood event simulation.
In the context of the two experiments, individual simulations in the Noah land surface model (LSM) yield outputs comprising mean areal precipitation, evapotranspiration, soil moisture variation, and runoff. The RE of water cycle elements modeled by the Noah LSM () is determined by
formula
(10)
where denotes the Noah LSM simulated mean areal water cycle elements under the influence of idealized scaled precipitation, while signifies the Noah LSM simulated mean areal water cycle elements forced by observed precipitation following the calibration of the WRF-Hydro model.
The RE of total streamflow at the Xixian hydrological station in Experiment 1 and Experiment 2 (QRE) is expressed as
formula
(11)
where (similar to its representation in Equation (4)) denotes the simulated total streamflow at the Xixian hydrological station under the influence of idealized scaled precipitation. In contrast to in Equation (4), represents the simulated total streamflow at the Xixian hydrological station under the influence of observed precipitation. The observed streamflow data at the Xixian hydrological station was solely utilized in the calibration and validation of the WRF-Hydro model. To mitigate model uncertainties, the water cycle element values from the calibrated WRF-Hydro model (inclusive of the Noah LSM) output, influenced by observed precipitation data, were considered as the true values in both Experiments 1 and 2.

Brief introduction

The WRF-Hydro model incorporates inputs such as precipitation, solar radiation, and temperature, along with channel routing dynamics, to generate an estimation of surface runoff. It is comprised of several components, including the Noah LSM/Noah-MP LSM, grid aggregation/disaggregation, subsurface flow routing, surface overland flow routing, channel routing, lake and reservoir routing, and a conceptual base flow model.

Within the Noah LSM, a simple water balance model is employed to delineate canopy interception and water permeation in subsurface layers, utilizing the Richards Equation (Schaake et al. 1996). The Grid aggregation/disaggregation module calculates an aggregation factor, aiding the implementation of routing sub-grids. This module leverages input datasets from large-scale climate models and LSMs to investigate small-scale overland and subsurface flow processes in hydrological models. In addition, a quasi-three-dimensional flow model is utilized to compute lateral subsurface flow, considering topography, saturated soil depth, and saturated hydraulic conductivity. A conceptual bucket model estimates changes in water storage within subsurface layers.

When the depth of ponded water surpasses the retention depth due to excess infiltration, exfiltration from the saturated soil layer, and water exchange between grids, the excess water is directed as surface runoff. Overland flow routing is determined using a simplified version of the Saint-Venant equations for shallow water waves, known as the diffusive wave formulation. This formulation has proven effective for fine terrain scales between 30 and 300 m. In this study, an aggregation factor of 10 was utilized for routing overland flow with a 300 m resolution. The time step for terrain routing grids in both overland flow and subsurface routing is directly related to the grid resolution. To prevent numerical diffusion, the Courant number should be maintained close to 1.0, with implementation achieved by
formula
(12)
where c is the assumed wave speed or celerity, Δt is the time step and Δx is the grid resolution. Gochis et al. (2020) provided a suggested routing time steps table for various grid spacings, and an 18 s terrain routing grid time step was employed by matching the 300 m resolution.

Upon reaching the channel network, overland flow is subsequently routed as channel flow. WRF-Hydro provides an explicit, one-dimensional, variable time-stepping diffusive wave formulation for gridded channel routing. Unlike terrain routing grid time step, which depends on grid resolution, the channel routing time step requires calibration before all model parameters to ensure model stability.

Main parameters

To enhance calibration efficiency, numerous scale factor parameters were incorporated into the model. The WRF-Hydro model and Noah LSM adopted a division of four soil layers, spanning default depths of 0–0.1, 0.1–0.4, 0.4–1, and 1–2 m. Nevertheless, the WRF-Hydro model was limited to establishing a uniform soil layer depth scheme for the entire research area. Previous investigations utilized fixed soil layer depth schemes, such as 0–0.05, 0.05–0.2, 0.2–0.45, and 0.45–0.8 m, alongside default layer depths (Senatore et al. 2015; Liu et al. 2021). It is imperative to acknowledge that soil moisture in the model is predominantly influenced by subsurface depth, and the pre-established depths may not be suitable for small and medium basins. In response to this challenge, Sun et al. (2020) introduced the ZSOILFAC parameter as a scale factor, ranging from 0.1 to 1, to calibrate the four soil layer depths.

The REFKDT parameter within the WRF-Hydro model serves as a hydrological parameter signifying the proportion of surface runoff that infiltrates into the soil. This parameter plays a pivotal role in the model's water cycle simulation by influencing both the volume of water available for runoff and the quantity that infiltrates into the groundwater system. The calculation for the maximum infiltration rate () is expressed as follows:
formula
(13)
formula
(14)
formula
(15)
where Px denotes rainfall intensity post-canopy interception, δi is the conversion coefficient of the integral time step Δt, Db represents the total diffusivity across the four soil layers, θs is the soil saturated water content, θi is the soil water content at the ith soil layer, ΔZi is the thickness of the ith soil layer, Ks is the saturated soil hydraulic conductivity, Kref is set to 2 × 106m/s, and Kdtref (REFKDT in the WRF-Hydro model) is a coefficient with a default value of 3.0 (Wood et al. 1998). Calibration of REFKDT is recommended for basins exhibiting diverse precipitation climatology and runoff generation mechanisms (Chen & Dudhia 2001). In the Noah LSM, REFKDT functions as a tunable parameter crucial for determining the partitioning of surface runoff into surface and subsurface runoff. It possesses a nominal range of 0.5–5.0 (Mitchell 2005).
Subsurface runoff is delineated as gravitational free drainage originating from the bottom layer of the Noah LSM, as expressed by
formula
(16)
where represents the soil water content of the bottom layer, denotes the hydraulic conductivity, and is a slope index within the range of 0–1. In the WRF-Hydro model, the parameter is contingent upon soil types delineated by Zobler (1986). The scale factor of , SLOPEFAC, exerts influence on the rate of upper saturated residual water flow to the lower unsaturated soil layer and the distribution of runoff from the land surface to the subsurface. A higher SLOPEFAC value correlates with an increased drainage rate.

RETDEPRTFAC, within the framework of the WRF-Hydro model, pertains to the ‘retention depletion factor,’ denoting the proportion of water retained in the soil as ‘retention’ and consequently unavailable for infiltration into the groundwater or contribution to runoff. Initially, both RETDEPRT and retention depletion are assigned a default value of 0.001 mm. RETDEPRTFAC operates as a sub-sensitive parameter within the first-order group, exhibiting a permissible range from 1 to 10 (Ryu et al. 2017).

OVROUGHRTFAC, an abbreviation within the WRF-Hydro model, represents the overland roughness factor. This factor plays a crucial role in shaping the dynamics of water flow across the land surface and significantly influences the precision of simulation outcomes. The specific value of the overland roughness factor is contingent upon the prevailing land cover in the modeled area. Within the WRF-Hydro model, the overland roughness factor is instrumental in computing the overland flow resistance, thereby exerting influence on both the speed and direction of water movement across the land surface.

Manning's roughness coefficient for channels is a crucial factor employed in the computation of open channel flow within hydrological modeling. This coefficient characterizes the roughness of the channel's land surface. The channel roughness of the land surface plays a pivotal role in influencing water flow dynamics, and Manning's roughness is specifically incorporated in the WRF-Hydro model to accommodate this effect. MANNFAC, a factor parameter, is utilized to scale the Manning's roughness across various channel levels within the model.

The saturated soil lateral conductivity (LKSAT), alternatively referred to as horizontal hydraulic conductivity, stands as a pivotal parameter within hydrological modeling. This parameter signifies the soil's capacity for horizontal water flow. Within the WRF-Hydro model, LKSAT is employed to characterize the lateral movement of water across grid cells. It is essential to recognize that the spatial and temporal variability of the saturated soil lateral conductivity is contingent upon factors such as soil texture, structure, and saturation. We introduce the saturated soil lateral conductivity factor (LKSATFAC), a scale factor specifically designed to modulate the saturated soil lateral conductivity. This factor allows for adjustments that capture variations in the lateral movement of water, accounting for spatial and temporal fluctuations in soil properties.

The conceptual groundwater bucket model integrated into the WRF-Hydro framework is a simplified yet computationally efficient tool designed to estimate groundwater discharge into the river network. This model operates under the assumption of a steady-state groundwater system and does not account for the spatial and temporal variations within the groundwater system. The outflow from the bucket model comprises two components: spilled flow when the conceptual water depth exceeds the bucket capacity and exponential storage discharge, commonly referred to as ‘exponential bucket’. The mathematical expression for the exponential bucket formulation is presented as follows:
formula
(17)
where denotes the outflow from the exponential bucket, C represents a constant, signifies the conceptual water depth at dt, corresponds to the depth of the bucket, and is a nondimensional exponential parameter.

The parameters were systematically categorized into two distinct groups, following the methodology detailed by Yucel et al. (2015). The first group, exerting a primary influence on the overall streamflow, included REFKDT, RETDEPRTFAC, ZSOILFAC (Sun et al. 2020), and SLOPEFAC (Senatore et al. 2020). The second group, predominantly impacting the hydrograph's shape, encompassed parameters such as OVROUGHRTFAC, MANNFAC, LKSATFAC (Naabil et al. 2017), and GWEXP (Liu et al. 2021).

Calibration for the standalone WRF-Hydro model

To mitigate numerical dispersion and enhance the stability of the solution, the diffusive wave channel routing module within the WRF-Hydro model incorporates a variable time-stepping technique. As an initial step in the calibration process, a series of flood simulations were conducted across multiple time steps to identify an optimal time step that strikes a balance between model stability and computational efficiency. While a larger channel time step (Δt) has the potential to reduce simulation time, it also poses a risk of compromising model stability. Therefore, the selection of the maximum time step is contingent upon ensuring the stability of the model.

Gochis et al. (2020) outlined a methodology that involves initially employing a large time step and subsequently halving the previous time step until model stability is achieved. Subsequently, Δt of 15, 9, 4, and 1 s were systematically tested to evaluate model stability across 23 flood events. For example, Figure 2 illustrates the hydrograph of the 030721 flood in relation to the corresponding channel time steps.
Figure 2

The hydrographs of the flood of 030721 simulated with different channel gridding time step Δt in the WRF-Hydro model.

Figure 2

The hydrographs of the flood of 030721 simulated with different channel gridding time step Δt in the WRF-Hydro model.

Close modal

Figure 2 exhibits a distinct wave pattern during the flood recession process when employing a 15 s channel time step, while a flattening of the flood peak is observed at Δt = 9 s. However, hydrograph shapes demonstrate consistency when utilizing Δt = 4 and 1 s. The model demonstrates stable simulation of the majority of flood events when Δt = 9 s, yet for the specific event 030721, stability is not achieved until Δt = 4 s. All 23 flood events successfully passed the model stability test at Δt = 4 s. Consequently, the time step for channel routing calculations in the XXW has been established at 4 s.

Table 3 presents the specific calibration ranges and increments for the eight parameters, while the corresponding calibration and validation results are depicted in Figure 3 and Table 4. The recalibrated value of REFKDT was notably smaller than the default setting. Notably, similar findings have been reported in most studies focusing on China, with REFKDT values consistently falling below 3 (Sun et al. 2020; Liu et al. 2021). The parameter ZSOILFAC was calibrated to 0.4, signifying soil layer depths of 0–0.04, 0.04–0.16, 0.16–0.4, and 0.4–0.8 m. Notably, studies by Ryu et al. (2017) and Liu et al. (2021) indicated that RETDEPRTFAC exhibited lower sensitivity compared to other parameters primarily influencing runoff generation. In our study, the RETDEPRTFAC retained its default value, indicating a corresponding RETDEPRT value of 0.001 mm. The observed minimal adjustment of OVROUGHRTFAC after calibration may be attributed to the extensive cultivation of crops within the basin.
Table 3

Information of the calibrated parameters in the WRF-Hydro model

ParameterMainly calculated moduleUnitDefaultCalibration rangeCalibration incrementCalibration result
REFKDT Noah LSM Unitless 3.0 0.1–5.0 0.1 1.5 
RETDEPRTFAC Overland flow routing Unitless, mm for RETDEPRT 1.0, 0.001 for RETDEPRT 1.0–10.0 1.0 
SLOPEFAC Noah LSM Unitless 1.0 0.1–1.0 0.1 0.6 
ZSOILFAC Noah LSM Unitless, mm for ZSOIL 1.0 0.1–2.0 0.1 0.4 
OVROUGHRTFAC Overland flow routing Unitless, m/s1/3 for OVROUGHRT 1.0 0.1–2.0 0.1 0.2 
LKSATFAC Subsurface flow routing Unitless, m/s for LKSAT 1,000 1,000–10,000 1,000 10,000 
GWEXP Groundwater Bucket model Dimensionless 3.0 1.0–5.0 3.0 
MANNFAC Channel routing Unitless, m/s1/3 for Manning's roughness 1.0 0.1–2.0 1.1 
ParameterMainly calculated moduleUnitDefaultCalibration rangeCalibration incrementCalibration result
REFKDT Noah LSM Unitless 3.0 0.1–5.0 0.1 1.5 
RETDEPRTFAC Overland flow routing Unitless, mm for RETDEPRT 1.0, 0.001 for RETDEPRT 1.0–10.0 1.0 
SLOPEFAC Noah LSM Unitless 1.0 0.1–1.0 0.1 0.6 
ZSOILFAC Noah LSM Unitless, mm for ZSOIL 1.0 0.1–2.0 0.1 0.4 
OVROUGHRTFAC Overland flow routing Unitless, m/s1/3 for OVROUGHRT 1.0 0.1–2.0 0.1 0.2 
LKSATFAC Subsurface flow routing Unitless, m/s for LKSAT 1,000 1,000–10,000 1,000 10,000 
GWEXP Groundwater Bucket model Dimensionless 3.0 1.0–5.0 3.0 
MANNFAC Channel routing Unitless, m/s1/3 for Manning's roughness 1.0 0.1–2.0 1.1 
Table 4

Total calibration and validation results in the WRF-Hydro model

EPR for total streamflow (%)EPR for peak flow rate (%)Mean absolute Mean absolute Mean NSE
Calibration 94.44 83.33 0.118 0.1524 0.79 
Validation 80 80 0.1504 0.1831 0.76 
Total 91.3 82.61 0.125 0.159 0.78 
EPR for total streamflow (%)EPR for peak flow rate (%)Mean absolute Mean absolute Mean NSE
Calibration 94.44 83.33 0.118 0.1524 0.79 
Validation 80 80 0.1504 0.1831 0.76 
Total 91.3 82.61 0.125 0.159 0.78 
Figure 3

Calibration and validation results for the 23 flood events.

Figure 3

Calibration and validation results for the 23 flood events.

Close modal

Figure 3 illustrates the , , and NSE values for all 23 floods following the calibration process. In general, the total streamflow simulated by the WRF-Hydro model tends to be higher than the observed values. The majority of and values for the floods fall within the range of −0.2 to 0.2. Overall, the error in total streamflow is lower than the error in peak flow rate. In addition, there is a higher occurrence of floods with high absolute values exceeding 0.2 compared to those with high absolute values. The NSE values for all 23 flood simulations consistently surpass 0.5. The flood event on 030630 exhibited the lowest absolute , while the flood event on 140928 achieved the lowest absolute and the highest NSE. Notably, both the absolute and absolute exceeded 0.2 for the flood events on 090928 and 160719. Conversely, the flood events on 070714 and 140829 had absolute values surpassing 0.2, while the absolute values remained below 0.2.

The performance of the WRF-Hydro model applied to our research basin is satisfactory, particularly in the representation of total streamflow. Both the EPRs of total streamflow and peak flow rate during the calibration phase were consistently higher than those during the validation phase, as indicated in Table 4. While the mean NSE for total streamflow, both in calibration and validation, exceeded 0.7 on average, it remained below 0.8. Notably, neither the EPR for total streamflow nor the peak discharge fell below 85% during validation. Despite these favorable aspects, the performance of the WRF-Hydro model in the XXW is not deemed excellent. This may be attributed to the lower resolution of geographic data in plain areas and the inherent uncertainty associated with meteorological forcing data. Considering these uncertainties, coupled with the model's intrinsic variability, we proceed under the assumption that the calibrated results reflect reality, with precipitation being the sole variable considered in subsequent idealized experiments.

Changing precipitation influenced flood processes in the WRF-Hydro model

This study undertakes a comprehensive analysis of 23 flood events calibrated and validated using the WRF-Hydro model. Specifically, our investigation centers on the total mean areal precipitation associated with single-peak hydrographs, ranging between approximately 50 and 160 mm. Among these events, the flood of 050903 exhibits the smallest total mean areal precipitation at 49.4 mm, while the flood of 170709 records the highest at 163.45 mm. To facilitate a comparative assessment, we strategically selected flood processes with absolute and absolute both smaller than 0.2. These floods represent a spectrum of precipitation magnitudes within the 50–160 mm range.

In addition, our study considers the influence of last time and total precipitation on flood characteristics. To discern the impact of short-time heavy precipitation versus long-time weak precipitation, we identified two flood events with comparable total precipitation but distinct last times. The criterion for distinguishing between long and short duration precipitation events is whether rainfall persists for more than 3 days. Notably, the flood event of 030630 features the largest total precipitation and an extended duration, while the flood event of 140928 exhibits the smallest total precipitation and a brief duration. Furthermore, we compared the floods of 030721 and 140928, which share similar total rainfall amounts but differ significantly in duration, with the former being of long duration and the latter of short duration. The four flood events in the idealized experiments and their characteristics are presented in Table 5. Short-time rainfall process with a ‘Large’ level total precipitation does not exist in the 23 flood events, while small flood events with long-time duration and ‘Small’ level total precipitation are not considered in our study.

Table 5

Rainfall characteristics of the four typical flood events

No.Rainfall last timeTotal precipitation
030630 Long Large 
030721 Short Middle 
140928 Short Small 
171002 Long Middle 
No.Rainfall last timeTotal precipitation
030630 Long Large 
030721 Short Middle 
140928 Short Small 
171002 Long Middle 

The hydrographs illustrating the dynamic interactions of four distinct flood events are presented in Figure 4. Within this figure, the variable P denotes the hourly mean areal precipitation, while Qreal and Qsim represent the observed and WRF-Hydro model-simulated streamflow at the Xixian hydrological station. A notable trend emerges from the comparative analysis of peak discharge values between observed and simulated data. The WRF-Hydro model consistently underestimates peak discharge in the floods of 030721 and 140928. In contrast, the model tends to overestimate peak discharge in the floods of 030630 and 171002. A unique observation is evident in the flood of 030721, where the modeled total streamflow consistently lags behind the observed total streamflow. Furthermore, an overarching principle is discerned regarding the relationship between total rainfall and flood peak flow rate. In general, flood peak flow rate aligns with the principle that a greater total rainfall corresponds to a higher flood peak flow. This principle is substantiated by the observed peak discharge values across the analyzed events. An intriguing anomaly is noted in the flood of 030721, where the peak discharge significantly surpasses that of the flood of 171002. This anomaly is attributed to the heightened rain intensity during the 030721 event, thereby contributing to the observed disparity in peak discharge values between these two floods.
Figure 4

Hydrographs for the four flood events and mean areal precipitation corresponding to the flood processes.

Figure 4

Hydrographs for the four flood events and mean areal precipitation corresponding to the flood processes.

Close modal
In Experiment 1, the relationship between precipitation and the simulated runoff depth driven by WRF-Hydro during four flood events is depicted in Figure 5. The red dashed line in the figure represents the standard line with a slope of 1, while the intersection points of the gray dashed line correspond to actual precipitation amounts and the simulated runoff depths driven by WRF-Hydro. The blue dashed line corresponds to the scaled experimental precipitation and the simulated runoff depth driven by WRF-Hydro. According to the runoff generation mechanism, even with different total rainfall amounts, the trend of runoff depth variation with rainfall is remarkably similar, increasing with increasing rainfall and decreasing with decreasing rainfall.
Figure 5

Relationships between mean areal precipitation and runoff depth forced by the scaled precipitation in the WRF-Hydro model.

Figure 5

Relationships between mean areal precipitation and runoff depth forced by the scaled precipitation in the WRF-Hydro model.

Close modal

Under increasing precipitation, the rate of increase in runoff depth gradually decreases, approaching the rate of precipitation increase. Conversely, as the driving precipitation decreases, the change in soil water formed by precipitation increases, and the runoff depth generated by precipitation decreases. In all four flood events, the slopes of the runoff depth-precipitation curves are consistently less than 1 and diminish progressively as ideal precipitation decreases. However, this trend is manifested differently in the relationship between QRE and RE of the mean areal precipitation (PRE).

The interrelationships between PRE and QRE for the four flood events are visually represented in Figure 6. Notably, the cumulative RE of total flood volume demonstrated a steeper increase compared to that of precipitation. The trends of PRE and QRE exhibit similarities across the four flood events, although the magnitudes of their respective increments differ. As precipitation increases, QRE experiences an accelerated rise. Conversely, in instances of decreasing precipitation, QRE demonstrates a slower decline, and the slope of QRE reduction suggests a downward trend. This implies that as precipitation decreases, the rate of QRE reduction diminishes gradually. Analyzing the QRE slopes in relation to PRE reveals nuanced patterns. The comparison of the QRE trends across the four events indicates that the flood of 030630 exhibits the most pronounced increasing slope, followed sequentially by the floods of 030721, 140928, and 171002. During 030630 and 030721 floods, precipitation absolute REs increased by 50%, while runoff absolute REs increased by more than 60%. In addition, a comparative analysis between the floods of 030721 and 171002 indicates that short-term heavy rainfall processes exert a more significant influence on total streamflow. This observation underscores the impact of precipitation intensity and duration on the sensitivity of QRE, providing valuable insights into the dynamics of these flood events. Different evaluation metrics exhibit varying trends in characterizing the relationship between streamflow and precipitation. As precipitation increases, the rate of increase in runoff depth slows down, eventually converging to the rate of precipitation increase. Simultaneously, the QRE rate increases with the rate of precipitation. Conversely, when precipitation decreases, the rate of decrease in runoff depth and the rate of decrease in RE both gradually diminish. The high sensitivity of QRE to PRE may be primarily attributed to variations in the proportion of water elements generated by precipitation and the calculation method of RE.
Figure 6

The relationships between QRE and PRE in Experiment 1.

Figure 6

The relationships between QRE and PRE in Experiment 1.

Close modal
To delve into the sensitivity of total streamflow errors, modeled by the WRF-Hydro model, to precipitation errors, we conducted a detailed analysis of key hydrological components influencing runoff calculations. These components, output by the Noah LSM, were compared and extracted for further examination. The water balance equation for a basin, considering precipitation (P), runoff (R), evapotranspiration (E), and changes in soil moisture (ΔW), is expressed as:
formula
(18)
To gain a comprehensive understanding of the water cycle elements' proportions in the idealized experiment, we examined the AE of mean areal runoff, evapotranspiration, and changes in soil moisture (ΔW), expressed as RAE, EAE, and WAE, respectively, with changing PRE for the four flood events (Figure 7). The evapotranspiration calculation module includes the calculation modules of the direct evaporation from the top shallow soil layer, evaporation of precipitation intercepted by the canopy, and transpiration via canopy and roots in the Noah LSM, based on a Penman-based energy balance approach that includes a stability-dependent aerodynamic resistance (Mahrt & Ek 1984) and a canopy resistance, which could be calculated with saturation-specific humidity, surface air temperature, and surface pressure (Chen & Dudhia 2001). The negligible EAE change in evapotranspiration may be attributed to the influence of forcing data in the Noah LSM, which remained relatively constant throughout the idealized experiment.
Figure 7

Changes in the proportion of AEs in runoff depth (R), evapotranspiration (E), and soil moisture variation (ΔW) within the scaled precipitation AE for the four typical flood events in Experiment 1.

Figure 7

Changes in the proportion of AEs in runoff depth (R), evapotranspiration (E), and soil moisture variation (ΔW) within the scaled precipitation AE for the four typical flood events in Experiment 1.

Close modal

The proportions of RAE and WAE were labeled in blue and orange, respectively. EAE proportions were not labeled due to their consistently low values. Notably, RAE dominated across all events, with RAE proportions in the flood of 140928 being consistently lower than the other three events, possibly due to its lower total precipitation. The flood of 030721 exhibited slightly higher RAE proportions compared to the event of 171002. In events with similar total rainfall, the sensitivity of RAE to PRE was more pronounced in short-time heavy rainfall processes.

Therefore, the main reason for the difference between the relationships of QRE and PRE compared to the relationship between runoff depth and precipitation lies in the fact that, as precipitation increases, the change in soil water caused by precipitation gradually increases but at a decreasing rate. When precipitation reaches a certain level, the change in soil water caused by precipitation no longer increases with increasing rainfall. At this point, the error in precipitation is entirely transformed into an error in runoff depth. Thus, under the condition of the same AE, QRE must be higher than PRE. The difference between QRE and PRE also becomes increasingly significant as the precipitation increases. Conversely, when rainfall decreases, the error in the decrease in precipitation leads to an increasing change in soil water, resulting in a gradual reduction in runoff depth. When precipitation is very low, the error may even be entirely retained in the soil. This situation, particularly in the context of flood events in humid areas and extreme precipitation scaling in experimental design, is not extensively discussed in this paper.

Sensitivity of flood processes to rainfall levels

The 12-h accumulated mean areal precipitation for four flood events is illustrated in Figure 8, with rainfall levels classified according to Table 2. The no-rain level, characterized by precipitation lower than 0.1 mm, was excluded from discussion to maintain a focus on flood events with substantial precipitation. Rainfall levels, including light rain, moderate rain, heavy rain, rainstorm, and heavy rainstorm, were analyzed for peaks below 80 mm, excluding torrential rainstorms.
Figure 8

12-h accumulated mean areal precipitation temporal distribution in the four flood events.

Figure 8

12-h accumulated mean areal precipitation temporal distribution in the four flood events.

Close modal

Figure 8 displays the temporal distribution of 12-h accumulated precipitation in the four flood events. Notably, heavy rainstorms occurred on 29 June 2003 (the 030630 flood) and 20 July 2003 (the 030721 flood), with peaks of 54.6 and 66.8 mm, respectively. Rainstorm levels were observed in three events, excluding the flood of 171002. Despite the total precipitation not being the lowest, the 171002 flood is discussed primarily in terms of light rain, moderate rain, and heavy rain. Temporally, the earliest and latest precipitation peaks were observed in the floods of 030630 and 171002, while the 030721 and 140928 events exhibited peaks in the middle of the rainfall processes. Total precipitation temporal distribution indicated similar trends for the floods of 030630, 030721, and 140928, with more rainfall distributed in the front of the process. In contrast, the flood of 171002 demonstrated more rainfall in the bottom half of the process. A comparison with Figures 4 and 8 revealed a correlation between the earlier precipitation peak in the rainfall process and the earlier flow rate peak in the corresponding flood event.

Utilizing the scaled precipitation method, Experiment 2 was conducted to assess the impact of PRE on flood events. The relationships between QRE forced by the newly scaled precipitation values at various rainfall levels and PRE are depicted in Figure 9. The PRE corresponding to QRE was renewed once due to the rate error in the process of precipitation scaling conversion.
Figure 9

Relationships between QRE and PRE with the misestimate precipitation at the different rainfall levels forcing.

Figure 9

Relationships between QRE and PRE with the misestimate precipitation at the different rainfall levels forcing.

Close modal

In general, QRE trends indicated an increase with positive PRE and a decrease with negative PRE, with varying rates. Higher positive PRE led to QRE increasing rates exceeding 1, emphasizing the sensitivity of QRE to PRE. Conversely, QRE exhibited a slower decrease with negative PRE due to the limitations of low precipitation levels to accommodate extremely low PRE. Sensitivity analysis revealed that the events of 030630 and 140928 were more sensitive to PRE than the floods of 030721 and 171002, with QRE forced by precipitation with errors at light and moderate rain levels exhibiting lower sensitivity compared to QRE forced by precipitation with errors at heavy rain, rainstorm, and heavy rainstorm rainfall levels. In general, sensitivities of QRE to PRE at high rainfall levels were not obviously increased with rainfall level rises. This suggests that total streamflow forecasts should prioritize accurate precipitation forecasting for high rainfall levels. In most cases, misestimation of precipitation tends to amplify the misestimation of runoff, especially for high rainfall levels, which makes the error in streamflow simulation more pronounced. Therefore, in regions with sparse distribution of rain gauges, the difficulty of flood forecasting increases. Exploring more accurate gridded precipitation data can reduce errors in hydrological simulations (Araghi et al. 2021).

A pivotal factor influencing the relationship between QRE and PRE is the variation in proportions of water cycle elements with PRE. Analogous to Figure 5, the red dashed line in Figure 10 represents the standard line with a slope of 1, and the intersection of the gray dashed lines corresponds to the observed total rainfall and its simulated runoff depth. Under conditions where evapotranspiration remains nearly constant, with the same total rainfall error, the change in soil moisture caused by ideal precipitation with a large deviation in high-level rainfall is lower than that caused by ideal precipitation with a large deviation in low-level rainfall. However, the runoff depth generated by ideal precipitation with a large deviation in high-level rainfall is high, a trend consistently observed in all four flood experiments. During a flood event, the change in soil moisture caused by ideal precipitation with a large deviation in high-level rainfall is more likely to reach saturation. When precipitation decreases, the runoff depth formed by ideal precipitation with a large deviation in high-level rainfall is smaller than that formed by ideal precipitation with a large deviation in low-intensity rainfall, but the change in soil moisture is greater. Deviations in the slope of runoff depth simulated by the idealized precipitation with the same errors at different rainfall levels are more pronounced in the 030630 and 140928 events, while the differences in slopes for the other two events are relatively small. In the 030721 event, the change in runoff depth increasing rates for ideal precipitation with same errors at different rainfall levels is minimal, as reflected in Figure 5, where the sensitivity of QRE to PRE under ideal precipitation with errors distributed at various rainfall levels is also very similar.
Figure 10

Relationships between runoff depth forced by the graded idealized rainfalls in Experiment 2 and mean areal precipitation.

Figure 10

Relationships between runoff depth forced by the graded idealized rainfalls in Experiment 2 and mean areal precipitation.

Close modal

This study investigates the sensitivity of flood runoff to precipitation in the flood-prone region of Eastern China, focusing on the XXW within the Upper HRB. Utilizing the WRF-Hydro model, we establish relationships between precipitation and water cycle elements, employing related or AEs as metrics for sensitivity evaluation. Through systematic parameter calibration, we ensure the model's applicability, followed by two idealized experiments to explore the impact of precipitation errors on total streamflow errors.

Parameters in the WRF-Hydro model were calibrated by GLDAS datasets and observed flow rate data at the Xixian hydrological station of 23 flood events in a flooding basin, Eastern China. Higher terrain slope and land cover character were important factors that cause the parameters in the XXW to be different from those applied to other plain regions. In the calibration process of the standalone WRF-Hydro model, a channel time step of 4 s was established as optimal for the XXW basin through systematic testing. Eight parameters were calibrated, and the values, particularly for REFKDT, were notably smaller than default settings. The model's performance was satisfactory, with EPR values consistently surpassing 0.8. The WRF-Hydro model demonstrates satisfactory representation of total streamflow, with notable underestimation of peak discharge in specific flood events.

In Experiment 1, we analyze the relationship between QRE and PRE, revealing similar trends but different sensitivities with the relationship between runoff depth and precipitation. The study delves into the sensitivity of total streamflow errors to precipitation errors, identifying nuanced patterns influenced by precipitation intensity and duration. In the process of flood with large streamflow, the absolute QRE is higher than the absolute PRE. This conclusion is applicable when the absolute PRE is not higher than 0.5. Furthermore, we explore the impact of different rainfall levels on flood processes. Comparative assessments of floods with similar total precipitation but varying durations highlight the influence of short-time heavy precipitation versus long-time weak precipitation. The study emphasizes the significance of precipitation forecasting accuracy for high rainfall levels in total streamflow predictions.

In Experiment 2, the sensitivities of total streamflow errors to precipitation errors at different rain levels are analyzed in detail, revealing varying rates of increase and decrease in QRE with positive and negative PRE. It is noteworthy that the impact of overestimating or underestimating precipitation on the formation of QRE is more sensitive at high rainfall levels than when inaccuracies occur at lower rainfall levels in predicting runoff. On lower rainfall levels, the likelihood of meeting the criteria for flood simulation qualification is higher when there are inaccuracies in estimating precipitation to form QRE. Therefore, enhancing the accuracy of precipitation forecasts at high rainfall levels emerges as particularly crucial.

In summary, the calibrated WRF-Hydro model demonstrated satisfactory performance in simulating flood events in the XXW. The analysis of precipitation sensitivity provided valuable insights into the dynamics of flood processes, emphasizing the need for accurate precipitation data, especially in high rainfall events. Furthermore, we would focus on more real precipitation forcing such as modeled precipitation with physical mechanism concerning precipitation distribution. More metrics of precipitation forecast evaluation will also be taken into account in future research.

This research was funded by the Natural Science Foundation of China (52379007; 42371045) and the Major Scientific and Technological Projects of Ministry of Water Resources of China (SKR-2022032).

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

The authors declare there is no conflict.

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