Assessment of the Impact of Spatial Variability on Streamflow Predictions Using High-Resolution Modeling and Parameter Estimation: Case Study of Geumho River Catchment, South Korea

Abstract

In this study, we analyzed the impact of model spatial resolution on streamflow predictions, focusing on high-resolution scenarios (<1 km) and flooding conditions at catchment scale. Simulation experiments were implemented for the Geumho River catchment in South Korea using Weather Research and the Forecasting Hydrological Modeling System (WRF-Hydro) with spatial resolutions of 100 m, 250 m, and 500 m. For the estimation of parameters, an automatic calibration tool based on the Model-Independent Parameter Estimation and Uncertainty Analysis (PEST) method was utilized. We assessed the hydrological predictions across different spatial resolutions considering calibrated parameters, calibration runtime, and accuracy of streamflow before and after calibration. For both Rainfall Events 1 and 2, significant improvements were observed after event-specific calibration in all resolutions. Particularly for 250 m resolution, NSE values of 0.8 or higher were demonstrated at lower gauging locations. Also, at a 250 m resolution, the changes in the calibrated parameter values ($REFKDT$) were minimized between Rainfall Events 1 and 2, implicating more effective calibration compared to the other resolutions. At resolutions of 100 m and 500 m, the optimal parameter values for the two events were distinctively different while more computational resources were required for calibration in Event 2 with drier antecedent conditions.

1. Introduction

Hydrological models are simplified representations of real-world hydrological processes with different levels of approximation, and a wide range of such models have been developed and implemented to improve understanding of these processes and to provide better support for making decisions. Among the various models with different spatial abstractions, distributed hydrological modeling has been gaining increased attention in various fields, including streamflow and drought forecasting, climate and land-use change assessment, and water resources management, due to its ability to handle spatial variations of hydrological variables based on the rapidly increasing spatial information. Some recent studies reported that the performance of distributed hydrological modeling could be improved through the use of high-resolution input (Maxwell et al. [1], Abbazadeh et al. [2]). For instance, Maxwell et al. [1] simulated surface and subsurface flows at a high spatial resolution (1 km) in illustrating the feasibility of continental-scale integrated modeling for enhancing our understanding of large-scale hydrological systems. In addition, Abbazadeh et al. [2] investigated the impact of soil moisture on streamflow prediction in the Houston catchment area in Texas, USA at varying spatial resolutions. Their simulation results indicated the improved streamflow with a finer spatial resolution of 1 km compared to coarser resolutions such as 36 km.

Regardless of the degree of input spatial detail, however, hydrological models inherently contain various uncertainties stemming from the parameters, model structure, input data, and initial and boundary conditions (Moges et al. [3]). Calibration and uncertainty estimation techniques, once developed for lumped models with simple model structures, have been modified and employed to reduce gaps between distributed modeling and reality. Chen et al. [4] proposed optimal parameters for a Physically Based Distributed Hydrological Model (PBDHM) using the Particle Swarm Optimization (PSO) technique in the southern region of China. Verri et al. [5] used the Weather Research and Forecasting Hydrological Modeling System (WRF-Hydro) model to reduce uncertainties, analyzing parameter sensitivity and developing an interpolation method for mitigating rainfall uncertainties. Tolson et al. [6] analyzed the sensitivity of model equations and the Nash–Sutcliffe coefficient of efficiency for daily flows in relation to parameters using the Soil and Water Assessment Tool (SWAT 2000) model. Setegn et al. [7] applied the SWAT model in flow analysis of the Tana Lake catchment in Ethiopia, implementing parameter estimation using the SUFI-2, GLUE, and ParaSol algorithms.

The WRF-Hydro adopted in this study is a distributed hydrological model developed by the U.S. National Center for Atmospheric Research (NCAR) that consists of land surface model, terrain routing, river, and reservoir components. This model offers flexible coupling between its components and has been used for diverse applications in various research studies. Most of the research using WRF-Hydro can be categorized into analyses of its integration with the Weather Research and Forecasting (WRF) atmospheric model and proposals for model improvements, including advances achieved through artificial intelligence (AI) and post-processing research. Examples of research on utilizing the integration between WRF and WRF-Hydro include a study by Senatore et al. [8] in which observations with simulations from standalone WRF and combined WRF/WRF-Hydro models were compared at Land Surface Model (LSM) 2.5 km-Routing 250 m resolution in the Crati river catchment in southern Italy. In their study, Naabil et al. [9] demonstrated the improved performance of the WRF/WRF-Hydro coupled model over standalone WRF in rainfall estimation for the Tono catchment. Moreover, Wang et al. [10] evaluated the simulated results of the WRF standalone model and the coupled WRF/WRF-Hydro model as hydrological elements for six different 24 h storm events with varying spatiotemporal homogeneity in rainfall distribution. Lee et al. [11] applied standalone WRF-Hydro to assess drought characteristics in South Korea. Several studies suggest that use of a hybrid model combining Long Short-Term Memory (LSTM) and the WRF-Hydro model enhances the accuracy of streamflow predictions. Cho et al. [12] proposed a hybrid model that combines LSTM and the WRF-Hydro model for improved streamflow prediction. They demonstrated that the predictive capabilities were enhanced using the proposed approach and various targeted model sensitivity analyses. Liu et al. [13] applied four traditional statistical post-processing methods based on Quantile Mapping (QM) and two proposed machine learning methods (SVR, CNN) to a distributed model (WRF-Hydro), aiming to reduce systematic biases in streamflow simulation. Zhang et al. [14] evaluated the impact of soil infiltration processes on simulation by calibrating the WRF-Hydro model using the Dynamically Dimensioned Search (DDS) technique and analyzing the importance of infiltration effects in urban areas. These studies collectively contribute to understanding the uncertainties within distributed hydrological models and their calibration, enabling more accurate interpretations of hydrological responses. Kim et al. [15] investigated the impact of the modeling resolution of WRF-Hydro on the land surface and streamflow in the built environment of Dallas–Fort Worth area, USA. Their findings showed that by increasing the spatial resolution from 100 m to 10 m in surface flow and river routing models, the duration of simulation was extended by over 100 times. As simulation time increased, a corresponding increase in the calibration time of automatic parameter estimation techniques became evident. Therefore, achieving higher accuracy through high-resolution input data requires additional computational resources for both simulation and calibration.

The Model-Independent Parameter Estimation (PEST) method applied in this study is a nonlinear parameter optimization technique that operates independently of the model itself. It requires only the preparation of necessary files for PEST without the need for additional programs. As an example of applying the PEST method to a hydrological model, Abbas et al. [16] applied the SWAT+ model and PEST based on the gwflow module combined with the Morris screening method to evaluate the effect of parameters on streamflow and groundwater head prediction. de Wit et al. [17] presented a dynamic modeling approach with combined SWAP and PEST to simulate groundwater levels and soil moisture. As some examples of the applications of PEST to WRF-Hydro modeling, Fersch et al. [18] implemented parameter optimization for six parameters of the WRF-Hydro across six sub-catchments utilizing PEST. Sofokleous et al. [19] investigated the influence of WRF-Hydro model parameters of soil moisture, groundwater, and vegetation on hydrological balance, employing grid-based calibration methods within PEST to mitigate overestimation and validate its applicability. Furthermore, Wang et al. [20] implemented PEST in a parallelized fashion for High-Performance Computing (HPC), integrating its functionality alongside WRF-Hydro, and assessed the suitability and computational advantages of parallel PEST techniques in a 2013 flooding case study in the Midwestern United States.

The main objective of this investigation is to evaluate the influence of model spatial resolution on parameter estimation in distributed hydrological modeling. To achieve this, we utilize WRF-Hydro models with model spatial resolutions of 100 m, 250 m, and 500 m for the Geumho River catchment, a medium-sized catchment in South Korea. First, we assess the impact of spatial resolution on the hydrological processes under the same default parameter conditions. Then, we evaluate how various resolutions of model impact parameter estimation using the PEST technique, taking into account streamflow prediction results and computational time. In addition, we investigate how the adjusted model affects the prediction results of streamflow at multiple observation gauges within the catchment. The paper is organized as follows: Section 2 describes the materials and methods in detail, including the study area, data, model configurations, simulations, and calibrations; the results with discussions are presented in Section 3; Section 4 presents the conclusions and directions for future research.

2. Materials and Methods

2.1. Study Area and Data

The study area is the Geumho River catchment (area: 2087.9 km²; river length: 69.3 km). Within the catchment, the Geumho River traverses Daegu Metropolitan City, the fourth largest city in South Korea in terms of population, and merges into the mainstream of the Nakdong River (Figure 1). There are multiple dam reservoirs in the study catchment, including the Yeongcheon Dam (235 km²), whose artificial controls are not explicitly considered in the hydrological simulation. Land use in the Geumho River catchment comprises 66.4% forested land and 28.8% agricultural land. The average annual temperature is at 13 °C with an annual rainfall of 1007 mm, less than the average annual precipitation of 1306.3 mm in South Korea where about 56% of the precipitation is concentrated during summer.

There are a total of 11 ground weather observation gauges within the Geumho River catchment, including 9 Automatic Weather Stations (AWS) and 2 Automated Synoptic Observing Systems (ASOS). The Inverse Distance Weighted (IDW) method was employed to build meteorological forcing data of WRF-Hydro with eight components (i.e., incoming shortwave radiation, incoming longwave radiation, specific humidity, air temperature, surface pressure, near-surface wind in the u- and v-components, and liquid water precipitation rate). IDW is one of the most widely selected techniques for interpolating spatial data in estimating the value of a point without data using the value of a point with data. The reciprocal of the distance between points is used as a weight to allow the values of closer points greater influence. The two selected events (

Table 1. Two selected Rainfall Events for simulation with warm-up periods to minimize the impact of initial conditions.

Rainfall Event	Warm-Up Period	Simulation Period
Event 1	1 July–5 August 2020	5–13 August 2020
Event 2	1 July–1 August 2022	1–9 September 2022

) are flood events, each with distinct characteristics. The rainfall event in 2020, referred to as Rainfall Event 1, was a concentrated heavy rainfall event characterized by antecedent rainfall before the event. In contrast, in the year 2022, during Rainfall Event 2, dry conditions were experienced from the beginning of the year until the event, with minimal antecedent rainfall. This event was triggered by the sudden landfall of Typhoon Hinnamnor, which led to heavy rainfall.

The Digital Elevation Model (DEM) data with resolutions of 100 m, 250 m, and 500 m were built based on the National Aeronautics and Space Administration (NASA) Shuttle Radar Topography Mission (SRTM) 1-Arc second dataset through resampling.

Table 2. Comparison of grid numbers by resolution, including details on the number of model input data grids determined by resolutions of 100 m, 250 m, and 500 m for comparison in this study.

Resolution	No. LSM Grids	No. Routing Grids	No. Channel Grids
100 m	459,441 (639 × 719)	459,441	9804
250 m	72,865 (247 × 295)	72,865	1484
500 m	18,081 (123 × 147)	18,081	378

provides detailed information regarding spatial dimensions, with varying resolution. We generated land cover and soil data in a WRF binary format by resampling based on datasets from the Ministry of Environment and the National Institute of Agricultural Sciences in Korea and according to United States Geological Survey (USGS) standards (Figure 2).

2.2. Methodology

2.2.1. WRF-Hydro

In this study, we used WRF-Hydro version 5.2 in conjunction with Noah-Multiparameterization (Noah-MP) (Niu et al. [21]) LSM model. The employed WRF-Hydro model (Figure 3) integrates atmospheric and hydrological processes, comprising LSM, hydrological, and separate-aggregate modules. Among various LSM models available within the current WRF-Hydro framework, Noah-MP LSM has an advantage over Noah LSM in replicating surface flux, surface temperature during dry periods, snow characteristics (snow water equivalent and depths), and runoff (Niu et al. [21]). The Noah-MP LSM operates as a spatially distributed 1D model based on four soil layers, addressing surface and subsurface flow paths vertically with respect to meteorological forcing. The ranges of soil depth configuration are 0–0.1 m, 0.1–0.4 m, 0.4–1 m, and 1–2 m. Both LSM resolution and hydrological routing resolution were consistently set at 100 m, 250 m, and 500 m. For instance, if the LSM resolution is 100 m, hydrological routing (i.e., overland flow and channel routing) also operates at 100 m resolution. The spatial resolution characteristics in the WRF-Hydro simulation experimental setup can be summarized in terms of the following: number of the grid (Table 2), channel grid (Figure 4), and streamflow order. Figure 5 is the distribution of streamflow order according to spatial resolution. The streamflow order in WRF-Hydro comprises parameters such as roughness coefficients and width, corresponding to orders from 1st to 10th. However, no channels higher than the 5th order have been generated in the medium-sized Geumho River catchment.

Hydrological modules enhance the descriptions of the infiltration excess process of Noah-MP and the lateral movement in saturated subsurface processes. Overland routing, subsurface flow, baseflow, and channel routing are incorporated. The methods for channel routing include vector-based routing such as Muskingum and Muskingum–Cunge, as well as grid-based routing based on diffusive wave approximation. Of these methods, the explicit, one-dimensional, variable time-stepping diffusive wave (Downer et al. [23]) was employed for the gridded channel network in this study. The equations for the variable time-stepping diffusive wave are as follows:

$$\frac{\partial A}{\partial t}+\frac{\partial Q}{\partial x}=q_{\mathrm{l}}$$

(1)

$$-\frac{\partial h}{\partial x}+S_{\mathrm{o}}=S_{\mathrm{f}}={\left(\frac{nQ}{A{R}^{2/3}}\right)}^2$$

(2)

where A denotes the wetted channel cross-sectional area, Q denotes the flow rate, $q_{\mathrm{l}}$ denotes the lateral inflow, h denotes the water depth, $S_{\mathrm{o}}$ denotes the channel bed slope, n denotes the Manning’s roughness coefficient for the channel bed, and R denotes the hydraulic radius of the channel cross-section.

To maintain computational stability and prevent numerical dispersion, a 6 s time interval was chosen for the overland and channel routing, satisfying the Courant condition criteria for diffusive wave routing at resolutions of 100 m, 250 m, and 500 m. Both one-way (standalone) and fully coupled integration of WRF and WRF-Hydro are supported within the current WRF-Hydro modeling system. In this study, a standalone version of WRF-Hydro was configured actively considering overland flow, saturated subsurface flow, gridded channel routing, and conceptual baseflow while without the lake and reservoir modules.

We adopt the following approach to focus on integrating PEST and WRF-Hydro in analyzing the impact of spatial resolution on model calibration. The aim is to identify the most influential parameters and adjust them with multiplicative scaling factors across the entire catchment to maintain spatial variation and model relationships, as suggested by Gupta et al. [24]. As a result of the literature review, decay coefficient ‘k’ is identified as the most influential parameter in Equation (3) for infiltration capacity (Kim et al. [15]; Lee et al. [11]; Zhang et al. [14]; Tolson et al. [6]; Chen et al. [4]). Infiltration capacity ‘$I_c$’ in this equation is modeled as follows (Schaake et al. [25]):

$$I_c=D_x(1-e^{-kt})$$

(3)

where $D_x$ represents the maximum water-holding capacity of the soil column, k indicates the decay coefficient, and t denotes the elapsed time. Decay coefficient k is defined by the following equation:

$$k=(REFKDT\frac{DKSAT}{REFDK})·(\frac{DT}{REFDK})$$

(4)

where $DKSAT$ represents the saturated hydraulic conductivity, while $REFKDT$ and $REFDK$ stand for parameters related to surface streamflow (Gochis et al. [26]). $DT$ denotes the time step in seconds. Both $REFKDT$ and $REFDK$ are adjustable parameters. As the effect of adjusting $REFDK$ is equivalent to the effect of adjusting $REFKDT$ for parameter ‘k’, it is not necessity to calibrate both (Kim et al. [15]). As such, we calibrate only $REFKDT$ in this work. Regarding Equation (4), if $REFKDT$ increases or decreases, k increases or decreases. k influences infiltration capacity when the maximum water holding capacity, $D_x$, is given. Accordingly, $REFDK$ may be considered as controlling the streamflow. For PEST calibration of $REFKDT$, the default values are set at 3, with minimum and maximum values of $1\times {10}^{-3}$ and $1\times {10}^2$, respectively. All other parameters in the LSM are set to default values in WRF-Hydro (Gochis et al. [26]).

$REFKDT$ is calibrated based on simulations spanning 8 days for Rainfall Event 1 (from 5th to 13th, August 2020) and Rainfall Event 2 (from 1st to 9th, September 2022). Prior to PEST calibration, we manually adjusted groundwater bucket model parameters by comparing them with observed streamflow at the gauge of Gangchang during the warm-up periods for each rainfall event to calibrate the initial conditions.

Table 3. Manual calibration parameters and ranges. The groundwater bucket model equation is as follows: $Qexp=C(exp\left(E(Z/Z_{\max })\right)-1)$. As E increases, C increases, and as $Z_{\max }$ decreases, discharge increases.

Calibrated Parameter	Range
$Z_{\max }$	50–200
C	0.5–1.5
E	1–4

outlines the parameters and their ranges that were tested in an effort to match model conditions.

2.2.2. PEST

We adopted an automated calibration procedure based on PEST software version 17.5 (Doherty et al. [27]). This procedure minimizes the objective function, which is the sum of the mean squared differences between the modeled and observed streamflow, employing the Gauss–Marquardt–Levenberg nonlinear least squares method. We calibrated a single parameter using 8-day observation data and one observation gauge along with prior information items. For each prior information item, we assigned a value equal to the default value provided by WRF-Hydro v5.2 (or the logarithm of that default value) to the adjustable parameter, assuming that the default parameter set is preferred.

2.2.3. Assessment Index

In this study, simulated streamflow is assessed using two statistical assessment criteria: Root Mean Square Error (RMSE) and the Nash–Sutcliffe Efficiency (NSE; Nash et al. [28], Moriasi et al. [29]). RMSE is a measure of the difference between the model-predicted and actual observed values in which the square root of the average of squared differences between predicted and observed values is calculated in evaluating how close the model is to the observed data. The equation defining the variables for RMSE calculation is

$$RMSE=\sqrt{\frac{1}{n}{\displaystyle \sum _{t=0}^n}{(Y_{\mathrm{t}}^{\mathrm{obs}}-Y_{\mathrm{t}}^{\mathrm{sim}})}^2}$$

(5)

where n represents the total number of observed data points, $Y^{\mathrm{obs}}$ denotes the observed discharge values, and $Y^{\mathrm{sim}}$ indicates the WRF-Hydro simulated results.

NSE quantifies the accuracy of modeled discharge by comparison to the mean of observed data. The equation defining the variables for NSE calculation is

$$NSE=1-\frac{n{\sum }_{t=0}^n{(Y_{\mathrm{t}}^{\mathrm{obs}}-Y_{\mathrm{t}}^{\mathrm{sim}})}^2}{n{\sum }_{t=0}^n{(Y_{\mathrm{t}}^{\mathrm{obs}}-{\overline{Y}}_{\mathrm{mean}}^{\mathrm{obs}})}^2}$$

(6)

where ${\overline{Y}}_{\mathrm{mean}}^{\mathrm{obs}}$ is the mean observed discharge. The NSE values range from $-\infty$ to 1. The closer the NSE value is to 1, the higher the accuracy of the evaluated model, and the higher the degree of agreement between the model prediction and the observed data. An NSE value below 0 means that the model’s performance is worse than the prediction by an average of the observed data.

3. Results

3.1. Comparative Analysis of Streamflow Predictions with Varying Spatial Resolution

In the analysis of streamflow predictions using WRF-Hydro, the model spatial input data were generated at resolutions of 100 m, 250 m, and 500 m, and simulations were performed for two rainfall events in 2020 and 2022, utilizing default parameters in all cases. This section analyzed the results of no-calibration streamflow predictions, with emphasis on the outcomes based on model spatial resolution. Figure 6 shows a comparison of the simulated streamflow for Rainfall Event 1, from 5th to 13th, August 2020, at three different model spatial resolutions in comparison with the observation at two gauges: Gangchang (in the lowermost region of the Geumho River) and Ansim (in the mid-lower region of the same river). The black solid, green dashed, light blue dashed lines illustrate the observation and the simulations at 100 m and 250 m resolutions, respectively. In Figure 6, the hydrograph at 100 m resolution has a similar pattern to the observed hydrograph with a slightly overestimated peak flow. At resolutions of 250 m and 500 m, the simulated hydrographs are found to be underestimated in a magnitude of approximately half of the observed data. For Event 1, the observed peak flow at Gangchang (lowermost location) was 2305 m³/s. Simulated peak flows at resolutions of 100 m, 250 m, and 500 m were 2775.3 m³/s, 1042.2 m³/s, and 1214.2 m³/s, respectively. While the peak flow at 100 m resolution was higher than the observed value, it showed the smallest difference. This trend is also evident in terms of NSE for no calibration cases in Event 1 shown in

Table 4. Evaluation metrics before (no calibration) and after calibration (calibrated) by PEST across different grid resolutions.

Event	Forecast Gauges	Resolution	RMSE (m3/s)		NSE
			No Calibration	Calibrated	No Calibration	Calibrated
Event 1	Gangchang	100 m	147.9	135.5	0.868	0.889
		250 m	245.1	168.5	0.266	0.843
		500 m	250.4	134.7	0.476	0.872
	Ansim	100 m	124.6	109.9	0.791	0.841
		250 m	160.6	111.9	0.255	0.794
		500 m	169.1	89.5	0.524	0.906
	Geumchang	100 m	85.5	85.4	0.832	0.848
		250 m	118.5	106.0	0.277	0.644
		500 m	108.8	83.2	0.427	0.808
Event 2	Gangchang	100 m	113.6	43.7	0.058	0.938
		250 m	127.0	37.5	−0.187	0.972
		500 m	153.4	33.5	−0.322	0.971
	Ansim	100 m	100.3	60.2	−0.053	0.742
		250 m	111.1	44.7	−0.145	0.934
		500 m	129.0	38.6	−0.244	0.928
	Geumchang	100 m	75.8	38.4	−0.058	0.684
		250 m	74.9	29.8	−0.087	0.903
		500 m	82.2	26.3	−0.142	0.830

, with the highest NSE value of 0.868 at 100 m resolution. The Root Mean Square Error (RMSE) and NSE values of the no-calibration cases were lower for Rainfall Event 2 than for Event 1. It was presumably because Rainfall Event 2 was triggered by a sudden heavy rain event due to Typhoon Hinnamnor in the absence of preceding rainfall implicating different hydrological initial conditions from Event 1 which could be characterized as a typical torrential rainfall during a monsoon season. Nonetheless, among the three resolutions, 100 m resolution demonstrated the smallest associated errors in no-calibration cases for Event 2.

3.2. Impact of Scale-Specific Parameter Estimation on Streamflow Simulation

To analyze the impact of spatial resolution and model calibration, event-specific calibration was implemented for Rainfall Events 1 and 2 using streamflow data from the Gangchang station (downstream observatory) while those from the Ansim and Geumchang gauges were not included in the calibration process.

Table 4 presents the results from evaluation of streamflow predictions before and after model calibration, utilizing performance metrics such as RMSE and NSE for each grid resolution. For Rainfall Event 1, the resolution that yielded the smallest RMSE (m³/s) error was 500 m for Gangchang and Geumchang and 250 m for Ansim. For Gangchang, the error was significantly reduced from 250.4 to 134.7 at 500 m resolution. In terms of NSE, the best results were 100 m for Gangchang and Geumchang and 500 m for Ansim, with the greatest improvement of NSE from 0.266 to 0.843 for Gangchang at a resolution of 250 m. In particular, the calibration for 250 m resolution enhanced the performance in terms of the NSE with values higher than 0.9, improved by about twofold compared to no-calibration cases in all three locations (Gangchang, Ansim, and Geumchang). In the case of 500 m resolution, the NSE increased by 80 % compared to no-calibration cases. At 100 m spatial resolution, the NSE varied by less than 5 % after calibration due to superior streamflow simulations without calibration for Event 1.

In Rainfall Event 2, the spatial resolution with the smallest RMSE error for each point was 500 m for Gangchang, Ansim, and Geumchang. The error was significantly reduced from 153.4 to 33.5 for Gangchang. In terms of NSE, the best results were 250 m for Gangchang, Ansim, and Geumchang, with the greatest improvement of NSE from −0.322 to 0.971 for Gangchang at a resolution of 500 m.

Upon comparing the pre- and post-calibration results of the two rainfall events, Rainfall Event 2 exhibited significant improvements based on NSE and RMSE, as shown in Table 4. When calibration was implemented, significant enhancements were observed in the results for grid resolutions of 250 m and 500 m in comparison to the 100 m grid resolution for Event 2.

Figure 7 presents streamflow simulations with and without calibration across varying grid resolutions. Figure 7a,c,e correspond to Rainfall Event 1 while Figure 7b,d,f correspond to Rainfall Event 2. The black solid, red dashed, and purple dashed lines indicate the observations, no-calibration, and calibrated simulations, respectively. No-calibration cases were simulated using a default $REFKDT$ parameter value of three. For both Rainfall Events 1 and 2, calibrated streamflow simulations exhibit significant improvement compared to no-calibration ones.

In Figure 8, the analysis is focused on the results of streamflow prediction before and after calibration at Ansim and Geumchang during Rainfall Event 1. Figure 8a,c,e display WRF-Hydro streamflow simulations at various grid resolutions in Ansim, both before and after calibration by PEST. Similarly, Figure 8b,d,f illustrates WRF-Hydro simulations in Geumchang at multiple resolutions. Comparable patterns to those observed in Gangchang were identified at both the Ansim and Geumchang locations for resolutions of 100 m, 250 m, and 500 m.

As depicted in Figure 8a,b, 100 m resolution showed the most improved predictions in terms of peak flow after calibration. The calibrated results at 250 m resolution, as illustrated in Figure 8c,d, also demonstrated significant improvements in both the maximum peak flow and its timing. In contrast, a higher peak flow for the previous rainfall was observed in the calibrated results. In Figure 8e,f, representing 500 m resolution, enhancements in both peak and post-peak flows were observed, despite the high peak for the prediction of previous rainfall streamflow, such as at the Ansim gauge.

Table 5. Optimized PEST parameters and calibration runtimes on different resolutions. With the same parameters, the single model runtimes were approximately 263 ± 10 s for 100 m, 84 ± 10 s for 250 m, and 68 ± 10 s for 500 m, respectively.

ID		Resolution
		100 m	250 m	500 m
Event 1	$REFKDT$	1.283	0.203	0.555
	PEST Runtime (min)	216	71	54
Event 2	$REFKDT$	0.079	0.158	0.070
	PEST Runtime (min)	695	90	125

presents the calibrated parameters for the WRF-Hydro model, differentiated by spatial resolution, for Rainfall Events 1 and 2, along with calibration runtime. The runtime for PEST parameter calibration exhibited significant variation across different resolutions and rainfall events. Specifically, during Rainfall Event 2, which had considerably less preceding rainfall compared to Rainfall Event 1, calibration runtime for 100 m and 500 m resolutions more than doubled. There was no clear pattern between the resolution and the calibrated parameters. In Rainfall Event 2, the calibrated parameters of 100 m and 500 m differed by more than twofold compared to Rainfall Event 1. For 250 m resolution, there was no significant difference in the calibrated parameters between Rainfall Events 1 and 2 and only a small variation in calibration time. This implies that with default parameters set for 250 m resolution, both the computational time and the required adjustments to parameter values are minimal. This suggests there is an advantage in using a 250 m resolution for constructing new models.

Our findings show differences and similarities compared to previous spatial resolution studies. Kim et al. [15] reported that in the absence of parameter calibration, 250 m spatial resolution was a good choice in terms of performance and calculation requirements for both LSM and routing models. Meanwhile, in our case, without calibration, the streamflow predictions were the most accurate at 100 m resolution. However, in terms of calibration performance and calibration calculation requirements, the strong advantage of a 250 m spatial resolution was found, in line with the suggestions of Kim et al. [15]. In other studies, such as Abbazadeh et al. [2], streamflow prediction accuracy was reported to increase with finer resolution from 36 to 9 to 1 km. However, simulation experiments in this study revealed that the accuracy did not increase linearly when the resolution became finer than 1 km such as 100 m, 250 m, and 500 m. At 250 m resolution, both calibration runtime and changes in the calibrated parameter values were minimized.

4. Conclusions

This study investigated the effects of spatial resolution on streamflow predictions by employing distributed hydrological modeling in conjunction with the parameter estimation tool, PEST. Simulation experiments for the Geumho River catchment in South Korea were performed using WRF-Hydro with spatial resolutions of 100 m, 250 m, and 500 m for land surface and routing components, focusing on flood periods. To assess the impact of model spatial resolution, no-calibration simulations were examined with default parameter sets at different model spatial resolutions. We then evaluated event-specific calibration results in terms of calibrated parameters and calibration runtimes. The key findings are summarized as follows:

• In the simulations without calibration using the default parameter set, 100 m resolution exhibited superior performance in terms of NSE, although calibration was deemed necessary for Rainfall Event 2 (Rainfall Event 1 NSE: 0.868; Rainfall Event 2 NSE: 0.058).
• For Rainfall Event 2, the NSE and RMSE results of calibrated simulations indicated significant improvement compared to those for Rainfall Event 1. In particular, at 250 m resolution, the NSE was 0.9 or higher at all gauges, with the evaluation index value more than doubled relative to no-calibration cases, thereby indicating more effective calibration compared to other resolutions.
• Calibration runtime for calibrating PEST parameters varied significantly across resolutions and rainfall events. In particular, for Event 2 with a drier hydrological initial condition, the calibration runtimes at 100 m and 500 m resolutions nearly doubled compared to those for Event 1. For 250 m resolution, there was no significant difference in the calibrated parameters between Rainfall Events 1 and 2 (calibrated parameter of Rainfall Event 1: 0.203; Rainfall Event 2: 0.158).

We evaluated the effect of spatial resolution on the parameters and streamflow simulations, postulating that there might be a pattern in the variation of calibrated parameter values as spatial resolution changes. However, no scale-dependent patterns were found in calibrated parameters at least for the two selected rainfall events. This phenomenon is partly due to the changes in configuration and interaction among hydrological components at a finer spatial resolution. Therefore, we propose that resolution-aware parameter regionalization schemes be developed as a potential future research area. Such schemes would enable effective calibration in high-resolution models by integrating insights from lower-resolution calibrations and taking into account resolution-specific discrepancies. In the era of digital twins and hyperconnectivity, distributed modeling using new information with increasing volume and finer spatial resolution is expected to provide an improved understanding of hydrological processes and their interactions.