Improving Flood Forecasting Skill by Combining Ensemble Precipitation Forecasts and Multiple Hydrological Models in a Mountainous Basin

Abstract

Ensemble precipitation forecasts (EPFs) derived from single numerical weather predictions (NWPs) often miss extreme events, and individual hydrological models (HMs) often fail to accurately capture all types of flows, including flood peaks. To address these shortcomings, this study introduced four “EPF + HM” schemes for ensemble flood forecasting (EFF) by combining two EPFs and two HMs. A generator-based post-processing (GPP) method was applied to correct biases and under-dispersion within the raw EPF data. The effectiveness of these schemes in delivering high-quality flood forecasts was assessed using both deterministic and probabilistic metrics. The results indicate that, once post-processed by GPP, all proposed schemes show improvements in both deterministic and probabilistic performances, with skillful flood forecasts for 1–7 lead days. The deterioration in forecast performance with extended lead times is also lessened. Notably, the results indicate that uncertainty within hydrological models has a more pronounced impact on capturing flood peaks than uncertainty in precipitation inputs. This study recommends combining individual EPF with multiple hydrological models for reliable flood forecasting. In conclusion, effective flood forecasting necessitates employing post-processing techniques to correct EPFs and accounting for the uncertainty inherent in hydrological models, rather than relying solely on the uncertainty of the input data.

1. Introduction

Floods are the most frequent natural disasters worldwide, posing significant threats to human lives and socio-economic development [1]. Research by Alfieri, Bisselink [2] indicates that intensifying hydrological cycles across global watersheds are causing large-scale flooding events, often exceeding the capacity of existing flood protection infrastructure, a trend likely exacerbated by climate change. Since the late 1980s, flood management strategies have shifted from reliance on structural measures to embracing non-structural approaches [3,4]. Among these, flood forecasting and early warning systems are considered the most effective and cost-efficient methods for mitigating flood risks and minimizing their impacts [5,6,7]. These systems provide critical information regarding water flow, levels, and the timing of peak floods. Timely warnings enable authorities and affected populations to implement effective response measures, underscoring the need to improve forecast accuracy and extend lead times.

Flood forecasting can be categorized into deterministic and probabilistic forecasts. Deterministic forecasts provide a specific prediction, representing one possible outcome from a range of possibilities. They typically do not consider inherent uncertainties and often have shorter lead times [8,9,10]. Despite being derived from optimal initial conditions, deterministic forecasts may underestimate or overestimate actual outcomes. To address these limitations, the integration of ensemble precipitation forecasts (EPFs) into flood forecasting has gained traction in hydrological and meteorological research [11,12,13]. EPFs are generated by running multiple simulations from numerical weather prediction (NWP) models with slightly varied initial conditions or different model physics. By incorporating EPFs from NWPs into hydrological models, ensemble hydrological forecasts can be produced, offering a range of possible future states rather than a single deterministic prediction. Studies have shown that EPFs can significantly improve the accuracy and reliability of flood forecasts by accounting for the uncertainty in precipitation inputs [14,15,16,17].

Uncertainties in ensemble hydrological forecasts primarily originate from input data and the hydrological simulation process [18]. The uncertainty in hydrological simulations stems mainly from boundary conditions and the structural and parametric characteristics of the employed models [19,20]. This paper focuses on uncertainties arising from these two sources. To quantify uncertainties in input data, utilizing multiple EPFs from various weather forecasting centers—a “grand ensemble” (GE)—has proven effective [21]. A GE assimilates a wider array of uncertainty sources in the inputs, creating a more robust forecast probability density function (PDF) [22]. Conversely, a single EPF may address uncertainties specific to NWP models, potentially overlooking extreme events [23]. Since 2006, the THORPEX Interactive Grand Global Ensemble (TIGGE), part of the THORPEX scientific program launched by the World Meteorological Organization, has gathered ensemble forecasts from over 10 global NWP centers [24]. The study by Pappenberger, Bartholmes [23] demonstrates that forecasts from a GE capture flood peaks more effectively than those based on a single EPF, providing more reliable predictions.

A single hydrological model, however, does not encompass all potential output errors nor does it capture every aspect of the flood hydrological process [25]. Therefore, employing multiple hydrological models with varied structures helps quantify model structure uncertainty while enhancing forecasting capability and accuracy [26,27]. Recently, ensemble forecasting integrating multiple hydrological models has gained prominence [28,29,30]. Addressing uncertainties in both input data and hydrological model structures can be effectively managed by combining various EPF and multiple hydrological models (“EPF + HM”). This approach harnesses the strengths of different models while mitigating their limitations, thus enhancing the precision and predictability of hydrological forecasts [31,32,33].

Additionally, systematic bias and insufficient dispersion in meteorological ensemble forecasts, coupled with low spatial and temporal resolution when integrated with hydrological models and flawed spatio-temporal correlation structures between variables, necessitate enhancements through statistical post-processing techniques [34,35]. Over the past two decades, a variety of statistical post-processing methods have been developed, including linear bias correction [36], rank histogram techniques [37], reliability diagram techniques [38], Bayesian model averaging [39], kernel density estimation [40], logistic regression [41], non-homogeneous Gaussian regression [42], and so on. Research has demonstrated that applying these post-processing techniques to raw meteorological ensemble forecasts significantly improves the accuracy and reliability of hydrological predictions [43,44,45].

In light of these advances, this study hypothesizes that integrating statistical post-processing methods with GE and multiple hydrological models (MHM) will significantly enhance flood forecasting accuracy and reliability. To test this hypothesis, we propose the following research objectives. (1) Evaluate the effectiveness of the statistical post-processing method: assess how post-processing improves EPF performance in flood forecasting by correcting biases and addressing insufficient dispersion. (2) Investigate the utility of a GE: determine if a GE, which aggregates EPFs from multiple numerical weather prediction centers, provides more accurate flood peak predictions than a single EPF. (3) Assess the potential of MHM: evaluate whether combining different hydrological models enhances flood forecasting reliability compared to a single hydrological model (SHM), particularly in capturing event variability and uncertainty. (4) Examine the benefits of integrating GE with MHM: explore whether the combined use of GE and MHM improves the overall quality of flood forecasting, leveraging the strengths of both approaches for more precise and dependable predictions. The primary objective of this research is to identify the most effective combination of EPF and hydrological models (EPF+HM) for improving flood forecasting. The novelty of this study lies in developing and implementing a comprehensive framework that integrates GE and MHM for ensemble flood forecasting (EFF). By applying this innovative framework to the Qingjiang River Basin in the mountainous central-western region of China—characterized by high population density and vulnerability to frequent rainstorms and floods—we aim to address challenges such as systematic biases, insufficient dispersion, and spatio-temporal discrepancies in traditional models. This research represents the first attempt to apply multi-model techniques for ensemble flood forecasting in this region. The outcomes are expected to contribute to developing more effective flood forecasts, particularly in regions with similar topographical and climatic challenges.

2. Study Area and Data

The Qingjiang River Basin (108°35′–111°35′ E, 22°33′–30°50′ N), situated in the southwestern part of Hubei Province, China, flows from west to east through ten counties and cities and joins the Yangtze River at Yidu. The main channel stretches approximately 423 km, encompassing a controlled drainage area of about 16,700 square km. The basin experiences a mid-subtropical monsoon climate, with an average annual temperature of about 14 °C and an annual precipitation of about 1400 mm, predominantly concentrated in the summer months. The terrain of the basin, primarily consisting of mountainous regions that account for over 80% of its area, slopes from west to east, forming a landscape of high mountains and deep valleys. This region, located in western Hubei, is known for its severe rainstorms. Influenced by the summer rainstorms, summer runoff accounts for about 40% of the annual runoff, with peak floods typically occurring in June and July. Given the significant impact of human activities, particularly dam construction, on the middle and lower reaches of the basin, this study focuses on the upper Qingjiang River Basin. This area is less affected by human interventions, with the Shuibuya Hydropower Station serving as the upstream catchment area (Figure 1).

This study incorporates meteorological and hydrological observation data, as well as EPFs from NWP centers. The observation dataset includes daily temperature, precipitation, potential evaporation, and runoff data spanning from 2014 to 2020. Meteorological data were sourced from 175 automatic meteorological stations distributed across the study area, and hydrological data were collected from the Shuibuya Hydropower Station (Figure 1). The EPFs utilized in this research were obtained from two highly regarded NWP centers within the TIGGE database, specifically ECMWF and NCEP. Detailed information about these models is provided in

Table 1. Overview of the datasets used in this study.

Datasets	Sources	Ensemble Members (Perturbed)	Temporal Resolution	Spatial Resolution	Temporal Span
Observed meteorological data	175 meteorological stations	-	Daily	Station	2014–2020
Ensemble precipitation forecasts (EPFs)	ECMWF (European Centre for Medium-Range Weather Forecasts)	50	7 lead days at 6 h	0.5 grid	2014–2020
	NCEP (National Centers for Environmental Prediction)	20
Observed discharge data	Shuibuya hydropower station	-	Daily	Station	2014–2020

.

3. Methodology

This study employs two EPFs and two hydrological models to conduct EFF, aiming to effectively manage the uncertainties in the flood forecasting process. These uncertainties originate from the input data and are propagated through various hydrological models, leading to uncertain outputs. Moreover, a statistical post-processing method is applied to correct biases and inadequate dispersion within raw EPFs. Finally, multiple evaluation metrics are utilized to assess the ensemble hydrological forecasts, encompassing both the raw and post-processed forecasts.

3.1. Post-Processing Method

In this study, the generator-based post-processing (GPP) method [36] was employed to correct EPFs. The GPP method is specifically designed for statistical post-process meteorological ensemble forecasts and has proven effective in previous research [45,46]. This method integrates meteorological forecast information into a weather generator, allowing for the regeneration of ensemble forecast outcomes that are consistent with both the ensemble meteorological forecasts and historical observational characteristics. The statistical distribution parameters for forecast variables within the weather generator are estimated from historical observational data. Firstly, the probability distribution function (PDF) for precipitation parameters is defined as follows:

$$y|x_1,\dots ,x_M~g(y|x_1,\dots ,x_k)$$

(1)

where y represents the precipitation variable, $x_1,\dots ,x_k$ corresponds to an ensemble of precipitation forecasts composed of K members. The PDF characterizes a mixed discrete/continuous distribution where the probability of zero precipitation is positive, and the probability of positive precipitation follows a continuous skewed distribution. The precipitation mixed distribution model proposed by [47] is as follows:

$$g(y|f_k)=P(y=0|f_k)\cdot I(y=0)+P(y>0|f_k)\cdot g_k(y|f_k)\cdot I(y>0)$$

(2)

where $g(y|f_k)$ denotes the probability distribution given the member forecasts; I() is the indicator function, which equals 1 if the expression inside the parenthesis holds true, and, otherwise, it equals 0; $P(y=0|f_k)$ and $g(y>0|f_k)$ represent the probabilities of no precipitation and precipitation, respectively; and $g_k(y|f_k)$ signifies a two-parameter gamma distribution. When applying the GPP method to correct precipitation, the probability density functions for precipitation in different seasons or of different intensities are independently calibrated to match observational data. Subsequently, using the forecast information from the original EPF, samples are redrawn from these calibrated probability density functions to generate the post-processed EPFs. For a detailed methodology, refer to Chen, Brissette [36].

3.2. Hydrological Models

Hydrological models are utilized for various applications. Previous studies comparing lumped and distributed models in outlet streamflow simulation have found minimal differences in performance between the two model types [48,49]. Given the scope of this study and the prevalent use of lumped models for hydrological simulation and forecasting, lumped models were selected. Distributed models were excluded due to their complexity and data demands. Two lumped hydrological models were used in this study: the Xinanjiang model (XAJ) [50] and the mod`ele du G’enie Rural `a 4 param`etres (GR4J) [51]. These two models are widely used for streamflow simulation and have proven effective in various hydrological contexts [52,53,54].

The XAJ proposed by [50] is a lumped hydrological model designed for humid and semi-humid regions. This model conceptualizes the catchment as a soil box, consisting of upper, lower, and deep soil layers. The XAJ model’s computational process consists of four modules (Figure 2): (1) Calculation of catchment evapotranspiration and soil moisture, using a three-layer evapotranspiration model—rainfall first replenishes the upper layer, then the lower and deep layers; evapotranspiration initially depletes the upper layer’s soil moisture, followed sequentially by the lower and deep layers. (2) Runoff generation, which utilizes a saturation excess runoff model where a storage capacity curve controls the distribution of precipitation throughout the catchment to calculate total runoff. (3) Water source partitioning, using a free water storage capacity curve to separate the total runoff into surface runoff, subsurface flow, and underground runoff. (4) Catchment routing, where surface runoff typically uses the unit hydrograph method, while interflow and groundwater flow use the linear reservoir method. The XAJ model is characterized by 15 parameters: 4 related to evaporation, 2 for runoff generation, and 9 for runoff routing. These parameters (

Table 2. Calibrated parameters in both XAJ and GR4J models.

	Parameters	Description	Range	Calibrated Value
XAJ	WM	Areal tension water capacity (mm)	Humid regions: 100~160	134.16
	WUM	Fraction of upper water in WM	0~0.6	0.26
	WLM	Fraction of lower water in WM	0.4~1	0.65
	K	Evaporation coefficient	0~0.6	0.55
	C	Coefficient of evapotranspiration in the lower soil layer	0.2~1	0.62
	IM	Impermeable coeflicient	0~0.2	0.07
	B	Tension water distribution index	0~0.02	0.01
	EX	Free water distribution index	1~1.5	1.39
	SM	Areal free water capacity (mm)	0~60	59.98
	KI	Fraction of free water to interflow	0~1	0.50
	KG	Fraction of free water to groundwater	0~1, KI + KG < 1	0.50
	CI	Interflow recession coefficient	0.8~1	0.80
	CG	Groundwater recession coefficient	0.8~1	0.90
	N	Number of reservoirs of the Nash model	0~5	0.27
	K	Storage constant of the Nash model	0~5	3.04
GR4J	X1	Production reservoir: storage of rainfall on the soil surface (mm)	1~750	187.07
	X2	Groundwater exchange coefficient: a function of groundwater exchange that influences the routing reservoir	−10~10	2.91
	X3	Routing storage: amount of water that can be stored in soil porous (mm)	1~400	68.84
	X4	Time peak: the time when the ordinate peak of flood hydrograph is created	0.5~10	1.33

) require calibration using observed streamflow to accurately reflect the hydrological characteristics of a specific watershed. Further details can be found in the study by Zhao [50].

Developed in 2003 by French scholar Perrin et al., based on the GR3J model [55], the GR4J model has a simple structure with only four free parameters (Table 2) and uses two nonlinear reservoirs for production and routing calculations (Figure 3): (1) The production reservoir first determines effective precipitation Pn and residual evaporation capacity En based on catchment precipitation P and evaporation capacity E, then calculates the precipitation Ps and replenishes the production reservoir and the evapotranspiration Es. (2) The routing reservoir employs time segment unit hydrographs for routing calculations. Different runoff components have different routing times; thus, rainfall is split into two parts: 90% of the rainfall is routed using unit hydrograph UH1, needing adjustment through the routing reservoir, and the remaining 10% flows directly to the catchment outlet section, routed using unit hydrograph UH2. More details are available from Perrin, Michel [51].

The basic inputs for both models include catchment-average precipitation, temperature, and potential evapotranspiration, with outputs being the runoff at the catchment outlet. Catchment-average precipitation is calculated using the Thiessen Polygon method. The model calibration period spans from 2014 to 2017, with a validation period that spans from 2018 to 2020. During calibration, the Nash–Sutcliffe Efficiency coefficient (NSE) and the volumetric error (RE) are used as objective functions, with optimization performed using the SCE-UA algorithm. The formulas for NSE and RE are as follows:

$$NSE=1-\frac{{\displaystyle \sum _{i=1}^n(Q_i^{obs}-Q_i^{sim})}}{{\displaystyle \sum _{i=1}^n(Q_i^{obs}-\overline{Q_i^{obs}})}}$$

(3)

$$RE(\%)=\frac{{\displaystyle \sum _{i=1}^n(Q_i^{obs}-Q_i^{sim})}}{{\displaystyle \sum _{i=1}^n(Q_i^{obs})}}\times 100$$

(4)

where $Q_i^{obs}$ represents the observed daily runoff, $Q_i^{sim}$ represents the simulated daily runoff, and ${\overline{Q}}^{obs}$ denotes the mean of the observed runoff over multiple days. The NSE value ranges from −∞ to 1, with 1 being the optimal value. The RE value ranges from 0 to ∞, with 0 being the optimal value.

3.3. Generation and Evaluation of Ensemble Flood Forecasting

The EFF is generated based on the following “EPF + HM” schemes: (A) ECMWF-driven XAJ, denoted as ECMWF + XAJ; (B) EPFs (ECMWF and NCEP) driving XAJ, referred to as GE + XAJ; (C) ECMWF driving multiple models (XAJ and GR4J), denoted as ECMWF + MHM; and (D) EPFs driving multiple hydrological models (XAJ and GR4J), known as GE + MHM. Scheme (D) represents the multi-ensemble, multi-model combination [27]. These four schemes generate ensemble members numbering 50, 70, 100, and 140, respectively. Additionally, ensemble forecast products corrected by the GPP method are used for flood ensemble forecasting in these four schemes. The results are evaluated and compared before and after post-processing.

This paper evaluates the performance of EFF using the ensemble mean and the 90% confidence interval (the difference between the 95th and 5th percentiles). The ensemble mean reflects the central tendency, while the 90% confidence interval quantifies the range, variability, and uncertainty within the ensemble. This dual assessment allows for a comprehensive evaluation of the ensemble’s accuracy in predicting flood events and in assessing the associated uncertainty. Both deterministic and probabilistic indicators are used. The deterministic indicators include the correlation coefficient (R) and the Relative Mean Error (RME), which measure the average deviation between the forecast mean and actual observations. Probabilistic indicators include the Continuous Ranked Probability Skill Score (CRPSS) and quantile histograms. To evaluate EFF uncertainty, three indicators are employed: Average Relative Interval Length (ARIL), the percentage of observations enclosed by the confidence interval (PCI), as well as the percentage of observations enclosed by the Unit Confidence Interval (PUCI) [56].

(1) R measures the correlation between forecasted and observed values, serving as an indicator of forecast reliability. It is calculated as follows:

$$R=\frac{{\displaystyle {\sum }_{i=1}^n(O_i-\overline{O})(F_i-\overline{F})}}{\sqrt{{\displaystyle {\sum }_{i=1}^n{(O_i-\overline{O})}^2}}\sqrt{{\displaystyle {\sum }_{i=1}^n{(F_i-\overline{F})}^2}}}$$

(5)

where O_i and F_i represent observed and ensemble forecasted precipitation, respectively, while $\overline{O}$ and $\overline{F}$ are the daily mean values of observed and forecasted precipitation over an n-day time series. R values range from [0, 1], with values closer to 1 indicating more reliable forecasts.

(2) RME reflects the relative deviation between forecast values and the observed mean, assessing the accuracy of the forecasts. It is expressed as follows:

$$RME=\frac{{\displaystyle {\sum }_{i=1}^n(F_i-\overline{O})}}{{\displaystyle {\sum }_{i=1}^n{Q}_i}}\times 100\%$$

(6)

RME values range from [−100%, 100%], with values closer to 0 indicating smaller errors between the ensemble mean and observations.

(3) CRPSS evaluates the performance of the quantitative precipitation forecast (QPF) ensemble distribution relative to the climatological distribution. It is defined for a variable n at time t, estimated from the ensemble forecast probability density function as follows:

$$CRP{S}_n\left(t\right)={\displaystyle \underset{-\infty }{\overset{+\infty }{\int }}{\left(F_{n,t}(y)-I\left(y\ge X\right)\right)}^2}{d}_y$$

(7)

The continuous skill score, CRPSS, is defined as follows:

$$CRPS{S}_n=1-\frac{CRP{S}_n}{CRP{S}_{n,ref}}$$

(8)

where $CRP{S}_{n,ref}$ is the CRPS obtained using a reference forecast. Higher CRPSS values approaching 1 indicate better ensemble forecast performance.

(4) Quantile histograms are used to check if the ensemble forecast values and observed values come from the same probability distribution. A flat, horizontal line shape indicates moderate dispersion within the ensemble; a concave shape with high sides and a low middle suggests under-dispersion; a convex shape with low sides and a high middle indicates over-dispersion. A flat histogram shape is a necessary condition for reliable ensemble forecasts. Additionally, the uniformity index of the quantile histogram is expressed as follows:

$$\Delta ={\displaystyle \sum _{\mathrm{i}=1}^{m+1}\left|F_i-\frac{1}{m+1}\right|}$$

(9)

as Δ approaches 0, the flatness of the histogram shape improves, indicating more reliable ensemble forecasts.

(5) ARIL assesses the resolution of the predictive distributions, defined over the entire duration of the simulation as follows:

$$ARIL=\frac{1}{n}{\displaystyle \sum _{i=1}^n\frac{Q_{upper,i}^{sim}-Q_{lower,i}^{sim}}{Q_i^{obs}}}$$

(10)

where n is the number of days in the observed record, $Q_{upper,i}^{sim}$ and $Q_{lower,i}^{sim}$ are the upper and lower simulated discharges of the 90% confidence interval, respectively, and $Q_i^{obs}$ is the observed discharge.

PCI quantifies the proportion of observed data falling within a specified range of simulated intervals, defined as follows:

$$PCI=\frac{1}{n}{\displaystyle \sum _{i=1}^n{Q}_{in,i}^{obs}}$$

(11)

where $Q_{in,i}^{obs}$ represents the number of observed discharges within the 90% confidence interval. A smaller ARIL indicates a narrower uncertainty interval, while a higher PCI suggests a greater reliability of the interval.

PUCI, derived from ARIL and PCI, is defined as follows:

$$PUCI=\frac{(1-Abs(PCI-0.9))}{ARIL}$$

(12)

Higher PUCI values generally indicate lower uncertainty in the 90% confidence interval of discharge.

4. Results

4.1. Calibration and Validation of Two Hydrological Models

Based on daily meteorological and hydrological observations within the study area, the periods from 2014 to 2017 were designated as the calibration period, and from 2018 to 2020 as the validation period. During these periods, the XAJ and GR4J hydrological models were calibrated and validated. Figure 4 displays the observed and simulated hydrological process graphs for both XAJ and GR4J hydrological models during the calibration and validation periods. The graphs indicate differences in the models’ abilities to capture flood peaks, which can be attributed to their distinct structural characteristics. However, both models effectively captured flood peaks during the calibration period.

Moreover, during the calibration and validation periods, the NSE values for the XAJ model are 0.86 and 0.88, respectively, and the RE values are 8.58% and 7.26%, respectively. For the GR4J model, the NSE values are 0.92 and 0.91, and the RE values are −0.15% and 8.26%, respectively. Compared to earlier studies [57,58], both the XAJ and GR4J models demonstrate good applicability, as indicated by NSE and RE values, which suggests that the models are well calibrated and reliable for further flood forecasting research. The calibrated parameters for both hydrological models are detailed in Table 2.

4.2. Evaluation of Ensemble Flood Forecasting Performance for Four Schemes

Figure 5 displays the R between the ensemble mean and observed runoff, generated by the four schemes, both before and after correction with the GPP method, over a forecast horizon of 1–7 days. As shown in the figure, the R values for the 1 lead day are relatively high, at approximately 0.7 before correction and about 0.8 after correction. As the forecast horizon extends, the R values gradually decrease. Scheme (C), which focuses solely on the uncertainty of the hydrological model, consistently shows relatively higher correlations both before and after correction. In contrast, schemes (B) and (D), which consider the uncertainty of the forecasting models, exhibit a rapid decline in R values after the third day of the forecast period. Overall, the R values in the right graph are higher than those in the left graph, indicating that runoff forecasts derived by the corrected EPF exhibit a higher degree of correlation with observed values. In conclusion, these results suggest that considering the uncertainty of hydrological models in runoff forecasting, coupled with effective post-processing methods, can enhance the performance of runoff forecasts.

Figure 6 illustrates the RME between the ensemble mean and observed runoff forecasted using the four schemes, both before and after correction with the GPP method. The plots indicate a general tendency of the ensemble mean to underestimate observed values, with schemes (A) and (C) showing a relatively lower degree of underestimation, about −40%, before correction. In contrast, schemes (B) and (D) exhibit a more significant underestimation of observed runoff, with RME ranging from −80% to −40%, and this underestimation intensifies as the forecast horizon extends. After correction, the underestimation in all schemes is markedly improved, reduced to within −20%, demonstrating that effective post-processing techniques can significantly enhance the accuracy of runoff forecasts.

Figure 7 presents the CRPSS of the forecasted runoff ensembles obtained from the four schemes, before and after correction with the GPP method. This evaluation measures the probabilistic skills of the ensemble forecasts. Using the classifications established by Harrigan, Prudhomme [59] and Bennett, Wang [60], the flood forecasting skill levels are defined as follows: very high if CRPSS is between 0.75 and 1; high if CRPSS is between 0.5 and 0.75; moderate if CRPSS is between 0.25 and 0.5; low if CRPSS is between 0 and 0.25; no skill if CRPSS equals 0; and negative skill if CRPSS is less than 0. Accordingly, it is evident that before correction, schemes (A) and (C) show moderate skills for 1–7 lead days. However, schemes (B) and (D) show low skills once the forecast period exceeds 3 days. After applying the GPP correction, the CRPSS for all schemes improves. All four schemes show high skills for the first two lead days and moderate skills for 3–7 lead days. What is more, scheme (A) exhibits the lowest CRPSS on 1 lead day, and the others show slightly higher CRPSS values.

Figure 8 shows the quantile histograms of the forecasted runoff ensembles obtained from the four schemes, both before and after correction with the GPP method. The ranks of schemes (A) through (D) are 50, 70, 100, and 140, respectively. Initially, the quantile histograms of the uncorrected EPF display a U-shape, with a large concentration of forecast values at the lowest and highest ranks, indicating a large concentration of forecast values at the lowest and highest ranks. This pattern indicates under-dispersion, reflecting an underestimation of forecast uncertainty. After applying GPP correction, the histograms become flatter, indicating a more uniform distribution. Specifically, the uniformity indices for the quantile histograms of schemes (A) through (D) decreased from 1.17 to 0.42, 1.11 to 0.26, 1.13 to 0.35, and 1.09 to 0.31, respectively. This demonstrates that the GPP method effectively mitigates the issue of under-dispersion in ensemble forecasts. Additionally, compared to scheme (A), the other schemes have slightly lower uniformity indices, which indicates that considering the uncertainty in both forecasting models and hydrological models can further enhance the probabilistic skills of ensemble forecasts, to a certain extent.

In addition,

Table 3. The Average Relative Interval Length (ARIL), the percentage of observations enclosed by the confidence interval (PCI), and the percentage of observations enclosed by the Unit Confidence Interval (PUCI) values for the 90% confidence interval of discharge for different schemes.

Schemes	Raw			GPP
	ARIL	PCI	PUCI	ARIL	PCI	PUCI
(A) CMWF + XAJ	1.304	0.331	0.330	2.615	0.764	0.331
(B) GE + XAJ	1.877	0.360	0.245	2.935	0.825	0.315
(C) ECMWF + MHM	1.765	0.450	0.312	2.671	0.816	0.343
(D) GE + MHM	2.317	0.470	0.246	2.980	0.863	0.323

presents three uncertainty metrics for evaluating 90% confidence intervals of discharge derived from different schemes. It can be determined that (1) generally, both ARIL and PCI values derived by raw EPFs are smaller than those derived by GPP post-processed EPFs, making it difficult to determine whether post-processing is useful or not; (2) considering the PUCI, those derived by GPP post-processed EPFs have larger values than those derived by raw EPFs, indicating that their results are more reliable and exhibit less uncertainty; and (3) the PUCI values of schemes (A) and (C) are generally larger than those of schemes (B) and (D), suggesting that former approaches yield more robust and reliable forecasts.

4.3. Application to a Typical Flood Event

On 17 July 2020, the Qingjiang River Basin experienced a significant torrential rain event, leading to a rapid rise in river levels. On 18 July, the flow rate at the Shuibuya station in the Qingjiang Basin reached a peak of 6767 m³/s, marking an extreme flood event. Figure 9 presents the EFFs for this flood event simulated by the four “EPF + HM” schemes on 1 lead day. Figure 9a,b shows the raw EPF simulation results and the post-processed EPF results using the GPP method, respectively. The schemes (A)~(D) generated ensemble member counts of 50, 70, 100, and 140, respectively. The figures display the ensemble mean and the 90% confidence interval to evaluate the EFFs’ performance in capturing the flood event.

From Figure 9a, it is evident that the EFFs generated using the raw EPF exhibit biases and under-dispersion. The ensemble mean and 90% confidence interval in scheme (A) underestimate the observed flood peak. Compared to scheme (A), scheme (B) shows no improvement in the ensemble mean and 90% confidence interval, while scheme (C) performs slightly better in capturing the observed peak event, indicating that GE does not necessarily enhance the accuracy of the EFFs. Schemes (C) and (D), compared to schemes (A) and (B), have a wider range of forecast ensembles, suggesting that incorporating hydrological uncertainty can improve the quality of the EFFs. Thus, including multiple hydrological models (MHM) results in a broader range of ensemble forecasts and reduces bias compared to using only single hydrological models (SHMs).

From Figure 9b, the flood forecasts conducted with the GPP-corrected EPF show improvements in the range of the forecast ensemble. The ensemble mean in scheme (A) is still underestimated, but the forecast range can better cover the observed flood. The performance of scheme (B) is similar to that of scheme (A), indicating that when using a single hydrological model, GE does not demonstrate an improvement over a single EPF. Schemes (C) and (D) outperform other schemes in terms of the ensemble mean, providing higher estimates for the flood peak. These results suggest that while post-processing of the EPF has been applied, using GE does not effectively enhance the performance of the EFFs, whereas using MHM better captures the flood event.

5. Discussion

In this study, EFFs were generated by integrating both raw and post-processed EPFs, i.e., ECMWF and NCEP, into calibrated hydrological models, i.e., XAJ and GR4J. The flood forecasts were produced from four ‘NWP + HM’ schemes, i.e., (A) ECMWF + XAJ, (B) GE + XAJ, (C) ECMWF + MHM, and (D) GE + MHM. The performance of both the raw and post-processed flood forecasts was evaluated using deterministic indicators such as R and RME, alongside probabilistic indicators like CRPSS and quantile histograms, as well as three uncertainty evaluation indicators—ARIL, PCI, and PUCI.

The analysis reveals that forecasts driven by raw EPFs yield satisfactory correlation and relative error, but are limited in probabilistic metrics such as CRPSS and quantile histograms. Results demonstrate that after GPP correction, all schemes show marked improvements in both deterministic and probabilistic terms, with high deterministic skills and moderate probabilistic skills over 1–7 lead days. This enhancement also mitigated the degradation of forecast quality over lead days, validating the effectiveness of the GPP method, consistent with the findings of Zhang, Chen [46]. These findings underscore the necessity of employing post-processing methods to enhance the reliability of flood forecasts.

A comparative analysis between schemes (A) and (B) shows that using a single hydrological model, flood forecasts based on GE do not show a significant improvement over those using a single EPF. Comparisons between schemes (A) and (C) reveal that when using a single EPF, forecasts based on MHM offer a broader ensemble range, a smaller ensemble mean error, and an increased accuracy of the ensemble mean. This improvement in flood forecast quality is credited to the integration of hydrological model uncertainty. Comparing scheme (A) with scheme (D) shows that although using multiple forecasting models and hydrological models yields forecasts with higher dispersion, they exhibit lower correlation, larger biases, and lower CRPSS. This suggests that while it is reasonable to use GE to quantify input uncertainty, compared to a single EPS, GE may not necessarily enhance flood forecasting performance, aligning with the findings of Teja, Manikanta [31]. Therefore, it is recommended to combine a single EPF with MHM (i.e., scheme (C)) to achieve reliable flood forecasting. Moreover, results indicate that compared to input uncertainty, the uncertainty in hydrological models can more effectively enhance the predictability of flood forecasts. Therefore, focusing on hydrological model uncertainty rather than input data uncertainty could decrease computational time and burden in flood forecasting.

6. Conclusions

This study assesses the efficacy of EFFs in accurately predicting streamflow and flood events using calibrated hydrological models driven by TIGGE ensemble forecasts. Two lumped models and two EPFs were employed to address uncertainties in hydrological model structures and input uncertainties, respectively. Four forecasting schemes combining different hydrological models and EPFs were analyzed to determine the most effective setup for delivering high-quality flood forecasts. The GPP method was used to correct bias and under-dispersion within raw EPFs. The performance of EFFs was assessed using both deterministic and probabilistic metrics.

The results underscore the significance of applying post-processing techniques like GPP to correct EPFs to improve the reliability of flood forecasting. The application of the GPP has proven effective in maintaining reliable forecast skills for 1–7 lead days and reducing quality degradation over extended periods.

A critical finding from this study is the limited improvement in flood forecasts when using a GE with a single hydrological model, which did not substantially outperform forecasts derived from a single EPF. However, the integration of MHM with a single EPF, as seen in scheme (C), markedly enhanced forecast accuracy by offering a wider range of ensemble forecasts, lower bias, and improved correlation. This suggests that uncertainty in hydrological models plays a more critical role in enhancing forecast predictability than input data uncertainty alone. Thus, addressing hydrological model uncertainty is crucial for optimizing flood forecasting systems.

Nonetheless, this study has limitations, as the GPP post-processing method corrects only temporal errors and does not consider spatial corrections. Scholars suggest that addressing errors from the spatial distribution of precipitation could further improve runoff forecast accuracy [61,62]. Moreover, given the complex terrain of the study area and lack of observational data, this study only used two lumped hydrological models. However, semi-distributed or distributed models, which better handle spatial variability in rainfall, might provide better hydrological forecasting outcomes [63]. Exploring how different hydrological models perform under varied geographic and climatic conditions in future research could provide valuable insights.

In conclusion, this research advocates for the strategic combination of a single EPF with multiple hydrological models to achieve more reliable flood forecasting. This approach not only harnesses the strengths of post-processing techniques but also aligns with the practical needs of reducing computational demands in flood forecasting practices.