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Runoff data is crucial for development of water resources. Runoff data is however rarely available for ungauged catchments, especially in developing countries. Geomorphological instantaneous unit hydrographs (GIUH) models can be used for predicting runoff in poorly gauged catchments, but a challenge with these models is estimating the dynamic velocity parameter. In this study, three GIUH models were developed based on estimation of flow velocity using calibration of Manning’s n (GIUH-cal), peak discharge (GIUH-pq) and 30-min rain intensity (GIUH-I30). The objectives of this study were to (a) assess suitability of a GIUH model for simulating runoff in Gule catchment, northern Ethiopia and (b) evaluate performance of three velocity parameter estimation methods in simulating runoff using GIUH models. Runoff hydrographs of the GIUH models matched well with observed hygrographs for most rain events. The GIUH-cal model had the best performance, 18 out of 20 rain events resulting in Nash–Sutcliffe model efficiency (NSE) values of 0.53 to 0.95. The GIUH-pq and GIUH-I30 models performed satisfactorily with 12 of the 20 rain events resulting in NSE values greater than 0.50. Overall, the GIUH models underestimated peak discharge compared to observed data. The GIUH models were moderately sensitive to changes in flow velocity. Peak discharge and time to peak discharge were highly sensitive to changes in flow velocity. The developed GIUH models could be used for simulating flood hydrographs of the Gule catchment. Particularly, the GIUH-I30 model will be very useful for estimating direct surface runoff in the absence of streamflow data.

Estimating peak discharge ( Q p ) and design flood in small tributary sub-basins is challenging owing to limited observed streamflow data. To address this, the synthetic unit hydrograph (SUH) concept was introduced that helps to estimate Q p of direct surface runoff (DSRO) hydrograph by routing the excess rainfall to the basin’s outlet, facilitating the construction of hydraulic structures in areas lacking observed rainfall-runoff data. Therefore, the present study evaluates the performances of three types of SUHs i.e., CWC-UH, Nash-GIUH and SCS-UH in estimating DSRO hydrographs, with an emphasis on Q p and time to peak ( T P ) during a storm event in ten tributary sub-basins of one of the most flood-affected river, Shilabati in Eastern India. The results of these three models exhibit striking similarities in the shapes of DSRO hydrographs derived from the SCS-UH and the Nash-GIUH models compared to the CWC-UH. The Nash-GIUH model stands out as the superior model due to the strong correlation (R 2  = 0.86) between the ratio of Q p and T p and the observed flood extents (flood-inundated area) for all sub-basins. In the Nash-GIUH-based DSRO hydrographs, Sub-basin-9 witnesses the highest Q p (334.64 m 3 s − 1 ) with short T p (19 h) ( Q p / T p ratio = 17.61) followed by Sub-basin-10 ( Q p / T p ratio = 13.50). Similarly, 31.67% and 19.51% of the total areas of Sub-basin-9 and − 10, respectively, were affected by flood inundation in the past. Therefore, the association between the shape of hydrographs and flood extents depicts that the Nash-GIUH-based rainfall-runoff model can effectively estimate floods in areas lacking streamflow data.

This research work significantly advances hydrological modelling in Greece by introducing Geomorphological Unit Hydrographs (GUH) tailored for ungauged basins. These GUHs, specifically adapted to the region’s intricate geomorphology and limited data resources, provide essential insights into hydrological behaviour. Utilising an innovative approach that integrates the time-area diagram method with Python’s ArcPy module, this paper examines the geomorphological metrics of 70 drainage basins and their relationships with hydrograph characteristics. Empirical relationships, expressed through simple forms like second-order polynomials and linear equations, are established and validated across 30 basins. System analysis reveals the efficacy of the 0.1–2.0 channel velocity range, supported by positive Nash–Sutcliffe Efficiency (NSE) values. Visual representations, including histograms, elucidate the intricate connections between hydrograph attributes and geomorphological parameters. Regression analysis produces predictive equations, demonstrating strong performance with models such as T-Polynomial for Q max and Cc-Linear for other hydrograph attributes, and their precision is confirmed through validation regression analysis, enhancing forecasting across various drainage basins.

The traditional instantaneous unit hydrograph (IUH) is very useful for theoretical analysis and practical forecasting of floods owing to its linear assumptions. Although various revised methods to overcome the unphysical assumptions have been proposed, it is still difficult to obtain efficiently a nonlinear IUH of diverse rainfall excess intensities in a watershed. In this study, we proposed practical and physical interpolation techniques to derive new IUHs from at least two existing IUHs corresponding to diverse rainfall excess intensities in a watershed. To interpolate the new IUHs, mass conservation law and power–law relationships between rainfall excess intensities and the peak flow and time to peak of IUHs were used. By employing convolution integration, surface rainfall–runoff hydrographs for timely varying rainfall events were derived. For verification, we applied the proposed technique to three real watersheds with different sizes ranging from 0.036 to 1,047 km2. All flood prediction procedures were completed instantly, stably and the prediction results showed the accuracy of Nash–Sutcliffe efficiency (NSE) = 0.55–0.93 and coefficient of determination (R2) = 0.72–0.94.

This study introduces two novel DEM-based distributed rainfall-runoff models derived from the existing Hidropixel model: Hidropixel TUH+ and Hidropixel DLR . These models account for spatial variations in direct runoff generation, translation, and storage within a watershed, considering spatial variability in rainfall and basin characteristics. In Hidropixel TUH+ , a Triangular Unit Hydrograph (TUH) is determined for each Digital Elevation Model (DEM) pixel and lagged to the watershed outlet based on the travel time from the pixel to the outlet. In Hidropixel DLR , a hydrograph is estimated for each pixel based on the travel time, which takes translation effects into account. To represent the storage effects, this hydrograph is attenuated by a linear reservoir at each pixel. Both approaches were applied to the Upper Medway catchment (250 km 2 ) in southeastern England, using rainfall data from a rain gauge network. The outcomes revealed that the proposed approaches provided a reasonably accurate prediction of the hydrographs and exhibited notably superior performance compared to the original version of Hidropixel, which has limited capabilities in capturing translation effects. Hidropixel TUH+ and Hidropixel DLR predicted peak flows with an average absolute error of 11% and 10%, respectively. The Hidropixel DLR achieved a more accurate time-to-peak estimation, with an average absolute error of 1 h, compared to the 1.5-h error from Hidropixel TUH+ . Additionally, the Hidropixel DLR predicted the full direct runoff hydrograph more accurately, achieving an average Nash–Sutcliffe coefficient ( NSE ) of 0.89, while the Hidropixel TUH+ had an NSE of approximately 0.84.

This paper presents a new flood modelling tool developed by coupling a full 2D hydrodynamic model with hydrological models. The coupled model overcomes the main limitations of the individual modelling approaches, i.e. high computational costs associated with the hydrodynamic models and less detailed representation of the underlying physical processes related to the hydrological models. When conducting a simulation using the coupled model, the computational domain (e.g. a catchment) is first divided into hydraulic and hydrological zones. In the hydrological zones that have high ground elevations and relatively homogeneous land cover or topographic features, a conceptual lumped model is applied to obtain runoff/net rainfall, which is then routed by a group of pre-acquired ‘unit hydrographs’ to the zone borders. These translated hydrographs will then be used to drive the full 2D hydrodynamic model to predict flood dynamics at high resolution in the hydraulic zones that are featured with complex topographic settings, including roads, buildings, etc. The new coupled flood model is applied to reproduce a major flood event that occurred in Morpeth, northeast England in September 2008. While producing similar results, the new coupled model is shown to be computationally much more efficient than the full hydrodynamic model.

This paper presents an energy model for determining the overland flow velocity in order to improve the low accuracy problem in flow concentration simulation. It furnishes a novel idea for studying flow concentration in ungauged basins. The model can be widely applied in analysis of spatial velocity field, extraction of instantaneous geomorphic unit hydrograph and development of distributed hydrological model. A distributed flood-forecasting model is constructed for Lianyuan Basin in Hunan Province of China. In the proposed method, gravitational potential energy is transformed into kinetic energy via an analysis of energy distribution of water particles in the basin. Based on the kinetic energy equation, the overland flow velocity simulating the geomorphic unit hydrograph is computed. Rainfall-runoff simulation is then performed by integrating with runoff yield and concentration model. Results indicate that the model based on energy conversion leads to more accurate results. The model has the following advantages: firstly, the spatial distribution of the velocity field is appropriate; secondly, the model has only one parameter, which is easily determined; and finally, flow velocity results can be used for the computation of river network flow concentration.

The probable maximum flood (PMF) is the flood caused by the probable maximum precipitation (PMP). A unit hydrograph (UH) is generally used to derive the PMF for the given PMP, but a method is needed to modify the UH parameters to reflect the PMP condition. This study presents a new method using the estimated channel velocity to modify the Clark UH parameters under the ordinary condition into those under the PMP condition. This study considers major dam basins in Korea and evaluates the application results in comparison to several previous studies. As application results of the proposed method, the Clark UH parameters under the PMP condition are found to be within the range 39–53% of those under the ordinary condition, with their mean of about 44%. The UH derived by applying this mean ratio shows that its peak time and the peak flow are just 44 and 227% of the UH under the ordinary condition, respectively. This change from the ordinary condition to the PMP condition is more extreme in Korea than that in Australia and the United Kingdom. This extreme change seems to be due to the climate in Korea, located in the Asian Monsoon region.

The probability distribution function (PDF)-based unit hydrographs (UHs) are gaining momentum in an application for more accurate rainfall-runoff transformation. Employing seven statistical performance indices, R2, NSE, MSE, RMSE, MAE, MAPE, and SE in generalized reduced gradient nonlinear programming (GRG-NLP) optimization, 18 known and 12 adaptable PDF-based UHs were assessed against UHs derived from 18 storms in 7 basins across the United States, Turkey, and India. To this end, 27 Maple codes were proposed for UH-application requiring only peak discharge (qp), time to peak (tp), and time base (tb) for derivation. The introduced PDFs, such as Dagum, Generalized Gamma, Log-Logistic, Gumbel Type-I, and Shifted Gompertz, replicated the observed data-derived UHs more closely than did the known PDFs, like Inverse Gaussian, two-parameter gamma distribution (2-PGD), Log-Normal, Inverse-Gamma, and Nagakami. Among the three-parameter (6 nos.), two-parameter (21 nos.), and single-parameter (3 nos.) PDFs, the Dagum, Log-Logistic, and Poisson consistently outperformed their respective counterparts in replication.

This study aims to assess various empirical synthetic unit hydrograph (SUH) methods and find the best method. Ideally, each river should have a definite rain gauge station (RGS) to get sufficient rainfall data that is available for carrying out meaningful analysis. The provisions of Indian Standard (IS) 4987:1994 determined the optimum number of RGS. In the absence of RGS, the SUH is recommended. SUHs have been developed using various methods such as Snyder's, Taylor and Schwarz, Soil Conservation Service, Mitchell's and Central Water Commission (CWC). In the present study, the Rel River Basin (RRB) is considered as the study area which has two existing RGS. IS 4987:1994 suggested that four RGS are required for more reliable rainfall data. Various efficiency criteria such as Correlation Coefficient, Pearson Coefficient, Nash Sutcliffe Efficiency, Index of Agreement, Normalized Root Mean Square Error, Mean Absolute Error, Root Mean Square Error and Kling-Gupta Efficiency have been used to compare SUH methods. The ranking of SUH methods was reported based on the compound factor (CF) through efficiency criteria. The 1.125 CF was observed as the minimum for the CWC method and recommended for determining peak discharge and timing for the study area.