Stage Discharge Research Articles

Discharge and sediment load modeling using rating curve-based missing data management

ABSTRACT Hydrological models are vital for water management to determine in-stream flow, irrigational water, domestic water supply, and biodiversity conservation. This study formulates a hydrological model with a novel approach for streamflow and sediment load in the QGIS-supported Soil and Water Assessment Tool for the Halda River catchment, a unique ecological habitat for natural carp spawning and freshwater sources. The daily simulation uses an innovative stage–discharge relationship technique from available 15-day interval flow data. The model evaluation parameters R2 values 0.80 and 0.62, and NS values 0.81 and 0.61 for calibration and validation of streamflow suggested excellent agreement in the seasonal cycle and most of the monsoon peak flow. The streamflow/precipitation ratio indicates a significant influence of groundwater through infiltration. The baseflow shows a decreasing trend. The sediment load based on suspended sediment concentration at a downstream location is 1,625 tons/day. On the contrary, the model prediction is 30 times lower. The scattered sediment load data support the model estimate by considering relatively lower intervention or land use change in its upstream. This model provides a baseline for daily flow and sediment load for scenario modeling (e.g., climate change, land use change) for environmental flow estimation of the fish habitat, freshwater supply, irrigation, and salinity intrusion.

A large-scale hydrological and hydrodynamic coupled model for flow routing in the Yangtze-Dongting system

In lowland alluvial river systems consisting of mainstream, distributaries, and floodplain lakes, the flow dynamics are characterized by changing backwater effects and seasonal water storage and release, and the bed morphology is unstable due to frequent sediment deposition and erosion. Hence, models that can accurately and efficiently simulate hydraulic interactions with low topographic data demands are required for such water systems. In this study, we present a coupled flow routing model for the Yangtze River-Dongting Lake system by coupling a 1D hydrodynamic model for the mainstream with hydrological models for distributaries and the lake. A new approach is proposed to generate a set of rating curves to represent the combined impacts of the inflow and outlet stage on the lake storage volume, thereby an innovative hydrological routing method fully considering backwater effects is established. Additionally, an implicit fully coupled algorithm is presented to integrate the hydrodynamic and hydrological models, which demonstrates ideal numerical stability and high computational efficiency. The coupled model is applied to flow routing in the Yangtze-Dongting system, with the Nash-Sutcliffe efficiency coefficients above 0.960, and most of the mean absolute error below 0.4 m (1000 m3/s) for stage (discharge). The model is also used to evaluate the impact of topographic changes during 1998–2016 on the flow process. The results indicate that the mainstream stage has decreased notably, while the reduction of the storage capacity of the lake is not yet remarkable. For the model proposed in this paper, only hydrological data and mainstream topographic data are necessary during model development, calibration, and application. In the context of continuous channel/lake bed adjustment in the middle reach of the Yangtze River Basin, the coupled model provides an effective tool for quantitatively evaluating the hydrological regime and flood process of a river system at a full scale.

Stage–discharge prediction in the multi-stage ice-covered compound channel

The multi-stage compound channel, which is a common pattern in natural alluvial rivers and the regulation projects of urban rivers, inevitably freezes in winter when it is situated in cold northern areas with high latitudes. Given that ascertaining the stage–discharge relationship for rivers is the foundation for the development of flood control schemes and water resources management, this study concentrates on proposing an analytical model for predicting the stage–discharge curves of multi-stage ice-covered compound channels. In deducing the analytical model, the cross section of the channel is first segmented into several homogeneous subregions that can be grouped into seven categories according to the geometric characteristics. Through analyzing the momentum transfer between adjacent subregions, the force balance equation for each subregion is then established to get the bulk mean velocity for the corresponding subregion, thereby obtaining the discharge by solving a tridiagonal matrix. Subsequently, measurements from two-stage and three-stage ice-covered compound channel experiments and three sets of experimental data from the literature are used to validate the performance of the proposed model. Good agreement between the predictions and the measured data suggests that the deduced model can accurately estimate the discharge for the multi-stage ice-covered compound channels when the flow depth is given. Finally, sensitivity analysis indicates that Manning's roughness coefficient of the channel bed has a more pronounced impact on the stage–discharge relationship than that of the ice cover. Moreover, when compared to the two-stage ice-covered compound channel, the multi-stage ice-covered compound channel offers greater potential for water resource utilization.

Stage–discharge relationship in an erodible compound channel with overbank floods

Due to environmental changes and anthropogenic activities, a dramatically diminished upstream sediment supply can promote riverbed erosion and alter the stage–discharge relationship in a channel with overbank flows, which can impact flood control. It is important to understand how the stage–discharge relationship in an erodible compound channel is affected and how to predict this relationship. In this study, we performed laboratory experiments in a straight compound channel with a mobile main channel under clear water scour. Stage–discharge relationships were measured before the destruction of the armor layer and after the formation of a new armor layer at the riverbed surface. The results indicated that the impact of riverbed erosion on the stage–discharge relationship cannot be ignored. Under the same discharge, the flow depth in the main channel increased, while the flow depth in the floodplains decreased after the new armor layer was formed relative to the case before armor layer destruction. Considering the impacts of the erosion depth and the variation in the bed resistance, we proposed a new method for predicting the stage–discharge relationship in an erodible compound channel after riverbed erosion. The predicted stage–discharge relationships agreed with the measurements, indicating that the proposed method could be used to precisely predict the stage–discharge relationship after riverbed erosion occurrence. The comparison of the results of the proposed method with and without considering the erosion depth supported the idea that the impact of riverbed erosion on the stage–discharge relationship must be included. Finally, the proposed method was further used to examine the influence of floodplain encroachment on flood control and riverbed erosion. Floodplain encroachment produced a larger flood flow depth on floodplains and a higher mean velocity in the main channel, suggesting that floodplain encroachment should be avoided to eliminate possible increases in flood disasters and riverbed erosion risks.

Sensitivity of small river channels in the North Carolina Piedmont to change in streamflow conditions, Atlantic Multi-decadal Oscillation, and land use/land cover change

Twenty-four years (1999–2022) of channel change is assessed using specific-gage analysis based on the United States Geological Survey (USGS) rating curve calibration data from thirteen sites (drainage area < 500 km2) to understand the sensitivity of discharge-specific stage (DSS) or its inverse, stage-specific channel capacity (SSCC) to streamflow regimes, hydroclimatological history, and land use in small Piedmont watersheds of North Carolina, USA. We compare observed channel changes to common streamflow and flood metrics, Atlantic Multi-decadal Oscillation Index (AMOI), and land use/land cover data using regression and correlation techniques to suggest drivers of change and infer sensitivity. In addition to interannual variability, our results at most sites reveal three coherent periods of DSS/SSCC variation at the sub-decadal scale as well as multidecadal trend variation. The magnitudes and frequencies of these changes indicative of potential sensitivity vary substantially amongst sites. The trendlines from the DSS plots for the full length of record indicate that six sites showed increased specific stage while the remaining seven sites showed either reduced or a near-zero change in specific stage. Coefficients of determination relating specific stage and the index of AMO are low (R2 = 0.14—0.38) with both positive and negative relationships exhibited. Multiple regression, coefficients of determination relating specific stage and average monthly discharge are more variable, ranging from 0.18 to 0.94. Both positive and negative correlations (r ≤ 0.7) are found between specific stage and basin land use/land cover intensity indices, although few are significant at 95 % confidence interval. Both qualitative observations and correlation analyses support inferences that drought and persistent low mean discharge conditions tend to increase discharge-specific stage values (decreasing SSCC), by aggradation of the bed and/or lower banks. At our sites, this may be responsible for a sub-decadal trend of increasing specific stage between roughly 2013 and 2018, followed by ongoing reductions over the subsequent period.

Modelling stage–discharge relationship of Himalayan river using ANN, SVM and ANFIS

Modelling stage–discharge relationship of Himalayan river using ANN, SVM and ANFIS

Evolutionary model for glacial lake-outburst fans at the ice-sheet front: Development of meltwater outlets and origins of bedforms

Large-scale landforms originated from jökulhlaups or glacial lake-outburst floods (GLOFs), and their small-scale components help in recognising the sedimentary environment of the flood. The GLOF fans that developed along the Pleistocene ice-sheet margin have not been investigated in detail, and north-eastern Poland, with its Megaflood Landform System and Bachanowo and Szeszupka fans, seems ideal for landform and sedimentary studies. This paper provides (1) an important opportunity to recognise the origins of glacier lake-outburst flood outlets and their evolution during two GLOFs and (2) a model of the origin of ice-marginal fans considering changes in sedimentary environment reflecting flood stages. During the first GLOF (GLOF1), the rising stage of meltwater burst triggered the formation of a supraglacial outlet and the development of the Szeszupka outburst fan. During the pulsed peak discharge, subglacial multi-channelised meltwater outburst caused the formation of the Bachanowo Gate, which was finally transformed at the flood waning stage. Such processes were associated with the widening of the floodwater subglacial routeway, when floodwater outlets rapidly spread across the glacier snout. In contrast, GLOF2 was responsible only for the Szeszupka fan erosion and development of outburst terraces. The small-scale bedforms continuum, recognised on the outburst fan surface, is associated with the development of streamlined erosional residuals, scours and their trains during the rising stage and peak discharge, while the waning stage and very end of flood conditions were favourable to the formation of pendant bars, distributive channels with erosional bars and chute bars, regardless of the feeding systems of the outburst fans.The fan deposits were OSL-dated and revealed either, likely, overly old ages or an age of 13.2 ± 0.9 ka. The latter age would imply the ‘normal’ meltwater outflow having a correlation with the events in the region. Nevertheless, this age might be considered a minimum age of the flood.

Impact of a concentrated lateral inflow and stage–discharge relation imposed at the downstream end of a finite channel for the diffusive wave model

Impact of a concentrated lateral inflow and stage–discharge relation imposed at the downstream end of a finite channel for the diffusive wave model

Remote sensing assessment of anthropogenic and climate variation effects on river channel morphology and vegetation: Impact of dry periods on a European piedmont river

AbstractRivers are subject to increasing human pressure, resulting in a loss of their natural characteristics, further enhanced by climate change. The present study focuses on a piedmont reach of the Italian Po River and combines Landsat satellite information with hydrological records to investigate changes in sandbars exposure and riparian vegetation coverage, considering the summer period of 1984–2022. Satellite data were handled via Google Earth Engine, looking at common indexes such as the Modified Normalized Difference Water Index, which was used to identify temporal variations in wetted channel area, and the Normalized Difference Vegetation Index, considered as a proxy of vegetation coverage variations. Changes in the river hydrology were analysed by looking at the annual minimum water levels, the discharge duration curve, the stage–discharge relationship and the yearly annual water volume. Results suggest that a process of oversimplification is affecting this reach of the Po River, showing how climate change can affect piedmont European watercourses. Indeed, after an initial period where bars tended to be barer and somehow stable over time, in the most recent decade a different trend appeared, with vegetation able to colonize the exposed sandbars more. Using the Po River as an exemplary case study, this work suggests that prolonged dry periods, which are more common in recent decades, might impact large and medium rivers located in temperate climates, favouring the development of vegetation on exposed sandbars, eventually resulting in a less dynamic active channel.

Rating curve development and uncertainty analysis in mountainous watersheds for informed hydrology and resource management

Accurate measurement of continuous stream discharge poses both excitement and challenges for hydrologists and water resource planners, particularly in mountainous watersheds. This study centers on the development of rating curves utilizing the power law at three headwaters of the lesser Himalayas—Aglar, Paligaad, and Balganga—through the installation of water level recorders for stage measurement and salt dilution for discharge measurement from 2014 to 2016. The stream stage–discharge relationship, crucially known as the rating curve, is susceptible to numerous factors in mountainous watersheds that are often challenging to comprehend or quantify. Despite significant errors introduced during the rating curve development, such as stemming from observations, modeling, and parameterization, they are frequently overlooked. In this study, acknowledging the inherent uncertainty, we employ the maximum-likelihood method to assess uncertainty in the developed rating curve. Our findings reveal substantial inconsistency in the stage–discharge relationship, particularly during high flows. A novel contribution of this study is introducing a weighing factor concept that correlates uncertainty with the morphological parameters of the watershed. The higher value of the weighting factor in Paligaad (0.37) as compared to Balganga (0.35) and less in the case of Aglar (0.27) will have more uncertainty. The authors contend that precise rating curves and comprehensive uncertainty analyses can mitigate construction costs, foster robust decision-making, and enhance the perceived credibility of decisions in hydrology and water resource management.

Research on stage–discharge relationship model based on random forest algorithm

Hydrological simulations and predictions are vital aspects of hydrological change research. Accurate predictions of hydrological factors such as stage and discharge are essential for water resources planning, reservoir dispatching and operation, shipping management and flood control. River discharge forecasting during flood seasons is an important issue in water resources planning and management. To improve the calibration accuracy and stability of the stage–discharge relationship model, the feasibility of integrated algorithms for studying the stage–discharge relationship was explored. A random forest (RF) algorithm based on a neural network (NN) was developed using a framework of integrated algorithms. First, the Levenberg–Marquardt (LM) algorithm was used to optimise the weight updating process of a back-propagation (BP) NN and improve the convergence speed. Then, the LM-BP algorithm was used as a decision tree to build an RF algorithm. The model was tested using hydrological data from Hongqi station on the Dadu River in China in the flood season. Results for the classical model, BP NN model, LM-BP NN model and optimised algorithm model were evaluated based on the mean absolute error (MAE), mean square error (MSE) and mean absolute percentage error (MAPE). The performance indicators showed that the optimised algorithm model (MAE = 3.13 m3/s, MSE = 19.28 m3/s and MAPE = 1.8%) was superior to the other models and showed high accuracy and good stability in flood-season flow forecasting.

River adjustments in response to human activities: A case study of the lower Beijiang River, China

AbstractIntensive human activity has caused significant changes in the river morphology and hydrological characteristics of the Pearl River Delta. Particularly, in‐channel mining and dam construction have induced remarkable levels of downward riverbed incision. Although strict control measures have been implemented for in‐channel sand mining, it remains unclear how the river has evolved since the abandonment of high‐intensity mining and its impact on flow diversion at the downstream confluence. This study presents the hydrological and morphological adjustments in the lower Beijiang River, the second largest tributary of the Pearl River, under the impacts of human interventions. A hydrodynamic model was developed to reveal the impacts of riverbed deformation on the flow diversion ratio at Sixianjiao, the confluence of the Beijaing River and the Xijiang River. The results showed that construction of cascade reservoirs upstream reach did not strongly influence run‐off, whereas incoming sediment loads were decreased. Because of upstream damming and in‐channel sand mining, a dramatic downward incision was observed in the lower Beijiang River, with a degradation volume of approximately 239.8 million m3 from 1999 to 2012. Particularly, in the upper reach, the incision depth was typically larger than 8 m. Riverbed incision caused continuous changes in the water stage–discharge relationship, and discharge increased remarkably under the same water level at the three hydrometric stations. During 2012–2020, because in‐channel sand mining was strictly controlled, rapid degradation was alleviated, deposition occurred in some cross‐sections and the deformation volume decreased by approximately 90% compared to that in the last period. A fast downward incision induced a change in flow exchange between the two rivers, and the flow diversion ratio of the Beijiang River increased from an average of 17% before 1998 to more than 21%.

Calibrating Complexity: A Comprehensive Approach to Developing Stage–Storage–Discharge Relationships for Geographically Isolated Wetlands (GIWs) in W-C Florida

Geographically isolated wetlands (GIWs) play a critical role in regional hydrology, streamflow, groundwater recharge, evapotranspiration, and water quality. Despite their importance, research on quantifying discharges from these wetlands remains scarce. This study focuses on the hydrological characterization of GIWs in W-C Florida, a region where they cover a significant proportion of the land surface. The paper introduces a new procedure for developing Stage–Storage–Discharge (rating) characteristics essential for deterministic hydrological modeling in larger geographic areas. The approach synthesizes and extends previous research methodologies and offers simplified key modeling coefficients (m and n), which act as intelligent calibration knobs. These coefficients, when coupled with easily derivable physical attributes such as areas, slopes, and elevations, allow for the accurate simulation of downstream discharge timings and magnitudes, including flood behavior. The proposed method was tested using observational data from well-calibrated models. The results indicated a relative error of −7.2% for stage–storage and 15% for stage–discharge. GIS-based techniques were evaluated against surveyed data, and the results showed an accuracy of 0.16 m (0.52 ft) in estimating both the invert elevation and the maximum depth of GIWs. This effort will ultimately contribute to a better understanding and management of these critical ecosystems.

Stage discharge relations of a trapezoidal broad-crested weir pierced by a circular culvert

The present work focusses on the stage discharge relationship of a trapezoidal broad-crested weir pierced by a circular shape culvert at its base. The objective is to evaluate the relevance of the experimental and of the predictive superposition approaches for this hydraulic structure frequently encountered at the outlet of flood prevention basins, combining a flow through the culvert and a flow over the weir. The “experimental” superposition consists of the linear sum of the experimental relations of both elementary structures. Compared to the stage discharge relation of the complete structure, this sum performs well with a difference in discharge that does not exceed 15 %. The sum of discharges through both elementary structures slightly exceeds the discharge through the complete structure for an upstream head slightly above the weir crest elevation; it slightly underestimates this discharge for a larger upstream head, as already reported in the literature. The “predictive” superposition approach consists in predicting the stage discharge relation of the hydraulic structure using the sum of the stage discharge relations, available in the literature, for the elementary structures. The predictive superposition proves to be highly accurate for our combined hydraulic structure, especially for flow conditions with an incoming head high enough, for which the flow over the weir dominates.

New proglacial meteorology and river stage observations from Inglefield Land and Pituffik, NW Greenland

Abstract. Meltwater runoff from the Greenland ice sheet (GrIS) is an important contributor to global sea level rise, but substantial uncertainty exists in its measurement and prediction. Common approaches for estimating ice sheet runoff are in situ gauging of proglacial rivers draining the ice sheet and surface mass balance (SMB) modeling. To obtain hydrological and meteorological data sets suitable for both runoff stage characterization and, pending the establishment of stage–discharge curves, SMB model evaluation, we established an automated weather station (AWS) and a cluster of traditional and experimental river stage sensors on the Minturn River, the largest proglacial river draining Inglefield Land, NW Greenland. Secondary installations measuring river stage were installed in the Fox Canyon River and North River at Pituffik Space Base, NW Greenland. Proglacial runoff at these sites is dominated by supraglacial processes only, uniquely advantaging them for SMB studies. The three installations provide rare hydrological time series and an opportunity to evaluate experimental measurements of river stage from a harsh, little-studied polar region. The installed instruments include submerged vented and non-vented pressure transducers, a bubbler sensor, experimental bank-mounted laser rangefinders, and time-lapse cameras. The first 3 years of observations (2019 to 2021) from these stations indicate (a) a meltwater runoff season from late June to late August/early September that is roughly synchronous throughout the region; (b) the early onset (∼ 23 June to 8 July) of a strong diurnal runoff signal in 2019 and 2020, suggesting minimal meltwater storage in snow and/or firn; (c) 1 d lagged air temperature that displays the strongest correlation with river stage; (d) river stage that correlates more strongly with ablation zone albedo than with net radiation; and (e) the late-summer rain-on-ice events appear to trigger the region's sharpest and largest floods. The new gauging stations provide valuable in situ hydrological observations that are freely available through the PROMICE network (https://promice.org/weather-stations/, last access: 14 September 2023).

The Processes of Aggradation and Incision in the Channels in the Terek River Basin, the North Caucasus: The Hydrological Fluvial Archives of the Recent Past

The rates of incision and aggradation in the channels in the Terek River basin (North Caucasus) for the last 50–85 years were estimated at 18 gauging stations. The stage–discharge method (annual low water stages at the same discharges) was applied. The stability of the Terek River channel was recorded on the tectonically subsiding Tersko–Kuma Lowland. On the subsiding Kabardian Plain, channel aggradation up to 14 mm a−1 was registered. The rapid (~32 mm a−1) incision of the Terek River occurs within the antecedent valley of the rising Sunzha Ridge, causing regressive erosion and incision (~25 mm a−1) of rivers on the Ossetian Plain, despite its tectonic subsiding. The rivers in the uplifting mountains of the North Caucasus transport the sediments delivered from slopes as climatically controlled debris flows. Aggradation and incision here alternate without a visible overall trend. The rates of modern channel bed deformations are 10 to 100 times higher than the mean rates of tectonic movements. The main effect of tectonics is the changes in river channel slopes, which cause changes in the bed load transport budget and channel bed deformation. Human-made constructions induce rapid deformations in the channels but have a local effect.

Influence of frequency on the partial discharge characteristics of biaxially oriented polypropylene film under nanosecond pulse voltage

Partial discharge (PD) is one of the key factors leading to premature insulation failure of film capacitors used in pulse power devices. To study the effect of frequency on the PD characteristics of biaxially oriented polypropylene (BOPP) film, a sphere-plate electrode was used to simulate defects of the air gap between the film layers. PD experiments of the BOPP film were carried out under 1, 10, 100, 500 Hz, and 1 kHz with a rising edge of 65 ns and a pulse width of 300 ns. The results show that the repetitive partial discharge inception voltage (RPDIV), the number of discharges, the rising stage discharge (RSD) amplitude, and the falling stage discharge (FSD) time-lag, all show an increase and then decrease with increasing pulse frequencies and reach a maximum value at a pulse frequency of 100 Hz. Moreover, the FSD discharge amplitude and the RSD discharge time-lag increase with an increasing pulse frequency. From the perspective of initial electron generation, the quantitative mathematical relationship between PD characteristics (RPDIV, PD amplitude, PD number, and PD time-lag) and frequency was established based on the Fowler–Nordheim field emission effect for the first time, which can reflect the influence of frequency on the memory effect and the development process of PD. The results can provide an experimental basis and a mechanistic explanation for the evaluation of PD characteristics for film capacitors under nanosecond pulse voltage.

Could a one-size-fits-all approach apply to the extension of stage-discharge relationships at flow-gauging weirs?

At a flow-gauging weir, the stage or flow depth is normally measured continuously and converted into discharge using a stage-discharge (SD) rating curve (RC). During flood events, the observed water levels often exceed the flow-gauging weir's designed measuring capacity or structural limit. Subsequently, the standard calibration of the flow-gauging weir becomes irrelevant and the extension of the SD RC for above-structure-limit flow conditions is required. This paper attempts to identify a one-size-fits-all approach for the extension of SD RCs by assessing seven indirect hydraulic extension methods and a one-dimensional HEC-RAS modelling approach against direct SD measurements or extension methods at selected flow-gauging sites in South Africa. In considering a ranking-based selection procedure and associated goodness-of-fit (GOF) criteria, the stepped backwater analysis, slope-area method, and 1-D HEC-RAS steady flow modelling proved to be the most appropriate. The other indirect extension methods resulted in larger statistical differences between the at-site benchmark and modelled values. Given that the extension of RCs is significantly more affected by the site and river reach geometry, initial hydraulic conditions, flow regimes, and level of submergence at high discharges than the actual extension method used, it was confirmed that a one-size-fits-all approach cannot be applied for the extension of SD RCs in South Africa.

Modelling and Numerical Simulation Approaches to the Stage–Discharge Relationships of the Lansheng Bridge

In recent years, extreme rainfall events with short delays and heavy rainfall have often occurred due to severe climate change. In 2015, Typhoon Soudelor caused a short-delayed heavy rainfall event in Nanshih River, which caused damage to a section of the Lansheng Bridge discharge station. The section was relocated upstream to rebuild the discharge station in 2019. However, the new discharge station cannot measure high flow due to the bridge structure. The flow observation range of Lansheng Bridge is therefore limited to normal flow, making it impossible to accurately estimate the flow during high-water stages. The purpose of this study is to use the past flow data of Nanshih River to estimate the flow rate under different return periods using frequency analysis. We used a Digital Elevation Model (DEM) to map the river’s topography, and used the 3D hydraulic calculations of the FLOW-3D model to estimate the water stage and discharge of the Lansheng Bridge. We then verified the accuracy of the model with the measured flow and water stage, and finally used the water stage and discharge data obtained from numerical simulation to construct the stage–discharge rating curve of the Lansheng Bridge. In addition to preventing flood disasters, this study approach can provide reliable data for use in water conservation. It may also be utilized to overcome the problem of measuring and estimating high flow during typhoon floods.

Laboratory Study of the Hydraulic Performance of the A-Type Triangular Piano Key Weir

A piano key weir (PKW), a new type of weir aiming to increase the discharge capacity of an existing dam, was recently designed. Despite a large body of research in this field, only a few studies were conducted on A-type triangular piano key weirs (TPKW) in straight channels. In this context, this present research sought to study the flow regime, stage–discharge relationship, and discharge coefficient. Experiments were carried out using nine TPKW models and three linear weirs (LW) as the control weirs. The results indicated that the triangular piano key weirs are capable of passing a higher discharge in similar laboratory conditions compared to linear key weirs due to their longer length. For a given h/P ratio (h is the water head over the weir crest, and P is the weir height) and constant length (Le), an increase in the weir height from 0.07 m to 0.15 m decreases the discharge coefficient by approximately 20%. From sensitivity analysis, the most influential parameters for the tested TPKW models are the h/Le dimensionless ratio, followed by the P/Le and Fr. Moreover, the discharge coefficient has a reverse trend when the dimensionless parameters h/P, h/Le, and Froude number are increased. However, with decreasing h/Le, the discharge coefficient of TPKW tends to that of a broad-crested weir because of local submergence. It is expected that the results obtained will be a reference for researchers who work in this field.