Regionalization of unit hydrograph Parameters: 2. Uncertainty analysis

Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.     

Regionalization of unit hydrograph Parameters: 2. Uncertainty analysis

Hydrologic model parameters obtained from regional regression equations are subject to uncertainty. Consequently, hydrologic model outputs based on the stochastic parameters are random. This paper presents a systematic analysis of uncertainty associated with the two parameters, N and K, in Nash's IUH model from different regional regression equations. The uncertainty features associated with N and K are further incorporated to assess the uncertainty of the resulting IUH. Numerical results indicate that uncertainty of N and K from the regional regression equations are too significant to be ignored.     

Correlation of the velocity parameter of three geomorphological instantaneous unit hydrograph models

Three geomorphological instantaneous unit hydrograph (GIUH) models are investigated. These GIUHs were derived as a function of watershed geomorphological characteristics. The geomorphological input parameters of the models were determined for 10 basins in Indiana, USA. The three GIUH models were used to simulate 187 observed runoff hydrographs of these basins. The non-measurable velocity parameters of the GIUH models were optimized and the relationships between them were investigated. The results of the investigation show that the velocity parameters of the three models are correlated. © 1998 John Wiley & Sons, Ltd.     

Introducing a new conceptual instantaneous unit hydrograph model based on a hydraulic approach

ABSTRACT

A novel approach is introduced for simulation of instantaneous unit hydrographs (IUHs). The model consists of a series of linear reservoirs that are connected to each other, and is referred to as the inter-connected linear reservoir model (ICLRM). By assuming the flow between two reservoirs is a linear function of the difference between the water levels in the reservoirs, a system of first-order linear differential equations is obtained as the ICLRM governing equation. By solving the equations, the discharge from the last reservoir is considered as an IUH. A small-scale laboratory device was constructed for the simulation of IUHs using the model. By studying four hydrographs extracted from the literature, and simulating them using both the ICLRM and the Nash model, it is concluded that the ICLRM can predict these hydrographs more accurately than the Nash model. Due to the simplicity of the construction and operation of the ICLRM and, more importantly, its visual aspect, the ICLRM may be considered as an effective educational tool for studying IUHs.     

The role of hydrograph indices in parameter estimation of rainfall–runoff models

A reliable prediction of hydrologic models, among other things, requires a set of plausible parameters that correspond with physiographic properties of the basin. This study proposes a parameter estimation approach, which is based on extracting, through hydrograph diagnoses, information in the form of indices that carry intrinsic properties of a basin. This concept is demonstrated by introducing two indices that describe the shape of a streamflow hydrograph in an integrated manner. Nineteen mid‐size (223–4790 km²) perennial headwater basins with a long record of streamflow data were selected to evaluate the ability of these indices to capture basin response characteristics. An examination of the utility of the proposed indices in parameter estimation is conducted for a five‐parameter hydrologic model using data from the Leaf River, located in Fort Collins, Mississippi. It is shown that constraining the parameter estimation by selecting only those parameters that result in model output which maintains the indices as found in the historical data can improve the reliability of model predictions. These improvements were manifested in (a) improvement of the prediction of low and high flow, (b) improvement of the overall total biases, and (c) maintenance of the hydrograph's shape for both long‐term and short‐term predictions. Copyright © 2005 John Wiley & Sons, Ltd.     

Application of the geomorphological instantaneous unit hydrograph theory to development of forecasting models in Poland

ABSTRACT

Geomorphological instantaneous unit hydrograph (GIUH) theory has been applied for the estimation of the parameters of two conceptual models: a linear cascade model and a Laurenson-type model. Conceptual models, especially the linear cascade model, are more convenient for operational forecasting than the original GIUH model. A single linear reservoir model is suggested, with limited storage to represent the subsurface flow component. Subsurface flow is significant in Polish mountainous river catchments. Preliminary results of applying the model to operational flood forecasting are described.     

Uncertainty estimates for surface runoff models

A lower bound for variance in surface runoff modelling estimates is advanced. The bound is derived using a linear unit hydrograph approach which utilizes a discretization of the catchment into an arbitrary number of subareas, a linear routing technique for channel flow effects, a variable effective rainfall distribution over the catchment, and calibration parameter distributions developed in correlating rainfall-runoff data by the model. The uncertainty bound reflects the dominating influence of the unknown rainfall distribution over the catchment and is expressed as a distribution function that can be reduced only by supplying additional rainfall-runoff data. It is recommended that this uncertainty distribution in modelling results be included in flood control design studies in order to incorporate a prescribed level of confidence in flood protection facilities.     

Uncertainty estimation of pathlines in ground water models

A method is proposed to estimate the uncertainty of the location of pathlines in two-dimensional, steady-state confined or unconfined flow in aquifers due to the uncertainty of the spatially variable unconditional hydraulic conductivity or transmissivity field. The method is based on concepts of the semianalytical first-order theory given in Stauffer et al. (2002, 2004), which allows estimates of the lateral second moment (variance) of the location of a moving particle. However, this method is reformulated in order to account for nonuniform recharge and nonuniform aquifer thickness. One prominent application is the uncertainty estimation of the catchment of a pumping well by considering the boundary pathlines starting at a stagnation point. In this method, the advective transport of particles is considered, based on the velocity field. In the case of a well catchment, backtracking is applied by using the reversed velocity field. Spatial variability of hydraulic conductivity or transmissivity is considered by taking into account an isotropic exponential covariance function of log-transformed values with parameters describing the variance and correlation length. The method allows postprocessing of results from ground water models with respect to uncertainty estimation. The code PPPath, which was developed for this purpose, provides a postprocessing of pathline computations under PMWIN, which is based on MODFLOW. In order to test the methodology, it was applied to results from Monte Carlo simulations for catchments of pumping wells. The results correspond well. Practical applications illustrate the use of the method in aquifers.     

Runoff estimation for an ungauged catchment using geomorphological instantaneous unit hydrograph (GIUH) models

A geomorphological instantaneous unit hydrograph (GIUH) is derived from the geomorphological characteristics of a catchment and it is related to the parameters of the Clark instantaneous unit hydrograph (IUH) model as well as the Nash IUH model for deriving its complete shape. The developed GIUH based Clark and Nash models are applied for simulation of the direct surface run‐off (DSRO) hydrographs for ten rainfall‐runoff events of the Ajay catchment up to the Sarath gauging site of eastern India. The geomorphological characteristics of the Ajay catchment are evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). The performances of the GIUH based Clark and Nash models in simulating the DSRO hydrographs are compared with the Clark IUH model option of HEC‐1 package and the Nash IUH model, using some commonly used objective functions. The DSRO hydrographs are computed with reasonable accuracy by the GIUH based Clark and Nash models, which simulate the DSRO hydrographs of the catchment considering it to be ungauged. Inter comparison of the performances of the GIUH based Clark and Nash models shows that the DSRO hydrographs are estimated with comparable accuracy by both the models. Copyright © 2007 John Wiley & Sons, Ltd.     

Comparative analysis of a geomorphology‐based instantaneous unit hydrograph in small mountainous watersheds

A conceptual insytnataneous unit hydrograph (IUH) based on geomorphologival association of linear reservoirs (GR) previously developed by the authors has been compared with other IUH models: a distributed GR variation (GR(v)), the Nash IUH, the Chutha and Dooge IUH, and the Troutman and Karlinger IUH for the analysis of direct runoff hydrographs recorded in three experimental watershed of the north of Spain. The comparison was made through a calibration‐validation process in which a leave‐one‐out cross‐validation method was applied. The results indicate the satisfactory performance of all the models, with the advantage for the GR model of the dependence on only one parameter, which can be identified from the watershed and event characteristics. This property makes its use easier than that of other models. Copyright © 2011 John Wiley & Sons, Ltd.     

Application of a land surface model for simulating rainfall streamflow hydrograph: 2. Comparison with hydrological models

Rainfall runoff hydrographs for 12 river basins ∼10³ km² in area, simulated using land surface model SWAP, are compared with analogous hydrographs obtained using hydrological models that took part in the International Model Parameter Estimation Experiment project and demonstrated the best results. All models were calibrated against data on daily river runoff from each basin over a 20-year period (1960–1979). Optimized model parameters were used to simulate runoff hydrographs for the following 19 years (1980–1998). The comparison of the modeled hydrographs for 12 basins in different calculational periods demonstrated that the SWAP model can simulate river runoff with an accuracy comparable with that of hydrological models.     

Petrological models of the oceanic lithosphere: Geophysical and geochemical tests

Petrological models of the oceanic lithosphere are tested to satisfy geophysical and geochemical constraints within the framework of plate tectonics. Quartz eclogite, olivine eclogite, peridotite and dunite are considered as the material of the lithosphere. The temperature at the base of the lithosphere is assumed to be the solidus temperature. This temperature, the thermal conductivity, and the heat flow and topography changes with age are used as the geophysical constraints. The compressional wave velocity-depth profile is used to select preferred models. Among geophysically successful models, high-temperature models are preferred to wet low-temperature models, because the low-temperature models have difficulties in explaining the mechanism of generation of oceanic basalt magmas. A preferred model is a two-layer model 70 km thick consisting of peridotite at the upper lithosphere and olivine eclogite at the lower lithosphere bounded at the base by the dry solidus.     

An extended Bayesian sediment fingerprinting mixing model for the full Bayes treatment of geochemical uncertainties

Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (JAGS and Stan) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and nonconservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and nonconservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with nonconservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies.     

Hydrograph and unit hydrograph derivation in arid regions

Arid and semi‐arid regions expose special hydrological features that are distinctive from humid areas. Unfortunately, humid‐region hydrological empirical formulations are used directly in the arid and semi‐arid regions without care about the basic assumptions. During any storm rainfall in arid regions, rainfall, infiltration and runoff components of the hydrological cycle have impacts on water resources. The basis of the methodology presented in this paper is the ratio of runoff increment to rainfall increment during an infinitesimally small time duration. This is the definition of runoff coefficient for the same infinitesimal time duration. The ratio is obtained through rational, physical and mathematical combination of hydrological thinking and then integrated with the classical infiltration equation for the hydrograph determination. The parameters of the methodology are explained and their empirical estimations are presented. The methodology works for rainfall and runoff from ungauged watersheds where infiltration measurement can be performed. The comparison of the new approach with different classical approaches, such as the rational formula and Soil Conservation Service method, are presented in detail. Its application is performed for two wadis within the Kingdom of Saudi Arabia. Copyright © 2006 John Wiley & Sons, Ltd.     

The meaning of oscillations in unit hydrograph S-curves

ABSTRACT

The Duhamel superposition integral is used to obtain some exact solutions for unit hydrograph applications. These equations and numerical examples are used to show that oscillations will occur in an S-curve when the time step is less than the excess rainfall duration if the measured hydrograph differs from a hydrograph that would be obtained by solving a linear differential equation with time-independent coefficients. The implications of this result with regard to the calculation of the instantaneous unit hydrograph (IUH) are discussed.     

An examination of geochemical modelling approaches to tracing sediment sources incorporating distribution mixing and elemental correlations

The identification of sediment sources is fundamental to the management of increasingly scarce water resources. Tracing the origin of sediment with elemental geochemistry is a well‐established approach to determining sediment provenance. Fundamental to the confident apportionment of sediment to their lithogenic sources is the modelling process. Recent approaches have incorporated distributions throughout the modelling process including source contribution terms for two end‐member sources. The shift from modelling source samples to modelling samples drawn from distributions has removed relationships, including potential correlations between elemental concentrations, from the modelling process. Here, we present a novel modelling approach that re‐incorporates correlations between elemental concentrations and models distributions for source contribution terms for multiple source end members. Artificial mixtures, based on catchment sources samples, were created to test the accuracy of this correlated distribution model and also examine modelling approaches used in the literature. The most accurate model incorporates correlations between elements, uses the absolute mixing model difference and does not use any weighting. This model was then applied to identify the sources of sediment in three South East Queensland catchments and demonstrated that Quaternary Alluvium is the most dominant source of sediment in these catchments (μ 44%, σ 12%). This study demonstrates that it is important to understand how different weightings may impact modelling results. Copyright © 2014 John Wiley & Sons, Ltd.     

Design hydrograph estimation in small and ungauged watersheds: continuous simulation method versus event‐based approach

The proper assessment of design hydrographs and their main properties (peak, volume and duration) in small and ungauged basins is a key point of many hydrological applications. In general, two types of methods can be used to evaluate the design hydrograph: one approach is based on the statistics of storm events, while the other relies on continuously simulating rainfall‐runoff time series. In the first class of methods, the design hydrograph is obtained by applying a rainfall‐runoff model to a design hyetograph that synthesises the storm event. In the second approach, the design hydrograph is quantified by analysing long synthetic runoff time series that are obtained by transforming synthetic rainfall sequences through a rainfall‐runoff model. These simulation‐based procedures overcome some of the unrealistic hypotheses which characterize the event‐based approaches. In this paper, a simulation experiment is carried out to examine the differences between the two types of methods in terms of the design hydrograph's peak, volume and duration. The results conclude that the continuous simulation methods are preferable because the event‐based approaches tend to underestimate the hydrograph's volume and duration. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of growing watershed imperviousness on hydrograph parameters and peak discharge

An increasing impervious area is quickly extending over the Wu‐Tu watershed due to the endless demands of the people. Generally, impervious paving is a major result of urbanization and more recently has had the potential to produce more enormous flood disasters than those of the past. In this study, 40 available rainfall–runoff events were chosen to calibrate the applicable parameters of the models and to determine the relationships between the impervious surfaces and the calibrated parameters. Model inputs came from the outcomes of the block kriging method and the non‐linear programming method. In the optimal process, the shuffled complex evolution method and three criteria were applied to compare the observed and simulated hydrographs. The tendencies of the variations of the parameters with their corresponding imperviousness were established through regression analysis. Ten cases were used to examine the established equations of the parameters and impervious covers. Finally, the design flood routines of various return periods were furnished through use of approaches containing a design storm, block kriging, the SCS model, and a rainfall‐runoff model with established functional relationships. These simulated flood hydrographs were used to compare and understand the past, present, and future hydrological conditions of the watershed studied. In the research results, the time to peak of flood hydrographs for various storms was diminished approximately from 11 h to 6 h in different decrements, whereas peak flow increased respectively from 127 m³ s^?1 to 629 m³ s^?1 for different storm intensities. In addition, this study provides a design diagram for the peak flow ratio to help engineers and designers to construct hydraulic structures efficiently and prevent possible damage to human life and property. Copyright © 2007 John Wiley & Sons, Ltd.     

Investigating sea-state effects on flash flood hydrograph and inundation forecasting

A common source of uncertainty in flood inundation forecasting is the hydrograph used. Given the role of sea-air-hydro-land chain processes on the water cycle, flood hydrographs in coastal areas can be indirectly affected by sea state. This study investigates sea-state effects on precipitation, discharge, and flood inundation forecasting implementing atmospheric, ocean wave, hydrological, and hydraulic-hydrodynamic coupled models. The Chemical Hydrological Atmospheric Ocean wave System (CHAOS) was used for coupled hydro-meteorological-wave simulations ‘accounting’ or ‘not accounting’ the impact of sea state on precipitation and, subsequently, on flood hydrograph. CHAOS includes the WRF-Hydro hydrological model and the WRF-ARW meteorological model two-way coupled with the WAM wave model through the OASIS3-MCT coupler. Subsequently, the 2D HEC-RAS hydraulic-hydrodynamic model was forced by the flood hydrographs and map the inundated areas. A flash flood event occurred on 15 November 2017 in Mandra, Attica, Greece, causing 24 fatalities, and damages was selected as case study. The calibration of models was performed exploiting historical flood records and previous studies. Human interventions such as hydraulic works and the urban areas were included in the hydraulic modelling geometry domain. The representation of the resistance caused by buildings was based on Unmanned Aerial System (UAS) data while the local elevation rise method was used in the urban-flood simulation. The flood extent results were assessed using the Critical Success Index (CSI), and CSI penalize. Integrating sea-state affected the forecast of precipitation and discharge peaks, causing up to +24% and from −8% to +36% differences, respectively, improving inundation forecast by 4.5% and flooding additional approximately 70 building blocks. The precipitation forcing time step was also highlighted as significant factor in such a small-scale flash flood. The integrated multidisciplinary methodological approach could be adopted in operational forecasting for civil protection applications facilitating the protection of socio-economic activities and human lives during similar future events.