Derivation of instantaneous unit hydrographs using linear reservoir models

In this research, a new conceptual model for producing instantaneous unit hydrographs (IUHs) is introduced by a linear combination of the Nash model, which assumes that the discharge from a reservoir is a linear function of its storage, and a model called inter-connected linear reservoir model (ICLRM), which assumes that the discharge from a reservoir is a linear function of the difference of its storage and its adjacent downstream reservoir. By employing these assumptions, a system of first-order linear differential equations with three degrees of freedom (storage coefficient, number of reservoirs, and weighting coefficient) is obtained as the governing equation for the proposed model. This model may be considered as the general form of the two models and is therefore capable of simulating IUHs laying between these two models. To show the capabilities of the model, linear and curvilinear soil conservation service (SCS) hydrographs are simulated using dimensionless hydrographs obtained by this model. Moreover, several real hydrographs were simulated by the proposed model and compared with hydrographs obtained by Nash, ICLRM, and SCS models. The results show that the model yields more accurate results compared to other studied models and may be considered as a new model for simulating IUHs.

The uncertainties of synthetic unit hydrographs applied for basins with different runoff generation processes

ABSTRACT Synthetic unit hydrographs (SUH) are useful tools for the estimation of maximum flows in basins lacking historical records of measurements. However, these methods have many uncertainties and do not always produce results consistent with reality. This study comparatively analyzed the uncertainty of the application of the Snyder, SCS, and Clark HUS methods, widely used, in relation to the observed hydrographs, in the Pequeno River and the Espingarda River basins, located in the State of Paraná, considered small from the point of view of the drainage area. The simulation was performed using the HEC-HMS 4.2.1 software considering a combination of parameters that produced the higher and lower peak flow, respectively named as conservative and bold approaches. It was verified that the SUH methods, in general, overestimated the peak flows for both basins under study. In addition, the results obtained showed that SUH are fundamentally conservative models so that a bold approach in estimating the parameters input leads to results with smaller errors in simulated peak flows. Even running the SUH with the real excess rainfall as input there is an overestimation of the peak flow. SCS SUH produced the highest peak flows and consequently the largest errors while Snyder’s SUH produced the smallest errors. The magnitude of the overestimation of the peak flow for the Pequeno River was up to 60 folds. Its geology features suggest a Dunnian runoff generation process, which explains the larger errors.

The Role of Topography on the Shape of Unit Hydrographs in Small and Medium Sized Watersheds through a Physical Model

This study intends to establish the main relations between topographic characteristics of the watershed and the main parameters of the unit hydrograph measured at the outlet. It looks to remove the subjectivity found in traditional synthetic methods and the trial and error setting of the main parameters of the hydrograph. The work was developed through physical experimentation of the rainfall-runoff process using the observed information of different watersheds of Chiapas, Mexico, as the reference. The experiments were carried out on a state-of-the-art semi-automatic runoff simulator, which was designed and built specifically for this study. Polynomial regression and fuzzy logic models were obtained to confirm the hypothesis of hydrological parameters being obtained from topographic data only by assuming uniform precipitation. Empirical relations were found for the peak flow, time to peak, base time and volume of the unit hydrograph and the watershed area, the main stream average slope, and the length of the stream of highest order. The main finding is that a unit hydrograph can be described based only on the watershed area when fuzzy logic models are applied.

Effectof Unit Hydrographs and Rainfall Hyetographs on Critical Rainfall Estimates of Flash Flood

To obtain critical rainfall (CR) estimates similar to the rainfall value that causes minor basin outlet flooding, and to reduce the flash flood warning missed/false alarm rate, the effect of unit hydrographs (UHs) and rainfall hyetographs on computed threshold rainfall (TR) values was investigated. The Tanjia River basin which is a headwater subbasin of the Greater Huai River basin in China was selected as study basin. Xin’anjiang Model, with subbasins as computation units, was constructed, and time-variant distributed unit hydrographs (TVUHs) were used to route the channel network concentration. Calibrated Xin’anjiang Model was employed to derive the TVUHs and to obtain the maximum critical rainfall duration (Dmax) of the study basin. Initial soil moisture condition was represented by the antecedent precipitation index (Pa). Rainfall hyetographs characterized by linearly increasing, linearly decreasing, and uniform hyetographs were used. Different combinations of the three hyetographs and UHs including TVUHs and time-invariant unit hydrographs (TIVUHs) were utilized as input to the calibrated Xin’anjiang Model to compute the relationships between TR and Pa (TR-Pa curves) by using trial and error methodology. The computed TR-Pa curves reveal that, for given Pa and UH, the TR corresponding to linearly increasing hyetograph is the minimum one. So, the linearly increasing hyetograph is the optimum hyetograph type for estimating CR. In the linearly increasing hyetograph context, a comparison was performed between TR-Pa curves computed from different UHs. The results show that TR values for different TIVUHs are significantly different and the TR-Pa curve gradient of TVUHs is lower than that of TIVUHs. It is observed that CR corresponds to the combination of linearly increasing hyetograph and TVUHs. The relationship between CR and Pa (CR-Pa curves) and that between CR and duration (D) (CR-D curves) were computed. Warnings for 12 historical flood events were performed. Warning results show that the success rate was 91.67% and that the critical success index (CSI) was 0.91. It is concluded that the combination of linearly increasing hyetograph and TVUHs can provide the CR estimate similar to the minimum rainfall value necessary to cause flash flooding.

Data-Driven Modeling and the Influence of Objective Function Selection on Model Performance in Limited Data Regions

The identification of unit hydrographs and component flows from rainfall, evapotranspiration and streamflow data (IHACRES) model has been proven to be an efficient yet basic model to simulate rainfall–runoff processes due to the difficulty in obtaining the comprehensive data required by physical models, especially in data-scarce, semi-arid regions. The success of a calibration process is tremendously dependent on the objective function chosen. However, objective functions have been applied largely in over daily and monthly scales and seldom over sub-daily scales. This study, therefore, implements the IHACRES model using ‘hydromad’ in R to simulate flood events with data limitations in Zhidan, a semi-arid catchment in China. We apply objective function constraints by time aggregating the commonly used Nash–Sutcliffe efficiency into daily and hourly scales to investigate the influence of objective function constraints on the model performance and the general capability of the IHACRES model to simulate flood events in the study watershed. The results of the study demonstrated the advantage of the finer time-scaled hourly objective function over its daily counterpart in simulating runoff for the selected flood events. The results also indicated that the IHACRES model performed extremely well in the Zhidan watershed, presenting the feasibility of the use of the IHACRES model to simulate flood events in data scarce, semi-arid regions.

Application of Gamma functions to the determination of unit hydrographs

There are many methods for calculating unit hydrograph, such as analysis method, trial algorithm and least squares method. But these methods have certain requirements for flood datas and the unit hydrograph may not be optimal. Based on the theory of composition, a hydrological system was viewed as a generalized collection in this study and Gamma functions were used to simulate the basin convergence process. At the same time, the Gamma function is parameterized and the parameters of Gamma function are optimized by genetic algorithm, which is based on the minimum error between the calculation of confluence process and the measurement process, before deriving the unit hydrograph. The Collins iteration method was used to compute the unit hydrograph. The results of actual calculated examples showe that this method is more precise than other methods, while it can also illustrate the law of runoff.