Use of Nash's IUH and DEMs to identify the parameters of an unequal‐reservoir cascade IUH model

Under the assumption that hydrograph generation was affected by n linear reservoirs with the same value of storage coefficient k, Nash proposed the formulation of the Instantaneous Unit Hydrograph (IUH), which has been widely used in rainfall–runoff simulation and flood forecasting. However, the assumption of the parameter k having the same value in all reservoirs is obviously unphysical as it results in the estimated value of n not being integral. In this study, for parameter n integral, the different k value for each reservoir was derived using the Laplace transform and developing a general rule for the equation of the IUH of any order. The relationship between parameter k and the slope of the river channel estimated using digital elevation model (DEM) data is established, the parameter estimation procedures are given. As in most unit hydrograph studies, only isolated storm events are considered here. Seventeen flood events in three catchments were selected for the case studies. Application results show that the proposed method is slightly better than Nash's IUH with higher model efficiency and smaller absolute relative errors. This work provides a new methodology for the formulation of the IUH. Copyright © 2008 John Wiley & Sons, Ltd.     

Analysis of geomorphologic and hydrological characteristics in watershed saturated areas using topographic‐index threshold and geomorphology‐based runoff model

The objective of this paper is to investigate the variation of geomorphology and runoff characteristics in saturated areas under different partial contributing area (PCA) conditions. Geomorphologic information and hydrologic records from two mid‐size watersheds in northern Taiwan were selected for analysis. The PCA ratio in the watershed during a storm was assumed equal to the ratio of the surface‐flow volume to the direct runoff volume from measured hydrologic data. The extents of PCA regions were then determined by using a topographic‐index threshold. Consequently, the geomorphologic factors in saturated and unsaturated areas could be calculated using a digital elevation model, and these factors could then be linked to a geomorphology‐based IUH model for runoff simulation, which can consider both the surface‐ and subsurface‐flow processes in saturated and unsaturated areas, respectively. The results show that geomorphologic characteristics in the saturated areas vary significantly with different PCA ratios especially for higher order streams. A large PCA ratio results in a sharp hydrograph because the quick surface flow dominates the runoff process, whereas the hydrologic response in a low PCA case is dominated by the delayed subsurface flow. Copyright © 2007 John Wiley & Sons, Ltd.     

Book Review

Abstract

The instantaneous unit hydrograph (IUH) of a watershed is the result of one instantaneous unit of rainfall excess distributed uniformly over the watershed. Although the geomorphological characteristics of the basin remain relatively constant, the variable characteristics of storms cause variations in the shape of the resulting hydrographs. It is, therefore, inadequate to use one typical IUH to represent the hydrological response generated from any specific storm. In this study, a variable IUH was derived that directly reflects the time-varying rainfall intensity during storms. The rainfall intensity used to generate the variable IUH at time t is the mean rainfall intensity occurring from the time t—T _c to t in which T _c is the watershed time of concentration. Hydrological records from three watersheds in Taiwan were used to demonstrate the applicability of the proposed model. The results show that better simulations can be obtained by using the proposed model than by using the conventional unit hydrograph method, especially for concentrated rainstorm cases.     

Application of the Kalman filter to the Nash model

The Nash model was used for application of the Kalman filter. The state vector of the rainfall–runoff system was constituted by the IUH (instantaneous unit hydrograph) estimated by the Nash model and the runoff estimated by the Nash model using the Kalman filter. The initial values of the state vector were assumed as the average of 10% of the IUH peak values and the initial runoff estimated from the average IUH. The Nash model using the Kalman filter with a recursive algorithm accurately predicted runoff from a basin in Korea. The filter allowed the IUH to vary in time, increased the accuracy of the Nash model and reduced physical uncertainty of the rainfall–runoff process in the river basin. © 1998 John Wiley & Sons, Ltd.     

Analysis of flow-sediment rating curve hysteresis based on flow and sediment travel time estimations

A flow-sediment rating curve is used to describe the relation between flow discharge and suspended-sediment concentration for a specific location. Five types of flow-sediment rating curves - single-valued line, clockwise loop, counterclockwise loop, single-valued line plus loop, and figure eight - were found to rely on the flow and available sediment arriving at the measuring site. In this study, equations for flow and sediment travel time were derived according to soil, rainfall, and watershed geomorphologic characteristics. The hysteresis of the rating curve was related to the travel times by a series of numerical tests. Field data collected from the Goodwin Creek Experimental Watershed, Mississippi, United States were used to verify the proposed rating curve hysteresis analysis. The results indicate that when the flow travel time is more extended than the sediment travel time, the rating curve shows a clockwise loop. A counterclockwise loop in the rating curve shows that the flow travel time is less extended than the sediment travel time. If the flow travel time exceeds the sediment travel time in specific runoff states and is less than the sediment travel time in other runoff states, then a single line plus a loop rating curve or a figure-eight rating curve is observed. The criterion for the model parameters to obtain equalization of the flow and sediment travel times was derived, which can identify the type of flow-sediment rating curve in a specific watershed.     

Application of a regionalized Clark IUH model with limited hydrologic data availability

To aid prediction of the flow hydrograph in a basin with limited data, a practical approach to determining a regionalized Clark instantaneous unit hydrograph (IUH) model is presented. The proposed model is described in terms of the synthetic time–area concentration curve, the concentration time, and a special regional similarity value that is valid in the whole basin. The latter was estimated from a Monte Carlo testing procedure based on the normal probability distribution of transformed regional similarity values composed of the time of concentration and the storage coefficient in gauged basins. The time–area concentration curve and the concentration time were calculated from a rational equation as in conventional methods. The method of transformation adopted was the Box–Cox power transformation, which is known to make non‐normal values resemble normal data. By introducing the regional similarity value into a Clark IUH, a statistically best estimate of IUH for given data conditions and its quantified degree of uncertainty were realized. The Wi River basin in Korea was used to test the applicability of the regionalized Clark IUH. The performance of the suggested methodology was evaluated by assuming an ungauged sub‐basin at the site. The results showed that the IUH model developed in this work was an effective tool, predicting a reliable hydrograph within the study area even though only limited data were available. Copyright © 2008 John Wiley & Sons, Ltd.