Estimation of Clark’s Instantaneous Unit Hydrograph Parameters and Development of Direct Surface Runoff Hydrograph

Abstract

We present a method to estimate Time of Concentration (T c ) and Storage Coefficient (R) to develop Clark's Instantaneous Unit Hydrograph (CIUH). T c is estimated from Time Area Diagram of the catchment and R is determined using optimization approach based on Downhill Simplex technique (code written in FOR-TRAN). Four different objective functions are used in optimization to determine R. The sum of least squares objective function is used in a novel way by relating it to slope of a linear regression best fit line drawn between observed and simulated peak discharge values to find R. Physical parameters (delineation, land slope, stream lengths and associated drainage areas) of the catchment are derived from SPOT satellite imageries of the basin using ERDAS: Arc GIS is used for geographic data processing. Ten randomly selected rainfall-runoff events are used for calibration and five for validation. Using CIUH, a Direct surface runoff hydrograph (DSRH) is developed. Kaha catchment (5,598 km 2 ), part of Indus river system, located in semiarid region of Pakistan and dominated by hill torrent flows is used to demonstrate the applicability of proposed approach. Model results during validation are very good with model efficiency of more than 95% and root mean square error of less than 6%. Impact of variation in model parameters T c and R on DSRH is investigated. It is identified that DSRH is more sensitive to R compared to T c . Relatively equal values of R and T c reveal that shape of DSRH for a large catchment depends on both runoff diffusion and translation flow effects. The runoff diffusion effect is found to be dominant. 2418 M.M. Ahmad et al.Keywords Time of concentration · Storage coefficient · Clark's instantaneous unit hydrograph · Direct surface runoff hydrograph · Hydrograph parameter estimation Nomenclature Q i+1 (i + 1)th ordinate of the CIUH i index varying from 1 to N, N is number of ordinates of the time area diagram RE uniformly distributed rainfall excess C 0 and C 1 are weighting coefficients R storage coefficient t computational time interval T c time of concentration L j length of stream of sub basin in km S j representative land slope of sub basin j j index varying from 1 to M and M is number of identified sub basins Q po observed peak discharge Q ps computed/simulated peak discharge Q oj jth ordinate of the observed hydrograph Q cj jth ordinate of the computed hydrograph j index varying from 1 to n, n being no. of ordinates of observed hydrograph Q po(i) peak discharge of observed hydrograph for ith event Q ps(i) peak discharge of simulated hydrograph for ith event T po(i) time to peak of observed hydrograph for ith event T ps(i) time to peak of simulated hydrograph for ith event NE number of calibration events η model efficiency NQ number of ordinates of the simulated hydrograph i index varying from 1 to NQ Q oi ith ordinate of the observed hydrograph Q ci ith ordinate of the computed/simulated hydrograph Q o mean of the ordinates of the observed hydrograph Z peak weighted root mean square (RMS) e...

Effects of urbanization variables on model parameters for watershed divisions

“…The system inputs and outputs are analogous to natural flows as rainfall and runoff. Mathematical formulations based on this approach have appeared in numerous models: for example, the Nash model (Nash 1957, Agirre et al 2005, Clarke model (Clarke 1973, Ahmad et al 2009, geomorphologic model (Jin 1992, Franchini and O'Connell 1996, Nourani et al 2009), distributed models based on parallel-type reservoirs (Hsieh and Wang 1999), a model of three serial linear reservoirs (Cheng 2010a(Cheng , 2010b(Cheng , 2010c and a linear cascade model of three serial reservoirs with one parallel reservoir (Yue andHashino 2000, Li et al 2012).…”

Development of geomorphologic instantaneous unit hydrograph for a large watershed

“…The conceptual models like the linear cascade model (Nash Model) and Clark Model are the most commonly used in this family of models. These models are very effective for operational forecasting (Ahmad 2009;Ahmad et al 2009;Zelazinski 1986). …”

Relating hydrograph components to rainfall and streamflow: a case study from northern Taiwan

“…These models, which are derived from a convolution integral, are generally known as unit hydrograph (UH)-based models and include: the Nash model (Nash 1957); Clarke's model (Clarke 1973, Ahmad et al 2009); the geomorphologic instantaneous unit hydrograph (GIUH) (Jin 1992, Franchini and O'Connell 1996, Nourani et al 2009, the distributed parallel model (Hsieh and Wang 1999), and sub-watershed divisions (Agirre et al 2005). Rainfall-runoff modelling with IUHs has been studied by O'Connell and Todini (1996), Melone et al (1998), Bhadra et al (2010) and others.…”