TR(BR)-18/99-2000 : Uncertainty analysis of GIUH based Clark model using first order analysis for a catchment of lower Godavari subzone 3(f)

Abstract

Uncertainty analysis outlines the inability to exactly model a real world hydrologic situation even if the best possible estimates of the input parameters of the model are utilized. An added complication with most of the hydrologic models is that in general these models are structured with several uncertain input parameters. The sources of uncertainty in model output are model structure itself and the uncertainty associated with the parameters of the model. Parametric uncertainty refers to a lack of knowledge of the exact values for model parameters. Parametric uncertainty can produce considerable uncertainty in the results generated from a hydrologic model. Hydrologic models generally require point or single estimates for model parameters. As modellers we generally provide point estimates but we do so recognising that we are not sure of the exact values of the parameters. Determining the uncertainty to be assigned to input parameters is one of major hurdles that must be addressed in the overall evaluation of uncertainty associated with hydrologic modelling. Hence, a single best estimate or expected value for each of the parameters should be obtained. Limits on parameters and suggested ranges of parameter values should be investigated. If the parameter is a physically measurable parameter, then the range of its values reported in literature and its variability should be examined with respect to the actual value of the parameter being utilised in a particular modelling study.

In this study, uncertainty analysis has been carried out for the parameters of the mathematical model developed at the National Institute of Hydrology for estimation of the Clark model parameters using the geomorphological characteristics of an ungauged catchment. The model has been applied for simulation of the direct surface runoff (DSRO) hydrographs of the catchment defined by bridge number 807 of the Lower Godavari Subzone 3 (f). The geomorphological parameters of the catchment have been evaluated using the GIS package, Integrated Land and Water Information System (ILWIS). The direct surface runoff hydrographs estimated by the GIUH approach have been compared with the observed direct surface runoff hydrographs as well as with the DSRO hydrographs simulated by the Nash model and the HEC-1 package. The performance of the GIUH model has also been evaluated by employing some of the error functions viz. (i) efficiency (EFF), (ii) absolute average error (AAE), (iii) root mean square error (RMSE), (iv) average error in volume (AEV), (v) percentage error in peak (PEP) and (vi) percentage error in time to peak (PETP) computed based on the observed and the simulated DSRO hydrographs. It is observed that the DSRO hydrographs computed by the GIUH based Clark model approach, which simulates the DSRO hydrographs of the catchment considering it to be ungauged, compare reasonably well with the observed and the simulated DSRO hydrographs.

For carrying out the uncertainty analysis, the geomorphological parameters viz. length ratio (RL), length of the highest order stream (L0), length of the main stream (L), and the velocity parameter (V) apart from the aforementioned geomorphological parameters, have been considered. Relative sensitivity analysis has been conducted for identifying the parameters of the GIUH based Clark model, which significantly affect peak of the unit hydrograph on the basis of their relative sensitivity coefficients. Uncertainty analysis has been carried out by first order analysis (FOA). Also, upper and lower 95% confidence limits for the peak of the unit hydrograph derived by the GIUH based Clark model have been computed. Uncertainty analysis has been carried out considering the following cases.

(i) Case I — Considering the uncertainty associated with length ratio (RL), length of the highest order stream (La), length of the main stream (L) and velocity (V),

(ii) Case II - Considering the uncertainty associated with length ratio (RL), length of the highest order stream (La) and Length of the main stream (L), and (iii) Case III- Considering the uncertainty associated with length ratio (RL) and length of the highest order stream (La).

As per Case-I, the uncertainty in the velocity parameter (V) leads to 72.7% uncertainty in peak of the unit hydrograph and it emerges to be the biggest contributor to the uncertainty in estimation of peak of the unit hydrograph. The uncertainty in parameters Lo, RL and L contribute to 15,3%, 8.4% and 3.6% uncertainty in the peak of the unit hydrograph respectively. Hence, the value of the velocity parameter (V) needs to be computed with the highest precision for accurate estimation of the peak of the unit hydrograph derived by the GIUH based Clark model. As uncertainty in 1_,Q and RL, also leads to 15.3% and 8.4% uncertainty in the peak of the unit hydrograph; therefore, effort should be made to estimate these parameters accurately, as well.

As per Case-II, when the three physically measurable geomorphological parameters, viz. RL, Lf1 and L are considered; the uncertainty in length of the highest order stream of the catchment (Lo) leads to 56.0% uncertainty in peak of the unit hydrograph and it emerges to be the biggest contributor to the uncertainty in estimation of peak of the unit hydrograph. The uncertainty in parameters RL and L contributes to 30.8%, 13.2% uncertainty in the peak of the unit hydrograph respectively. Hence, the values of LQ needs to be measured with precision for accurate estimation of the peak of the unit hydrograph derived by the GIUH based Clark model. As uncertainty in RL leads to 30.8% uncertainty in the peak of the unit hydrograph; therefore, effort should be made to estimate the parameter RL also as accurately as possible.

As per Case-III, when the two parameters, viz. RL and L0 are considered; the uncertainty in length of the highest order stream of the catchment (Lu) leads to 64.5% uncertainty in peak of the unit hydrograph and it emerges to be the biggest contributor to the uncertainty in estimation of peak of the unit hydrograph. The uncertainty in parameter RL contributes to 35.5% uncertainty in the peak of the unit hydrograph. Hence, the values of both of these geomorphological parameters, Ln and 121 need to be precisely measured for accurate estimation of the peak of the unit hydrograph derived by the GIUH based Clark model.

The confidence intervals (CIs) i.e. the intervals which contain the true value of the model output with the indicated degree of confidence or probability have been computed for the 95% confidence level for the three cases assuming that peak of the unit hydrograph is normally distributed. Using the GIUH based Clark model, the actual peak of the unit hydrograph and the time to peak have been estimated as 46.37 cumec and 5 hours respectively. For this peak of the unit hydrograph, the lower and upper 95% confidence limits for Case-I have been computed as 35.33 cumec and 57.41 cumec respectively. The lower and upper 95% confidence limits for Case-II have been computed as 40.60 cumec and 52.14 cumec respectively. The lower and upper 95% confidence limits for Case-III have been computed as 40.99 cumec and 51.75 cumec respectively.

The geomorphological parameters which contribute to higher degree of unceratinty in derivation of unit hydrograph using the GIUH based Clark model as outlined above, are to be estimated more precisely for reducing the uncertainty associated with the flood estimates computed by the GIUH based Clark model. Also, in order to decrease or increase upper and lower confidence limits, the parameters leading to greater uncertainty in the peak of the unit hydrograph need to be estimated more accurately.