Computational framework for flood routing through ogee spillway and investigation of the effect of storage-level relationship on design quantities

This diploma thesis investigates the effect of the selected mathematical form of the stage–storage relationship on flood routing results in reservoirs. The stage–storage relationship links the water surface elevation of a reservoir to the corresponding stored volume and constitutes a key component in the computational representation of reservoir response during the passage of a flood wave. Three fitting models are compared: a simple power-law relationship, a two-branch piecewise power-law relationship, and a two-parameter shape relationship (hereafter referred to as the “Kumaraswamy relationship”, as it is inspired by the distribution function of the same name). The methodology was applied to seventeen dams in Greece. Eleven were examined as individual reservoirs, while six were included in two cascade systems located on the Acheloos and Aliakmonas rivers. For each case, the three models were fitted to the available stage–storage data and were subsequently incorporated into the same flood-routing framework in order to assess the effect of model selection on the main routing results. In terms of fitting performance, the Kumaraswamy relationship provided the best overall results, yielding the lowest root mean square error (RMSE) in 14 of the 17 cases. In the remaining three cases, the piecewise power-law relationship achieved the best fit, while the simple power-law relationship generally exhibited larger fitting errors and greater sensitivity to the extension of the available data at high stage values. The influence of the selected stage – storage model on flood-routing results varied considerably among reservoirs. In some cases, the three relationships produced very similar values of peak outflow and maximum water level, while in others noticeable differences were observed. In the cascade systems, it was also found that differences generated at an upstream reservoir may propagate downstream through the resulting inflow hydrograph. The statistical analysis indicated a strong and statistically significant positive correlation between the variation in goodness of fit, expressed by ΔNRMSEorig, and the variation in the ratio of peak outflow to peak inflow, a. In addition, the exponent of the piecewise power-law relationship and the first shape parameter of the Kumaraswamy relationship showed a very strong positive correlation. This suggests that they capture related characteristics of reservoir geometry. Overall, the results show that the mathematical form selected for the stage–storage relationship can influence both fitting performance and flood-routing results, although the magnitude of this effect varies among reservoirs. The comparative application of more than one fitting model can therefore provide a more complete assessment of result sensitivity and reduce the dependence of the analysis on a single mathematical assumption.