Advanced sensitivity analysis of the impact of the temporal distribution and intensity of rainfall on hydrograph parameters in urban catchments
Authors: Fatone Francesco , Szeląg Bartosz , Kiczko Adam , Majerek Dariusz , Majewska Monika , Drewnowski Jakub , Łagód Grzegorz 
Published: October 2021

Abstract. Knowledge of the variability of the hydrograph of outflow from urban catchments is highly important for measurements and evaluation of the operation
of sewer networks. Currently, hydrodynamic models are most frequently used for hydrograph modeling. Since a large number of their parameters have to
be identified, there may be problems at the calibration stage. Hence, sensitivity analysis is used to limit the number of parameters. However, the
current sensitivity analytical methods ignore the effect of the temporal distribution and intensity of precipitation in a rainfall event on the
catchment outflow hydrograph. This article presents a methodology of constructing a simulator of catchment outflow hydrograph parameters (volume and
maximum flow). For this purpose, uncertainty analytical results obtained with the use of the GLUE (generalized likelihood uncertainty estimation)
method were used. A novel analysis of the sensitivity of the hydrodynamic catchment models was also developed, which can be used in the analysis of
the operation of stormwater networks and underground infrastructure facilities. Using the logistic regression method, an innovative sensitivity
coefficient was proposed to study the impact of the variability of the parameters of the hydrodynamic model depending on the distribution of
rainfall, the origin of rainfall (on the Chomicz scale), and the uncertainty of the estimated simulator coefficients on the parameters of the outflow
hydrograph. The developed model enables the analysis of the impact of the identified SWMM (Storm Water Management Model) parameters on the runoff
hydrograph, taking into account local rainfall conditions, which have not been analyzed thus far. Compared with the currently developed methods, the
analyses included the impact of the uncertainty of the identified coefficients in the logistic regression model on the results of the sensitivity
coefficient calculation. This aspect has not been taken into account in the sensitivity analytical methods thus far, although this approach
evaluates the reliability of the simulation results. The results indicated a considerable influence of rainfall distribution and intensity on the
sensitivity factors. The greater the intensity and rainfall were, the lower the impact of the identified hydrodynamic model parameters on the
hydrograph parameters. Additionally, the calculations confirmed the significant impact of the uncertainty of the estimated coefficient in the
simulator on the sensitivity coefficients. In the context of the sensitivity analysis, the obtained results have a significant effect on the
interpretation of the relationships obtained. The approach presented in this study can be widely applied at the model calibration stage and for
appropriate selection of hydrographs for identification and validation of model parameters. The results of the calculations obtained in this study
indicate the suitability of including the origin of rainfall in the sensitivity analysis and calibration of hydrodynamic models, which results from
the different sensitivities of models for normal, heavy, and torrential rain types. In this context, it is necessary to first divide the rainfall
data by origin, for which analyses will be performed, including sensitivity analysis and calibration. Considering the obtained results of the
calculations, at the stage of identifying the parameters of hydrodynamic models and their validation, precipitation conditions should be included
because, for the precipitation caused by heavy rainfall, the values of the sensitivity coefficients were much lower than for torrential ones. Taking
into account the values of the sensitivity coefficients obtained, the calibration of the models should not only cover episodes with high rainfall
intensity, since this may lead to calculation errors at the stage of applying the model in practice (assessment of the stormwater system operating
conditions, design of reservoirs and flow control devices, green infrastructure, etc.).