Prediction of runoff hydrographs has been being a long-standing topic of hydrology. It is well recognized that the surface runoff from a watershed depends on the hydro-meteorological characteristics of the rainfall and the physiographic properties of the watershed (Yen and Chow, 1969). Physiographic properties includes watershed properties including area, slope, geometry and land use of a watershed and drainage network properties. Physiographic properties can be divided into surface and subsurface features. Infiltration and antecedent conditions can also be regarded as additional factors affecting a flow hydrograph (Singh, 1997). The temporal and spatial rainfall variation caused by the rainstorm movement, which results in significant difference in hydrologic response at the outlet of a watershed for a given amount of rainfall.
This research involves understanding how spatio-temporal rainfall variation affects the hydrologic response of a catchments, particularly in urbanized areas. The focus this research is on the relation between rainfall variation and network configutaion, which is one of the characteristics of a catchment. The Gibbsian model is introduced to represent the property of a network. One-parameter Gibbsian model is a stochastic network model suggested by Troutman and Karlinger (1992). It covers uniform model and the Scheidegger model. 30 catchments in Seoul, South Korea were examined to investigate the applicability of the Gibbsian model to urban drainage networks and difference from natural river networks. In addition, observed radar rainfall and flow data were used to evaluate the relation between sensitivity of urban drainage networks and spatio-temporal rainfall variability depending on network configuration.
The sensitivity of urban drainage networks has a close relation with spatio-temporal rainfall variability in terms of peak flow (Seo and Schmidt 2012, 2013). Especially, this study focusing on network configuration because the sensitivity of drainage networks depends on it. We adopted the Gibbsian model. The parameter value of the Gibbsian model represents the overall sinuosity of the network. As the parameter value increases, the network becomes less sinuous and vice versa. Typically, it was believed that urban drainage systems are efficient in terms of drain efficiency and drainage time.
First, we analyzed the network characteristics of 30 drainage networks of Metropolitan City of Seoul, South Korea. Areas of catchments considered in this study range from 0.51 to 8.59 square kilometers. The procedure used in this study in order to generate the Gibbsian model given a parameter, β is as follows: First, start from a network, s1 generated by the Uniform model and randomly select a point, v in the network and assign a new flow direction from v to generate adjacent network s2. Second, check whether the new network, s2 is acyclic. If not, repeat the first step. Third, draw a random probability x between zero and one and check that x is greater than exp(-β[ΔH]) where H is sinuosity, ΔH is equal to H(s2) - H(s1). If this holds, then take s2 as a new network. In the next step use s2 as the starting network and repeat these steps sufficiently number of times that the resulting tree has the distribution close to the stationary Gibbs' distribution. In order to obtain the network configuration of drainage networks, 100 networks for each parameter value were generated for a catchment. Comparing the average width function from the simulation, the representative parameter value of the corresponding catchment was obtained.
Second, radar rainfall and flow data were collected for the period of 2011-13 to evaluate the relation between sensitivity of urban drainage networks and spatio-temporal rainfall variability depending on network configuration.
Results and discussion
One of the key findings of this study is that the network configuration of urban drainage network is not much efficient compared to river in Nature. Especially, compared with the results from Troutman and Karlinger (1992), some of the drainage networks in Seoul are less efficiency than river in nature. This is contrary to typical common sense that a man-made drainage system is efficient in terms of drainage time mainly due to decreased roughness in artificial drainage systems. However, in terms of overall network configuration, the results of this study show that man-made drainage systems can be less efficient than river in nature. This is consistent with the results from Seo and Schmidt (2012).
The results of this study also show that more efficient (less sinuous) drainage network is more sensitive to spatio-temporal rainfall variability than less efficient (more sinuous) drainage network. The observation from 2012 to 2013 shows that more efficient networks showed higher peaks compared to less efficient networks. This is important in that it implies a network configuration which is both efficient and less sensitive to spatio-temporal rainfall variation. It implies an optimum network configuration which potentially mitigate flood risks in urban environments.
The results show that an efficient drainage network in terms of drainage time is much more sensitive to rainstorm movement in terms of peak flows compared to less efficient or highly sinuous drainage networks. As a consequence, peak flows of a drainage network are higher and the corresponding catchment becomes more sensitive to temporal and spatial variation of rainfall as the network is efficiently organized further and further. This is a paradox between efficiency and safety of urban drainage networks. Depending on dominant storm kinematics and flow direction of a catchment, the network configuration can be an important factor affecting the safety of the catchment from flood risks. The preliminary result shows the layout of urban drainage networks is crucial and a compromise between network efficiency and the security of urban catchments from flood risks is required. In this regard, this study suggests the need to consider network configuration as one of the alternative nonstructural measures to mitigate the flood risks in urban environments.
Seo, Y. and Schmidt, A. R. (2012) The effect of rainstorm movement on urban drainage network runoff hydrographs. Hydrological Processes, 26(25), 3830-3841. doi: Doi 10.1002/Hyp.8412
Seo, Y. and Schmidt, A. R. (2013) Network configuration and hydrograph sensitivity to storm kinematics. Water Resources Research, 49(4), 1812-1827. doi: Doi 10.1002/Wrcr.20115
Singh, V. P. (1997) Effect of spatial and temporal variability in rainfall and watershed characteristics on stream flow hydrograph. Hydrological Processes, 11(12), 1649-1669.
Troutman, B. M. and Karlinger, M. R. (1992) Gibbs distribution on drainage networks. Water Resources Research, 28(2), 563-577.
Yen, B. C. and Chow, V. T. (1969) A laboratory study of surface runoff due to moving rainstorms. Water Resources Research, (5), 989-1006.