Hydrologically Enhanced Distributed Urban Drainage Model and Its Application in Beijing City

Anjun Pan1; Aizhong Hou2; Fuqiang Tian3; Guangheng Ni4; and Heping Hu5

Abstract: Heavy rainfall-induced inundation is becoming more serious in urban areas making it necessary to urgently appraise and redesign the infrastructure system to drain the storm water more efficiently. For the complex urban drainage systems that include street, sewer, and ditch/river networks, a sophisticated urban drainage model is required to facilitate optimal planning and management. Although most existing models simulate the runoff generation process in a simpler manner and treat the drainage connections between runoff generation cells and the corresponding drainage links in a rigid/static manner, this study proposes a new hydrologically enhanced distributed urban drainage model. In the new model, the urban area is discretized into a four-layer network, i.e., two-dimensional (2D) grid network, 1D street network, 1D sewer network, and 1D ditch/river network. Physically based equations are utilized to describe water movement along the four networks, i.e., the 1D Richards equation is used to simulate the infiltration process along the vertical direction in the grid network, the 2D Saint-Venant equation is used to simulate the overland flow process along the planar direction in the grid network, and the 1D Saint-Venant equation is used to simulate the street, sewer, and river flows in the remaining networks. The new model incorporates the state-of-the-art physical descriptions about hydraulic and hydrological processes during the urban storm inundation period, which allows a more realistic depiction of the runoff generation processes, automatic alteration of overland flow routing path, direct and easier usage of gridded radar rainfall data readily available recently, and real-time hydrodynamic flux exchanges between surface and sewer pipes. The model is validated in a hypothetical application by comparing with the published literature results. Also, a real urban watershed application shows the capacity of the model to provide reasonable predictions of the outlet hydrograph, which indicates its potential for planning and real-time management of urban drainage systems. DOI: 10.1061/(ASCE)HE.1943-5584.0000491. © 2012 American Society of Civil Engineers. CE Database subject headings: Urban areas; Drainage; Hydrodynamics; Rainfall; China. Author keywords: Urban drainage; Dual drainage system; Hydrodynamic interaction; Richards equation; Saint-Venant equation.

Introduction of China) produced 2 m of inundation under more than 10 flyovers leading to extensive traffic jams. Another example is the 3-h heavy Heavy rainfall is more likely to occur as a consequence of global rainfall on July 18, 2007 in Jinan (capital of Shandong Province, warming (Mcbean 2006; Mailhot et al. 2007), and heavy rainfall China), which claimed the lives of at least 34 people. For most induced inundation is becoming more serious in urban areas severe urban inundations, the rainfalls often exceed design rainfall (Mcbean 2006). China is in a stage of fast growth, and the urbani- values. But for many other minor cases where the rainfalls are zation ratio will probably reach up to 50% by 2020. Cities are areas below design standard, the urban inundations are caused by failure with highly concentrated populations and assets. Once inundation or improper operation of street inlets, pipe systems, and drainage occurs, it will cause tremendous property damage and loss of lives. river systems. It is, therefore, necessary to redesign and reoperate For example, the heavy rainfall on July 10, 2004 in Beijing (capital infrastructure systems to drain the storm water more efficiently. To facilitate the optimal design and operation of urban drainage 1Doctoral Student, Dept. of Hydraulic Engineering, State Key Labora- systems, a sophisticated urban drainage model is required. In fact, tory of Hydroscience and Engineering, Tsinghua Univ., Beijing 100084, the urban storm water flows through considerable complex path- China. E-mail: [email protected] 2 ways such as roofs, parking lots, squares, yards, roads, drainage Doctoral Student, Dept. of Hydraulic Engineering, State Key Labora- pipelines, flyovers, and pump stations. (Hsu et al. 2000), and tory of Hydroscience and Engineering, Tsinghua Univ., Beijing 100084, the flow regime changes substantially as the water moves along China. E-mail: [email protected] 3Associate Professor, Dept. of Hydraulic Engineering, State Key the various boundaries, which makes the urban storm water mod- Laboratory of Hydroscience and Engineering, Tsinghua Univ., Beijing eling a challenging task. A lot of research work has been done, and

Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. 100084, China (corresponding author). E-mail: [email protected] a large number of urban storm flow simulation models were pro- 4Professor, Dept. of Hydraulic Engineering, State Key Laboratory of posed. Because of the interrelated nature of storm water flow in the Hydroscience and Engineering, Tsinghua Univ., Beijing 100084, China. closed sewer pipeline and in the open street channel, the simulation E-mail: [email protected] of urban drainage has changed from the simple calculation of flow 5 Professor, Dept. of Hydraulic Engineering, State Key Laboratory of rate in sewer networks to the simulation of dual drainage systems Hydroscience and Engineering, Tsinghua Univ., Beijing 100084, China. containing both street and sewer networks (Smith 2006a, b). The E-mail: [email protected] last two decades have seen a steady progress in the dual urban Note. This manuscript was submitted on October 10, 2010; approved on August 15, 2011; published online on August 18, 2011. Discussion period drainage model motivated by the swift advances of Geographic open until November 1, 2012; separate discussions must be submitted for Information System (GIS) tools and computational capacity (Smith individual papers. This paper is part of the Journal of Hydrologic Engi- 2006a). The following are a few examples among many others. Hsu neering, Vol. 17, No. 6, June 1, 2012. ©ASCE, ISSN 1084-0699/2012/6- et al. (2000) used the Storm Water Management Model (SWMM) 667–678/$25.00. and the two-dimensional (2D) diffusive flow model for the coupled

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J. Hydrol. Eng. 2012.17:667-678. simulation of surface inundation in the downtown area of Taipei caused by the overflow of the sewer network. Schmitt et al. (2004) built a dual drainage model RisUrSim that incorporated the detailed surface flow simulation and the interaction between surface and sewer flow. Nasello and Tucciarelli (2005) built a dual model of a double network formed by an upper network of open channels (street gutters) and a lower network of closed conduits (sewer pipes). Fang and Su (2006) built a coupled model of the surface and sewer network to simulate the inundation in the city of Beaumont, Texas caused by a tropical storm. However, most existing urban drainage models simulate the runoff generation process in a simpler manner and subsequently always assume the rigid/static affiliation between runoff generation cells (i.e., small drainage catchment) and the corresponding drainage links (i.e., street channel, sewer pipe, and river channel). The runoff generation model holds an important position in catchment hydrological models but has been oversimplified in current urban drainage models. For example, in the model proposed by Nasello and Tucciarelli (2005), the runoff generation is calculated on the basis of the rational method with predetermined division of drainage areas. Also, the urban area is usually featured by the flat terrain, and therefore, the routing path of overland flow can be substantially changed when the water level rises in the street, sewer, or river. Some other abnormal situations could also alter the routing paths of overland flow and street flow especially when the rain gutters, Fig. 1. Discretization diagram of urban area sewer pipes, or the other water pathways are blocked for various reasons. Most of the existing urban drainage modeling work ignores the dynamic features of overland flow routing and the var- networks are two overlapping computational cells with the same ied relation between drainage catchments and drainage links. They planar location, whereas the spatial resolution of discretization usually assume that water in surface units can only flow along the schemes for 2D grid network, 1D street/sewer networks, and 1D predetermined routing path and could only enter into the sewer pipe ditch/river network are independent, which allows more flexibility. through the particular rain inlet and cannot flow to the adjacent Among the four networks, the street network serves as a transfer units or channels (with the exception of surcharged condition, network, i.e., the node of street network is virtually connected to e.g., in Fang and Su 2006; Nasello and Tucciarelli 2005; and the center of the grid cell at the top through a virtual inlet and physi- Hsu et al. 2000). cally linked to the corresponding node of sewer network at the In this paper, originally a hydrologically enhanced urban drain- bottom through a grated inlet/manhole. For the ditch/river network, age model was proposed by combining the one-dimensional (1D) water in all the other three networks, i.e., grid network, street Richards equation for soil water movement along the vertical network, and sewer network, can flow to it directly through the direction, the 2D Saint-Venant equation (diffusive wave model) corresponding neighbor links. for overland flow, and 1D Saint-Venant equation (dynamic wave When the storm reaches top layer grids, the loss is removed from model) for street flow, sewer flow, and ditch/river flow. This grid- the total rainfall and the net rainfall is obtained, which will cause based distributed model could easily utilize the high-resolution the overland flow on the grid network. The overland flow will then Digital Elevation Model (DEM), land use, and radar rainfall data, enter the street nodes and form the street flow when it reaches the which have already become commonly available at lower cost. By virtual inlet between the grid cell and street node, and the street this way, the model can automatically alter the routing path of overflow will further enter the sewer network and add to the sewer flow land flow and, thus, no need exists to predetermine the small drain- when it reaches rain inlets/manholes. All the water will go into the age catchment manually. The incorporation of Richards equation in ditch/river network from sewer/street networks or directly from the net rainfall calculation allows more realistic depiction of runoff grid network and ultimately route to the watershed outlet. The in- generation processes. Subsequently, a description will first be given teractions among the street network, sewer network and ditch/river of model structure and the equations/methods used in the model, network are taken into account in the model at least in the following and then a hypothetical experiment will be implemented to show two aspects: (1) when the sewer network is surcharged, the water the capacity of the proposed model. This will be followed by a case will continue to flow along the streets until it reaches the next rain

Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. study in a typical urban watershed in Beijing, the capital of China. inlet or forms street inundation, as depicted in many urban dual The paper will be closed by a summary of the main results and drainage models (e.g., Fang and Su 2006; Nasello and Tucciarelli subsequent conclusions. 2005; Hsu et al. 2000); (2) when the water level in the ditch/river network is higher than the elevation of sewer network outlet, a backwater effect will reduce the drainage efficiency dramatically. Model Structure The loss from total rainfall to net rainfall includes interception, evaporation, detention of impervious area, and infiltration, of which In the model, the urban area is discretized into a four-layer network the infiltration accounts for most part of the total loss for the in- (Fig. 1). The top layer is a 2D grid network representing various undation modeling. In the model proposed in this paper, the infil- urban landscapes (runoff generation areas), the middle and bottom tration process is simulated by solving Richards equation within the layers are a 1D street network and sewer network, respectively, and framework of the HYDRUS model (Simunek and van Genuchten the side layer is a 1D ditch/river network. The street and sewer 2008). The detention of the impervious urban residential area is

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J. Hydrol. Eng. 2012.17:667-678. assumed to be constant and will be fixed at 3 mm in the following Application to a Hypothetical Example real watershed application in Beijing (an empirical value used in the unpublished technical report by Tang 2004); whereas, the intercep- The hypothetical dual network example used in Nasello and tion and evaporation are neglected. The simulation of overland flow Tucciarelli (2005) is adopted by introducing a new grid network adopts the diffusive wave model of the 2D Saint-Venant equation; (see Fig. 2). Following Nasello and Tucciarelli (2005), the street whereas, the simulation of 1D street/sewer/river flow adopts the and sewer networks are divided into 2 × 36 links, i.e., 73 computa- dynamic wave model of the 1D Saint-Venant equation. The 2D tional nodes arranged every 50 m. The lowest position of sewer ¼ diffusive wave equation is numerically solved by the explicit differ- network is at node 1 [i.e., z 0, Fig. 2(d)], and the elevation of ence method with adaptive time step, and the numerical scheme the corresponding street node (34) is 1.7 m [Fig. 2(c)]. The street (explicit difference) of the 1D Saint-Venant equation is imple- flow enters into the sewer network through seven inlets (nodes 42, mented on the basis of the ‘link-node’ concept used in the SWMM 45, 48, 51, 54, 60, and 63) at reaches of IV, V, and VI. The inlets model (Roesner et al. 1988), and thus the addition/subtraction have a square shape with a side length of 0.45 m. The sewer network has a round shape with a diameter of 0.6 m and the Manning of source/sink terms (such as rainfall and hydrodynamic flux roughness coefficient of 0:013 m1∕3∕s. The street is conceptual- exchange between surface and sewer pipes) are significantly sim- ized as a trapezoid with the minimum and maximum width of 0.3 m plified, and the flow can be solved sewer by sewer by using the and 10 m, respectively, side slope of 1%, and the Manning rough- one-sweep explicit solution method with no need for simultaneous ness coefficient of 0:017 m1∕3∕s. At the outlet nodes 1 and 34, the solution of the sewer network. The explicit scheme makes program- free outfall boundary conditions are imposed. ming easier although acknowledging that the stability and conver- The cell size of the newly introduced grid network is arbitrarily gence aspects are inferior to implicit schemes (Yen and Akan chosen as 10 m, which are totally discretized into 5,921 pixels 1999). The exchange flux at grated inlet between the street network [Figs. 2(a) and 2(b)] For the sake of simplification, in this hypo- and sewer network is calculated by the weir equation for lower thetical example the landscape properties (e.g., land use and soil water levels or the sluiced gate equation for higher water levels types) and elevation of all pixels are set to be uniform. Similar to as used by Nasello and Tucciarelli (2005), and the influx through the street and sewer network, the free outfall boundary conditions the virtual inlet between the grid network and street network is are imposed to the southern border pixels; whereas, no flow boun- calculated by the broad-crest weir equation. The closed pipe flow dary conditions are imposed to the other border pixels. in the sewer network could experience a transition between free In terms of initial condition and climate forcing, an initial dry surface flow and pressure flow at the different stages of a heavy street network was set, and a constant inflow of Q ¼ 0:003 m3∕s storm event, which is handled by the Preissmann narrow slot for all the computational sewer nodes, which is same as Nasello and method (Preissmann and Cunge 1961). The main equations used Tucciarelli (2005). Additionally, an initial 1 mm water depth is set in the model are summarized in Table 1. for all pixels in the grid network to facilitate the numerical stability. For the time domain discretization, the same time step is applied To show the effect of spatial heterogeneity of rainfall on flow in to all equations of the four layers. Water exchanges within and the drainage networks, two nonuniform rainfall scenarios are used. among pixels, street segments, pipe links, and channel reaches As in Figs. 2(a) and 2(b), the darker part of the grid network throughout the way, and thus all equations are coupled together at indicates the rainfall area whereas no rain falls over the remain- each time step. The self-adaptive time-step strategy is implemented ing lighter part. In two scenarios, we have the same total rainfall by setting the predetermined convergent water head increment, area, i.e., 130;000 m2. This value equals the total drainage area which leads to longer time steps during between-storm periods in the hypothetical example in Nasello and Tucciarelli (2005), whereas, shorter time steps during the within-storm periods. i.e., 26 × 5;000 ¼ 130;000 m2 (see subsequent details). The time

Table 1. Equations Used in the Model Eq. Name Equation Note Number ∂θ ∂ h ∂ψ i Richards equation ¼ þ Used for infiltration modeling. ψ ∼ Pressure head, [L]; (1) ∂ ∂ K ∂ 1 S t x x θ ∼ Volumetric water content, [L3L3]; S ∼ Source or sink term, [L3L3T1]; K ∼ Unsaturated hydraulic conductivity, [LT1] ∂h ∂½uh ∂½vh Diffusive wave model þ þ ¼ q Used for overland flow modeling. H ∼ Water level, [L]; (2) ∂t ∂x ∂y of 2D Saint-Venant h ∼ water depth, [L]; u, v ∼ flow rate at directions of x, y,[LT1] ∂H ∂H equation S þ ¼ 0; S þ ¼ 0 n ∼ Manning roughness coefficient, [L1∕3T1]; q ∼ lateral in flow, fx ∂x fy ∂y pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi [LT1]; S ; S ∼ friction slope along direction ofx, y Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. n2u u2 þ v2 n2v u2 þ v2 fx fy S ¼ ; S ¼ fx h4∕3 fy h4∕3 ∂A ∂Q Dynamic wave model þ ¼ 0 Used for street/ sewer/river flow modeling. Q ∼ flow rate, [L3T1]; (3) ∂t ∂x of 1D Saint-Venant A ∼ cross section area, [L2]; H ∼ water level, [L]; S ∼ friction slope ∂Q ∂ðQ2∕AÞ ∂H f equation þ þ gA þ gAS ¼ 0 ∂t ∂x ∂x f pffiffiffiffiffi pffiffiffiffiffi ¼ ð : 1:5; : 0:5Þ ∼ ∼ Weir, sluiced gate Qexch min 0 385 2gLinh 0 67 2gAinh Lin interceptional length, [L]; Ain the opem area of the inlet gate, (4) 2 ∼ equation for exchange orpffiffiffiffiffi [L ]; h water depth above ground level, [L]; H1 and j j¼ð : Þ2ð Þ ∼ flux between street and Qexch Qexch 0 67 2gAin H1 H2 H2 water levels of the upper and the lower nodes, [L] sewer nodes

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J. Hydrol. Eng. 2012.17:667-678. Fig. 2. A hypothetical drainage network [adapted from Nasello and Tucciarelli (2005)]: (a) grid network with rainfall at north part; (b) grid network with rainfall at south part; (c) street network; (d) sewer network

series rainfall data is described by the following piecewise function indeed the pressure flow, and the water level at nodes 9, 12, 15, (Nasello and Tucciarelli 2005): and 27 at t ¼ 40;000 s is higher than the street’s elevation indicat- 8 ing a surcharged situation. < 0mm; t ¼ 0 ∼ 12000 s For the nonuniform rainfall scenarios, we used the same initial ¼ ; ¼ ∼ R : 10 mm t 12001 30000 s and boundary conditions mentioned above. The simulated hydro- 50 mm; t ¼ 30001 ∼ 72000 s graphs at outlet nodes and water level profiles at different times are shown in Figs. 5 and 6, respectively. Fig. 5 shows that the flow is To demonstrate that the new model can produce results consis- obviously delayed for the rainfall scenario at the north part (far side tent with the published literature (i.e., Nasello and Tucciarelli from the drainage outlet). For the rainfall scenario at the south part 2005), the runoff generation layer will first be ignored and it will (near the side from the drainage outlet), the routing of storm water be simply assume that each node in reaches V, VI, and VII (totally through street and sewer networks forms a flood peak that looks 26 nodes) will drain the rain in an area of 5;000 m2. In other words, different from the hydrographs in Figs. 3(a), 3(b), and 5(a). Also, no infiltration or other losses occur, and water falling over an area the street outflow in the north rainfall scenario (1:25 m3∕s) is much of 5;000 m2 will directly enter into the corresponding node in higher than that in the south rainfall scenario (0:55 m3∕s). This is

Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. reaches V, VI, and VII, which is same as the configuration in attributed to the distance of the overland flow routing path, i.e., the Nasello and Tucciarelli (2005). The simulated hydrographs at short routing path in the south rainfall scenario reduces the possibil- outlet nodes 1 and 34, and water level profiles at different times ity of water routing into the street network. Correspondingly, the (t ¼ 9;000 s, t ¼ 24000 s, and t ¼ 40;000 s) are shown in Figs. 3 surface outflow in the north rainfall scenario (0:24 m3∕s) is much and 4 respectively together with the published results in Nasello lower than that in the south rainfall scenario (0:92 m3∕s). and Tucciarelli (2005). The two sets of results are almost identical Fig. 6 shows that the water level profile at t ¼ 40;000 s is higher which indicates the good performance of the new model in simu- than the pipe’s top elevation for the north rainfall scenario indicat- lating the dual drainage process. Fig. 4 shows that the water level of ing a pressure sewer flow [refer to Fig. 6(a)]. Although, the pipe has the pipeline at t ¼ 9;000 s is lower than the pipeline’s top elevation, a free surface flow at the same time for the south rainfall scenario and the sewer flow is actually the free surface flow, whereas the [refer to Fig. 6(b)]. The simulated inundation maps are also shown water level at nodes 9, 12, 15, 27, and 30 at t ¼ 24;000 s is higher for two rainfall scenarios in Fig. 7. The results show the distinct than the pipeline’s top elevation indicating that the sewer flow is discrepancy of inundation location while the trivial difference of

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J. Hydrol. Eng. 2012.17:667-678. (a) (b)

Fig. 3. Consistency comparison of hydrographs at outlet nodes with Nasello and Tucciarelli (2005): (a) flow hydrographs obtained in this paper; (b) flow hydrographs obtained in Nasello and Tucciarelli (2005)

(a) (b)

Fig. 4. Consistency comparison of water level profiles at different times with Nasello and Tucciarelli (2005): (a) water level profiles obtained in this paper; (b) water level profiles obtained in Nasello and Tucciarelli (2005)

(a) (b) Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. Fig. 5. Comparison of flow hydrographs at outlet nodes for different rainfall scenarios: (a) for rainfall scenario at the north part; (b) for rainfall scenario at the south part

maximum inundation depth, which is attributed to the uniform i.e., 10 and 20 m. When the grid size becomes larger, the flow rate elevation configuration for this hypothetical example. This could at the street outlet increases obviously. The grid resolution should be expanded by setting the real or stochastic topography, which be, therefore, one of the uncertainty sources of modeling. In fact, is left for future research. the modeling uncertainty originates from many sources including To be noted, the cell size of the grid network has a significant rainfall input, model structure, landscape heterogeneity which de- influence on the simulated hydrographs. Fig. 8 shows the paired serves careful study. For the real applications, parameter calibration flow hydrographs obtained at the different grid resolutions, can compromise these uncertainties. As this paper is concerned

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J. Hydrol. Eng. 2012.17:667-678. (a) (b)

Fig. 6. Comparison of water level profiles at different times for different rainfall scenarios: (a) for rainfall scenario at the north part; (b) for rainfall scenario at the south part

Fig. 7. Comparison of surface inundation depth for different rainfall scenarios: (a) for rainfall scenario at the north part; (b) for rainfall scenario at the south part Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved.

Fig. 8. Comparison of flow hydrographs at outlet nodes for different grid resolutions

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J. Hydrol. Eng. 2012.17:667-678. primarily about model development, the uncertainty associated the length varying from 5.25 to 217.59 m. The sewer pipe has either with the proposed model including grid resolution is left for future a round or rectangular cross section according to the field investi- research. gation data. The ditch/river network has 47 nodes and 46 links with the length varying from 100 to 2,000 m, and the cross section is conceptualized as a trapezoid or a rectangle. There are in total 400 Application to a Real Urban Watershed virtual inlets and 237 grated inlet/manholes to connect the grid network, street network, and sewer network according to the inves- The real urban study area is the upstream catchment of the Qinghe tigation data. All inlets have a square shape with a side length of watershed in Beijing, where Tsinghua University campus, Peking 0.45 m. At the outlet nodes, the free outfall boundary conditions are University campus, and Zhongguancun Science Park are located imposed. (Fig. 9). Qinghe watershed is a subwatershed of the Beiyunhe River The primary parameter of calibration is Manning roughness co- basin, and it has two main branches, i.e., the Wanquanhe branch efficients for the surface grid network and for street/sewer/river net- and Xiaoyuehe branch, of which the former flows through the works. The manual calibration strategy is implemented on the basis Tsinghua University campus. The total area of the catchment is of the visual inspection criteria upon the stream flow hydrograph about 100 km2. As shown in Figs. 10(a) and 10(b), the topography at the Qinghe gauging station. Several well-gauged storm-runoff is quite flat in the east part of the catchment where the principal events exist that are selected for model calibration and validation land use type is an urbanized residential area, and the west part is the hilly area (Fragrance Hill). The east part will be focussed (see Table 2). The Manning roughness coefficients for grid network on to set up the urban drainage system as shown in Fig. 10(c). pixels are grouped according to land use types. The range and A total of four rain-gauge stations (Wenquan, Yangfang, Haidian, finally used values of different parameters are listed in Table 3. and Songlin stations) exist within and around the study area. The To be noted, the saturated hydraulic conductivity and other soil stream flow gauge station, i.e., Qinghe gate station, is located at hydraulic parameters in the Van Genuchten model (Van Genuchten a water sluice gate on the Qinghe stream just upstream of the 1980) for different soil types were chosen from the literature Xiaoyuehe outlet. The stream flow record is not continuous (Carsel and Parrish 1998) in a previous independent study by Tang throughout the year and is only available during flood season (June (2004), which produced reasonable hydrological modeling results to September) for some years (not continuous either). in an adjacent small watershed (Wenyu river). They are adopted in The spatial resolution of the grid network is 200 m (same as the this study (see Table 4) without further calibration for the same cell size of DEM, land use, and soil type, again the influence of grid kinds of soil types in the two watersheds. resolution is not considered in this study), and the study area is The resultant hydrographs at different locations for calibration totally discretized into 2,464 pixels. The street network consists and validation events are shown in Figs. 11–14, respectively. The of 587 nodes and 615 links with the length varying from 56.4 figures show the general agreement between simulated and ob- to 284.4 m. The street is assumed to have a rectangular cross sec- served flow rates at Qinghe gate station. To be noted, in the results tion with different widths determined by field investigation data. for validation storm event (5) (Fig. 13), the observed hydrograph The sewer network is made up of 588 nodes and 587 links with experienced a sudden drop after the flood peak time. This was the Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved.

Fig. 9. Location of the study area (upstream catchment of Qinghe watershed)

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J. Hydrol. Eng. 2012.17:667-678. Fig. 10. (a) DEM, (b) land use, (c) soil type, and (d) drainage system of the study area

Table 2. Statistics of Several Gauged Storm-Runoff Events in the Study Table 4. Parameters of Van Genuchten Model for the Three Soil Types Area (adapted from Carsel and Parrish 1988) 3 3 3 3 Duration Maximum Soil type α n θs (L L ) θr (L L ) Ks ðcm∕hÞ Storm time rainfall depth event No. Date Start time–End time (hours) in 1 h (mm) Clay 0.008 1.09 0.38 0.068 0.2 Loam 0.036 1.56 0.43 0.078 1.04 – 1 Jul 3, 1998 22:00 0:00 2 34.7 Sand 0.145 2.68 0.43 0.045 29.7 2 Jul 5, 1998 15:00–6:00 15 84.4 3 Jul 30, 2007 15:00–4:00 13 15 4 Aug 1, 2007 20:00–1:00 5 40.5 consequence of manually gate controlling indicated by the original hydrologic records. However, it could not be considered in the 5 Jun 13, 2008 17:00–4:00 11 40.5 current simulation for lack of detailed manipulation information; 6 Aug 10, 2008 8:00–6:00 22 44.5 although, the model does have the capacity to mimic some flood mitigation operations including gate regulation and pumping (Pan 2010). Furthermore, the simulated inundation water depth from the calibration event is shown in Fig. 15. It is evident that the maximum Table 3. Range and Calibrated Values of Model Parameters simulated inundation depth is about 1.5 m, which is less than the Parameter Land use type Min Max Calibrated actual value (about 2.0 m). In fact, the maximum inundation depth always occurred in the flyovers, and the model did not go into too Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. n-Manning Forest 0.03 0.16 0.04 much detail of the flyovers, which could be further extended by roughness Open forest 0.03 0.08 0.035 refining the local discretization scheme. coefficient Grassland 0.03 0.07 0.03 Following Nasello and Tucciarelli (2005), the sensitivity analy- Arable 0.01 0.045 0.022 sis is performed on the following model output variables: the maxi- Residential land 0.011 0.03 0.025 mum water depth at grid node 470, maximum water depth at street River 0.01 0.05 0:01–0:015 node 140, the peak flow rate at the sewer pipe node 1113, and the Street 0.011 0.018 0.015 peak flow rate at the river node 21 (see Fig. 15). The perturbed parameters are the side length of grated inlet and the Manning Sew pipe 0.011 0.03 0.015 roughness coefficients of different routing paths including the grid L , see Eq. (4) in Table 1 0.1 1.2 0.9 in network, street, sewer pipe, and river channel. The sensitivities, A , see Eq. (4) in Table 1 0.1 1.0 0.9 in defined as the ratio of incremental and original values of output

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J. Hydrol. Eng. 2012.17:667-678. Fig. 11. Comparison of measured and simulated hydrographs in the study watershed for calibration storm events 1 and 2

Fig. 12. Comparison of measured and simulated hydrographs in the study watershed for validation storm events 3 and 4 Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved.

Fig. 13. Comparison of measured and simulated hydrographs in the study watershed for validation storm event 5

J. Hydrol. Eng. 2012.17:667-678. Fig. 14. Comparison of measured and simulated hydrographs in the study watershed for validation storm event 6

Fig. 15. Simulated inundation map in the study watershed for calibration events 1 and 2

variables, are shown in Table 5. The results show that increasing the between the street and sewer pipe, which further raises the peak grid roughness detains more water on the grid surface and, thus, flow rate of sewer pipes and river reaches. The increasing of sewer reduces the peak flow rate in the sewer pipes and river reaches. pipe and river reach roughness results in a reduced peak flow rate as However, the increasing of street roughness leads to deeper surface expected. Also, the results show that the sensitivities of negative or inundation in the street nodes and, thus, a larger exchange flux positive perturbation on inlet size are significant and approximately

Table 5. Results of Sensitivity Analysis Maximum water Maximum water Peak flow rate at Peak flow rate Parameters depth at grid node 470 depth at street node 140 sewer pipe node 1113 at river node 21 Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. Roughness Coefficient of grid Network 20% 13:2% 0 3.7% 6.4% 20% 7.3% 0 12:0% 17:0% Roughness Coefficient of street 20% 0 0:3% 12:1% 12:0% 20% 0 0.1% 5.0% 1.1% Roughness Coefficient of Sewer pipe 20% 0 0 0.8% 1.3% 20% 0 0 7:4% 13:8% Roughness Coefficient of river 20% 0 0 1.7% 3.3% 20% 0 0 0:7% 0:8% Side length of Grated inlet 20% 0013:1% 7:9% 20% 0 0 16.7% 7.6%

J. Hydrol. Eng. 2012.17:667-678. symmetrical, which is different than the roughness sensitivities: the Notation sensitivity of negative perturbation is much smaller than that of positive perturbation for the grid network and sewer pipe; whereas, The following symbols are used in this paper: the trend is reversed for the street and river. The sensitivity analysis A = cross section area, [L2]; 2 results could provide useful guidelines for understanding model Ain = open area of the inlet gate, [L ]; behavior and, thus, parameter calibration. g = acceleration of gravity, [LT2]; h = water depth, [L]; H = water level, [L]; Conclusion H1 = water levels of the upper node, [L]; H2 = water levels of the lower node, [L]; A hydrologically enhanced distributed urban drainage model is K = unsaturated hydraulic conductivity, [LT1]; proposed by introducing a runoff generation layer (grid network) Lin = interception length, [L]; into the dual drainage model. The principal components of urban n = Manning roughness coefficient, [L1∕3T1]; drainage processes are represented by physically based equations, q = lateral inflow, [LT1]; i.e., the infiltration process is simulated by Richards equation, the Q = flow rate, [L3T1]; 2D overland flow, and 1D street/sewer/river flow processes are 3 1 Qexch = exchange flux between street and sewer nodes, [L T ]; described by the Saint-Venant equation. The dynamic wave model S = source or sink term, [L3L3T1]; of the Saint-Venant equation is adopted so that the surcharge con- Sf = friction slope, []; dition and backwater effect can be simulated. The routing path of Sfx = friction slope along direction of x, []; overland flow along the grid network is defined automatically ac- Sfy = friction slope along direction of y, []; cording to fixed topography and real-time varying water depth, and t = time, [T]; by this way the arbitrary predetermination of small drainage catch- u = flow velocity at directions of x, [LT1]; ment is not required any more. Also, the model is flexible in terms v = flow velocity at directions of y, [LT1]; of discretization scheme, i.e., the four networks are discretized sep- x = x coordinate, []; arately and subsequently linked by their hydraulic connections. y = y coordinate, []; Furthermore, the gridded format of surface network is compatible ψ = pressure head; and [L]; and to the new generation of rainfall production such as radar. θ = volumetric soil moisture content, [L3L3]. The model can be potentially applied to real-time management purposes of urban drainage systems other than the planning and designing purpose. The applications to the hypothetical example References and real urban watershed showed the capacity of the model to provide reasonable predictions of the outlet hydrograph. Of course, Carsel, R. F., and Parrish, R. S. (1988). “Developing joint probability the model application does require precise DEM data and detailed distributions of soil water retention characteristics.” Water Resour. physical representation of surface areas within the drainage system, Res., 24(5), 755–769. “ which could be more and more easily available as the remote sens- Cheng, C. T., Ou, C. P., and Chau, K. W. (2002). Combining a fuzzy ing technology is developing. optimal model with a genetic algorithm to solve multiobjective rainfall-runoff model calibration.” J. Hydrol., 268(1–4), 72–86. The model can be further improved (1) by adopting nested spa- Cheng, C. T., Wang, W. C., Xu, D. M., and Chau, K. W. (2008). “Opti- tial discretization to account for important detail topography during mizing hydropower reservoir operation using hybrid genetic algorithm urban inundation such as in flyovers, (2) by jointly utilizing GIS and chaos.” Water Resour. Manage., 22(7), 895–909. and AutoCAD tools to facilitate fast preprocessing of various data Cheng, C.-T., Zhao, M.-Y., Chau, K. W., Wu, X.-Y. (2006). “Using genetic including DEM, sewer network, road network, and river network, algorithm and TOPSIS for Xinanjiang model calibration with a single (3) by employing data assimilation methods such as the 4D varia- procedure.” J. Hydrol., 316(1–4), 129–140. tional method (4DVar, Hostache et al. 2010; Lai and Monnier 2009) Dietz, M. E. (2007). “Low impact development practices: A review of and ensemble Kalman Filter (EnKF) (Reichle et al. 2002) to reduce current research and recommendations for future directions.” Water – – uncertainties associated with model parameters and forcing data Air Soil Poll., 186(1 4), 351 363. “ (Salamon and Feyen 2010), (4) by incorporating state-of-the-art Duan, Q. Y., Sorooshian, S., and Gupta, V. K. (1992). Effective and effi- cient global optimization for conceptual rainfall—Runoff models.” optimization tools to realize the automatic parameter calibration Water Resour. Res., 28(4), 1015–1031. such as the shuffled complex evolution (SEC-UA) algorithm (Duan Fang, X., and Su, D. (2006). “An integrated one-dimensional and two- et al. 1992), Markov Chain Monte Carlo (MCMC) sampler entitled dimensional urban stormwater flood simulation model.” J. Am. Water Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) Resour. Assoc., 42(3), 713–724. (Vrugt et al. 2003), Genetic Algorithm (GA) (Cheng et al. 2002, Hostache, R., Lai, X. J., Monnier, J., and Puech, C. (2010). “Assimilation 2006, 2008) and (5) by integrating various catchment processes of spatially distributed water levels into a shallow-water flood model. (natural or unnatural) such as many kinds of low impact develop- Part II: Use of a remote sensing image of mosel river.” J. Hydrol.,

Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved. ment (LID) practices recommended as an alternative to traditional 390(3–4), 257–268. “ stormwater design (Dietz 2007). These are left for future research. Hsu, M. H., Chen, S. H., and Chang, T. J. (2000). Inundation simulation for urban drainage basin with storm sewer system.” J. Hydrol., 234(1–2), 21–37. “ Acknowledgments Lai, X., and Monnier, J. (2009). Assimilation of spatially distributed water levels into a shallow-water flood model. Part I: Mathematical method ” J. Hydrol. – – The data used in this study is provided by Beijing Water Authority and test case. , 377(1 2), 1 11. Mailhot, A., Duchesne, S., Caya, D., and Talbot, G. (2007). “Assessment and Beijing Meteorological Agency, and the research funding of future change in intensity—duration—frequency (IDF) curves for comes from the National Natural Science Foundation of China southern quebec using the canadian regional climate model.” J. Hydrol., (NSFC, 50823005) and from the State Key Laboratory of Hydro- 347(1–2), 197–210. science and Engineering, Tsinghua University (20089-TC-1, 2012- Mcbean, E. A. (2006). Projections of climate change on precipitation KY-03). Their support is greatly appreciated. intensities, and implications to urban infrastructure, in water: Global

J. Hydrol. Eng. 2012.17:667-678. common and global problems, V. I. Grover, ed., Science Publisher, Simunek, J., and van Genuchten, M. Th. (2008). “Modeling nonequili- Enfield, NH, 189–199. brium flow and transport with HYDRUS.” Vadose Zone J., 7(2), Nasello, C., and Tucciarelli, T. (2005). “Dual multilevel urban drainage 782–797. model.” J. Hydraul., Eng., 131(9), 748–754. Smith, M. B. (2006a). “Comment on ‘analysis and modeling of flooding in Pan (2010). “Study on distributed multi-layer urban flood model: Case urban drainage systems.” J. Hydrol., 317(3–4), 355–363. study in Beijing urban area.” Ph.D. thesis, Tsinghua Univ., Beijing, Smith, M. B. (2006b). “Comment on ‘potential and limitations of 1D China. modeling of urban flooding’ by O. Mark et al. [J. Hydrol. 299 Preissmann, M. A., and Cunge, J. A. (1961). “Calculation of wave (2004)284-299].” J. Hydrol., 321(1–4), 1–4. propagation on electronic machines.” Proc., 9th Congress, IAHR, Tang, L. H. (2004). “Study on the rule of precipitation-runoff in regions Dubrovnik, 656–664. under changing landscapes.” Technical Rep. at Institute of Hydrology Reichle, R. H., McLaughlin, D. B., and Entekhabi, D. (2002). “Hydrologic and Water Resources, Tsinghua Univ., Beijing, China. data assimilation with the ensemble kalman filter.” Mon. Weather Rev., Van Genuchten, M. T. (1980). “A closed-form equation for predicting the 130(1), 103–114. hydraulic conductivity of unsaturated soils.” Soil Sci. Soc. Am. J., 44(5), Roesner, L. A., Aldrich, J. A., and Dickinson, R. E. (1988). “Storm water 892–898. management model user’s manual, version 4, EXTRAN addendum.” Vrugt, J. A., Gupta, H. V., Bouten, W., and Sorooshian, S. (2003). “A EPA/600/3-88/001b (NTIS PB88236658/AS), EPA, Athens, GA. shuffled complex evolution metropolis algorithm for optimization Salamon, P., and Feyen, L. (2010). “Disentangling uncertainties in distrib- and uncertainty assessment of hydrologic model parameters.” Water uted hydrological modeling using multiplicative error models and Resour. Res., 39(8), 1201–1215,. sequential data assimilation.” Water Resour. Res., 46(12), 501–519. Yen, B. C., and Akan, A. O. (1999). “Hydraulic design of urban drainage Schmitt, T. G., Thomas, M., and Ettrich, N. (2004). “Analysis and modeling systems.” Hydraulic design handbook, L. W. Mays, ed., McGraw-Hill, of flooding in urban drainage systems.” J. Hydrol., 299(3–4), 300–311. New York. Downloaded from ascelibrary.org by TSINGHUA UNIVERSITY on 03/14/15. Copyright ASCE. For personal use only; all rights reserved.

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