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ERROR: type should be string, got "https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. A Time-Varying Distributed Unit Hydrograph considering soil \n1 \nmoisture content \n2 \nBin Yi1,2, Lu Chen1,2*, Hansong Zhang3, Ping Jiang4, Yizhuo Liu1,2, Hongya Qiu1,2 \n3 \n1 School of Civil and Hydraulic Engineering, Huazhong University of Science and Technology, Wuhan, \n4 \n430074, China \n5 \n2 Hubei Key Laboratory of Digital Valley Science and Technology, Wuhan 430074, China \n6 \n3 PowerChina Huadong Engineering Corporation Limited，Hangzhou 310014, China \n7 \n4 Meizhou Hydrological Bureau, Guangdong Province, Meizhou 514000, China \n8 \nCorrespondence: Lu Chen (chen_lu@hust.edu.cn) \n9 \nAbstract: The distributed unit hydrograph (DUH) method has been widely used for \n10 \nflood routing simulation, because it can well characterize the underlying surface \n11 \ncharacteristics and various rainfall intensities. The core of the DUH is the calculation \n12 \nof flow velocity. However, the current velocity formula assumed a global equilibrium \n13 \nof the watershed and ignored the impact of time-varying soil moisture content on flow \n14 \nvelocity, which leads to a larger flow velocity value. The goal of this study is to identify \n15 \na soil moisture content factor, which was derived based on the water storage capacity \n16 \ncurve, to explore the responses of DUH to soil moisture content in unsaturated areas. 17 \nThus, an improved distributed unit hydrograph based on time-varying soil moisture \n18 \ncontent was proposed in this paper. The proposed method considered the impact of both \n19 \nthe time-varying rainfall intensity and soil moisture content on the flow velocity, and \n20 A Time-Varying Distributed Unit Hydrograph considering soil \n1 2 Hubei Key Laboratory of Digital Valley Science and Technology, Wuhan 430074, China \n6 3 PowerChina Huadong Engineering Corporation Limited，Hangzhou 310014, China \n7 4 Meizhou Hydrological Bureau, Guangdong Province, Meizhou 514000, China \n8 Correspondence: Lu Chen (chen_lu@hust.edu.cn) \n9 Correspondence: Lu Chen (chen_lu@hust.edu.cn) \n9 Abstract: The distributed unit hydrograph (DUH) method has been widely used for \n10 \nflood routing simulation, because it can well characterize the underlying surface \n11 \ncharacteristics and various rainfall intensities. The core of the DUH is the calculation \n12 \nof flow velocity. However, the current velocity formula assumed a global equilibrium \n13 \nof the watershed and ignored the impact of time-varying soil moisture content on flow \n14 \nvelocity, which leads to a larger flow velocity value. The goal of this study is to identify \n15 \na soil moisture content factor, which was derived based on the water storage capacity \n16 \ncurve, to explore the responses of DUH to soil moisture content in unsaturated areas. 17 \nThus, an improved distributed unit hydrograph based on time-varying soil moisture \n18 \ncontent was proposed in this paper. The proposed method considered the impact of both \n19 \nthe time-varying rainfall intensity and soil moisture content on the flow velocity, and \n20 1\nAbstract: The distributed unit hydrograph (DUH) method has been widely used for \n10 \nflood routing simulation, because it can well characterize the underlying surface \n11 \ncharacteristics and various rainfall intensities. The core of the DUH is the calculation \n12 \nof flow velocity. However, the current velocity formula assumed a global equilibrium \n13 \nof the watershed and ignored the impact of time-varying soil moisture content on flow \n14 \nvelocity, which leads to a larger flow velocity value. The goal of this study is to identify \n15 \na soil moisture content factor, which was derived based on the water storage capacity \n16 \ncurve, to explore the responses of DUH to soil moisture content in unsaturated areas. 17 \nThus, an improved distributed unit hydrograph based on time-varying soil moisture \n18 \ncontent was proposed in this paper. The proposed method considered the impact of both \n19 \nthe time-varying rainfall intensity and soil moisture content on the flow velocity, and \n20 1 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. the watershed is assumed not to be equilibrium but vary with the soil moisture. A Time-Varying Distributed Unit Hydrograph considering soil \n1 The Qin \n21 \nRiver Basin was selected as a case study, and results of the time-varying distributed unit \n22 \nhydrograph (TDUH) and current DUH methods were used as comparisons with that of \n23 \nproposed method. Influence mechanism of time-varying soil moisture content on the \n24 \nflow velocity and flood forecasts were explored. Results show that the proposed method \n25 \nperforms the best among the three methods. The shape and duration of the unit \n26 \nhydrograph can be mainly related to the soil moisture content at initial stage of a storm. 27 \nWhen the watershed is approximately saturated, the grid flow velocity is majorly \n28 \ndominated by the excess rainfall. 29 Keywords: Time-varying distributed unit hydrograph, Runoff routing, Flow velocity, \n30 \nSoil moisture content, Excess rainfall \n31 Keywords: Time-varying distributed unit hydrograph, Runoff routing, Flow velocity, \n30 \nSoil moisture content, Excess rainfall \n31 1. Introduction \n32 Flood is a natural disaster with strong suddenness, high frequency and serious \n33 \nharm (Jongman et al., 2014; Alfieri et al., 2015; Munich, 2017). Global flood losses \n34 \naccount for about 40% of the total losses of all kinds of natural disasters. High accuracy \n35 \nflood forecasts can provide decision-making basis for reservoir operation, flood control, \n36 \nand optimal allocation of water resources, which plays a significant role in water \n37 \nresources management, development and utilization, and national economic \n38 \nconstruction. 39 Watershed routing calculation is an important procedure in hydrological model, \n40 2 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. whose accuracy directly affects flood forecasts results. The Unit Hydrograph (UH), \n41 \nproposed by Sherman (1932), is one of the methods most widely used for development \n42 \nof flood prediction and warning systems for gauged basins with observed rainfall–\n43 \nrunoff data (Singh et al., 2014). The UH is a surface runoff hydrograph resulting from \n44 \none unit of rainfall excess uniformly distributed spatially and temporally over the \n45 \nwatershed for the entire specified rainfall excess duration (Chow 1964). Usually, the \n46 \nUH can be categorized into 4 major types, including the traditional models, probability \n47 \nmodels, conceptual models, and geomorphologic methods (Bhuyan et.al. 2015). 48 First, the traditional models were discussed. The traditional methods established \n49 \nthe relationships between parameters used to describe the UH (e.g. peak flow, time to \n50 \npeak and time base) and parameters used to describe the basin. Snyder (1938), Mockus \n51 \n(1957), and U.S. Soil Conservation Service (SCS) (2002) proposed some traditional \n52 \nmethods,, which are still available to hydrologists nowadays. The disadvantages of \n53 \nthese methods are that they do not yield satisfactory results, and their application to \n54 \npractical engineering problems is tedious and cumbersome (Nigussie et al., 2016). 55 First, the traditional models were discussed. The traditional methods established \n49 \nthe relationships between parameters used to describe the UH (e.g. peak flow, time to \n50 \npeak and time base) and parameters used to describe the basin. Snyder (1938), Mockus \n51 \n(1957), and U.S. Soil Conservation Service (SCS) (2002) proposed some traditional \n52 \nmethods,, which are still available to hydrologists nowadays. The disadvantages of \n53 \nthese methods are that they do not yield satisfactory results, and their application to \n54 \npractical engineering problems is tedious and cumbersome (Nigussie et al., 2016). 1. Introduction \n32 55 Furthermore, Most UHs have steeper rising limbs than their receding sides, which \n56 \ncan be well characterized by the probability distribution functions (pdfs). Many pdfs \n57 \nwere used for derivation of UHs due to their similarity in the shape of statistical \n58 \ndistributions to UHs. The difficulties of these methods are that the distribution functions \n59 \nare diverse, and the parameters depends on numerous hydrological data (Bhuyan et al., \n60 \n2015). 61 Furthermore, Most UHs have steeper rising limbs than their receding sides, which \n56 \ncan be well characterized by the probability distribution functions (pdfs). Many pdfs \n57 \nwere used for derivation of UHs due to their similarity in the shape of statistical \n58 \ndistributions to UHs. The difficulties of these methods are that the distribution functions \n59 \nare diverse, and the parameters depends on numerous hydrological data (Bhuyan et al., \n60 \n2015). 61 3 3 Another modeling technique for deriving UHs is conceptual model. Nash (1957) \n62 \nproposed a conceptual model characterized as a succession of n linear reservoirs \n63 \nconnected in series with the same storage coefficient K, for the derivation of the \n64 \ninstantaneous unit hydrograph (IUH). After that, Dooge (1959) derived a mathematical \n65 \nmodel for the IUH based on linear reservoirs. Bhunya et al. (2005) and Singh et al. 66 \n(2007) represented a hybrid and extended hybrid model based on the linear reservoir \n67 \nmodel. Singh (2015) proposed a new simple two-parameter IUH with conceptual and \n68 \nphysical justification. Khaleghi et al. (2018) suggested a new conceptual model namely \n69 \nthe inter-connected linear reservoir model (ICLRM). However, the conceptual model \n70 \nneglects the impact of uneven spatial distribution of the basin’s underlying surface on \n71 \nthe UHs. 72 62 On the bases of time-area method developed by Clark (1945), Rodriguez-Iturbe \n73 \n(1979) proposed a geomorphologic instantaneous unit hydrograph (GIUH) method, \n74 \nwhich couples the hydrologic characteristics of a catchment with more detailed \n75 \ngeomorphologic parameters (Kumar et al., 2007). In the model, the IUH corresponds \n76 \nto the probability density function of travel times from the locations of runoff \n77 \nproduction to the outlet of a watershed (Gupta et al., 1980). With the development of \n78 \ndigital elevation models (DEMs) and geographic information system (GIS) technology, \n79 \nthe formulation of width function-based geomorphological IUH methods are available, \n80 \nthe rigidity of which is reflected in its incapacity to account properly (i.e. 1. Introduction \n32 to respect the \n81 \ngeometry) for the distribution of rainfall (Rigon et al., 2016). 82 4 4 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. The methods mentioned above are based on the UH linear assumption. However, \n83 \nit is well-known that the rainfall-runoff process is nonlinear due to the dependence of \n84 \nthe flood wave celerity on the excess rainfall intensity (Robinson et al., 1995). Minshall \n85 \n(1960) showed that different rainfall intensities significantly correspond to different \n86 \nUHs for a small watershed. After that, Rodríguez-Iturbe et al. (1982) extended the \n87 \nGIUH to the geomorphoclimatic IUH (GcIUH) to cope with this nonlinearity by \n88 \nincorporating excess rainfall intensity in the determination of the IUH. Lee et al. (2008) \n89 \nproposed a variable Kinematic wave GIUH corresponding to time-varying rainfall \n90 \nintensity for the calculation of the runoff concentration, which warrants consideration \n91 \nfor rainfall-runoff modelling in ungauged catchments that are influenced by high \n92 \nintensity rainfall. 93 83 5\nFurthermore, it is difficult for the previous methods (traditional models, \n94 \nprobability models, conceptual models, and geomorphologic models) to fully consider \n95 \nthe geomorphic characteristics of the watershed while incorporating the nonlinearity of \n96 \nrainfall-runoff process (e.g. time-varying rainfall intensities). Thus, the spatially \n97 \ndistributed unit line hydrograph (DUH) method has been attached much attention. The \n98 \nconcept of a DUH is based on the fact that the unit hydrograph can be derived from the \n99 \ntime-area curve of a watershed by the S-curve method (Muzik, 1996). The DUH can be \n100 \nessentially classified as a type of geomorphoclimatic unit hydrograph, since its \n101 \nderivation depends on watershed geomorphology, rainfall and hydraulics (Du et al., \n102 \n2009). The spatially distributed flow celerity and temporally varying excess rainfall \n103 5 intensities can be considered in this method (Bunster et al., 2019). 104 In DUH models, the travel time of each grid cell can be calculated by dividing the \n105 \ntravel distance of a cell to the next cell by velocity of flow generated in that cell (Paul \n106 \net al., 2018). And the travel times are then summed along the flow path to obtain the \n107 \ntotal travel time from each cell to the outlet. The DUH can be derived using the \n108 \ndistribution of travel time from all grid cells in a watershed (Bunster et al., 2019). 1. Introduction \n32 Some \n109 \nDUH models assumed a time-invariant travel time field and ignored the dependence of \n110 \ntravel time on excess rainfall intensity (Melesse & Graham, 2004; Noto and La Loggia, \n111 \n2007; Gibbs et al., 2010), while others suggested various UHs correspond to different \n112 \nstorm events, namely time-varying distributed unit hydrograph (TDUH) (Martinez et \n113 \nal.,2002; Sarangi et al., 2007; Du et al., 2009). Compared to the fully distributed models \n114 \nbased on the momentum equation, DUH model is a more efficient approach that allow \n115 \nthe use of distributed terrain information in a purely ungauged region. The DUH \n116 \nmethods are better than the traditional UHs because the spatially information of \n117 \nwatershed and time-varying rainfall-runoff process was considered, and have been \n118 \ndeveloped as an alternative method to semi-distributed and fully distributed methods \n119 \nfor rainfall-runoff modelling (Bunster et al., 2019). 120 6\nMany researchers have also focused on the upstream contributions to the travel \n121 \ntime estimation besides excess rainfall intensity in TDUH method. For instance, \n122 \nMaidment et al. (1996) defined the velocity in the cell also as a function of the \n123 \ncontributing area to take into accounts the velocity increase observed downstream in \n124 6\nMany researchers have also focused on the upstream contributions to the travel \n121 \ntime estimation besides excess rainfall intensity in TDUH method. For instance, \n122 \nMaidment et al. (1996) defined the velocity in the cell also as a function of the \n123 \ncontributing area to take into accounts the velocity increase observed downstream in \n124 6 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. river systems (Gironás et al., 2009). Gad (2014) applies a grid-based technique \n125 \nimplementing the stream power formulation to relate flow velocity to the hydrologic \n126 \nparameters of the upstream watershed area through simplistic parametric approaches. 127 \nMany similar works have been done by Saghafian and Julien (1995), Bhattacharya et \n128 \nal. (2012) and Chinh et al. (2013). Yet, they assumed that the watershed was global \n129 \nequilibrium. After that, Bunster et al. (2019) developed a spatially TDUH model that \n130 \naccounts for dynamic upstream contributions and characterized the temporal behavior \n131 \nof upstream contributions and its impact on travel times in the basin. 1. Introduction \n32 However, this \n132 \ntime-varying DUH model also adopted the assumption that equilibrium in each \n133 \nindividual grid cell can be reached before the end of the rainfall excess pulse. When \n134 \nthere accrues continuous excess-rainfall in a watershed, the soil moisture content and \n135 \nsurface runoff increase, and the infiltration rate decreases, leading to an acceleration of \n136 \nthe routing velocity. Until the entire basin is saturated and the routing velocity reach its \n137 \nmaximum. Accepting the assumption of equilibrium in global or the grid cell yields \n138 \nslower travel times, shorter times to peak, and higher peak discharges. However, all the \n139 \naforementioned approximations neglect the impact of dynamic changes of soil moisture \n140 \nexchange and water storage in unsaturated regions. 141 7\nThe objective of this study is therefore to propose a time varying distributed unit \n142 \nhydrograph runoff routing method that accounts for dynamic rainfall intensity and soil \n143 \nmoisture content based on the existing Xinanjiang (XAJ) model. The main \n144 \ncontributions and innovations of the present study are as follows. First, the soil moisture \n145 The objective of this study is therefore to propose a time varying distributed unit \n142 \nhydrograph runoff routing method that accounts for dynamic rainfall intensity and soil \n143 \nmoisture content based on the existing Xinanjiang (XAJ) model. The main \n144 \ncontributions and innovations of the present study are as follows. First, the soil moisture \n145 7 7 content proportional factor in the unsaturated area was identified and expressed based \n146 \non the water storage capacity curves. Second, the travel time expression function based \n147 \non the Kinematic wave theory was modified by considering a soil moisture content \n148 \nproportional factor. Besides the rain intensity, the influence of the time-varying soil \n149 \nmoisture storage on the confluence velocity was considered in the watersheds, where \n150 \nthe runoff generation is dominated by saturation-excess mode. Finally, the Qin River \n151 \nBasin in Guangdong Province, China, was selected as a case study. The TDUH and \n152 \nDUH methods were compared with the proposed method. 153 8 8 2. Establishment of flood forecasts model \n155 The flood forecast modelling frame work mainly consists the calculation of excess \n156 \nrainfall and the derivation of DUH. In this study, the XAJ model was adopted to \n157 \ncalculate the excess rainfall and a new routing method was developed to incorporate \n158 \nthe behavior of dynamic changes of soil moisture content and rainfall intensity. The soil \n159 \nmoisture content factor in unsaturated regions was expressed by the water storage \n160 \ncapacity curves. Thus, the individual gird cell was not assumed to be equilibrium but \n161 \nvariable in time. The general formula of velocity proposed by Madidement (1993) \n162 \ncombining with the soil moisture content factor was proposed for considering the \n163 \nimpact of underlying spatially heterogeneous on the watershed equilibrium. 164 2.1 Calculation of runoff generation \n165 The Xinanjiang (XAJ) model was used for the calculation of excess rainfall in this \n166 \nstudy. It is a conceptual hydrologic model proposed by Zhao et al. (1980) for flood \n167 \nforecasts in the Xinan River Basin. After that, the XAJ model has been widely used in \n168 \nhumid and semi-humid watersheds all over the world (Zhao, 1992). It mainly consists \n169 \nof four modules, namely evapotranspiration module, runoff generation module, runoff \n170 \npartition module and runoff routing module (Zhou et al., 2019). Usually, a large \n171 \nwatershed is divided into several sub-watersheds to capture the spatial variability of \n172 \nunderlying surface, precipitation, and evaporation. In each sub-basin, the inputs of the \n173 \nXAJ model are the average areal rainfall as well as evaporation, and the output is \n174 9 9 streamflow. The schematic diagram of the XAJ model is shown in Figure 1. 175 streamflow. The schematic diagram of the XAJ model is shown in Figure 1. 175 \nFirst, for the evapotranspiration module, the soil profile of each sub-basin is \n176 \ndivided into three layers, the upper, lower and deeper layers, and only when the layer \n177 \nabove it exhausted water does evaporation from a next layer occur. Second, as for the \n178 \nRunoff generation in the XAJ model, a catchment is divided into two parts by the \n179 \npercentage of impervious and saturated areas, namely permeable and impervious areas \n180 \nrespectively. Since the soil moisture deficit is heterogeneous, runoff distribution is \n181 \nusually nonuniform across a basin. 2. Establishment of flood forecasts model \n155 Thus, a storage capacity curve was adopted by the \n182 \nXAJ model to accommodate the nonuniformity of the soil moisture deficit or the tension \n183 \nwater capacity distribution. Third, the runoff partition of the XAJ model divides the \n184 \ntotal runoff into three components by a free reservoir, which consists of surface runoff \n185 \n(RS), interflow runoff (RI) and groundwater runoff (RG). More details can be found in \n186 \n(Zhao et al., 1980). Finally, the linear reservoir method was adopted for calculation of \n187 \ncatchment routing (Lu et al., 2014), and the TDUH considering soil moisture content, \n188 \nDUH, TDUH were used to calculate the routing of river net. The Maskingen method \n189 \nwas employed to produce the streamflow from each sub-basin to the outlet of the entire \n190 \ncatchment. Various runoff routing methods were introduced in Section 2.2. 191 2.2 Calculation of runoff routing based on TDUH considering time-\n192 \nvarying soil moisture content \n193 2.2 Calculation of runoff routing based on TDUH considering time-\n192 \nvarying soil moisture content \n193 10 \nThe routing calculation adopted the GIS-derived DUH method, which allowed the \n194 \nvelocity to be calculated on a grid cell basis over the catchment. The core of the DUH \n195 10 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. method is to equate the probability density distribution function of the time at which \n196 \nthe rainfall flows to the outlet of the basin to the IUH, in which the time-area \n197 \nrelationship was derived using the velocity field with spatial distribution characteristics. 198 \nLaurenson (1964) identified that the concept of DUH was due to time-area histogram. 199 \nAfter that, Madidement (1993) proposed the travel time formula for each grid cell, \n200 \nwhich are relating to the length, slop, velocity coefficient of any reach of the flow path, \n201 \nexpressed as Equations. (1) and (2). The diagram of travel time calculation is shown as \n202 \nFigure 2(a). 203 method is to equate the probability density distribution function of the time at which \n196 \nthe rainfall flows to the outlet of the basin to the IUH, in which the time-area \n197 \nrelationship was derived using the velocity field with spatial distribution characteristics. 198 \nLaurenson (1964) identified that the concept of DUH was due to time-area histogram. 2. Establishment of flood forecasts model \n155 The time-area diagram values are at \n219 discrete time points, and the specific formula is given by \n220 (\n)\n(\n)\n(\n)\n1\nA i t\nA\ni\nt\nUH i t\nt\n\n−\n−\n\n\n\n\n\n\n=\n\n (4) \n221 (\n)\n(\n)\n(\n)\n1\nA i t\nA\ni\nt\nUH i t\nt\n\n−\n−\n\n\n\n\n\n\n=\n\n (4) \n221 (4) where (t\ni t\n=  and i = 0, 1, 2, ..., n); UH is the ordinate value of the DUH; \n(\n)\nA i t\n\n is \n222 where (t\ni t\n=  and i = 0, 1, 2, ..., n); UH is the ordinate value of the DUH; \n(\n)\nA i t\n\n is \n222 the total area of the watershed; \nt\n is the time interval. 223 However, the methods above only consider the influence of the spatial \n224 \nheterogeneity of the underlying surface on the catchment routing process and adopt a \n225 \nsingle UH for each sub-watershed, ignoring the effect of time-varying rain intensity. 226 \nThus, the TDUH can be derived by combining the continuity and Manning equations \n227 \n(Noto & Loggia, 2007). Compared to the traditional DUH method, the TDUH method \n228 \nis more consistent with the routing process. The concrete derivation process of this \n229 \nmethod is as follows. 230 However, the methods above only consider the influence of the spatial \n224 \nheterogeneity of the underlying surface on the catchment routing process and adopt a \n225 \nsingle UH for each sub-watershed, ignoring the effect of time-varying rain intensity. 226 \nThus, the TDUH can be derived by combining the continuity and Manning equations \n227 \n(Noto & Loggia, 2007). Compared to the traditional DUH method, the TDUH method \n228 \nis more consistent with the routing process. The concrete derivation process of this \n229 \nmethod is as follows. 230 However, the methods above only consider the influence of the spatial \n224 \nheterogeneity of the underlying surface on the catchment routing process and adopt a \n225 \nsingle UH for each sub-watershed, ignoring the effect of time-varying rain intensity. 226 \nThus, the TDUH can be derived by combining the continuity and Manning equations \n227 \n(Noto & Loggia, 2007). Compared to the traditional DUH method, the TDUH method \n228 \nis more consistent with the routing process. 2. Establishment of flood forecasts model \n155 199 \nAfter that, Madidement (1993) proposed the travel time formula for each grid cell, \n200 \nwhich are relating to the length, slop, velocity coefficient of any reach of the flow path, \n201 \nexpressed as Equations. (1) and (2). The diagram of travel time calculation is shown as \n202 \nFigure 2(a). 203 0.5\nV\nkS\n=\n (1) \n204 \ni\ni\ni\nL\nV\n\n\n=\n or \n2\ni\ni\ni\nL\nV\n\n\n=\n (2) \n205 0.5\nV\nkS\n=\n (1) \n204 \ni\ni\ni\nL\nV\n\n\n=\n or \n2\ni\ni\ni\nL\nV\n\n\n=\n (2) \n205 (1) (2) where V is the flow velocity; S is the slope of the watershed unit; k is the coefficient of \n206 \nthe flow velocity which is related to the vegetational form of the watershed unit; \ni\n\n \n207 \nis the retention time of the unit i; \niL is the path length of the stream; and m is the \n208 \nnumber of the watershed unit. 209 where V is the flow velocity; S is the slope of the watershed unit; k is the coefficient of \n206 Then the simulation is performed along the flow path from the gird cell to the \n210 watershed outlet (Muzik, 1996), and the formula is given by \n211 1\nm\ni\ni\n\n\n=\n=\n\n\n (3) 1\nm\ni\ni\n\n\n=\n=\n\n\n (3) \n212 1\nm\ni\ni\n\n\n=\n=\n\n\n (3) \n212 (3) where \ni is the travel time from the unit i to the outlet of the sub-watershed. 213 In addition, the time-area histogram of the watershed can be obtained after the \n214 In addition, the time-area histogram of the watershed can be obtained after the \n214 \narrival time of each cell being calculated as shown in Figure2 (b), which indicates the \n215 arrival time of each cell being calculated as shown in Figure2 (b), which indicates the \n215 11 distribution of partial watershed areas contributing to runoff at the watershed outlet as \n216 a function of travel time (Muzik, 1996). The time-area diagram can be obtained based \n217 on the distribution of travel time, namely S-hydrograph, as shown in Figure 2(c). Then, \n218 the DUH can be derived from the S-hydrograph. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 2\n1\n3\n2\n1\nV\nh S\nn\n=\n (6) \n236 236 (6) 0.4\n0.4\n0.3\n0.6\n1\nV\nI\nL S\nn\n=\n (7) \n240 (7) Denote the discrete rainfall intensity and the reference rainfall intensity as \nsI and \n241 \ncI respectively (Kong et al., 2019). The flow velocity of the discrete rainfall intensity \n242 Denote the discrete rainfall intensity and the reference rainfall intensity as \nsI and \n241 \ncI respectively (Kong et al., 2019). The flow velocity of the discrete rainfall intensity \n242 \ns\nV can be written by \n243 2/5\n2/5\ns\ns\ns\nc\nc\nc\nc\nV\nI\nV\nV\nV\nV\nI\n=\n\n=\n\n (8) \n244 2/5\n2/5\ns\ns\ns\nc\nc\nc\nc\nV\nI\nV\nV\nV\nV\nI\n=\n\n=\n\n (8) \n244 (8) where \nc\nV is the flow velocity of the reference rainfall intensity. 245 Combining Equations. (6) and (8), the flow velocity formula considering rainfall \n246 \nintensity is given by \n247 2\n2\n2\n1\n1\n5\n5\n3\n2\n2\n1\n1\ns\ns\ns\nc\nc\nI\nI\nV\nh S\nv\nkS\nn\nI\nI\n\n\n\n\n=\n=\n\n\n\n\n\n\n\n\n (9) \n248 2\n2\n2\n1\n1\n5\n5\n3\n2\n2\n1\n1\ns\ns\ns\nc\nc\nI\nI\nV\nh S\nv\nkS\nn\nI\nI\n\n\n\n\n=\n=\n\n\n\n\n\n\n\n\n (9) \n248 (9) where k is the velocity coefficient. 249 13 \nEquation. (5) assumes that equilibrium in each individual grid cell is reached \n250 \nbefore the excess rainfall pulse. However, the DUH derived based on this assumption \n251 \nmay be higher, leading to larger forecast errors. For instance, in a continues storm event, \n252 \ndue to the spatial heterogeneity of the underlying surface, the surface runoff increases \n253 \nin the unsaturated regions, and the infiltration rate decreases. As is known that the more \n254 13 \nEquation. (5) assumes that equilibrium in each individual grid cell is reached \n250 \nbefore the excess rainfall pulse. However, the DUH derived based on this assumption \n251 \nmay be higher, leading to larger forecast errors. 2. Establishment of flood forecasts model \n155 The concrete derivation process of this \n229 \nmethod is as follows. 230 \nThe continuity equation of water flow is given by \n231 \nVLh\nIA\n=\n (5) \n232 \nwhere V is the velocity of the flow; L is the length of the unit; h is the depth of the \n233 \nstream; I is the intensity of the excess rainfall; and A is the area of the unit, \n2\nA\nL\n=\n. 234 \nThe Manning formula is described by \n235 (5) 12 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. For instance, in a continues storm event, \n252 \ndue to the spatial heterogeneity of the underlying surface, the surface runoff increases \n253 \nin the unsaturated regions, and the infiltration rate decreases. As is known that the more \n254 13 surface runoff, the greater the velocity. Until the entire basin is saturated and the routing \n255 \nvelocity reach its maximum. However, the traditional velocity calculations do not \n256 \nconsider the influence of the proportion of water sources in the unsaturated area on the \n257 \nflow velocity. To solve this issue, an improved TDUH method considering soil moisture \n258 \ncontent was proposed in this paper. The proposed equations for calculation of the flow \n259 \nvelocity of each cell was discussed below. 260 First, combining the soil moisture content and watershed storage capacity curve to \n261 \ncalculate \nt\n (the fraction of basin with the soil storage capacity less than \nt\nW ); \n262 \nFurthermore, for the (\n)\n1\nt\n\n−\n part, calculating the proportion of \ntA ( the current soil \n263 \nmoisture content) to \nt\nt\nA\nB\n+\n (the corresponding maximum soil moisture storage for \n264 \npart of (\n)\n1\nt\n\n−\n). The schematic diagram is shown in Figure 3, in which \n'\n~WM\n\n is \n265 \nthe watershed storage capacity curve; \nt\nW is the current soil moisture storage; and \n266 \n(\n)\n1\nt\n\n−\n is the part of the watershed that the soil moisture storage dose not reach the \n267 \nmaximum. 268 First, combining the soil moisture content and watershed storage capacity curve to \n261 \ncalculate \nt\n (the fraction of basin with the soil storage capacity less than \nt\nW ); \n262 \nFurthermore, for the (\n)\n1\nt\n\n−\n part, calculating the proportion of \ntA ( the current soil \n263 \nmoisture content) to \nt\nt\nA\nB\n+\n (the corresponding maximum soil moisture storage for \n264 \npart of (\n)\n1\nt\n\n−\n). The schematic diagram is shown in Figure 3, in which \n'\n~WM\n\n is \n265 \nthe watershed storage capacity curve; \nt\nW is the current soil moisture storage; and \n266 \n(\n)\n1\nt\n\n−\n is the part of the watershed that the soil moisture storage dose not reach the \n267 \nmaximum. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 268 For the watershed storage capacity curve \n'\n~WM\n\n, the specific formula is given \n269 \nby \n270 '\n1\n1\nb\nWM\nWMM\n\n\n\n= −\n−\n\n\n\n\n (10) \n271 (10) where \n'\nWM is the soil storage capacity of the watershed; WMM is maximum \n272 \nwatershed soil storage capacity;  is fraction of basin with the soil storage capacity \n273 \nless than \n'\nWM ; and b is exponent of the curve. 274 less than \n'\nWM ; and b is exponent of the curve. 274 14 For the current soil moisture storage content of the (\n)\n1\nt\n\n−\n part, the specific \n275 \nformula is given by \n276 \n1\nt\nt\nt\nA\nW (11) \n277 \nFor the maximum soil moisture storage of the (\n)\n1\nt\n\n−\n part, the specific formula \n278 \nis given by \n279 \n1\n1\n1\n1\nt\nb\nt\nt\nA\nB\nWMM\nd (12) \n280 For the current soil moisture storage content of the (\n)\n1\nt\n\n−\n part, the specific \n275 1\nt\nt\nt\nA\nW (11) \n277 (11) For the maximum soil moisture storage of the (\n)\n1\nt\n\n−\n part, the specific formula \n278 \ni\ni\nb\n279 For the maximum soil moisture storage of the (\n)\n1\nt\n\n−\n part, the specific formula \n278 \nis given by\n279 For the maximum soil moisture storage of the (\n)\n1\nt\n\n−\n part, the specific formula \n278 \ni\ni\nb\n279 is given by \n279 1\n1\n1\n1\nt\nb\nt\nt\nA\nB\nWMM\nd (12) \n280 (12) Thus, the proportion \ntw of the current soil moisture content to the corresponding Thus, the proportion \ntw of the current soil moisture content to the corresponding \n281 Thus, the proportion \ntw of the current soil moisture content to the corresponding \n281 maximum soil moisture content is expressed by maximum soil moisture content is expressed by \n282 1\n1\n1\n1\n1\n1\n1\n1\n1\nt\nt\nt\nt\nt\nt\nt\nt\nb\nb\nt\nW\nA\nW\nw\nb\nA\nB\nWMM\nd\nWMM\nb\n (13) (13) It can be seen from Equation. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. (13) that as the rainfall continuous, the soil moisture \n284 content in the unsaturated area continues to increase and the non-runoff area continues \n285 \nto decrease. With the gradual increase of soil moisture content wt, (1-\nt ) approaches 0 \n286 \nd\nd\n1\nh\nh b\ni\nh\nh f ll\n287 content in the unsaturated area continues to increase and the non-runoff area continues \n285 to decrease. With the gradual increase of soil moisture content wt, (1-\nt ) approaches 0 \n286 and wt tends to 1 when the basin reaches the full storage. 287 Combining Equations. (9) and (13), and considering the impact of both rainfall \n288 \nintensity and time-varying soil moisture content on the watershed velocity, the velocity \n289 \nequation is assumed to be \n290 2\n1\n5\n2\n2\ns\ns\nt\nc\nI\nV\nk S\nw\nI\n\n\n=\n\n\n\n\n\n\n\n (14) \n291 2\n1\n5\n2\n2\ns\ns\nt\nc\nI\nV\nk S\nw\nI\n\n\n=\n\n\n\n\n\n\n\n (14) \n291 2\n1\n5\n2\n2\ns\ns\nt\nc\nI\nV\nk S\nw\nI\n\n\n=\n\n\n\n\n\n\n\n (14) \n291 (14) Similar to the studies on dynamic upstream contributions by Bhattacharya et al. 292 15 \n \n(2012), Bunster et al. (2019), a power law can be used to improve the applicability of \n293 15 \n(2012), Bunster et al. (2019), a power law can be used to improve the applicability of \n293 15 2\n1\n5\n2\n2\ns\ns\nt\nc\nI\nV\nk S\nw\nI\n\n\n\n=\n\n\n\n\n\n\n\n (15) \n295 (15) where  is an exponent smaller than unity, which needs to be determined by trial and \n296 \nerror method. Hence, the fraction of the current soil moisture content \ntw that \n297 \ncontributes to the flow velocity decreases as \ntw increases. 298 where  is an exponent smaller than unity, which needs to be determined by trial and \n296 \nerror method. Hence, the fraction of the current soil moisture content \ntw that \n297 \ncontributes to the flow velocity decreases as \ntw increases. (c) Objective function of the Nash-Sutcliffe efficiency: \n316 (\n)\n(\n)\n2\n2\n,\n,\n,\n1\n1\n1\n/\nn\nn\nobs i\nsim i\nobs i\nobs\ni\ni\nNSE\nQ\nQ\nQ\nQ\n=\n=\n\n\n\n\n= −\n−\n−\n\n\n\n\n\n\n\n\n\n\n\n (18) \n317 (\n)\n(\n)\n2\n2\n,\n,\n,\n1\n1\n1\n/\nn\nn\nobs i\nsim i\nobs i\nobs\ni\ni\nNSE\nQ\nQ\nQ\nQ\n=\n=\n\n\n\n\n= −\n−\n−\n\n\n\n\n\n\n\n\n\n\n\n (18) \n317 (18) 3\n1\nObj\nNSE\n= −\n (19) \n318 3\n1\nObj\nNSE\n= −\n (19) \n318 (19) (d) The optimized objective function: \n319 (d) The optimized objective function: \n319 (d) The optimized objective function: \n319 1\n2\n3\nmin(\n)\nObj\naObj\nbObj\ncObj\n=\n+\n+\n (20) \n320 1\n2\n3\nmin(\n)\nObj\naObj\nbObj\ncObj\n=\n+\n+\n (20) \n320 (20) where \n,\nobs i\nQ\n is the value of actual flood flow; \n,\nsim i\nQ\n is the value of predicted flood \n321 where \n,\nobs i\nQ\n is the value of actual flood flow; \n,\nsim i\nQ\n is the value of predicted flood \n321 \nflow; \n'\n,\nobs i\nQ\n is the value of actual flood peak; \n'\n,\nsim i\nQ\n is the value of predicted flood \n322 \npeak; \n,\nobs i\nT\n is the time of actual flood peak; \n,,\nsim i\nT\n is the time of predicted flood peak; \n323 \nobs\nQ\n is the average of actual flood flow; N is the number of the flood; a, b and c are \n324 \nconstants. 325 where \n,\nobs i\nQ\n is the value of actual flood flow; \n,\nsim i\nQ\n is the value of predicted flood \n321 \nflow; \n'\n,\nobs i\nQ\n is the value of actual flood peak; \n'\n,\nsim i\nQ\n is the value of predicted flood \n322 \npeak; \n,\nobs i\nT\n is the time of actual flood peak; \n,,\nsim i\nT\n is the time of predicted flood peak; \n323 \nobs\nQ\n is the average of actual flood flow; N is the number of the flood; a, b and c are \n324 \nconstants. 325 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 298 Therefore, the proposed method considering both the rainfall intensity and soil \n299 \nmoisture content was proposed, in which soil moisture content is regarded as an \n300 \nimportant factor affecting the TDUH. When the soil moisture content of the whole basin \n301 \nreaches the saturation, \n2\ns\nV is equal to \n1\ns\nV . 302 Therefore, the proposed method considering both the rainfall intensity and soil \n299 \nmoisture content was proposed, in which soil moisture content is regarded as an \n300 \nimportant factor affecting the TDUH. When the soil moisture content of the whole basin \n301 \nreaches the saturation, \n2\ns\nV is equal to \n1\ns\nV . 302 2.3 Model calibration \n303 \nThe SCE-UA (Shuffled Complex Evolution Algorithm) method, developed by the \n304 \nUniversity of Arizona in1992 (Duan et al., 1992), is suitable for the nonlinear, high \n305 \ndimension optimization problems. The method has been widely used for the calibration \n306 \nof hydrological model (Vrugt et al., 2006; Beskow et al., 2011; Zhou et al., 2018). 307 \nHence, the SCE-UA method was used to optimize the parameters of XAJ model in this \n308 \nstudy. The relative flood peak error, relative peak time error, and Nash-Sutcliffe \n309 \nefficiency of floods were chosen as the criteria, the specific functions of which are given \n310 \nas follows. 311 \n(a) Objective function of the flood peak: \n312 (a) Objective function of the flood peak: \n312 16 16 '\n'\n,\n,\n1\n'\n1\n,\n1\nN\nobs i\nsim i\ni\nobs i\nQ\nQ\nObj\nN\nQ\n=\n\n\n−\n=\n\n\n\n\n\n\n\n (16) \n13 (16) (b) Objective function of the peak time error: \n314 (b) Objective function of the peak time error: \n314 (b) Objective function of the peak time error: \n14 (\n)\n2\n,\n,,\n,\n1\n1\n/\nn\nn\nobs i\nsim i\nobs i\ni\ni\nObj\nT\nT\nT\n=\n=\n\n\n=\n−\n\n\n\n\n\n\n (17) \n315 (\n)\n2\n,\n,,\n,\n1\n1\n/\nn\nn\nobs i\nsim i\nobs i\ni\ni\nObj\nT\nT\nT\n=\n=\n\n\n=\n−\n\n\n\n\n\n\n (17) \n315 (17) (c) Objective function of the Nash-Sutcliffe efficiency: \n316 3 Study area and data \n326 The Qin River basin was selected as a case study. This river is the tributary of the \n327 \nMei jiang River, which originates from Guangdong Province, China. The Qin River is \n328 \n91 km long with a basin area of 1578 km2. The mean slope of the basin is 1.1‰. There \n329 \nare 21 meteorological stations and 1 flow station (Jianshan station) in this area. The \n330 \nlocation and stations of the Qin River Basin are shown in Figure 4. 331 17 18 \n \nAccording to the DEM data of the Qin River Basin, the whole basin can be divided \n332 \ninto 9 sub-watersheds based on the natural water system, namely watershed 1-9 from \n333 \nupstream to downstream as shown in Figure 5. The details of each sub-watershed are \n334 \ngiven in Table 1. 335 \nThe rainfall and evaporation data from meteorological stations was collected \n336 \nwith the length from the years 2013 to 2018. The simultaneous hourly runoff data for \n337 \nthe Jianshan station was collected as well. The soil moisture content before the floods \n338 \nwas calculated based on the daily recession coefficient of water storage in the basin. 339 \n4. Results and discussions \n340 \n4.1 Calibration of parameters \n341 \n4.1.1 Parameters Calibration of the runoff generation using the XAJ Model \n342 \nThe accuracy of runoff generation calculation is of great importance in the rainfall- \n343 \nrunoff forecasts. The higher the accuracy of the runoff calculation is, the smaller the \n344 \nimpact on the error of the routing calculation is. Because the Qin River Basin is in the \n345 \nhumid area of southern China, the saturation-excess method with three-source runoff \n346 \nseparation of the XAJ model was adopted to calculate the excess rainfall in this study. 347 \nDozens of floods were selected to calibrate the parameters of the XAJ model by the \n348 \nshuffled complex evolution algorithm method. In addition, to make the simulation \n349 \nresults of the XAJ model more accurate, the unit hydrograph was used for flood routing, \n350 \nwhich was derived by historical rainfall runoff process. The time interval is 1 hour. The \n351 332 4. Results and discussions \n340 18 \nThe accuracy of runoff generation calculation is of great importance in the rainfall- \n343 \nrunoff forecasts. The higher the accuracy of the runoff calculation is, the smaller the \n344 \nimpact on the error of the routing calculation is. Because the Qin River Basin is in the \n345 \nhumid area of southern China, the saturation-excess method with three-source runoff \n346 \nseparation of the XAJ model was adopted to calculate the excess rainfall in this study. 347 \nDozens of floods were selected to calibrate the parameters of the XAJ model by the \n348 \nshuffled complex evolution algorithm method. In addition, to make the simulation \n349 \nresults of the XAJ model more accurate, the unit hydrograph was used for flood routing, \n350 \nwhich was derived by historical rainfall runoff process. The time interval is 1 hour. The \n351 18 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 19 \nflood peak, flood volume, and the occurrence time of flood peak are three main basic \n352 \nelements for describing the flood events, and Equation (20) was used as the objective \n353 \nfunction. The average Nash-Sutcliffe efficiency, relative flood peak error, and peak \n354 \noccurrence time error obtained in the calibration period of the XAJ model are 0.92, \n355 \n26.1%, and 1.5 hours respectively, indicating a good performance of the XAJ model. 356 \nThe detailed information of the calibrated parameters of the XAJ model is shown in \n357 \nTable 2. 358 \n4.1.2 Parameters determination of the proposed flood routing method \n359 \nAs mentioned in Section 2.2, the core of the DUH is the calculation of grid flow \n360 \nvelocity. As shown in Equation (15), the parameters that need to be calibrated are K, S, \n361 \nIc and , in which Ic can be determined according to the hourly mean rainfall intensity \n362 \nand flood forecast accuracy of the target basin. For the Qin River Basin, the Ic is set to \n363 \n20 mm/h, because the mean rainfall intensity of multiple floods is about 20mm/h. 364 \nAdditionally, parameter  reflects the influence of soil moisture content in \n365 \nunsaturated regions on flow velocity. The smaller of parameter  is, the smaller the \n366 \ninfluence of soil moisture content has on the flow velocity. 4. Results and discussions \n340 When the value of  is \n367 \nequal to 1, the flow velocity of grid cell is proportional to the soil moisture content \n368 \nfactor wt. According to the previous research on the flow velocity, the effect of upstream \n369 \ncontributions on the flow velocity is adjusted by a coefficient, which is set to 0.5. 370 \nInspired by the research, the parameter  of soil moisture content is assumed to be 0.5 \n371 \nto reflect the influence of soil moisture content on flow velocity in this study \n372 flood peak, flood volume, and the occurrence time of flood peak are three main basic \n352 \nelements for describing the flood events, and Equation (20) was used as the objective \n353 \nfunction. The average Nash-Sutcliffe efficiency, relative flood peak error, and peak \n354 \noccurrence time error obtained in the calibration period of the XAJ model are 0.92, \n355 \n26.1%, and 1.5 hours respectively, indicating a good performance of the XAJ model. 356 \nThe detailed information of the calibrated parameters of the XAJ model is shown in \n357 \nTable 2. 358 4.1.2 Parameters determination of the proposed flood routing method \n359 19 \n \nAs mentioned in Section 2.2, the core of the DUH is the calculation of grid flow \n360 \nvelocity. As shown in Equation (15), the parameters that need to be calibrated are K, S, \n361 \nIc and , in which Ic can be determined according to the hourly mean rainfall intensity \n362 \nand flood forecast accuracy of the target basin. For the Qin River Basin, the Ic is set to \n363 \n20 mm/h, because the mean rainfall intensity of multiple floods is about 20mm/h. 364 \nAdditionally, parameter  reflects the influence of soil moisture content in \n365 \nunsaturated regions on flow velocity. The smaller of parameter  is, the smaller the \n366 \ninfluence of soil moisture content has on the flow velocity. When the value of  is \n367 \nequal to 1, the flow velocity of grid cell is proportional to the soil moisture content \n368 \nfactor wt. According to the previous research on the flow velocity, the effect of upstream \n369 \ncontributions on the flow velocity is adjusted by a coefficient, which is set to 0.5. 370 \nInspired by the research, the parameter  of soil moisture content is assumed to be 0.5 \n371 \nto reflect the influence of soil moisture content on flow velocity in this study \n372 https://doi.org/10.5194/hess-2021-470\nPreprint. 4. Results and discussions \n340 Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. (Bhattacharya et al., 2012; Bunster et al., 2019). In order to determine the grid cell slope \n373 \nS, the slope distribution of the study areas is obtained from the DEM data of the target \n374 \nbasin as shown in Figure 6(a). Parameter k is the velocity coefficient, which can be \n375 \ndetermined based on different underlying surface types or different flow states (Ajward \n376 \n& Muzik, 2000). Parameter k changes with different underlying surface types and the \n377 \ndetailed k values are given in Table 3. The land type of the Qin River Basin is shown in \n378 \nFigure 6(b). Then the k values of each grid cell can be determined combining Figure \n379 \n6(b) and Table 3. 380 The grid flow velocity can be calculated by Equations (1) and (9) with the above \n381 \nparameter settings. In this basis, the flow travel time can be determined by Equation \n382 \n(2). It is noteworthy that the raster size of the basin was divided by 1km×1km, and the \n383 \nrasterized flow direction of each sub-watershed is shown in Figure 6(c), where L is 1 \n384 \nwhen the rasterized flow is flowing along the edges of the grid, and L is \n2 when it is \n385 \ndiagonally. 386 20 \n \n4.2 Derivation of TDUH considering time-varying soil moisture content \n387 \nAfter determining the parameters above, the flood routing can be calculated based \n388 \non the proposed TDUH considering time-varying soil moisture content. Meanwhile, in \n389 \norder to improve the efficiency and effectiveness of the routing method, the rainfall \n390 \nintensity and soil moisture content parameters were discretized in present study (Kong \n391 \net al., 2019). Then a simplified TDUH considering time-varying soil moisture content \n392 \nand TDUH can be obtained in a certain range of rainfall intensities or soil moisture \n393 20 contents, the division ranges of which are presented in Tables 4 and 5. Furthermore, to \n394 \nevaluate the flood simulation effect of the proposed method, the traditional DUH and \n395 \nTDUH methods were used for comparisons. 396 The DUH without considering rainfall intensity and soil moisture can be obtained \n397 \nbased on Equations (1) to (4). Results of the DUH for each sub-watershed of the Qin \n398 \nRiver Basin are shown in Figures 7. 4. Results and discussions \n340 There is only one DUH for a specific sub-watershed \n399 \ndue to the simplification of the underlying surface such as slope and land covers. The \n400 \ndifferences among the DUHs are mainly reflected in the flood peaks and their \n401 \noccurrence time. It can be also seen from Figure 7 that the peaks of DUHs in Sub-\n402 \nwatersheds 4 and 6 are significantly lower than others. The reasons may be that the \n403 \nsmaller mean slop values of Sub-watersheds 4 and 6 lead to lower flow velocity, \n404 \nresulting in lower peaks of DUH. 405 Moreover, the TDUHs corresponding to different rainfall intensities of 9 sub-\n406 \nwatersheds are shown in Figure 8. It can be seen from Figure 8 that different rainfall \n407 \nintensities correspond to different TDUHs. The increased rainfall intensity leads to \n408 \nhigher peak and earlier peak occurrence time of the TDUH. This is because that larger \n409 \nrainfall intensity causes larger flow velocity according to Equation (9). In the practical \n410 \nuse of TDUH, the unit hydrographs need to be selected according to the rainfall \n411 \nintensities. 412 The TDUH of each sub-watershed can be further divided according to the soil \n413 \nmoisture content. The TDUHs considering soil moisture contents of Sub-watershed 1 \n414 21 are shown in Figure 9. Obviously, under the same rainfall intensity conditions, the soil \n415 \nmoisture content is of great importance to the shape, peak value and duration of the \n416 \nTDUH. Specifically, when the proportion of soil moisture content wt increases, the \n417 \nproposed method considering soil moisture content is accompanied with steeper rising \n418 \nlimb, higher peak and shorter duration. After the whole basin is saturated, the TDUH \n419 \nconsidering the time-varying soil moisture content is the same with the TDUH. 420 4.3 Comparisons of flood routing methods \n421 4.3 Comparisons of flood routing methods \n421 The runoff generation module of the XAJ model was used to calculate the excess \n422 \nrainfall, and the DUH, TDUH and improved TDUH considering soil moisture content \n423 \nwere employed for flood routing calculation, respectively. Dozens of floods for the Qin \n424 \nRiver Bains were applied for model validation. Simulated results of the three methods \n425 \nare shown in Table 6. Three criterions given in Equations (16), (17) and (19) were used \n426 \nfor model performance evaluation. It is demonstrated that the proposed method shows \n427 \nthe best performance. 4. Results and discussions \n340 The relative flood peak error of the proposed method ranges from \n428 \n-3.9% to 9.5%. The mean peak occurrence time error of the proposed is 1.2h, which is \n429 \nthe smallest among the three methods. The average NSE coefficients of floods for \n430 \nvalidation are above 0.8. Figure 10 shows the flood hydrographs of three routing \n431 \nmethods for part of the flood events (Event No. 20130720, 20130817, 20150709, \n432 \n20160128, 20161021 and 20180916). It generally shows the proposed method performs \n433 \nthe best among the three routing methods. 434 22 The flood events No.20161021 and 20180916 were conducted in-depth analyses \n435 \nfor the reason that the forecast results of the both floods using proposed method are not \n436 \nas good as TDUH. For the flood event No.20161021, the simulation result of the \n437 \nproposed method are basically consistent with that of the DUH method. The rainfall in \n438 \nthe previous 30 days before the flood event No.20161021 was calculated, and the result \n439 \nshows that the soil moisture content was close to saturation. As mentioned above, for \n440 \nwatershed where the soil moisture content is completely saturated, the proposed method \n441 \nperforms the same as the TDUH method. Thus, the simulation results of the proposed \n442 \nmethod and TDUH are almost consistent and better than that of the DUH method for \n443 \nthe flood No.20161021. For the flood event No.20180916, there is a lag in the peak \n444 \ntime of the proposed method, and the rainfall in the previous time of this flood is \n445 \nrelatively small. The possible reason for the inaccurate flood simulation is that the \n446 \nrunoff generation is not dominated by the saturation-excess, and it is therefore not \n447 \nappropriate to calculate runoff with the XAJ model. 448 435 23 \n \n4.4 Influence of time-varying soil moisture content on floods forecasts \n449 \nIn order to explore the mechanism of time-varying soil moisture content on the \n450 \nflood forecasts, three typical flood forecasting results of the proposed method were \n451 \nchosen for comparison. Specifically, compared with the forecasting results using \n452 \nTDUH, the result of the flood event No.20130817 using the proposed method is \n453 \nrelatively similar, the results of the flood events No.20150709 and 20160128 have a \n454 \nbetter performance, and the result of the flood event No.20180916 is poor. Their \n455 23 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 4. Results and discussions \n340 corresponding temporal evolution processes of soil moisture content in unsaturated \n456 \nregions were obtained. The box-and-whisker plots of soil moisture contents of all sub-\n457 \nwatersheds for flood events No.20130817, 20150709, 20160128 and 20180916 are \n458 \nshown in Figure 11. It can be seen from Figure 11 that the soil moisture content of each \n459 \nsub-watershed is initially low, then the soil moisture content of the sub-watershed \n460 \ngradually increases. Meanwhile, it is obviously that the wt is hard to reach the maximum. 461 \nFor all the 4 floods, only the flood event No.20130817 does the saturation of 9 sub-\n462 \nwatersheds eventually reach. The mean values of wt for the flood events No.20150709, \n463 \n20160128 and 20180916 range from 0.5 to 0.8, and the soil moisture content does not \n464 \nreach the maximum during the storm events. As shown from the observed flood in \n465 \nFigure 10, the peak discharge of the flood event No.20130817 is larger than those of \n466 \nother floods, reaching 3500 m³/s, which means that the watershed is more probably \n467 \nreach the saturation during the flood period. 468 As discussed in Section 4.3, the result of the flood event No.20130817 using the \n469 \nproposed routing method shows the same behavior as that of TDUH. This is because \n470 \nthe simulation performance of the proposed method considering time-varying soil \n471 \nmoisture content is the same as the TDUH when the soil moisture contents are closer \n472 \nto 1. Additionally, the forecasting results of the flood events No.20150709, 20160128 \n473 \nwith the proposed routing method are obviously better than those of DUH and TDUH. 474 \nThe reason can be summarized as follows. The mean values of wt range from 0.5 to 0.6 \n475 \nfor the two floods and the initially wt values are low as shown in Figure 11. Thus, the \n476 24 soil moisture content has a significant impact on the shape of hydrographs. For the flood \n477 \nevent No.20180916, the sub-watersheds do not reach a global saturation eventually, and \n478 \nthe time-varying values of wt are generally high, which leads to lower flow velocity \n479 \nthan that of the TDUH method. 4. Results and discussions \n340 The peaks occurrence time of unit hydrographs used \n480 \nfor the runoff routing calculation are general later, and therefore leading to a lag time \n481 \nbetween the maximum rainfall intensity and the peak discharge for the forecasting \n482 \nresult of the flood event No.20180916. The flood peak discharge is higher, which may \n483 \nbe due to the inaccurate calculation of excess rainfall. 484 25 \n \n4.5 Comparisons of velocity calculated by the three routing methods \n485 \nThe routing method considering both time-varying rainfall intensity and soil \n486 \nmoisture content is more accurate as discussed in Section 4.3. To explore the effect of \n487 \ntime-varying soil moisture content on flow velocity, we selected a grid cell in the Sub-\n488 \nwatershed 3, in which slope and land type parameters are constants. Then, the flow \n489 \nvelocity was calculated under different storm conditions. The storm events \n490 \nNo.20130817 and 20150709 were selected and compared, because the storm event \n491 \nNo.20130817 is with a high intensity and long duration, and the storm event No. 492 \n20150709 is with a short period of heavy rainfall. Thus, soil moisture contents during \n493 \nthe two storm events are significantly different. Figure 12 shows time-varying velocity \n494 \nvalues of a grid cell for storm events No.20130817 and 20150709. For the two storm \n495 \nevents, the mean velocity of the DUH method is the largest among the three methods, \n496 \nfollowed by the TDUH method. The velocity calculated by the proposed method \n497 25 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. considering soil moisture content is the smallest. The velocity of DUH method is a \n498 \nconstant in two storms, and that of the TDUH method varies with the changes of the \n499 \nexcess rainfall. Meanwhile, the flow velocity of the proposed method is not only \n500 \ndominated by rainfall intensity, but also related to soil water content. 501 considering soil moisture content is the smallest. The velocity of DUH method is a \n498 \nconstant in two storms, and that of the TDUH method varies with the changes of the \n499 \nexcess rainfall. Meanwhile, the flow velocity of the proposed method is not only \n500 \ndominated by rainfall intensity, but also related to soil water content. 501 considering soil moisture content is the smallest. 4. Results and discussions \n340 The proposed method \n519 \ncomprehensively considered the changes of time-varying soil moisture content and \n520 \nrainfall intensity. The response of underlying surface to the soil moisture content was \n521 \nconsidered as an important factor in this study. The Qin River Basin was selected as a \n522 \ncase study. The DUH, TDUH and proposed routing methods were used for flood \n523 \nforecasts, and the simulated results were compared and discussed. The main \n524 \nconclusions are summarized as follows. 525 \n(1) The proposed runoff routing method considering both time-varying rainfall \n526 \nintensity and soil moisture content was proposed, and the influence of the \n527 \ninhomogeneity of runoff generation on the confluence process was considered. It is \n528 \nsuggested that the soil moisture content is a significant factor affecting the accuracy of \n529 \nflood forecasts, especially in the catchment dominated by saturation-excess runoff, and \n530 \nthe flow velocity increases gradually with more surface runoff after considering the soil \n531 \nmoisture content in unsaturated regions. 532 \n(2) The time-varying characteristics of the DUH can be further considered by \n533 \nintroducing both the factors such as rainfall intensity and soil moisture content to the \n534 \nflow velocity formula, which can effectively improve the accuracy of flood forecasts. 535 \nThe simulation hydrographs and criterions of ten floods show that the accuracy of the \n536 \nproposed method is the highest, followed by the TDUH method, and then the DUH \n537 An improved distributed unit hydrographs routing method considering time-\n518 \nvarying soil moisture content was proposed for flood routing. The proposed method \n519 \ncomprehensively considered the changes of time-varying soil moisture content and \n520 \nrainfall intensity. The response of underlying surface to the soil moisture content was \n521 \nconsidered as an important factor in this study. The Qin River Basin was selected as a \n522 \ncase study. The DUH, TDUH and proposed routing methods were used for flood \n523 \nforecasts, and the simulated results were compared and discussed. The main \n524 \nconclusions are summarized as follows. 525 (1) The proposed runoff routing method considering both time-varying rainfall \n526 \nintensity and soil moisture content was proposed, and the influence of the \n527 \ninhomogeneity of runoff generation on the confluence process was considered. 4. Results and discussions \n340 The velocity of DUH method is a \n498 \nconstant in two storms, and that of the TDUH method varies with the changes of the \n499 \nexcess rainfall. Meanwhile, the flow velocity of the proposed method is not only \n500 \ndominated by rainfall intensity, but also related to soil water content. 501 For the storm event No.20130817, the initial soil moisture content is large, and it \n502 \nreaches the maximum rapidly. The flow velocity of the proposed method is slightly \n503 \nsmaller than that of TDUH method at the initial stage of storm events. When the whole \n504 \nbasin reaches saturation, the flow velocity of the two methods is equal. Therefore, the \n505 \ndifferences of hydrographs are small when using TDUH method and the proposed \n506 \nmethod for flood routing calculation, which leads to similar forecasting results. 507 For the storm event No.20130817, the initial soil moisture content is large, and it \n502 \nreaches the maximum rapidly. The flow velocity of the proposed method is slightly \n503 \nsmaller than that of TDUH method at the initial stage of storm events. When the whole \n504 \nbasin reaches saturation, the flow velocity of the two methods is equal. Therefore, the \n505 \ndifferences of hydrographs are small when using TDUH method and the proposed \n506 \nmethod for flood routing calculation, which leads to similar forecasting results. 507 For the storm event No.20150709, the initial soil moisture content is small, and \n508 \nthe entire basin cannot reach the saturation after the rainstorm. Therefore, the grid \n509 \nvelocity in the early stage of a storm is greatly affected by the soil moisture content. In \n510 \nthe later stage of the rainstorm, the wt of the watershed does not reach the maximum, \n511 \nand it is nearly close to 1. Thus, the impact of later soil moisture content on the flow \n512 \nvelocity value is small. From the analyses above, it can be concluded that the shape and \n513 \nduration of the unit hydrograph is mainly related to the soil moisture content at the \n514 \ninitial stage of a storm, and when the watershed is approximately saturated, the grid \n515 \nflow velocity is majorly dominated by the excess rainfall. 516 26 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 4. Conclusions \n517 \nAn improved distributed unit hydrographs routing method considering time-\n518 \nvarying soil moisture content was proposed for flood routing. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 28 \nmethod. 538 \n(3) The shape and duration of the improved TDUH considering soil moisture are \n539 \nmainly affected by the rainfall intensity. Meanwhile, soil moisture content at initial \n540 \nstage of a storm also plays a significant role in the characteristics of the improved \n541 \nTDUH. When the watershed is approximately saturated, the grid flow velocity is \n542 \nmajorly dominated by the excess rainfall. 543 \nData availability \n544 \nDue to the strict security requirements from the departments, some or all data, models, \n545 \nor code generated or used in the study are proprietary or confidential in nature and may \n546 \nonly be provided with restrictions (e.g. anonymized data). 547 \nAuthor contributions \n548 \nLu Chen conceived the original idea, and Bin Yi designed the methodology. Ping Jiang \n549 \ncollected the data. Bin Yi developed the code and performed the study. Bin Yi, Lu Chen, \n550 \nand Hansong Zhang contributed to the interpretation of the results. Bin Yi wrote the \n551 \npaper, and Lu Chen revised the paper. 552 \nCompeting interests \n553 \nThe authors declare that they have no conflict of interest. 554 \nAcknowledgments \n555 \nThis research has been supported by the key project of Natural Science Foundation of \n556 (3) The shape and duration of the improved TDUH considering soil moisture are \n539 \nmainly affected by the rainfall intensity. Meanwhile, soil moisture content at initial \n540 \nstage of a storm also plays a significant role in the characteristics of the improved \n541 \nTDUH. When the watershed is approximately saturated, the grid flow velocity is \n542 \nmajorly dominated by the excess rainfall. 543 Due to the strict security requirements from the departments, some or all data, models, \n545 \nor code generated or used in the study are proprietary or confidential in nature and may \n546 \nonly be provided with restrictions (e.g. anonymized data). 547 Author contributions \n548 \nLu Chen conceived the original idea, and Bin Yi designed the methodology. Ping Jiang \n549 \ncollected the data. Bin Yi developed the code and performed the study. Bin Yi, Lu Chen, \n550 \nand Hansong Zhang contributed to the interpretation of the results. Bin Yi wrote the \n551 \npaper, and Lu Chen revised the paper. 552 \nCompeting interests \n553 \nThe authors declare that they have no conflict of interest. 4. Results and discussions \n340 It is \n528 \nsuggested that the soil moisture content is a significant factor affecting the accuracy of \n529 \nflood forecasts, especially in the catchment dominated by saturation-excess runoff, and \n530 \nthe flow velocity increases gradually with more surface runoff after considering the soil \n531 \nmoisture content in unsaturated regions. 532 27 \n \n(2) The time-varying characteristics of the DUH can be further considered by \n533 \nintroducing both the factors such as rainfall intensity and soil moisture content to the \n534 \nflow velocity formula, which can effectively improve the accuracy of flood forecasts. 535 \nThe simulation hydrographs and criterions of ten floods show that the accuracy of the \n536 \nproposed method is the highest, followed by the TDUH method, and then the DUH \n537 27 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 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D.: On the relative roles of hillslope processes, \n676 \nchannel routing, and network geomorphology in the hydrologic response of \n677 \nnatural \ncatchments. Water \nResources \nResearch, \n31(12), \n678 \nhttps://doi.org/10.1029/95WR01948, 1995. 679 31 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. Rigon, R., Bancheri, M., Formetta, G. and Lavenne, A.: The geomorphological unit \n680 \nhydrograph from a historical-critical perspective[J]. Table 1. Detailed information of sub-watersheds \n719 References \n558 Earth Surface Processes & \n681 \nLandforms, 41(1):27-37, https://doi.org/10.1002/esp.3855, 2016. 682 Sherman, L. K.: Streamflow from rainfall by the unit-graph method. Engineering News \n683 \nRecord, 108:501-505, 1932. 684 Snyder, F. F.: Synthetic unit-graphs. Transactions American Geophysical Union, 19, \n685 \n447-454, https://doi.org/10.1029/TR019i001p00447, 1938. 686 Saghafian, B., Julien, P. Y.: Time to equilibrium for spatially variable watersheds. 687 \nJournal of Hydrology, 172 (1–4):231-245, https://doi.org/10.1016/0022-\n688 \n1694(95)02692-I, 1995. 689 SCS. Design of hydrograph. Washington, DC: US Department of Agriculture, Soil \n690 \nConservation Service. 2002. 691 Singh, P. K., Bhunya, P. K., Mishra, S. K. and Chaube, U. C.: An extended hybrid model \n692 \nfor synthetic unit hydrograph derivation. Journal of Hydrology, 336(3-4):347-360, \n693 \nhttps://doi.org/10.1016/j.jhydrol.2007.01.006, 2007. 694 Singh, P. K., Mishra, S. K. and Jain, M. K.: A review of the synthetic unit hydrograph: \n695 \nfrom the empirical UH to advanced geomorphological methods. International \n696 \nAssociation \nof \nScientific \nHydrology \nBulletin, \n59(2):239-261, \n697 \nhttps://doi.org/10.1080/02626667.2013.870664, 2014. 698 Sarangi, A., Madramootoo, C. A., Enright, P. and Prasher, S. O.: Evaluation of three \n699 \nunit hydrograph models to predict the surface runoff from a Canadian watershed. 700 \nWater Resources Management, 21(7):1127-1143, https://doi.org/10.1007/s11269-\n701 \n006-9072-9, 2007. 702 Singh, S. K.: Simple Parametric Instantaneous Unit Hydrograph. Journal of Irrigation \n703 \n& \nDrainage \nEngineering, \n141(5):04014066.1-04014066.10, \n704 \nhttps://doi.org/10.1061/(ASCE)IR.1943-4774.0000830, 2015. 705 Vrugt, J. A., Gupta, H. V., Dekker, S. C., Sorooshiand, S., Wagenere, T. and Boutenf, \n706 \nW.: Application of stochastic parameter optimization to the Sacramento Soil \n707 \nMoisture Accounting model. Journal of Hydrology, 325(1-4),288-307, \n708 \nhttps://doi.org/10.1016/j.jhydrol.2005.10.041, 2006. 709 Zhao, R. J., Zuang, Y., Fang, L.: The xinanjiang model. IAHS AISH Publ. 129, 351-\n710 \n356, 1980. 711 Zhao, R. J.: Xinanjiang model applied in China. J. Hydrol. 135(1-4), 371-381, \n712 \nhttps://doi.org/10.1016/0022-1694(92)90096-E, 1992. 713 Zhou, Q., Chen, L., Singh, V. P., Zhou, J. Z., Chen, X. H. and Xiong, L. H.: Rainfall-\n714 \nrunoff simulation in Karst dominated areas based on a coupled conceptual \n715 \nhydrological \nmodel. Journal \nof \nHydrology, \n573: \n524-533, \n716 \nhttps://doi.org/10.1016/j.jhydrol.2019.03.099, 2019. 717 Table 1. Detailed information of sub-watersheds \n719 Table 1. Detailed information of sub-watersheds \n719 32 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. References \n558 Sub-watersheds \nDrainage area/km2 \nNumber of grids \nAverage slope \nSub-watershed 1 \n175.64 \n176 \n13.29 \nSub-watershed 2 \n195.86 \n197 \n9.27 \nSub-watershed 3 \n154.97 \n156 \n12.50 \nSub-watershed 4 \n153.08 \n151 \n9.57 \nSub-watershed 5 \n147.79 \n147 \n12.49 \nSub-watershed 6 \n249.36 \n253 \n11.74 \nSub-watershed 7 \n213.34 \n211 \n10.56 \nSub-watershed 8 \n122.28 \n129 \n10.77 \nSub-watershed 9 \n166.51 \n161 \n9.74 \nTable 2. Calibrated parameters of the XAJ model \n720 \nParameters \nPhysical meaning \nValue Unit \nUM \nAveraged soil moisture storage capacity of the upper layer \n18.87 \nmm \nLM \nAveraged soil moisture storage capacity of the lower layer \n73.67 \nmm \nDM \nAveraged soil moisture storage capacity of the deep layer \n39.29 \nmm \nB \nExponential of distribution of tension water capacity \n0.27 \n- \nIM \nRatio of impervious to total areas in the catchment \n0.01 \n- \nK \nRatio of potential evapotranspiration to pan evaporation \n0.85 \n- \nC \nEvapotranspiration coefficient of the deeper layer \n0.12 \n- \nSM \nFree water capacity of the surface layer \n46.29 \nmm \nEX \nExponent of the free water capacity curve influencing the \ndevelopment of the saturated area \n0.50 \n- \nKI \nOutflow coefficient of free water storage to interflow \n0.41 \n- \nKG \nOutflow coefficient of free water storage to groundwater \n0.28 \n- \nCI \nRecession constant of the lower interflow storage \n0.87 \n- \nCG \nRecession constant of the ground water storage \n0.99 \n- \nCS \nRecession constant in the lag and rout method for routing through \nthe channel system within each sub-watershed \n0.46 \n- \nKE \nMuskingum time constant for each sub-reach \n23.90 \n- \nXE \nMuskingum weighting factor for each sub-reach \n0.13 \n- \nTable 3. The specific values of k for different vegetational types \n721 721 33 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 34 \nLand Type \nVegetational Form \nk (m/s) \nCrop land \nfallow \n1.37 \ncontour tillage \n1.40 \nstraight plough \n2.77 \nGrass and plow land \ntrample \n0.30 \nlush \n0.46 \nsparse \n0.64 \npasture \n0.40 \nForest \ndense \n0.21 \nsparse \n0.43 \nfull of dead leaves \n076 \nImpervious surface \n\\ \n6.22 \nTable 4. The rainfall intensity It of each period corresponds to the discrete rain intensity \n722 \nIs \n723 \nNet rainfall intensity It (mm/h) \n0 < It ≤ 15 \n15 < It ≤ 25 \n25 < It ≤ 35 \nIt >35 \nDiscrete rainfall intensity Is(mm/h) \n10 \n20 \n30 \n40 \nTable 5. References \n558 The soil moisture content wt of each period corresponds to the discrete soil \n724 \nmoisture content ws \n725 \nSoil moisture \ncontent wt \n0 < wt ≤ 0.2 \n0.2 < wt ≤ 0.4 \n0.4 < wt ≤ 0.6 \n0.6 < wt ≤ 0.8 \nwt > 0.8 \nDiscrete soil \nmoisture content \nws \n0.1 \n0.3 \n0.5 \n0.7 \n0.85 \nTable 6. The results of three criterions for all routing methods \n726 \nEvent \nnumber \nObj1 (%) / Obj2 (h) / Obj3 (-) \nDUH \nTDUH \nProposed \n20130720 \n13.3/5/0.47 \n12.5/3/0.52 \n-3.9/1/0.73 \n20130817 \n4.7/7/0.69 \n0.5/4/0.81 \n4.9/2/0.82 \n20130922 \n15.9/-3/0.57 \n-11.1/-3/0.54 \n2.4/2/0.85 \n20150709 \n27.1/-3/0.56 \n-18.8/0/0.54 \n9.5/-1/0.83 \n20160128 \n1.7/1/0.32 \n-6.6/-1/0.48 \n1.5/0/0.92 \n20160827 \n8.8/2/0.75 \n4.9/1/0.81 \n3.3/0/0.91 Land Type \nVegetational Form \nk (m/s) \nCrop land \nfallow \n1.37 \ncontour tillage \n1.40 \nstraight plough \n2.77 \nGrass and plow land \ntrample \n0.30 \nlush \n0.46 \nsparse \n0.64 \npasture \n0.40 \nForest \ndense \n0.21 \nsparse \n0.43 \nfull of dead leaves \n076 \nImpervious surface \n\\ \n6.22 \nTable 4. The rainfall intensity It of each period corresponds to the discrete rain intensity \n722 34 20161021 \n15.7/3/0.56 \n4.6/-1/0.78 \n8.8/-2/0.72 \n20180606 \n4.8/2/0.64 \n-2.4/1/0.72 \n2.6/0/0.84 \n20180830 \n4.2/-2/0.71 \n-0.3/-1/0.82 \n2.4/1/0.79 \n20180916 \n6.5/8/0.52 \n-4.8/3/0.69 \n4.4/-3/0.54 \nAverage \n|9.5|/|3.3|/0.58 \n|7.4|/|2.1|/0.67 \n|4.4|/|1.2|/0.80 \nList of Figures \n727 \n \n728 \nFigure 1. Schematic diagram of the XAJ model \n729 \nhttps://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 20161021 \n15.7/3/0.56 \n4.6/-1/0.78 \n8.8/-2/0.72 \n20180606 \n4.8/2/0.64 \n-2.4/1/0.72 \n2.6/0/0.84 \n20180830 \n4.2/-2/0.71 \n-0.3/-1/0.82 \n2.4/1/0.79 \n20180916 \n6.5/8/0.52 \n-4.8/3/0.69 \n4.4/-3/0.54 \nAverage \n|9.5|/|3.3|/0.58 \n|7.4|/|2.1|/0.67 \n|4.4|/|1.2|/0.80 \nList of Figures \n727 \n \n728 \nFigure 1. Schematic diagram of the XAJ model \n729 \n \n730 \nFigure 2. Schematic diagram of the DUH \n731 \n( ) 20161021 \n15.7/3/0.56 \n4.6/-1/0.78 \n8.8/-2/0.72 \n20180606 \n4.8/2/0.64 \n-2.4/1/0.72 \n2.6/0/0.84 \n20180830 \n4.2/-2/0.71 \n-0.3/-1/0.82 \n2.4/1/0.79 \n20180916 \n6.5/8/0.52 \n-4.8/3/0.69 \n4.4/-3/0.54 \nAverage \n|9.5|/|3.3|/0.58 \n|7.4|/|2.1|/0.67 \n|4.4|/|1.2|/0.80 \nList of Figures \n727 20161021 \n15.7/3/0.56 \n4.6/-1/0.78 \n8.8/-2/0.72 \n20180606 \n4.8/2/0.64 \n-2.4/1/0.72 \n2.6/0/0.84 \n20180830 \n4.2/-2/0.71 \n-0.3/-1/0.82 \n2.4/1/0.79 \n20180916 \n6.5/8/0.52 \n-4.8/3/0.69 \n4.4/-3/0.54 \nAverage \n|9.5|/|3.3|/0.58 \n|7.4|/|2.1|/0.67 \n|4.4|/|1.2|/0.80 \nList of Figures \n727 728 Figure 1. Schematic diagram of the XAJ model \n729 Figure 1. Schematic diagram of the XAJ model \n729 \n730 g\ng Figure 2. Schematic diagram of the DUH \n731 35 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 732 \nFigure 3. Watershed storage capacity curve \n733 \n \n734 \nFigure 4. Distribution diagram of meteorological and flow stations in Qin river basin \n735 732 \nFigure 3. Watershed storage capacity curve\n733 732 Figure 3. References \n558 Watershed storage capacity curve \n733 Figure 3. Watershed storage capacity curve \n733 734 \nFigure 4. Distribution diagram of meteorological and flow stations in Qin river basin \n735 734 \nFigure 4. Distribution diagram of meteorological and flow stations in Qin river basin \n735 Figure 4. Distribution diagram of meteorological and flow stations in Qin river basin \n735 36 \n \n \n736 736 36 36 Figure 5. The sub-watershed of the Qin River Basin. (Note. The satellite imagines for \n737 the study area are available at http://www.gscloud.cn) \n738 \n \n739 \n \n740 \nFigure 6. Slope, Land types and rasterized flow direction of the Qin River Basin. (a) \n741 the study area are available at http://www.gscloud.cn) \n738 the study area are available at http://www.gscloud.cn) \n738 739 739 Figure 6. Slope, Land types and rasterized flow direction of the Qin River Basin. (a) \n741 Slope distribution. (b) Land types. (c) Rasterized flow direction. 742 743 \nFigure 7. The DUH for the Qin River Basin \n744 Figure 7. The DUH for the Qin River Basin \n744 37 37 745 \n \n746 \n \n747 \nFigure 8. The TDUH for the Qin River Basin. (a) Sub-watershed 1. (b) Sub-watershed \n748 \n2. (c) Sub-watershed 3. (d) Sub-watershed 4. (e) Sub-watershed 5. (f) Sub-watershed 6. 749 \ntps://doi.org/10.5194/hess-2021-470\neprint. Discussion started: 29 September 2021\nAuthor(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 745 \n \n746 \n \n747 \nFigure 8. The TDUH for the Qin River Basin. (a) Sub-watershed 1. (b) Sub-watershed \n748 \n2. (c) Sub-watershed 3. (d) Sub-watershed 4. (e) Sub-watershed 5. (f) Sub-watershed 6. 749 745 6 7 Figure 8. The TDUH for the Qin River Basin. (a) Sub-watershed 1. (b) Sub-watershed \n748 Figure 8. The TDUH for the Qin River Basin. (a) Sub-watershed 1. (b) Sub-watershed \n748 \n2. (c) Sub-watershed 3. (d) Sub-watershed 4. (e) Sub-watershed 5. (f) Sub-watershed 6. 749 g\nQ\n( )\n( )\n2. (c) Sub-watershed 3. (d) Sub-watershed 4. (e) Sub-watershed 5. (f) Sub-watershed 6. 749 (g) Sub-watershed 7. (h) Sub-watershed 8. (i) Sub-watershed 9. 750 751 \n \n752 \nFigure 9. The TDUH considering soil moisture content for sub-watershed 1 of Qin \n753 \nRiver Basin. (a) \n10mm/h\nsI =\n. (b) \n20mm/h\nsI =\n. (c) \n30mm/h\nsI =\n. (d) \n40mm/h\nsI =\n. 754 Figure 9. References \n558 The TDUH considering soil moisture content for sub-watershed 1 of Qin \n753 Figure 9. The TDUH considering soil moisture content for sub-watershed 1 of Qin \n753 \nRiver Basin. (a) \n10mm/h\nsI =\n. (b) \n20mm/h\nsI =\n. (c) \n30mm/h\nsI =\n. (d) \n40mm/h\nsI =\n. 754 Figure 9. The TDUH considering soil moisture content for sub-watershed 1 of Qin \n753 \nRiver Basin. (a) \n10mm/h\nsI =\n. (b) \n20mm/h\nsI =\n. (c) \n30mm/h\nsI =\n. (d) \n40mm/h\nsI =\n. 754 River Basin. (a) \n10mm/h\nsI =\n. (b) \n20mm/h\nsI =\n. (c) \n30mm/h\nsI =\n. (d) \n40mm/h\nsI =\n. 754 38 https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 755 \n756 \n \n757 \nFigure 10. Comparisons of flood hydrograph obtained by three methods. (a) Flood \n758 \nevent No.20130720. (b) Flood event No.20130817. (c) Flood event No.20150709. (d) \n759 \nFlood event No.20160128. (e) Flood event No.20161021. (f) Flood event No.20180916. 760 5 756 756 \n757 Figure 10. Comparisons of flood hydrograph obtained by three methods. (a) Flood \n758 Figure 10. Comparisons of flood hydrograph obtained by three methods. (a) Flood \n758 \nevent No.20130720. (b) Flood event No.20130817. (c) Flood event No.20150709. (d) \n759 \nFlood event No.20160128. (e) Flood event No.20161021. (f) Flood event No.20180916. 760 Flood event No.20160128. (e) Flood event No.20161021. (f) Flood event No.20180916. 760 39 761 \n \n762 \nFigure 11. Distributions of time-varying wt at different times in each sub-watershed \n763 \n/doi.org/10.5194/hess-2021-470\nnt. Discussion started: 29 September 2021\nthor(s) 2021. CC BY 4.0 License. 761 \n \n762 \nFigure 11. Distributions of time-varying wt at different times in each sub-watershed \n763 761 \n \n762 761 Figure 11. Distributions of time-varying wt at different times in each sub-watershed \n763 40 768 \nFigure 12. Time-varying velocity values of a grid cell in different storm events. (a) \n769 \nTime-varying velocity in storm event No.20130817. (b) Time-varying velocity in storm \n770 \nevent No.20150709. The rainfall content is \ns\nc\nI\nI , and the soil moisture content is \ntw . 771 \nps://doi.org/10.5194/hess-2021-470\nprint. Discussion started: 29 September 2021\nAuthor(s) 2021. CC BY 4.0 License. https://doi.org/10.5194/hess-2021-470\nPreprint. Discussion started: 29 September 2021\nc⃝Author(s) 2021. CC BY 4.0 License. 768 \nFigure 12. Time-varying velocity values of a grid cell in different storm events. (a) \n769 \nTime-varying velocity in storm event No.20130817. References \n558 (b) Time-varying velocity in storm \n770 \nevent No.20150709. The rainfall content is \ns\nc\nI\nI , and the soil moisture content is \ntw . 771 768 Figure 12. Time-varying velocity values of a grid cell in different storm events. (a) \n769 \nTime-varying velocity in storm event No.20130817. (b) Time-varying velocity in storm \n770 \nevent No.20150709. The rainfall content is \nsI\nI , and the soil moisture content is \ntw . 771 Figure 12. Time-varying velocity values of a grid cell in different storm events. (a) \n769 \nTime-varying velocity in storm event No.20130817. (b) Time-varying velocity in storm \n770 Figure 12. Time-varying velocity values of a grid cell in different storm events. (a) \n769 event No.20150709. The rainfall content is \ns\nc\nI\nI , and the soil moisture content is \ntw . 771 41"