## Preliminary Results of Hydrologic Reconstruction of the May 2014 Kolubara River Flood - page 03

 Effective Rainfall Modelling The SCS (now NRCS) method of estimating direct runoff from heavy rainfall was the method of choice for rainfall-runoff calculations in this paper. This method was developed by the Soil Conservation Service (now National Resources Conservation Service) as a procedure for estimating runoff in small, ungauged agricultural watersheds (SCS 1985), and has since become one of the most popular methods for computing surface runoff for a given rainfall event in small to medium sized watersheds (Mishra and Singh 1999). A very brief overview of the method is presented in the next few paragraphs. For a more complete description of the method, the reader is referred to the NRCS National Engineering Handbook (2002), which is available online. The basis of the method is the runoff equation:                            (Eq. 1) where Q = depth of direct runoff, P = depth of total rainfall, Ia = initial abstraction, and S = potential maximum retention or infiltration. The initial abstraction, defined as the rainfall that occurs before runoff begins, is assumed to be a function of the maximum potential retention S, estimated with the following empirical relationship:                             (Eq. 2) The rainfall-runoff equation obtained by substituting Eq. 2 for abstraction into Eq. 1 is:                            (Eq. 3) Maximum potential retention S is estimated using the runoff curve number CN value:                        (Eq. 4) for obtaining S in millimeters. In this study, the CN for each catchment was calibrated to agree with observed hydrographs at downstream profiles, whilst also bearing in mind the hydrologic soil group, land use, treatment and hydrological condition of each catchment.   Direct Runoff Modelling To simulate the process of direct runoff of excess precipitation in the catchment, or the transformation of precipitation excess into point runoff, the Clark unit hydrograph model (Clark, 1945) was used. Clark's model derives a watershed unit hydrograph by explicitly representing two critical processes in the transformation of excess precipitation to runoff: translation of excess precipitation from its origin throughout drainage to the watershed outlet, and attenuation of the magnitude of the discharge as the excess is stored throughout the watershed. The Clark unit hydrograph is represented with two parameters: time of concentration Tc and the watershed storage coefficient R. In the Clark unit-hydrograph method, TC is the time from the end of effective precipitation to the inflection point of the recession limb of the runoff hydrograph. The inflection point on the runoff hydrograph corresponds to the time when overland flow to the channel network ceases and beyond that time the measured runoff results from drainage of channel storage. Attenuation of flow can be represented with a simple, linear reservoir for which storage is related to outflow as                            (Eq. 5) where S is the watershed storage, R is the watershed-storage coefficient, and O is the outflow from the watershed. The parameters of the Clark unit hydrograph were calibrated to observed hydrographs at control profiles. Initial values for Time of concentration were estimated using the digital terrain model to obtain the longest flow path and slope for the modified Kirpich formula (Kirpich, 1940) proposed by Zelenhasic (1970). Initial values for the storage coefficient R were estimated as a linear relation to Tc, as proposed by Russel et al. (1979). Channel Flow Modelling The Muskingum-Cunge model was used for modelling flood wave propagation. The model is based upon solution of the continuity equation                          (Eq. 6) and the diffusion form of the momentum equation                          (Eq. 7) using a linear approximation that yields the convective diffusion equation               (Eq. 8) where c = wave celerity, and μ = hydraulic diffusivity (Miller and Cunge, 1975). As both c and μ change over time, they are recomputed at each time and distance step, Δt and Δx, using the algorithm proposed by Ponce (1986). The Muskingum-Cunge model included in HEC-HMS was used, where (for each river reach) the principal dimensions of the section were specified, along with channel roughness, energy slope, and length. The length was estimated using the flow network derived from the digital terrain model, channel roughness was estimated based on a field survey and aerial photographs, and the energy slope was estimated as the channel slope, also derived from the digital terrain model.   Temporal and Spatial Interpolation of Daily Rainfall Data Into Hourly Data During the May 2014 Kolubara flood, hourly precipitation data in the basin were available only at the main meteorological station Valjevo and on two automatic gauges Majinovići and Štavica. Тhis was not sufficient to properly represent the spatial and temporal distribution of hourly rainfall in the entire basin; therefore, a method of spatial and temporal interpolation was applied that uses all available data from rain gauges in the basin with daily data, as well as hourly rainfall data both within the basin and nearby (from Loznica, Sremska Mitrovica, Belgrade, Smederevska Palanka, Kragujevac, and Požega). The Thiessen polygon method was used for spatial interpolation.   Results and Discussion The results of hydrologic modelling are shown visually as hydrographs, both observed (official data from RHMSS) and computed results. The results are shown for three control profiles at hydrologic stations on the Kolubara River: Valjevo, Slovac and Beli Brod, as well as on the output profile, the hydrologic station Draževac. Significant differences can be seen between the computed and observed hydrographs, which are mainly due to the following: The observed hydrographs show discharges measured by the hydrologic gauging stations. However, on almost all locations of gauging stations, the river overflowed into the floodplain and completely bypassed the gauges, or in some cases the embankments were breached upstream and significant amounts of water flowed outside of the regulated river profile. At all of these river gauging stations, the water level either reached or completely flooded the limnigraphs, in some places completely destroying the equipment (e.g. Valjevo and Belo Polje). On many locations, after the flood peak had passed, i.e. the falling limb of the hydrograph was reconstructed based on additional measurements. In some cases, significant river bed erosion during the flood event considerably altered the stage-discharge relationship in the vicinity of the gauging station. In such circumstances, it is evident that during the May 2014 flood, the total discharge of the Kolubara River was much higher than measured by the RHMSS hydrologic stations. Figure 3 shows the computed and observed hydrographs of the Kolubara River at the hydrologic station Valjevo. The rising limbs of the hydrographs show agreement, as well as the peak discharge and total volume, while the falling limbs show some difference. This is due to upstream overflows and flooding previously noted.

Figure 3: Computed and observed hydrograph for the hydrologic station Valjevo (Kolubara River).

The computed and observed hydrographs of the Kolubara River at the hydrologic station Slovac are shown in Figure 4. The rising limbs of the hydrographs show agreement, as was the case with Valjevo. The peak of the computed hydrograph seems to be "missing" the volume that uncontrollably flowed in the floodplain around the gauging station.

Figure 4: Computed and observed hydrograph for the hydrologic station Slovac.