Methodology for Estimation of Maximum Probable Flood (MPF) Hydrograph in the Jadar River Basin Aleksandra Ilic1, Stevan Prohaska2, Vesna Tripkovic2 1Faculty of Civil Engineering and Architecture, Nis, Serbia 2Institute for the Development of Water Resources "Jarosalav Cerni", Belgrade, Serbia [email protected] Abstract This paper presents methodology for assessing the maximum runoff hydrograph on natural watercourses. The basis for the estimation of hydrograph is estimated maximum precipitation, as a dominant factor for the formation of high flows in natural conditions. Theoretically, maximum probable precipitation or MPP is the largest amount of rainfall for a specific duration, which is physically possible over catchment area in certain parts of the year. For determining maximum probability of rainfall, in the given case, a statistical approach developed by Hershfield (1961) was used. The approach was modified in 1965. For the assessment of maximum high flows we used deterministic “rainfall-runoff“ model, which is based on boundary intensity runoff method, which uses maximum precipitation as input data, taking into account most unfavorable combination of other critical factors that affect the river runoff. The paper will be illustrated through specific example of maximum probable hydrograph calculation in the Jadar river basin in the western part of Serbia. Keywords: maximum probable precipitation, maximum probable flood, boundary intensity runoff method Introduction Maximum probable flood (MPF) represents runoff that can be expected as a result of the most unfavorable combination of critical meteorological and hydrological conditions in the analyzed basin. The procedure for the determination of the maximum probable flood is based on previously obtained probable maximum precipitation (PMP), which can occur in critical climatic conditions. Meteorological conditions include those parameters that have a predominant role in the formation of the probable maximum precipitation over examined area in a particular period of the year. According to the definition it follows that the probable maximum flood may be determined using maximum probable precipitation as input for deterministic “precipitation-runoff” model. Considering the above, we can say that maximum probable rainfall, determined this way, has infinite return period. The subject of this paper is the review of the procedures in hydrologic practice in Serbia. Such procedures include the determination of maximum probable flood hydrograph and its main components, a procedure for determination maximum probable precipitation and a procedure used to perform transformation of the probable maximum precipitation into maximum probable runoff. The paper is illustrated by a practical example of estimation of maximum probable runoff hydrograph of the Jadar River, right tributary of the Drina River in Serbia. Input data The territory considered is Jadar river basin, the right tributary of the Drina River, which is located in the northwest part of Serbia. This catchment area is completely ungauged, as there is no systematic monitoring of water levels and flow measurements. The map of the examined part of Jadar River basin which is the main focus of this paper is given in Figure 1. BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 1 Figure 1 Map of Jadar River Basin area with meteorological stations As flood waves are consequences of rainfall it is necessary to define them as the main input into the deterministic model "precipitation-runoff". To determine the total rainfall in the basin, the latest available data on daily precipitation in Serbia for the postwar period up to year 2006 were used. The spatial distribution of the analyzed stations can be seen in Figure 1. During updating of Water Management Master Plan of the Republic of Serbia for the period 1946- 2006, statistical analyses were performed for a series of maximum daily rainfall from which the results were used for this study. Theoretical values of maximum daily rainfall for stations near the area of Jadar River are presented in Table1. Table1 Theoretical values of maximum daily precipitation P0,01% P0,1% P1% Precipitation station max max max (mm) (mm) (mm) Desić 252.9 152.7 90.5 Dvorska 125.8 107.1 86.7 Donje Crniljevo 112.1 92.3 74 Draginac 126.8 103.8 81.7 Joševa 255.4 172.5 113.6 Kozjak 143.9 118.6 93.9 Krupanj 206.1 152.3 108.3 Loznica 198.7 148.1 106.2 Majinović 113.7 99.6 83.5 Osečina 135.8 112.3 88.7 Pecka 168.1 136.5 104.8 BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 2 P0,01% P0,1% P1% Precipitation station max max max (mm) (mm) (mm) Planina 213.8 169.4 128.7 Stave 340.4 205.2 121.5 Tekeriš 204.1 151.3 107.7 Zajača 222.6 163 114.6 Zavlaka 160.6 123.9 92.2 Valjevska Kamenica 137.7 116.7 94.3 For defining short duration rainfall, high intensity rainfall reduction curves for pluviograph stations Valljevo and Loznica were used. The considered period was 1953-2008 (figures 2 and 3). 1 10 100 1000 10000 10 1 ψ(τ) ) τ ( ' 0.1 ψ ), ψαϖ(τ) τ " !) ( av( av ψ ), τ ( ψ 0.01 %%%%%" '(!) 0.001 0.0001 τ (min) Figure 2. High intensity rainfall reduction curves for P. S. Loznica 1 10 100 1000 10000 10 1 ψ(τ) 0.1 ) τ ( ' ψ ), τ ( av "ψαϖ!)(τ) av( ψ 0.01 ), τ ( ψ 0.001 "%%%%% '(!) 0.0001 0.00001 τ (min) Figure 3. High intensity rainfall reduction curves for P. S. Valjevo BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 3 Methodology for Maximum Probable Flood Hydrograph determination The determination procedure for the probable maximum flood hydrograph is based on the boundary intensity runoff method, which can be applied to the similar hydrologic basins. The essence of this method is in the practical use of the genetic formula of runoff which takes into account surface runoff genesis in a watershed. Actually, genetic runoff formula gives, more or less, details of the basic principles for maximum runoff formation: • Inflow to the catchment surface • Loss of water through infiltration and determination of the direct runoff • Runoff on the slopes • Transformation of flow hydrograph from slopes into the runoff hydrograph as a result of the water transformation through the drainage network. Inflow to the catchment surface To describe the principles of forming the catchment runoff, the reduction curves of heavy rains are most frequently used. As it is already known, they represent the dependence of the maximum mean rainfall intensity as a function of time averaging interval τ. They are formed on the basis of the recorded data on pluviograph stations. P ψ(τ)P i ( ) τ max,day ( )P (1) max τ = = = ψ τ max,day τ τ where: imax (τ) – maximum average rainfall intensity for duration τ; P ψ(τ) = τ – reduction curve of the maximum rainfall intensity for the duration of rain τ; P max,day ψ (τ) ψ(τ) = – reduction curve for maximum mean rainfall for the duration τ; τ Pτ – precipitation depth for duration τ; Pmax,day – depth of maximum daily precipitation sum. Studies have shown that these curves, whose ordinates are relative to the daily rainfall, are very stable in space. Also to a less degree, they depend on the length and quality of the sample. Finally, the transition from relative to absolute coordinates is easier because the network of meteorological stations for daily precipitation measure has far more density than the pluviograph station network. Effective rainfall determination The determination of effective rain can be done in two ways: 1. As the difference between total rainfall and the size of infiltration or 2. As product of the total rain in the catchment area and runoff coefficient α. The coefficient of runoff depends on soil types, characteristics and state of vegetation and its determination is based on the empirical values or the use of observations on analogue catchments. If it is assumed that during the occurrence of heavy rainfall evaporation is negligible, then the total effective precipitation can be obtained as the difference between total precipitation P (total rain fall in the basin) and the sum of infiltration G, i.e.: BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 4 t t P P G idt fdt (2) ef = − = ∫ − ∫ 0 0 where: i – Intensity of rainfall; f – Intensity of infiltration. The ratio of effective and total rainfall, so called runoff coefficient α i.e.: P α = ef (3) P In this paper in order to study the infiltration losses during rainfall the phi - index method is used, which essentially represents the average intensity of infiltration during the storm, provided that the other losses are negligible (Figure 4). Phi- index method assumes that the losses are constant for the duration of the rain. Figure 4. Schematic review of phi-index determination τk (i − φ)Δt = P (4) ∑ τ ef τ=0 where: – rainfall duration; τk Δt – discretization period. If: (i − φ) ≤ 0 (5) τ then the difference equals zero, so the equation becomes: (i − φ)Δt = 0 (6) τ i.e. total amount of rainfall during the Δt period is "spent" on infiltration. Value of phi- index depends on the structure of soil, rainfall intensity and duration, as well as soil moisture. Estimation of inflow time and maximum flow module from slopes The existing formulas for estimation inflow time on the slopes, , and the module of maximum flow τslope from the slopes (q = 16.67a ) were obtained with the following assumptions: τslope. BALWOIS 2012 - Ohrid, Republic of Macedonia - 28 May, 2 June 2012 • The water flow over the slopes is considered in the form of water depth, equally distributed over the surface of slope, with constant roughness • A depth of effective rainfall is considered only as a function of time.