CHAPTER 3 HYDROLOGICAL MODELING 3.1 Introduction 3.2
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The Study on Flood and Debris Flow Supporting Report I (Master Plan) Paper IV in the Caspian Coastal Area Meteo-Hydrology focusing on the Flood-hit Region in Golestan Province CHAPTER 3 HYDROLOGICAL MODELING 3.1 Introduction An integrated and distributed MIKE SHE hydrological model is used to evaluate rainfall-runoff process in the Madarsoo River basin. The model is able to analyze impacts of watershed management practices, land use, soil types, topographic features, flow regulation structures, etc. over the basin on river flows. For this, MIKE SHE model was coupled with MIKE 11 river modeling system to simulate flows in the river system. Inflows and hydrodynamic processes in rivers are taken into consideration for model development. The model computes river flows taking account of overland flow, interflow and base-flow. An integrated and distributed hydrological model MIKE SHE was set up for the Madarsoo River basin for the following reasons: (1) To generate probable or design discharges precisely in the river system to assist on flood control master plan development, (2) To analyze the impacts of watershed management practices and biological measures of flood mitigation by quantifying river flows under these circumstances, and (3) To analyze the impact of incorporation of flood regulation structures like dam in the river system to reduce peak flows. 3.2 MIKE SHE MIKE SHE is an integrated hydrological model because all components of hydrological cycle (precipitation, evapotranspiration, surface flow, infiltration, groundwater flow, etc.) are incorporated into the model. Similarly, and it is also a distributed model because the model can handle spatial and temporal distributions of parameters. Therefore, MIKE SHE is an integrated and physically based distributed model. It consists of a number of components called modules, where each module represents a particular flow process. The modules of MIKE SHE used in this study are: overland flow, river flow, unsaturated-zone flow, saturated-zone flow, and evapotranspiration modules. As mentioned above, MIKE SHE evaluates the rainfall-runoff process in the basin in a fully distributed and integrated manner, and generates river flows considering overland flow, interflow and base-flow (Figure 3.1). Overland Flow It occurs when rainfall intensity exceeds infiltration rate of soils, which causes water stagnation on surface. The ponded water starts flow overland routed down gradient to river system. The overland flow is estimated in MIKE SHE by diffusive wave approximation of Saint Venant equations. Let horizontal plane coordinates are (x,y), ground surface level be z(x,y), flow depth be h(x,y), flow velocities in the x- and y-directions be u(x,y) and v(x,y), respectively, and q(x,y) be the net input to overland flow (net rainfall less infiltration). Then the conservation of mass gives: ∂h ∂(uh) ∂(vh) + + = q (1) ∂t ∂x ∂y JICA CTI Engineering International Co., Ltd. IV - 39 Supporting Report I (Master Plan) Paper IV The Study on Flood and Debris Flow Meteo-Hydrology in the Caspian Coastal Area focusing on the Flood-hit Region in Golestan Province Figure 3.1 Conceptual MIKE SHE Model The momentum equations are: ∂h u ∂u 1 ∂u qu S = S − − − − (2) fx ox ∂x g ∂x g ∂t gh ∂h v ∂v 1 ∂v qv S = S − − − − (3) fy oy ∂x g ∂y g ∂t gh where, Sfx and Sfy are the friction slopes in x- and y-directions, respectively. So is the surface slope. The dynamic solution of the two-dimensional St. Venant equations is numerically challenging. Therefore, it is common to reduce the complexity of the problem by dropping the last three terms of the momentum equations. Thereby, ignoring momentum loss is ignored due to local and convective acceleration and lateral inflows perpendicular to the flow direction. This is known as the diffusive wave approximation, which is implemented in MIKE SHE. Hence, a Strickler/Manning-type law for each friction slope is used with Strickler coefficients Kx and Ky in x- and y-directions. u 2 S fx = 2 4 / 3 (4) K x h v 2 S fy = 2 4 / 3 (5) K y h IV - 40 CTI Engineering International Co., Ltd. JICA The Study on Flood and Debris Flow Supporting Report I (Master Plan) Paper IV in the Caspian Coastal Area Meteo-Hydrology focusing on the Flood-hit Region in Golestan Province The governing equations (Eqs. 1, 2 & 3) are solved with initial and boundary conditions to get a fully dynamic description of shallow two-dimensional overland flow. For initially dry land surface, initial conditions are: h(x,y,0) = 0; u(x,y,0) = 0; and v(x,y,0) = 0; and boundary conditions applied on watershed boundary are: u = 0 and v = 0. River Flow To enable estimation of total river flow from overland flow, inter flow and groundwater flow, it is necessary to use the river model together with the hydrological model in a fully coupled mode. This is done through an explicit coupling between the MIKE SHE and MIKE 11 models where the two models run simultaneously and exchanges information in each time step. This coupling estimates one-dimensional river flows and water levels using fully dynamic Saint Venant equation. The conservation of mass can be expressed as: ∂A ∂Q + = q (6) ∂t ∂x The momentum equation is: ∂Q ∂(Q 2 / A) ∂h + + gA( + S ) = 0 (7) ∂t ∂x dx f where, Q is discharge, A is cross-section area of flow, h is water surface elevation, q is lateral inflow, g is acceleration due to gravity, t is time elapsed, x is longitudinal distance and Sf is friction slope. The friction slope Sf can be expressed in the following form using Manning’s equation. n 2 | Q | Q S = (8) f A2 R 4 / 3 The governing equations (Eqs. 6 & 7) are solved with initial and boundary conditions to estimate one-dimensional river flows and water levels in the river system. Unsaturated-Zone Flow The unsaturated flow is considered to occur in vertical direction in soil profile. The driving force for transport of water in the unsaturated zone is the gradient of the hydraulic head (h), which includes a gravitational component (z) and pressure component (ψ). h = z +ψ (9) The volumetric flux in soil profile is estimated by Darcy’s equation. ∂h q = −K(θ ) (10) ∂z where q is water flux, h is hydraulic head, K(Ө) is unsaturated hydraulic conductivity. Assuming that the soil matrix is incompressible and the soil water has a constant density, the continuity equation is considered as written below. ∂θ ∂q = − − S(z) (11) ∂t ∂z JICA CTI Engineering International Co., Ltd. IV - 41 Supporting Report I (Master Plan) Paper IV The Study on Flood and Debris Flow Meteo-Hydrology in the Caspian Coastal Area focusing on the Flood-hit Region in Golestan Province where Ө is volumetric water content and S is root extraction sink term. Saturated-Zone Flow The governing three-dimensional saturated flow equation in saturated porous media is considered as presented below. ∂ ⎛ ∂h ⎞ ∂ ⎛ ∂h ⎞ ∂ ⎛ ∂h ⎞ ∂h ⎜ K x ⎟ + ⎜ K y ⎟ + ⎜ K z ⎟ − Q = S (12) ∂x ⎝ ∂x ⎠ ∂y ⎝ ∂y ⎠ ∂z ⎝ ∂z ⎠ ∂t where, Kx, Ky, and Kz are hydraulic conductivities on x, y and z directions, Q is source or sink term, h is hydraulic head and S is specific storage coefficient. Evapotranspiration Evapotranspiration is one of the main components in the water balance, and it often contributes to water loss in a considerable amount of the total rainfall. The evapotranspiration is estimated based on empirically derived by Kristensen and Jensen’s equation (1975). However, in this study already computed monthly reference evapotranspiration rate is input in the model to calculate actual crop evapotranspiration based on soil moisture content, root distribution and leaf area index. 3.3 Model Application The developed MIKE SHE hydrological model is used in design flow estimation in the Madarsoo River to assist on the flood control master plan development. 3.3.1 Study Area Study area is the Madarsoo River basin of which drainage area is about 2,300 km2. The Madarsoo River originates from the north side on the Alborz Mountains and runs from the east to the west through northern part of the country, and merge with the Gorgan River that finally empties into the Caspian Sea. The length of the Madarsoo River is about 142 km. The mean annual rainfall in the middle part of basin (at Tangrah) is 695 mm, but the upper part of the river basin has quite lower rainfall. The elevation of the basin ranges from 79 m to 2,474 m from the mean sea level (MSL). 3.3.2 Data Requirements Primary data requirements of the model are basin boundary map, topographic map and rainfall data. As mentioned earlier, various modules are used to develop MIKE SHE hydrological model so that data requirements of one module differs from other. Basically data requirements of used modules are presented in Table 3.1. IV - 42 CTI Engineering International Co., Ltd. JICA The Study on Flood and Debris Flow Supporting Report I (Master Plan) Paper IV in the Caspian Coastal Area Meteo-Hydrology focusing on the Flood-hit Region in Golestan Province Table 3.1 Data Requirements for the Model Module Data Requirements Overland Flow Manning's roughness coefficient, Detention storage, Initial water depth, Rainfall, DEM, Land use River Flow River network data, River cross-sectional data Unsaturated Zone Flow Soil map, Soil physical properties like: Hydraulic conductivities, Water contents at saturation, Field capacity and wilting points Saturated Zone Flow Storage coefficient, Specific yields, Hydraulic conductivities Evapotranspiration Evaporation, Crop coefficients, Leaf area index (LAI), Rooting depth (RD) Topographic Data The topographic map of the study area is produced in a 30 m x 30 m grid resolution.