Kinematic Routing Model and its Parameters Definition

Real HRAP Cell Hillslope model Cell-to-cell channel routing Routing Model

Separate Treatment of Fast and Slow Runoff HRAP Cell

Hillslope Routing q = discharge per unit area of hillslope h = average overland flow depth R s = fast runoff from water balance S h = hillslope slope n h = hillslope roughness D = drainage density L h = hillslope length Momentum: Conceptual Hillslope x Continuity: Kinematic Wave –Koren et al. (2004) Independent routing for each hillslope element Only routes fast runoff Grid Pixel

Channel Routing Momentum: x Continuity: Kinematic Wave –Koren et al. (2004) Routes –fast runoff from hillslope –Slow runoff Grid Pixel Q = channel discharge A = channel cross-sectional area q Lh = overland flow rate at the hillslope outlet R g = slow runoff component from the water balance F c = grid cell area L c = channel length within a cell

Kinematic Wave Advantages Require few parameters Easy to generate fast implicit numerical scheme compared, e.g., to diffusive model Flexible in selection of simulation time-space increments Allows selection of larger time increments compared to other models

Kinematic Wave Disadvantages Lack of attenuation specifically for very flat basins RDHM defines a simple one-shape channel cross- section Potential effect on results comparing other models –When channel properties vary in space, attenuation may occur –Any numerical scheme introduces some attenuation. So use, e.g., diffusive model will accelerate physical attenuation by numerical –There are few criteria that allows estimation of potential errors –In headwater basins, wave form change depends mostly on lateral inflow contribution and joining channels, not attenuation –One-shape channel can affect significantly on simulation results if there is a flood plane. It might be difficult to get a reasonable peak timing for high and low floods

HL-RDHM Routing Parameters There are three basic parameters –Hillslope depth-discharge relationship parameter, q s –Two parameters of channel discharge-cross-section relationship, q o and q m Parameters have to be defined at each grid cell above selected basin These parameters are not directly measurable Combination of local basin properties (topography, soil, vegetation) and an integrated basin response at the outlet (discharge measurement information)

Hillslope Routing Parameter Derivation Four hillslope property grids have to be defined –Surface slope, S h –Manning’s roughness coefficient, n h –Channel density as a ratio of total channel length to area, D –Pixel area, f HL-RDHM calculates the basic parameter q s at each grid cell during run-time from

Channel Routing Parameters Derivation Two methods are available in RDHM –‘Rating curve’ method that estimates the parameters q 0 and q m directly using hydraulic measurements at an outlet gauging station –‘Channel shape’ method assumes a simple parabolic channel geometry and uses outlet hydraulic measurements to estimate shape parameters at outlet –then basic routing parameters at outlet –Grids of S c (channel slope) and n c (channel Manning’s roughness coefficient) should be available above outlet

R Scripts Provided to Assist with Flow Measurement Analysis Outletmeas_manual.R automatically generates several plots and computes reqressions User can specify plotting and regression weight options Directly to Q = q 0 *A qm 1.Generate A =a*B b 2.Q = v*A = q 0 *A qm

Typical Channel Shape Depending on β  = 1  < 1  > 1  = 0

Assumptions on Derivation Parametric Grids Two assumptions from channel geometry laws are adopted for interpolation outlet parameters to upstream –The ratio of channel-forming flows at different cells equals ratio of drainage areas above the cells –The ratio of channel cross-sectional areas of different cells is a known function of stream orders Also, parameters q m (rating curve method) and β (channel shape method) assumed to be constant above selected outlet

Generating Distributed Routing Parameters Information needed Parameters estimated at an outlet pixel Drainage area Connectivity Geomorphologic relationship Channel slope and roughness for the channel shape only method q0q0 qmqm Extrapolate Estimate Rating Curve method Channel Shape Method

‘Measured’ and estimated channel bank width

Distribute Parameters Upstream using Genpar Features of Genpar –Needs a base grid –Modifies the entire area upstream of an outlet –Able to handle multiple outlets Assign values to entire upstream area Overwrite values for sub-basins

Specific discharge grids generated using different number of outlets: 1,2,6 Arkansas river, USA 1 2 6