Kinematic Routing Model and its Parameters Definition

Overland flow routed independently for each

hillslope

(adapted from Chow et al., 1988)

HRAP Cell (~ 4 km x 4 km) Uniform, conceptual hillslopes within a modeling unit are assumed

• Drainage density illustrated is ~1.1 km/km2• Number of hillslopes depends on drainage density

Conceptual channel provides cell-

to-cell link

Overland flow routed independently for each

hillslope

(adapted from Chow et al., 1988)

HRAP Cell (~ 4 km x 4 km) Uniform, conceptual hillslopes within a modeling unit are assumed

• Drainage density illustrated is ~1.1 km/km2• Number of hillslopes depends on drainage density

Conceptual channel provides cell-

to-cell link

Real HRAP Cell

Hillslope model

Cell-to-cell channel routing

Routing Model

Fast runoff components• Surface• Direct• Impervious

Slow runoff components• Interflow• Supplemental baseflow• Primary baseflow

Hillslope routing

Channel routing

Separate Treatment of Fast and Slow Runoff

HRAP Cell

Hillslope Routing

sh Rx

qL

t

h

35

352

hqhn

SDq s

h

h

q = discharge per unit area of hillslopeh = average overland flow depthRs = fast runoff from water balanceSh = hillslope slopenh = hillslope roughnessD = drainage densityLh = hillslope length

Momentum:

Conceptual Hillslope

DLh 2

1x

Continuity:

• Kinematic Wave– Koren et al. (2004)

• Independent routing for each hillslope element

• Only routes fast runoffGrid Pixel

Channel Routing

Momentum:

cLx

Continuity:

• Kinematic Wave– Koren et al. (2004)

• Routes – fast runoff from hillslope

– Slow runoffGrid Pixel

c

cgL L

fRq

x

Q

t

Ah

mqAqQ 0

Q = channel dischargeA = channel cross-sectional areaqLh = overland flow rate at the hillslope outletRg = slow runoff component from the water balanceFc = grid cell areaLc = 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, qs– Two parameters of channel discharge-cross-section relationship,

qo and qm

• 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, Sh– Manning’s roughness coefficient, nh– Channel density as a ratio of total channel length to area, D– Pixel area, f

• HL-RDHM calculates the basic parameter qs at each grid cell during run-time from

h

hs

n

SDq

2

Channel Routing Parameters Derivation

• Two methods are available in RDHM– ‘Rating curve’ method that estimates the parameters q0 and qm

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 Sc (channel slope) and nc (channel Manning’s

roughness coefficient) should be available above outlet

mqobsoobs AqQ

obsobs HB

)1(3

2

1

c

co n

Sq 1

3/5

mq

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 = q0*Aqm

1. Generate A =a*Bb

2. Q = v*A = q0*Aqm

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 qm (rating curve method) and β (channel shape method) assumed to be constant above selected outlet

iQoioi rFFQQ ,//

),,(/, oiloiiA kkRfAAr

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

q0 qm

Extrapolate

Estimate

Rating Curve method

Channel Shape Methodo

iqiAoi F

Frqq m ,,0,0

),,,,,( ,,,, iciciQiAooi nSrrf

‘Measured’ and estimated channel bank width

-30

-20

-10

0

10

20

30

To

p w

idth

, m

0 50 100 150 200Distance, km

Estimated Bank width from c.-s.

Channel top width of the Blue riverderived from channel structure

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 differentnumber of outlets: 1,2,6 Arkansas river, USA

1

2

6