kinematic routing model and its parameters definition
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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