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![Page 1: LL-III physics-based distributed hydrologic model in Blue River Basin and Baron Fork Basin Li Lan (State Key Laboratory of Water Resources and Hydropower.](https://reader035.fdocuments.in/reader035/viewer/2022062422/56649ecb5503460f94bd94c6/html5/thumbnails/1.jpg)
LL-III physics-based distributed hydrologic model in Blue River Basin and Baron Fork Basin
Li Lan(State Key Laboratory of Water Resources
and Hydropower Engineering Science,Wuhan University, China ,430072)
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1. Model Introduction
The LL-I physics-based distributed hydrologic model was produced by Lan Li in Wuhan University in 1997 , and in 2002 the LL-II model was put forward based on LL-I when taking part in DMIP-I, then in 2004 the LL-III model was developed.
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2. structure of the model
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Slope concentration calculus
between grids
withinSub-basin
Saturated and unsaturated slope concentration calculus
Confluence calculus of underground runoff
Unsaturated Zone
concentration calculation
inflow of unit-width river network
convergence calculus of all levels of sub-basin river
network
Gradually evolving
DEM Land use Soil textrue NDVI
Slope grid calculation priority ranking
Sub-basin priority calculations ranking
Slope
GIS platform
Soil moisture Saturated Hydraulic Conducti-
-vity
Leaf area index,
Vegetation coverage
treatment of Rader-rain-
measurement or rain-interpolation
Precipitationradiation snow
Grid rainfall
Snow calculation
Hydrologic analysis
Flows, the catchment area,
sub-basin division, the extraction of
drainage networks
River grid priority calculations ranking Sub-basin priority calculations
ranking slope
Categories of Surface
Water body, high and low
plants, building on bare soil, Impermeable
area
Roughness
Runoff forecast Spring flood forecastSnowmelt forecast
Flood Forecast Daily runoff forecast Reservoir Operation
Ice forecast Water process forecast
Forecast of blue water
process
Forecast of unit
grid green water
process
Evapotranspiration calculation of high vegetation Evapotranspiration calculation of low vegetation
Evapotranspiration calculations of soil Evapotranspiration calculations of underground water
Evapotranspiration calculations of water body Evapotranspiration calculations of urban
Water resources assessment
Concentration calculation in saturated and unsaturated soil Layer 1
Concentration calculation in saturated and unsaturated soil Layer 2
…Concentration calculation in
saturated and unsaturated soil Layer n
(Calculation of regressive runoff)Mesh integrated
runoff patterns
Soil moisture calculationSoil / water temperature calculation
Categories calculating of evapotranspiration
Categories surface interception calculations
N-layer classification net rain calculating
N-layer classification infiltration calculation
Energy balance calculat-
-ion
N-layer cell net rain calculation
Distributed water use
model Irrigation water
distributed computing Factory wastewater
Distributed Computing Sewage discharge
Distributed Computing Livestock Sewage
discharge Distributed Computing
Affect of human activity
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3. Model Equations
(1)Evaporation
1 ) Evaporation capacity
The plant canopy evapotranspiration is taken Jensen and Haise formula.
)]([
)()()()()
001(1 tTL
tRC
t
LAI
tLAItVCFKtET T
)]([
)()()](1[)(
022 tTL
tRC
ttVCFKtET T
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Where is the plant canopy evapotranspiration( mms-1 ) , is evaporation of soil, VCF(t) is vegetation cover rate, LAI(t)/LAI0 is relative leaf area index , is available ratio of soil moisture,
is soil moisture, is soil porosity, K1 is evapotranspiration coeffition of plant canopy, K2 is evaporation coefficient of soil, is the water vapor density ( kg·m-3 ) , L is latent heat of water evaporation(kj·kg-1), is net surface solar radiation, T is temperature (℃) , CT is correction factor of the impact that temperature makes on evaporation.
)(1 tET
)(2 tET
0/)( t
)(t 0
R
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2 ) The actual soil evaporation rates
The equation of actual soil evaporation rates is as follows:
And the max evaporation capacity:
)()( Kdz
dDEs
21
2
max 4 HaEs
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Where is diffusivity, is the porosity, is hydraulic conductivity, is a coefficient,
is coefficient of recharge by rainfall penetration, is rainfall penetration, is rainfall volume.
)(D )(K
sE
a 1
P
Pf
fP P
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( 2 ) Interception
Valley interception and effective rainfall is related to vegetation cover and the depth of water accumulation of the basin. Use the following nonlinear formula:
)(])1([ 211 Eivegveg
dt
dP
t
PP rrtrt
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Where is retention coefficient of bare soil
is retention coefficient of vegetation
88.01 )](2.0[61.2 Eia
045.1]2.0)[(21.02 Eivega
2a
1a
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( 3 ) Infiltration
Where is diffusivity, is the porosity, is hydraulic conductivity.
)()( Kdz
dDf
)(D )(K
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(4) Net rainfall
Where is precipitation, is evaporation,
is infiltration, is interception.
rPfEiR
i E
f rP
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(5)Calculation of overland runoff The calculation of overland runoff is based
on the convection-diffusion equation derived from shallow water dynamic wave equation and continuous equation, the following forms:
Where r stands for precipitation
rcc 11 x
q
t
q
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(6) Subsurface flow
Where : is storativity of aquifer, is unit discharge of subsurface runoff, is actual infiltration rate ( ),
is wave velocity of subsurface flow, is outflow coefficient of subsurface flow, is evaporation of soil layer i, is the depth of soil layer i, is infiltration rate of soil layer i, is water death of subsurface soil layer.
)],,(),,(),,([][t
q2212111
w tzxEtzxftzxfx
qqk iii
ww
),,(),,(),,( 22121 tzxEtzxftzxfx
q
t
hs iii
ww
1s wq
2f hmm /
1 1k2E
iz ),,(2 tzxf i
wh
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(7) Underground runoff The path of underground runoff is parallel
with the overland flow. Underground runoff equation is obtained through continuous equation and the equation of motion:
)],(),,([ 312 txEtzxfqkx
q
t
qmgg
gg
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Where is unit discharge of underground runoff, is wave velocity of underground runoff, is outflow coefficient of undergrou--nd runoff, is the actual infiltration rate when , is evaporation of underground runoff.
gq
gk
2f2f
zi lz 3E
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(8) Confluence of sub-basin Reflect the inter-basin links through the
boundary conditions
Where is wave velocity, D is Diffusivity, q is unit-width inflow of this sub-basin.
cqx
QD
x
DD
x
Dtxc
t
Q
2
2
),(
),( txc
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(9) Flow calculation
The convergence model uses hydrodynamic equations, continuous equations and momentum equations to calculate the runoff to the space grid nodes of each layer, and uses numerical differential format and numerical analysis to establish relationship of adjacent grid between time and space.
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Includes slope convergence and river network convergence.
Slope convergence includes processes of overland flow, subsurface flow, underground runoff etc.
The total of overland flow, subsurface flow, underground runoff is called unit-width inflow. And river network convergence is the convergence process of the unit-width inflow which runs into the river.
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4. Parameters calibration
The parameters that need to be determined can be related with the topography parameters, such as DEM, Land cover, NDVI, Soil texture, etc. Only overland flow wave velocity and river wave velocity need to be calibrated by measured data.
The overland flow wave velocity, is the function of Roughness, gradient and strength of net rain.
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River confluence is the function of Roughness, hydraulic gradient and unit-width flow.
Establish the empirical formulas of interception coefficient and evaporation coefficient according to each month of year 2000 respectively.
And the interception coefficient and is related with effective rainfall (i-E), evaporation coefficient
and is related with rainfall strength by calibrated parameters of 2000 year,.
1a 2a
1kX2kX
Parameters calibration
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5. Simulation results
1. Comparison of calculated discharge among the three gauges of Blue River with calibration. See figure 5-1 and figure 5-2.
2. Comparison of calculated discharge among the three gauges of Baron Fork with calibration. See figure 5-3 and figure 5-4.
3. Comparison of calculated discharge and observed flow of Blue River. See figure 5-5 and figure 5-6.
4. Comparison of calculated discharge and observed flow of Baron Fork. See figure 5-7 and figure 5-8.
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Figure 5.1
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Figure 5-2
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Figure 5-3
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Figure 5-4
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Figure 5-5
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Figure 5-6
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Figure 5-7
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Figure 5-8
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