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)

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.

2. structure of the model

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

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

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

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

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

（ 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

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

（ 3 ） Infiltration

Where is diffusivity, is the porosity, is hydraulic conductivity.

)()( Kdz

dDf

)(D )(K

(4) Net rainfall

Where is precipitation, is evaporation,

is infiltration, is interception.

rPfEiR

i E

f rP

(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

(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

(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

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

(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

(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.

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.

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.

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

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.

Figure 5.1

Figure 5-2

Figure 5-3

Figure 5-4

Figure 5-5

Figure 5-6

Figure 5-7

Figure 5-8