Download - M Bittelli Water Balance
Water balance at the field and watershed scale.
Marco Bittelli
Department of Agro-Environmental Science and Technology, University of Bologna, Italy
Water Balance
Water Balance: computed processes
3D Richards’ equation
3D Darcy’s law
2D St. Venant and
Manning equations
Penman Monteith equation
Soil Evaporation and Plant Transpiration
Computation of the water balance
∆S= P+I-ETP-D-R
where:
∆S= Change in soil water storage1. P= Precipitation and I=Irrigation2. ETP= Evapotranspiration3. DP= Drainage4. R= Runoff
1.Precipitation
Measurement (tipping bucket)
Weather Station
Tipping bucketExample of daily rainfall, max and min temperature,(Bologna, 2005)
2. Evapo-Transpiration
Continuum Continuum SoilSoil--PlantPlant--AtmosphereAtmosphere
Ψa = atmosphere (-150,000 J/kg)
Ψl = leaf (-2000 J/kg)
Ψx = xilem (-800 J/kg)
Ψr = roots (-700 /kg)
Ψs = soil (-300 /kg)
The driving forceis the water
potential gradient
RHMRT
w
ln=ψ
ψ = Water Potential [J kg-1]R = Gas constant, 8.31 [J mole-1 K-1]T = Temperature [K]Mw = Molecular weight of water, 0.018 [kg mole-1]RH = relative humidity [-]
2.Computation of Evapo-transpirationET0 = Priestley-Taylor equation
Penman-Monteith equation
Kc = Crop coefficient (varies with croptype and cultivar)
Ksx Kc = Crop coefficient (varies with croptype and cultivar) and correctedKs for environmental stress
2.Estimating ET0
Penman-Monteith equation1. most advancedand reliable model2. physically based3. radiation, turbulence, stomatal and aerodynamic resistance, vapour
pressure deficit
Priestley Taylor equation1. reliable model2. physically based3. radiation, vapour pressure deficit.
Comparison between Priestley-Taylor and Penman Monteith
ET0
0
50
100
150
200
250
1 2 3 4 5 6 7 8 9 10 11 12
Month
ET0
(mm
Priestley-Taylor
Penman Monteith
( )
⎟⎟⎠
⎞⎜⎜⎝
⎛++∆
−+−∆
=
a
s
a
aspan
rr
reecGR
ET1
)(
γ
ρλ
( )γ
αλ +∆
∆−=
GRET n
Rn = Net RadiationG = Soil heat flux(es-ea) = vapor pressure deficitρα= air densitycp= specific heat of air∆= slope of the saturation vapor pressure/temperature curveγ = psychrometric constantra= aerodynamic resistancers= surface resistanceα= factor which account for the resistance term
Infiltration = movement of water from soilsurface into soil
Water input production = rainfall + snowmelt + irrigationPonding and overland flow (runoff) occurs when water input production > infiltration capacityInfiltration capacity depends on: surface roughness (retention) – ground vegetation, surface organic layer, by-pass pathwaysSurface soil water content (saturation,depth of water table)Permeability (hydraulic conductivity) of soil (rate at which water moves through soil)Slope
3. Drainage
Matrix flowRoot, burowing animals,insects and worms, cracks, wetting/drying (clay),freeze/thaw cracks,stoneTextural preferential flowpaths. Result in rapid flow of infiltrating water that is preferential and bypasses the soil matrixImportant during storm flow.
3.Quantification of drainage
Water Potential-hydraulic conductivity: modelsbased on Darcy’s Law for flow through homogeneous porous media, physically, process based models
Soil Water Capacity (“bucket” or “cascade”) models based on field capacity and wilting point: simple, empirical models, but reflect hydraulic processes.
3.Richards equation
Fluxin
Fluxout
• Continuity equation applied to soil water flow• Applicable for continuos systems•Water flow is based on Darcy’s law
dθ/dt⎟⎠⎞
⎜⎝⎛ −= Kg
zK
ztw δδψψ
δδ
δδθρ )(
θ= volumetric soil water content (m3 m-3)ψ = soil water potential (J kg-1)z= vertical dimension (m)K(ψ)= Hydraulic conductivity ()g= gravitational constant ()
3. Example of 1D flow model
Saturated Water Content(groundwater)
Plant transpiration and soil evaporation
Percolation
Percolation
4.Runoff
Experimental systems
Derivation from soil balanceequation
4. Runoff experimental systems
Department of Agro-Environmental Science and Technology, University of Bologna, Italy
Department of Biological and AgriculturalEngineering, Texas A&M, USA
4. Runoff models
∆S (Change in Soil Water Content)
Total Soil water storage= amount of water stored in layer of soil= water held between field capacity (θfc) and
the permanent wilting point (θpwp)= θ · thickness
where θ is the volumetric soil water content
Approaches to solve the water balance equation
Direct Direct experimentalexperimental measurementmeasurement of the of the differentdifferent water water balancebalance termsterms
ModelingModeling ((withwith variousvarious levelslevels of of experimentalexperimentalinput data)input data)
CombinedCombined useuse of of experimentalexperimental data and data and modelingmodeling
Example of water balance forcorn
Example of Water balance (mm)
for corn plots in the Emilia Romagna region
22100
919270.202
Runoff
778901994519
1048540643800
Prec+Irr
1999200020012002200320042005Mean
Year
1318836740515115262400399127152413934561681115435533413213215368392153101143273691451011333149112214216394396209
DrainageLateralFlows
SoilWater
Content
PlantTranspiration
SoilEvaporation
Computation performed with the model WEPP model(Water Erosion Prediction Project)