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  • 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 Darcys law

    2D St. Ve

    nant an

    d

    Manning

    equatio

    ns

    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

    a = atmosphere (-150,000 J/kg)

    l = leaf (-2000 J/kg)

    x = xilem (-800 J/kg)

    r = roots (-700 /kg)

    s = soil (-300 /kg)

    The driving forceis the water

    potential gradient

    RHMRT

    w

    ln=

    = 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

    )(

    ( )

    +

    =

    GRET n

    Rn = Net RadiationG = Soil heat flux(es-ea) = vapor pressure deficit= air densitycp= specific heat of air= slope of the saturation vapor pressure/temperature curve = psychrometric constantra= aerodynamic resistancers= surface resistance= 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 Darcys 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 systemsWater flow is based on Darcys law

    d/dt

    = Kg

    zK

    ztw

    )(

    = volumetric soil water content (m3 m-3) = soil water potential (J kg-1)z= vertical dimension (m)K()= 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 (fc) and

    the permanent wilting point (pwp)= thickness

    where 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)