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)