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 Penman Monteith equation Soil Evaporation and Plant Transpiration 2D St. Venant and Manning equations 3D Richards equation 3D Darcy s law
Computation of the water balance S= P+I-ETP-D-R where: S= Change in soil water storage 1. P= Precipitation and I=Irrigation 2. ETP= Evapotranspiration 3. DP= Drainage 4. R= Runoff
1.Precipitation Measurement (tipping bucket) Weather Station Example of daily rainfall, max and min temperature, (Bologna, 2005) Tipping bucket
2. Evapo-Transpiration Continuum Soil-Plant Plant-Atmosphere Ψ a = atmosphere (-150,000 J/kg) Ψ l = leaf (-2000 J/kg) Ψ x = xilem (-800 J/kg) Ψ r = roots (-700 /kg) Ψ s = soil (-300 /kg) The driving force is the water potential gradient ψ = RT M w ln RH ψ = Water Potential [J kg -1 ] R = Gas constant, 8.31 [J mole -1 K -1 ] T = Temperature [K] M w = Molecular weight of water, 0.018 [kg mole -1 ] RH = relative humidity [-]
2.Computation of Evapo-transpiration ET 0 = Priestley-Taylor equation Penman-Monteith equation K c = Crop coefficient (varies with crop type and cultivar) K s x Kc = Crop coefficient (varies with crop type and cultivar) and corrected K s for environmental stress
2.Estimating ET 0 Penman-Monteith equation 1. most advancedand reliable model 2. physically based 3. radiation, turbulence, stomatal and aerodynamic resistance, vapour pressure deficit Priestley Taylor equation 1. reliable model 2. physically based 3. radiation, vapour pressure deficit.
Comparison between Priestley-Taylor and Penman Monteith 250 200 ET0 ET = ( R G) n α λ + γ ET0 (mm 150 100 Priestley-Taylor Penman Monteith 50 0 1 2 3 4 5 6 7 8 9 10 11 12 Month R n = Net Radiation G = Soil heat flux (e s -e a ) = vapor pressure deficit ρ α = air density c p = specific heat of air = slope of the saturation vapor pressure/temperature curve γ = psychrometric constant r a = aerodynamic resistance r s = surface resistance α= factor which account for the resistance term λet = ( R G) n + ρ c a + γ 1 + p r r s a ( e s e r a a )
Infiltration = movement of water from soil surface into soil Water input production = rainfall + snowmelt + irrigation Ponding and overland flow (runoff) occurs when water input production > infiltration capacity Infiltration capacity depends on: surface roughness (retention) ground vegetation, surface organic layer, by-pass pathways Surface soil water content (saturation,depth of water table) Permeability (hydraulic conductivity) of soil (rate at which water moves through soil) Slope
3. Drainage Matrix flow Root, burowing animals,insects and worms, cracks, wetting/drying (clay),freeze/thaw cracks,stone Textural preferential flowpaths. Result in rapid flow of infiltrating water that is preferential and bypasses the soil matrix Important during storm flow.
3.Quantification of drainage Water Potential-hydraulic conductivity: models based 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 Continuity equation applied to soil water flow Applicable for continuos systems Water flow is based on Darcy s law δθ δ δψ ρ w = K( ψ ) Kg δt δz δz Flux in dθ/dt θ= volumetric soil water content (m 3 m -3 ) ψ = soil water potential (J kg -1 ) z= vertical dimension (m) K(ψ)= Hydraulic conductivity () g= gravitational constant () Flux out
3. Example of 1D flow model Percolation Plant transpiration and soil evaporation Percolation Saturated Water Content (groundwater)
4.Runoff Experimental systems Derivation from soil balance equation
4. Runoff experimental systems Department of Agro-Environmental Science and Technology, University of Bologna, Italy Department of Biological and Agricultural Engineering, 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 (θ fc ) and the permanent wilting point (θ pwp ) = θ thickness where θ is the volumetric soil water content
Approaches to solve the water balance equation Direct experimental measurement of the different water balance terms Modeling (with various levels of experimental input data) Combined use of experimental data and modeling
Example of water balance for corn
Example of Water balance (mm) for corn plots in the Emilia Romagna region Year Prec + Irr Runoff Soil Evaporation Plant Transpiration Soil Water Content Lateral Flows Drainage 1999 800 2 209 396 394 216 14 2000 643 0 122 491 331 113 10 2001 540 0.2 145 369 327 114 10 2002 1048 27 153 392 368 215 13 2003 519 19 132 334 355 154 11 2004 994 9 168 456 393 241 15 2005 901 100 127 399 400 262 15 Mean 778 22 151 405 367 188 13 Computation performed with the model WEPP model (Water Erosion Prediction Project)