Soil Water Atmosphere Plant (SWAP) Model: I. INTRODUCTION AND THEORETICAL BACKGROUND

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1 Soil Water Atmosphere Plant (SWAP) Model: I. INTRODUCTION AND THEORETICAL BACKGROUND Reinder A.Feddes Jos van Dam Joop Kroes Angel Utset,

2 Main processes Rain fall / irrigation Transpiration Soil evaporation + Solute transport Crop growth Drainage/infiltration Seepage/percolation

3 SWATR and CROPR (1978) Feddes, Kowalik and Zaradny Emphasis on soil physical aspects Application to heterogeneous soil profiles New simple description of water uptake by roots Groundwater table fluctuating with time Meteorological data on daily practical basis New boundary conditions at soil surface Focus on crop dry matter yield Disadvantages of SWATR/CROPR: Treatment of unsaturated zone only Crop development prescribed in time User s unfriendly

4 SWATRE (1983) Belmans, Feddes and Wesseling Modified numerical scheme 6 different types of conditions at the bottom of this zone including flux from the saturated zone to calculate the depth of the groundwater table, or vice versa if soil system remains unsaturated: 3 different conditions SWATR SWATRE SWAP

5 SWAP philosophy Interaction between water flow, solute transport, heat flow and plant growth Processes at field scale level physical base scenario analysis soil heterogeneity Long term simulations, with multiple crops in a year Employ experience with SWATRE and its derivatives SWATR SWATRE SWAP

6 Current SWAP features Simulation period up to 70 years Three crops a year, simple and detailed crop model (WOFOST) Irrigation scheduling criteria Actual rainfall intensities are used to generate surface runoff Interaction between water flow, solute transport, heat flow and crop growth Soil heterogeneity options: scaling of soil hydraulic functions, mobile/immobile concept, swelling and shrinking of clay soils Multi-level drainage Interaction with surface water management Graphical User s Interface Documentation Structured Fortran code spread with program

7 Theory on soil-water movement: The one-dimensional soilwater flow equation or Richards equation Darcy Continuity dz q S q q H K q S z t z

8 The flow equation for the vertical soil-water movement (Richards, 1931) Darcy equation: q K ( h) Mass conservation: t q z h z S z h q = soil water flux (cm d -1 ) h = pressure head (cm) = water content (cm 3 cm -3 ) K = hydraulic conductivity (cm d -1 ) z = depth (cm) t = time (d) C = /h (cm -1 ) S = root water extraction (d -1 ) Flow equation: t C h h t K h h z z 1 S h

9 Solution soil water flow equation h K h h 1 z C h t z Field conditions require numerical solution Numerical solution needs: water retention function (h) hydraulic conductivity function K() root water extraction function S(h) initial conditions top and bottom boundary conditions S h

10 Analytical retention function (Van Genuchten, 1980) Soil water pressure head (cm) n res sat res sat res n 1 h m 1 m 1 n Water content (cm 3 cm -3 )

11 Hysteresis of retention function Soil water pressure head (cm) Main drying curve ( d, n, res, sat ) Drying scanning curve ( d, n, res, sat * ) Main wetting curve ( w, n, res, sat ) md Water content (cm 3 res act * sat sat cm -3 ) * sat sat Current status Scaling: res res act md res res

12 Analytical hydraulic conductivity function hydraulic conductivity (cm d -1 ) Increase, steeper slope K K sat 1 m 1 1 m K sat S e S e S e sat res res 2 water content (cm 3 cm -3 )

13 Process of Evapotranspiration, the SWAP top boundary condition Three basic physical requirements: a continuous supply of water; energy available to change liquid water into vapour; a vapour gradient to maintain a flux from the evaporating surface to the atmosphere. Penman (1948) was the first to introduce the combination method for water surfaces: energy balance plus heat and mass transfer

14 Energy balance of a water surface Q* = H + E + G Where: Q* = energy flux density of net incoming radiation (W m-2) E = flux density of latent heat into the air (W m-2) H = flux density of sensible heat into the air (W m-2) G = heat flux density into the water body (W m-2)

15 Transport of sensible heat The flux of sensible heat into the air: H Where: a c p T( 0) r a T( z) a = density of the air (kg m -3 ) c p = specific heat of the air at constant pressure (J kg -1 K -1 ) T(0) = temperature at the evaporating surface (K) T(z) = air temperature at a certain height z above the surface (K) r a = aerodynamic resistance for heat (s m -1 ) problem: generally the surface temperature, T(0), is unknown

16 Transport of latent heat The flux of latent heat into the air: Where: = ratio of molecular weight of water vapour to dry air ( =0.622) e s (0) = saturated vapour pressure at the evaporating surface (hpa) e(z) = prevailing vapour pressure at height z at temperature Ta (hpa) r a H a p a e s ( 0) r a e( z) = aerodynamic diffusion resistance, assumed to be the same for heat and water vapour (s m -1 )

17 Saturated water vapour pressure curve Saturated water vapour pressure es as a function of (air) temperature es (0) es ( z ) des s T (0) T ( z ) dt The slope s in figure can be determined at temperature T(z), provided that T(0)-T(z) is small

18 Water surfaces: Evaporation equation of Penman (1948) where: E 0 * es ( z) e( z) s( Q G) cp a ra ( Wm s E 0 = open water evaporation rate (kg m -2 s -1 ) s = proportionality constant de a /dt a (hpa K -1 ) Q* = net radiation flux density for open water surface (W m -2 ) G = water heat flux density (W m -2 ) = latent heat of vaporization (hpa K -1 ) = psychrometric constant (hpa K -1 ) E a = isothermal evaporation rate (kg m -2 s -1 ) radiation term: s s ( Q G) / * p a s s ra 2 aerodynamic term c e ( z ) e( z ) )

19 Evapotranspiration of dry crops with full soil cover: The Penman-Monteith-Rijtema approach We treat the dry vegetation layer simply as one big leaf

20 The Penman-Monteith equation: dry crops with full soil cover ET * es( z) e( z) s( Q G) cp a ra ( Wm r s 1 c ra 2 ) Under conditions of optimal water supply, i.e. potential evapotranspiration ET p, the canopy resistance, r c,, has a minimum value, e.g.: arable crops r c = 30 s m -1,grass r c = 70 s m -1, forest r c =150 s m -1. Under conditions of water stress, r c, increases rapidly, and actual evapotranspiration could be calculated. This option however is not used in SWAP, because r c is not known!!!!!

21 ET p of Dry Crops with full soil cover: Monthly average lysimeter data for 11 locations

22 Different ETp cases ETp of Wet Crops with full soil cover Canopy resistance r c = 0 Albedo of a wet crop surface r (say 0.23) Roughness of a crop surface (dependent on crop height and wind speed), resulting in an aerodynamic resistance, r a ETp of Bare soils Canopy resistance r c = 0 Albedo of a bare soil r (say 0.15) Roughness of a bare soil (dependent on surface structure and wind speed), resulting in an aerodynamic resistance, r a

23 Evaporation of intercepted rainfall (E i =) P i where: = interception (mm) P i a ai P i = bp = a physical parameter, representing the crop-dependent saturation value (mm) LAI = leaf area index (-) b = degree of soil cover (-) P = precipitation (mm) P Von Hoyningen-Hüne (1983) and Braden (1985) measured interception for various crops. P i a LAI b P a LAI As maximum interception capacity a = 0.28 can be taken for most crops

24 T p = S C * ET p S C = fraction ground cover (-) Partitioning of ET p in potential soil evaporation E p and potential plant transpiration T p in SWAP Detailed crop growth model E p = ET p * e -*LAI = extinction coefficient (-) LAI = leaf area index (m 2 m -2 ) T p = ET p - E p Simple crop growth model Same approach as above, or: E p = (1 - S C ) * ET p

25 Potential root water extraction Root length density l root (cm cm -3 ) Potential root water extraction S p (d -1 ) z (cm) z (cm) 0 S D root z p T p Potential transpiration In case of uniform root distribution: S p T D p root

26 Actual water uptake by roots T act D root T act S d 0 z D root s s s s s

27 Actual root water extraction 1.0 rs T low T high h 4 h 3l h 3h h 2 h 1 Soil water pressure head EC slop e 1.0 rw EC max Soil water electrical conductivity Actual root water S z ) extraction: ( S ( z a rw rs p )

28 Simulation of flow and transport in cracked clay soils Empirical models can be calibrated for specific conditions, but can not be used for predictive purposes Detailed physical simulation of flow and transport processes requires too much input data SWAP aims to simulate the field average flow and transport processes with a limited number of physically based parameters

29 Shrinkage characteristic V pore / V solid = void ratio e Shrinkage stages: 1 Structural 2 Normal 3 Residual 4 Zero e sh e e sh sh V water / V solid = moisture ratio

30 Crack geometry Geometry factor describes shrinkage direction: V 1 1 V z z r s r s = 1: only subsidence 1 < r s < 3: subsidence dominates cracking r s = 3: isotropic shrinkage r s > 3: cracking dominates subsidence Crack wall area with respect to surface area: zi A 4 Polygon diameter d pol wall, rel Perimeter 23 d d pol pol Surface area ½3 d 2 pol

31 Water flow simulation in cracked clay Precipitation P Runoff P - I max Infiltration I max Crack inflow I c Clay matrix Darcy flux q Infilt. q c,m Crack water level GW c Crack water storage W c Bypass flow q c,d Crack depth Z c Groundwater table Drainage flux q drain

32 Water repellency Hydrofiel Hydrofoob

33 SWAP also simulates solute movement through the soil profile Diffusion in liquid phase tortuosity factor: 7/3 / ( POR ) 2 soil column

34 As well as soil heat flow

35 SWAP can be used in a GIS environment

36 SWAP and AGRIDEMA Could we use SWAP to provide irrigation recommendations under global change and variable-climate conditions 1 ECiw = 3 ds/m relative transpiration depth of applied irrigation water (cm) LS SL SiCL SiL

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