Soil – Water – Atmosphere – Plant (SWAP) Model:
I. INTRODUCTION AND THEORETICAL BACKGROUND
Reinder A.Feddes
Jos van Dam
Joop Kroes
Angel Utset
AGRIDEMA COURSE,
Vienna, November 2005
Main processes
Rain fall / irrigation
Transpiration
+ Solute transport
Drainage/infiltration
Soil evaporation
Crop growth
Seepage/percolation
AGRIDEMA COURSE
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SWATR and CROPR (1978)
Feddes, Kowalik and Zaradny
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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
AGRIDEMA COURSE
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SWATRE (1983)
Belmans, Feddes and Wesseling
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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
1978
SWATR
1983
SWATRE
1998
SWAP
AGRIDEMA COURSE
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SWAP philosophy
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Interaction between water flow,
solute transport, heat flow and
plant growth
Processes at field scale level
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physical base
scenario analysis
soil heterogeneity
Long term simulations, with
multiple crops in a year
Employ experience with
SWATRE and its derivatives
1978
SWATR
1983
SWATRE
1998
SWAP
AGRIDEMA COURSE
Vienna, November 2005
Current SWAP features
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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
AGRIDEMA COURSE
Vienna, November 2005
Theory on soil-water movement: The one-dimensional soilwater flow equation or Richards equation
Darcy
dz
q
Continuity
?
q
?H
q ? ?K
?z
??
?q
? ?
?S
?t
?z
AGRIDEMA COURSE
Vienna, November 2005
S
The flow equation for the vertical soil-water movement
(Richards, 1931)
Darcy equation:
? ?h ? z ?
q ? ? K ( h)
?z
Mass conservation:
??
?q
? ?
? S ?h ?
?t
?z
q = soil water flux (cm d-1)
h = pressure head (cm)
? = water content (cm3 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:
?
? ?h
??
? ?K ?h ??
? 1 ??
??
?h
? ?z
??
?
? C ?h ? ?
? S ?h ?
?t
?t
?z
AGRIDEMA COURSE
Vienna, November 2005
Solution soil water flow equation
?
? ? h ??
? ?K ?h?? ? 1??
?h
? ?z ??
?
C ?h? ?
? S ?h?
?t
?z
?
?
Field conditions require numerical solution
Numerical solution needs:
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–
–
–
–
water retention function ?(h)
hydraulic conductivity function K(?)
root water extraction function S(h)
initial conditions
top and bottom boundary conditions
AGRIDEMA COURSE
Vienna, November 2005
Soil water pressure head (cm)
Analytical retention function (Van Genuchten, 1980)
? ? ? res ?
? sat ? ? res
?1 ? ? h ?
n m
1
m ? 1?
n
n
?
? res
? sat
Water content (cm3 cm-3)
AGRIDEMA COURSE
Vienna, November 2005
Soil water pressure head (cm)
Hysteresis of retention function
Main drying curve (? d , n, ? res, ? sat)
Drying scanning curve (? d, n, ? res, ? sat*)
Main wetting curve (? w, n, ? res, ? sat)
? md
Current status
Scaling:
*
? sat
? ? res
? ? ? res
? act
? sat ? ? res
? md ? ? res
? res
? act
? sat*
? sat
Water content (cm3
cm-3)
AGRIDEMA COURSE
Vienna, November 2005
hydraulic conductivity (cm d-1)
Analytical hydraulic conductivity function
Ksat
K ? K sat S e
Increase ? ,
steeper slope
?
?
?1 ?
??
1
?
?1 ? S em
?
?
?
?
?
?
? ? ? res
Se ?
? sat ? ? res
water content (cm3 cm-3)
AGRIDEMA COURSE
Vienna, November 2005
m
?
?
??
2
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
AGRIDEMA COURSE
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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)
AGRIDEMA COURSE
Vienna, November 2005
Transport of sensible heat
The flux of sensible heat into the air:
T (0) ? T ( z)
H ? ? acp
ra
Where:
?a
cp
T(0)
T(z)
ra
= density of the air (kg m-3)
= specific heat of the air at constant pressure (J kg-1 K-1)
= temperature at the evaporating surface (K)
= air temperature at a certain height z above the surface (K)
= aerodynamic resistance for heat (s m-1)
problem: generally the surface temperature, T(0), is unknown
AGRIDEMA COURSE
Vienna, November 2005
Transport of latent heat
The flux of latent heat into the air:
?? a? es (0) ? e( z)
?H ?
pa
ra
Where:
?
= ratio of molecular weight of water vapour to dry air (? =0.622)
es(0) = saturated vapour pressure at the evaporating surface (hPa)
e(z) = prevailing vapour pressure at height z at temperature Ta (hPa)
ra
= aerodynamic diffusion resistance, assumed to be the same for
heat and water vapour (s m-1)
AGRIDEMA COURSE
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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
AGRIDEMA COURSE
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Water surfaces:
Evaporation equation of Penman (1948)
es ( z) ? e( z )
s(Q ? G) ? c p ? a
ra
? E0 ?
(Wm? 2 )
s??
*
where:
E0 = open water evaporation rate (kg m-2 s-1)
s = proportionality constant dea/dTa (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)
Ea = isothermal evaporation rate (kg m-2 s-1)
radiation term:
s
(Q * ? G ) / ?
s??
aerodynamic term
c p ? a es ( z) ? e( z)
s??
ra
AGRIDEMA COURSE
Vienna, November 2005
Evapotranspiration of
dry crops with full soil cover:
The Penman-Monteith-Rijtema approach
We treat the dry
vegetation layer
simply as one big leaf
AGRIDEMA COURSE
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The Penman-Monteith equation:
dry crops with full soil cover
es ( z) ? e( z)
s(Q ? G) ? cp ? a
ra
? ET ?
(Wm? 2 )
? rc ?
s ? ? ??1 ? ??
? ra ?
*
Under conditions of optimal water supply, i.e. potential
evapotranspiration ETp, the canopy resistance, rc,, has a
minimum value, e.g.:
–
arable crops rc = 30 s m-1,grass rc = 70 s m-1, forest rc =150 s m-1.
Under conditions of water stress, rc, increases rapidly, and actual
evapotranspiration could be calculated. This option however is
not used in SWAP, because rc is not known!!!!!
AGRIDEMA COURSE
Vienna, November 2005
ETp of Dry Crops with full soil cover:
Monthly average
lysimeter data for
11 locations
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Different ETp cases
ETp of Wet Crops with full soil cover
?
?
?
Canopy resistance rc = 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, ra
ETp of Bare soils
?
?
?
Canopy resistance rc = 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, ra
AGRIDEMA COURSE
Vienna, November 2005
Evaporation of intercepted rainfall
Von Hoyningen-Hüne (1983) and
Braden (1985) measured
interception for various crops.
(Ei=) P i
aI
Pi = bP
P
?
?
?
?
1
?
Pi ? a LAI?1?
bP ?
?
? 1? a LAI ?
?
?
where:
Pi = interception (mm)
a = a physical parameter, representing the crop-dependent saturation
value (mm)
LAI = leaf area index (-)
b = degree of soil cover (-)
P = precipitation (mm)
As maximum interception capacity a = 0.28 can be taken for most crops
AGRIDEMA COURSE
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Partitioning of ETp in potential soil evaporation
Ep and potential plant transpiration Tp in SWAP
?
Detailed crop growth model
–
Ep = ETp * e-?*LAI
? = extinction coefficient (-)
LAI = leaf area index (m2 m-2)
–
?
Tp = ETp - Ep
Simple crop growth model
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Same approach as above, or:
–
Ep = (1 - SC) * ETp
Tp = SC * ETp
SC = fraction ground cover (-)
–
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Potential root water extraction
z (cm)
z (cm)
Root length density lroot (cm cm-3)
Potential root water extraction Sp (d -1)
0
?S
p
?z ? Tp
? D root
Potential transpiration
In case of uniform root distribution:
Sp ?
Tp
D root
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Actual water uptake by roots
Tact
T act ?
D root
? S ?d z
0
s
s
Droot
s
s
s
AGRIDEMA COURSE
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Actual root water extraction
1.0
Tlow
? rw
Thigh
h4
1.0
? rs
h3l
h2 h1
h3h
Soil water pressure head
0.0
ECslop
e
ECmax
Soil water electrical conductivity
Actual root water
Sa (z) ? ?
extraction:
0.0
rw
?
rs
S p (z)
AGRIDEMA COURSE
Vienna, November 2005
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
AGRIDEMA COURSE
Vienna, November 2005
Shrinkage characteristic
Vpore / Vsolid = void ratio e
2
4
3
1
Shrinkage stages:
1 Structural
2 Normal
3 Residual
4 Zero
e??
e ? ? sh e
? ? sh?
? ? sh?
Vwater / Vsolid = moisture ratio ?
AGRIDEMA COURSE
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Crack geometry
• Geometry factor describes shrinkage direction:
1?
•
?V ?
? z?
? ?1 ?
?
V
z ?
?
rs
rs = 1: only subsidence
1 < rs < 3:
subsidence dominates cracking
rs = 3: isotropic shrinkage
rs > 3: cracking dominates subsidence
Crack wall area with respect to surface area:
Polygon diameter dpol
4? z
Awall, rel ?
i
d pol
Perimeter 2? 3 dpol
Surface
area
½? 3 dpol2
AGRIDEMA COURSE
Vienna, November 2005
Water flow simulation in cracked clay
Precipitation P
Runoff P - Imax
Crack inflow Ic
Infiltration Imax
Crack water level GWc
Clay matrix
Infilt. qc,m
Darcy flux q
Groundwater table
Crack water storage Wc
Bypass flow qc,d
Crack depth Zc
Drainage flux qdrain
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Water repellency
Hydrofiel
Hydrofoob
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SWAP also simulates solute
movement through the soil profile
Diffusion in liquid phase
tortuosity factor: ? 7/3 / (? POR ) 2
soil column
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As well as soil heat flow
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SWAP can be used in a GIS environment
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SWAP and AGRIDEMA
Could we use SWAP to provide irrigation recommendations
under global change and variable-climate conditions?
ECiw = 3 dS/m
relative transpiration
1
0.9
0.8
0.7
LS
SL
SiCL
SiL
0.6
0.5
70
80
90
100
110
120
130
140
depth of applied irrigation water (cm)
AGRIDEMA COURSE
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