Toward a More Comprehensive and
Mechanistic Approach to Simulation
of Interacting Plant and Soil
Processes
Dennis Timlin1, David Fleisher1, Soo-Hyung
Kim2, V.R. Reddy1
1USDA-ARS Crop Systems and Global Change
Laboratory2University of Washington
How can Soil Physics Contribute to Crop
Modelling?
You also need to know about Biology and
how the components interact
Cloud cover
Rain
Transpiration
Evaporation
Gravity flow
Initiation,
Expansion,
Abscission of
Shoot organs
Capillary flow
Root distribution
Root growth and death
uptake Water
and
Minerals
N2O2
Organicmater
NH4
NO3
Photoperiod
Light interception
PhotosynthesisRespiration
Heat balanceat soil surface
Carbon partitioning
Soil heat flux
Nodule growthand death
Nitrogen fixation
CO2
Overview
Research Approach
Quantification of temperature effects
Coupled gas exchange models for photosynthesis and energy
balance
Water stress effects on plants
Some examples
MODELING STARTS WITH DATA AND
QUANTIFIABLE RELATIONSHIPS
Data Are First Obtained from Controlled
Experiments in Growth Chambers
Characteristics of Sunlit Controlled
Environment Chambers
Use natural sunlight and
soil volume (larger units)
Control and monitor aerial
and soil environments
Monitor whole canopy gas
exchange (Pg, Respiration,
Transpiration)
Measure gas leakage rates
with a N2O system to
maintain accuracy
Sunlit; controls air T, CO2, RH,
fertigation; measures CER, ET,
canopy T, soil water content, root
growth
A: Clear plexiglas cuvette (2.2
*1.4*2.5 m)
B: One cubic meter soil bin
C: Air handler
D: Soil surface
E: Doors
SPAR chamber
Field Experiments Are Also Carried Out
Collecting Potatoes for a Spatial Nitrogen
Study
Sampling is a Busy Time
TEMPERATURE RESPONSE
Temperature Response Functions
Temperature is a key environmental variable regulating growth
and development of plants
Biological organisms respond to temperature in nonlinear
fashion
Temperature responses best modeled using non-linear
temperature functions
Non-linear temperature dependence vs
thermal time (GDD)
Slopes are
not
consistent
over varying
mean
temperatures
Temperature (C)
0 10 20 30 40
Ra
te
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Topt Tceil
Rmax
Simplified beta function Beta distribution models mimic
the response well only with
biologically meaningful
parameters
Non-Linear Temperature Response
Modified beta-distribution function (Yan and Hunt, 1999)
r – leaf appearance rate, [leaves plant-1 day-1]
Rmax – maximum r, [leaves plant-1 day-1]
Tceil – ceiling temperature (r = 0), [oC]
Topt – optimal temperature (r = Rmax), [oC]
Similar Topt (≈31.4) and Tceil (≈41.0) for various growth and developmental events in maize
optceil
opt
TT
T
optoptceil
ceil
T
T
TT
TTRr
max
Temperature dependence of leaf initiation
and appearance in corn(a) Leaf initiation
Mean ambient temperature (C)
10 20 30 40
Prim
ord
ia d
-1
0.0
0.2
0.4
0.6
0.8
1.0
1.2Warrington & Kanemasu
(1983b)
Line fit using data from SPAR chambers
(b) Leaf appearance
Mean ambient temperature (C)
10 20 30 40
Leaves d
-1
0.0
0.1
0.2
0.3
0.4
0.5
0.6Tips
Ligules
Canopy or leaf
area in corn as a
function of
temperature
Data from our growth
chambers.
Ke is relative leaf
growth rate
Te determines how
fast a leaf reaches its
maximum size
Data from the literature
Shows similar
temperature
dependence
PHOTOSYNTHESIS
Response to CO2 in EPIC
CO2 (ppm)
0 200 400 600 800 1000
RU
E [(k
g h
a-1
) / (M
J m
-2)]
0
10
20
30
40
50
Rice
Corn
Photosynthesis (leaf level) in Maize as a
function of CO2 and temperature
0 500 1000 1500 2000 2500
Le
af A
net (
mo
l m
-2 s
-1)
0
10
20
30
40
50
Ambi
Elev
0 200 400 600 800 1000 1200
Le
af A
net (
mo
l m
-2 s
-1)
0
10
20
30
40
50
Ambi / 19 C
Elev / 19 C
Ambi / 35 C
Elev / 35 C
31 C
Ci (mol mol
-1)
0 200 400 600 800 1000 1200
gs (
mo
l m
-2 s
-1)
0.0
0.2
0.4
0.6
0.8
1.0
PAR (mol m-2
s-1
)
0 500 1000 1500 2000 2500
gs (
mo
l m
-2 s
-1)
0.0
0.1
0.2
0.3
0.4
0.5
31 C
A
B D
C
35 C
19 C
Large decrease in
stomatal
conductance and
thus transpiration
Small difference in
net Photosynthesis
with increasing CO2
Light limited
Carbon limited
http://supercoolandawesome.blogspot.com/2013/05/gas-exchange-in-
aquatic-and-terrestrial.html
Photosynthesis can be considered a
series of gas exchange processes.
CO2 diffuses into the leaf interior and
water vapor diffuses out.
The higher the CO2 concentration, the
less the water vapor diffusion. Stomata
do not open as widely
Diffusion
Enzymatic based reactions to take up CO2
Photosynthesis
CO2 supply (source)
Diffusion equation
Biochemical demand (sink)
Uses Michaelis-Menton kinetics
von Caemmerer (2000)
Accounts for the CO2 concentrating mechanism and related
leakage
Function of Ci, leaf temperature and PAR
The sink component
Model for leaf gas-exchange (source
component)
Transpiration and leaf temperature: Penman’s linearized
energy budget equation
Numerically solved for convergence
Calculation of Stomatal Conductance (gs) and
Transpiration (E)
a
aaLsv
P
TeTegE
)()(2
)()/(
10 l
as
s
s fPC
hAggg
hs is relative humidity, Cs is leaf surface CO2 concentration Pa is air pressure, A
is net photosynthesis, go and g1 are parameters, f(Ψ) adjusts for water stress
gv is conductance to water vapor (a function of (gs), es is vapor
pressure of the leaf surface at leaf temperature (TL), ea is vapor
pressure of the atmosphere at air temperature (Ta).
An accurate estimation of leaf
temperature is important
Challenges in modeling gas exchange
Photosynthesis, transpiration, stomatal conductance, and leaf
energy balance are closely linked to each other
These processes should be coupled to make realistic
predictions
Coupling enables estimation of unknown variables
)()/(
10 l
as
s
s fPC
hAggg
)(exp
exp1)(1
lff
ff
ls
sf
ET Demand
ET Supply
Jw = (s - l)/Rp
Rp=Rsr+Rr+Rstem
))(
(2a
aLsvpotential
P
eTegE
Energy balance equation
Rabs = L + H + E
Rabs: Absorbed radiation
L: Long-wave radiation
H: Sensible heat loss
E: Latent heat loss (evaporative cooling)
Long-wave radiation
Sensible heat
Evaporative cooling
Calculation of Leaf Temperature
*
4
*
*
aphr
aabsaL
p
D
cg
TR
sTT
v
hr
g
g
*rhhr ggg
Where Ta is air temperature, Rabs is absorbed long-wave and short-wave radiation
per surface leaf area, is leaf thermal emissivity (set to 0.97), is the Stefan-
Boltzmann constant (5.67x 10-8 Watts m-2 K-4), D is vapor pressure deficit, s is the
slope of the slope of the vapor pressure deficit-temperature curve Δ divided by
atmospheric pressure. γ is the psychrometric constant (6.66 x 10-4). Total water
vapor conductance per surface leaf area, gv, is calculated from stomatal
conductance and heat conductance at the boundary layer:
bws
bws
vgg
ggg
5.0
Note that gv requires gs and is
needed to calculate leaf
temperature. Hence iteration is
required
Temperature dependence of transpiration
at elevated CO2
Transpiration
Leaf temperature (oC)
20 25 30 35 40
E (
mm
ol m
-2 s
-1)
2
4
6
8
10
12
Ambient
Elevated
Consistent decrease in transpiration. Dependence on leaf
temperature is similar.
Maize transpiration response – CO2
Time of the Day (Central Standard Time)
0 2 4 6 8 10 12 14 16 18 20 22 24
Ca
no
py W
ate
r U
se
, g
H2O
m-2
s-1
0.0
0.1
0.2
0.3
0.4
0.5
PP
FD
, µ
mo
l m
-2 s
-1
0
500
1000
1500
2000
2500
720 µmol CO2 mol-1
360 µmol CO2 mol-1
Solar Radiation
Maize, DAE 36
Canopy Evapotranspiration (Diurnal, DAE 36)
Adapted from: Kim, S.-H., Sicher R.C., Bae H., Gitz, D.C., Baker, J.T., Timlin, D.J. and Reddy.
V.R. Canopy photosynthesis, evapotranspiration, leaf nitrogen, and transcription profiles of maize in
response to CO2 enrichment. Global Change Biol. 12:588-600. 2006.
Reduced ET rates under
elevated CO2
Daily and season WUE
higher with elevated CO2
Leaf temperature of maize at
elevated CO2
(a)
Local time
3 6 9 12 15 18 21
Ta
ir-T
lea
f (o
C)
-2.0
-1.0
0.0
1.0
2.0Ambient Ca
Elevated Ca
Increased leaf temperature
Leaf A-Ci response of corn and rice
Ci (mol mol
-1)
0 200 400 600 800 1000
A (
mol m
-2 s
-1)
0
20
40
60
80
Corn Obs from Bunce (1990)
Rice Obs from Baker
Corn Pred
Rice Pred
Biomass Calculated by MAIZSIM from Farms on the Eastern
Shore of MD
MD, 2006
Days after emergence
0 20 40 60 80 100120140
MD, 2007
Days after emergence
0 20 40 60 80 100 120
100
200
300
400
500
MD, 2008
Days after emergence
0 20 40 60 80 100120140
Shoot dry
matter,
g p
lant-
1
100
200
300
400
500
DE, 2006
Days after emergence
0 20 40 60 80100120140160
DE, 2007
Days after emergence
0 20 40 60 80 100120140
Kim, S-K, Y. Yang, D.J. Timlin, D. Fleisher, A. Dathe, V.R.
Reddy. Modeling Nonlinear Temperature Responses of
Leaf Growth, Development, and Biomass in MAIZSIM.
Agron. J. 104:1523-1537. 2012
WATER STRESS
Simple Method to Model Water Stress
Relative available water content (AW)
0.0 0.5 1.0Rela
tive tra
nspiration r
atio (
Ta/T
p)
0.0
0.5
1.0
Stress No stress
AW
wp
fc wp
Limitations of Current Modeling
Approaches
These are empirical approaches that mimic the impact of water stress on growth and yield not the mechanism.
Energy balance is not always modeled
No stomatal response (effects on carbon assimilation) to increased CO2 or temperature
Assumes stomata control transpiration and photosynthesis (and growth) proportionally
Response of Plants to Water Availability
Stomatal closure decreases water loss more than it decreases
carbon assimilation
Linking water loss and photosynthesis as a linear relationship
to model water stress will result in underprediction of yields.
Osmotic adjustment
Soil water potential
Potential transpiration rate
Leaf water potential
Stomatal conductance
Carbon partitioning to roots
Leaf expansion rate
Leaf water potential is a basis for water stress calculations.
Simulating carbon assimilation rates and
transpiration in growth chambers
400 ppm
Hour of day
0 5 10 15 20 25
PN
et
mo
l C
O2 m
-2 s
-1
-40
-20
0
20
40
60
80
100
120
140
160Measured 25%
Measured 100%
Simulated 25%
Simulated 100%
800 ppm
Hour of day
0 5 10 15 20 25
PN
et
mo
l C
O2 m
-2 s
-1
-40
-20
0
20
40
60
80
100
120
140
160
Water Use, Observed and from Simulations
with SPAR Environment Data
Irrigation treatment (% of control)
20 40 60 80 100
Wa
ter
use
, l p
lan
t-1
0
5
10
15
20Measured ambient CO2
Measured elevated CO2
Simulated ambient CO2
Simulated elevated CO2
Biomass
Irrigation treatment (% of control)
20 40 60 80 100
Bio
mass,
g p
lant-1
0
20
40
60
80
100
120
Measured ambient CO2
Measured elevated CO2
Simulated ambient CO2
Simulated elevated CO2
TESTING AND SOME APPLICATIONS
Nitrogen uptakeWater content
Water uptakeRoot growth
Water uptakeRoot growth
Radiation use efficiency from simulations
for three temperature scenarios
What is the reason for the temperature
effect?
Temperature Regime
Avg +3 +6
22.0 25.0 27.5
Photosynthesis
Leaf temperature (oC)
20 25 30 35 40
A (
mol m
-2 s
-1)
25
30
35
40
45
Elevated
Ambient
High temperatures -> rapid growth
and smaller leaves-> rapid
senescence.
Mean Water Content at 60 cm Depth
Closing notes
Complex models are possible.
Our experience indicates that although they require more parameters,
many of the parameters have physical meaning and can be fit
independent of the environment.
Growth chambers are useful to provide finally controlled
conditions to investigate environmental effects on plant growth
and development –
Very quantitative
Fine time scales
We have a potato (SPUDSIM) and a maize (MAIZSIM) model.
soybean and wheat are under development
Closing notes (cont’d)
MAIZSIM is open source
and available on GitHub.
Search using keywords
Github and MAIZSIM.
THANK YOU!
Jw = (s - l)/Rp
)(
4
Harp
stemasabsl
ggc
JTRT
gs=f(A, hs, ci, leaf )
A = f(gs, Tl, Rabs, ci)
A, gs,, ci
gs=f(A, hs, ci, leaf )
A = f(gs, Tl, Rabs, ci)A, gs,, ci, Tl
))(
(2a
aLsvpotential
P
eTegE
Rstem
Rp=Rsr+Rr+Rstem
The Coupled Model
Current Modeling Approaches Can be
Improved
We need a more physiologically based approach that takes
into account processes that plants have developed to optimize
carbon assimilation and minimize water loss under all
conditions of water availability and especially water deficit
situations.
