National Research Centre
Agricultural and Biological Research Division
Field Crops Research Department
Crop Modeling
By
Dr. Omar Maghawry Ibrahim
Researcher
2012
Definitions and purposes
• Crop is defined as an “Aggregation of individual plant species
grown in a unit area for economic purpose”.
• Growth is defined as an “Irreversible increase in size and
volume and is the consequence of differentiation and
distribution occurring in the plant”.
• Model is a set of equations, which represents the behavior of a
system .
• Simulation is defined as “Reproducing the essence of a system
without reproducing the system itself ”.
• The purpose is usually to aid in explaining, understanding or
improving performance of a system
Models in agriculture
• Agricultural models are mathematical equations that represent
the reactions that occur within the plant and the interactions
between the plant and its environment.
• Owing to the complexity of the agricultural system and the
incomplete of present knowledge, it becomes impossible to
completely represent the system in mathematical terms and
hence, agricultural models images of the reality.
• Unlike in the fields of physics and engineering, universal
models do not exist within the agricultural sector.
• Agricultural models are very site specific and can only applied
to other sites where climate, soil parameters and crop
management are similar to those used in developing the
original model.
A schematic representation of interactions between a
plant and its environment
Climate and weather factors co-determine the potential
and attainable crop yields
Types of crop models
• Statistical models:
• These models express the relationship between yield or yield
components and weather parameters or other limiting factors
such as fertilizers and irrigation.
Different relationships
Linear relationships
Y
Curvilinear relationships
Y
X
Y
X
Y
X
X
Models of regression
Linear in parameters
Polynomial
regression
Multiple regression
Y=b0+b1x1+b2x2 ….
1st order, Simple regression
Y=b0+b1x
Model 1
Variable X is fixed
Variable Y is random
Model 2
Variable X is random
Variable Y is random
2nd order ( Quadratic )
Y=b0+b1x+b2x2
3rd order (cubic)
Y=b0+b1x+b2x2+b3x3
Non-linear in parameters
Intrinsically linear
Logarithmic
Y=b0+b1ln(x)
Non-Intrinsically
Non-linear
Gompertz model
Y= b1 * exp(–b2 * exp(–b3 * x))
Models of linear regression
Name
Equation
Linear
Y=b0+b1x
Quadratic
Y=b0+b1x+b2x2
Cubic
Y=b0+b1x+b2x2+b3x3
where
b0 = a constant , bn = regression coefficient, x= independent variable or time value, ln = the natural logarithm
u = upperbound value for LOGISTIC
Models of non linear regression
(intrinsically linear)
Name
Equation
Linear equation
Compound
Y=b0b1x
ln(Y)=ln(b0)+xln(b1)
Power
Y=b0xb1
ln(Y)=ln(b0)+b1ln(x)
Growth
Y=eb0+b1x
ln(Y)=b0+b1x
Exponential
Y=b0eb1x
ln(Y)=ln(b0)+b1x
Logistic
Y=(1/u+b0b1x)−1
ln(1/Y−1/u)=ln(b0)+xln(b1)
where
b0 = a constant , bn = regression coefficient, x= independent variable or time value, ln = the natural logarithm
u = upperbound value for LOGISTIC
Models of nonlinear regression
(non intrinsically linear)
Name
Model expression
Asymptotic Regression
b1 + b2 * exp(b3 * x)
Asymptotic Regression
Gompertz
Metcherlich Law of
Diminishing
Michaelis Menten
b1 – (b2 * (b3 ** x))
b1 * exp(–b2 * exp(–b3 * x))
b1 + b2 * exp(–b3 * x)
b1 * x / (x + b2)
Mechanistic and empirical models
• Mechanistic models use mathematical functions to represent
physical, biological, and chemical processes . Although these
models are suitable for areas outside the data range used for
development, they tend to be complex and require many input
parameters .
•
Empirical models are based on correlative factors between
variables, are relatively simple, and require less data although
such models cannot be used in areas outside the data range for
which they were created.
Static and dynamic models
• A static model is one that does not contain time as a variable
even if the end-products of cropping systems are accumulated
over time.
• In contrast dynamic models explicitly incorporate time as a
variable and most dynamic models are first expressed as
differential equations.
Deterministic and stochastic models
• Deterministic models: These models estimate the exact value
of the yield or dependent variable. These models also have
defined coefficients.
• Stochastic models: A probability element is attached to each
output. For each set of inputs different outputs are given along
with probabilities. These models define yield or state of
dependent variable at a given rate.
Descriptive and explanatory models
• A descriptive model defines the behavior of a system in a
simple manner. Example of this model is biomass production
of any crop under optimum conditions as a function of time by
using simple regression equation.
• Explanatory model consist of quantitative description of the
mechanisms and processes that cause the behavior of the
system. To create this model, a system is analyzed and its
processes and mechanisms are quantified separately. The
model is built by integrating these descriptions for the entire
system. It contains descriptions of distinct processes such as
leaf area expansion. Crop growth is a consequence of these
processes.
Simulation models
• Simulation models, in general, are a mathematical
representation of a real world system. One of the main goals of
crop simulation models is to estimate agricultural production
as a function of weather and soil conditions as well as crop
management. These models use one or more sets of
differential equations.
Crop Simulation Models Software
Software
Details
CERES-Rice
Rice, water
GRAZPLAN
Pasture, water, lamb
EPIC
Erosion Productivity Impact Calculator
CERES
Series of crop simulation models
DSSAT
Framework of crop simulation models including
modules of CERES, CROPGRO and CROPSIM
QCANE
Sugarcane, potential conditions
AUSCANE
Sugarcane, potential & water stress, erosion
CANEGRO
Sugarcane, potential & water stress
APSIMSugarcane
Sugarcane, potential growth, water and nitrogen stress
NTKenaf
potential growth, water stress
Crop Simulation Models Software
Software
SLAM II
Details
SPICE
REALSOY
Whole plant water flow
Soya bean
MODVEX
IRRIGATE
COTTAM
Model development and validation system
Irrigation scheduling model
Cotton
APSIM
GWM
Modeling framework for a range of crops
General weed model in row crops
MPTGro
GOSSYMCOMAX
Acacia spp.and Leucaena Spp.
Forage harvesting operation
Cotton
Crop Simulation Models Software
Software
SIMCOM
LUPINMOD
Details
Crop (CERES crop modules) & economics
Lupin
TUBERPRO Potato & disease
SIMPOTATO Potato
WOFOST
Wheat & maize, Water and nutrient
WAVE
SUCROS
ORYZA1
Water and agrochemicals
Crop models
Rice, water
SIMRIW
SIMCOY
Rice, water
Corn
Overview of the components and modular structure of the
DSSAT cropping model
Model validation
• The model validation stage involves the confirmation that the
calibrated model closely represents the real situation. The
procedure consists of a comparison of simulated output and
observed data that have not been previously used in the
calibration stage.
CONCLUSION
• Crop models are based on mechanistic or empirical approaches.
• Mechanistic models use mathematical functions to represent
physical, biological, and chemical processes. Although these
models are suitable for areas outside the data range used for
development, they tend to be complex and require many input
parameters.
• Empirical models are based on correlative factors between
variables, are relatively simple, and require less data although
such models cannot be used in areas outside the data range for
which they were created.