Crop Modeling By Dr. Omar Maghawry Ibrahim Researcher 2012 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 Curvilinear relationships Y Y X X Y Y X X

Non-linear in parameters Y= b1 * exp(–b2 * exp(–b3 * x)) Models of regression Linear in parameters Non-linear in parameters Polynomial regression Multiple regression Y=b0+b1x1+b2x2 …. Intrinsically linear Logarithmic Y=b0+b1ln(x) 1st order, Simple regression Y=b0+b1x Model 1 Variable X is fixed Variable Y is random Non-Intrinsically Non-linear Gompertz model Y= b1 * exp(–b2 * exp(–b3 * x)) 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

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) b1 – (b2 * (b3 ** x)) Gompertz b1 * exp(–b2 * exp(–b3 * x)) Metcherlich Law of Diminishing b1 + b2 * exp(–b3 * x) Michaelis Menten 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 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 APSIM-Sugarcane Sugarcane, potential growth, water and nitrogen stress NTKenaf potential growth, water stress

Crop Simulation Models Software Details SLAM II Forage harvesting operation SPICE Whole plant water flow REALSOY Soya bean MODVEX Model development and validation system IRRIGATE Irrigation scheduling model COTTAM Cotton APSIM Modeling framework for a range of crops GWM General weed model in row crops MPTGro Acacia spp.and Leucaena Spp. GOSSYM-COMAX

Crop Simulation Models Software Details SIMCOM Crop (CERES crop modules) & economics LUPINMOD Lupin TUBERPRO Potato & disease SIMPOTATO Potato WOFOST Wheat & maize, Water and nutrient WAVE Water and agrochemicals SUCROS Crop models ORYZA1 Rice, water SIMRIW SIMCOY 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.

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