University of Florida

ABE 5015
Empirical Models of Crop Growth and Yield Response

Semester Taught - Spring

Catalog Description

Credits: 3

Analytical models useful for engineering design and management decisions, including water reuse. Emphasis on analytical functions. Modeling strategy based on patterns of data, functional relationships, connections among various factors, consistency among data sets, and mathematical beauty.


Permission of Instructor

Course Objectives

  • Illustrate patterns in data from graphical format.
  • Suggest relationships which are compatible with the patterns.
  • Discuss characteristics of alternative relationships.
  • Calibrate the chosen model for a set of data.
  • Develop connections between components of the system (such as dry matter and plant nutrients).
  • Apply model to other data sets to search for consistency.
  • Search for commonality among parameters for similar data sets.
  • Interpret implications of the models for application and basic processes.


Allen R. Overman
Rogers Hall Room 273
392-1864 x273

Material/Supply Fees


Course Outline

Mathematical models have been developed to describe the dependence of crop growth and yields on various factors such as stage of growth, harvest interval (for perennial grasses), water availability, and others (such as tillage).

The models are constructed around analytical functions which are well known and easily evaluated. Connections are shown between dry matter and plant nutrient uptake through phase relationships. Principles (learned from mathematics, physics, and chemistry) which have guided the development of these models include: (1) Patterns (data), (2) Relationships (equations), (3) Connections (among system components), (4) Consistency (among data sets), and (5) Mathematical beauty (such as symmetry).

The course progresses from simple ideas to more complex analysis. Data from studies with a variety of crops, soils, and environmental conditions are used to illustrate practical applications. Significance of model parameters as related to the physical system is explored. Importance of models to analysis, design, operation, and evaluation of systems is emphasized.

Topics Covered

  1. Introduction
    1.1    Historic Background
    1.2    Yield Response Models
    1.3    Growth Models
    1.4    Environmental Input
    1.5    Summary
  2. Seasonal Response Models
    2.1    Background
    2.2    Extended Logistic Model
    2.3    Extended Multiple Logistic Model
    2.4    Water Availability
    2.5    Legume/Grass Interaction
    2.6    Summary
  3. Growth Response Models
    3.1    Background
    3.2    Empirical Growth Model
    3.3    Extended Empirical Growth Model
    3.4    Phenomenological Growth Model
    3.5    Expanded Growth Model
  4. Mathematical Characteristics of Models
    4.1    Background
    4.2    Phenomenological Growth Model
    4.3    Expanded Growth Model
    4.4    Rational Basis for Logistic Model
    4.5    Coupling Among Applied, Soil, and Plant Components
    4.6    Accumulation of Dry Matter and Plant Nutrients
  5. Pasture Systems
    5.1    Background
    5.2    Quadratic Model
    5.3    Linear Exponential Model
    5.4    Summary
  6. Nonlinear Regression for Mathematical Models
    6.1    Background
    6.2    Logistic Model
    6.3    Probability Model
    6.4    Confidence Contours
    6.5    Sensitivity Analysis
    6.6    Dimensionless Plots
    6.7    Correlation Coefficient


Instructor will provide information

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