Types Of Models

Depending upon the purpose for which it is designed the models are classified into different groups or types. Of them a few are :

a. Statistical models: These models express the relationship between yield or yield components and weather parameters. In these models relationships are measured in a system using statistical techniques (Table 1).

Example: Step down regressions, correlation, etc.

b. Mechanistic models: These models explain not only the relationship between weather parameters and yield, but also the mechanism of these models (explains the relationship of influencing dependent variables). These models are based on physical selection.

c. Deterministic models: These models estimate the exact value of the yield or dependent variable. These models also have defined coefficients.

d. Stochastic models: A probability element is attached to each output. For each set of inputs different outputs are given alongwith probabilities. These models define yield or state of dependent variable at a given rate.

e. Dynamic models: Time is included as a variable. Both dependent and independent variables are having values which remain constant over a given period of time.

f. Static: Time is not included as a variables. Dependent and independent variables having values remain constant over a given period of time.

g. Simulation models: Computer 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, and calculate both rate and state variables over time, normally from planting until harvest maturity or final harvest.

Table 1. Prediction models for crop growth, yield components and seed yield of soybean genotypes with meteorological observations

GENOTYPE

MACS-201

MACS-58

Plant height

-0.09 HTU3 R2 = 0.97

57.60-0.24 MIT1 -0.06 RH12 -0.07 HTU3 R2 = 0.92

Branches per plant

2.97+0.08 SS1 +0.08 MAT2 -0.01 HTU2-0.07 MAT3 R2 = 0.91

6.44-0.01 RH21 +0.03 MAT2 -0.12 MAT3 R2 = 0.83

Green leaves

-1.20-0.20 MT1 -0.03 RH11 +0.19 GDD2 -0.18 RH13 +0.13 RH23 +2.92 MT3 -3.55 GDD3 R2 = 0.98

19.95-0.29 MIT2 -0.05 RH12 -0.602 SS3 R2 = 0.78

Leaf area (dm2 m-2)

754.01-25.97 SS1 -20.65 MAT2 -29.85 SS2 +0.15 HTU2 -23.23 MIT3 -5.66 RH13 -0.73 RH23 R2 = 0.99

451.89-2.28 RH11 -7.06 SS1 -1.90 MIT2 +1.02 RH22 +1.34 HTU2-2.04 GDD3 R2 = 0.99

Leaf area index

-13.46+0.40 SS1 -0.09 MAT2 +0.17 MAT3 +0.15 RH23 +1.02 SS3 -0.02 HTU3 R2 = 0.98

18.30-0.03 RH11 -0.03 RH21 -0.02 HTU1 +0.((2 HTU2 -0.35 MAT3 R2 = 0.96

Canopy dry weight

-1610.10+3.16 RH11 +16.65 MT1 +2.73 HTU2 +76.0^1 MAT3 -6.77 RH13 + 126.81 SS3 -14.12 HTU3 R2 = 0.99

2018.40-7.14 RHU -2.21 HTU. -1.74 RH12 -16.14 MAT3 R2 = 0.94

No. of pods per plant

-697.79+4.14 MIT1 +0.94 RH11 +13.01 SS1 +11.14 MAT3 +2.2(1 RH23 +29.93 SS1 -1.65 HTU3 R2 = 0.99

56.89+3.86 SS1-0.33 HTU3 R2 = 0.88

Seeds per pod

-5.08 + 0.03 MAT. + 0.94 RHn +0.05 MIT2 -0.03 RH13 +0.04

4.13-0.07 MIT. -0.02 GDD. -0.86 GDD3 R2 = 0.95 RH23 +0.11 SS3 -0.07 gdd3 R2 = 0.99

100 seed weight

3.18-0.05 rhJJ -0.09 GDD2 +1.95 MT3 -2.34 GDD3 R2 = 0.93

15.32-0.11 RHn -0.06 RH21 -0.10 HTU. -0.04 RH22 +0.((2 HTU2 +0.74 MT3 -1.2-4 GDD3 R2 = 0.97

Harvest index

56.16 +0.11 rhjj -0.13 RH21 +0.38 MAT2 -0.07 HTU2 -0^9 MAT3 R2 = 0.94

151.36-0.20 RHU -0.06 RH21 -0.10 HTU. -0.63 MAT2 +0.17 HTU2 -2.30 MAT3 -0.06 RH13 R2 = 0.98

Yield

6370.20-7.73 RH21 -5.57 HTU2 -93.85 MAT3 R2 = 0.93

6899.70-21.84 RHU -62.83 MT.-10.89 HTU3 R2 = 0.95

Plant height

42.38+0.70 SS1 -0.07 HTU3 R2 = 0.92

110.89-0.36 MIT.-0.05 RH21 +0.042 HTU. -0.11 RH12 -0.03 RH22 -0.01 H1TU2 -0.91 1M2 AT3 -0.12 RH13-1.1 SS3 R2 = 0.99

GENOTYPE

MACS-201

MACS-58

Branches per plant

6.31-0.01 RH12 +0.02 MT2 -0.09 MAT3 R2 = 0.91

5.79-0.01 RH12 -0.01 RH22 -0.06 MAT3 R2= 0.81

Green leaves

2.81+0.68 MAT -0.05 RH21 -0.04 HTU1 -0.215 MIT2 -0.23 MAT3 R2 = 0.77

28.68-0.72 RH21 +0.05 SS1 -0.73 MIT2 +0.(01 RH12 -0.48 SS2 +0.67 (2 DD2 -0.051 2RH13 -0.72 SS3 -0.27 GDD3 R2 = 0.99

Leaf area (dm2 m-2)

190.28-2.01 RH11 +1.02 RH21 -6.68 SS1 -4.98 MAT2 +1.19 HTU2 +26.48 MT3 -40.32 GDD3 R2 = 0.99

346.96-0.20 RH21 +0.02 HTU1 -0.53 RH12 -0.32 RH22 +0.013 HTU2 +1.16 MIT3 -0.64 RH13 -3.80 SS3 -10.10 GDD3 R2 = 0.99

Leaf area index

17.47-0.01 RH21 -0.25 SS1 -0.02 HTU1 -0.36 MA21T2 +0.06 H1 TU2 -0.35 MAT3 +0.06 RH23 +0.39 SS3 R2 = 0.99

6.21-0.02 RH22 -0.02 HTU3 R2 = 0.87

Canopy dry weight

751.46+19.21 MIT -4.19 RHn -2.16 HTU1 -18.80 MAT2 +1.47 RH12 +4.36 HTU2 +70.36 SS3 -4.71 HTU3 R2 = 0.99

1568.40-5.00 MAT -6.30 RHn -0.91 HTU1 +2.20 1MAT2 +0.8011 MT2 +5.40 GDD2 +0.49 HTU2 +2.68 RH13 -14.91 SS3 -22.65 MJ1 R2 = 0.99

No. of pods per plant

152.48-0.25 RH21 -0.28 RH12

-1.24 MIT2 R2 = 0.89

56.54+3.39 MAT +6.44 SS1 +2.80 MT2 -0.70 HTU1 -0.53 RH12 -0.72 RH13 -0.32 HTU3 R2 =0.98

Seeds per pod

4.93-0.00 HTU1 -0.01 RH12 +0.01 HTU2 -0.05 mat3 R2 = 0.86

RH12 -0.04 HTU2 -0.02 IMAT3

-0.03 RH13 +0.02 RH23 R2 = 0.9913 23

100 seed weight

15.45+0.06 MAT2 -0.28 GDD3 R2 = 0.90

28.08-0.12 MAT -0.02 RH„ -0.03 RH21 +0.01 MAT2 -0.02 RH12 +0.02 RH23 -0.45 SS3 -0.4^ GDD3 +0.02 HTU3 R2 = 0.99 3 3

Harvest index

44.25+1.10 SS1 -0.10 HTU3 R2 = 0.92

58.90 +1.02 MAT -0 07 RH21 -0.10 HTU1 -0.11 RH22 -0.31 SS22 -0.62 GDD2 -0.65 MAT3 -0.322 GDD3 R2 = 1.000

Yield

6373.5-128.52 MAT3 R2 = 0.90

7115.90-27.53 MIT1 -22.21 RHn -4.51 HTU1 -3.22 RH12 -3.00 HTU2 -66.31 MAT3 -7.-45 HTU3 R2 =2 0.99

GENOTYPE -MACS-330

Plant height

85.15-0.67 MAT1 +0.77 SS1 -1.10 MAT2 -0.42 RH12 +0.09 RH22 +1.07 SS2 -0.14 RH13 +1.64 MT3 -0.14 HTU3 R2 = 0.99

Branches per plant

-5.05-0.32 MTj +0.39 GDD1 +1.03 MT2-1.04 GDD2 -0.06 MIT3 R2 = 0.85

Green leaves

12.40-0.64 RH21 +0.032 SS2 -0.037 HTU2 R2 = 0.81

Leaf area (dm2 m2)

-203.25-0.47 RHU -1.06 RH12 +40.96 MT2 -41.82 GDD2 -0.17 HTU2 +6.01 MAT3 -1.12 RH13 -1.04 HTU3 R2 = 0.83

Leaf area index

-2.17+0.0067 RH21 +0.39 SSj -0.09 GDD! +0.016 RH22 +0.18 SS2 +0.22 MAT3 +0.00(39 RH13 -0.60 SS3 -0.17 GDD3 R2 = 0.87

Canopy dry weight

144.72-6.41 MATj -3.51 RHU +1.33 RH21 -9.53 RH12 +3.58 RH22 +48.55 SS2 -3.84 HTU2 -29.11 SS3 +1.61 HTU3 R2 = 0.99

No. of pods per plant

24.67-2.29 MIT1 +0.63 RHU +6.79 SS1 -3.37 MAT2 +0.32 HTU2 +4.17 MAT3 -10.42 SS3 -0.35 HTU3 R2 = 0.95

Seeds per pod

7.47-0.09 SS1 -0.08 MAT2 -0.04 RH12 +0.10 MAT3 -0.01 RH13 -0.01 HTU3 R2 = 0.96

100 seed weight

-2.02-0.07 RHU +0.03 RH21 +0.26 SS1 +0.68 MAT2 +0.08 RH22 -0.67 GDD2 +0.02 RHn -0.022 MT3 -0.013 HTU3 R2 = 0.99

Harvest index

24.39-0.22 RHn +0.06 RH21 -0.12 MT1 +1.75 MAT2 -0.20 RH12 +0.24 RH22 -1.64 GDD2 +0.55 MAT3 -0.10 HTU3 R2 = 0.99

Yield

1899+1.27 RH23 -5.63 HTU3 R2 = 0.77

ABBREVIATIONS

SSj - Sunshine hours in phase 1

552 - Sunshine hours in phase 2

553 - Sunshine hours in phase 3 GDD 1 - Growing degree days in phase 1 GDD2 - Growing degree days in phase 2 GDD3 - Growing degree days in phase 3 HTU1 - Heliothermal units in phase 1 HTU2 - Heliothermal units in phase 2 HTU3 - Heliothermal units in phase 3

RHn - Relative humidity in the morning in phase 1 RH12 - Relative humidity in the morning in phase 2 RH13 - Relative humidity in the morning in phase 3 RH21 - Relative humidity in the evening in phase 1 RH22 - Relative humidity in the evening in phase 2 RH23 - Relative humidity in the evening in phase 3

MATj - Maximum temperature in phase 1 MAT2 - Maximum temperature in phase 2 MAT3 - Maximum temperature in phase 3 MIT1 - Minimum temperature in phase 1 MIT2 - Minimum temperature in phase 2 MIT3 - Minimum temperature in phase 3 MT1 - Mean temperature in phase 1 MT2 - Mean temperature in phase 2 MT3 - Mean temperature in phase 3

h. Descriptive model: A descriptive model defines the behaviour of a system in a simple manner. The model reflects little or none of the mechanisms that are the causes of phenomena. But, consists of one or more mathematical equations. An example of such an equation is the one derived from successively measured weights of a crop. The equation is helpful to determine quickly the weight of the crop where no observation was made.

i. Explanatory model: This consists of quantitative description of the mechanisms and processes that cause the behaviour 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, tiller production, etc. Crop growth is a consequence of these processes.

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