A Simplified Linear Transformation to Calculate N Application Rates in Corn and Wheat

Dr. Brenda Ortiz Who Built The Unique Corn Optical Sensor Data Set Required for This Investigation

And Dr. Bill Raun Who Kept this Investigation going Through Hell and High Water

Dr. Jim Schepers Whose argument for measuring NDVI at Two Different Locations Without an N Rich Strip caused me to Modify my approach to the problem.

Corn at three growth stages symmetric sigmoid model

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

1.00

2.00

3.00

4.00

5.00

6.00

Meas.GS V-6Meas.GS V-8Meas.GS V-10GS V-6GS V-8GS V-10

Normalized Difference Vegetative Index

Yiel

d G

oal,

mg/

Ha

Difficulty with the symmetric sigmoid for predicting grain yield• This equation is Parametric – each parameter is a function of an

equation. • This means that you cannot directly solve for any value of the yield

equation.• This isn’t good. We must adjust the parameters until the equation

predicts known yield values. Consequently, we can’t directly solve the yield equation for exact values.• We need a simpler approach which replaces parameters with

constants and linearizes the relationship between the independent dependent variable (FP ndvi) and the dependent variable yield.

We can make the following assumptions when developing a model to predict grain yield with optical sensors

• Yield without additional N is proportional to Farmer Practice NDVI.• NRich NDVI is independent of location within an area in a field where

production variables exhibit geostatistical relatedness.• A straight line can be constructed between the maximum value of

NRich NDVI and the minimum value of Farmer Practice NDVI.• Because NDVI is linearly proportional to crop yield, a straight line can

be fit through NDVI and crop Yield. (Dr. Jim Schepers)

Corn and Wheat there is a region where symmetric sigmoid exhibits high linearity

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.00

1.00

2.00

3.00

4.00

5.00

6.00

Normalized Difference Vegetative Index

Yiel

d G

oal,

mg/

Ha

linearization• Despite the concerns about using sophisticated non-linear models, agronomist

have need to use N-Lin models to describe and predict complex biological phenomena. One of these model is the symmetric sigmoid which is a step function i.e. growth models. Many of these models are parametric requiring input of data to change values of coefficients as inputs change. In effect, two, three, or more additional equations are needed to define the coefficients required to implement the non-linear model. • One approach often used by engineers when creating models to control

machines and processes, is to break the model up into segments which can be treated as independent models within the range of interest. In the case of symmetric sigmoid, most of the change in the value of the dependent variable occurs for NDVI values ranging form 0.20 and 0.80. Nearly all change occurs between 0.10 and 0.90 NDVI.

•Consistently, yield data were linear functions of NDVI

Data Linearization

• Fit a straight line (linear regression) through the data• Fit a straight line through at least two N-Rich reference strips• Locate one NRich strip in the highest yielding portion of the field and

one from the natural occurring lowest producing area of the field. Exclude alkali spots, pot-holes, abnormally low producing regions, etc.• Although only two carefully selected areas are needed to establish

the linear regression line, additional N-Rich strips will improve the accuracy and precision of the fitted straight line.

Linearized Generalized N Rate Algorithm AONR Corn Experiment - 2014

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normalized Difference Vegetative Index

Nor

mal

ized

Yie

ld Yield Goal Plateau

Linearized Yield Goal

NDVI Farmer Practice vs NRich NDVI 23 Site Years

0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.90000.00000.10000.20000.30000.40000.50000.60000.70000.80000.90001.0000

f(x) = 0.541140981762285 x + 0.436441429996342R² = 0.395595723889611

Farmer Practice NDVI

N R

ich

NDV

I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6f(x) = NaN x + NaNR² = 0 LCB 2004 109 1416

Farmer Practice NDVI

Whe

at Y

ield

, t/H

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

f(x) = 10.9413329110403 x − 1.10688981025813R² = 0.588201321680053

Efaw 2004 75 846

NDVI

Corn

Yie

ld m

T/H

A

Why Linearize Data

• Establishes a straight line relationship between NDVI and Grain Yield.• Differences between NDVI values are equivalent to differences in

yield.• Yield goal is the maximum expected yield

Additional Steps

• NDVI of the yield goal for the most productive area and for the least productive area must be determined using an N-Rich reference strip. Although peak yield generally occurs at approximately 0.80 NDVI, there is no guarantee that it will. A second N-Rich reference strip must be established in the least productive area in the field. • Yield goals must be established at each location. The literature

contains several methods for establishing reasonable yield goals.• A linear curve must be fitted to the data with NDVI being the

independent variable and yield goal being the dependent variable. Use standard regression equations for linear curves.

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.850.00

2.00

4.00

6.00

8.00

10.00

12.00f(x) = 15.490957166217 x − 2.07751052886588R² = 0.733395331398094

Corn - 57-gd,Haskell 2004, 99day

NDVI

Corn

Yie

ld m

T/H

a

Yield Goal

MinYld=Yld Goal*0.48/0.81

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.850.00

2.00

4.00

6.00

8.00

10.00

12.00f(x) = 15.490957166217 x − 2.07751052886588R² = 0.733395331398094

Corn - 57-gd,Haskell 2004, 99day

NDVI

Corn

Yie

ld m

T/H

a

Defines the yield limit without additional N. Increase in yield will be proportional to increase in NDVI

0.55 0.6 0.65 0.7 0.75 0.8 0.850.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

f(x) = 26.3479876494689 x − 10.1010213430281R² = 0.398551397364693

56-gd, Efaw OFFIt, 2006

NDVI

Expe

cted

Yie

ld m

T/H

a

Circles are approximate locations for Nrich NDVI and minimum NDVI

Appendix – Additional Examples

0.5 0.55 0.6 0.65 0.7 0.750.00

2.00

4.00

6.00

8.00

10.00

12.00

f(x) = 24.3214698368749 x − 9.58547198352701R² = 0.476975959402944

52-gd, LCB N Study 2006

NDVI

Corn

Yie

ld m

g/H

a

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.90.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

f(x) = 21.1784884284347 x − 6.35228842374134R² = 0.587767675888738

57-gd, Haskel 2004, 113 Day Corn

NDVI

Corn

Yie

ld m

T/H

a

0.78 0.79 0.8 0.81 0.82 0.83 0.84 0.85 0.86 0.870.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

f(x) = 54.3617135734723 x − 33.4088283309241R² = 0.460569905171288

53-gd, LCB Catchup 2005

NDVI

Corn

Yie

ld m

T/H

a

0.6 0.65 0.7 0.75 0.8 0.850.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

f(x) = 28.1917558701544 x − 12.3570232575276R² = 0.547442182216558

61-gd, Haskell 2004, 115 Day

NDVI

Corn

Yie

ld m

T/H

a

0.3000 0.3500 0.4000 0.4500 0.5000 0.55000.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

f(x) = 12.734059960024 x + 1.20198718075123R² = 0.23114625158361

GCS ST 2009- 712 GDD

Farmer Practice NDVI

Corn

Yie

ld, m

T/ha

0.2000 0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.55000.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

f(x) = 36.3435419107933 x − 6.56526316972054R² = 0.628652712972206

TVS BT 2009- 709 GDD

Farmer Practice NDVI

Corn

Yie

ld, m

T/ha

0.2500 0.3000 0.3500 0.4000 0.4500 0.5000 0.5500 0.6000 0.65000123456789

10

f(x) = 26.4314199585823 x − 7.84088720580132R² = 0.738191453552352

EVS ST 2010- 883 GDD

Farmer Practice NDVI

Corn

Yie

ld ,

mT/

Ha

0.4000 0.4500 0.5000 0.5500 0.6000 0.6500 0.7000 0.7500 0.80000.01.02.03.04.05.06.07.08.09.0

10.0

f(x) = 18.8335140940794 x − 5.63572216630152R² = 0.318210691557767

EVS BT 2010- 1106 GDD

Farmer Practice NDVICo

rn Y

ield

, mT/

Ha

0.5500 0.6000 0.6500 0.7000 0.7500 0.80000.0

1.0

2.0

3.0

4.0

5.0

6.0

f(x) = 9.00086056891097 x − 2.79579539526449R² = 0.189615109735662

EVS BT 2011- 879 GDD

Farmer Practice NDVI

Corn

Yie

ld, m

T/H

A

0.5000

0.5500

0.6000

0.6500

0.7000

0.7500

0.8000

0.85000.02.04.06.08.0

10.012.0

f(x) = 24.7057438384165 x − 12.036510436785R² = 0.446900877769618

TVS BT 2011- 844 GDD

Farmer Practice NDVI

Corn

Yie

ld, m

T/H

a

0.6000 0.6500 0.7000 0.7500 0.8000 0.85000.0

2.04.06.0

8.010.012.0

f(x) = 30.8780314989637 x − 17.4980957293479R² = 0.608167587484256

EVS BT 2012 - 773 GDD

Farmer Practice NDVI

Corn

Yi,e

ld, m

T/H

a

0.7000

0.7200

0.7400

0.7600

0.7800

0.8000

0.8200

0.84000.0

2.0

4.0

6.0

8.0

10.0

f(x) = − 3.16910180616986 x + 9.35978941420811R² = 0.00664652182816239

EVS ST 2012- 773 GDD

Farmer Pactice NDVI

Corn

Yie

ld, m

T/H

a

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.850.00

2.00

4.00

6.00

8.00

10.00

12.00f(x) = 15.490957166217 x − 2.07751052886588R² = 0.733395331398094

Corn - 57-gd,Haskell 2004, 99day

NDVI

Corn

Yie

ld m

T/H

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6f(x) = NaN x + NaNR² = 0 LCB 2004 109 1416

Farmer Practice NDVI

Whe

at Y

ield

, t/H

a

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

1

2

3

4

5

6

7f(x) = NaN x + NaNR² = 0 Efaw 2004 124 1521

124-GD Linear (124-GD)

TC Model

NDVI

Corn

Yld

, m

T/H

a