a simplified linear transformation to calculate n application rates in corn and wheat
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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
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