Transcript Generalized Algorithm for Variable Rate Nitrogen Application on Cereal Grains John B. Solie, Regents Professor Biosystems and Agri.

Generalized Algorithm for Variable
Rate Nitrogen Application on
Cereal Grains
John B. Solie, Regents Professor Biosystems and Agri. Engineering Dept.
William R. Raun, Regents Professor, Plant and Soil Sciences Department
Dean Monroe, PhD, Formerly Biosystems and Agri. Engineering Department
Randall K. Taylor, Professor, Biosystems and Agri. Engineering Department
D. Brian Arnall, Assistant Professor, Plant and Soil Sciences Department
Physiological Basis for Spectral
Sensing
Near Infrared
Reflectance (%)
0.5
Visible
870
780
960
0.25
550
670
460
Plant Reflectance
450 500 550 600 650 700
750 800
850 900 950 1000 1050 1100 1150
Wavelength (nm)
Normalized Difference Vegetative
Index - NDVI
• Calculated from the red
and near-infrared bands
NDVI 
• Equivalent to a plant
physical examination
• Correlated with:
–
–
–
–
–
–
–
Plant biomass
Crop yield
Plant nitrogen
Plant chlorophyll
Water stress
Plant diseases
Insect damage
 NDVI   Re d
 NDVI   Re d
OSU Original N Rate Algorithm
Bill’s Postulates
1. Crop yield potential can be
predicted from NDVI
2. A maximum potential yield
exists that is a function of the
weather and soil type
3. A fertilizer response index
exists that defines the
response to additional
fertilizer and varies from year
to year and site to site.
4. Response to N fertilizer is
independent of potential
yield.
5. YPN = f(YP0, RI)
1. Measure
RI NDVI 
NRNDVI
Fp NDVI
2. Predict YP0 YP  Ae
B
NDVI
GD
3. Predict YPN YPN  RI YP0
4. NRate 
(YPN  YP 0)% N
NUE
1
4
3
2
Problems with OSU Original
Algorithm
• Discontinuities in yield & response index models
• Yield model dos not satisfy boundary conditions
– zero yield on bare soil (FpNDVI =0,
– Maximum potential yield at FPNDVI=1,
• Failure to account for bare soil NDVI.
• Inability to fully account for crop growth stage and
varying biomass levels.
• Lack of a scientifically based procedure to determine
maximum potential yield.
• Inability to account for interaction between Nrich
NDVI and yield model
Proposed Generalized Algorithm
• Fix maximum value of potential yield curve with best
estimate of maximum potential yield, YPmax.
• Use bounded (sigmoid) model to predict grain yield as
function of NDVI.
• Incorporate RIFert into YP0 yield prediction to calculate
YPN
• Calculate potential yields with and without additional
fertilizer with bounded yield model, response index, and
maximum estimated yield.
• Calculated N application rate based on difference
between potential yield.
• Improve methodology for mid-season prediction of
maximum yield
Potential Yield Models
(8)
• Straight Line
YP  a NDVI  b
• Exponential
YP  a e b NDVI
• Sigmoid
YP 
YPMAX
1 e

FpNDVI  inf
K
Unit Sigmoid Model
1.2
1 e
Maximum Potential Yield
1
FpNDVI  inf

K
Inflection Point
½ Max Yield
0.8
Yield
YP 
YPMAX
0.6
+
Bare Soil
Yield
Radius of
Curvature
0.4
0.2
0
0
0.2
0.4
0.6
FpNDVI
0.8
1
Max. Yield and Inflection Point
3.5
3
Yield
2.5
2
1 X Yield
2 X Yield
1.5
3 X Yield
Infl. Pt.
1
0.5
0
0
0.2
0.4
0.6
Fp NDVI
0.8
1
1.2
Curvature Change with Unit Max.
Yield And Variable Inflection NDVI
1.2
1
Unit Crop Yield
0.8
Inf = 0.3 NDVI
0.6
In = 0.5 NDVI
Inf = 0.7 NDVI
0.4
0.2
0
0
0.2
0.4
0.6
FpNDVI
0.8
1
1.2
Corn Sigmoid Model Parameters
0.8
"Inf"
"K"
Linear ("Inf")
Linear ("Inf")
Poly. ("K")
0.7
Parameter value
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
0.6
Average NDVI
0.8
1
Optimization & Sensitivity Analysis
Sigmoid Model Parameters for Corn
1.2
TC R^2
Model R^2
1
TC Error
0.8
Model Error
0.6
0.4
0.2
0
0
0.05
0.1
"K" Value
0.15
Bare Soil Factor
0.2 0.8
R2 or Absolute Error
R2 or Absolute Error
Curvature "K"
0.7
0.6
0.5
0.4
TC R^2
0.3
Model R^2
0.2
TC Error
0.1
Model Error
0
0
0.02
0.04
0.06
Bare Soil Factor
0.08
0.1
Sigmoid Yield Model Parameters
Coeficient of Determination
R2
Absolute Error
TC NLIN
Regression
Sigmoid Yield
Model
TC NLIN
Regression
Sigmoid Yield
Model
Model Factor
Crop
Optimum
Value
"K"
Corn
0.123
0.429
0.402
0.582
0.680
Wheat
0.124
0.537
0.502
0.423
0.523
Corn
0.045
0.429
0.402
0.582
0.665
Wheat
0.077
0.537
0.502
0.423
0.524
"BSF"
Corn Zero Intercept Sigmoid Model:
Measured and Predicted Values
Perkins 2006 OFFIT Trial 56 Days
Perkins 2006 OFFIT Trial 65 Days
Corn Grain Yield, Mt/ha
6
5
4
3
TC Model
2
Sigmoid Model
1
56-gd Data
0
5
4
TC
Model
Model
Yield
3
2
1
0
0
0.2
0.4
0.6
0.8
1
0
NDVI
0.2
0.4
0.6
NDVI
Perkins 2006 OFFITT Trial 78 Days
6
Corn Grain Yield, Mt/ha
Corn Grain Yield, Mt/ha
6
TC Model
5
4
3
2
1
0
0
0.2
0.4
0.6
NDVI
0.8
1
0.8
1
Corn Zero Intercept Sigmoid Model:
Measured and Predicted Values
Efaw 2006 OFFIT Trial 62 Day
12
TC
Model
Model
Yield
10
8
6
Efaw 2006 OFFIT Trial 69 Days
4
18
2
16
0
0
0.2
0.4
0.6
NDVI
0.8
1
Corn Grain Yield, Mt/ha
Corn Grain Yield, Mg/ha
14
TC Model
14
Model
Yield
12
10
8
6
4
2
0
0
0.2
0.4
0.6
NDVI
0.8
1
Wheat Perkins 2006
Wheat Grain Yield, Mt/ha
6
51-gd TC Model
51-gd Sigmoid Model
120-gd TC Model
120-gd Sigmoid Model
51-gd Data
120-gd Data
5
4
3
2
1
0
0
0.2
0.4
0.6
NDVI
0.8
1
Step 1 Estimate maximum potential
yield within field for current year
Winter Wheat Yield of Cumulative Pot. Etos
10 days before to 30 days after planting
7
Max Yield
6
Wheat Yield, Mg/ha
• Field yield
records
• Farmer
and/or
consultant’s
informed
opinion
• Growth
models
• Other
Dry Weather
Freeze Damage
5
Excessive Rain
4
Unknown
Linear (Max Yield)
3
2
y = 0.0437x + 0.0223
R² = 0.8999
1
0
0
50
100
150
Cumulative Potential ETos, mm
200
Fully Bounded Sigmoid Yield
Model Parameters
"inf" & "K" Coefficient Values
0.8
"K"-Curvature
"inf" Inflection Pt.
0.7
0.6
y = 0.9739x - 0.0884
R² = 0.8927
0.5
0.4
0.3
y = -0.3556x2 + 0.4654x - 0.0764
R² = 0.1231
0.2
0.1
0
0
0.2
0.4
0.6
Average NDVI
0.8
1
NRich Strip
Sense NDVI from NRich and adjacent farmer
practice strip in a portion of the field exhibiting the
highest response to pre-plant fertilizer.
Potential Yield Calculations
YPmax
YP0 
1 e
FpNDVI  inf

K
YPmax
YPN 
1 e
RI NDVI FpNDVI  inf

K
Fertilizer Application Rate
(YPN  YP0) % N
NRate 
NUE
N Fertilizer Rate kg/ha
Nrate
100
90
80
70
60
50
40
30
20
10
0
0
0.2
0.4
0.6
NDVI
0.8
1
Conclusions
• With the possible exception of winter wheat, the process
for estimating crop yield in-season is more art than
science.
• Research is needed to improve maximum yield estimates
for crop, year, and location.
• The proposed sigmoid yield model for calculating yield
accounts for location, year, and crop growth prior to
sensing.
• Model parameters are the same for corn and wheat (NUE
and % N in grain are crop specific).
• Seven years of tests confirm that the model for
calculating N application rate from yield estimates works
well.
Questions
Ivan Ortiz-Monasterio Farmer training,
Ciudad Obregon, Mexico, January 2007
Visible
Near Infrared
Reflectance (%)
50
25
Plant Reflectance
0.0
450 500
550 600
650
780
880
950
Wavelength (nm)
1000
Spectral Signature: Two N Levels
Set One Winter Wheat
1
0.9
0.8
0.7
0.6
High N
0.5
Low N
Set Two Winter Wheat
0.4
0.3
1
0.2
0.9
0.1
0.8
0.7
0
650
700
750
800 0.6
0.5
High
N
0.4
0.3
0.2
0.1
0
650
700
750
800
Red Edge
Red Edge High and No N Rates
Curves are Shift and Normalized
0.5
0.4
Reflectance
0.3
0.2
Adj High
Adj Low
0.1
0
640
-0.1
660
680
700
720
740
Wavelength, nanometers
760
780
800
Comparisons of Various Indices
RedNDVI vs Green/Red
RedEDGE vs Green/Red
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
Green/Red Ratio
5
721
720
719
718
717
716
715
714
713
712
711
7
0
6
0.5
1
1.5
RedEDGE vs red NDVI
721
720
719
718
717
716
715
714
713
712
711
RedEDGE
0
0.2
0.4
0.6
0.8
2
2.5
3
3.5
N Concentration (Minolta SPAD)
Spad vs RedEdge
724
y = 0.1883x + 709.49
R² = 0.2975
722
720
718
RedEDGE
716
Linear (RedEDGE)
714
712
710
0
20
40
Spad vs RedNDVI
60
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
y = -0.0014x + 0.5219
R² = 0.0019
RedNDVI
Linear (RedNDVI)
0
10
20
30
40
50
60