Nitrogen Use Efficiency, Nitrogen Fertilizers, NUE, Nitrogen and the EnvironmentLibrary of Yield Prediction Equations

This page and all associated mathematical equations have been shared with anyone interested in the development of sensor based algorithms, and has been shared since 2002.  No other research group has gone to the effort of sharing all their data with others so as to improve our science.   

Mathematical equations and the  associated units (English or Metric) have not, will not, and cannot change as this would be fraudulent.  All yield prediction equations, and the units for which they were developed, have remained the same since the inital loading date and year specified. 

Clarifying "southern" for algorithms developed in Oklahoma has become necessary so as to communicate our region/environment. 

This page and all others within our NUE website continues to change as new additions and formatting have been required, thus the requirement for citing a date when visiting web pages.  We will continue to share everything we do, because it is right.  No other N-management project in the world has been this transparent.

Last update: November 05, 2018
Sensor Based Nitrogen Rate Calculator, Topdress and Sidedress N rates for Corn and Wheat, Nitrogen management

Generalized Algorithm

Winter wheat algorithm 2017 (option 1) YP0=590*EXP(INSEY*258.2)

Corn algorithm (Southern US Grain Belt, options 21 (English units), 22 (Metric units))

INDEPENDENCE of Yield Potential and Nitrogen Response

(2013) 1. Relationship between Grain Crop Yield Potential and Nitrogen Response.  Agron. J. 105:1335-1344.

(2010) 2. Independence of Yield Potential and Crop Nitrogen Response. Prec. Agric. DOI 10.1007/s11119-010-9196-z

Manuscripts Addressing Sensor Based Nitrogen Algorithms

(2001) 3. In-Season Prediction of Yield Potential Using Wheat Canopy Reflectance,  Agron. J. 93:131-138(pdf)

(2001) 4. Nitrogen Fertilization Optimization Algorithm Based on In-Season Estimates of Yield and Plant Nitrogen Uptake  J. Plant Nutr. 24:885-898

(2002) 5. Improving Nitrogen Use Efficiency in Cereal Grain Production with Optical Sensing and Variable Rate Application. Agronomy Journal, 94:815-820

(2002) 6.
Real-Time Sensing and N Fertilization with a Field Scale GreenSeeker Applicator

(2002) 7. Improving Nitrogen Use Efficiency in Cereal Grain Production with Optical Sensing and Variable Rate Application. Agron J. 94:815-820.

(2003) 8. Identifying an In-Season Response Index and the Potential to Increase Wheat Yield with Nitrogen(pdf) Agron J. 95:347-351

(2004) 9. Evaluation of Green, Red, and Near Infrared Bands for Predicting Winter Wheat Biomass, Nitrogen Uptake and Final Grain Yield  J. Plant Nutr. 27:1431-1441.

(2005) 10.
Optical Sensor Based Algorithm for Crop Nitrogen Fertilization  Commun. Soil Sci. Plant Anal. 36:2759-2781 (pdf)

(2005) 11. Growth Stage, Development, and Spatial Variability in Corn Evaluated Using Optical Sensor Readings  J. Plant Nutr. 28:173-182 (pdf)

(2005) 12. Relationship Between Response Indices Measured In-Season and at Harvest in Winter Wheat.  J. Plant Nutr. 28:221-235.

(2006) 13. Relationship Between Coefficient of Variation Measured by Spectral Reflectance and Plant Density at Early Growth Stages J. Plant Nutr. 29:1983-1997 (pdf)

(2006) 14. Mid-Season Prediction of Wheat Grain Yield Potential Using Plant, Soil, and Sensor Measurements. J. Plant Nutr. 29:873-897 (pdf)

(2006) 15. In-season prediction of corn grain yield potential using normalized difference vegetation index(Agron. J. 98:1488-1494)(pdf)

(2006) 16. Spectral Reflectance Indices as a Potential Indirect Selection Criteria for Wheat Yield under Irrigation. Crop Sci. 2006 46: 578-588.

(2007) 17. Use of In-Season Reflectance for Predicting Yield Potential in Bermudagrass.  Commun. Soil Sci. Plant Anal. 38:1519-1531

(2007) 18.  By-Plant Prediction of Corn Forage Biomass and Nitrogen Uptake at Various Growth Stages Using Remote Sensing and Plant Height Measures (Agron J. 99:530-536) (pdf)

(2007) 19.  Potential Use of Spectral Reflectance Indices as a Selection Tool for Grain Yield in Winter Wheat under Great Plains Conditions. Crop Sci. 2007 47: 1426-1440.

(2008) 20.
Adjusting Midseason Nitrogen Rate Using a Sensor-Based Optimization Algorithm to Increase Use Efficiency in Corn. J. Plant Nutrition. 31:1393-1419.

(2008) 21.
Determination of optimum resolution for predicting corn grain yield using sensor measurements.  Arch. Agron. Soil Sci. 54:481-491.

(2008) 22. Relationship between Nitrogen Use Efficiency and Response Index in Winter Wheat (J. Plant Nutr.) (pdf)

(2009) 23. In-season optical sensing improves nitrogen-use efficiency for winter wheat.

(2011) 24. Assessment of the nitrogen management strategy using an optical sensor for irrigated wheat.  Agronomy Sust. Development. DOI 10.1007/s13593-011-0005-5

(2011) 25. Red edge as a potential index for detecting differences in plant nitrogen status in winter wheat. J. Plant Nutr. 35:1526-1541.

(2011) 26. By-plant prediction of corn grain yield using optical sensor readings and measured plant height.J. Plant Nutr. 35: 1429-1439.

(2012) 27. Generalized algorithm for variable-rate nitrogen application in cereal grains. Agron. J. 104:378-

(2012) 28. Evaluation of a reduced cost, active, NDVI sensor for crop nutrient management. J. of Sensors. doi:10.1155/2012/582028

(2012) 29. Use of soil moisture data for refined GreenSeeker sensor based nitrogen recommendations in winter wheat (Triticum aestivum L.).  J. Prec. Agric. 14:343-356.

(2013) 30. Use of Optical Sensor Technology for the Fertilization of Wheat (Triticum aestivum L.) Terra Latinoamericana 31:95-103

(2014) 31. In season prediction of nitrogen use efficiency and grain protein in winter wheat, Triticum aestivum L.. Commun. Soil Sci. Plant Anal. 00:1-15. DOI:10.1080/00103624.2014.904337

(2015) 32. Algorithms for in-season Nutrient Management in Cereals. Agron J. 108:(5) 

(2016) 33. Evaluation of mid-season sensor based nitrogen fertilizer recommendations for winter wheat using different estimates of yield potential

(2016) 34.
Development of an in-season estimate of yield potential utilizing optical crop sensors and soil moisture data for winter wheat.

(2016) 35. Variability in Optimum Nitrogen Rates for Maize. Agron. J. 108:2165-2173. (doi:10.2134/agronj2016.03.0139)

(2017) 36. Predicting early season nitrogen rates of corn using indicator crops. Agron. J. 109:1-8 (2017

(2018) 37.
Effect of nitrogen fertilizer source on corn (Zea mays L.) optical sensor response index values in a rain-fed environment.  J. Plant Nutr.

Outline for Generating New Crop Algorithms for N Fertilization
Link for computing cumulative GDD by ZIP Code (Syngenta)
What Do N Rich Strips Say About N Rate Algorithms, and Geostatistics and Sampling NDVI, John Solie, University Perspective
Yield Potential Prediction Equations:  Coefficients
Wheat:  INSEY = (NDVI / days from planting to sensing where GDD>0)
Corn:  NDVI  / cumulative GDD

NUE Conference, Generalized Algroithm (excel file), J. Solie, August 4, 2012

  #  Condition Crop Year Equation Units NUE RI Adjustment Equation
1 Dryland Winter Wheat  2002 YP0=344*EXP(INSEY*267.65) kg/ha 50
2 Dryland Winter Wheat  2003 YP0=500*EXP(INSEY*267.65) kg/ha 50
3 Dryland Winter Wheat 2004 YP0=359*EXP(INSEY*324.4) kg/ha 50
4 Dryland Winter Wheat 2005 YP0=522*EXP(INSEY*274.7) kg/ha 50 RI Harvest = 1.69(RI-NDVI) -0.70
5 Dryland Winter Wheat 2006 YP0=532*EXP(INSEY*270.1) kg/ha 50 RI Harvest = 1.69(RI-NDVI) -0.70
6 Dryland Winter Wheat 2016 YP0=590*EXP(INSEY*258.2) this includes 1SD kg/ha 50 RI Harvest = 1.69(RI-NDVI) -0.70
7 Dryland Winter Wheat 2007 Mod CoefA = 0.383516x2 - 91.989634x + 6214.147063
CoefB = -0.000423x2 + 0.099424x - 3.746111
YP0 = (CoefA * EXP (CoefB * NDVI))
kg/ha 50 RI Harvest = 1.69(RI-NDVI) -0.70
8 Dryland Winter Wheat, KSU-OSU 2015 YP0=734.57*EXP(INSEY*212.14) kg/ha 50 RI Harvest = 1.11(RI-NDVI) + 0.11
9 Dryland Winter Wheat-Forage 2007 YP0 = 159.57*EXP(3.909*NDVI) kg/ha 50
10 Dryland & Irrigated Durum Wheat 2006 YP0=322*EXP(INSEY*211.5) kg/ha   RI Harvest = 1.69(RI-NDVI) -0.70
11 Dryland & Irrigated Durum Wheat (for increased protein) 2006 YP0=322*EXP(INSEY*211.5)* *apply 20 kg N/ha when projected yield exceeds 4000 kg/ha kg/ha  
12 Rainfed Wheat-Southern Australia, David Cox 2006 YP0=1800*EXP(INSEY*85) kg/ha 60 RI Harvest = 1.69(RI-NDVI) -0.70
13 Rainfed Wheat, E. Australia, R. Heath 2006 YP0=580*EXP(INSEY*244.94) kg/ha 60 RI Harvest = 1.69(RI-NDVI) -0.70
14 Rainfed Bolivia Maiz (Corn), Bolivia 2017 YP0=201.62*EXP(INSEY*195.09) kg/ha 60 INSEY= NDVI / dias desde la siembra a la medida
15 Irrigated Corn 2003 YP0=2332.9*(EXP(INSEY*132.46) kg/ha 50
16 Dryland Corn 2003 YP0=1633*(EXP(INSEY*132.46) kg/ha 50
17 Dryland & Irrigated Corn 2004 YP0=1565*(EXP(INSEY*154.7) kg/ha 50 RI Harvest = 1.64(RI-NDVI) - 0.5287
18 Rainfed Corn (1st planting, Argentina) 2005 YP0=1941*(EXP(INSEY*162) kg/ha 50 RI Harvest = 1.64(RI-NDVI)-0.5287
19 Irrigated Corn (2nd planting, Argentina) 2005 YP0=624*(EXP(INSEY*149.41) kg/ha 50
20 Rainfed Corn (USA) 2006 YP0=1202*(EXP(INSEY*169.6) kg/ha 50 RI Harvest = 1.64(RI-NDVI)-0.5287
21 Irrigated/Rainfed Corn USA, Cummulative GDD, Southern US Grain Belt

** because of the misuse of these equations for northern US regions, we can work with you to generate YP0 functions specific to your state/area.  This version is in Metric units and has been metric since 2007.  (in All_2018_CornYield_GDD.xls)
2007 YP0=2592*(EXP(NDVI/Sum of GDD*1775.6) kg/ha 50 RI Harvest = 1.64(RI NDVI) -0.5287
22 Irrigated/Rainfed Corn USA, Cummulative GDD, Southern US Grain Belt

* because of the misuse of these equations for northern US regions, we can work with you to generate YP0 functions specific to your state/area.  This version is in English units and has been in English  units (bu/ac) since 2009.
2009 YP0=1.291*(EXP(NDVI/Sum of GDD*2649.9) bu/ac RI Harvest = 1.64(RI NDVI) -0.5287
USA link for computing cumualtive GDD
23 Corn Colombia 2014 YP0 =1633*(EXP(INSEY*132.4)) 60
24 Corn Colombia (Llanos orientales) 2015 YP0=60.9*(EXP(INSEY*252.6)) kg/ha 60
25 Rainfed Corn Ohio 2008 YP0=1287*(EXP(NDVI/Sum of GDD*2655) kg/ha   RI Harvest = 1.64(RI NDVI) -0.5287
26 Irrigated/Rainfed Corn (USA), days from planting to sensing 2007 CoefA = 11.777*(days*days) - 1485.4*(days)+48533
CoefB = -0.0008(days*days) + 0.1402*(days)-3.3851
YP0 = (CoefA * EXP (CoefB * NDVI))

days = days from planting to sensing

kg/ha RI Harvest = 1.64(RI NDVI) -0.5287


Corn (USA) Using Cumulative GDD



(x = cumulative GDD)
YP0 = (CoefA * EXP (CoefB * NDVI))



RI Harvest = 1.64(RI NDVI) -0.5287

28 Rainfed Sorghum 2005 YP0=72*(EXP(INSEY*296.2) kg/ha   none
29   Sorghum KSU-OSU 2006 YP0=633*(EXP(INSEY*141.94)      
30 Sorghum KSU  2007 new YP0=58.689*(EXP(INSEY*273.47) kg/ha RI-Harvest=2.104*RI NDVI -1.044
31 Rainfed, 50% NUE Sorghum OSU-KSU 2008 2008 YP0=183.37*(EXP(INSEY*217.7) kg/ha   RI Harvest = 1.69*RI NDVI -0.7
32 Irrigated Spring Wheat Mexico 2003 YP0=701*EXP(INSEY*154.91) kg/ha 60  
33 Irrigated Spring Wheat Mexico 2006 YP0=989*EXP(INSEY*130.65) kg/ha 60
34 Irrigated Spring Wheat
Mexico (Melgas)
2007 YP0=1250*EXP(INSEY*106.12) kg/ha 60  
35 Irrigated Spring Wheat,
Baja California, Jesus Santillano
2014 YP0=1087.9*EXP(INSEY*134.69) kg/ha 60  
36 Irrigated Spring Wheat, Baja California, Jesus Santillano 2015

y = 1.0811e(INSEY*135.134)

kg/ha 60 RI Harvest = 1.69*RI NDVI - 0.7
37 Rainfed Spring Wheat INDIA (67-73 days after planting) 2006 YP0=838*EXP(INSEY*177.12) kg/ha 60
38 Rainfed Spring Wheat
2007 YP0=680,547*EXP(NDVI*2701) NDVI a inicios de encanazon kg/ha 60  
39 Rainfed Canada, Spring Wheat 2009 YP0=853.2*exp902.9x  where x=NDVI/GDD0 where GDD0= Sum of daily GDD, base-temp = 0C RI=(RINDVI*1.105)+0.02(max of 2)
40 Dryland Spring Wheat Canada 2005 YP0 = 1659*(exp(732.72*INSEY)) kg/ha 60
41 Dryland Spring Wheat
2008 YP0 = 996.3*(exp(1779*INSEY)) INSEY = NDVI/sum of GDD in F kg/ha 60 RI Harvest = 1.69(RI-NDVI) -0.70
42 Dryland Bermudagrass 2006 YP0 = 728.8*(exp(639.5*(INSEY)) kg/ha 40 none
43 Dryland Canola Canada 2005 YP0=1408.3*exp(744.61*INSEY) kg/ha  
44 Dryland Canola Canada 2008 YP0=885.7*exp(881.5*INSEY), INSEY = NDVI/sum of GDD kg/ha   RI-Harvest=1.69*RI-NDVI - 0.7
45 Dryland Canola Canada 2009 YP0=701.9*exp(632.9x) x=NDVI/GDD0, sum of daily GDD, baste temp = 5C      
46 Rainfed Rice INDIA, 64-28 days after planting 2006 YP0=2104*EXP(INSEY*124.96) kg/ha 60
47 Rainfed North Central
2010 YP0=29.32*EXP(INSEY*4725) INSEY = NDVI/ cum GDD kg/ha 50 RI harvest = 3.33*RI NDVI - 2.315
48 Irrigated South West
Irrigated Cotton
2010 YP0=231.6*EXP(INSEY*3668.1) INSEY = NDVI/ cum GDD kg/ha   RI harvest = 3.33*RI NDVI - 2.315
49 Dryland Cotton 2008 YP0= 235.96*EXP(INSEY*2216.2)  INSEY = NDVI/ cum GDD, with 60F as lower threshold (range of 50 to 80) 50 RI harvest = 1.8579*RI NDVI - 0.932
50 Dryland Malting Barley 2006


Percent N, %

Test weight, lb/bu

Maize (Colombia)



Maize (Argentina)



Maize (USA)



Maize (Minnesota)



Winter Wheat



Winter Wheat (Kansas)



Winter Wheat Forage



Spring Wheat (Ciudad Obregon)



Spring Wheat (Baja California)



Spring Wheat (Dakota's)



Wheat Argentina






Sorghum KANSAS



Spring Wheat (Canada)



Wheat S-Australia



Wheat E Australia






Spring Wheat Argentina



Spring Wheat (India)



Rice (India)



Cotton Lint



Durum Wheat



Canola (Canada)







Spring Wheat



Hopkins, J.W. 1968. Protein content of western canadian hard red spring wheat in relation to some environmental factors. Ag. Meteorology.

Winter Wheat



Debaeke, P., Aussenac, T., Fabre, J.L., Hilaire, A., Pujol, B., and Thuries, L. 1996. Grain nitrogen content of winter bread wheat (Triticium aestivum L.) as related to crop management and to the previos crop. Europen Journal of Agronomy. 5(1996) 273-286.




Heckman, J.R., J.T. Sims, D.B. Beegle, F.J. Coale, J. Herbert, T.W. Bruulsema, and W.J. Bamka. 2003. Nutrient removal by corn grain harvest. Agronomy Journal. 95: 587-591.

Corn (grain)

 0.7 to 1.25 (lb/bu)


Potash and Phosphate Institute. 2001. Nutrients removed in the harvest portion of a crop [Online]. Available at (verified 30 Jan. 2012). Potash and Phosphate Inst., Norcross, GA.

Corn (silage, 67% water)



Potash and Phosphate Institute. 2001. Nutrients removed in the harvest portion of a crop [Online]. Available at (verified 30 Jan. 2012). Potash and Phosphate Inst., Norcross, GA.




Jones C. A. 1983. Field Crop Research 6: 133-147




Mucho R. 1990. Effect of nitrogen on partitioning and yield in grain sorghum under differing environmental conditions in the semi-arid tropics. Field Crop Research 25: 265-278




Mucho R. 1990. Effect of nitrogen on partitioning and yield in grain sorghum under differing environmental conditions in the semi-arid tropics. Field Crop Research 25: 265-278




R. F. Brennan, M. G. Mason & G. H. Walton (2000). Effect of nitrogen fertilizer on the concentrations of oil and protein in canola (brassica napus) seed 23:3, 339-348




E. Assadi, H. Janmohammadi, A. Taghizadeh, and S.Alijani (2011). Nutrient composition of different varities of full-fat canolaseed and nitrogen-corrected true metabolizable energy of full fat canola seed with or without enzyme addition and thermal processing :20:95-101




O.Ozturk, S. Soylu, R. Ada, S. Gezgin, and Babaoglu (2010).Studies on  Differential Response of Spring Canola Cultivars to Boron Toxicity .33 :1141-1154

Sunflower (seed)



Robinson, R.G.1975.Amino Acid and Elemental Composition of Sunflower and Pumpkin Seeds. Ag.J Vol.67 pg.541-544

N to protein factor  (6.10)




Gholinezhad, E., Aynaband, A., Ghorthapeh, A.H., Noormohamadi, G., and Bernousi, I. 2011.Effect of drought stress and nitrogen rates on grain yield, quality traits and physiological indices in sunflower hybid iroflor at different plant density. World Applied Sciences J. 14(1): 131-139.

N to protein factor (6.10)

Protein =%N x 6.25 or %N x 5.7 in case of wheat grain

1 percent N = 10,000 ppm
1 percent N = 10,000 mg/kg
1 percent N = 10,000 ug/g
1 percent N = 10 g/kg
g/kg = percent

In the figure above, 6 yield potential equations are reported for winter wheat, spring wheat, dryland corn and irrigated corn.  As is noted, the 6 equations are really quite similar.  This is important when considering that the winter wheat equation came from data in Oklahoma, spring wheat from North Dakota, South Dakota, and Mexico, and Corn (both irrigated and dryland), from Mexico, Nebraska, and Oklahoma.  Each production region (country or state specific) may well have minor adjustments that are needed (variety, planting date, etc.), but for the most part these yield potential predictive equations should be accurate.  Regardless, what is apparent here is that all grain yield prediction equations will have the same form. The importance of the yield potential equations is that they accurately reflect what the "yield potential" will be for the growing conditions encountered within a specific year.  "Yield potential" changes from year to year in the exact same field, largely due to temporal variability.  Also, looking at the graphs, our estimate of yield potential is the "yield" you hope to grow given the "current" growth rate (on the day of sensing), thus, the outer edge of the data set is used, and estimated by adding 1 standard deviation along the entire exponential curve.  For all crops (see figures below), very few data points were encountered in the upper left hand corner, noting that this outer edge represented a rather clean upper boundary.  As is noted above, the YP0 equation for wheat is somewhat different that the other crops, largely because many of the days from planting to sensing have GDD<0 (growing degree days or Tmin+Tmax/2 - 4.4C), where growth is not possible.  The growth curve (biomass produced per day), estimated using NDVI (excellent predictor of biomass) has proven to be a reliable parameter for estimating harvested grain yield in winter wheat, spring wheat, and corn (both dryland and irrigated). Actual data for all equations is shown below.  

Spring wheat (Ciudad Obregon), employs a different strategy whereby "maximum yields" can theoretically be achieved from in-season N applications, regardless of how severe the N stress is.  This is consistent with previous studies conducted by Ivan Ortiz-Monasterio showing that the plants can completely recover, provided that the N is applied before Feekes 5, or Zadoks 30 to 31.  Also, the spring wheat algorithm adjusts for "projected N removed" based on an equation established at CIMMYT (figure below).

Figure 2.  Relationship between grain N removed in spring wheat, and grain yield, developed at Ciudad Obregon.

Spring Wheat, Canada, 2004-2007

Corn (V8 to V10)
Winter Wheat (Feekes 5 to Feekes 7)
Spring Wheat (prior to Feekes 7)

INSEY versus Winter Wheat Grain Yield, for 1998-1999 (9 Loc's) and 1998-2004 (35 Loc's), and 2004 (5 Loc's) versus 1998-2004 (35 Loc's).   The ability to establish a yield prediction equation from only one year of data (5 Loc's in 1994) is delineated in the above graph when compared to the yield predication equation for all 35 sites from 1998 to 2004 and that spanned 7 years.

            corn yield prediction

Trimble Pocket Sensor, Greenseeker, NDVI, nitrogen
Comprehensive information on Nitrogen Use Efficiency for cereal crop production