N Fertilizer Optimization Algorithm (NFOA)

1.   Predict potential grain yield or YP₀ (grain yield achievable with no additional N fertilization) from the grain yield-INSEY equation, where;

INSEY = NDVI (Feekes 4 to 6)/days from planting to sensing (days with GDD>0)
YP₀ = 0.74076 + 0.10210 e ^{577.66(INSEY)}   units: (YP₀ in Mg/ha)

2.   Predict the magnitude of response to N fertilization (In-Season-Response-Index, or RI_NDVI).  RI_NDVI, computed as; NDVI from Feekes 4 to Feekes 6 in non-N-limiting fertilized plots divided by NDVI Feekes 4 to Feekes 6 in the farmer check plots (common fertilization practice employed by the farmer).  The non-N limiting (preplant fertilized) strip will be established in the center of each farmer field.

3.   Determine the predicted yield that can be attained with added N (YP_N) fertilization based both on the in-season response index (RI_NDVI) and the potential yield achievable with no added N fertilization, computed as follows:

YP_N       = (YP₀)/ (1/RI_NDVI)
= YP₀ * RI_NDVI  units: (YP_N in Mg/ha)

Limits must be imposed on the above whereby RI_NDVI cannot exceed 2.0, and where YP_N cannot exceed the maximum obtainable yield (YP_MAX). YP_MAX is determined by the farmer, or previously defined as a biological maximum for a specific cereal crop, grown within a specific region, and under defined management practices (e.g., YP_MAX for dryland winter wheat produced in central Oklahoma would be 7.0 Mg/ha).

4.   Predict percent N in the grain (PNG) based on YP_N (includes adjusted yield level)

PNG = -0.1918YP_N  + 2.7836
units: (PNG in %)

5. Calculate predicted grain N uptake (predicted percent N in the grain multiplied times YP_N)

GNUP = PNG*(YP_N/1000)   units: (GNUP in kg/ha)

6. Calculate predicted forage N uptake from NDVI 

FNUP_NDVI = 14.76 + 0.7758 e ^5.468NDVI
units: (FNUP_NDVI in kg/ha)

7. Determine in-season topdress fertilizer N requirement (FNR)= (Predicted Grain N Uptake - Predicted Forage N Uptake)/0.70

FNR = GNUP – FNUP   units: (FNR in kg/ha)

Definitions

INSEY                  In Season Estimated Yield = NDVI (Feekes 4 to 6)/days from planting to sensing (days with GDD>0) = YP₀

GDD                    Growing Degree Days = (Tmin + Tmax)/2 – 4.4°C

RI_NDVI                         = NDVI from plots receiving adequate but not excessive preplant N, divided by NDVI from the farmer check (specific to that field) where preplant N may or may not have been applied.

RI_HARVEST                 = Maximum observed grain yield (treatment average with N fertilizer) divided by the observed grain yield from plots where no N was applied either preplant or topdress

RI_SV                      = Estimate of RI (spatial variability), using the average NDVI value from a random sensor sample (100 m in length) collected in a farmers field + 1 standard deviation, divided by the average NDVI value minus 1 standard deviation.

YP_MAX                  = Maximum obtainable yield level for a specific environment determined by the farmer, or previously defined as a biological maximum by research agronomists for that crop, and for that region (units: Mg/ha)

YP₀                       = Predicted or potential yield based on growing conditions up to the time of sensing, that can be achieved with no additional (topdress) N fertilization  (units: Mg/ha)

YP_N                             = Predicted or potential yield that can be achieved with additional (topdress) N fertilization based on the in-season response index (RI_NDVI) (units: Mg/ha)

                             = (YP₀)/ (1/RI_NDVI)

                             = (YP₀)*(RI_NDVI)

PNG                     = Percent nitrogen in the grain estimated from multiple observations, over years, using various different wheat varieties (likely to be region specific) (units: %)

GNUP                  = Predicted grain N uptake (predicted percent N in the grain multiplied times YP_N/1000) (units: kg/ha)

FNUP                   = Predicted forage N uptake estimated from the calibrated relationship with NDVI  (units: kg/ha)

FNR                     = Fertilizer nitrogen requirement estimated by subtracting predicted forage N uptake (FNUP) from predicted grain N uptake (GNUP) (units: kg/ha)

Restrictions

                     YP_N cannot be > YP_MAX

                             RI_NDVI cannot be > 2.0

Figure 1.  Predicted yield achievable with added N fertilization (YP_N) based on RI_NDVI as a function of predicted yield that can be achieved with no added N fertilization (YP0), where YP_N = (YP₀)/ (1/RI_NDVI).

Lukina, E.V., K.W. Freeman, K.J. Wynn, W.E. Thomason, R.W. Mullen, G.V. Johnson, R.L. Elliott, M.L. Stone, J.B. Solie, and W.R. Raun. 2001. Nitrogen fertilization optimization algorithm based on in-season estimates of yield and plant nitrogen uptake. J. Plant Nutr.