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Garden with Insight v1.0 Help: Plant Growth - Nitrogen

Supply and Demand

Crop use of N is estimated by using a supply and demand approach. The daily crop N demand is the difference between the crop N content and the ideal N content for that day. The demand is estimated with the equation [Equation 276] where UND is the N demand rate of the crop in kg/ha*day, c(NB) is the optimal N concentration of the crop in kg/t, B is the accumulated biomass in t/ha for day i, and UN is the actual N uptake rate in kg/hg*day.

Equation 276

UND = c(NB) * B - (sum with k from 1 to i-1 of) UN
UND = min(4 * bn(3) * deltaB(p), c(NB) * B - (sum with k from 1 to i-1 of) UN)
UND = PlantNitrogenDemandForOptimalGrowth_kgPha
c(NB) = plantOptimalNConc_kgPkg
B = totalPlantBiomass_tPha
sum of UN(k) = cumNUptake_kgPha

Optimal N concentration for crop

The optimal crop N concentration declines with increasing growth stage (Jones, 1983a) and is computed as a function of growth stage by using the equation [Equation 277] where bn(1), bn(2) and bn(3) are crop parameters expressing N concentration and HUI (heat unit index) is the fraction of the growing season.

Equation 277

c(NB) = bn(1) + bn(2) * exp(-bn(3) * HUI)
c(NB) = (bn(1) - bn(3)) * (1.0 - HUI / (HUI + exp(bn(1) - bn(2) * HUI))) + bn(3)
c(NB) = PlantoptimalNConc_kgPkg
bn(1) = plantOptimalNConcParams[0
bn(2) = plantOptimalNConcParams[1
bn(3) = plantOptimalNConcParams[2
HUI = heatUnitIndex

Supply of N in the soil layers

Soil supply of N is assumed to be limited by mass flow of NO3-N to the roots [Equation 278] where UN is the rate of N supplied by the soil in kg/ha*day, WNO3 is the amount of NO3-N in kg/ha, SW is the soil water content in mm, u is water use rate in mm/day, and subscript l refers to the soil layers.

Equation 278

UN(l) = u(l) * WNO3 / SW
GWI change: added upper bound of 0.9 * nitrate to n supply (now is similar to P)
UN(l) = NSupplyForLayer_kgPha
u(l) = plantWaterUse_mm
WNO3 = nitrate_kgPha
SW = waterContent_mm

Totaling the N available in the layers

The total mass flow supply is estimated by summing the layer supplies: [Equation 279] where UNS is the N supply rate from soil to plants in kg/ha.
special equation not needed. done in other code.

Adjusting the N available in the layers for high or low amounts

Since mass flow uptake can produce questionable results when N concentrations are extremely high or low, UN values obtained from equation 278 are adjusted: [Equation 280]. Equation 280 assures that actual N uptake cannot exceed the plant demand when mass flow estimates are too large. It also provides for increased N supply when mass flow estimates are too low despite the availability of NO3.

Equation 280

UN(a) = UN * UND / UNS, UN(a) <= WNO3
seemingly much different.
UN(a) = ActualNUptakeByLayer_kgPha
UN = nUptake_kgPha
UND = nDemand_kgPha
UNS = totalSupply_kgPha
WNO3 = nitrate_kgPha

Nitrogen Fixation (for legumes)

Daily N fixation is estimated as a fraction of daily plant N uptake for legumes: [Equation 281] where WFX is the amount of N fixation in kg/ha and FXR is the fraction of uptake for day i.

Equation 281

WFX = FXR * UN, WFX <= 6.0
no bound here, but it is bounded at 20 kg/ha later in the code
WFX = NFixation_kgPha
FXR = nFixationFraction_frn
UN = nDemand_kgPha

The fraction, FXR, is estimated as a function of soil NO3 content and water content and plant growth stage [Equation 282] where FXG is the plant growth stage factor, FXW is the soil water content factor, and FXN is the soil NO3 content factor.

Equation 282

FXR = min(1.0, FXW, FXN) * FXG
FXR = NFixationFraction_frn
FXW = nFixationFractionWaterFactor
FXN = nFixationFractionNitrateFactor
FXG = nFixationFractionGrowthStageFactor

The growth stage factor inhibits N fixation in young plants prior to development of functional nodules and in old plants with senescent nodules (Patterson and LaRue, 1983) [Equation 283], [Equation 284], [Equation 285] and [Equation 286] where HUI is the heat unit index for day i.

Equation 283, 284, 285, 286

if HUI <= 0.15 or HUI > 0.75, FXG = 0.0
if 0.15 < HUI <= 0.3, FXG = 6.67 * HUI - 1.0
if 0.3 < HUI <= 0.55, FXG = 1.0
if 0.55 < HUI <= 0.75, FXG = 3.75 - 5.0 * HUI
FXG = min((HUI - 0.1 * 5), min(4 - 5 * HUI, 1))
the first case (HUI < 0.15 or > 0.75) is avoided by an if statement outside of this
the other three cases match (not exactly) the cases below
FXG = NFixationFractionGrowthStageFactor
HUI = heatUnitIndex

The soil water content factor reduces N fixation when the water content at the top 0.3 m of soil is less than 85% of field capacity (Albrecht et al., 1984, Bouniols et al., 1991) using the equation [Equation 287] where SW3, WP3, and FC3 are the water contents in the top 0.3 m of soil on day i, at wilting point, and at field capacity.

Equation 287

if SW3 < 0.85 * (FC3 - WP3) + WP3,
FXW = (SW3 - WP3) / (0.85 * (FC3 - WP3))
FXW = 1.3 * (SW3 - WP3) / (FC3 - WP3) - 0.3
FXW = NFixationFractionWaterFactor
SW3 = soilWaterContentTop30cm_mm
WP3 = wiltingPointTop30cm_mm
FC3 = fieldCapacityTop30cm_mm

The amount of NO3 in the root zone can affect N fixation (Harper, 1976; Bouniols et al., 1985) and determines the soil NO3 factor, FXN [Equation 288], [Equation 289] and [Equation 290] where WNO3 is the weight of NO3-N in the root zone in kg/ha*m and RD is the root depth in m. This approach reduces N fixation when the NO3-N content of the root zone is greater than 100 kg/ha*m and prohibits N fixation at N contents greater than 300 kg/ha*m.

Equation 288, 289, 290

if WNO3 > 300, FXN = 0
if 100 < WNO3 < 300, FXN = 1.5 - 0.005 * WNO3 / RD
if WNO3 < 100, FXN = 1.0
bounds checking is not as complex in code
FXN = NFixationFractionNitrateFactor
WNO3 = totalNitrateInRootZone_kgPha
RD = rootDepth_m

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Updated: May 4, 1998. Questions/comments on site to
Copyright © 1998 Paul D. Fernhout & Cynthia F. Kurtz.