Note: This page is no longer being maintained and is kept for archival purposes only. For current information see our main page. Kurtz-Fernhout Software Developers of custom software and educational simulations. Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company
Garden with Insight
Product area
Help System
Contents
Quick start
Tutorial
How-to
Models

#### 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
Code:
UND = min(4 * bn(3) * deltaB(p), c(NB) * B - (sum with k from 1 to i-1 of) UN)
Variables:
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)
Code:
c(NB) = (bn(1) - bn(3)) * (1.0 - HUI / (HUI + exp(bn(1) - bn(2) * HUI))) + bn(3)
Variables:
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
Code:
same
GWI change: added upper bound of 0.9 * nitrate to n supply (now is similar to P)
Variables:
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
Code:
seemingly much different.
Variables:
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
Code:
no bound here, but it is bounded at 20 kg/ha later in the code
Variables:
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
Code:
same
Variables:
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
Code:
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
Variables:
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))
Code:
FXW = 1.3 * (SW3 - WP3) / (FC3 - WP3) - 0.3
Variables:
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
Code:
bounds checking is not as complex in code
Variables:
FXN = NFixationFractionNitrateFactor
WNO3 = totalNitrateInRootZone_kgPha
RD = rootDepth_m

 Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company Updated: March 10, 1999. Questions/comments on site to webmaster@kurtz-fernhout.com. Copyright © 1998, 1999 Paul D. Fernhout & Cynthia F. Kurtz.