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Appendix 1: Sugarbeet model - equations and parameters

BiomBarley(t) = BiomBarley(t - dt) + (GrowBarley + BarleySeed - HarvBarley) * dt

INIT BiomBarley = 0

GrowBarley = IF(MaxBarley>TotalBiom) THEN (RGRBarley*BiomBarley*(MaxBarley-TotalBiom)/MaxBarley) ELSE 0

BarleySeed = 0.18*BeginBarley

HarvBarley = IF EndBarley=1 THEN (BiomBarley+1)/DT ELSE 0

BiomSubeet(t) = BiomSubeet(t - dt) + (GrowSuBeet + SugarbeetSeed - HarvSugarBeet) * dt

INIT BiomSubeet = 0

GrowSuBeet = IF (RotationYear=1) AND (MaxSuBeet>TotalBiom) THEN(RGRSuBeet*BiomSubeet*(MaxSuBeet-TotalBiom)/(MaxSuBeet)) ELSE 0

SugarbeetSeed = 0.005*BeginSugarBeet

HarvSugarBeet = IF EndSugarBeet=1 THEN (BiomSubeet+1)/DT ELSE 0

BiomWheat(t) = BiomWheat(t - dt) + (GrowWheat + WheatSeed - HarvWheat) * dt

INIT BiomWheat = 0

GrowWheat = IF(MaxWheat>TotalBiom) THEN (Winterperiod*(RGRWheat*BiomWheat*(MaxWheat-TotalBiom)/MaxWheat))/DT ELSE 0

WheatSeed = 0.18*BeginWheat

HarvWheat = IF EndWheat=1 THEN (BiomWheat+1)/DT ELSE 0

MaxBarley = 15

MaxSuBeet = 15

MaxWheat = 18

RGRBarley = 0.075

RGRSuBeet = 0.06

RGRWheat = 0.04

BiomCHEAL(t) = BiomCHEAL(t - dt) + (GrowCHEAL + GermCHEAL - ControlCHEAL - DebriCHEAL) * dt

INIT BiomCHEAL = 0

GrowCHEAL = IF(MaxCHEAL>TotalBiom) THEN(Winterperiod*RGRCHEAL*BiomCHEAL*((MaxCHEAL-TotalBiom)/MaxCHEAL)) ELSE 0

GermCHEAL = DELAY(BeginWeed,1)*SeedbankCHEAL

ControlCHEAL = BiomCHEAL*EffiCHEAL

DebriCHEAL = EndWeed* (BiomCHEAL)

BiomELYRE(t) = BiomELYRE(t - dt) + (GrowELYRE + InitialELYRE - ControlELYRE - DebriELYRE) * dt

INIT BiomELYRE = 0

GrowELYRE = IF(BiomassCrop>0 AND MaxELYRE>TotalBiom) THEN(Winterperiod*RGRELYRE*BiomELYRE*((MaxELYRE-TotalBiom)/MaxELYRE)) ELSE 0

InitialELYRE = 0.05*ELYREinField*BeginWeed

ControlELYRE = BiomELYRE*EffiELYRE

DebriELYRE = EndWeed* (BiomELYRE)/DT*0.92

BiomSTEME(t) = BiomSTEME(t - dt) + (GrowSTEME + GermSTEME - ControlSTEME - DebriSTEME) * dt

INIT BiomSTEME = 0

GrowSTEME = IF(MaxSTEME>TotalBiom) THEN(Winterperiod*RGRSTEME*BiomSTEME*((MaxSTEME-TotalBiom)/MaxSTEME)) ELSE 0

GermSTEME = DELAY(BeginWeed,1)*SeedbankSTEME

ControlSTEME = BiomSTEME*EffiSTEME

DebriSTEME = EndWed* (BiomSTEME)

BiomVIOAR(t) = BiomVIOAR(t - dt) + (GrowVIOAR + GermVIOAR - ControlVIOAR - DebriVIOAR) * dt

INIT BiomVIOAR = 0

GrowVIOAR = IF(MaxVIOAR>TotalBiom) THEN(Winterperiod*RGRVIOAR*BiomVIOAR*((MaxVIOAR-TotalBiom)/MaxVIOAR)) ELSE 0

GermVIOAR = DELAY(BeginWeed,1)*SeedbankVIOAR

ControlVIOAR = BiomVIOAR*EffiVIOAR

DebriVIOAR = EndWeed* (BiomVIOAR)

SeedPoolCHEAL(t) = SeedPoolCHEAL(t - dt) + (NewSeedCHEAL - DeadSeedCHEAL) * dt

INIT SeedPoolCHEAL = 45297435.89744

NewSeedCHEAL = (DebriCHEAL)/DT*30000*1000/0.5

DeadSeedCHEAL = IF(BeginWeed=1) THEN SeedPoolCHEAL/3 ELSE 0

SeedPoolSTEME(t) = SeedPoolSTEME(t - dt) + (NewSeedSTEME - DeadSeedSTEME) * dt

INIT SeedPoolSTEME = 40333333.33333

NewSeedSTEME = (DebriSTEME)/DT*7000*1000/0.200

DeadSeedSTEME = IF(BeginWeed=1) THEN SeedPoolSTEME/3 ELSE 0

SeedPoolVIOAR(t) = SeedPoolVIOAR(t - dt) + (NewSeedVIOAR - DeadSeedVIOAR) * dt

INIT SeedPoolVIOAR = 35369230.76923

NewSeedVIOAR = (DebriVIOAR)/DT*600*1000/0.05

DeadSeedVIOAR = IF(BeginWeed=1) THEN SeedPoolVIOAR/3 ELSE 0

ELYREinField = 1

MaxCHEAL = 9.5

MaxELYRE = 14

MaxSTEME = 6

MaxVIOAR = 5

RGRCHEAL = 0.073

RGRELYRE = 0.034

RGRSTEME = 0.08

RGRVIOAR = 0.07

SeedbankCHEAL = SeedPoolCHEAL*0.01/1000000*0.05

SeedbankSTEME = SeedPoolSTEME*0.015/1000000*0.05

SeedbankVIOAR = SeedPoolVIOAR*0.02/1000000*0.05

BiomassCrop = BiomBarley+BiomSubeet+BiomWheat

BiomSenWeed = BiomCHEAL+BiomELYRE+BiomSTEME+BiomVIOAR

BiomSUResWeed = BiomSTEME_2

BioVolunteer = BiomBarley_2+BiomSubeet_2+BiomWheat_2

DicotWeeds = BiomCHEAL+BiomSTEME+BiomVIOAR+BiomSubeet_2+BiomSTEME_2

MonocotWeeds = BiomELYRE+BiomBarley_2+BiomWheat_2

SitePotential = 20

TotalBiom = (BiomassCrop+BiomSenWeed+BioVolunteer+BiomSUResWeed)

BiomSTEME_2(t) = BiomSTEME_2(t - dt) + (GrowSTEME_2 + GermSTEME_2 - ControlSTEME_2 - DebriSTEME_2) * dt

INIT BiomSTEME_2 = 0

GrowSTEME_2 = IF(MaxSTEME>TotalBiom) THEN(Winterperiod*RGRSTEME*BiomSTEME_2*((MaxSTEME-TotalBiom)/MaxSTEME)) ELSE 0

GermSTEME_2 = DELAY(BeginWeed,1)*SeedbankSTEME_2

ControlSTEME_2 = IF SU=0 THEN BiomSTEME_2*EffiSTEME ELSE 0

DebriTEME_2 = EndWeed* (BiomSTEME_2)

SeedPoolSTEME_2(t) = SeedPoolSTEME_2(t - dt) + (NewSeedSTEME_2 - DeadSeedSTEME_2) * dt

INIT SeedPoolSTEME_2 = 0

NewSeedSTEME_2 = (DebriSTEME_2)/DT*7000*1000/0.200

DeadSeedSTEME_2 = IF(BeginWeed=1) THEN SeedPoolSTEME_2/3 ELSE 0

IniSuSTEME_2 = 1/10000000

SeedbankSTEME_2 = (IniSuSTEME_2*SeedPoolSTEME*0.015/1000000*0.05)+(SeedPoolSTEME_2*0.015/1000000*0.05)

RotationYear(t) = RotationYear(t - dt) + (RotationYearRate - RotationYearReset) * dt

INIT RotationYear = 0

RotationYearRate = IF DaysInYear=1 THEN DaysInYear/DT ELSE 0

RotationYearReset = IF RotationYear>4 THEN ((RotationYear-1)/DT) ELSE(0)

Years(t) = Years(t - dt) + (YearRate) * dt

INIT Years = 0

YearRate = If DaysInYear=1 THEN DaysInYear/DT ELSE 0

BeginBarley = IF RotationYear=2 AND DaysInYear=75 THEN 1 ELSE 0

BeginSugarBeet = IF RotationYear=1 AND DaysInYear=90 THEN 1 ELSE 0

BeginWeed = IF (BeginBarley=1 OR BeginSugarBeet=1 OR BeginWheat=1) THEN 1 ELSE 0

BeginWheat = IF RotationYear>1 AND RotationYear<4 AND DaysInYear=258 THEN 1 ELSE 0

DaysInYear = COUNTER(1,366)

DaysTotal = TIME

EndBarley = IF RotationYear=2 AND DaysInYear=229 THEN 1 ELSE 0

EndSugarBeet = IF RotationYear=1 AND DaysInYear=304 THEN 1 ELSE 0

EndWeed = IF(EndBarley=1 OR EndSugarBeet=1 OR EndWheat=1) THEN 1 ELSE 0

EndWheat = IF RotationYear>2 AND DaysInYear=239 THEN 1 ELSE 0

Winterperiod = IF DaysInYear>325 OR DaysInYear<60 THEN 0 ELSE 1

BiomBarley_2(t) = BiomBarley_2(t - dt) + (GrowBarley_2 + BarleySeed_2 - HarvBarley_2 - WinterMortalityBarley_2 - ControlBarley_2) * dt

INIT BiomBarley_2 = 0

GrowBarley_2 = IF(MaxBarley_2>TotalBiom) THEN (Winterperiod*RGRBarley_2*BiomBarley_2*(MaxBarley_2-TotalBiom)/MaxBarley_2)/DT ELSE 0

BarleySeed_2 = DELAY(BeginWeed,1)*(SeedPoolBarley_2*0.7*0.05/1000000)

HarvBarley_2 = IF EndWeed=1 THEN (BiomBarley_2+1)/DT ELSE 0

WinterMortalityBarley_2 = IF Winterperiod=0 THEN BiomBarley_2*0.8 ELSE 0

ControlBarley_2 = BiomBarley_2*EffiBarley

BiomSubeet_2(t) = BiomSubeet_2(t - dt) + (GrowSuBeet_2 + SugarbeetSeed_2 - HarvSugarBeet_2 - ControlSBeet_2) * dt

INIT BiomSubeet_2 = 0

GrowSuBeet_2 = IF(MaxSuBeet_2>TotalBiom) THEN (Winterperiod*RGRSuBeet_2*BiomSubeet_2*(MaxSuBeet_2-TotalBiom)/(MaxSuBeet_2)) ELSE 0

SugarbeetSeed_2 = DELAY(BeginWeed,1)*(SeedPoolSugarBeet_2*0.7*0.04/1000000)

HarvSugarBeet_2 = IF EndWeed=1 THEN (BiomSubeet_2+1)/DT ELSE 0

ControlSuBeet_2 = BiomSubeet_2*EffiSugarBeet

BiomWheat_2(t) = BiomWheat_2(t - dt) + (GrowWheat_2 + WheatSeed_2 - HarvWheat_2 - ControlWheat_2) * dt

INIT BiomWheat_2 = 0

GrowWheat_2 = IF(MaxWheat_2>TotalBiom) THEN (Winterperiod*RGRWheat_2*BiomWheat_2*(MaxWheat_2-TotalBiom)/MaxWheat_2)/DT ELSE 0

WheatSeed_2 = DELAY(BeginWeed,1)*(SeedWheat_2*0.7*0.05/1000000)

HarvWheat_2 = IF EndWeed=1 THEN (BiomWheat_2+1)/DT ELSE 0

ControlWheat_2 = BiomWheat_2*EffiWheat

SeedPoolBarley_2(t) = SeedPoolBarley_2(t - dt) + (NewSeedBarley_2 - DeadSeedBarley_2) * dt

INIT SeedPoolBarley_2 = 0

NewSeedBarley_2 = (HarvBarley+HarvBarley_2-2)/DT*SeedLossBarley*0.5*1000000/0.05

DeadSeedBarley_2 = IF(BeginWeed=1) THEN SeedPoolBarley_2*95/100 ELSE 0

SeedPoolSugarBeet_2(t) = SeedPoolSugarBeet_2(t - dt) + (NewSeedSugarBeet_2 - DeadSeedSugarBeet_2) * dt

INIT SeedPoolSugarBeet_2 = 0

NewSeedSugarBeet_2 = (HarvSugarBeet+HarvSugarBeet_2-2)*(85000*2000*SeedLossSugarBeet/MaxSuBeet_2)

DeadSeedSugarBeet_2 = IF(BeginWeed=1) THEN SeedPoolSugarBeet_2*7/10 ELSE 0

SeedWheat_2(t) = SeedWheat_2(t - dt) + (NewSeedWheat_2 - DeadSeedWheat_2) * dt

INIT SeedWheat_2 = 0

NewSeedWheat_2 = (HarvWheat+HarvWheat_2-2)/DT*SeedLossWheat*0.5*1000000/0.05

DeadSeedWheat_2 = IF(BeginWeed=1) THEN SeedWheat_2*95/100 ELSE 0

MaxBarley_2 = 15

MaxSuBeet_2 = 15

MaxWheat_2 = 18

RGRBarley_2 = 0.07

RGRSuBeet_2 = 0.06

RGRWheat_2 = 0.04

SeedLossBarley = 0.05

SeedLossSugarBeet = 0.0025

SeedLossWheat = 0.05

DicotBarley(t) = DicotBarley(t - dt) + (SprayDicotBarley) * dt

INIT DicotBarley = 0

SprayDicotBarley = IF (BiomBarley>0) AND (DicotWeeds>1) THEN (DoseDicotBarley+DoseXtraBarley) ELSE 0

DicotWheat(t) = DicotWheat(t - dt) + (SprayDicotWheat) * dt

INIT DicotWheat = 0

SprayDicotWheat = IF(BiomWheat>0 AND BiomWheat<2) AND (DicotWeeds>0.5) THEN (DoseDicotWheat+DoseXtraWheat) ELSE 0

GlufHerbicidSugarBeet(t) = GlufHerbicidSugarBeet(t - dt) + (SprayGlufSugarBeet) * dt

INIT GlufHerbicidSugarBeet = 0

SprayGlufSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=1 AND SUResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<2) AND ((DicotWeeds+MonocotWeeds)>1.5) THEN DoseGlufSugarBeet ELSE 0

GlyphHerbicidSugarBeet(t) = GlyphHerbicidSugarBeet(t - dt) + (SprayGlyphSugarBeet) * dt

INIT GlyphHerbicidSugarBeet = 0

SprayGlyphSugarBeet = IF (GlyphResSugarBeet=1 AND GlufResSugarBeet=0 AND SUResSugarBeet=0 AND BiomSubeet>0.01 AND BiomSubeet<2 AND (DicotWeeds+MonocotWeeds)>1.5) THEN DoseGlyphSugarBeet ELSE 0

MonocotBarley(t) = MonocotBarley(t - dt) + (SprayMonocotBarley) * dt

INIT MonocotBarley = 0

SprayMonocotBarley = IF (BiomBarley>0) AND (DaysInYear=228) AND (BiomELYRE>1) THEN DoseMonocotBarley ELSE 0

MonocotHerbicidSugarBeet(t) = MonocotHerbicidSugarBeet(t - dt) + (SprayMonocotSugarBeet) * dt

INIT MonocotHerbicidSugarBeet = 0

SprayMonocotSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<2.5) AND (MonocotWeeds>0.3) THEN DoseMonocotSugarBeet ELSE 0

MonocotWheat(t) = MonocotWheat(t - dt) + (SprayMonocotWheat) * dt

INIT MonocotWheat = 0

SprayMonocotWheat = IF (BiomWheat>10) AND (DaysInYear=238) AND (BiomELYRE>1) THEN DoseMonocotWheat ELSE 0

SUHerbicidSugarBeet(t) = SUHerbicidSugarBeet(t - dt) + (SpraySUSugarBeet) * dt

INIT SUHerbicidSugarBeet = 0

SpraySUSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0 AND SUResSugarBeet=1) AND (BiomSubeet>0 AND BiomSubeet<0.9) AND (DicotWeeds>0.4) THEN (DoseSUSugarBeet+DoseXtraSugarbeet) ELSE 0

TradHerbicidSugarBeet(t) = TradHerbicidSugarBeet(t - dt) + (SprayTradSugarBeet) * dt

INIT TradHerbicidSugarBeet = 0

SprayTradSugarBeet = IF (GlyphResSugarBeet=0 AND GlufResSugarBeet=0 AND SUResSugarBeet=0) AND (BiomSubeet>0 AND BiomSubeet<0.9) AND (DicotWeeds>0.4) THEN DoseTradSugarBeet ELSE 0

DoseDicotBarley = WeedControl*0.007

DosDicotWheat = WeedControl*0.007

DoseGlufSugarBeet = 0.6*WeedControl

DoseGlyphSugarBeet = 0.72*WeedControl

DoseMonocotBarley = 3*0.360*WeedControl

DoseMonocotSugarBeet = 0.219*WeedControl

DoseMonocotWheat = 3*0.360*WeedControl

DoseSUSugarBeet = 0.007*WeedControl

DoseTradSugarBeet = 1.07*WeedControl

DoseXtraBarley = IF Problem=1 THEN 0.126 ELSE 0

DoseXtraSugarbeet = IF Problem=1 THEN 0.360 ELSE 0

DoseXtraWheat = IF Problem=1 THEN 0.144 ELSE 0

EffiBarley = EfGluBarley+EfGlyBarley+EfHalBarley

EffiCHEAL = EfGluCHEAL+EfGlyCHEAL+EfSUCHEAL+EfTradCHEAL+EfSUXtraCHEAL

EffiELYRE = EfGluELYRE+EfGlyELYRE+EfHalELYRE

EffiSTEME = EfGluSTEME+EfGlySTEME+EfSUSTEME+EfTradSTEME+EfSUXtraSTEME

EffiSugarBeet = EfGluSuBeet+EfGlySuBeet+EfSUSuBeet+EfSUXtraSuBeet

EffiVIOAR = EfGluVIOAR+EfGlyVIOAR+EfSUVIOAR+EfTradVIOAR+EfSUXtraVIOAR

EffiWheat = EfGluWheat+EfGlyWheat+EfHalWheat

EfGluBarley = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGluCHEAL = IF Glufosinate>0 THEN 0.95 ELSE 0

EfGluELYRE = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGluSTEME = IF Glufosinate>0 THEN 0.95 ELSE 0

EfGluSuBeet = IF GlufResSugarBeet=0 AND Glufosinate>0 THEN 0.7 ELSE 0

EfGluVIOAR = IF Glufosinate>0 THEN 0.75 ELSE 0

EfGluWheat = IF Glufosinate>0 THEN 0.7 ELSE 0

EfGlyBarley = IF SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfGlyCHEAL = IF SprayGlyphSugarBeet>0 THEN 0.95 ELSE 0

EfGlyELYRE = IF SprayGlyphSugarBeet>0 OR GlyphosatePreHarv>0 THEN 0.99 ELSE 0

EfGlySTEME = IF SprayGlyphSugarBeet>0 THEN 0.95 ELSE 0

EfGlySuBeet = IF GlyphResSugarBeet=0 AND SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfGlyVIOAR = IF SprayGlyphSugarBeet>0 THEN 0.75 ELSE 0

EfGlyWheat = IF SprayGlyphSugarBeet>0 THEN 0.99 ELSE 0

EfHalBarley = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfHalELYRE = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfHalWheat = IF Haloxyfob_ethoxyethyl>0 THEN 0.95 ELSE 0

EfSUCHEAL = IF SU>0 THEN 0.8 ELSE 0

EfSUSTEME = IF SU>0 THEN 0.8 ELSE 0

EfSUSuBeet = IF SUResSugarBeet=0 AND SU>0 THEN 0.98 ELSE 0

EfSUVIOAR = IF SU>0 THEN 0.75 ELSE 0

EfSUXtraCHEAL = IF SU&Xtra>0 THEN 0.9 ELSE 0

EfSUXtraSTEME = IF U&Xtra>0 THEN 0.9 ELSE 0

EfSUXtraSuBeet = IF SUResSugarBeet=0 AND SU&Xtra>0 THEN 0.98 ELSE 0

EfSUXtraVIOAR = IF SU&Xtra>0 THEN 0.8 ELSE 0

EfTradCHEAL = IF TradMixture>0 THEN 0.80 ELSE 0

EfTradSTEME = IF TradMixture>0 THEN 0.75 ELSE 0

EfTradVIOAR = IF TradMixture>0 THEN 0.60 ELSE 0

Glufosinate = SprayGlufSugarBeet

GlufResSugarBeet = 0

Glyphosate = SprayGlyphSugarBeet+GlyphosatePreHarv

GlyphosatePreHarv = SprayMonocotWheat+SprayMonocotBarley

GlyphResSugarBeet = 1

Haloxyfob_ethoxyethyl = SprayMonocotSugarBeet

HerbUseBarley = DicotBarley+MonocotBarley

HerbUseSugarBeet = GlufHerbicidSugarBeet+GlyphHerbicidSugarBeet+MonocotHerbicidSugarBeet+SUHerbicidSugarBeet+TradHerbicidSugarBeet

HerbUseWheat = DicotWheat+MonocotWheat

Problem = IF BiomSUResWeed/BiomSenWeed>0.25 THEN 1 ELSE 0

SU = IF Problem=0 THEN (SprayDicotBarley+SprayDicotWheat+SpraySUSugarBeet) ELSE 0

SU&Xtra = IF Problem=1 THEN (SprayDicotBarley+SprayDicotWheat+SpraySUSugarBeet) ELSE 0

SUResSugarBeet = 0

TotalHerbUse = HerbUseBarley+HerbUseSugarBeet+HerbUseWheat

TradMixture = SprayTradSugarBeet