Testing models to destruction

1. Testing models to destruction Neil Crout Environmental Science School of Biosciences University of Nottingham UK

2. Models and falsification • Can’t prove something is true • So standard approach is to falsify • Models are simplified approximations • So we know they are wrong • Hard to falsify in a regular way • Models are an assembly of relationships • Hard to separate their influence on one another • Hard to falsify in a regular way • So, model evaluation is dependent on purpose • Surely correct, but is this sufficient?

3. Can we falsify the model design through reduction? For each model relationship test the hypothesis, H, Reducing the relationship to a constant will increase the discrepancy between prediction and observation H =

4. Reduction by variable replacement

5. Reduction by variable replacement

6. Roots Vernalisation EVAPO CANOPY SOIL.AW[1..30] TempMax TempMin exw[1..30] Rootlen Potlfno TTOPT TTFIX TTOUT SLOSL ECUM TTOUT Amnlfno Soilmax aw[1..30 AVWATER WATCON SHOUT CanTemp PrimordNo Vprog TTROOT SoilMin Def Leafnumber HSLOP(Tmean) TTCAN LAIStage PHENO TTOUT DrFacLAI Rootlength Areamax PTSOIL RN Rad PTAY WINTER Leafarea Alpha Reduc CROPUP PENMAN TAU GAKLIR Areaopt Lastleaf FleafNo SF Anthesis PotTrans Deadleaves Maxgaklir leafarea IPHASE Anthesis TTOUT Transp AreaANTH BIOANTH EVSOIL GRAIN Therm Biomass Reduc EVAP ENAV Grainstart CropN CONDUC Hcrop BiomassBGF BiomassBGF Demand Hsoil Grainend BIOANTH TCMax TTOUT TCmin Biomass TDeepsoil DrFacLai Inputs SF DrFacgrowth Soilmin GrainDM Temp Min Temp Max GrainNoverGrainDm tadj Tmean Soilmax LeafNc TTOUT TDeepsoil MinGrainDemand Temp Max Temp Max Water balance Rain GrainDemand UptakeN AvN VARIETY Si Soil leafarea Radiation AreaANTH leafarea Dry matter SoilN DeadLeafN GrainN PoolN Lastleaf EarWt Therm RUE ExStemNc StemNc ExLeafNc Anthesis SF Biomass Tau PAR drfacgrowth rad CropN Equilibrium leafarea uw[1..30] exw[1..30] aw[1..30] Naw[1..30] Nex[1..30] biomass dn stembiomass MaxStemdemand AvN Rootlen Naw[1..30] Nuw[1..30] Nex[1..30] Soil moisture SF Percolation StemN N’Pulses anforP Wateruptake Rain+Irr exw[1] SumP Fert minstemDemand UptakeN Rootlen Norganic Tmean aw[1] Q Nf Q exw[1..30] StemNc AW[1..30] Waterbalance.Si Ta Nm Ts Ni aw[1..30] Ndp uw[1] CropN si Naw[1] Qwp LeafNc WP(Pottrans) RZexw uw[1..8] Soil evap aw[1..30] Qr x[1..8] WP (Rain +irrigation) x Leafdemand StemExN si aw[1..8] Qwp Qfc Q EVAPO.evsoil exw[1..30] x AW[1] Qfc TransP EVAPO.pottrans leafarea leafarea Nuw[1..8] Naw[1..8] aw[1..5] SOIL.EXW[1..30] exw[1..5] evsoil Nex[1..30] SF Results

7. Compare to observations, calculate likelihoods etc

8. Should we accept the reduction hypotheses? Vernalisation 99% N-mineralisation Temp/moisture adjustment~99% Crop N physiology 50% Canopy Temperature 96% Nitrogen Leaching 50% Diurnal adjustment of thermal time 99% 40 other variables <<50%

9. Co-workers • Davide Tarsitano • Glen Cox • James Gibbons • Andy Wood • Jim Craigon • Steve Ramsden • Yan Jiao • Tim Reid NMJ Crout, D Tarsitano, AT Wood. Is my model too complex? (2009) Evaluating model formulation using model reduction.Environmental Modelling & Software, 24:1-7 with thanks to BBSRC and Leverhulme