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

Models and falsification Cant 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?

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

Reduction by variable replacement

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

Compare to observations, calculate likelihoods etc

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

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