Modeling the Land Carbon Cycle. Please see h5p://biocycle.atmos.colostate.edu/shiny/land/
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- Giles McCormick
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1 Modeling the and Carbon Cycle Please see h5p://biocycle.atmos.colostate.edu/shiny/and/
2 What is a Model? Models are simplifica?ons of reality which we use to organize and make sense of what we see in the world around us Models are abstrac?ons which seek to capture the essence of real processes Simple models are not intended to be perfect representa?ons of the real world Models help us understand
3 evels of Abstrac?on 6. Computer program (Stella, MATAB, Python, R) More abstract 5. Numerical algorithm (arithme?c procedure) 4. Discrete model (algebra) 3. Mathema?cal model (differen?al equa?ons) 2. Conceptual model (in our heads, maybe with a diagram) 1. Real world (impossibly complicated) More realis?c
4 Exponen?al Growth dp = gp P(t) = P(0)e gt et g = % Popula?on increases 20x in 30?me steps! Rate of growth of new stuff (plants, popula?ons) propor?onal to the amount of old stuff Rate rises faster and faster uickly exceeds any reasonable limit Not very realis?c!
5 h5p://biocycle.atmos.colostate.edu/shiny/logis?c/ dp = g 1 P K ogis?c Growth P et growth rate depend on popula?on Exponen?al growth when popula?on is small Growth rate shrinks as popula?on approaches carrying capacity
6 Cascading Carbon Pools Conceptual Model Mathema?cal Model df ds d dp Symbols used: = NPP MORT = MORT = (1 ϵ) [ τ F = (1 ϵ) [ τ F ] S ] τ S NPP = Net primary production (photosynthesis minus plant respiration, in GtC/yr) MORT = plant mortality (transfers carbon from live plants to dead litter, GtC/yr) τ,, τ S = turnover time for carbon in litter, fast, and slow soil pools (years) ϵ = efficiency of microbial respiration (fraction of what they eat that turns into CO2) = fractional increase in decomposition rates per degrees of warming T = temperature (Celsius), prescribed from a simple climate model using the IPCC SRES A2 emissions scenaro. h5p://biocycle.atmos.colostate.edu/shiny/and/ Plants grow logis?cally limited by nutrients Carbon from dead plants becomes li5er i5er decomposes quickly into fast and then slow soil organic ma5er
7 Discre?ze the Model Replace all the differen(als with differences Mathema?cal Model (differen?al equa?ons) df ds d dp = NPP MORT = MORT = (1 ϵ) [ τ F = (1 ϵ) [ τ F ] S ] τ S Discrete Model (algebraic equa?ons) ΔP =(NPP MORT )Δt Δ = ΔF = ΔS = MORT τ τ ( 1 ε ) F F F( 1 ε ) S τ τ S Δt Δt Δt Approximate calculus with algebra
8 Algorithm (Recipe) Write down a procedure to update (P,,F,S) Discrete Model (algebraic equa?ons) ΔP =(NPP MORT )Δt Δ = ΔF = ΔS = MORT τ τ ( 1 ε ) F F F( 1 ε ) S τ τ S Δt Δt Δt Algorithm (arithme?c to update pools) qmult = (T- T0)/ t P new = P old + (NPP MORT) t new = old + (MORT- old / ) qmult F new = F old + ((1- ) old / F old / F ) qmult S new = S old + ((1- )F old / F S old / S ) qmult h5p://biocycle.atmos.colostate.edu/shiny/and/
9 Computer Program Convert arithme?c recipe into programming language Algorithm (arithme?c to update pools) Computer Program (instruc?ons in R) P new = P old + (NPP MORT) t plant[i+1] <- plant[i] + NPP[i] - mortality[i] new = old + (MORT- old / ) qmult litter[i+1] <- litter[i] + mortality[i] litter[i]/tau.litter * resp.enhancement F new = F old + ((1- ) old / F old / F ) qmult fast.soil[i+1] <- fast.soil[i] + resp.enhancement * ( (1.-eff.microbes) * litter[i]/tau.litter - fast.soil[i]/tau.fast) S new = S old + ((1- )F old / F S old / S ) qmult slow.soil[i+1] <- slow.soil[i] + resp.enhancement * ( (1.-eff.microbes) * fast.soil[i]/tau.fast - slow.soil[i]/tau.slow) h5p://biocycle.atmos.colostate.edu/shiny/and/
10 Results Try it yourself and test the effects of CO 2 fer?liza?on, nitrogen deposi?on, deforesta?on, and climate! h5p://biocycle.atmos.colostate.edu/shiny/and/
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