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Using R to Model Complex Biogeochemical Systems Chris Wood

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Introduction to the science Why are we interested in sediments? – 71% of Earth’s surface (335,258,000 km 2 ) – Very dynamic environments Why are we interested in shelf-seas? – Globally important sinks & sources for nutrients – High rates of primary productivity

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Main reactions Oxic zone – O 2 mineralisation NO denitrification MnO 2 reduction Fe(OH) 3 reduction Froelich et al. (1979) SO 4 2- reduction

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The maths… Despite the complexity, it can be described mathematically(!): Oxic breakdown of organic matter: Change in concentration of i Transport of chemical species Rate of consumption of i, but dependent on j

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Transport ReacTran package written for ecological and biogeochemical models; the examples in the vignette reflect this Grid <- setup.grid.1D(N=100,dx.1=0.1,L=15) – Grid$x.mid, Grid$x.int, Grid$dx O2tran <- tran.1D (C=O2, C.up=bwO2, dx=Grid) – Other arguments allow specific transport terms to be used

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Solving the maths The deSolve and rootSolve packages – rootSolve: ‘Nonlinear root finding, equilibrium and steady-state analysis of ordinary differential equations’ – deSolve: ‘General solvers for initial value problems of ordinary differential equations (ODE), partial differential equations (PDE), differential algebraic equations (DAE), and delay differential equations (DDE).’

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Solving the maths (cont…) – Simple to implement modelFunction <- function(t, y, pars){ #implementation of transport and differential #equations; e.g: OC <- y[1:100]; O2 <- y[101:200] oxicMin <- r*OC*(O2/(O2+ksO2oxic)) } ss.output <- steady.1D(y=rep(10,2*100), func=modelFunction, parms=c(r=10, ksO2oxic=1)) dyn.output <- ode.1D(y=ss.output$y, times=0:364, func=modelFunction, parms=pars)

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Output

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Data management Data – Multiple sites, cruises, repeat measurements & parameters R + MySQL (+ RJDBC/rJava) Post-processing / data consistency checking carried out in R Allows model calibration to be carried out

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Model testing & model calibration Sensitivity analysis – Allows us to discover the most sensitive model parameters Genetic algorithm – (Relatively) efficient method of making model output fit real data

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Future ideas / personal interests Web-based model-runs via R + python (mod_python / rpy2) – R would provide better graphics than currently available via PHP libraries – Greater access for non-modeller researchers – Public engagement of science

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Any questions? Acknowledgements: – Funding: NERC & Defra – University of Southampton Boris Kelly-Gerreyn, Peter Statham, Adrian Martin, Andy Yool, John Hemmings, Charlie Thompson, Carl Amos – Netherlands Institute of Ecology Karline Soetaert, Filip Meysman – University of Portsmouth Gary Fones, Fay Couceiro, Adam Hamilton – Cefas John Aldridge, Ruth Parker, Dave Sivyer, Johan van Molen, Naomi Greenwood, Elke Neubacher – UEA Keith Weston – Partrac Ltd Kevin Black, Rachel Helsby – Crew of Cefas Endeavour Main aims Main aims Objectives Objectives The importance The importance Initial considerations Initial considerations Multidisciplinary approach Multidisciplinary approach Our model Our model Current results Current results Observations Observations Conclusions Conclusions

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The importance of nutrients in the coastal ocean Shelf seas: – Globally important sinks & sources for nutrients – High rates of primary productivity Knowledge of nutrient origin & fate is key to understanding primary productivity Sediments are potentially important sources of nutrients in shelf seas Need to be able to model sediment systems to predict nutrient exchanges

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Results from genetic algorithm

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Analysis of genetic algorithm output Are values sensible? ParameterOMEXDIA valueGA result Mean flux (g C m -2 yr -1 )-16 Bioturbation (cm 2 d -1 )1/36517/365 rFast (d -1 ) rSlow (d -1 ) pFast NCrFdet (mol N : mol C)0.16

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Evaluation of outputs Are all processes well explained by model? – How important is the benthic fluff layer? – Do more mineralisation reactions need to be included in the model? – Should other biogeochemical processes be included? Has model been ‘over-fitted’?

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Conclusions & future work The GA is able to give a good fit with sensible parameter values, but: – How much predictive ability does this model have? – Effect of increasing number of biogeochemical processes? Incorporate a simple sediment resuspension model into current model The model could help in calculating nutrient budgets of shelf seas?

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Sensitivity analysis 3 simple sensitivity analysis experiments were carried out – each with an upper and lower value: – Literature data – Double and halve the default values – Order of magnitude above and below the default value Non-linearity of model leads to unexpected results

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Sensitivity analysis results

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Observational data

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Comparison with observations

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Sensitivity analysis results Increased cost function implies more sensitive parameter Ranking all results into a single list allows us to pick an arbitrary number of parameters to use in future experiments o Mean Flux o pFast o rFast o NCrFdet o rSlow o biot

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Optimising model to data: Genetic Algorithm The population is the set of free parameters A generation is a set of model runs equal to the number of free parameters Initial run: randomly generated parameter set from a range given to the algorithm Parameter values are converted into binary to allow ‘genetic crossover’ between random pairs of parameters Subsequent runs: The model is run for n generations * m unconstrained parameters – 5000 * 30 = (~28 hrs) Parents: Children: Crossover point

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Example of inhibition

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Current understanding of early diagenesis Euphotic zone Thermocline has little effect, although cells sink out… with a short delay at the pycnocline (1) PP = 250 g C m -2 yr -1 (1) 370 g C m -2 yr -1 (2) 1.Brockmann et al. (1990) 2.Wollast (1991) 3.Kuhn & Radach (1997) 4.Billen et al. (1990) 5.van Raaphorst et al. (1990) 6.Hall et al. (1996) 7.van der Weijden (1992) 8.Fang et al. (2007) 9.Canfield et al. (1993) 10.Wijsmann et al. (2002) 11.Ussher et al. (2007) 12.Overnell (2002) 13.Rysgaard et al. (2001) 14.Price et al. (1994) 15.Jorgensen (1977) 16.Slomp et al. (1998) C org : 50-90% recycled [1) NO NO 3 - : -160 – 309 µmol m -2 d -1 (5, 6) NH 4 + : -400 – 66 µmol m -2 d -1 (5, 6) 10-50% (1, 2) ‘Normal’: ~340 mg Spring bloom: 185 mg C m -2 d -1 (12-21%) (3) Shelf sea C org content = 1-5% C org metabolism: 12 – 23 mmol C cm -2 day -1 (4) C org ~1% (2) Nitrate reduction: 0.7 mmol m -2 d -1 (7) Z Z < 1 cm: 113 – 401 nmole cm -2 d -1 [9] 1 < Z (cm) < 4: 387 – 1987 nmole cm -2 d -1 [9] Fe 3+ reduction rates: (12) / (13) nmol cm -2 d -1 C org metabolism: 18 mmol C m -2 d -1 (9) SO 4 2- reduction: nmol cm -3 d -1 (15) C org : 2 µmol cm -2 d -1 [2] Si(OH) 3 – 0.05 – 0.2 µmol cm -2 d -1 [6] Fe 2+ flux increases (7 – 22 [modelled] / 46 [in situ measurement] nmol cm -2 d -1 ) as O 2 of BW decreases (300 -> 0 µM) [6] PO 4 : µmol m -2 d -1 (16) 1.1 5.2 ΣCO 2 (g d.w.) -1 d -1 CFA: 5.8 % (8) Pyrite formation: 8.9 x10-6 µmol l -1 d -1 (10) Permanently buried: Sediment-water interface (SWI) Fluxes: Z

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Multidisciplinary approach NOCS, University of Portsmouth, CEFAS & Partrac Ltd

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Why include resuspension? Previous work has concentrated on other sources of nutrients Frequent resuspension events – Release of nutrients – Sink for nutrients Resuspension may be involved in regulating primary production

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What is early diagenesis? The physical, biological & chemical changes which occur to deposited material during burial in sediment Oxidation of organic matter and reduced species Transport (advection, diffusion & bioturbation)

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Main Aims & Objectives How do resuspension events impact nutrient concentrations in overlying waters? Modify an existing one-dimensional non- steady state sediment biogeochemistry model with a view to include resuspension Validate and calibrate the model with literature and experimental data Use the model to investigate the role of resuspension on nutrient dynamics

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Objectives Modify an existing one-dimensional non- steady state early diagenetic model to include resuspension Validate and calibrate the model with literature and project data Study changes in nutrient (organic and inorganic) concentrations in the sediment and bottom waters following resuspension Study role of exchanges between particles and macro- and micro-nutrients

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Initial considerations Understand early diagenetic processes associated with degradation of organic matter in shelf-seas Acquire data for calibration and validation Recognise potential limitations of modelling approaches Decide on model and programming language to use

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Experimental aspects : 9 cruises Porewater profiles and fluxes across the sediment-water interface of O 2, NO 3, NH 4 +, TOC measured in-situ resuspension experiments using Voyager II Lab-based resuspension experiments using a mini-flume

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Experimental aspects 9 cruises Diffusive fluxes and porewater profiles of major nutrients and other species measured

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Secondary reactions Oxidation of reduced species –O2–O2 – MnO 2 Sink of species – Adsorption – Fe H 2 S FeS 2 + 2H 2 – Formation of apatites (e.g. carbonate fluorapatite [CFA])

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Processes to be included Sediment-water interface cm - m POC Resuspension Erosion depth Benthic fluff DOC DON DOP OM + O 2 NH PO CO 2 OM + HNO 3 CO 2 + NH 3 + H 3 PO 4 OM + Fe 2 O 3 Fe 2+ + CO 2 + NH 3 + H 3 PO 4 OM + SO 4 2- CO 2 + NH 3 + S 2- + H 3 PO 4 OM = (CH 2 O) 106 (NH 3 ) 16 (H 3 PO 4 ) Concentrations, fluxes and profiles Fe 2+ S 2- NH 4 + C org / FeS z ≅ 50 cm

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The General Diagenetic Equations Change in concentration of i Bioturbation Advection Rate of addition of i, but dependent on j

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The diagenetic model used OMEXDIA (Soetaert et al. 1996) – Written in the R programming language 1-dimensional Multi-G TOC, O 2, NO 3 -, NH 4 + & ODU OMEXDIA (Soetaert et al. 1996) – Written in the R programming language 1-dimensional Multi-G TOC, O 2, NO 3 -, NH 4 + & ODU Fe(OH) 3 SO 4 2-

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ODU

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With no ODU component…

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Addition of Fe(OH) 3 & SO 4 2-

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Overview of nitrate

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Comparison with observations

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Beck et al. (2008) Bottcher et al. (1998) Slomp et al. (1997)

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Nitrogen Nitrate shows clear classical profile – including increasing concentrations in the oxygen penetration zone Ammonium shows expected increase in concentration towards depth Comparison with observations

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Conclusions & future work (Some) general features in the model are consistent with real data but need better fitting to match the data Incorporate a simple sediment resuspension model into current model The model could help in calculating nutrient budgets of shelf seas?

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Future work Implement the remaining biogeochemical processes into the model Incorporate a sediment transport model into OMEXDIA Upscale model into ERSEM Carry out scenario testing

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Summary A combined experimental and observational approach is being taken to improve our knowledge about nutrient cycling An early diagenetic model has been shown to recreate the profiles found in experimental work Resuspension will be added to the model and calibrated using experimental results

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