1. Biogeochemical modelling Corinne Le Quéré University of East Anglia and the British Antarctic Survey

2. project the future test hypothesis (e.g. CLAW) quantify feedbacks formalize your ideas e.g. F CO2 = k g ·(pCO 2 )

3. SOLAS Science

4. Model dimensions: 0D F CO2 = k g ·(pCO 2 ) 1D depth/height 2D depth/height + latitude 3D depth/height + latitude + longitude 4D depth/height + latitude + longitude + time

5. Outline of lecture: 1.Introduction 2.Chemical processes 3.Biological processes 4.Physical processes 5.Model evaluation and benchmarking 6.One example (ocean CO 2 sink) 7.The modellers psychology

6. Outline of lecture:

7. SOLAS Science

8. known processes measured species derived rates Parameterisation of chemical processes are 0-Dimensional:

9. Typical chemical processes in the atmosphere: 1.ozone 2.NOx 3.hydrocarbon (Volatile Organic Carbon) 4.OH - 5.aerosols 6.CO, CH 4

10. NO x AND VOC processes (D. Jacobs) Emission NO h (420 nm) NO 2 HNO 3 1 day NITROGEN OXIDES (NO x ) VOLATILE ORGANIC COMPOUNDS (VOC) Emission VOC OH HCHO h (340 nm) hours CO hours BOUNDARY LAYER ~ 2 km Deposition

11. Tropospheric ozone processes (D. Jacobs) O3O3 O2O2 h O3O3 OHHO 2 h, H 2 O Deposition NO H2O2H2O2 CO, VOC NO 2 h STRATOSPHERE TROPOSPHERE 8-18 km

12. !================================================================= ! ! The decay for CH4 is calculated by: ! OH + CH4 -> CH3 + H2O ! k = 2.45E-12 exp(-1775/T) ! ! This is from JPL '97. JPL '00 does not revise '97 value. (jsw) !================================================================= DO L = 1, MAXVAL( LPAUSE ) DO J = 1, JJPAR DO I = 1, IIPAR ! Only consider tropospheric boxes IF ( L < LPAUSE(I,J) ) THEN !jsw Is it all right that I'm using ! 24-hr avg temperature to calc. rate coeff.? KRATE = 2.45d-12 * EXP( -1775d0 / Tavg(I,J,L) ) ! Conversion from [kg/box] --> [molec/cm3] ! [kg CH4/box] * [box/cm3] * XNUMOL_CH4 [molec CH4/kg CH4] STT2GCH4 = 1d0 / AIRVOL(I,J,L) / 1d6 * XNUMOL_CH4 ! CH4 in [molec/cm3] GCH4 = STT(I,J,L,1) * STT2GCH4 ! Sum loss in TCH4(3) (molecules/box) TCH4(I,J,L,3) = TCH4(I,J,L,3)+ & ( GCH4 * BOXVL(I,J,L) * KRATE * BOH(I,J,L) * DT ) ! Calculate new CH4 value: [CH4]=[CH4](1-k[OH]*delt) GCH4 = GCH4 * ( 1d0 - KRATE * BOH(I,J,L) * DT ) ! Convert back from [molec/cm3] --> [kg/box] STT(I,J,L,1) = GCH4 / STT2GCH4 ENDIF ENDDO example of model code from GEOS-CHEM

13. Typical chemical processes in the ocean: 1.C cycle (CO 2, CO 3 2-,HCO 3 -,CaCO 3,H 2 CO 3 ) 2.pH 3.Si cycle (SiO 2 to Si(OH) 4 - ) 4.Fe cycle (Fe 3+ to Fe 2+ ) 5.photochemistry (degration of Organic C by light)

14. The Fe cycle in the oceans Fe(III)L Fe 2+ Fe 3+ pFe dissolved Fe hμhμ P, B organic or inorganic sedimentation Coagulation Dissociation L growth hμhμ hμ = photoreduction dissolved, colloidal

15. carbon cycle CO 2 CO 2 + H 2 O + CO 2- 3 2HCO - 3 chemical reactions 90 numbers in PgC/yr atmosphere ocean

16. ! Set volumetric solubility constants for co2 in mol/l*atm (Weiss, 1974) ! ------------------------------------------------------------------------------------ ! c00 = -58.0931 c01 = 90.5069 c02 = 22.2940 c03 = 0.027766 c04 = -0.025888 c05 = 0.0050578 ! ! ln(k0) of solubility of co2 (eq. 12, Weiss, 1974) ! --------------------------------------------------------- ! cek0 = c00+c01/qtt+c02*zqtt+sal*(c03+c04*qtt+c05*qtt2) ak0 = exp(cek0) * smicr ! ! this is Wanninkhof (1992) equation 8 (with chemical enhancement), in cm/h ! ------------------------------------------------------------------------- ! kgwanin(ji,jj) = (0.3*ws*ws + 2.5*(0.5246+ttc*(0.016256+ttc*0.00049946))) ! ! convert from cm/h to m/s and apply ice cover ! -------------------------------------------- ! kgwanin(ji,jj) = kgwanin(ji,jj) /100./3600. * (1-freeze(ji,jj)) ! Set Schmit constants ! -------------------------------------------------------------------------- schmico2 = 2073.1-125.62*ttc+3.6276*ttc**2-0.043126*ttc**3 ! ! compute gas exchange kg in mol/m2/yr/uatm ! -------------------------------------------------------------------------- gasex = kgwanin * (660/schmico2)**0.5 kg = gasex * ak0 * 1.e3 * (3600.*24.*365.25) example of model code for CO 2 gas exchange formulation

17. Outline of lecture:

18. SOLAS Science

19. Typical biological processes in the ocean: 1.phytoplankton growth 2.zooplankton grazing 3.bacterial remineralisation 4.particulate dynamics

20. poorly known processes some measured rates vertical transport of particles Parameterisation of biological processes are 1-Dimensional:

21. carbon cycle 45 34 CO 2 CO 2 + H 2 O + CO 2- 3 2HCO - 3 chemical reactions 90 numbers in PgC/yr biological activity 11 atmosphere ocean

22. surface mixed layer depth atmosphere 100 m biological activity

23. real surface atmosphere 100 m biological activity

24. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers Primary Production 45 PgC/y what they do

25. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers what they do these bloom

26. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers what they do these form shells

27. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers what they do these respond to pH

28. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers what they do these float

29. phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers what they need Fe PN P N P N PN PN PNSi

30. Respiration 34 PgC/y Primary Production 45 PgC/y pico-heterotrophs bacteria phyto- plankton pico-autotrophs N 2 -fixers calcifiers DMS-producers mixed silicifiers zoo- plankton proto meso macro

31. Respiration 34 PgC/y pico-heterotrophsbacteria zoo- plankton proto meso macro what they do

32. pico-heterotrophsbacteria zoo- plankton proto meso macro what they do these control blooms

33. pico-heterotrophsbacteria zoo- plankton proto meso macro what they do these produce big feacal pellets

34. pico-heterotrophsbacteria zoo- plankton proto meso macro what they need FOOD F O O D FOOD F O O D

35. time scale a few +1 days a few days

36. NO 3 NH 4 Si DIC Fe PO 4 light T predation mortality, sedimentation environment biogeochemistry biology maximum growth rate phytoplankton growth

37. growth rate (1/d) Buitenhuis et al., 2006 temperature (˚C) pico phytoplankton diatoms micro zooplankton meso zooplankton

38. growth rate (1/d) Buitenhuis et al., 2006 temperature (˚C) pico phytoplankton diatoms micro zooplankton meso zooplankton

39. Modelling strategy: diagnostic models (Najjar et al., 1992; OCMIP2 1998-200) biogeochemical models (Maier-Reimer et al., 1990-1993) ecosystem models (Fasham et al., 1993) NP ZD Calcifiers PO 4 Fe Nutrient Phytoplankton Zooplankton Detritus (NPZD) Dynamic Green Ocean Models (DGOM)

40. ! ! Evolution of Mesozooplankton ! ------------------------ ! trn(ji,jj,jk,jpmes) = trn(ji,jj,jk,jpmes) & & +mesoge(ji,jj,jk)*gramet(ji,jj,jk) & & -tortz2(ji,jj,jk)-respz2(ji,jj,jk) ! ! Evolution of DOC ! ---------------- ! trn(ji,jj,jk,jpdoc) = trn(ji,jj,jk,jpdoc) & & +rn_sigpoc*orem(ji,jj,jk)-olimi(ji,jj,jk) & & +grarem(ji,jj,jk)*(1.-rn_sigmic)+grarem2(ji,jj,jk) & & *(1.-rn_sigmes)-xaggdoc(ji,jj,jk)-xaggdoc2(ji,jj,jk)& & +depdoc(ji,jj,jk) ! ! Evolution of POC ! ------------------------------------------------------------------ ! trn(ji,jj,jk,jpgoc) = trn(ji,jj,jk,jpgoc) & & +grapoc2(ji,jj,jk)+resphy(ji,jj,jk,jpdia,1)+xagg(ji,jj,jk) & & +tortz2(ji,jj,jk)-orem2(ji,jj,jk)-grazgoc(ji,jj,jk) & & +xaggdoc2(ji,jj,jk) & & +(sinking2(ji,jj,jk)-sinking2(ji,jj,jk+1))/e3t_0(jk) ! ! Evolution of dissolved IRON ! ------------------------------------------------------------------ ! trn(ji,jj,jk,jpfer) = trn(ji,jj,jk,jpfer)- & & xbactfer(ji,jj,jk)+ferat3*( & & respz2(ji,jj,jk)+respz(ji,jj,jk))+grafer(ji,jj,jk) & & +grafer2(ji,jj,jk)+ofer(ji,jj,jk) & & +(1.-rn_siggoc)*ofer2(ji,jj,jk) & & -xscave(ji,jj,jk)+irondep(ji,jj,jk) & & +depfer(ji,jj,jk)-xaggdfe(ji,jj,jk) ! example of model code from PlankTOM ecosystem model

41. Outline of lecture:

42. SOLAS Science

43. Typical physical processes in the atmosphere and ocean: 1.advection 2.diffusion 3.mixing 4.convection

44. well known processes with physical equations difficult to represent because of size of grid sub-grid scale parameterisations developed and tuned to give reasonable physical transport Parameterisation of physical processes are 3-Dimensional:

45. convection and horizontal advection

46. vertical advection

47. Eddies and mixing

48. ! Horizontal advective fluxes ! ----------------------------- ! ! =============== DO jk = 1, jpkm1 ! Horizontal slab ! ! =============== DO jj = 1, jpjm1 DO ji = 1, fs_jpim1 ! vector opt. ! upstream indicator zcofi = MAX( zind(ji+1,jj,jk), zind(ji,jj,jk) ) zcofj = MAX( zind(ji,jj+1,jk), zind(ji,jj,jk) ) ! volume fluxes * 1/2 zfui = 0.5 * e2u(ji,jj) * pun(ji,jj,jk) zfvj = 0.5 * e1v(ji,jj) * pvn(ji,jj,jk) ! centered scheme zcenut = zfui * ( tn(ji,jj,jk) + tn(ji+1,jj,jk) ) zcenvt = zfvj * ( tn(ji,jj,jk) + tn(ji,jj+1,jk) ) zcenus = zfui * ( sn(ji,jj,jk) + sn(ji+1,jj,jk) ) zcenvs = zfvj * ( sn(ji,jj,jk) + sn(ji,jj+1,jk) ) END DO ! Tracer flux divergence at t-point added to the general trend ! -------------------------------------------------------------- DO jj = 2, jpjm1 DO ji = fs_2, fs_jpim1 ! vector opt. zbtr = btr2(ji,jj) ! horizontal advective trends zta = - zbtr * ( zwx(ji,jj,jk) - zwx(ji-1,jj,jk) & & + zwy(ji,jj,jk) - zwy(ji,jj-1,jk) ) zsa = - zbtr * ( zww(ji,jj,jk) - zww(ji-1,jj,jk) & & + zwz(ji,jj,jk) - zwz(ji,jj-1,jk) ) ! add it to the general tracer trends ta(ji,jj,jk) = ta(ji,jj,jk) + zta sa(ji,jj,jk) = sa(ji,jj,jk) + zsa END DO ! example of model code from NEMO ocean physical model

49. carbon cycle 45 34 physical transport 11 33 CO 2 CO 2 + H 2 O + CO 2- 3 2HCO - 3 chemical reactions 90 numbers in PgC/yr biological activity 11 atmosphere ocean

50. Outline of lecture:

51. validation: process of checking if something satisfies a certain criterion evaluation: systematic determination of merit, worth and significance of something using criteria against a set of standards benchmarking: process of comparing the quality of a product to another that is widely considered to be a standard. Benchmarking provides a snapshot of the performance of your model, and helps to keep track of model evalution.

52. 4 1.e-5 Example benchmark for marine carbon cycle model: CO 2 sink in 1990 between 1.8-2.6 PgC/y export of carbon between 9-12 PgC/y primary production between 40-70 PgC/y CO 2 variability in equatorial Pacific between 0.6-1.0 PgC mezo-zooplankton grazing << micro-zooplankton grazing all phytoplankton biomass > 0.02 PgC no phytoplankton biomass dominate globally

53. Carbon-cycle model intercomparison Project (OCMIP) visual evaluation of model results

54. formal evaluation of model results using a Taylor diagram Carbon-cycle model intercomparison Project (OCMIP)

55. Model Bias M: Model Results D: Observational Data

56. Cost functions N: Number of Observations D: Observational Data σ D : Standard deviation Data CF < 1 = very good,1–2 = good, 2–5 = reasonable,>5 = poor OSPAR Commission (1998). CF < 1 = very good, 1–2 = good, 2–3 = reasonable, >3 = poor Radach and Moll (2006). examples: ERSEM Courtesy of I.Allen

57. Model efficiency D: Observational Data D_bar: Mean of Data M: Model Results

58. Outline of lecture:

59. carbon cycle 45 34 physical transport 11 33 CO 2 CO 2 + H 2 O + CO 2- 3 2HCO - 3 chemical reactions 90 numbers in PgC/yr biological activity 11 atmosphere ocean

60. Smith and Reynolds 2005 and IPCC 2007 water energy winds observed warming trend 1979-2005

61. physical transport chemical reactions ocean biological activity

62. sea-air CO 2 flux anomaly

63. PISCES-T ecosystem model 2 phyto, 2 zoo., 2 sinking particles limitation by Fe, P, and Si initialise with observations in 1948 (Buitenhuis et al., GBC 2006) OPA model OPA General Circulation model 0.5-1.5 o x2 o resolution 31 vertical levels calculated vertical mixing NCEP daily forcing

64. PISCES-T ecosystem model 2 phyto, 2 zoo., 2 sinking particles limitation by Fe, P, and Si initialise with observations in 1948 (Buitenhuis et al., GBC 2006) OPA model OPA General Circulation model 0.5-1.5 o x2 o resolution 31 vertical levels calculated vertical mixing NCEP daily forcing for year 1967

65. Change in Southern Ocean CO 2 sink in model real forcing

66. 1967 forcing Change in Southern Ocean CO 2 sink in model changes in winds

67. Outline of lecture:

68. truth time The modellers psychology

69. truth time illusion (everybody is happy)

70. truth illusion (everybody is happy) time

71. truth time chaos (everybody is happy) illusion (everybody is happy)

72. truth illusion (everybody is happy) chaos (everybody is happy) relief (need a new job) time

73. truth illusion (everybody is happy) chaos (everybody is happy) relief (need a new job) climate models land ecosystem models ocean biogeochemistry models climate models time

74. do your best, but simplify to answer your question use benchmarking to i) validate, and ii) follow improvements in your model EVERYTHING must make sense Putting it all together: