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

Biogeochemical modelling

Corinne Le Quéré

University of East Anglia and the British Antarctic Survey

• project the future

• test hypothesis (e.g. CLAW)

• quantify feedbacks

• formalize your ideas e.g. FCO2 = kg·(∆pCO2)

SOLAS Science

Model dimensions:

0D FCO2 = kg·(∆pCO2)

1D depth/height

2D depth/height + latitude

3D depth/height + latitude + longitude

4D depth/height + latitude + longitude + time

Outline of lecture:

1. Introduction

2. Chemical processes

3. Biological processes

4. Physical processes

5. Model evaluation and benchmarking

6. One example (ocean CO2 sink)

7. The modeller’s psychology

Outline of lecture:

1. IntroductionIntroduction

2. Chemical processes

3. Biological processesBiological processes

4. Physical processesPhysical processes

5. Model evaluation and benchmarkingModel evaluation and benchmarking

6. One example (ocean CO2 sink)One example (ocean CO2 sink)

7. The modeller’s psychologyThe modeller’s psychology

SOLAS Science

• known processes

• measured species

• derived rates

Parameterisation of chemical processes are 0-Dimensional:

Typical chemical processes in the atmosphere:

1. ozone

2. NOx

3. hydrocarbon (Volatile Organic Carbon)

4. OH-

5. aerosols

6. CO, CH4

NOx AND VOC processes (D. Jacobs)

Emission

NOh (420 nm)

NO2

HNO3

1 day

NITROGEN OXIDES (NOx) VOLATILE ORGANIC COMPOUNDS (VOC)

Emission

VOC

OHHCHOh (340 nm)

hoursCO

hours

BOUNDARYLAYER

~ 2 km

Deposition

Tropospheric ozone processes (D. Jacobs)

O3

O2h

O3

OH HO2

h, H2O

Deposition

NO

H2O2

CO, VOC

NO2

h

STRATOSPHERE

TROPOSPHERE

8-18 km

!================================================================= !

! 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 ENDDO ENDDO

example of model

code from GEOS-

CHEM

Typical chemical processes in the ocean:

1. C cycle (CO2, CO32-,HCO3

-,CaCO3,H2CO3)

2. pH

3. Si cycle (SiO2 to Si(OH)4-)

4. Fe cycle (Fe3+ to Fe2+)

5. photochemistry (degration of Organic C by light)

The Fe cycle in the oceans

Fe(III)L

Fe2+

Fe3+

pFe

dissolved Fe

hμ

P, B

organic or inorganic

sedimentationCoagulationDissociation

L

growth

hμ

hμ = photoreduction

dissolved, colloidal

carbon cycle

CO2

CO2 + H2O + CO2-3 2HCO-

3

chemical reactions

90

numbers in PgC/yr

atmosphere

ocean

! 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 CO2 gas

exchange

formulation

Outline of lecture:


2. CChemicalhemical processes processes

3. Biological processes

4. PhysicalPhysical processes processes




SOLAS Science

Typical biological processes in the ocean:

1. phytoplankton growth

2. zooplankton grazing

3. bacterial remineralisation

4. particulate dynamics

• poorly known processes

• some measured rates

• vertical transport of particles

Parameterisation of biological processes are 1-Dimensional:

carbon cycle

45

34

CO2

CO2 + H2O + CO2-3 2HCO-

3

chemical reactions

90

numbers in PgC/yr

biological activity

11

atmosphere

ocean

surface

mixed layer depth

atmosphere

100 m

biological activity

real surface

atmosphere

100 m

biological activity

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

Primary Production

45 PgC/y

what they do

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

what they do

these bloom

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

what they do

these form shells

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

what they do

these respond to

pH

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

what they do

these float

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producersmixed

silicifiers

what they need

Fe P N

Fe P N

Fe P NFe P NFe P N

Fe P N Si

Respiration

34 PgC/y

Primary Production

45 PgC/y

pico-heterotrophsbacteria

phyto-plankton

pico-autotrophs

N2-fixers

calcifiers

DMS-producers

mixed

silicifiers

zoo-plankton

proto

meso

macro

Respiration

34 PgC/ypico-heterotrophsbacteria

zoo-plankton

proto

meso

macro

what they do


zoo-plankton

proto

meso

macro

what they do

these control blooms


zoo-plankton

proto

meso

macro

what they do

these produce big

feacal pellets


zoo-plankton

proto

meso

macro

what they need

F O O D

F O O D

F O O D

F O O D

time scale

a few +1 days

a few days

NO3

NH4

Si

DICFe

PO4

light

T

predation

mortality, sedimentation

environment

biogeochemistry

biology

maximum growth rate

phytoplankton growth

gro

wth

rate

(1/d

)

temperature (˚C)

pico phytoplankton

diatoms

micro zooplankton

meso zooplankton

gro

wth

rate

(1/d

)

temperature (˚C)

pico phytoplankton

diatoms

micro zooplankton

meso zooplankton

Modelling strategy:

diagnostic models (Najjar et al., 1992; OCMIP2 1998-200)

Pt

max 0, Pobs Pmod

biogeochemical models (Maier-Reimer et al., 1990-1993)

Pt

r g T g EP2

KP P

ecosystem models (Fasham et al., 1993)

N P

ZD

Calcifiers

PO4Fe

Nutrient Phytoplankton Zooplankton Detritus

(NPZD)

Dynamic Green Ocean Models

(DGOM)

!! 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

Outline of lecture:



3. BiologicalBiological processes processes

4. Physical processes




SOLAS Science

Typical physical processes in the atmosphere and ocean:

1. advection

2. diffusion

3. mixing

4. convection

• 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:

convection and horizontal advection

vertical advection

Eddies and mixing

! 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 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 END DO !

example of model

code from NEMO

ocean physical model

carbon cycle

45

34

physical transport

11

33

CO2

CO2 + H2O + CO2-3 2HCO-

3

chemical reactions

90

numbers in PgC/yr

biological activity

11

atmosphere

ocean

Outline of lecture:





5. Model evaluation and benchmarking



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.

41.e-5

Example benchmark for marine carbon cycle model:

• CO2 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

• CO2 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

Carbon-cycle model intercomparison Project (OCMIP)

visual evaluation of model results

formal evaluation of model results using a Taylor

diagram

Carbon-cycle model intercomparison Project (OCMIP)

Model Bias

100*

D

MDPbias

M: Model Results

D: Observational Data

-50

-40

-30

-20

-10

0

10

20

30

40

50

% M

odel

Bia

s Excellent

Excellent

Very Good

Very Good

Good

Good

Poor

Poor

Cost functions

D

MD

nCF

1

N: Number of Observations


σD: 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).

0

0.2

0.4

0.6

0.8

1

1.2

Cos

t Fun

ctio

n

Very Good

Good

examples: ERSEMCourtesy of I.Allen

Model efficiency

2

2

1

DD

MDME


D_bar: Mean of Data

M: Model Results

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Mod

el E

ffici

ency

Excellent

No Skill

Poor

Very Good

Good

Outline of lecture:






6. One example (ocean CO2 sink)


carbon cycle

45

34

physical transport

11

33

CO2

CO2 + H2O + CO2-3 2HCO-

3

chemical reactions

90

numbers in PgC/yr

biological activity

11

atmosphere

ocean

Smith and Reynolds 2005 and IPCC 2007

water

energy

winds

observed warming trend 1979-2005

physical transport

chemical reactions

ocean

biological activity

sea-air CO2 flux anomaly

• 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 • 0.5-1.5ox2o resolution• 31 vertical levels • calculated vertical mixing• NCEP daily forcing

• 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 • 0.5-1.5ox2o resolution• 31 vertical levels • calculated vertical mixing• NCEP daily forcing for year 1967

Change in Southern Ocean CO2 sink in model

real forcing

real forcing

1967 forcing

Change in Southern Ocean CO2 sink in model

changes in winds

Outline of lecture:






6. One example (ocean COOne example (ocean CO22 sink) sink)

7. The modeller’s psychology

truth

time

The modeller‘s psychology

truth

time

illusion (everybody is happy)

truth


time

truth

time

chaos (everybody is

happy)


truth


chaos (everybody is

happy)

relief (need a new job)

time

truth


chaos (everybody is

happy)

relief (need a new job)

climate modelsland ecosystem

modelsocean biogeochemistr

y models

climate models

time

• 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:

Documents

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