Saroja Polavarapu

Climate Research Division, Environment Canada

RPN seminar, 6 Feb. 2015

Greenhouse gas simulation with GEM: The story of mass

conservation

CRD: Michael Neish, Douglas Chan, Shuzhan RenMRD: Monique Tanguay, Claude Girard, Michel RochAQRD: Jean de Grandpré, Sylvie Gravel

OUTLINE

• What are we trying to do and why?

• The mass conservation story of GEM for CO2

• Ensemble Kalman Filtering

1. THE FLUX ESTIMATION PROBLEM

• The natural carbon cycle involves CO2 exchange between the terrestrial biosphere, oceans/lakes and the atmosphere.

• Fossil fuel combustion and anthropogenic land use are additional sources of CO2 to the atmosphere.

8.6 Pg C/yr

http://www.scidacreview.org/0703/html/biopilot.html

The Global Carbon Cycle

Earth’s crust 100,000

1 Pg = 1 Gt = 1015 g

Net surface to atmosphere flux for biosphere or ocean is a small difference between two very large numbers

Net perturbations to global carbon budget LeQuere et al. (2013, ESSDD)

• Based on 2002-2012

• 50% of emissions remain in atmosphere

• 25% is taken up by terrestrial biosphere

• 25% is taken up by oceans

Interannual variability

• The uncertainty and interannual variability in the global CO2 uptake is mainly attributed to the terrestrial biosphere

• Thus, we must first learn more about biospheric sources/sinks

http://www.carboscope.eu/?q=co2_budget

50% to atmosphere

25% uptake by land

25% uptake by ocean

But what is the spatial distribution of the fluxes and how is it changing?

Figure courtesy of Elton Chan, CCMR

With the increased coverage from new satellite data, can we get flux estimates at higher spatial resolution?

Mean XCO2 Aug. 2009 GOSAT Greenhouse Gas Observing Satellite

v2.0 averaged at 0.9°x0.9°

Figure courtesy of Ray Nassar, CCMR

OCO-2 launch July 2014

http://oco.jpl.nasa.gov/

Atmospheric observations give feedback on model forecasts

• If forecast does not match observation, difference could be due to errors in CO2 initial conditions, meteorological analyses, prescribed fluxes, model formulation, representativeness, or observation errors.

CO2 forecast Fluxes

caaf ScxMc ),(Meteorologyanalysis

CO2

analysis

Forecast model Model error

The inverse problem for Carbon Flux estimation

• In flux inversions, if one solves for fluxes only, the transport model is needed to relate the flux to the observation: model is a strong constraint

• Exact mass conservation in transport model over years of simulation is needed to attribute model-data mismatch to fluxes.

• Techniques used to solve inverse problem: 4D-Var, EnsKF, Bayesian Inversion, Markov Chain Monte Carlo (MCMC)

• Perfect model assumption since forecast model is used as a strong constraint• No allowance for imperfect meteorological analyses• Extension for imperfect tracer initial conditions is not hard

ScHcScHcSSSSSJ fobsTfobsbTb 11 RB2

1

2

1)(

flux conc obs

Spatial interpolation Forecast model

Prior flux

Conventional inverse problem setup

World Data Centre for Greenhouse Gases (WDCGG)

http://gaw.kishou.go.jp/cgi-bin/wdcgg/map_search.cgi http://transcom.project.asu.edu

22 TransCom regions

Weekly avg obs

One or more years

J F M A M J J A S O N D J F M A M J JMonthly mean flux

Inversions using surface network

• Inversion methods differ in:

– Methodology– Observations

▪ Sfc: 100 flask + continuous

– A priori fluxes– Transport models

• Interannual variability is similar and due to land

Peylin et al. (2013)

1 5-62 7-83 94 10 11

Mean XCO2 Aug. 2009 GOSAT Greenhouse Gas Observing Satellite

The changing observing system

World Data Centre for Greenhouse Gases

http://gaw.kishou.go.jp/cgi-bin/wdcgg/map_search.cgi

• ~100 highly accurate surface stations with weekly or hourly data

• Regular aircraft obs over Pacific

• Satellites: GOSAT (2009), OCO-2 (2014) +…

v2.0 averaged at 0.9°x0.9°

GOSAT figure courtesy of Ray Nassar, EC

Environment Canada Carbon Assimilation System (EC-CAS)

• An advanced, state-of-the-art assimilation system which will use ensemble forecasts to directly simulate various sources of model error. Comparable to systems in development for Japan, US, etc.

• Will be run routinely but behind real time since it takes time for flux to reach measurement locations

• Forward model: global operational air quality model 0.9° x 0.9°

• Statistical method: Ensemble Kalman Smoother (ext. of oper.)

• Observations: GAW global surface-based in-situ and remote sensing stations, satellite, aircraft, Total Carbon Column Observing Network (TCCON)

• Emissions: biosphere (Canadian Terrestrial Ecosystem Model from CCCma), ocean, fossil fuel, biomass burning

13

forecast step

Analysis step

EC-CAS Carbon Assimilation System

Perturb initial conc., met fields, fluxes

Flask, continuous, aircraft, satellite

Perturb obs

The future vision: Comprehensive Carbon Data Assimilation System

Comprehensive carbon assimilation systems are being built by NASA, NOAA, agency-consortiums in Europe, Japan and EC.

GEO Carbon Strategy Report (2010)

EC-CAS team

• Saroja Polavarapu: (lead) data assimilation• Mike Neish: system development• Ray Nassar: satellite observations, modeling anthropogenic

and other emissions• Douglas Chan: carbon cycle science and modeling• Bakr Badawy: biospheric modeling• University collaborators:

– Prof. Dylan Jones (U Toronto), Feng Deng– Prof. John Lin (U Waterloo), Myung Kim (U Waterloo)

2. MASS CONSERVATION WITH GEM

Operational model forecasts

• 10-day forecasts from the current operational model (experiment K4H1RA2B: Strato2B final cycle) also show a steady drop in global mean surface pressure

• About 0.1 hPa is lost in 10 days

Global mean surface pressure

Date

Pre

ssur

e (h

Pa)

10-day forecasts

0-day forecasts

Why do we need mass conservation?

• When we assimilate greenhouse gas observations, mass conservation will not be possible. So no need for this if we want to estimate the CO2 or CH4 state only.

• However, we need mass conservation for– Accurate forward simulations of CO2/CH4. With a good initial

state and good source/sink inputs, can match observations.

– Estimation of sources/sinks of CO2/CH4 with inverse methods. Such methods will serve as a benchmark for the non-traditional EnKF state/flux estimation scheme.

Greenhouse gas simulation with GEM-MACH

• Need good simulation of GHG with exact mass conservation

• Priorities: (1) CO2 global (2) CH4 global (3) CO2, CH4 regional

• CH4 chemistry: (D.Chan, CCMR)

• stratosphere – LINOZ (de Grandpré, McLinden, AQRD), • troposphere:

• [OH] climatology from CMAM (D. Plummer, CCCma)

• Start with global CO2 simulation

GEM RPN MACH

Dynamics emis+v.diff

GEM RPN MACH

Dynamics emis+v.diffPhysics Physics

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CHOHkdt

CHd

Model validation: experiment setup

• How well can GEM-MACH simulate Carbon? – Simulation for January 1 – December 31, 2009

– Initial condition from CarbonTracker for Jan. 1, 2009

– Meteorology: surface fields (archived surface analyses), 3D winds, archived analyses from 4D-Var

– Set up: series of 24h forecasts, no CO2 assimilation

– Emissions: ▪ Every 3 hours (area type) though GEM-MACH set up for monthly fields with

diurnal variation▪ biosphere (CarbonTracker a posteriori)▪ ocean (CarbonTracker a posteriori)▪ Fossil Fuel (CarbonTracker but based on CDIAC)▪ Biomass burning (GFED v3)

• Idea: With CarbonTracker emissions and initial conditions, simulation should match CarbonTracker if transport is similar

Lack of global mass conservation

Increasing KTmin reduces increase in global CO2

10

50

• Because of emissions, large gradients near the surface are created. The semi-Lagrangian advection scheme does not conserve mass.

• The poor vertical mixing of CO2 from the surface exacerbates the non-conservation issues.

20

Pet

agra

ms

C

Time

Hypothesis

• Hypothesis: Adding fluxes at the surface creates large horizontal gradients. Without sufficient vertical mixing in the boundary layer, these unrealistically large gradients are smoothed by the semi-Lagrangian advection scheme (nonconservative flavour). With fast vertical mixing, horizontal gradients are reduced before the SL scheme can act.

• To prove this: Check global mass before and after advection and before and after diffusion

– Mass change due to diffusion is machine precision– Mass changes due to advection!

Further proof: Turn off advection

No advection

control

Annual growth is 7.7 Pg but should be ~4

4.5 Pg C = 2.1 ppm too much

Pet

agra

ms

C

Time

How did we accumulate so much CO2?

• The mass change due to advection over 24h is shown

• 7.7 Pg C per year is 0.0004 Pg C per time step for monotonic changes.

• For global CO2 of 818 Pg C only 0.00006 Pg C can be represented with 32-bits.

• The error we are looking for is only 6.7 times machine epsilon

Hour

0.028 Pg CM

ass

chan

ge (

Pg

C)

Mass change due to advection over 24 h

Mass conservation: Semi-Lagrangian advection

• ECMWF IFS (red) shows spurious increase of 1 ppm (Recall GEM spurious increase of 2.1 ppm in one year)

• South Pole (or Darwin) shows background CO2 values best and better illustrates annual trend

IFSLMDZ

TM3 TM5obs

Houweling et al. (2010, ACP)

1 ppm

Simulated and observed XCO2

Pg

C

EC-CAS version: GEM v4.6.0-rc8

Factors found to reduce spurious mass gain:• Reducing time step• Adding horizontal diffusion to tracers consistent with meteorological fields• Including convective transport of tracers (Zhang-McFarlane scheme)• Adding tracer mass conservation scheme with global mass fixer

(Bermejo-Conde)

Without tracer mass conservation scheme

With Bermejo-Conde+ILMC scheme

After one year, difference in mass from expected mass is 0.04 Pg C

Mismatch in summer when global water vapour cycle peaks

Pet

agra

ms

C

Time

Global mass of water vapour in GEM analyses during 2009

Pet

agra

ms

Time

The total mass of the atmosphere varies mainly due to water vapour loading.

Trenberth and Smith (2005, J.Clim.)•The mass of dry air is constant•Water vapour cycle amplitude is 0.36 hPa or 0.00037 rel. to dry air•Here amplitude is 1900/5E6=0.00038

Next puzzle

• Why don’t we get exact mass conservation even after we (Monique Tanguay) implemented a tracer mass conservation scheme?

• Tracer variable in model– Presently a pseudo moist mixing ratio (mass CO2/mass moist

air). (Mixing ratio is NOT adjusted whenever water vapour changes, e.g. after physics step.)

– Tracer mixing ratios defined w.r.t. dry air is another way

– Observations are of mixing ratio w.r.t. dry air (mass CO2/mass dry air)

• Let’s check global mass of CO2, air and water vapour at various points in the model time step.

Terminology used here

Adv+? Physics Emis+diffus

Dynamics

Adv+? Physics Emis+diffus

Dynamics

“Diffusion”error

“Advection”change

“Diffusion”error

“Advection”change

Mass change due to “advection” actually includes any changes anywhere in the dynamics or physics steps.

GEM does not conserve global moist air mass without use of switch PSADJ

• About 2500 Pg of moist air is lost in 10 days.

• This is a relative loss of 0.0005

PSADJ=on

PSADJ=off

Global moist air mass

12ss pp

jiji

airair

A

MMg

,,

12

PSADJ scheme

Pet

agra

ms

Day in January 2009

Impact of switch PSADJ

PSADJ=onPSADJ=off

PSADJ=onPSADJ=off

PSADJ seems to remove water!Air mass include H2O signal

• Turning PSADJ on removed the H2O signal from moist air mass

Moist air Water vapour

Ideally red curve should look like this

Mass change due to dynamics+physics steps

2

0

-2

-4

-6

-8

-10

Pet

agra

ms

1 3 5 7 9January 2009

1 3 5 7 9January 2009

10

5

0

-5

-10

-15

-20

A missing source of mass for Ps

• Claude Girard (RPN-A) determined that the changes in global water vapour due to physics impact GEM’s thermodynamic equation but the flux of water across the Earth’s surface was not properly accounted for.

• We need to use the surface pressure to compute the total air mass and we assume that the water vapour mass is accounted for when computing tracer mass. If the surface pressure does not reflect the current mass of water vapour, global tracer mass calculations will not be accurate.

• Claude devised a means of adding this source of mass to surface pressure at the end of the physics time step (see his Note from August 19, 2014). http://iweb.cmc.ec.gc.ca/~armasmp/docs/mass-cons/Total_mass_variation_iin_GEM_girard.pdf

• Monique Tanguay (RPN-A) implemented this in GEM v4.7.0 and v4.6.0-rc8

Impact of new mass source of Ps

• With adw_source_ps=True, moist air mass change from one time step to the next resembles water vapour mass change, as hoped

Adw_source_ps=True

Adw_source_ps=False

Moist air Water vapour Hours from May 1, 2009 0UTC Hours from May 1, 2009 0UTC

Mass change due to dynamics+physics steps

Impact of ps_source on air mass

• PSADJ acts on moist air• We actually need PSADJ to act on dry air

PS_source onPS_source off

Moist air mass Dry air mass

Hours from Jan. 1, 2009 00Z Hours from Jan. 1, 2009 00Z

PS_source onPS_source off

Pe

tag

ram

s

Air mass evolution over 10 days

New ps_source term will impact meteorological forecasts

2 day forecast valid 3 Jan 2009Difference in surface pressure due to new Ps mass source

• Differences are largest in the tropics and in synoptic scale systems over the ocean

• Max differences are about 3 hPa!• There may be an impact on meteo forecasts

Expt by Monique Tanguay

Forecast impact of ps_source: NH summer/winter (neg/neutral)

Summer

Winter

NH Tropic SHGYY15 96h

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

Expts by Michel Roch

ControlPs_source

Another new flag: PSADJ-dry

• For both experiments: PS_source is on• Good conservation in first 24 hours

Dry air mass

Better but not perfect conservation of dry air

PSADJ on moist airPSADJ on dry air

Hours from Jan. 1, 2009 00Z

Spurious increase in dry air mass

Pe

tag

ram

s 10 day change is 100/5.1E6=2E-5

10 day change is 10/5.1E6=2E-6

Impact of ps_dry: Neutral

Summer

Winter

NH Tropic SHGYY15 96h

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

u uv

GZ T

Expts by Michel Roch

Need a dry mixing ratio for tracers

Change in CO2 mass

CO2 mixing ratio w.r.t. moist airCO2 mixing ratio w.r.t. dry air

• No tracer mass conservation. Keep PSADJ-dry=on, PS_source=on.

• Define CO2 mixing ratio as 𝜒=𝜌CO2/𝜌dry-air instead of 𝜒=𝜌CO2/𝜌air • Dry mixing ratio removes water

signal, and CO2 is more constant but still need to add tracer mass conservation scheme for this variable.

• This was done by Monique Tanguay

• Spin-up problem• CO2 change is ~0.0001 Pg C• Diffusion error is <0.0000005 PgC

Hours from Jan. 1, 2009 00Z

Pe

tag

ram

s

• With a tracer mixing ratio w.r.t. dry air, mass conservation is good until October then drifts

• Accounting for local changes in air mass (surface pressure) when analyses are inserted every 24h yields exact conservation! But CO2 fields are terrible—so the story is not over...

CO2 global mass with a dry tracer mixing ratio

Dry tracer mixing ratio

Local offset schemeDry tracer mixing ratio normalizedExpected mass

Pet

agra

ms

C

Time

Good agreement with surface obs

Alert

Sable Island

Toronto

Without assimilation, CT fluxes

Obs GEM

Dry tracer mixing ratio, global offset scheme

CO2 transport with GEM compared to chemistry transport models

GEM

CarbonTracker (NOAA)

GEOS-CHEM(US academia)

Column mean CO2 for 2009 The model runs use the same initial state and fluxes

Relevance of greenhouse gas modeling work to GEM

• Feedback to GEM-MACH:– https://wiki.cmc.ec.gc.ca/wiki/EC-CAS_Technology_Transfer

– Vertical diffusion equation– Emissions coding error– Assessing vertical diffusion equation in dry mixing ratio

• Feedback to GEM– Helping to test tracer conservation schemes– Illustrated a missing source of mass for surface pressure– Involved in redesign of global mean surface pressure fix– Helping to convert tracer equation to dry mixing ratio

GEM RPN MACH

Dynamics emis+v.diff

GEM RPN MACH

Dynamics emis+v.diffPhysics Physics

3. ENSEMBLE KALMAN FILTER

Ensemble Kalman Filter – first look

• No tracer assimilation, only passive advection

• Testing with 64 ensemble members, 0.9° grid spacing

• Start on 28 Dec 2008. Run for 4 weeks to 23 Jan 2009

• All members have same initial CO2 and same fluxes. Spread is due to spread in winds only.

• Winds differ among ensemble members due to differences in: model parameters (convection scheme, parameters involved in PBL model, diffusion of potential

temperature, etc. ), observation error perturbations

• How does uncertainty in winds affect CO2 spread?

Evolution of ensemble spreadAnimation of column mean CO2

Dec. 28, 2008 to Jan. 23, 2009

Ensemble mean

Ensemble spread

Other coupled meteorology/tracer forecast systems• ECMWF:

Real time operational 5-day CO2 forecasts since 2013. No

assimilation of CO2 obs. Updated initial conditions from flux inversions every Jan. 1. Plans: Near-real time assimilation of surface obs of CO2 with coupled meteorological/tracer assimilation

• NASA/Goddard GEOS5: Coupled CO and CO2 assimilation to meteorological assimilation. Weakly couple ocean and land data assimilation systems to atmospheric assimilation system.–Provide boundary conditions for regional modelling and flux inversions.–Improve modelling of radiative transfer, evapotranspiration–Feedback on modeling of boundary layer, convection, advection

–Provide a prioris for satellite retrievals of CO2 and CH4

Future work

• EnKF development (Polavarapu/Neish)

– compare to obs without CO2 assimilation

– Extend EnKF for tracer assimilation

• Global methane simulations (D.Chan)

– Tropospheric chemistry uses CMAM OH climatology (D.Plummer)

– Stratospheric chemistry from Jean deGrandpré (LINOZ)

• OCO-2 OSSE work (Ray Nassar)

• Regional greenhouse gas simulations to support inverted Lagrangian trajectory work

– supports measurement network interpretation work of Elton Chan and Douglas Chan

• Coupling with CTEM (CCCma ecosystem model) (Bakr Badawy)

– Evaluate CTEM with GEM meteorology

EXTRA SLIDES

Interannual variability: 1870-2013LeQueré et al. (ESSD, 2014)

Atmospheric accumulation has strong variability due to land uptake. This is due to climate variability.

Ocean uptake is not as variable.

Wet and dry air components of GEM analyses during 2009

This peak is due to water vapour

• Removing the water vapour from the air mass reduces the peak variation from 3000 to 1500

• However, long time scale variations still exist

Kalman Filter for coupled system

• System equations (truth):

• Equations for all 3 uncertainties also evolved, but not shown here

s

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CO2 tracers

Sources (Fluxes)

Weather forecast model

Transport model

Flux evolution model

Kalman Filter for coupled system

• System equations (truth):

• Model errors separated into: meteorology, transport, flux

• Model errors can be explicitly modelled and accounted for in actual forecast step (from analysis)

s

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CO2 tracers

Sources (Fluxes)

Weather forecast model error

Transport model error

Flux evolution model error

Kalman Filter for coupled system

• Analysis step:

• Meteorology and tracer analysis steps decoupled, initially

• CO2 obs used to update CO2 and flux estimates

• Analysis step includes observation and representativeness errors

• Equations for uncertainties not shown

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fk

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Meteorology step already done operationally

CO2 tracers

Sources (Fluxes)

GHG obs

Weight matrix based on error models

EC-CAS mass conservation: progress in the past year

GEM 4.5.0-a10 (7.2)

GEM 4.5.0-b7 (5.5)GEM 4.5.0 (4.8)

Expected mass (3.3)

GEM 4.5.0+mass cons(3.7)

Latest run has:•Surface fields from archives with Liebman filtering•Physics recycling•Half time step = 900s•Hor diffusion of tracers•Bermejo-Conde+ILMC

GEM 4.6.0-rc8 (3.3)

May 2013July 2013Nov 2013Jan 2014July 2014

By the end of one year, the mass gain is exactly right!

Polavarapu, Neish, deGrandpre, Gravel

Change in global mass due to advection

24h run of GEM-MACH• Even with the flux boundary condition the global mass changes during 24 h

• The mass change due to advection is shown here

Experiment=fluxBCtry2

Change in global mass due to diffusion

24h run of GEM-MACH• The mass change due to the

diffusion step is isolated here• The maximum error of 0.0008

Pg C is 13 times machine epsilon

• The typical error of 0.0002 Pg C is 3.3 times machine epsilon

• This plot reflects only the precision of the diagnostic calculation. No conclusions about model behaviour can be drawn.

Experiment=fluxBCtry2

Jump of machine epsilon

Impact of greenhouse gas modeling work on GEM-MACH

• Using a model in a different way often leads to insights/feedback on the model

• GEM-MACH was designed for air quality forecasts: regional scale up to 2 days, or global scale up to 10 days.

• But we used it for greenhouse gas simulations. Unlike the air quality problem, (1) we have no reactive chemistry to hide behind, and (2) we are looking at long time scales.

• We saw problems because of this different focus and we were able to provide feedback to GEM-MACH:

– https://wiki.cmc.ec.gc.ca/wiki/EC-CAS_Technology_Transfer – Vertical diffusion equation– Emissions coding error– Assessing vertical diffusion equation in dry mixing ratio (in progress)