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Physical knowledge to improve
and extend machine learning
pCO2 reconstructions
Galen A. McKinley
Valerie Bennington, Lucas Gloege, Amanda Fay
Columbia University, Earth and Environmental Science
Lamont-Doherty Earth Observatory
ICOS Science Conference
September 13, 2022
2
Uncertainties remain significant for the ocean carbon sink.
And observation-based products are temporally limited.
Friedlingstein et al., 2022
sink
sink
Fluxes since 1850 (in GtCO2/yr)
Ocean flux since 1960 (in GtCO2/yr)
3
Limitations of observation-based reconstructions of pCO2
• Few observations in 1980s and none prior
• Limited explain-ability from machine
learning
• Existing knowledge about CO2 dynamics is
often not incorporated into algorithms
Gloege et al., JAMES 2021
µatm
4
Limitations of observation-based reconstructions of pCO2
• Few observations in 1980s and none prior
• Limited explain-ability from machine
learning
• Existing knowledge about CO2 dynamics is
often not incorporated into algorithms
Gloege et al., JAMES 2021
µatm
5
The impact of temperature on pCO2 is very well
established
6
Method #1: pCO2-Residual
• Sea Surface Temperature has a known direct impact on
ocean pCO2
• Biogeochemistry and physical processes drive the
remaining variability
• By removing the temperature component, we focus the
statistics on biogeochemical-physical impacts on pCO2
Takahashi et al., 1993
pCO2-T
Bennington et al. 2022, in review
Mean pCO2
7
Mean pCO2
+
pCO2-T (blue) and observed pCO2 (red)
pCO2 Residual = (pCO2-pCO2-T)
monthly SST
8
pCO2-Residual values
make physical sense
and are approximately
normally distributed
Bennington et al. 2022, in review
9
Reconstruct pCO2-Residual with XGBoost
pCO2 – T = pCO2
pCO2 - Residual
1. XGB learns pCO2-Residual as
function of features
2. Combine with
pCO2-T for final
result Input data (“Features”)
• Satellite data
− Sea Surface Temp. (SST)
− Chlorophyll-a (Chl-a)
▪ Monthly climatological
− Mixed layer depth
− Sea Surface Salinity (SSS)
▪ Location and time
− Day of year (DOY)
− Latitude, Longitude (n-
vector)
▪ xCO2
Bennington et al. 2022, in review
10
pCO2-Residual performs well against independent data
Bennington et al 2022, in review
11
Flux timeseries, 1985-2019
Bennington et al. 2022, in review
12
Ocean models have long been used as the basis
for the Global Carbon Budget.
Can these be used to support reconstruction of
real ocean pCO2?
13
Method #2: Hybrid Data Physics
• Use GCB Hindcast models as a first
guess (or “prior”)
• Calculate the difference between
the model pCO2 and SOCAT data
• Apply XGB algorithm to reconstruct
a full-field model correction
• Get final estimate of real-world
pCO2 by adding this estimated
correction at each point
© 222 Lamont-Doherty Earth Observatory
Hindcast ocean biogeochemical models
+ SOCAT Data
Gloege et al. 2022, JAMES
14
Full-coverage misfit individually estimated for each model,
month
Gloege et al. 2022, JAMES pCO2
misfit (uatm)
15
Climatological misfits are much larger than interannual
Princeton Model, others similar Bennington et al. 2022 GRL
16
Since climatological misfit dominates, how much skill is gained by applying
only this as correction, as opposed to an interannual?
• HPDClimTest applies the 2000-2020 climatology of the model-observation misft
1959 2020
1982
LDEO-HPD = Model pCO2 + Interannual Misfit
HPD: Model pCO2 + Climatological Misfit
Observations
Begin
Model Period
Begins
HPDClimTest = Model pCO2 +
Climatological Misfit
Bennington et al. 2022 GRL
17
Most improvement over original models is climatological
Comparison data (1990-2020) not
used in algorithm training: GLODAP
and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
18
Most improvement over original models is climatological
Comparison data (1990-2020) not
used in algorithm training: GLODAP
and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
19
Most improvement over original models is climatological
Comparison data (1990-2020) not
used in algorithm training: GLODAP
and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
20
Most improvement over original models is climatological
Comparison data (1990-2020) not
used in algorithm training: GLODAP
and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
21
Apply climatological misfit to extend back to 1959
• HPDClimTest applies the 2000-2020 climatology of the model-observation misfit
• Since it dominates, apply this in the pre-observed period
1959 2020
1982
LDEO-HPD = Model pCO2 + Interannual Misfit
LDEO-HPD = Model pCO2 +
Climatological Misfit
Observations
Begin
Model Period
Begins
HPDClimTest = Model pCO2 +
Climatological Misfit
Bennington et al. 2022 GRL
22
LDEO-HPD: Air-sea CO2 flux, 1959-2020
Bennington et al. 2022 GRL
23
Conclusions
• Physical knowledge can be incorporated into machine learning algorithms, and
leads to improved reconstruction skill
• pCO2-Residual
• Focuses the statistics on the biogeochemical-physical component of pCO2
• LDEO-HPD
• Uses suite of hindcast ocean models as a prior, corrects with SOCAT data
• Climatological correction most impactful; supporting extension back to 1959
24
THANK YOU
mckinley@ldeo.columbia.edu
25
26
Flux timeseries, 1985-2019
Bennington et al. 2022 in review

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McKinley, Galen: Physical knowledge to improve and extend machine learning pCO2 reconstructions

  • 1. Physical knowledge to improve and extend machine learning pCO2 reconstructions Galen A. McKinley Valerie Bennington, Lucas Gloege, Amanda Fay Columbia University, Earth and Environmental Science Lamont-Doherty Earth Observatory ICOS Science Conference September 13, 2022
  • 2. 2 Uncertainties remain significant for the ocean carbon sink. And observation-based products are temporally limited. Friedlingstein et al., 2022 sink sink Fluxes since 1850 (in GtCO2/yr) Ocean flux since 1960 (in GtCO2/yr)
  • 3. 3 Limitations of observation-based reconstructions of pCO2 • Few observations in 1980s and none prior • Limited explain-ability from machine learning • Existing knowledge about CO2 dynamics is often not incorporated into algorithms Gloege et al., JAMES 2021 µatm
  • 4. 4 Limitations of observation-based reconstructions of pCO2 • Few observations in 1980s and none prior • Limited explain-ability from machine learning • Existing knowledge about CO2 dynamics is often not incorporated into algorithms Gloege et al., JAMES 2021 µatm
  • 5. 5 The impact of temperature on pCO2 is very well established
  • 6. 6 Method #1: pCO2-Residual • Sea Surface Temperature has a known direct impact on ocean pCO2 • Biogeochemistry and physical processes drive the remaining variability • By removing the temperature component, we focus the statistics on biogeochemical-physical impacts on pCO2 Takahashi et al., 1993 pCO2-T Bennington et al. 2022, in review Mean pCO2
  • 7. 7 Mean pCO2 + pCO2-T (blue) and observed pCO2 (red) pCO2 Residual = (pCO2-pCO2-T) monthly SST
  • 8. 8 pCO2-Residual values make physical sense and are approximately normally distributed Bennington et al. 2022, in review
  • 9. 9 Reconstruct pCO2-Residual with XGBoost pCO2 – T = pCO2 pCO2 - Residual 1. XGB learns pCO2-Residual as function of features 2. Combine with pCO2-T for final result Input data (“Features”) • Satellite data − Sea Surface Temp. (SST) − Chlorophyll-a (Chl-a) ▪ Monthly climatological − Mixed layer depth − Sea Surface Salinity (SSS) ▪ Location and time − Day of year (DOY) − Latitude, Longitude (n- vector) ▪ xCO2 Bennington et al. 2022, in review
  • 10. 10 pCO2-Residual performs well against independent data Bennington et al 2022, in review
  • 12. 12 Ocean models have long been used as the basis for the Global Carbon Budget. Can these be used to support reconstruction of real ocean pCO2?
  • 13. 13 Method #2: Hybrid Data Physics • Use GCB Hindcast models as a first guess (or “prior”) • Calculate the difference between the model pCO2 and SOCAT data • Apply XGB algorithm to reconstruct a full-field model correction • Get final estimate of real-world pCO2 by adding this estimated correction at each point © 222 Lamont-Doherty Earth Observatory Hindcast ocean biogeochemical models + SOCAT Data Gloege et al. 2022, JAMES
  • 14. 14 Full-coverage misfit individually estimated for each model, month Gloege et al. 2022, JAMES pCO2 misfit (uatm)
  • 15. 15 Climatological misfits are much larger than interannual Princeton Model, others similar Bennington et al. 2022 GRL
  • 16. 16 Since climatological misfit dominates, how much skill is gained by applying only this as correction, as opposed to an interannual? • HPDClimTest applies the 2000-2020 climatology of the model-observation misft 1959 2020 1982 LDEO-HPD = Model pCO2 + Interannual Misfit HPD: Model pCO2 + Climatological Misfit Observations Begin Model Period Begins HPDClimTest = Model pCO2 + Climatological Misfit Bennington et al. 2022 GRL
  • 17. 17 Most improvement over original models is climatological Comparison data (1990-2020) not used in algorithm training: GLODAP and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
  • 18. 18 Most improvement over original models is climatological Comparison data (1990-2020) not used in algorithm training: GLODAP and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
  • 19. 19 Most improvement over original models is climatological Comparison data (1990-2020) not used in algorithm training: GLODAP and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
  • 20. 20 Most improvement over original models is climatological Comparison data (1990-2020) not used in algorithm training: GLODAP and LDEO pCO2 (not in SOCAT) Bennington et al. 2022 GRL
  • 21. 21 Apply climatological misfit to extend back to 1959 • HPDClimTest applies the 2000-2020 climatology of the model-observation misfit • Since it dominates, apply this in the pre-observed period 1959 2020 1982 LDEO-HPD = Model pCO2 + Interannual Misfit LDEO-HPD = Model pCO2 + Climatological Misfit Observations Begin Model Period Begins HPDClimTest = Model pCO2 + Climatological Misfit Bennington et al. 2022 GRL
  • 22. 22 LDEO-HPD: Air-sea CO2 flux, 1959-2020 Bennington et al. 2022 GRL
  • 23. 23 Conclusions • Physical knowledge can be incorporated into machine learning algorithms, and leads to improved reconstruction skill • pCO2-Residual • Focuses the statistics on the biogeochemical-physical component of pCO2 • LDEO-HPD • Uses suite of hindcast ocean models as a prior, corrects with SOCAT data • Climatological correction most impactful; supporting extension back to 1959
  • 25. 25